Interpretations of Quantum Mechanics

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Interpretations of Quantum Mechanics

«New interpretations appear every year. None ever disappear.»

— Quantum mechanics: Fixing the shifty split. N. D. Mermin in Physics Today 65:8 (2012).

Very little is known about quantum mechanics besides its formalism and that it works (it describes the world around us) but much has been written about it. For many, what we know is more than enough. This is known as the shut up and calculate school. Although nobody is sure who the headmaster is, the school definitely exists. Others are not satisfied and would like to have, at least, answers such as:

• Is the world local or nonlocal?
• Is the world deterministic or probabilistic?
• Is there even a "world"? (elements of reality)
• Is the observer special? Are we special?
• Where is the "shifty split" and what does it split?

The schism occurred with Born "interpreting" Schrödinger's wavefunction as a probability amplitude, thus bringing a dichotomy between what is "real" and what is physical (what Bell would later call the "beable").

Providing an alternative starting point, or theory, to address satisfactorily such questions pauses the problem of quantum foundations. The main difficulty of this delicate question is that all competing interpretations, even when they differ wildly, cannot be discriminated through the prism of experiments, thus placing the point out of reach of the scientific method.

One possible approach to such problems which present no way towards their resolution, is to envision all possible alternatives. We do not know which one is correct, but we know that—being imaginative and systematic enough—we will have come to toy with the actual one. Sherlock Holmes would proceed to remove what is impossible to single out what is true, but his quantum counterpart would oppose to that that while

Sherlock Holmes observed that once you have eliminated the impossible then whatever remains, however improbable, must be the answer. I, however, do not like to eliminate the impossible.

— Douglas Adams, Dirk Gently's Holistic Detective Agency.

A recurrent clue from the various formulations is that something which is not measured, needs not have a value anyway.

“spooky action at a distance.”

This is a topic which has been much debated by many authors and there exists a huge literature on the topic, see for instance .

Realism: scientific observations are caused by some physical (objective) reality whose existence is independent of human observers.

Path integrals

This could be called the first interpretation, since Feynman's path integral formalism came after the two independent approaches to quantum mechanics (that of Schrödinger and Heisingberg) proved to be different versions of the same thing. Initially, there was no attempt at an interpretation, it just happened that various people found various way to formulate the theory. Feynman was the first to provide an alternative way to look at what was already known, not adding any new result, just a different viewpoint. Hence the first "interpretation".

Hugh Everett III's many-words

This is by far the most exotic interpretation despite also being the simplest and most devoid of superfluous assumptions, thus passing Occam's razor test. In fact, according to DeWitt, it is the only formalism ««that takes the mathematical formalism as it stands, without adding anything to it, and that at the same time assumes that this formalism provides a complete description of quantum phenomena.»». It postulates that there is a full (total, universal) wavefunction of the universe, which obeys Schrödinger's equation, thus being irreversible and deterministic and not involving any measurement, let alone collapse. All those complications are removed by a painfully obvious remedy: the observer is included as part of the physical system under study, to be treated within the theory exactly on the same footing as the rest of the environment. Everything is quantum: there is no cut between the classical macroscopic world and the quantum microscopic one, no cut between an atom and a conscious observer. And why not? Are we not subject to Newton's equations of motion? Why would we escape Schrödinger's? It also enjoys all the attributes which Einstein had deemed necessary for a physical theory: it is realist, deterministic and local.

This comes at the price, though, that all the possible outcomes of experiments are realized as part of this giant wavefunction of all possibilities, in which we (as observers) coexist in as many alternate realities (or parallel universes) as needed to satisfy unitary evolution.

A typical QM measurement, such as that of a spin component in the Stern–Gerlach experiment, is a local and very low energy event. It is not credible that the measurement could have the huge cosmological effect of bifurcating the universe.

— Reviews of quantum foundations. D. Ballentine in Physics Today 73:11 (2020).

When I first heard of the world-splitting assumed in the MWI, I went back to Hugh Everett’s paper to see if he had really said anything so absurd.

— Reviews of quantum foundations. D. Ballentine in Physics Today 73:11 (2020).

"what is most difficult in the Everett interpretation is to understand exactly what one does not understand." Indeed, it may look simple and attractive at first sight, but turns out to be as difficult to defend as to attack.

— Do we really understand quantum mechanics? Strange correlations, paradoxes and theorems. F. Lalöe in Am. J. Phys. 69:655 (2001).

Everett sometimes referred to his own many-worlds approach as the "pure wave theory", removing the necessity for everything else (particles, collapses, observers, measurement, etc.) The basic idea is that of relative states: the observer becomes relative to his observation. This is why various observations drag their respective observers in their own reality. The features of Copenhagen arise when see from within: ««the formal theory is objectively continuous and causal, while subjectively discontinuous and probabilistic»».

Proponents include David Deutsch, who came up with the idea of a quantum computer based on his belief that universes were indeed splitting. An early supporter was Wheeler, the PhD advisor of Everett, so much so that he even was initially counted as one of its developers, although he later personally distanced himself from the theory. He wrote an "assessment" of the theory to accompany Everett's paper. This is a short and nice paper, with little formalism and defending the approach.

Opponents include L. Ballentine, A. Peres, R. Penrose, J. Bell and almost everybody who studied the problem and did not come to the conclusion that this is the correct formulation. Opposition ranges from rabid (as is the case of Rosenfeld who thought Everett was stupid) to moderate acceptation (e.g., Bell, who thinks this is an inferior version of Bohm's theory).

Links & Further reading

• 🕮The Everett Interpretation of Quantum Mechanics: Collected Works 1955-1980 with Commentary. Jeffrey A. Barrett and Peter Byrne. Princeton University Press, 2012. [ISBN: 978-0691145075] Probably the best source as containing Everett's papers (including the two theses) plus comments and contextualization.
• 🕮The Many Worlds of Hugh Everett III: Multiple Universes, Mutual Assured Destruction, and the Meltdown of a Nuclear Family. Peter Byrne. Oxford University Press, 2013. [ISBN: 978-0199659241] Mainly biographical.
• Quantum mechanics and reality. B. DeWitt in Physics Today 23:30 (1970). This is the paper that popularized the theory. Comments and replies (by DeWitt) can be found in Ref. .
• The origin of the Everettian heresy. S. Osnaghi, F. Freitas and O. Freire in Stud. Hist. Philos. Sci. B 40:97 (2009). On the historical early developments of the theory.
• Everettian Quantum Mechanics on the Stanford Encyclopedia of Philosophy.
• Everett's son (Mark) on Nova. Material include Everett's PhD thesis.

Pilot wave

This theory, first proposed by De Broglie and then later extended by Bohm (it is also popularly known as Bohm's pilot wave or Bohmian mechanics) is the best illustration of an interpretation of quantum mechanics, in that it is fully equivalent as far as the final results go, but in complete opposition regarding what is actually going on. *

The Bohmian version posits that an underlying wave (which follows Schrödinger's equation) guides physical particles, the latter being well-defined in terms of their positions and velocities in 3D space, like classical particles. Given that the particles' behaviour is piloted by the wave, which is itself nonlocal and, this time, in the configuration space (of very high dimensions), albeit deterministic, this theory thus retains all the wonders of quantum mechanics (with which it agrees on all results, remember). It is, therefore, a matter of taste whether to abide by this version which "solves" problems such as wave or particle (it is both) and which slit the particle went through (this is not observer-dependent anymore but is well-defined as the theory is both realistic and objective, particles being physical objects). It also gets rid of the measurement problem and the wavefunction collapse. Since it is deterministic, if one would know the initial condition perfectly, one would know where the particle would eventually end up. The lack of knowledge of the initial condition gives rise to the probabilistic aspect, just like in classical mechanics, except that the wavefunction determines both such an initial condition as well as the quantum potential, which drives the particles, so tightening one's knowledge would alter the fate of the particles. The wavefunction itself, and not the particles, rules the dynamical evolution of the system. Crucially, the particles do not act back onto the wavefunction, and are thus mere realization of the scenario acted by the wavefunction. Although there is only one wavefunction, which never collapses, this dual relationship in fact allows to derive the collapse of the wavefunction, to retain only the "branches" inhabited with particles, so that the possibilities not realized carry on an empty evolution in a ghostly fashion. This makes a direct link with Everett's multiverses. Bohm's theory is of the hidden-variables type, the hidden variables being, funnily, the particles themselves!

There are various ways to formulate the theory.

Bohm rewrites Schrödinger's equation in a way that gives rise to a quantum potential $Q$ (proportional to~$\hbar$):

$$Q=-{\hbar^2\over 2m}{\nabla^2 R\over R}$$

where $R$ is the (real-valued) modulus of the wavefunction $\psi=R\exp(i S/\hbar)$. Schrödinger's equation applied to this decomposition yields

$$\partial_tS+{(\nabla S)^2\over 2m}+V+Q=0$$

with $V$ the (physical) potential, and

$$\partial_tP+\nabla\left(P{\nabla S\over m}\right)=0$$

where $P\equiv R^2=\psi^*\psi$.

Philippidis et al. studied the quantum potential for the two-slits experiment and produced the now-famous figure actually showing the trajectories of the individual particles, interfering as waves:

This, remarkably, resembles very much the trajectories reconstructed through weak measurements by Kocsis et al. and other works brought even stronger support.

Interestingly, Einstein discussed a "Führungsfeld" (guiding field) for photons, in terms of the electromagnetic field, to account for his revival of the particle-theory of light, even before quantum mechanics itself, and also worked out a quantum version. In a letter to Born, he observed that Bohm's solution seemed "too cheap". He probably did not like the embedded nonlocality, but would have he lived enough to accept its inescapability (post-Bell), no doubt that he would have embraced Bohm's (nonlocal) realistic version.

The interesting feature of Bohm's theory is that it shows that physics is local in configuration space, but not necessarily in ordinary space. That suggests that real space is a projection of a broader reality.

A dialogue covers the basics in Ref. . See also the introduction by Goldstein.

Proponents include Bell and others (S. Goldstein, J. Bricmont, etc.)

Opponents include Heisenberg (who called it a "superfluous 'ideological superstructure'), Englert, Scully et al. who described "surreal" trajectories, would the theory be true. (as it seems to be).

Quantum Bayesianism (QBism)

Another broad school of information-interpretation

This extends to the quantum realm the Bayesian school of probabilities. Jaynes being both an ardent proponent of the latter as well as a proficient quantum physicist, .

A drawback of these interpretations is that if the wavefunction is a reflection of one's knowledge, then it is incomplete and does not capture the deeper, underlying element of reality:

Assume that, indeed, $

— \Psi\rangle$ is affected by an imperfect knowledge of the system; is it then not natural to expect that a better description should exist, at least in principle? If so, what would be this deeper and more precise description of the reality?, Template:Laloe10a

If so, what would be this deeper and more precise

description of the reality?

quantum states consistently as (subjective) information

One of the things that sets QBism apart from the other interpretations is its reliance on the technical details of quantum information to amplify Feynman’s point—that the modification of the probability calculus in quantum theory indicates that something new is created in the universe with each quantum measurement.

— Quantum foundations. D. P. DiVincenzo and C. A. Fuchs in Physics Today 72:50 (2019).

An advocate of QBism is David Mermin. An ennemy is Ballentine.

Consistent histories

Also known as "decoherent histories", it was first proposed by R. B. Griffiths and shortly after by R. Omnès. It was also studied by M. Gell-Mann and J. B. Hartle.

It regards quantum mechanics as intrinsically probabilistic, and substitutes the deterministic wavefunction (still used for computational purposes) for probable histories of the observables, which are possible scenarios of what could have happened, generalizing for that purpose Born's rule so that entire sequences of events can be attributed probabilities. It provides a realistic and objective interpretation with no nonlocal (action at a distance) effects. It also flushes the mysteries of quantum mechanics down to single-particle non-commuting observables, or the principle of complementarity. In this sense, the theory has been described as "Copenhagen done right". The EPR paradox, for instance, is resolved by attributing settled correlations from the start, with all various possibilities consisting of coherent histories, removing the need of an observer or of a measurement. A "weakness" of the theory is that it does not settle which set of histories actually happen, only those which can happen. Histories are "consistent" precisely because there can be "quantum incompatibility" which rule out certain alternatives. It also does not settle the problem of the complementarity principle for a single particle, which cannot have a well-defined value for incompatible observables.

Griffiths and Omnès wrote an introductory piece, in which they write:

The central idea is that the rules that govern how quantum beables relate to each other, and how they can be combined to form sensible descriptions of the world, are rather different from what one finds in classical physics

— Consistent Histories and Quantum Measurements. R. B. Griffiths and R. Omnès in Physics Today 52:26 (1999).

The theory is also introduced by Goldstein.

Quantum Decoherence

This theory, by Wojciech H. Zurek, is independent from the "decoherent histories" of Griffiths & Omnès above (although for a macroscopic system, the latter justify the so-called consistency of families of histories central to their interpretation with Zurek's decoherence). It explains the act of observation from the environment, which acts as an effective observer, thereby effectively making a model of what constitutes "observation" in quantum mechanics.

Superdeterminism

https://en.wikipedia.org/wiki/Superdeterminism

Enlightened ones

Besides or beyond the "agnostic" approach of not worrying about the interpretation because this is either futile or unnecessary, one can also find the view that it is actually not needed at all, since there is no problem of interpretation in the first place and everything is accounted for by the theory, since it works in producing what it aims to describe.

Quantum Theory Needs No ‘Interpretation’. C. A. Fuchs and A. Peres in Physics Today 53:70 (2000).

Still others

• Time-symmetric theories: putting past and future on an equal footing. Proposed by Schottky in 1921.
• Transactional interpretation: both the field $\psi$ and its complex conjugage $\psi^*$ are real (physical) objects which describe a "possibility wave" from the source to the receiver and vice-versa, whose mutual interaction realizes a transaction.
• Quantum logic: positing that logic as we know it is not suitable to describe the quantum regime. Possibly related to Feynman's negative probabilities.
• Quantum Darwinism: a well-packaged and wrapped-up version of decoherence.
• Stochastic quantum mechanics: Newton's equations with stochastic terms lead to Schrödinger's equation.

Not all interpretations are exactly equivalent to orthodox (Copenhagen) version. For instance, Spontaneous Localization predicts small energy increases with time, but too small to be detected.

Still, still others

Modal interpretations of quantum theory, Many-minds interpretation, Quantum mysticism, magic, a prank by God, etc.

Copenhagen Interpretation

We put it last while it ranks first from historical, practical and didactic points of view. Impulsed by Bohr (mainly) and Heisenberg (in his shadow, though not without disagreements), it is also the oldest formulation of some form of interpretation (in the mid-20s). It is in fact so predominant as to be known as the "orthodox" view of quantum mechanics! It relies chiefly on the principle of complementarity, which states that not everything can be known about a quantum object. The observation is irreversible in that it causes a collapse of the wavefunction. The interpretation was much discussed at the 5th Solvay conference. Its proponents include Bohr, whose paper replying to EPR (with the same title) can be regarded as the Copenhagen-interpretation paper, and also von Neumann, who formulated the Mathematical axioms of the theory. Its detractors include Einstein and everybody siding with any of the alternative interpretations above.

If that were so then physics could only claim the interest of shopkeepers and engineers; the whole thing would be a wretched bungle.

— Einstein, In a letter to Schrödinger [2]

No reasonable definition of reality could be expected to permit this.

— Einstein as cited by Pais

The point is no longer that quantum mechanics is an extraordinarily (and for Einstein, unacceptably) peculiar theory, but that the world is an extraordinarily peculiar place.

— Bringing home the atomic world: Quantum mysteries for anybody. N. D. Mermin in Am. J. Phys. 49:940 (1981).

If there is spooky action at a distance, then, like other spooks, it is absolutely useless except for its effect, benign or otherwise, on our state of mind.

— Is the Moon There When Nobody Looks? Reality and the Quantum Theory. N. D. Mermin in Physics Today 38:38 (1985).

In speaking of the adherents of this interpretation, it is important to distinguish the active adherents from the rest, and to realize that even most textbook authors are not included among the former. If a poll were conducted among physicists, the majority would profess membership in the conventionalist camp, just as most Americans would claim to believe in the Bill of Rights, whether they had ever read it or not.

— Quantum mechanics and reality. B. DeWitt in Physics Today 23:30 (1970).

The name comes from Heisenberg despite his personal reluctance to complementarity. The reason might be as an atonement following his WWII break-up with Bohr.

M. Jammer, The Conceptual Development of Quantum Mechanics 共McGraw–Hill, New York, 1966兲; second edition 共1989兲.

Proponents include Bohr himself, not quite Heisingberg, interestingly, but rather fanatics like L. Rosenfeld who commented as follow on the Copenhagen interpretation:

there has never been any such thing and I hope there will never be. The only distinction is between physicists who understand quantum mechanics and those who do not.

Links

• From the Wikipedia.
• Feynman speaking about it (and part 2)
• Other links: [3]

References

• Quantum (Un)speakables: From Bell to Quantum Information, Ed. by R.A. Bertlmann and A. Zeilinger.