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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.^[1] For many, what we know is more than enough. This is known as the shut and calculate school. 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?^[2]

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 _^[3].

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

Path integrals

Feynman's path integral formalism^[4].

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 Occasm's razor test. It postulates indeed that there is a full (total, universal) wavefunction of the universe^[5], 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. And why not? Are not we subject to Newton's equations of motion? Why would we escape Schrödinger's?

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).

Proponents include David Deutsch, who came up with the idea of a quantum computer based on his belief that universes were indeed splitting

^[6]

^[7]

Pilot wave

This theory, first proposed by De Broglie and then later extended by Bohm^[8][9] (it is also popularly known as Bohm's pilot wave or Bohmian mechanics) posits an underlying wave (which follows Schrödinger's equation) that guides the particles, the latter being well-defined in terms of their positions in 3D space, like classical particles, and thus being of the hidden-variable type, but given that their behavior is piloted by the wave, which is itself nonlocal and, this time, in the configuration space (of very high dimensions), albeit deterministic, thus have all the wonders of quantum mechanics. A dialogue covers the basics in Ref. _^[10].

‘‘quantum velocity term,’’ which has a value defined in configuration space and not in ordinary space

quantum phenomena are local in configuration space, but not necessarily in ordinary space.

See also ^[11]

Proponents include Bell. Opponents include Englert, Scully et al.^[12].

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 ^[13]

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^[2]. An ennemy is Ballentine.^[14]

Superdeterminism

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

Consistent histories

(Quantum contextuality?) R. B. Griffiths and R. Omnès, ‘‘Consistent histories and quantum mea- surements,’’ Phys. Today 52, 26–31 共August 1999兲.

Relational quantum mechanic

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.^[15]

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.^[16]

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[1]. Its proponents include Bohr, von Neumann. 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).

^[17] and ^[18]

^[19]

^[20]

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

^[21]

Links

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

References

1. ↑ Resource letter IQM-2: Foundations of quantum mechanics since the Bell inequalities. L. E. Ballentine in Am. J. Phys. 55:785 (1987).
2. ↑ ^{2.0 2.1} Quantum mechanics: Fixing the shifty split. N. D. Mermin in Physics Today 65:8 (2012).
3. ↑ Do we really understand quantum mechanics? Strange correlations, paradoxes and theorems. F. Lalöe in Am. J. Phys. 69:655 (2001).
4. ↑ Space-Time Approach to Non-Relativistic Quantum Mechanics. R. P. Feynman in Rev. Mod. Phys. 20:367 (1948).
5. ↑ "Relative State" Formulation of Quantum Mechanics. H. Everett III in Rev. Mod. Phys. 29:454 (1957).
6. ↑ The structure of the multiverse. D. Deutsch in Proc. R. Soc. Lond. A 458:2911 (2002).
7. ↑ Quantum mechanics and reality. B. DeWitt in Physics Today 23:30 (1970).
8. ↑ A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. I. D. Bohm in Phys. Rev. 85:166 (1952).
9. ↑ A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. II. D. Bohm in Phys. Rev. 85:180 (1952).
10. ↑ Understanding Bohmian mechanics: A dialogue. R. Tumulka in Am. J. Phys. 72:1220 (2004).
11. ↑ Quantum interference and the quantum potential. C. Philippidis, C. Dewdney and B. J. Hiley in Nuov. Cim. B 52:15 (1979).
12. ↑ Surrealistic Bohm Trajectories. B.-G. Englert, M. O. Scully, G. Süssmann and H. Walther in Zeitschrift für Naturforschung A 47:1175 (1992).
13. ↑ Quantum-Bayesian coherence. C. A. Fuchs in Rev. Mod. Phys. 85:1693 (2013).
14. ↑ Reviews of quantum foundations. D. Ballentine in Physics Today 73:11 (2020).
15. ↑ The scandal of quantum mechanics. N. G. van Kampen in Am. J. Phys. 76:989 (2008).
16. ↑ Derivation of the Schrödinger Equation from Newtonian Mechanics. E. Nelson in Phys. Rev. 150:1079 (1966).
17. ↑ Quantum Theory without Observers-Part One. S. Goldstein in Physics Today 51:42 (1998).
18. ↑ Quantum Theory without Observers-Part Two. S. Goldstein in Physics Today 51:38 (1998).
19. ↑ Quantum-mechanics debate. L. E. Ballentine, P. Pearle, E. H. Walker, M. Sachs, T. Koga, J. Gerver and B. DeWitt in Physics Today 24:36 (1971).
20. ↑ Still more quantum mechanics. G. L. Trigg, M. Hammerton, Jr R. Hobart Ellis, R. Goldston and H. Schmidt in Physics Today 24:11 (1971).
21. ↑ Role of the Observer in Quantum Theory. A. Shimony in Physics Today 31:755 (1963).