Is Quantum Mechanics “Crazy enough”?

A bit of context

Quantum Mechanics alongside the General theory of Relativity are theories developed in the first half of the 20th century that have shattered both common sense conceptions of the world and more technical “laws of Nature” that scientists of the time (and to some extent of today) were holding as unquestionable truths. The way they came about and the conceptual ripples these theories have generated in their wake are however quite different.

While General Relativity may have benefitted from various contributions from both the mathematical and physical communities, for the purpose of this post, I will be bold enough to claim that its conceptual inception is mostly due to A. Einstein. As far as I am aware, the way people understand General Relativity today is not very different from Einstein’s original paper back in 1915: there is a clear connexion between the mathematics and “objects out there” making reality. From there, technical advances in General Relativity have permitted astrophysicists and cosmologists to reflect deeper on concepts of space, time, frames of observation and so forth. For Quantum Mechanics however, the story is very different. Prominent figures such as Planck, Einstein, Sommerfeld, de Broglie, Bohr, Pauli, Dirac, Born, Heisenberg or Schrodinger would have contributed by the end of the 1920s, each in their own original way, to the conceptual and technical development of what we call today Quantum Mechanics. Maybe the fact that so many talented physicists participated in the elaboration of a single theory to capture the microscopic world explains in part why Quantum Mechanics, to this day, does not seem to carry a clear vision about what the theory is supposed to tell about the world. This confusion has been illustrated in 2011 by a poll conducted at a conference on the foundations of Quantum Mechanics. The results were published in an article with a quite telling conclusion:

Quantum theory is based on a clear mathematical apparatus, has enormous significance for the natural sciences, enjoys phenomenal predictive success, and plays a critical role in modern technological developments. Yet, nearly 90 years after the theory’s development, there is still no consensus in the scientific community regarding the interpretation of the theory’s foundational building blocks. Our poll is an urgent reminder of this peculiar situation.

What is even more telling is that, according to the article, experts do not even agree on the conceptual and metaphysical content of the most popular formulation of Quantum Mechanics, the so-called Copenhagen interpretation.

“Craziness” as a guide for progress?

In his fascinating book 137: Jung, Pauli and the Pursuit of a Scientific Obsession, the historian of science Arthur I. Miller recalls how glorious was the beginning of the atomic theory as proposed by Bohr’s atomic model. As a brief reminder, in 1913 Bohr proposed a model to explain the electromagnetic spectra emitted and absorbed by hydrogen atoms in which a negatively charged electron would orbit a positively charged proton, like a planet would orbit the Sun in a Heliocentric model. The twist was that orbits had to obey additional, non-classical rules. In particular, Bohr gave up on classical ideas among which were that closed orbits of classical mechanics can have in principle a radius of arbitrary size and that an accelerated charge necessarily radiates light. The model was very bold indeed but at the same time was incredibly appealing: the microscopic world could be thought of as a “mini-universe” in and of itself which is a constitutive part of  a larger universe. This “boldness” of Bohr’s when tackling difficult problems in physics — and possibly in other dimensions of his life — seemed to have been a guide throughout his life. Miller recounts that Bohr would often label new theories he would be reported on by his peers as being not “crazy enough” if he meant that they were probably false. One marking example of this attitude is when Pauli suggested in 1924 a fourth quantum number (corresponding to a fourth degree of freedom in a three dimensional space) to characterise the state of an electron around a proton: Bohr allegedly said that it was a completely insane idea; meaning probably correct in his terms. This fourth degree of freedom is what we identify as the intrinsic spin nowadays. Craziness could have value after all!

In this post, I would like to review some of the most known interpretations of Quantum Mechanics and, rather than discarding a view based on standard assumptions of the “scientific method” such as falsifiability or Ockham’s sharp razor, I would like us to try to gauge the plausibility for it to describe nature based on how crazy it appears.

The 2018 Crazy Interpretations of Quantum Mechanics Contest

1st contestant: the Copenhagen interpretation

The Copenhagen interpretation of Quantum Mechanics is understood to be mostly Bohr’s and Heisenberg’s view on the Quantum Theory as it was being developed at the end of the 1920s. Whether what we call today the Copenhagen interpretation has anything to do with what either Bohr or Heisenberg had in mind is difficult to know of course. For starters, they did not necessarily agree on everything about Quantum Mechanics. As an example, when Heisenberg came up with his famous uncertainty principle/relation, the idea was welcome by a great number of physicists except for Niels Bohr. He would actually reproach that the uncertainty relation implied that an electron was a particle while it need not be the case. Bohr had no problem thinking of an electron as being somehow a particle and a wave through a philosophical principle of complementarity very much like the Yin-Yang principle in Eastern philosophy. Bohr, and later Pauli through his covert collaboration with Jung, thought that this principle would be the key to unjam physics from its stalled state and merge it peacefully with the humanities (no need to say, this programme has been far from successful as attested by the Science Wars in the 1990s). For a closer inspection of what one might think of Bohr’s view on Quantum Mechanics, this article is quite illuminating. For Heisenberg’s view, I believe his Nobel prize lecture summarises it quite neatly.

Regardless of what it is exactly, roughly speaking the Copenhagen interpretation is the material being taught since the 1930s in universities for students to learn how to solve problems with the theory. Since textbooks don’t even agree on which postulates to use and since I am French, I will present here Quantum Mechanics as I was taught it through  the textbook by Claude Cohen Tannoudji, Franck Laoe and Bernard Diu (in a slightly simplified vocabulary):

  1. At any time the state of a system is characterised by a mathematical object called wave function,
  2. To any measurable property of a system corresponds a mathematical (linear) operator that can act on the wave function,
  3. Only certain prescribed values can result from the measurement of a given property,
  4. The wave function relates to the probability of obtaining a given outcome upon measurement of a given property,
  5. Upon measurement, the wave function collapses so as to give exactly the same outcome upon immediate repetition of the same measurement,
  6. In absence of measurement, the wave function evolves according to the so-called Schrodinger equation.

This set of postulates is somewhat minimal but lays out the mathematical tools being employed when working with the theory of Quantum Mechanics. Some textbooks might add more postulates like the existence of incompatible measurable properties such as position and momentum; but this could also be considered as a model of the theory so I prefer to leave it outside of the list.

As for the interpretation of what these postulates mean or represent, a majority of textbooks carefully avoid discussing some difficult questions such as A) what is a measurement? B) Why is there two modes of evolution depending on the context? C) What is a wave function? D) Why/How are macroscopic objects — like a cat — not subject to the laws of Quantum Mechanics? E) Why the rules to obtain probabilities are different from that of usual probability theory?

When they do mention these questions however, the argument will often revolve around the idea that Quantum Mechanics has enabled physicists to finally understand that the sole role of physics as a discipline was to predict the outcome of experiments; no more, no less. On that view then Quantum Mechanics is a very efficient recipe at doing just that and any further question is deemed meaningless and a waste of time. In spite of having initiated a full re-assessment of the goals and objectives of physics as a discipline, the lack of introspection from some of its proponents has lead some authors, like former theoretical physicist and philosopher of physics D. Z. Albert, to humorously summarise this interpretation as exemplified in the video clip below.

2nd contestant: the de Broglie-Bohm pilot wave interpretation

This interpretation of Quantum Mechanics attempts to find answers to questions C) and E) mentioned above which can provide then a range of opportunities to address the other questions.

It relies on an initial hypothesis that de Broglie presented in 1927 stating that, in the microscopic world, particles appear to behave as if they were waves and that there could be an invisible wave piloting the trajectories of normal classical particles. By 1952, Bohm refined de Broglie’s theory to respond to various criticisms. More technically, the theory claims that there is a hidden, extended stuff that we don’t see that continuously interacts with particles so as to make them behave like waves themselves in some circumstances. For this reason the de Broglie-Bohm interpretation belongs to the class of hidden-variables theories. This suggests as well that the reason why probabilities emerge in the Quantum Mechanics formalism is simply due to the lack of information about this unaccessible material and it can be retrieved within the theory without being postulated (postulate 4 above is then not needed and the wave function collapse is not really mysterious any longer).

While hidden variables theories have received a great blow with the observed violations of Bell’s inequalities notably by Aspect et al.’s 1882 experiment — that have been even more refined in the past years —, these violations at most enable one to discard so-called local hidden variables theories.  Such theories will have the specific feature that any two space-time events that are not within the same light cone are necessarily statistically independent. Bohm’s theory however permits such things as faster-than-light correlations as trajectories of particles depend on the state of the “pilot wave” in the whole universe.

The de Broglie-Bohm interpretation has recently gained in popularity thanks to classical macroscopic realisations of the theory reproducing Quantum Mechanics results and other phenomena commonly attributed to the quantum realm. Here is a nice video discussing some of these recent exciting studies.

A further basis to regain interest in the de Broglie-Bohm interpretation, in my opinion, is also due to a recent paper by Aharanov et al. interestingly titled “Finally making sense of the double slit experiment” in which the authors argue for a deterministic theory where positions and momenta of particles are determined as in classical mechanics but with additional non-local interactions. Although this study does not endorse per se the de Broglie-Bohm theory, it supports most of its major claims that are usually thought to be completely at odds with the Copenhagen view of Quantum Mechanics.

3rd contestant: the Many World Interpretation

This interpretation of Quantum Mechanics takes issue with questions B), D) and E) having to do with the collapse of the wave function and what appears, to its proponents, as being ad hoc probability rules. This interpretation of Quantum Mechanics, initiated by Everett and improved further to this day, is somehow the “simplest” as it just decides to discard postulates 4 and 5 of the Copenhagen interpretation presented above and attempts at deriving them from a proper understanding of the other postulates supplemented by a priori assumptions on what are probabilities (it thus involves a great deal of mathematics and philosophy of probabilities).

There are two fundamental ingredients to this interpretation: one is a commitment to realism and to the view that we have to follow and trust the world view emerging from the mathematical formalism and the other is to follow a single form of time evolution for the quantum state of a system. The commitment to realism may appear reminiscent of the Quine and Putnam argument for a form of epistemic deontology with regards to mathematical objects (that we have a duty to consider them as what really constitute the world so to speak) but in essence it appears more as a refusal to use a double standard of interpretation when judging the mathematics of quantum mechanics when compared to how we interpret the mathematical formalism of more classical subjects like electromagnetism for example. Physicist and philosopher David Wallace makes a compelling argument for this position in this paper very much worth the read.

These assumptions seem fair enough from outside but this interpretation starts collecting a strong look of disapproval from some physicists when the aforementioned commitments are followed through, up to their natural conclusion: the word view emerging from this version of quantum mechanics is that of a very large universe in which physical objects constantly interact with copies of themselves until a “branching” occurs whereby the world splits into non-interacting worlds where copies cannot interfere with others’ existence anymore; hence many worlds. In this view, when one makes a quantum measurement with a random outcome, all outcomes happen in the universe but only one outcome is effectively observed in each branching parallel sub-universe. The probability rule can then be deduced, provided some assumptions are satisfied, by simply counting (that’s an oversimplification) the number of branches in which a given outcome occurs.

If you want to know more about this interpretation, you can have a look at Oxford physicist David Deutsch’s attempt at explaining it during an interview.

Last contestant: consciousness-caused collapse

This interpretation deals with questions A), B) and D) mentioned above. The core idea is that the common denominator of these three questions is that of a final measurement by a conscious observer. This was initially emphasised by John Von Neumann when attempting to discuss how a measurement could be understood following only postulate 6 above. He realised that if one follows only the Schrodinger equation then macroscopic objects like measuring apparatus, the building in which the experiment is carried out, the car in which the experimentalist comes to work etc… will be in some superposition of incompatible quantum states like the now famous Schrodinger’s cat. As Von Neumann saw it, this infinite regress (please see section 2 to of this article for more on this idea) only stops when a conscious observation is performed ; thereby defining a measurement in quantum mechanics as a conscious act of observation.

This interpretation is not furiously popular nowadays mostly, it appears, for the departure that it takes from more traditional naturalistic and materialistic philosophies, where subjective experience can play no role and which in a sense underpin physics as a scientific discipline. Some eminent scientists such as Von Neumann, Eugene Wigner, Andrei Linde or Henry Stapp have supported the view. One appealing aspect it has, in my opinion, is that it somehow takes seriously the problem of (phenomenal) consciousness from a physics standpoint. It could be that there are in fact more than a few closeted scientists or interested people who do share this particular interpretation of quantum mechanics but it seems quite difficult to be too vocal about it as it can be at the expense of one’s academic reputation as recounted by cosmologist Andrei Linde in the interview below

Other contestants worth mentioning:

Other interpretations which I do not have time to go over in this post or may overlap with some other views already mentioned comprise Qbism for Quantum Bayesianism  which can be viewed as a limiting case of the Copenhagen interpretation, Quantum Logic, which, as an interpretation, replaces classical logic with a new logic thus changing the kind of sentences that can be written at all about the world and Spontaneous Collapse interpretation according to which the measurement postulate 5 is but an approximation of a more complicated mechanism objectively and really causing a dramatic change in the state of a system and finally the Ur theory of von Weizsacker with his temporal logic whose goal is to provide the scaffolding for a theory of everything (according to von Weizsacker, a neo-Kantian at heart, as it were, a theory of everything is a theory which provides the preconditions of (all) experience).

And the winner is?

Among the interpretations I have mentioned, I have obviously my own favourite interpretations but I do not want to share them here; that’s not the objective. Instead I would like to pause for a moment, contemplate the rich landscape of interpretation opportunities and prefer to leave it for you to decide whether any of those is crazy enough to be right!


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