Tankar

Ernst Stueckelberg came up with many of the most fundamental ideas in 20^th century theoretical physics but got little recognition. I learned about him when I realised that an evolution equation I derived from philosophical musings was introduced by him already in 1941. Stueckelberg was a modest man who struggled with life.

Ernst Stueckelberg was born in Basel in 1905. His mother Alice belonged to an aristocratic German family. That explains his impressive but cumbersome full name: Johann Melchior Ernst Karl Gerlach Stückelberg von Breidenbach zu Breidenstein und Melsbach.

When Alice’s father died, Ernst inherited the title Baron Souverain of the Holy Roman Empire of the Teutonic Nations of Breidenbach at Breidenstein and Melsbach. Ernst’s father Alfred was a lawyer, and his family had been citizens of the canton of Basel since the 14^th century. Alfred gave his son a strict upbringing, seemingly to live up to his noble maternal heritage.

After obtaining his Ph.D. in physics in Basel at the young age of 22, Ernst was offered to come to Princeton as a research associate. There he applied the recently invented quantum mechanics to analyse the properties of molecules. The American physicist Philip Morse recollects [1]:

I also came to know a rather stiff young man, tall and thin, with an aristocratic profile and a Prussian manner and carriage. […] We came to be close friends, perhaps because opposites attract. [… He] could not help his name, nor could he help his mannerisms, which had been drilled into him by his father. He once told me his father would not allow him to take off his coat or tie even when he was studying by himself in his own room.

One of Stueckelberg’s achievements at Princeton was to explain the continuous spectrum of the hydrogen molecule H₂. Later in life he expressed pride that this feat got it into the New York Times.

Available accounts differ on the order of events, but it seems that the Depression forced Princeton to let Stueckelberg go [2]. Back in Switzerland he could only get a job as a poorly paid Privatdozent.

Ernst married in 1931. Not long afterwards he seems to have lost a considerable wealth that belonged to his wife in naïve investments. To earn their living, Stueckelberg was forced to enlist in the army.

The pressing circumstances may have contributed to the fact that Stueckelberg began to express symptoms of mental illness around this time. These problems would haunt him for the rest of his life. His condition has been described as manic-depressive psychosis. He was often balanced and brilliant, but from time to time he had to retreat to the asylum for a few weeks.

The financial situation improved in spring 1935, when Stueckelberg was promoted to professor at the University of Geneva. When he returned to Europe, he had abandoned molecular physics and started working in the quickly developing fields of quantum theory and elementary particle physics.

Nevertheless, he was quite isolated, partly because of his personal situation. This is illustrated by the fact that between 1935 and 1943 Stueckelberg published 42 papers, 40 of which as the sole author.

He didn’t travel much and published most of his work in the local journal Helvetica Physica Acta, which was not widely read in the international physics community, partly because the articles were written in French.

His main lifeline to the scientific world was his friend Wolfgang Pauli, who, on the other hand, was central to the world of theoretical physics in the early to middle 20^th century.

During fits of depression, Stueckelberg repeatedly submitted resignation letters to his university. They were always ignored, except once. In 1950 he had to be reinstated as professeur honoraire.

Despite his hardships, Stueckelberg came up with several groundbreaking ideas and results [3]. Some of them went unnoticed until they were rediscovered by others several years later. At least three of these ideas led to Nobel prizes – but not to Stueckelberg. Here are some examples of his achievements:

• In 1934, Stueckelberg devised a relativistically invariant perturbation method for quantum fields that preserves the gauge invariance of the full equations. It was mostly ignored. In retrospect, these general properties would have made his scheme suitable as a starting point to understand the divergences that plague perturbation expansions in quantum field theory.

• In 1935, he developed a model where nuclear forces were mediated by exchange particles (bosons), in a similar way as electromagnetic forces are mediated by photons. Stueckelberg dropped the idea since Pauli thought it was ridiculous. The idea was rediscovered by Yukawa, who got the Nobel prize for this work in 1949.

• In 1938 Stueckelberg discovered a special case of the Higgs mechanism that provides mass to the nuclear exchange particles he postulated in 1935. The corresponding Higgs particle was discovered in the LHC accelerator at CERN in 2013. Peter Higgs and François Englert received the Nobel prize the same year for their theoretical prediction of the particle.

• In 1941, he proposed the law of conservation of baryon number. Very simply speaking it says that matter can be transformed, but it cannot appear or disappear – just like energy.

• In 1941, Stueckelberg proposed that antiparticles may be seen as particles travelling backwards in time, an idea later utilised and popularised by Feynman. In doing so, Stueckelberg introduced a novel evolution equation that separates two aspects of time. This equation is the reason I learned about Stueckelberg (see postscript).

• In 1943, he outlined the idea of renormalisation to come to terms with the divergences to infinity that plague quantum field theory. Stueckelbergs’s paper was rejected by Physical Review as too sketchy. Later, Schwinger and Feynman published their version of the idea, which was more detailed and contributed to their Nobel prize in 1965.

• Stueckelberg’s work on renormalisation was formalised in 1953 together with the mathematician Andrée Petermann, with whom Stueckelberg discovered the renormalisation group. It expresses in general terms the effects of a scale change on the description of a physical system. Kenneth Wilson was awarded the Nobel prize in 1982 for his work in this field, which has wide-ranging applications, including phase transitions and critical phenomena in thermodynamics.

• Heisenberg came up with the idea of the scattering matrix (S-matrix) to represent the probabilities that initial sets of particles transform into other sets of particles. He hoped that the S-matrix could be used as a fundamental description of the microscopic world, thus getting rid of the mathematical problems associated with interacting quantum fields. Stueckelberg and Feynman independently published useful perturbation recipes based on the S-matrix programme in 1949. The two approaches are basically equivalent. Feynman illustrated his method by means of the famous Feynman diagrams of particle reactions.

A few weeks after receiving the Nobel prize in 1965, Feynman gave a lecture at CERN outside Geneva. Stueckelberg attended. Afterwards, Stueckelberg was making his way out alone from the amphitheatre. Feynman, surrounded by admirers, made the remark [4]:

“He did the work and walks alone toward the sunset; and, here I am, covered in all the glory, which rightfully should be his!”

Research and teaching seem to have been the focus of Stueckelberg’s life – perhaps like clear, calm lakes in the messy and troubled landscape of life. He didn’t seek recognition and seemed uninterested in administration, or in building a research group around his own ideas.

According to colleagues and students, Stueckelberg had a peculiar and careful style of writing and teaching. He is known for the generality and depth of his ideas, but also for idiosyncratic notation and convoluted expression. Therefore, his work was sometimes hard to understand and appreciate – even for highly gifted colleagues like Pauli.

Wolfgang Pauli was a harsh critic of the work of other physicists, Stueckelberg included. According the their colleague Konrad Bleuler: “[F]or Pauli, a lecture hall was a kind of a holy place where only truth was allowed. And a wrong statement was a sacrilege.” Bleuler recalls [5]:

“Stueckelberg always knew really special — I might say prophetic — ideas. He gave a lecture and of course Pauli — it happened very often — didn’t agree. And said ‘you are not allowed to say such things.’ But you see, Stueckelberg being a prophet, he’s not so easily stopped uttering his prophecies. So Pauli in despair menaced Stueckelberg with a stick and it seemed — I was not present myself but I was told — that the seminar ended like the war of Troy, Pauli, rather corpulent, with his stick after Stueckelberg around the table in the lecture hall.”

Stueckelberg’s health deteriorated in the 1960s. Electroshocks and experimental medication for his mental illness slurred his speech and sometimes affected his thinking. Crippled by arthritis, he was carried to seminars in the arms of younger colleagues [2].

He brought his dog Carlo III to his lectures and often talked to the animal about the subject at hand. Some claimed that the dog seemed to understand tensor calculus, since it barked when Stueckelberg made an error at the blackboard. The sceptic part of the audience suspected that the dog rather reacted to the hesitation of his master when he was about to commit a mistake.

In the final part of his life Stueckelberg embraced the Roman Catholic Church. He turned away from quantum theory and elementary particles to study relativistic thermodynamics. That subject may have had existential significance to Stueckelberg as it relates to the arrow of time. He devoted an entire book to it. According to fellow Swiss physicist Charles Enz [6]:

“[H]is book on thermodynamics makes arduous reading, defying the traditions of pedagogy, language, and notation. It is a logical construct without compromise, a cathedral of the spirit erected to prove with the aid of the notion of entropy that the time of physics is indeed the ‘biblical time’ having a beginning and an end, and not the ‘Greek time’ that flows uniformly from an infinitely distant past to an infinitely distant future.”

Stueckelberg had to end an interview a few months before his death because he was tired [2]. He painfully lifted himself out of his chair with two canes. A heavy gold cross dangled from his thin neck. “I look forward every day to my eventual journey to Heaven”, he said. “We live too long.”

Postscript

Here I describe how I came into contact with Stueckelberg and his work. In so doing I sketch some of my own ideas relating to time.

I pursue the idea that it should be possible to reconstruct the structure of physical law from epistemic principles. To this end, it is assumed that the structure of knowledge and the structure of the world reflect each other. A thorough analysis of what can be know about the world and what cannot provides lessons about the world itself.

According to this idea, one-to-one correspondence should appear between fundamental forms of appearances and the degrees of freedom in proper physical models. Here, the term forms of appearances is understood in the Kantian sense as categories of perception that are given a priori, into which all sensory impressions and all other elements of consciousness are placed.

Time is such a form of appearance. Kant viewed time as an essential such form, stating that it is a necessary representation that grounds all intuitions.

We can actually separate two aspects of the temporal form of appearance. The most basic one is the perceived flow of time, the directed sequence of events. This aspect of time may be parametrized by the variable T. On top of that we can measure temporal distances between events. Such distances may be expressed by means of the variable t. At each point in time T, which we may call now, we have knowledge of temporal distances t between an entire set of events, stretching from the present arbitrarily far back into the past. Of course, we may also know about the spatial distances between these events. Therefore, an entire space-time

$(x,y,z,t)$

can be associated to each T, representing the known spatio-temporal relations at the present point in time. From the assumed epistemic perspective, the variables T and t should be treated as independent degrees of freedom in our physical models, even though they are related. From more careful considerations of this kind, it is possible to derive a quantum mechanical evolution equation

$i\hbar\frac{\partial}{\partial T}\Psi(x,y,z,t,T)=R \Psi(x,y,z,t,T)$

where R is some Hermitean operator. This equation corresponds to the Schrödinger equation with a second temporal variable. The temporal metric is contained in t, meaning that relativistic transformations apply to t, but not to T. This makes the above evolution equation relativistically invariant, in contrast to the Schrödinger equation.

A few years ago I learned that Stueckelberg had arrived at the same equation already in 1941. He did not start out with philosophical musings like I did, but with his well-known desire for symmetry and relativistic invariance.

Stueckelberg used the evolution parameter T to be able to create particle trajectories that bended backwards in time t. He interpreted such trajectories as the creation or the annihilation of a particle-antiparticle pair, according to the figure below (taken from Ref. [7]).

The weakness of Stueckelberg’s approach is that he never provided any physical motivation for the introduction of the evolution parameter (which he called λ).

From the subjective point of view, it is very natural to unfold the now, represented by a given value of T, into an entire temporal axis t. Suppose that you listen to music. The appreciation of harmonies, and the emotional response they give rise to in the present, depend crucially on memories of sounds in the immediate past, and their metric intervals, to the extent that the music would cease to exist without these memories. That is, each present state of the listener contains both the present and the past in a crucial way.

At the formal level of physical description, the very perception of a sound at a given moment T relies on sensory recording during an extended period of time t, since such a temporal interval is needed to determine the frequencies that define the sound that we hear at a given moment. The same goes for spatial perceptions, since they arise when light with different frequencies enter the eye.

References

[1] Philip M. Morse, In at the Beginnings: A Physicist’s Life (MIT Press, 1977)

[2] Robert P. Crease and Charles C. Mann, The Second Creation, pp. 140-144 (Macmillan, 1986)

[3] Jan Lacki, Henri Ruegg, and Gérard Wanders (eds.) E. C. G. Stueckelberg, An Unconventional Figure of Twentieth Century Physics (Birkhäuser, 2009)

[4] Jagdish Mehra, The Beat of a Different Drum: The Life and Science of Richard Feynman, pp. 573-577 (Oxford University Press, 1994)

[5] Lillian Hoddeson, Interview with Konrad Bleuler, January 20, 1984 (Transcript by American Institute of Physics)

[6] Charles P. Enz, Ernst Stueckelberg, obituary, Physics Today 39(3), pp. 119-121 (1986)

[7] Ernst Stueckelberg, Remarque à propos de la création de paires de particules en théorie de relativité, Helvetica Physica Acta 14, pp. 588-594 (1941)

Everything has to be based on observation, provided observation is understood correctly. Observation includes grasp of essence, which is simply left out of what is called experience most of the time – in particular, by the empiricists.

Kurt Gödel [1]

This blog post was originally submitted to the FQXi Essay Contest 2020.

Introduction

This essay points to hidden premises in the arguments demonstrating the existence of mathematical propositions that are formally unprovable. It is argued that blindness to such premises has confused the interpretation of unprovability and uncomputability theorems. The same blindness has led many to assign improper and too prominent roles to codes and computation, roles they cannot play regardless these theorems.

Similarly, there are hidden premises in the rules we use to extract predictions from quantum theory. The source of the hidden premises is the same in the mathematical and the physical cases: we have to assume outside agents who act on the system being studied – be it a formalisation of arithmetic, or an experimental setup designed to test Bell’s inequalities.

The relation between the agent and the system has a specific form. Everything with specific form can be used as a handle to new insights. In this case the claimed common source allows us to find common traits of formal unprovability in mathematics and physical indeterminism.

To find these common traits, we need to open our eyes. We are blind to the nature of the relation between ourselves and the world since we are born with it, and thus take for granted – just like we are deaf to the harmony of the spheres since we always hear it, or so it is said.

In the beginning was time

There are some premises of reasoning we cannot do away with, but which we often ignore. One such premise is the existence of time. Ignorance of this premise sometimes leads to contradictions in terms. There are physicists who deny the fundamental nature of the directed flow of time. We may imagine one of them saying: “Yesterday I realised that there is no need for time in physics, today I’m writing my result up, and tomorrow I’ll explain it at a seminar.”

Time is a premise even in logic. The prefix in the very word premise is temporal in itself (which is also the prefix of prefix). The premise comes before the conclusion. And the steps in our reasoning leading to the conclusion are like the ticking of a clock. We cannot shuffle the axioms used in a mathematical proof with the intermediate lines and the theorem, without destroying the logic. The order and direction of the elements in the proof are fundamental.

Computer games

I see a similar blindness to the premises of the reasoning when I hear some people discuss coding, and the idea that the laws of nature are like a computer program – so that life becomes a simulation. The very concept of a code requires two things external to the code itself: the structure or message that is coded, and a key or dictionary that translates message to code and back. If we use the word object in a very general sense, we may say that as soon as we talk about codes, we presuppose the three objects in Figure 1. We also presuppose a set of relations between them. The key must be placed conceptually between the message and the code.

As a first observation, it becomes self-contradictory to try to describe the universe as a code, since then we presuppose the existence of objects outside the universe, which there cannot be, by definition.

This argument can be made more concrete. If we are materialists, we must assume that the code, the key and the message are imprinted in physical objects. A computer code is imprinted in computer hardware, and the key is ultimately imprinted in the brain of the programmer. The structure that is coded may be, for example, the atmosphere. Then the code corresponds to a climate model, and we are performing a climate simulation. If we analogously claim to be able to simulate the entire universe, and entertain the idea that the universe is equivalent to such a simulation, we clearly presuppose physical objects outside the universe, making the idea incoherent.

No object is an island

Let us turn to the relations between the three objects code, key, and message. They are also presupposed as soon as you speak about codes. These relations often lack direction, since the roles of the code and the message can sometimes be interchanged. They may, for example, correspond to two different languages. The key is then a dictionary. Such relations are implicitly presupposed whenever we speak about a set of objects. In fact, the very concept of a set implies a directed relation from the set to its elements, expressing the hierarchic relation between the object that corresponds to the set to the objects that correspond to its elements.

When we encode mathematical structures such as sets in a computer program, we sometimes forget that we also encode the relations between the elements in this structure. Look at matrices, for example. We encode the magnitude of the numerical elements, of course, but also their relations via the indices that specify the position of the elements in the matrix. The rows and columns are overlapping sets of elements. In the above figure, object C may correspond to column 1 of a 2 x 2-matrix, and objects A and B to elements e_12 and e_22, respectively.

It and bit

A computer code can be seen as a string of symbols that translates to a sequence of bits fed into the computer. Such a code is completely flat, lacking any hierarchical structure, and there are no inherent distinctions between objects and relations in the code itself. Therefore we might get the following idea: since we can encode and store in a computer memory a structure such as a matrix as a string of bits, hierarchies and relations among objects are not fundamental.

However, these hierarchies and relations are not grinded into nothing in the coding process – they just move to the key. They have to be there in order to regain the structure of the matrix when it is retrieved from the computer memory. And since the key is indispensable whenever we speak about codes, relations and hierarchies defend their fundamental role in any meaningful representation of reality.

This conclusion is reinforced by the simple observation above that the existence of a code implies a key and a message, with certain relations between them. These relations are shown in Figure 1, and constitute meta-relations as compared to the relations within the encoded message. It is tempting to try to grind all these relations and meta-relations to a structureless heap by creating a meta-code that translates the entire setup of code, key and message – and all the relations within this triad – to a string of bits. But it’s easy to see that we just end up in infinite regress: the meta-code inevitably gives rise to a meta-key and a meta-message, introducing new interesting relations. To me, these simple considerations show the incoherence of the idea it from bit, and its younger sibling it from qubit.

Again, let’s be a little bit more concrete. Currently, informational approaches to quantum mechanics are popular, where information is understood in its binary form. It is true that the simplest quantum mechanical systems have two possible states, and therefore may be called qubits. But it does not follow that all other quantum mechanical systems can described as collections of qubits. Indeed, this is not the case, since there are other fundamental quantum mechanical systems which have more than two possible states, such as quarks with their three possible colour charges.

Of course we may try to encode these more complex systems as a collection of qubits, but then we inevitably presuppose something external to the heap of qubits, as discussed above. And then the model is incomplete. In this case we need a key telling us which sets of qubits describe a truly two-state system, and which describe systems with more than two states. In other words, the qubits need to be marked, just like the elements of an encoded matrix need to be marked with indices telling us which rows and columns they belong to. Again, we may try to encode these markings into a meta-code, but we will just chasing our own tail in the never-ending dance of infinite regress.

The conceptual tower

The scientific ideal is to be able to explain as much as possible from as little as possible. This ideal can be taken too far, however. One lesson from the above considerations is, I think, that we cannot choose a too small or too simplistic set of assumptions and building blocks if we want to construct a complete model of the world. We must take all of its fundamental structures and relations into account.

The spatio-temporal relations between physical objects can hardly be reduced to something more fundamental, even if some physicists try. I argued that attempts to get rid of temporal relations lead to self-contradiction. Equally fundamental are the set-theoretical relations between physical objects that we most often take for granted.

We gladly speak of composite objects like a set of three quarks in a nucleon, a set of nucleons in an atomic nucleus, a nucleus and electrons in an atom, a set of atoms in a molecule, and so forth. Yet it is a profound state of affairs that perceived physical objects can always be arranged in this hierarchical, set-theoretical manner, a fact that makes the reductionist scientific method possible. These relations between physical objects define a proto-space of relative spatial scales. Kurt Gödel referred to set-theoretical relations as quasi-spatial [1].

The perceptions of temporal relations and the perception of some physical objects being parts of others are as fundamental to our perception of reality as the perception of the objects themselves. We may call them forms of perception (or forms of appearances, like Kant did [2]). To make more refined interpretations of what we see, to understand it and to build scientific models that account for it, we need still more advanced concepts, such as algebra and analysis. Therefore, there is a sense in which the entire tower of conceptual tools at our disposal has an equally fundamental position in our scientific worldview as the physical objects.

Kurt Gödel embraced this kind of conceptual realism. He claimed that we perceive concepts directly in a similar way as we perceive physical objects. He arrived at this Platonism at the age of nineteen, and said that it led him to his groundbreaking work in mathematical logic in his twenties. Naturally, he vehemently opposed the logical positivists of his day, who claimed that simple facts verified by empirical observation were a sufficient basis for philosophy and science.

Evidently, I agree with Gödel in this respect. We cannot derive simple concepts from facts, or all higher concepts from the lower ones. If we try to do it, we will have to use the concepts we try to derive, making the arguments circular. No conceptual bootstrapping is possible. If we just try to encode the concepts, we end up in infinite regress just like before.

Think again about the idea it from bit. It is indeed an idea. The idea that the world can be described as a binary code is very abstract, yet simple and indivisible. It cannot itself be decomposed in binary form. Then this idea does not belong to the world. Then what kind of world are we talking about?

Some self-reflection is needed

If we accept the fundamental nature of all elements in the tower of abstraction, all the way up from simple observations, then what kind of reality does this tower represent? Clearly, it cannot correspond to a naive materialistic world-view, in which the only things granted fundamental significance are physical objects or fields distributed in space and time, and where everything else can be explained in terms of these.

We need to find a common denominator for all levels in the tower, just like the common denominator for all physical objects is that they are located in the same three-dimensional space.  To me, the only conceivable common denominator is that all levels in the tower are perceived or appreciated by someone; they are all integrated in the mind of an observer. In other words, all building blocks of the conceptual tower are located in the same mental space. This makes perceiving subjects equally fundamental as perceived objects. The relation between the observer and the observed becomes one of the fundamental relations of the world. This relation may be represented as follows.

When you think about this figure, it’s a bit paradoxical. In order to emphasize that subjects are equally fundamental as objects, we represent the subject as an object related to another object. You, the reading subject, look at this picture from the outside, and thus escapes the representation. We might try to represent this predicament like in the figure below.

However, you still look at this meta-representation from the outside. Clearly, whenever you want to catch the subject in order to incorporate it in an objective description, it always flies higher, escaping the butterfly net. If we repeatedly try to catch the subject in the objectification net we just end up in a similar kind of infinite regress as we already discussed in relation to messages and codes. The relation between subject and object also escapes this objectification net, emphasizing the fundamental nature of this relation. These reflections are examples of self-reference. The subject looks at itself from the outside as an object of study, and reflects on its own nature, and its relation to the objects it perceives. In such a case we may divide the single bi-directional relation between subject and object in Figure 4 into two directed relations that form a loop. We may read the upper relation as: The subject looks at an object, and the lower relation as: This object represents the subject.

In a more concrete setting, the representation of the subject may simply be our mirror image. Generally speaking, self-reference does not require a self in the sense of a personal subject, but just two or more objects with directed relations that form a loop. We may take acoustic feedback as an example, where the two objects that are related in a loop are the microphone and the loudspeaker. We need at least two objects in such a loop of self-reference; a single object referring to itself makes no sense, I think. We need the mirror image to see ourselves; I cannot see my face directly with my own eyes.

Semantic self-references may seem genuinely self-referring, but this is not really so. Consider the famous liar paradox: This statement is false. This sentence is actually the set of two parts that carry meaning: a subject and a predicate, where the predicate refers to the subject.

A: This statement (subject)

B: is false (predicate)

C: This statement is false (sentence)

The first part A does not refer to itself, but to C. Referring to Figure 2 we may draw the following figure. Here we have two loops: one with two objects A and C, and another one with three objects A, C and B.

With the liar paradox we approach Gödel’s famous first theorem about the incompleteness of axiomatic arithmetic.

Looking at a theorem

Let me try to illuminate the structure of Gödel’s proof in the light of the discussion so far. Much more detailed – but still generally accessible – accounts can be found in several places, for example in the charming little book What is mathematical logic? [3]

The basic idea is just to modify the Liar paradox in the following way.

A: This statement (subject)

B: cannot be proved (predicate)

C: This statement cannot be proved (sentence)

This statement is self-referential in the same way as the Liar paradox, as expressed in Figure 8. Clearly, it must be true to avoid contradiction. Thus we have a true statement that cannot be proved, and thus truth goes beyond proof.

This is just cheap semantics, of course. To make a precise mathematical theorem out of it, we first have to replace the word statement with formula. Further, we must refer to a specific formula, which we may call F. Since the word statement defines part A above, but also refers to the entire sentence C, the entire claim This statement cannot be proved must itself correspond to formula F. To create such a correspondence we must find means to code sentences such as C as formulas of the same type as F. We may then write

A: Formula F

B: cannot be proved

C: This statement can be coded as a formula F, which cannot be proved.

The above formulation makes the hierarchical, set-theoretical difference between A and C explicit: whereas A is a formula, C is a statement about a formula (which in turn can be coded as a formula).

The formulas and proofs we are talking about here belong to the realm of formal systems. Below is shown an alphabet of 13 symbols that is sufficient to express any arithmetic proposition as a string of these symbols called a formula. For example, the number two is expressed as s(s(0)),where the symbol s can be interpreted as the successor of. The number two is clearly the successor of the successor of zero.

To a formal system also belongs a set of axioms and a set of allowed inferences. The axioms are just a set of formulas, and the inferences are mechanical rules that allow us the get new formulas from an old one. A proof of a formula F becomes a sequence of formulas, where the first one is an axiom, and the last one is F.

To code a statement about formulas and the possibility to prove them into a formula, as required in sentence C, Gödel introduced a method to code formulas and proofs as integers, now called Gödel numbers. One way to do it is shown above. It uses the uniqueness of the decomposition of an integer into a product of primes.

The coding makes it possible to say whether a given integer is the Gödel number of a formula, or a proof, or neither. If it is the Gödel number of a formula, the formula can be decoded, and if it is the Gödel number of a proof, the proof can be decoded.

With the help of the coding schemes expressed in Figures 9 and 10 we can close the semantic loop in Figure 8 in a mathematically well-defined sense.

We have to find a formula F that closes this loop and makes it self-consistent. Such a formula is not too hard to formulate [4]. As a consequence we get Gödel’s first incompleteness theorem: In any consistent formal system with an interpretation that contains arithmetic, there is a formula F that cannot be proved or disproved within the system. Since the arithmetic interpretation of any formula is either true or false, it follows that in any formalisation of arithmetic, there is a true proposition that cannot be formally proved. Here truth is defined within element D in Figure 11, whereas provability is defined within element C.

A common but controversial inference is that human reasoning is something else than the mechanical procedures of formal proofs and the execution of computer programs. We seem to have access to more truth than a computer can ever have, and therefore we must stand outside and above the mechanics.

What I want the reader of this essay to take to heart is the following: we make use of the last statement in order to prove Gödel’s theorem. It is a presupposition. The inference is therefore a tautology. (Gödel’s theorem itself is certainly not.)

If we want the proof of Gödel’s theorem to stay within the formal system it analyses, the formula F must speak about itself. But there is no genuine self-reference in the sense of Figure 7. Instead, to make the argument in the proof go through, we presuppose three elements in a loop, where the formal system under study is just one of them. We also use the hierarchical nature of set theory according to Figure 2. Such hierarchies are non-existent within a formal system.

Hey you

Elements C and D in the loop in Figure 12 correspond to propositions and statements. They carry meaning, which must be defined subjectively. What we presuppose in the proof of Gödel’s theorem is therefore an agent who observes the formal system from the outside. We presuppose ourselves, naturally.

In this picture, the arrows pointing to and from A in Figure 12 correspond to a relation between the observer and the observed. In his proof, Gödel demonstrates that this relation is fundamental in order to understand mathematics, and the limitations of its formalisation.

There is an analogous situation in physics. It was realised in the beginning of the twentieth century that there is a limitation to classical, Newtonian physics: it cannot account for all observed phenomena. Quantum theory was therefore invented. A decisive difference between classical physics and quantum theory is that the latter treats the relation between the observer and the observed as fundamental. This is so since we find a rule among its postulates that tells us which values of a quantity can actually be observed in a given situation, and also a rule that gives us the probability to observe each of the allowed values.

Many physicists want to explain away this fact, trying to derive these postulates from the others. What they want to do, in effect, is to objectify the act of observation. They argue that as far as physics concerns, it is sufficient to consider ‘observations’ made by a measuring apparatus. Such an ‘observation’ just amounts to an interaction between the system of interest and the apparatus. I have argued in relation to Figure 5 that it is logically impossible to erase the subject in this way; we just end up in infinite regress. The messiness and incompleteness of the mathematical frameworks that come out of these attempts suggest that it is a dead end in physics as well.

Self-dissection

At the same time, the truly materialistic approach to the physical world has proven immensely fruitful in the past. And neuroscientists have unravelled close neural correlates to our subjective mental states. How do these facts go together with all of the above?

We may try to make all these things fit together by introducing an operational version of materialism, in which each shift in our subjective perception corresponds to a shift in the brain state. The odd thing in our predicament is that the brain state is a state we observe according to the laws of quantum theory, just like all the other things around us. The brain state is therefore itself a subjective perception, in a sense. We get a self-referential loop in physics similar to the one in mathematics that Gödel pointed out.

We have to pause for a minute, though. If operational materialism is interpreted very strictly, it should be possible to explain each of our actions as a result of the processes going on in the brain. There are two potential problems with this picture – one mathematical and one physical.

Let us start with the mathematical problem. In this picture, the brain should be seen as analogous to a computer. But then it could also be seen as analogous to a formal system, mechanically processing input like axioms, producing output like true formulas. However, we have argued that the structure of Gödel’s proof presupposes something fundamental that is external to the formal system itself, yet interrelated to it. There is no place for such subjective externalities in this strict version of operational materialism.

The physical problem has to do with causality. Quantum theory is expressed in the following form: Given that we observe a certain system in a certain way, the probability to see this or that is so and so. If I look to my right I will see this or that with certain probabilities, and if I look to my left I will see this or that with other probabilities. But the theory does not say anything at all about which direction I will actually look. This is often called Heisenberg’s choice, and it lies outside the scientific description, as far as quantum theory can tell. There are not even any probabilities associated with it.

Heisenberg’s choice is fundamental within the theory and has tangible consequences; it affects the future evolution of the physical world. Yet it is impossible to account for it in a picture where all choices reflect the actions of a brain whose state evolves according to the laws of physics. This is true even if those laws are probabilistic, like in quantum theory. (We may, of course, try to express Heisenberg’s choice as the outcome of a probabilistic quantum experiment, but we just run into the arms of our old friend infinite regress.)

To make the idea of operational materialism consistent with known mathematics and physics we clearly have to find its limitations. Again, there is one mathematical and one physical side of the coin.

Mathematically, or rather logically, we may construct a self-referential loop where a subject observes her own brain state F as she is about to make a choice. The choice may then be such that it contradicts the state F supposed to give rise to it. The set-up is similar to the circuit shown in Figure 11 in order to motivate Gödel’s theorem.

In this case the conclusion would be that there are brain states F such that a choice is made by the owner of the brain that cannot be accounted for by F.

We may try to find the physical source of the limitation to operational materialism in the architecture of the brain. We should clearly search for a microscopic structure that is crucial for information processing, having the potential to influence macroscopic action. It must further be able to hide its inner state from outside scrutiny, at the same time as this inner state may influence the information processing being performed by the structure.

The so called microtubules are intriguing candidates. These extremely thin tubes are abundant inside neurons. Their circular circumference is composed of just thirteen tubulin molecules, whereas their length can stretch to the centimetre scale. The tubulin molecule has a discrete set of possible conformations. Conformational changes can spread like waves along the tube, suggesting that the surface of the microtubule acts as a cellular automaton, performing computations relevant to brain function.

The interior of the microtubule is filled with water. One may speculate that the state of this water is unknowable to a large extent. This may be so because the rigid lattice formed by the tubulin molecules only allows a discrete number of collective states of the entire microtubule surface, whereas the possible states of the water inside the tube is probably much higher. If this is the case, some information about the inside of the microtubule is necessarily lost at the surface.

In this way we may be able to avoid the possibility to gain perfect knowledge of our own brain state. Such a limitation would make the idea of operational materialism consistent with the limitations of computability and determinism highlighted by Gödel’s theorem and quantum theory, respectively. It would also make operational materialism conform with the fundamental role given in this connection to the observer and her relation to the observed world. I come to think of a quote by Niels Bohr:

The idea suggests itself that the minimal freedom we must allow the organism will be just large enough to permit it, so to say, to hide its ultimate secrets from us. [5]

Stuart Hameroff and Roger Penrose have argued forcefully for the idea that microtubules play a crucial role for the appearance of consciousness. [6] Their perspective is somewhat different from the one I present here, however. Several recent studies [7] point to the important role of microtubules for the higher brain functions, even though the underlying mechanisms are still unknown.

The conceptual clock tower universe

The world view promoted in this essay incorporates the observing subject in a never-ending dance with the observed world. The couple is forever interconnected by a fundamental relation. It also incorporates fundamental forms of perception such as time and set-theoretical hierarchies into which the naked sense impressions are placed, and also some more abstract concepts used to interpret and relate them. It is claimed that such a world view is often implicitly presupposed even by those who explicitly deny it.

Sense impressions, forms of perception, and higher concepts are seen as equally fundamental in this world view, and define different floors of a conceptual tower. It is suggested that the world is this tower, with all its inhabitants and furniture. Then the outline of the tower, together with the stairs that run between the floors, the pipes and ventilation shafts, must correspond to the laws of physics, as well as to the structure of the mathematics used to express these laws. If this is true, forms of perceptions and the structure of mathematical concepts should give clues to the laws of physics, and vice versa.

Since the perception of physical objects in three-dimensional space is just one of the floors in the tower, the tower itself is not built in this concrete, ordinary space, but is located in a more abstract space, which cannot be separated from awareness.

The objectivity of such a world does not reside in the physical objects that are observed in three-dimensional space. Rather, it resides in the parts of the conceptual tower and how they fit together. The tower has its rotating cogwheels, like a mental mill, or a clock. True, this is another kind of clockwork universe than that suggested in the seventeenth century. Even so, it is not for us to decide how the conceptual clock tower operates in its abstract space, what the pieces look like and how they fit together. That cannot be changed by our wishes. We can still get crushed between its cogwheels. In that sense such a universe is still objective.

References and notes

[1] Hao Wang, A logical journey: From philosophy to Gödel, The MIT Press (1996).

[2] Immanuel Kant, Critique of pure reason, translated by P. Guyer, and A. W. Wood, Cambridge University Press (1998).

[3] John N. Crossley et al., What is mathematical logic? Oxford University Press (1972).

[4] Since element C in this loop is a statement about a formula whose nature can be varied, we should consider corresponding formulas F’(x) with a free variable x. We may then specify F as follows, as an arithmetic proposition within element D in the loop: There is no y such that y is the Gödel number of the proof of formula F with Gödel number z, where F is defined as F’(x) with x replaced by z, as expressed symbolically in the formal alphabet.

[5] Niels Bohr, Light and life, Nature 131, 421-23 (1933).

[6] Stuart Hameroff, and Roger Penrose, Consciousness in the universe: a review of the ‘Orch OR’ theory, Physics of Life Reviews 11, 39-78 (2014). [7] Travis J. A. Craddock et al., Anesthetic Alterations of Collective Terahertz Oscillations in Tubulin Correlate with Clinical Potency: Implications for Anesthetic Action and Post-Operative Cognitive Dysfunction, Scientific Reports 7, 9877 (2017); María del Rocío Cantero et al., Bundles of Brain Microtubules Generate Electrical Oscillations, Scientific Reports 8, 11899 (2018).

This is an English translation of a blog post in Swedish published in 2017.

A summer day in the mid 70s I was sitting in my parent’s Volvo PV outside a public swimming pool in our home town Lund, Sweden, listening to the radio. My big sister attended swimming school. The voice on the radio talked about a space probe which had investigated Jupiter and its moons. In hindsight I conclude it must have been Pioneer 11. The existence of alien planets and the infinite space struck me with wonder and fear.

Much later I have pondered the strange fact that our familiar landscape with towns, fields and forests floats on top of bottomless seas of glowing magma. But this thought has not led to the same feeling of striking wonder as the thought of the planets in space did when I was three or four years old. It has not grown to much more than a thought.

To some extent it certainly has to do with age. Most of us become less receptive to immediate impressions as we grow up. We spin a cocoon around us weaved of thoughts about the world. On the inside of this cocoon we paint pictures of the outside. As time goes by we paint layer on top of layer of conceptions. They make it harder and harder to see and perceive the world – what we see are just our own conceptions of it.

It is the same thing with memories. Throughout my life I have been thinking about the radio broadcast about alien planets that made such an impression on me. That makes it hard to know if I really remember the event by now, or if I just reach my previous attempts to remember it, the pictures of the event I have painted as I lost access to the proper memory.  

The ever thicker layers of paintings on the inside of the cocoon make it almost opaque. It becomes hard to feel the wind of the world through the threads out of which it is spun. Of course, that makes it harder and harder to paint accurate pictures of the world. Finally we just reproduce the pictures we have already painted, since that is the only thing we see. Even though we may the best of intentions, our world view deviates more and more from the world as it really is.

It seems to me that much of the follies in the world, and much of its misery, has its root in the fact that people ceases to see the world, ceases to see themselves, seeing only their own conceptions, hearing only their own statements about it. People who are blindly convinced of the goodness of the ideology they have painted in front of themselves and each other, can step on and crush innocent people without noticing it, feeling like walking on air, with a blessed smile on their face.

The blind conviction that you belong to the good side is most often associated with religion, but is sometimes ascribed to the political left. But the right suffers from a blindness of its own. People on the right can become so convinced that their own perspective is the only rational one that they do not see that other perspectives can be equally reasonable. They do not see that they, with reason as a beacon, go astray in ideological quagmires and sink into the irrational swamp.

If the political right sometimes confuses ideology with reason, materialists sometimes confuse their own world view with science. But science is just a method to gain knowledge. Whether science supports a materialistic world view can only be decided empirically. The answer is not given beforehand.

From the days of Newton until the previous turn of the century science provided ever more support to such a materialistic or realistic world view. The objects that we look at are really out there, regardless whether we observe them or not. The observer is secondary, and is equivalent to the intricately cemented piece of matter that constitutes its body.

But since the beginning of the 20th century science have started to point in another direction. The theories of relativity and quantum mechanics demand an observer to make it possible to motivate and understand its equations in a simple way. To express it more vividly: the living subject seems to be a fundamental part of the world.

I cannot help following the debate on these matters among physicists and philosophers of science. Even though science no longer provides support to a naively materialistic world view, many physicists and philosophers refuse to accept that this is so. They feel so comfortable with the pictures they have painted on the inside of their cocoons – pictures of objects that dance about independent from themselves – that they hold their ears if you knock on the outside of the cocoon and tell them that the world out there seems to be organized in a different way.

At this point someone will surely object that I contradict myself when I talk about a world outside the cocoon when I have just said that science suggests there are no objects independent from the living subject. But I use the term the world out there in a somewhat more subtle sense. For instance, the absence of objectively existing stuff does not preclude the existence of objectively existing laws of nature which govern what we see. We may be right or wrong when we interpret the world and its behaviour. To borrow the motto from The X-Files: The truth is out there.

My impression is that physicists who persist in their narrow materialistic world view rarely responds to, in a sober and pertinent way, those empirical facts and theoretical models that point in another direction. They do not even want to consider that they are wrong, or play for a minute with alternative world views to see where they lead. Instead, these are discarded with contempt, silence or with far-fetched theories with the sole purpose to uphold the preconceived world view despite all the facts that speak against it.

As an example of such a far-fetched theory I want to mention superdeterminisim. This idea has surfaced in order to explain away the strange behaviour of pairs of particles which are quantum mechanically entangled. Let me make a detour to explain what this means, and the return to superdeterminism, which has been called the final conspiracy theory.

That two particles are entangled may mean that if we examine one of the particles and find it in a certain state, the probability to see the other particle in a similar state immediately increases, regardless how far away it is located – be it in another galaxy. In a certain sense, this probability increase travels infinitely fast from one of the entangled particles to the other. Einstein called this phenomenon spooky action at a distance. The increased probability that the other particle will be found in a similar state as the first one means that the states of the two entangled particles becomes strongly correlated when we examine both of them.

There is not necessarily anything mystical or strange about such behaviour. We may imagine that the two particles have definite states to begin with, before we observe them, and that the probabilities we use to describe these states just reflects our ignorance about their actual states. In that case we may say that there are hidden variables whose values determine the state of each particle. Such a model is deterministic and the probabilities play no fundamental role. Therefore there is no need for a probability transfer from one particle to the other with infinite speed. The state we observe in one of the particles is already determined by the hidden variables. The increased probability to observe a similar state in the other particle is due to our increased knowledge about the values of the hidden variables as we observe the first particle, which, logically, affects the probability to observe a similar state in the second particle. But the fact of the matter is that this state is determined in advance, even if we do not know until we observe it.

A more detailed statistical analysis reveals, however, that such a deterministic explanation with hidden variables cannot give rise to such strong correlations between the entangles particles as seen in experiment. (This is true, at least, in all normal models with hidden variables, where these describe properties of the particles themselves, and go along with them as they move.) On the other hand, the experimental results agree perfectly with the predictions of quantum mechanics.

But in quantum mechanics there is no determinism; the state of the entangled particles are not given before we observe them, and the probabilities are fundamental quantities. We have returned to a model where an observation of one of the entangled particles immediately changes the state of the other, in terms of changed probabilities.  

Ever more refined experiments rule out almost all other explanations of these phenomena than the quantum mechanical one. One of few remaining possibilities to avoid quantum mechanics and Einstein’s spooky action at a distance is to imagine that it is determined beforehand which observations of the entangled particles we are going to make. Then it may be determined that we are always going to do observations that seemingly confirm the strong correlation predicted by quantum mechanics, even though the correlation would have been weaker if we were able to choose our mode of observation freely.

But how on earth could something like that be determined beforehand, and when would it be determined? A research group in Vienna has recently challenged this idea by letting random colour variations in the light from a star located 600 light years away determine the way in which one of the particles in the entangled pair was observed, while colour variations in the light from another star located 2 000 light years away in the opposite direction determined the way in which the other particle was observed. The idea behind this arrangement was to push back the point in time at which the mode of observation has to be determined as far as possible. Since the light from the nearest of the two stars was emitted 600 years ago it must have been determined during the middle ages how the experiment in Vienna in 2016 would be carried out. An absurd thought.

Now we come back to superdeterminism. Rather than to imagine it was determined in an obscure way during a secret counsel below medieval vaults how scientists in Vienna would observe pairs of entangled particles in 2016, we may transcend to a general law of nature that we must always do observations that seemingly confirms quantum mechanics. In reality, though, the world is deterministic and can be described by a mathematical model with hidden variables. This would become clear if only the scientists could choose freely which experiments they are going to perform. Mother Nature is conspiring against us. She consistently hides her true face by just showing us carefully chosen glimpses, which we collect to a distorted portrait.

The truth is that very few physicists take superdeterminism seriously. But among those who do we find the Nobel laureate Gerard’t Hooft and some other highly talented people. How is it possible? I can only understand it psychologically. The metaphysical world view they have painted at the inside of  their cocoons means so much to them emotionally that they refuse to accept that the world out there looks different when they look through the peep-hole in the wall of the cocoon drilled by science.

Aided by that metaphor we may express the idea of superdeterminism as follows. The physicist who is prisoner in her own world view does not want to believe what she sees when she looks at the world through a hole in the wall of the cocoon. She therefore gets the brilliant idea that what she sees, what seemingly contradicts her world view, is just a small picture that someone out there holds in front of the peep-hole. If this someone moved away this little picture so that the physicist inside her cocoon could look out freely, the world would look exactly like she imagined to begin with. But it never happens.

It is easy to make fun of other people’s follies. But each one of us carries a world view that gives meaning and direction to our lives, to our striving. If somebody tries to take it away we react instinctively and forcefully since we risk losing our foothold. We all know the firm grip of religious or political convictions, the impossibility to make someone change her mind by argumentation and finding examples contradicting this conviction. As long as possible we tweak our argumentation and reinterpret empirical facts to defend our position. Those who know me might say that I defend my standpoints more vigorously than most other people, whatever objections I face.

What is interesting is that this forceful and irrational (or rather a-rational) reaction is as evident in scientific battles as in religious or political ones. Evidently, the progression of science since the days of Newton has inspired a metaphysical materialism among Westerners that we adhere to and refuse to let go regardless what science itself suggests. We have become dependent on Newtonian materialism; to question it is to touch something very sensitive in our inner self.

I am psychologising. That is another habit of mine, apart from defending my positions stubbornly. Maybe it is because my dad was a psychologist. Freud, Adler and Skinner were often present at the dinner table when I was a kid, and they looked down on me from the book shelves.

As I grew up, I pulled the books from the shelves and started to read, Freud made a strange impression on me. He wrote with exquisite clarity, control and apparent logic, but the reasoning sometimes led to conclusions that seemed far-fetched or just nuts. I never managed to bridge the gap I sensed between the secure, authoritative voice that you like to listen to, and the fixated querulant who pursues strange theses in absurdum. Conspiracy theorists have a similar trait; they put forward facts and circumstances that support their theories in a seemingly waterproof way, and you are easily caught in the web they spin, but if you take a step back all of it appears far-fetched and stupid.

It is the same thing with superdeterminism. Those physicists who take this final conspiracy theory seriously must suffer from some kind of fixation; they must carry something they feel that they cannot afford letting go, someting that leads these highly intelligent people deep into the irrational quagmire with science and rationality as a beacon.

In his autobiographical book Memories, Dreams, Reflections Carl Gustav Jung devotes an interesting chapter to Freud and their interrupted friendship. Jung relates a conversation that he had in his youth with Freud, where the latter expresses a serious urging:

”My dear Jung, promise me never to abandon the sexual theory. That is the most essential thing of all. You see, we must make a dogma of it, an unshakable bulwark” He said that to me with great emotion, in the tone of a father saying, “And promise me this one thong, my dear son: that you will go to church every Sunday.” In some astonishment I asked him, “A bulwark – against what?” To which he replied, “Against the black tide of mud” – and here he hesitated for a moment, then added – “of occultism.”

I cannot help associating Freud’s conviction of his own sexual theory to some physicists’ conviction of the materialistic world view. Jung analyses Freud’s fixation to his own theory, and I would like to apply a similar analysis to these physicists:

One thing was clear: Freud, who had always made much of his irreligiosity, had now constructed a dogma; or rather, in the place of a jealous God whom he had lost, he had substituted another compelling image, that of sexuality. It was no less insistent, exacting, domineering, threatening, and morally ambivalent than the original one. […] The advantage of this transformation for Freud was, apparently, that he was able to regard the new numinous principle as scientifically irreproachable and free from all religious taint. At bottom, however, the numinosity, that is, the psychological qualities of the two rationally incommensurable opposites – Yahweh and sexuality – remained the same.

We just have to exhange the word sexuality for materialism. The latter should rather be described as amoral than morally ambivalent, though. But both are equally exacting. The former explains the entire human psyche, according to Freud, and the latter explains the entire world, according to its adherents.

But why would we, Westerners, like to exhange God for Materialism? Sexuality is an attraction of its own, apart from being scientifically irreproachable. But what is the allure of materialism? A possible explanation is that it is soothing. It teaches us that life is just some molecules that happen to gather into a human body for a short period of time, that love is just chemistry, that happiness is just a cocktail of neurotransmitters in the brain. The recurrent word just turns into a lullaby that makes us relax. We do not have to wrestle like Jacob with God, we cannot chose freely between good and bad, we have no responsibility for our choices before God or eternity. To question materialism becomes, in that light, an attempt to try to snatch a quilt from somebody’s bed, a quilt that makes life lukewarm and comfortable.  

The world can be described as materialists say that it is, but it is not just like that, even though this description is a very effective tool to manipulate the world as we know it. The closer we examine matter itself, the more it dissolves before our eyes to mathematical abstractions that cannot be interpreted materialistically. The behaviour of the entangled pair of particles is an example of this fact.

Another explanation why belief in materialism stays strong despite these insights is its limitation; its keyword just spares us from infinity. When you think about it, there is hardly any other myth about the world that is easier to understand, and at the same time gives us the feeling that we understand everything. We get the feeling that we are done with the world. It allows us to lock ourselves into a small cocoon where we feel safe, at the same time as it creates the illusion to behold the entire cosmos thanks to the easily comprehensible world view that is painted on its inner walls.

I started this reflection by telling how infinity and the unknown outer space made me tremble as a little kid. A similar trembling and dread can be seen in the laboratory dogs in the Youtube film below, when their cages are opened and the see for the first time ever a large lawn in front of them, and the sky above. A came across this film a long time ago on Facebook, among all the touching and funny animal films that circulate there. But this film stayed in my memory. It is not only touching, but also existential. Just look how the dog watches the outside world with fear and wonder one minute and thirty seconds into the film, and look how the dogs hardly dare to touch the strange grass with their paws to begin with.

The advantages I see to stay in the cage of materialism are, as noted above, that it is soothing and that infinity is shielded. But there are serious drawbacks as well. First and foremost it becomes necessary to deny yourself and your fellow human beings. The living subject has no place in such a world view. Sure, some people say that consciousness can be explained as a collective result of the many intricate processes going on in certain complex systems, like the human brain. According to this line of thought, consciousness is emergent. But that is an empty word in this connection, even though it sounds beautiful. A five year old who has not yet been stuck in materialistic conceptions realises that subjective perceptions and the objective items of these perceptions are qualitatively distinct aspects of the world. It is impossible to deduce the ones from the others, just like it is impossible to deduce colours from sounds or letters from figures.

It is odd that so many people turn to materialism despite the self-denial that is required. It was logical as long as science suggested a strictly materialistic world; you had to try to accept that the world is as cold and mechanistic as it seemed to be. But science no longer points in that direction. Therefore there has to be an irrational force that makes us want to deny ourselves.

Is it psychologically necessary? Don’t we have the guts to look into each other’s eyes and say ”Hey, you exist and your existence means something! You are, you are not just. You cannot be reduced to something else, you are a miracle!” Are we so frightening that we better close our eyes before the mirror? Most of us have brushed our teeth in front of the bathroom mirror and suddenly happened to look into our own eyes. Then it may happen that your self-consciousness is heightened, like in an acoustic feedback; the primitive sensation that you exist causes vertigo. Then you are pushed away from yourself again, like if somebody pulled the cord from the socket to put an end to the feedback loop.

That the living subject is a fundamental aspect of the world does not necessarily mean that there is providence, warmth, a benevolent God. Is the thought of a cold and living world more frightening than the thought of a cold and dead world? Is that the reason why we turn to the second alternative? A living monster maybe scares us more than a mechanical monster?

When I categorically claim that materialists deny the living subject, I do not claim that they are cold and ruthless towards themselves and other people. Luckily, most of them do not live as they preach. To speak psycho-language again, they are mentally dissociated. Thought, feeling and action do not fit together. This dissociation is equally grave among materialists as among Christian creationists who at the same time are interested in science, and enjoy the fruits in the form of modern technology.

As I see it, the entire Western society is dissociated in this way. Newton concluded that the same laws of nature applied in heaven and on earth. The angles had to land on the ground, cut off their wings and make their living just like anybody else. From this insight there is a line of development to the ideal of equality that was forcefully expressed in the French revolution and in the U.S. constitution. We are equal before the law and have the same rights and obligations. The society of privileges crumbled. Rulers answered to the people rather than to heaven. The individual started to be seen as the fundamental unit of society and all individuals were assigned the same value.

At the same time there is no place for the living individual in a materialistic world view inspired by Newton’s physics. The word individual derives from Latin and means indivisible, but the only unit that is indivisible in a materialistic world is the atom, which is the Greek version of the same word. Man does not possess an indivisible soul but is equivalent to his body, which can be divided into ever smaller parts until we reach the level of the atoms. The behaviour of these atoms is determined by the laws of nature, and therefore the behaviour of human beings are completely determined by the same laws of nature. There is no place for the free will that is a prerequisite for Western justice, which is based on individual responsibility. The laws of society are therefore dissociated from the laws of nature that have inspired them.

Such dissociation at the root of a society cannot be sustainable in the long run. Then the right hand of the societal body does not know what the left hand does. When one of the dissociated conceptions finally crumbles under the pressure from the other, there will be confusion and aggression because of the lack of understanding of the underlying forces that has led to this situation.

The incompatible traits of individualism and atomistic materialism are exposed most clearly in the abortion debate. When does the foetus stop being just a collection of atoms in the womb of a woman, becoming an individual of its own? When does it acquire the right to its own life? The most stubborn abortion advocates do not even seem to realise that it is an existential problem that we have to tackle in one way or the other. Instead they repeat as a mantra that the woman has the right to her own body. But that answer is an non sequitur since it does not address the question. That is the way a dissociated individual reacts, a person unable to let two aspects of her conceptions meet and chafe.

Many people who lock onto a certain type of conception and refuse to try other perspectives are probably just afraid what will happen if they let go. Seas never sailed are filled by fantasy with sea monsters. If you admit that abortion is an existentital problem you are afraid that you are immediately transformed into a fanatical pro-life acitivst in the U.S. who foams with rage, waving placards referring to the Bible outside abortion clinics. If you would admit that personal existence is unfathomable, that we cannot explain the spark of life, you are afraid that you are immediately transformed into a spaced out new age type who cannot think straight.

Wolfgang Pauli is an example showing that this does not have to be the case. He is one of my favourite physicists. When he was thirty years old he underwent a crisis. He divorced, his mother committed suicide; he started to drink, quarrelled, and had intense dreams that worried him. To get help he contacted Carl Gustav Jung, who worked in Zürich, just like Pauli. Jung is considered to be the great mystic among the psychologists, with his ideas about the collective unconscious, about archetypes and synchronicity. Pauli embraced these ideas despite his scientific outlook, and he seemed to need them to understand himself and his dreams.

What is more, Pauli had no problems whatsoever to accept the new direction away from materialism that physics took as a result of the quantum mechanics that he helped to develop himself. He even predicted that future physics would move even farther away from these conceptions. Even so, Pauli was anything but a spaced out new age type who could not think straight. He was commonly known as the conscience of physics, and ruthlessly criticised colleagues who wrote papers, which lacked exact result and predictions, or which were logically and mathematically obscure.

Sure, his exact scientific personality and his need to explore subjective states of mind reveal a double face. But at least he tried to get the two mental poles to cooperate more harmoniously, to avoid dissociation. In a letter to Jung from 1934 he describes his dreams about wasps, and interprets the separate dark and bright stripes on their bodies as symbols of the two diametrically opposed attitudes in his own psyche. In the same letter he also writes:

The specific threat to my life has been that in the second half of life I swing from one extreme to the other […]. In the first half of my life I was a cold and cynical devil to other people and a fanatical atheist and intellectual ”enlightener”. The opposite to that was, on the one hand, a tendency toward being a criminal, a thug (which could have degenerated into me becoming a murderer), and, on the other hand, becoming detached from the world – a totally unintellectual hermit with outbursts of ecstasy and visions.

One may ask whether Western society has to go through another convulsion before the two incompatible principles of individualism and materialism that it is built upon become reconciled, in the same way as Pauli started to tackle the incompatible aspects of his personality only after a personal crisis. Let us hope that it is possible to dissolve the societal dissociation in a more harmonious way.

I always write much longer texts than I plan to do. I have talked about people who voluntarily live their lives in small cocoons to get peace and quiet, who paint pictures on their inner walls, which they confuse with the outside world. I have psychologised people and called them dissociated when they do not dare see all aspects of the world at once. Am I any better myself? No and yes! I am equally afraid of the world in which happen to find ourselves as anybody else, or maybe even more so. I have an equally large need to shield it, to sort the perceptions so that I only receive as many and as strong ones as I can handle. Probably I have spun thicker walls in my cocoon than most other people. But I try to avoid filling its inner walls with fantasy images, with myths. I rather stare at the bare walls. Now and then a ray of light finds its way through the threads which make up the wall, sometimes I see the contours of something moving outside. In that way I might learn something about the world. That is the way I want to live, that is the way I am able to live.

(to myself and others)

Michel de Montaigne:

The frontiers of our research are lost in dazzling light. Plutarch, writing of the fountain-heads of history, says that when we push our investigations to extremes, they all fall into vagueness, rather like maps where the margins of known lands are filled in with marshes, deep forests, deserts and uninhabitable places. That explains why the most gross and puerile of rhapsodies are to be found among thinkers who penetrate most deeply into the highest matters: they are engulfed by their curiosity and their arrogance.

The beginnings and the ends of our knowledge are equally marked by an animal-like stupor: witness Plato’s soarings aloft in clouds of poetry and the babble of the gods to be found in his works. Whatever was he thinking about when he defined Man as an animate creature with two legs and no feathers? He furnished those who wanted to laugh at him with an amusing opportunity for doing so. For, having plucked a live capon, they went about calling it `Plato’s man’. [1]

Detail of Carta Marina by Olaus Magnus (1539)

Tomas Tranströmer:

The truth is there on the ground
but nobody dares take it.
The truth lies on the street.
Nobody makes it his own. [2]

[1] From Apologie de Sebond in the Essais (1580/1589). Translation to English by M. A. Screech, Penguin Books (1987).

[2] From the poem Air Mail in the collection För levande och döda (1989). Translation to English by Don Coles in the collection For the Living and the Dead, Buschek Books (1996).

Nature has tried to tell us for a hundred years that we should remove from the scientific world-view the idea that the world around us is still there even if all aware inhabitants disappear. As I see it, we must finally learn the lesson that reality as we know it is observer-dependent in order to develop physics further.

Many physicists refuse to accept this conclusion, in part because they fear the implications. But there is no need to be afraid. To say that reality is observer-dependent does not imply that everything is subjective, nor does it imply solipsism. And it is still possible to do science in such a world. At least, this is what I argue in the present blog post.

Fruitful thoughts

It is not possible to prove that observers are indispensable in modern physics. But all attempts to understand the structure of relativity and quantum mechanics in a straightforward way without referring to observers have failed so far.

An even stronger hint that observers are indeed crucial is the fact that the original ideas that led to these theories revolve around observers, and the question what they can see, feel and measure. The fact that such ideas bear fruit must mean something.

The spark that inspired Einstein to formulate the special theory of relativity was a disturbing question that came to him already when he was sixteen years old. What would it be like to bicycle along a beam of light, at virtually the same speed? Would the cyclist observe a frozen light wave? In his Autobiographical Notes [1] Einstein writes

“From the very beginning it appeared to me intuitively clear that, judged from the standpoint of such an observer, everything would have to happen according to the same laws as for an observer who, relative to the earth, was at rest. For how should the first observer know or be able to determine, that he is in a state of fast uniform motion? One sees in this paradox the germ of the special relativity theory is already contained.”

In a lecture in Kyoto in 1922 Einstein described how “the luckiest thought” of his life came to him in 1907 [2], a thought that eventually led to general relativity in 1915.

“The breakthrough came suddenly one day. I was sitting on a chair in my patent office in Bern. Suddenly a thought struck me: If a man falls freely, he would not feel his weight. I was taken aback. This simple thought experiment made a deep impression on me. This led to the theory of gravity.”

The breakthrough in the mathematical formulation of quantum mechanics was a paper written by Heisenberg in 1925 [3]. Its abstract simply reads, in English translation:

“The present paper seeks to establish a basis for theoretical quantum mechanics founded exclusively upon relationships between quantities which in principle are observable.”

Heisenberg goes on to write:

“It is well known that the formal rules which are used in quantum theory for calculating observable quantities such as the energy of the hydrogen atom may be seriously criticized on the grounds that they contain, as basic element, relationships between quantities that are apparently unobservable in principle, e.g., position and period of revolution of the electron.”

The immense fruitfulness of these ideas is a hint as clear as any hint can be that we should walk further along the same road as we try to develop physics further.

Not so fruitful thoughts

Nevertheless, in recent decades many physicists have tried to walk in the opposite direction.

Some have supplemented the established formalism of modern physics with ‘hidden variables’ that describe entities with no direct relation to observations. Sometimes these entities are called ‘beables’, in contrast to the ‘observables’ that are sufficient to formulate standard quantum mechanics. (An example of a beable would be an electron which always possesses the well-defined position. This position would then be the corresponding hidden variable.)

Others are gluing the label ‘real’ on the mathematical tools that are used to express the laws of modern physics, like the wave function or quantum fields. These tools then become a more abstract form of beables.

Physicists playing with such models hope that they will be able to weave a fundamental layer of observer-independent reality from the thread defined by these beables. Observables and actual observations are imagined to emerge somehow as secondary phenomena out of the woven fabric. However, in order to conform with all the empirical facts, it seems that this fabric necessarily becomes very messy and ugly. Furthermore, as far as I am aware, such models have not led to a single new prediction confirmed by experiment.

The fact that these beables are imagined to be the only building blocks of the fundamental layer of reality means that observers are locked out from the construction by assumption. No surprise, then, that it is very hard to let them in afterwards through the locked door. Philosophers and physicists bang their heads against the hard walls defined by the fabric of beables, pondering the ‘hard problem of consciousness’ they have created themselves.

Some theoretical physicists concede that it is impossible to solve this ‘hard problem’. They admit that consciousness is an essential element of the world, but argue that it cannot be understood or described by science. In so doing they look upon conscious observers as immaterial spirits that can float through the walls of beables to become inhabitants in their house. It is odd that physicists accept the idea that there are essential elements in the world that lie outside science. It is even more odd that they seem blind to the fact that modern science already incorporate consciousness, in the sense that the basic postulates of quantum mechanics are formulated as a relationship between the observer and the observed.

Jenny Hasselquist and Lars Hanson as Marianne Sinclair and Gösta Berling, respectively, in the movie “Gösta Berlings saga” from 1924.

Trying to escape from oneself

Instead of introducing beables in order to evade the conclusion that conscious observers are fundamental one may try to objectify the act of observation.

Naively, an observation always has a subjective side to it: someone observes something. Many physicists deny this fact by saying that it is sufficient as far as physics concerns to consider ‘observations’ made by a measuring apparatus. Such an ‘observation’ just amounts to an interaction between the system of interest and the apparatus. We might introduce a conscious physicist who in turn observes the pointer readings of the measuring apparatus after the interaction, but that is immaterial, they say. Alternatively, they claim that the observing physicist is equivalent to such an apparatus. This is the hard-core materialist approach. In either case, the driving force is the wish to objectify the observing subject.

But we fool ourselves if we think that it is possible to look upon ourselves as observers from an outside objective position. The best you can do to transcend yourself is to hold up a mirror in front of you. But the picture that you see will still be created from within. You may position a second mirror to capture the image of yourself holding the first mirror, thus analyzing the interaction between a system of interest – yourself – and a measuring apparatus – the mirror. But the picture that you see is still created from within. You may introduce a third mirror to capture the entire scene, and so on. The more mirrors you introduce the smaller and more shattered will be the picture of yourself that you see in this hall of mirrors. But you are still stuck within yourself, even though your heart is shrinking. Genuine objectification of observations is impossible.

I come to think of the unhappy heroine Marianne Sinclair in Selma Lagerlöf’s novel Gösta Berling’s saga [4]. She played the mirror game all her life, trying to escape from herself, looking upon herself from the outside as an object of analysis – except one night when Gösta Berling came right at her and crushed all the mirrors.

“But we thought of the strange spirit of self-consciousness which had already taken possession of us. We thought of him, with his eyes of ice and his long, bent fingers,—he who sits there in the soul’s darkest corner and picks to pieces our being, just as old women pick to pieces bits of silk and wool.

Bit by bit had the long, hard, crooked fingers picked, until our whole self lay there like a pile of rags, and our best impulses, our most original thoughts, everything which we had done and said, had been examined, investigated, picked to pieces, and the icy eyes had looked on, and the toothless mouth had laughed in derision and whispered,—

‘See, it is rags, only rags.’

—

And if one looks carefully, behind him sits a still paler creature, who stares and sneers, and behind him another and still another, sneering at one another and at the whole world.

And while Marianne lay and looked at herself with all these staring icy eyes, all natural feelings died within her.

She lay there and played she was ill; she lay there and played she was unhappy, in love, longing for revenge.

She was it all, and still it was only a play. Everything became a play and unreality under those icy eyes, which watched her while they were watched by a pair behind them, which were watched by other pairs in infinite perspective.

All the energy of life had died within her. She had found strength for glowing hate and tender love for one single night, not more.”

Lagerlöf expresses how our “best impulses” and “most original thoughts” are picked to pieces by the pale creature. We may compare to the traditional scientific analysis of free will, where each impulse and choice is considered to be predetermined by the physical processes that go on in our brains. We look at the pale mirror image of ourselves and conclude that there is nothing original in our whims and ideas, that they are all secondary to electrochemical activity, which can be investigated and picked to pieces until nothing is left unexplained.

But this picture is challenged by quantum mechanics. The reason is the simple fact that its formalism take our own observations as a starting point, rather than processes that can be analyzed from a hypothetical objective, external position.

Quantum mechanics deviates from determinism at two levels. The observable outcome of a given experiment is not always determined beforehand. All we can do then is to assign probabilities to the different outcomes. We can apply this fact to our own brains and argue that some of our impulses and thoughts are not predetermined, but appear by chance with a given probability. We are dices in God’s hands.

But there is an even deeper lack of determinism in quantum mechanics, which is not so often discussed. To be able to decide the probabilities for different outcomes, we must first choose which experiment we are going to do. And quantum mechanics remains silent about this choice. The theory is expressed in the form “Given that we observe a certain system in a certain way, the probability to see this or that is so and so.” If I look to my right I will see this or that with certain probabilities, and if I look to my left I will see this or that with other probabilities. But quantum mechanics does not say anything at all about which direction I will actually look. This is often called Heisenberg’s choice, and it lies outside the scientific description, as far as quantum mechanics can tell. Even so, it has tangible consequences; it affects the future evolution of the physical world.

Now we may try to evade this conclusion by calling on the pale creature to observe ourselves from the outside. Then we may say that there is a meta-experiment performed by the pale creature whose outcome determines which experiment we are going to choose. In the above example the outcome of this meta-experiment decides whether we are going to look to the right or to the left. If our pale creature dissects our brain well enough, he might be able to decide the probability of each outcome, saying that we will look to the right with probability 2/3 and to the left with probability 1/3.

But as the creature focuses on this task we must ask ourselves what on earth made the creature choose the particular meta-experiment that decides whether we are going to look to the left or to the right. We have to consider a meta-meta-experiment that decides whether we are going to do either of those things, or something completely different, like singing a song. Ah, but let’s call upon the still paler creature that sits behind the first creature to perform this meta-meta-experiment.

We may go on forever, creating an infinite tower of self-observing creatures, placing an infinite number of mirrors in the mirror hall. We still cannot escape the conclusion that we start with an original choice that is beyond scientific description, simply because this is the premise when we apply the deepest scientific theory that we have – quantum mechanics. Thus we can sweep away all these pale creatures and mirrors from the mind, like Gösta Berling did. We can acknowledge ourselves and the fact that there seems to be “original thoughts” and “best impulses” coming to us from God knows where.

This liberation of the mind is not possible in classical, Newtonian physics. It presupposes the existence of a external, objective position from which everything can be observed and analyzed in detail, and everything that happens can be determined beforehand, at least in principle.

We may thus characterize the difference between classical and modern physics by saying that the former disregards that we cannot escape from ourselves, whereas the latter acknowledges it.

Don’t be afraid

Are we deserted within ourselves if this interpretation of modern physics is true? Whom or what can we hold on to? My impression is that the unease caused by these questions, and the instinctive unwillingness to look for answers that follow, is an important reason why many physicists try to find another interpretation of modern physics, an interpretation that keeps close to the safe and familiar shore of classical physics instead of heading straight into deep waters. But there are tentative answers to the questions above, answers that point to another shore that may be more interesting and appealing than the one we left more than a hundred years ago.

What may an observer-dependent world mean?

Here’s my attempt to answer the pressing questions. My arguments are tentative, and some of them may appear ‘poetic’ or even obscure. My only aim is to make one or two readers say to themselves: “Maybe this might be reasonable after all. Let’s explore these matters further.”

To summarize, I will try to motivate seven claims about the observer-dependent world suggested by modern physics:

1) The truth is still out there
2) Science survives
3) We can still pick the radio to pieces to learn how it works
4) There is still an external world
5) You are not alone
6) It is not anthropocentric
7) It is as little mystical as a world can ever be

Let’s discuss these claims one by one.

1) The truth is still out there

Quantum mechanics suggests that we should not imagine physical objects with properties that transcend our ability to perceive them. Basically, all objects are objects of perception. But there must be something that transcends the mere perceptions in any well-defined world view. The very statement that all objects are objects of perception is a statement about the nature of the world that transcends the perceptions to which it refer. In fact, any statement about the world as we perceive it is a transcendental statement in this sense. And we must be able to talk about what we see, hear and feel. We must also assume the distinction between true such statements and false ones. This is perfectly possible in an observer-dependent world.

There are also forms of perception such as the passage of time into which all perceptions are placed. We cannot break these forms; they are immutable. In this respect they resemble the laws of physics. In my own research I try to establish a certain one-to-one correspondence between physical laws and forms of perceptions. These rules of the game define an objective world into which we are thrown.

2) Science survives

I talked about the laws of physics. Despite what some people think, we can still do science in an observer-dependent world. Science and realism have no direct relation to each other – science is a method to accumulate and structure knowledge based on observations, realism is a metaphysical idea that says that the objects that we see somehow exist even if there is nobody there to look at them.

3) We can still pick the radio to pieces to learn how it works

It is easy to arrive at the conclusion that if the objects do not have an independent existence, the things that we see are nothing more than visual effects in a kaleidoscope, random reflections in the pieces of a broken mirror. There is no depth to the picture, no underlying order, no persistence.

But this conclusion is false. It is possible to assign an identity to an observed object, and to uphold this identity as time passes if we track it continuously. We can speak about this given object disappearing out of sight, and then returning again, like the sun in the morning. If we let physical law act on an object that is observed at some point in time this law may simply tell us that the object will play hide and seek as time goes. But physical law will act differently on a hypothetical object that we have not yet observed. And it cannot be applied at all to an imagined object that is not observable in principle. That’s how I see it, at least.

We can learn more about such an identifiable object that we just take a superficial glance at to begin with. We may pick it apart to see what it is made of. This is still possible in an observer-dependent world. Just like it is possible to define the identity of an observed object in such a world, it is also possible to define the notion that it consists of smaller parts. In other words, if we consider two objects it is sometimes possible to say that one is a part of another. In mathematical language, we can uphold the notion of sets and subsets.

In the picture I am suggesting, the physical state of the object is defined by the knowledge we have about it, and physical law acts on this state to determine how the object evolves. The possibility to increase the knowledge about the object as time goes by makes it necessary to allow for a formulation of physical law that acts on the smallest parts of the object we can ever know about. Therefore the principle of reductionism may be valid in an observer-dependent world just like in an observer-independent one.

The notion that one observable object is a physical part of another defines a directed relation between them. One object points to the other. There are many more examples of such arrows between objects of perception. A generalization is an abstract object of perception that refers to the set of concepts it generalize. A memory is an object of perception that refers to an event in the past. A symbol is an object of perception that refers to the object it symbolizes, which is also an object of perception. A statement refers to a set of other objects and their internal relations. I think that the existence of such arrows between objects must be seen as part of the fundamental structure of the world. We cannot make them ‘emerge’ from the objects themselves – just as we cannot make conscious observers emerge from a fabric of beables. The world is simply delivered with a bag of such arrows, and also with a fundamental relation between the observers and the observed. The arrows make it possible to weave a world with rich structure, containing hierarchies and depths. Without them we are left with the structureless heap of pieces from the broken mirror I started out with.

4) There is still an external world

We all instinctively make the distinction between our own body and the external world. In the observer-independent world suggested by classical physics, the external world continues to exist even if the bodies of all conscious observers disappear. This is not so in the observer-dependent world suggested by modern physics. Nevertheless it is still possible to make the distinction between your own body and external objects in such a world. However, both your body and the external objects are basically objects of perception.

5) You are not alone

The most common reaction to the idea of an observer-dependent world is: “But that means solipsism!” This is not so.

The incorrect conclusion follows from the idea that observers should be identified with their bodies. As stated above, all objects are assumed to be objects of perception. But the only observer whose perceptions I have firsthand knowledge about is myself. Therefore I may argue that all objects are objects of my perception, including the bodies of other potential observers. If the bodies and the observers are identified their existence depends on my perceptions, and is therefore secondary to me.

However, there is a crucial difference between the idea that a person should be identified with her body, and the idea that everything she perceives corresponds to activity in her body. The latter idea contains the operationally relevant aspect of the concept of materialism. This type of ‘operational materialism’ may survive and thrive in an observer-dependent world.

In fact, the idea that an observer should be identified with her body is not consistent with the premise of the discussion, that the world is observer-dependent. Your own body is then an object of your own perception, just like body of everybody else. And you cannot identify yourself with a part of your own perceptions.

Let us therefore continue the discussion with the assumption that there is an aspect of ourselves that cannot be identified with our bodies. This means that we acknowledge both poles in the observer-observed pair, or the subject-object pair, and treat them both as fundamental. This does not mean that they can be separated from each other, like Descartes tried to do with his dualistic notions of res cogitans and res extensa; quantum mechanics is expressed as a relation between the observer and the observed, and if quantum mechanics is fundamental, so is this relation.

Then the subjective aspect of another observer can have an existence that is independent of your existence, even though her body is an object of your perception. She may have original thoughts and make original choices, in the sense discussed above, just like you. Having liberated the ‘souls’ of our fellow beings in this way, their bodies are also let free. Even though the body of the other observer may still seem secondary to you since it is an object of your perception, your body correspondingly becomes an object of her perception. You and your fellow beings are then placed at the same level ‘body and soul’.

Let us explore these symmetries a little bit more. We have argued that it is perfectly possible to have a set of several subjects, which are equal in the sense that the existence of any one of them is not conditioned on the existence of any other. In an analogous way we know that we have a set of several objects in the physical world that are independent in the same sense: there are many apples in an apple tree, and if we eat one of them, the others do not vanish as well.

However, even if the members of the set of subjects are independent, just like the members of the set of objects, the two sets are not independent of each other. This is the core idea of a materialistic observer-dependent world. We have argued that all objects are objects of perceptions, and therefore they cease to exist if the set of subjects disappear. And experience tells us that our perceptions depend on our bodies. If the set of objects in our bodies disappear, so does the set of subjects.

Just like one subject may observe several objects, one object may be observed by several subjects. This symmetry between the subjective and objective aspects of the world may seem self-evident from everyday experience, but to promote it to a postulate makes it possible to use it to define the fundamental notion that several subjects live in the same world. They do so if and only if they sometimes observe the same object, be it an apple tree or each other’s bodies.

We may say then that this common world is defined by the sum or union of the perceptions of all the subjects that live in it, together with all the true statements they can make about their perceptions. In such a world physical law becomes a rule according to which this common state of knowledge about the world evolves.

We are clearly not alone in such a world. Our individual experiences and observations become a small part of its fabric. Just as we can divide the objective aspect of the world into small atoms, we may divide the subjective aspect into ‘small’ individuals. The word atom derives from the Greek word atomon, which means indivisible. The word individual is derived from the Latin word individuus with the same meaning. The fact that both the objective and the subjective aspects of the world can be described in a similar atomistic way supports the idea that they are symmetric to a considerable degree.

I have argued that it is possible to accomodate several observers in an observer-dependent world. But I have not yet given any argument why there should be several observers, apart from saying that it is natural for reasons of symmetry. I know of one such argument, at least.

In special relativity, two observers can measure different spatial and temporal distances between a given pair of events, depending on how they move in relation to each other. The Lorentz transformation provides the recipe for how distances measured by one observer are related to the distances measured by the other. All equations that express physical law remain the same when a Lorentz transformation is applied to the spatio-temporal coordinates that are used to express them. This means that the measurements of all observers are equally valid, regardless their relative velocity, and that they are ruled by the same laws of physics.

My reading of all of this is that the world is constructed in order to accommodate several observers and to make them all equal – meaning that their measurements are equally valid even if they happen to differ from each other. The argument that leads to the Lorentz transformation presupposes two or more observers who observe the same object or event. The fact that the form of physical law remains the same when a Lorentz transformation is applied means that such situations are built into the structure of the world.

6) It is not anthropocentric

A common objection to the idea of an observer-dependent world is to say that it is anthropocentric. The reasoning goes something like this:

“Some people say that an experiment does not have a definite outcome before a physicist observes the result. Consciousness collapses the wave function and gets rid of its spooky superpositions. In other words, the state of the specimen that is studied in the experiment becomes real under the eyes of the physicist. But it’s ridiculous to think that we have to rely on human physicists performing experiments to make the world around us real.“

This reasoning is inaccurate in two respects.

First, consciousness cannot be seen as an agent that acts on something else, like a wave function. Such a dualistic conception is untenable. Rather, everything must be looked upon as consciousness, in the sense that all objects basically are objects of perception. The wave function collapse is just a formal description of the subjective increase of knowledge that occurs due to an observation in a controlled experimental setting.

Second, there are many other situations than scientific experiments in which our knowledge increases in a similar way. In fact, it occurs whenever a conscious creature makes a new observation, regardless whether it is a physicist, another human or an aware animal. Together we make the world real by our observations. We learn more about the perceived objects and new objects of perception come into our field of vision.

Not even in the lab does it matter who is making the observation. It is irrelevant whether the observer passed all her physics exams, whether she put on the white lab coat, or whether she is human at all. I would like to quote the prominent physicist Wolfgang Pauli [5], speaking about quantum mechanics:

“[T]here remains still in the new kind of theory an objective reality, inasmuch as these theories deny any possibility for the observer to influence the results of a measurement, once the experimental arrangement is chosen. Therefore particular qualities of an individual observer do not enter the conceptual framework of the theory.”

My working hypothesis is that the immutable forms of perception reflect the laws of physics, and vice versa. Examples of such forms of perception are the directed flow of time and the fact that objects can be divided into parts. If this hypothesis is correct, these forms are common to all conscious creatures that live in the same world, since all such creatures are governed by the same laws of physics. This is a comforting thought, I think. It would mean that all beings are brothers and sisters that look in a similar way at the world into which we are thrown. We can then understand each other at a basic level.

7) It is as little mystical as a world can ever be

Another common objection to the idea of an observer-dependent world is that it is mystical or approaches the ideas associated with ‘new age’. Some even say that it cannot be combined with science.

Such reactions do not in themselves form an argument against the idea. Rather, they express distaste. Science does not rely upon a specific metaphysical idea like realism, but on the empirical method, rationality, and the coherence and clarity of the concepts that are used to build models. I come to think about a quote by Darwin [6]:

“In scientific investigations it is permitted to invent any hypothesis, and if it explains various large and independent classes of facts it rises to the rank of a well-grounded theory.”

Put differently, it is not the content of a hypothesis that makes it scientific or not, rather its form. The new age movement has made a great disservice to hypotheses about the physical world that are centred around observations and consciousness, since they have become associated with the intellectual sloppiness and wishful thinking that is abundant in that milieu.

In an observer-dependent world, the history of the universe before the appearance of the first aware beings must be seen as an abstract extrapolation backwards in time using the laws of physics. The true creation is not the Big Bang but the first dim perception. There is no pre-existent physical world into which the first aware creature was born. Some people are repelled by this fact, and look upon it as a kind of creationism. The repulsion is another expression of the fear that science and spirituality will become intermingled.

I can understand the feeling that we lose firm ground to stand on if there is no pre-existent physical world into which we were born. But the firm, objective ground is still there, albeit in a more abstract form, as discussed under the headline “The truth is still out there” and onwards.

In fact, I would like to argue that such a ‘creationism’ is less mystical than the ordinary realistic and scientific story about the creation of the world. In that story we have two creations that cannot be explained in terms of something that was there before. First, we have the creation of the physical world in the Big Bang. Second, we have the appearance of consciousness when the first sufficiently complex creatures had evolved in this physical world. This second creation cannot be explained in terms of the first. That would amount to a solution to the hard problem of consciousness. This is impossible in principle since that problem is not properly posed, but the result of the untenable idea that it is possible to separate the observer from the observed in the dualistic spirit of Descartes. If we accept that the poles in this pair are distinct but inseparable we are left with just one mystery instead of two – the creation of both poles together.

I would say that the question whether an observer-dependent world is ‘mystical’ is a different one than the question whether consciousness is central. I would like to define mysticism as a belief in entities and realms of which we have no every day, tangible perception, and also the belief that these entities and realms are necessary to account for ourselves and the world in which we live.

In this sense those who feel the need to emphasize the existence of an observer-independent world are clearly mystics, since the realm in which they believe by definition cannot be reached by observation. Those of us who think that an observer-dependent world is sufficient are not necessarily mystics, on the other hand. We do have to believe in truth, objective physical laws and immutable forms of perception. Otherwise we fall in the trap of postmodernism. But these entities can be sensed and analyzed by ordinary means of perception, even though we do not have free access to the truth in which we believe, unfortunately.

Comfort: An observer-independent reality can never be ruled out

The statement that there is an observer-independent world is metaphysical. But so is the statement that there is no such world. From a scientific point of view both statements are meaningless. Anyone who wants to persist in the faith that there is an observer-independent world out there can therefore continue to do so regardless where science takes us in the future.

Even if the freedom to invent scientific hypotheses is large, as Darwin pointed out in the quote above, it clearly cannot be applied directly to such metaphysical statements. However, it can be used to address a related question.

It seems to me that one of the main lessons of quantum mechanics is that we should not represent the physical state of the world as if we know everything about it, as if we know the exact positions and velocities of all particles in the universe. If we do that we get the wrong answer when we ask physical law how the world evolves. This means that physical law acts on a state that corresponds to our incomplete knowledge about the world rather than on a state that corresponds to a perfect image of a hypothetical observer-independent world where all particles have definite positions and velocities. Simply put, physical law seems to act on our knowledge about the world, not on a hypothetical world in itself. If we try to feed it with metaphysics, it spits it out.

This idea can be promoted to a scientific hypothesis that can indeed be tested: physical law is such that if we feed it with data and entities that cannot be known or observed, then it spits out wrong predictions. I have given this simple principle a fancy name – explicit epistemic minimalism – and I claim that it explains various large and independent classes of facts in the words of Darwin.

This is a hypothesis that constrains the form of physical law; it is not a hypothesis about the world as such. However, if it is correct then the observed world of knowledge becomes self-sufficient to a considerable degree. Then we cannot use the laws of physics as a handle to open the door to the underlying observer-independent “real” world, since physics just refers to what we already know. But we do need such a handle to the underlying real world to be able to say anything intelligible about it; it must send an ambassador to our world of knowledge that can tell us some of its secrets.

But the ambassador has not yet revealed herself. The underlying real world, if it exists in some sense of the word, therefore seems to have very little to do with the world that we actually observe. Many philosophers and scientists have arrived at the same conclusion. For example, Erwin Schrödinger wrote the following in his essay “My view of the world” [7]:

“Kant having established that the “tree in itself” is not only (as the English philosophers knew already) colourless, odourless, tasteless, and so on, but also belongs entirely to the realm of things-in-themselves which must in absolutely every respect remain inaccessible to our experience, we are in a position to declare once and for all that this thing-in-itself holds no interest for us whatever; that we are going, if necessary, to disregard it. Now, in the realm of things which do interest us, the tree presents itself just once, and we can just as well call this single datum a tree as a perception-of-a-tree – the first having the advantage of brevity. This one tree, then, is the one datum we have: it is at one and the same time the tree of physics and the tree of psychology. As we observed at an earlier point, the same elements go to make up both the Self and the external world, and in various complex forms are sometimes described as constituents of the external world – things – and sometimes as constituents of the Self – sensations, perceptions. These thinkers call this the restoration of the natural concept of the world, or the vindication of naïve realism. It does away with a whole mass of pseudo-problems, in particular the famous ignorabimus of Du Bois Reymond, of how feeling and consciousness could arise from a movement of atoms.”

Let the dead ones go

I don’t know if any believer in an observer-independent real world found comfort in the preceding section. Considering the development of physics during the last hundred years, such a belief, to me, resembles the belief that a beloved person who has died lives on somewhere, in some other realm. I do entertain such thoughts myself, sometimes.

I don’t want to give the impression that it is easy to give up beliefs of this kind. Even those physicists who developed and championed the Copenhagen interpretation of quantum mechanics in the twenties did not arrive easily at the conclusion that physics only deals with appearances, with what we can say about the world rather than what is. For example, Werner Heisenberg expressed himself in the following way [8]:

“During the months following these discussions an intensive study of all questions concerning the interpretation of quantum theory in Copenhagen finally led to a complete and, as many physicists believe, satisfactory clarification of the situation. I remember discussions with Bohr which went through many hours till very late at night and ended almost in despair; and when at the end of the discussion I went alone for a walk in the neighbouring park I repeated to myself again and again the question: Can nature possibly be so absurd as it seemed to us in these atomic experiments?”

Maybe the shock felt by the physicists in the twenties when classical physics finally died after a long period of illness resembled the shock that we feel when an ill family member or friend finally passes away.

When a beloved person dies, the world as we know it is torn apart. But after a while we reconstruct it again so that it becomes similar to what it was before, but not quite the same. The latter process has been going on in the physics community in the last decades. Many physicists have recently turned their backs on the Copenhagen interpretation and tried to construct new interpretations of quantum mechanics that rely on modified observer-independent models of the world. They are not quite the same as the old Newtonian model, but they may nevertheless be called “classical”.

They cannot accept the death of classical physics, they cannot let go of the picture of the world that it painted. And now they think that they can bring it to life again. As we have discussed above we can never exclude the possibility that they are right. We can never exclude the possibility that the deceased loved one suddenly is knocking on our door again. But there is no sign of any such resurrection.

In the end, the metaphysical picture of the world associated with classical physics was just an imaginary friend. It was never there, it was all in our heads. There is no real loss. The world remains the same after it passed away. The only thing that has changed is our perspective. Physics can move forward only if we accept this new perspective wholeheartedly, I think.

References

[1] Albert Einstein, Autobiographical notes, translated and edited by Paul A. Schilpp, Open Court (1949)

[2] Albert Einstein, How I created the theory of relativity, translated by Yoshimasi A. Ono, Physics Today 35(8) pp. 45-47 (1982)

[3] Werner Heisenberg, Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen, Zeitschrift für Physik 33(1) pp. 879–893 (1925)

[4] Selma Lagerlöf, Gösta Berlings saga, Frithiof Hellbergs förlag (1891). English translation: Pauline Bancroft Flach, The story of Gösta Berling, Gay and Bird (1898)

[5] Wolfgang Pauli, Matter, in: Writings on Physics and Philosophy, edited by Charles P. Enz, and Karl von Meyenn, Springer-Verlag (1994)

[6] Charles Darwin, The variation of animals and plants under domestication, Volume 1, John Murray (1868)

[7] Erwin Schrödinger, Meine Weltansicht, Zsolnay (1961). English translation: Cecily Hastings, My view of the world, Cambridge University Press (1964)

[8] Werner Heisenberg, Physics and philosophy: the revolution in modern science, HarperCollins (1958)

Schrödinger looked into the future and the past at the same time, just like Janus. He opened the door to modern physics, and then tried to close it. He wanted to return to the secure world of classical physics at the same time as he dismissed as childishly naïve the materialistic world view at its core.

The story about Erwin Schrödinger is often told as follows. He discovered the Schrödinger equation and became one of the founding fathers of quantum mechanics. But then he came to dislike his own creation intensely. “I don’t like it, and I’m sorry I ever had anything to do with it”, he said about the standard probabilistic interpretation of his own equation. To emphasize the absurdity of the implications of quantum mechanics he came up with the Schrödinger’s cat thought experiment, which has become part of the wider culture of the modern world.

I was therefore surprised and confused when I started reading Schrödinger’s essay My View of the World, the first part of which he wrote in the autumn of 1925, just a couple of months before he formulated the Schrödinger equation. Schrödinger describes his philosophical journey from Schopenhauer to the Vedantic ideas of ancient India. He presents convincing arguments why it makes no sense to talk about a world of objects without any observers. All objects are objects of perception, he argues, and you cannot separate the perceiving subject from the perceived object like Descartes tried to do with his dualistic notions of res cogitans and res extensa.

It seemed to me that such a view would make it quite easy to accept the implications of quantum mechanics, as they are usually presented: if it is impossible by assumption to observe an object (Schrödinger’s cat), it makes no physical sense to ascribe any definite properties to it (such as being alive or dead).

How come, then, that Schrödinger didn’t accept quantum mechanics – and more than that, was deeply upset about it? To find out, I read more about his life and work. I got some clues, but I cannot say that I have resolved the paradox. Here I collect pieces of the puzzle, and express some meandering thoughts about how they may fit together.

The development of Schrödinger’s philosophy

Towards the end of his life, Schrödinger wrote in the foreword to My View of the World that as a young man he looked forward to the chair of theoretical physics in Czernowitz, which he expected to be offered in 1918. There he could do a decent job as a lecturer, and devote himself to philosophy. However, history intervened, the Dual Monarchy split, and Czernowitz became part of Romania.

Schrödinger’s interest in philosophy went back at least to the time as a student in Vienna. Together with his best friend, the botany student Franz Frimmel, he used to discuss philosophical questions during long evening walks about the city, which sometimes lasted till the early hours of the morning.

Schrödinger’s first major philosophical influence was a book by Richard Semon from 1904 called The Mneme as Conservative Principle, which put forward the curious hypothesis of psycho-lamarckism. According to this theory, memories can be inherited. Schrödinger and Frimmel read this book together and discussed it in detail. Their shared youthful enthusiasm may well have been the starting point for Schrödinger’s life-long interest in the origin and nature of life. This interest led to the famous book What is life? from 1944, which inspired Watson and Crick in their search for the DNA molecule.

At the end of World War I Schrödinger’s philosophical studies intensified. He read every word of Schopenhauer, whose dark but systematic outlook may have created some coherence for the searching mind to the shattered society and painful experiences of the time. Schopenhauer led Schrödinger to Indian philosophy. He came to believe in Vedanta, a belief that lasted for the rest of his life. From now on, his philosophical views remained remarkably fixed.

Maybe the memories of the war created a deep need for the more harmonious realm beyond the personal and wordly that Vedantic philosophy offered. The deaths of Erwin’s father in 1919 and mother in 1921 may have contributed to this need.

Arthur Schopenhauer

Schrödinger’s views of the world

Such feelings and motivations are absent from his philosophical manifesto My view of the world. It is abstract yet personal. Its temporal proximity to his breakthrough in quantum mechanics suggests that it was written in the same surge of energy during the second half of 1925.

Nevertheless, he never publicly associated his philosophy with his physics, as far as I know. Later in life he emphasized that they had little to do with each other. My view of the world was not published until 1961. Schrödinger wrote in the foreword:

“Not a word is said here of acausality, wave mechanics, indeterminacy relations, complementarity, an expanding universe, continuous creation, etc. Why doesn’t he talk about what he knows instead of trespassing on the professional philosopher’s preserves? Ne sutor supra crepidam. On this I can cheerfully justify myself: because I do not think that these things have as much connection as is currently supposed with a philosophical view of the world.”

As a bystander interested in the same fundamental questions as Schrödinger was, it is hard to understand this position. It suggests a strange dissociation between two aspects of his intellect, between the two roads towards understanding that he followed with passion, two roads that ought to lead to the same destination. To me, a central passage in My view of the world that has bearing on exactly those questions about the nature of the physical world that quantum mechanics forces us to ask is the following:

“Kant having established that the “tree in itself” is not only (as the English philosophers knew already) colourless, odourless, tasteless, and so on, but also belongs entirely to the realm of things-in-themselves which must in absolutely every respect remain inaccessible to our experience, we are in a position to declare once and for all that this thing-in-itself holds no interest for us whatever; that we are going, if necessary, to disregard it. Now, in the realm of things which do interest us, the tree presents itself just once, and we can just as well call this single datum a tree as a perception-of-a-tree – the first having the advantage of brevity. This one tree, then, is the one datum we have: it is at one and the same time the tree of physics and the tree of psychology. As we observed at an earlier point, the same elements go to make up both the Self and the external world, and in various complex forms are sometimes described as constituents of the external world – things – and sometimes as constituents of the Self – sensations, perceptions. These thinkers call this the restoration of the natural concept of the world, or the vindication of naïve realism. It does away with a whole mass of pseudo-problems, in particular the famous ignorabimus of Du Bois Reymond, of how feeling and consciousness could arise from a movement of atoms.”

This quote pinpoints from a philosophical perspective the essential lesson of quantum mechanics: that it is empirically meaningless to talk about things-in-themselves, and that they should therefore not be introduced into physical models. If one tries to do it, the model ends up erroneous; it disagrees with the empirical evidence.

At the end of the quote Schrödinger refers to one of the insoluble world-riddles that the physiologist Emil du Bois-Reymond presented before the Prussian Academy of Sciences in 1880, namely the origin of simple sensations. Du Bois-Reymond characterised this riddle as ignoramus et ignorabimus (we do not know and will not know).This ignorabimus is now rebranded as the hard problem of consciousness.

(As a side note, David Hilbert famously shot back fifty years later with militant optimism before the Society of German Scientists and Physicians in Königsberg: “In opposition to the foolish ‘ignorabimus’ our slogan shall be: We must know – we will know.” This sounds even better in German: “Wir müssen wissen — wir werden wissen.”)

It should be stressed that the naive realism of Schrödinger is rather the opposite of what may be referred to as naive scientific realism – the idea that the world is no more and no less than a collection of small objects that dance about in space, independently of any aware observers.

Instead, the naive realism of Schrödinger, or his natural concept of the world, is a world view in which existence and experience go hand in hand, where the aware observer is indispensable. All of this seemingly fits like a glove on the hand of the Copenhagen interpretation of quantum mechanics. How come, then, that Schrödinger disliked that approach to quantum mechanics deeply?

After some reflection I concluded that one philosophical reason may be the little weight Schrödinger assigned to the individual, in so doing following a long tradition in eastern philosophy. In contrast, in our attempts to come to terms with quantum mechanics from the Copenhagen angle, we often introduce as a crucial element individual observers who interact with their environment.

The inability in practice of a single observer to gain simultaneous knowledge about everything around her is transcended in the Copenhagen interpretation of quantum mechanics to the statement that there is no such complete knowledge to be gained even in principle. This fact is encoded in the physical formalism as superpositions of different possibilities that cannot be excluded given the actual incomplete knowledge.

The Heisenberg uncertainty relations can be seen from the Copenhagen perspective as a reflection of this predicament: the individual who interacts with her environment to learn something new inevitably perturbs the same environment so that she loses knowledge about something else. She is like the elephant in the glass shop: when she enters the shop to take a closer look at a beautiful vase at the back, she cannot help breaking a lot of other items, forever losing the possibility to learn anything about them.

In short, the intuitive understanding of quantum mechanics from the Copenhagen perspective relies on the individuality of the observers and the sharp distinction between the observer and the environment. Schrödinger, on the other hand, considered this individuality and this distinction to be illusions. Regarding individuality he writes:

“For philosophy, then, the real difficulty lies in the spatial and temporal multiplicity of observing and thinking individuals. If all events took place in one consciousness, the whole situation would be extremely simple. There would then be something given, a simple datum, and this, however otherwise constituted, could scarcely present us with a difficulty of such magnitude as the one we do in fact have on our hands.”

“I do not think that this difficulty can be logically resolved, by consistent thought, within our intellects. But it is quite easy to express the solution in words, thus: the plurality that we perceive is only an appearance; it is not real. Vedantic philosophy, in which this is a fundamental dogma, has sought to clarify it by a number of analogies, one of the most attractive being the many-faceted crystal which, while showing hundreds of little pictures of what is in reality a single existent object, does not really multiply that object.”

It may be noted that these ideas go together quite well with the psycho-lamarckism that fascinated Schrödinger in his youth: if personal memories are inherited the dividing line between yourself and your ancestors is blurred.

Having erased the distinction between different observers, Schrödinger goes on to erase the distinction between the multi-faceted single observer and the world.

“[I]nconceivable as it seems to ordinary reason, you – and all other conscious beings as such – are all in all. Hence this life of yours which you are living is not merely a piece of the entire existence, but is in a certain sense the whole; only this whole is not so constituted that it can be surveyed in a single glance. This, as we know, is what the Brahmins express in that sacred, mystic formula which is yet really so simple and so clear: Tat tvam asi, this is you. Or again, in such words as ‘I am in the east and in the west, I am below and above, I am this whole world’.”

In this picture, the mind merges with the world in a similar way as the mind of the mystic merges with God. This picture of the mind is very different from that of individual elephants trying to make sense of the items in the glass shop without breaking too many of them.

Another way to put the difference is to say that the mind imagined by Schrödinger is passive, whereas the mind of the observer in the Copenhagen interpretation of quantum mechanics is active: it chooses a way to interact with the external world, thereby choosing which knowledge it may gain, and which may be lost in the process.

The Copenhagen mind gains knowledge in a stepwise fashion. It may choose to open a letter to see what’s inside. It may decide to measure the frequency of light emitted by an atom and record the result. The discrete nature of such knowledge gain is closely related to the “quantum jumps” that Schrödinger detested, and wanted to remove from quantum mechanics. First we detect one state of an atom, then another. It is impossible to say what happens in between these detections, and it is impossible to predict which state the atom will jump to. All we can do is to associate a probability to each possible jump.

Instead Schrödinger wanted to use the wave mechanics that he invented to model a continuous and smooth evolution of the world. Such an evolution goes well together with the idea of smooth and ondulating changes of the state of mind of an observer whose consciousness merges with the world around her. Schrödinger might have had a picture of his wave function as a cosmic field of vision.

Vishvarupa, the universal form of Vishnu, where he displays all faces, creatures and forms as parts of him.

Schrödinger’s wave mechanics

A couple of months after completing My view of the world Schrödinger went to the Villa Herwig in Arosa for Christmas vacation. There he took decisive steps towards his new wave mechanical formulation of quantum mechanics. In a letter to his fellow physicist Wilhelm Wien he wrote on December 27 in 1925:

“At the moment I am struggling with a new atomic theory. If only I knew more mathematics! I am very optimistic about this thing and expect that if I can only… solve it, it will be very beautiful.”

At this time Erwin’s marriage with Annemarie Bertel was strained. She did not accompany him to Arosa. Instead he was joined by “an old girlfriend from Vienna”, whose identity is still unknown. Schrödinger’s biographer Walter Moore compares her to the mysterious dark lady who inspired Shakespeare’s sonnets.

It seems that Schrödinger’s philosophical, scientific and erotic explorations culminated at the same time during this period in his life. The famous mathematician Hermann Weyl, who was a colleague of Schrödinger at the University of Zürich, once said that Schrödinger “did his great work during a late erotic outburst in his life”.

The academic circle in Zürich they belonged to seems to have been avant garde in more than one respect. Extramarital affairs were not only accepted, but expected. Annemarie found in Hermann Weyl a lover that she was devoted to. Weyl’s wife Hella was in turn romantically involved with another physicist, Paul Scherrer. Nevertheless, despite these adventures – and more to come – Annemarie and Erwin remained companions for life.

After the return from Arosa in January 1926, Schrödinger completed four groundbreaking papers within half a year. During this period of intense activity there was probably not much time for him to think about what the concepts he used in his equations actually meant. First he thought that the wave function Y represented some kind of matter wave or a new type of aether, then he settled at a picture in which it corresponds to a continuous charge distribution. In that picture the charge of the electron circling around the nucleus of the hydrogen atom is smeared out in a cloud with a density proportional to the square modulus |Y|2 of the wave function Y.

Max Born and others quickly realised that |Y|2 must rather correspond to the probability to find a single electron at the given location, in order for the theory to account for all the discrete or quantum aspects of atomic matter and radiation that are seen in experiments. Given the state of the electron at time A, the theory then specifies the probability to find it at another state at time B. The electron jumps between the two states, and all the theory can say about the process is the probability that it will happen.

Schrödinger could not accept this idea. He seems to have settled on a picture in which the smooth and deterministic evolution of the wave function devised by his own Schrödinger equation corresponded to a smooth and deterministic evolution of the world as a whole. He wrote to Wilhelm Wien in August 1926:

“[T]oday I no longer like to assume with Born that an individual process of this kind is absolutely random, i.e., completely undetermined. I no longer believe today that this conception (which I championed so enthusiastically four years ago) accomplishes much.”

The opposing view that he championed before is clearly revealed in his inaugural lecture at the University of Zürich in December 1922, where he exclaimed the following:

“It is quite possible that the laws of Nature without exception have a statistical character. […] The burden of proof lies upon the advocates of absolute causality, not upon those who doubt it. For to doubt it is today by far the more natural viewpoint.”

In preparing for this lecture he wrote a letter to Wolfgang Pauli in which he even suggested that conservation laws were not absolute but statistical:

“Can the conservation of energy-momentum not be merely a macroscopic valid average relation, of which atomic physics knows nothing, like the 2nd law [of thermodynamics]? At least it can be that way, and I see almost no other way out.”

How come Schrödinger changed his mind so drastically? In the meantime he had contributed a lot to the efforts to provide a solid mathematical foundation to quantum mechanics. Naively, one might therefore think that he would conclude that these theoretical successes reinforced the tentative conclusions from empirical quantum mechanics – that there was no way to get rid of randomness in atomic physics.

One may speculate that Schrödinger instead fell so much in love with his own wave equation and the waves in it that he lost his sober judgment. The acclaim of his achievements was immediate, and the success must have been overwhelming.

Schrödinger had previously done a fair amount of research on waves. During World War I he served as a lieutenant in the fortress artillery. He probably contemplated the so called “outer zone of abnormal audibility” of large explosions. As one moves away from the explosion the perceived sound is first attenuated, but may then rise again in a zone at a distance of 50-100 km, before dying out at even larger distances. At any rate, Schrödinger wrote a paper on the subject in 1917.

In November 1925 Schrödinger welcomed as his assistant the young physicist Erwin Fues from Stuttgart. Schrödinger suggested that Fues should work on the interaction of atmospheric shock waves. Fues’ professor in Stuttgart was not happy about this seemingly outdated topic, and strongly advised him to ask for a problem connecting to the rapidly developing quantum mechanics.

But maybe the connection was already there in Schrödinger’s mind. He might have played with the idea that “everything is waves”, just like an economist may sometimes feel that “everything is economy”, or a psychologist concludes that “everything is psychology”. If so, this hunch probably grew into a full-blown vision after his discovery of wave mechanics during the Christmas vacation at Villa Herwig in Arosa. Then all other ideas, such as that of randomness and discreteness, may have been swept away.

Villa Dr. Herwig in Arosa, Switzerland

Back to philosophy

Also, what had changed between the years 1922 and 1925 was that Schrödinger’s vedantic philosophy had matured, and it conformed more to a continuous and deterministic picture of the world than to a discrete and random one.

As noted above, the idea that the world consists of nothing but smooth waves evolving continuously fit well together with the philosophical ideas that he formulated just months before he discovered wave mechanics. Maybe this discovery appeared to him as a sign from above that the thoughts expressed in My view of the world were converging towards the truth. His scientific research seemed to confirm his deeper thoughts within a couple of months. It could well have given him a shock of joy and self-confirmation.

As far as I know, however, Schrödinger never during these years tried to connect in public his vedantic ideas about the self and the world with his wave mechanics. This is not surprising, considering that he kept his philosophical writings to himself and did not publish My view of the world until 1961, perhaps fearing that his reputation as a scientist would be hurt if he talked too openly about such matters.

But there was a rift in his vision of physics. He could not help seeing it, but he could never really accept it. His wave mechanics did not get rid of the randomness and the “damned quantum jumps”. Throughout his life he made several attempts to patch up this rift and recreate a smooth, deterministic physics. But he could never really present a coherent alternative to the predominant Copenhagen interpretation of quantum mechanics, which was based on the randomness and inherent incompleteness of knowledge that he detested.

As a psychological speculation, one might understand the strange statement in the preface from 1960 to My view of the world that physics has nothing to do with philosophy as a defence mechanism. During the months of intense scientific creativity after his Christmas holidays 1925 in Arosa, Schrödinger may have dreamed about a quick and happy marriage between his vedantic philosophy and his physics. When that marriage never came true, he may have concluded that it was not meant to be, that it could never happen. Schrödinger’s philosophical views seem to have been vital for him, conquered at a difficult time in his life after World War I. To preserve them, he may have been forced to encapsulate and isolate them from a physics that developed in a different direction.

The scene in Bhagavad-Gita where Krishna teaches Arjuna before the battle

Reflections

It seems to me that Schrödinger is somewhat inconsistent in his take on individuality. He uses the individuality of perception when he rules out an underlying objective reality and arrives at the natural concept of the world described in the long quote above, where the perceived tree is the only meaningful tree there is. At the same time, in the vedantic tradition, he dismisses individuality as an illusion.

In Schrödinger’s natural concept of the world, two individuals A and B share the same perception of this tree. There is no need for an underlying layer of reality which causes the perceptions of A and the perception of B, possibly via emissions of one set of photons from the tree-in-itself that hit the retina of A and another set of photons from the underlying tree-in-itself that hit the retina of B.

In My view of the world Schrödinger argues against an underlying, objective reality by the following thought experiment. He imagines one individual A who looks at an interesting scenery and an identical individual B who is placed in a dark room. From the objective perspective, nothing changes if A and B change places, but from the subjective perspective both A and B perceive a drastic change. According to Schrödinger, the inability to account for this individually perceived asymmetry proves that the picture with an underlying objective reality can never be sufficient to account for the world as we know it.

At the same time he plays down the individuality of perception as an illusion. In one of the quotes above he compares it to one of the hundreds of little pictures that a many-faceted crystal creates of a single object. This single object would then correspond to a single, universal consciousness. These ideas certainly go together well with a physical model where the world consists of smoothly interacting waves, without sharp distinctions between this and that, between different objects or between different subjects.

But to me it seems too easy to dismiss individuality by name-calling and metaphors. Even an “illusion” requires a “real” mechanism to make it appear. A hallucination requires an over-heated brain. The multiplication of the image of the single object requires an multi-faceted crystal. In the same way, there must be a substrate of the individuality of perception in the fabric of the world, regardless whether you call this individuality an illusion or not.

If we take Schrödinger’s argument about the non-existence of individuality seriously, then we also invalidate his own argument against the existence of an underlying objective reality that we sketched above. In other words, Schrödinger’s idealistic vision of a single cosmic consciousness goes well together with a realistic vision of a single materialistic world. Pure idealism and pure realism are not so different when it comes to model building. Les extremes se touchent.

An example would be the Schrödinger and Einstein. As we have seen, Schrödinger was inspired by vedantic mysticism with visions of a unified consciousness that breaks the distinctions of earth-bound perceptions. Einstein had seemingly a very different realistic vision of a deterministic and materialistic world characterized by harmony and order. But in realizing their different visions, they seem to have come to love the same type of field models. They joined forces against the common enemy – the Copenhagen school of Niels Bohr, Werner Heisenberg and Wolfgang Pauli. The Copenhagen vision was rather that of a world consisting of observers who interact with and try to learn about the world around them at the same time as they crush it, like clumsy elephants.

The common feature of the purely idealistic and the purely realistic camps of Schrödinger and Einstein is that they both focus on just one of the poles in the observer-observed pair or the subject-object pair. In the wording of Descartes, they focus on either res cogitans or res extensa, and deny the other.

To me, the only reasonable position is the middle ground between idealism and realism represented by the Copenhagen school. We have to acknowledge both the observer and the observed, and treat the relation between them as fundamental. Perhaps like the two sides of a coin. You cannot characterise the coin accurately by just describing one of its sides. At the same time you cannot consider one side in isolation from the other. As Schrödinger correctly noted, the strict dualism of Descartes is untenable.

In quantum mechanics the fundamentality of the relation between the observer and the observed becomes explicit via the measurement postulate and the operator rule that tells which property values are observable in a given situation. The measurement postulate describes the discrete and probabilistic transition from possibility to actuality. Schrödinger could not accept this deviation from continuity and determinism. Countless modern
thinkers follow in his footsteps and call it the “measurement problem”. This is a misnomer. Rather than a problem, it’s the pearl at the core of quantum mechanics, opening up the necessary depth dimension of the theory as compared to the flat class of theories that aims to be either purely idealistic or purely realistic.

I described the universal mind imagined by Schrödinger as passive. Its lack of limits means that it does not have a world to interact with. It just is. But this is not life, this is not physics. It’s a dream that might come true in afterlife or in Nirvana. To do science means to struggle with the world. We hunt Nature down and force it to deliver the answers that we seek. We defy the cold and go to Antarctica to learn about inland ice and paleoclimate, and we build massive accelerators to learn about elementary particles. It’s like Jacob’s wrestling with God.

In the vedantic vocabulary of Schrödinger the struggles of life is part of Maya, the illusory and multi-faceted material world, whereas the unification of man with cosmos is Brahman. Maybe Schrödinger made a category mistake. He may have dreamt of a physics that reflects Brahman. But as far as I understand it must reflect Maya. It is only in such a world that we do physics.

Roy de Maistre, Jacob wrestling with the angel, 1958