Causality, determinism, and physics

“Felix, qui potuit rerum cognoscere causas,” (“Fortunate, who was able to know the causes of things”), Virgil, Georgica (II, v. 490), has been taken to refer to Lucretius' work “De Rerum Natura” (“On the nature of things”).

See, e.g.,

J. D.

Jackson

, , 2nd ed. ( , , ), Sec. 7.10.

M.

Pawłowski

,

T.

Paterek

,

D.

Kaszlikowski

,

V.

Scarani

,

A.

Winter

, and

M.

Żukowski

, “ ,” , – ().

D.

Pitalúa-García

, “ ,” , ().

R.

Jones

, “ ,” , ().

M.

Frisch

, “ ,” , Spring 2022th ed., edited by

Edward N.

Zalta

( , , ).

B.

Russell

, “ ,” , – ().

N.

Bohr

, “ ,” , – ().

C.

Hoefer

, “ ,” , Spring 2016th ed., edited by

Edward N.

Zalta

( , , ).

J.

Earman

, “ ,” in , edited by

J.

Butterfield

and

J.

Earman

( , , ), pp. –.

Earman's review (Ref. 10) is, in fact, a very good example of the strong association, in physics at least, of “determinism” with, essentially, differential equations. It covers many intriguing examples of non-unique or “pathological” solutions to problems in classical mechanics, classical field theories, and both special and general relativity. Unfortunately, I do not find this a very useful approach to the problem of determinism in quantum mechanics. Rather, to me, as I will try to make clear in Sec. V, the one-to-many relation between state vectors and measurement outcomes, as posited in the “orthodox” formalism and observed in actual experiments, is the very definition of indeterminism.

, Physics, Book 2, Chap. 3, available online in the Internet Classics Archive: <http://classics.mit.edu/Aristotle/physics.2.ii.html>

D.

Hume

, A Treatise of Human Nature, Book III, Sec. II, available online as part of the Project Gutenberg <https://www.gutenberg.org/files/4705/4705-h/4705-h.htm>

The emphasis on these kinds of causes and effects is a characteristic of mechanistic explanations of the world, which became widespread in the 17th century. See, for a historical perspective and many valuable insight,

D.

Dieks

, “ ,” in , edited by

B.

Falkenburg

and

G.

Schiemann

( , , ), pp. –.

It may seem that I am conflating here determinism and predictability, something which philosophers are always warning us not to do (Refs. 9 and 10). The question is subtle, but I believe it is certainly legitimate to ask for evidence from any model that calls itself deterministic before we lend it any credence. Otherwise, we might as well believe that everything that happens in the universe is determined by invisible causes of which we cannot know anything. Of course, we may want to cut our physical theories some slack: There may be many cases where exact prediction is an extremely challenging mathematical problem, but we otherwise have no reason to doubt the underlying model, because it has proved itself sufficiently (through verifiable predictions) elsewhere. On the other hand, an impossibility to come up with verifiable predictions in practice by a model that calls itself deterministic may also be an indication that this particular model has reached the limits of its applicability. This is, in my opinion, the case of so-called “deterministic chaos” the moment an accurate prediction requires the initial conditions to be specified to greater precision than allowed by quantum mechanics (see Sec. IV C).

In fact, Newton's theory was criticized in his time by no less than Leibnitz and Huygens for not being “mechanistic” enough on this point! See S. Psillos and S. Ioannidis, “Mechanisms, Then and Now: From Metaphysics to Practice,” in the book cited in Ref. 14.

According to Section 2 of Ref. 6, this has been used in philosophy to argue against the usefulness of the notion of cause itself. If so, this seems like backwards reasoning to me. The world as we experience it is time-asymmetric. If our notion of cause reflects this, and our physical theories do not, this is rightfully a problem for our physical theories, not the other way around.

E.

Schliesser

and

T.

Demeter

, “ ,” in , Summer 2020th ed., edited by

Edward N.

Zalta

(Metaphysics Research Lab, Stanford University, Stanford, CA), see <https://plato.stanford.edu/archives/sum2020/entries/hume-newton/>.

P. S.

de Laplace

, , translated into English from the original French 6th ed. by

F. W.

Truscott

and

F. L.

Emory

( , , ).

This reference, like the terms “Laplace's demon” and “Laplacian determinism,” has become standard, yet, interestingly, Earman (Ref. 10, p. ) quotes a very similar statement made by Leibnitz over a century earlier.

F.

Del Santo

and

N.

Gisin

, “ ,” , ().

A.

Einstein

, “ ,” , – (), reprinted in

A.

Einstein

, , edited by

R.

Fürth

, translated by A. D. Cowper ( , , ). Also available online as part of the Collected Einstein Papers <https://einsteinpapers.press.princeton.edu/vol2-trans/137>

R.

Kubo

, “ ,” , ().

R. P.

Feynman

,

R. B.

Leighton

, and

M.

Sands

, ( , , ), Vol. , Sec. 39-4.

G. H.

Wannier

, , revised ed. ( , , ), Chap. 18.

R. P.

Feynman

,

R. B.

Leighton

, and

M.

Sands

, ( , , ), Vol. , Secs. 40-6 and 41-2.

S. H.

Strogatz

, ( , , ).

W. H.

Zurek

, “ ,” , – ().

A.

Einstein

, “ ,” originally published in , ();

reprinted in , edited by

B. L.

van der Waerden

, Classics of Science, Vol. ( , , ).

A.

Einstein

,

B.

Podolsky

, and

N.

Rosen

, “ ,” , – ().

The comprehensive article review article by

F.

Laloë

, “ ,” , () covers a number of alternative “interpretations” (many of which are actually extensions, and, as such, really different physical theories) of quantum mechanics. Note that most of them are, at best, only indirectly concerned with questions of causality or determinism: in most cases, their primary purpose is to address questions like the ontological status of the wavefunction, or to make sense of the collapse postulate.

In a class by itself is the Everettian, or “many-worlds” interpretation, which does not involve hidden variables. This interpretation, in effect, embraces the indeterminism implied by the one-to-many correspondence between quantum states and possible outcomes, by asserting that every single possible outcome is actually realized in one of a multitude of “worlds” that come into being whenever a system in a state such as Eq. (6) is “observed.” (Depending on the interpretation, these may be either true physical or purely “mental” worlds.) As these worlds are, by assumption, inaccessible to each other, this, the only truly deterministic prediction of the theory, is neither verifiable nor disprovable. Within the single-world perspective that is the only one available to any observer, it remains a fact that identically prepared systems will yield different, unpredictable results, for which no causal explanation is given.

A. M.

Gleason

, “ ,” , – (), see http://www.jstor.org/stable/24900629.

J. S.

Bell

, “ ,” , – ().

S.

Kochen

and

E. P.

Specker

, “ ,” , – (), see https://www.jstor.org/stable/24902153.

For a very accessible presentation of some of these results, see

N. D.

Mermin

, “ ,” , – ().

In practice, however, experiments to check the predictions of Bell's theorems (Ref. 36) have been carried out on simpler kinds of entangled states, such as a superposition of states of polarization, H and V (for horizontal or vertical) of two photons, of the form $1 / 2 ( | H ⟩ | H ⟩ + | V ⟩ | V ⟩ )$⁠, or a superposition of the states of two atoms of the form $1 / 2 ( | e ⟩ | g ⟩ + | g ⟩ | e ⟩ )$⁠.

C. J.

Wood

and

R. W.

Spekkens

, “ ,” , ().

This, of course, does not make these correlations any less mysterious! In a recent paper, Spekkens and co-workers have argued for what they call “Quantum Causal Models” as a possible way to deal with them:

J.-M.

Allen

,

J.

Barrett

,

D. C.

Horsman

,

C. M.

Lee

, and

R. W.

Spekkens

, “ ,” , ().

L. D.

Landau

and

E. M.

Lifshitz

, , 3rd ed. ( , , ).

D.

Drahi

,

N.

Walk

,

M. J.

Hoban

,

A. K.

Fedorov

,

R.

Shakhovoy

,

A.

Feimov

,

Y.

Kurochkin

,

W. S.

Kolthammer

,

J.

Nunn

,

J.

Barrett

, and

I. A.

Walmsley

, “ ,” , ().

H. J.

Briegel

, “ ,” , ().

, “ ,” , ().

The general question of “mechanistic” explanations in science is currently the subject of an active debate. According to the article cited in Ref. 16, this includes proposals to expand the concept of “mechanism” to make it essentially synonymous with “causal pathways.”

See

N. D.

Mermin

, “ ,” , (), Sec. 3.3.3: “When I act on the world, the action I take is my free choice. Reciprocally, when the world acts back on me in response to my action, quantum mechanics can tell me nothing more than the probability of the response I can expect: the world's reaction to my action is the world's free choice.” While this was written from the perspective of one specific interpretation of quantum mechanics (QBism), it may be taken to apply in the “standard” (Copenhagen) interpretation as well.