Public Library Talk: Einstein and the Atom

I'm giving a talk tomorrow (Wednesday, October 28), at the Central Branch of the London Public Library, (251 Dundas Street), 7 PM, Stevenson & Hunt Room.   The talk will be non-technical, and accessible to all.  Please join me, if you can!

Einstein and the Atom.

 Abstract:
Einstein’s name is widely associated with the “atom bomb,” via the formula E = mc². Less widely known is that he played a key role in providing evidence that atoms exist at all. One of Einstein’s early papers was an analysis of Brownian motion, the ceaseless dance of tiny particles, such as pollen grains, suspended in a fluid. The dance of pollen grains, Einstein realized, was evidence that they are being buffeted by smaller particles, beyond microscopic resolution. This talk will be about the ingenuity required to turn the visible into evidence about the invisible.

Was Einstein Wrong?

Some headlines from the past day or so:

• Dutch News: Dutch scientists show Einstein was wrong about ‘spooky action’
• Time magazine, What Einstein Got Wrong About the Speed of Light
• The New York Times, Sorry, Einstein.Quantum Study Suggests ‘Spooky Action’ Is Real.

This sort of thing is nothing new, of course.  Many  discussions of Einstein's attitude towards quantum mechanics suggest that Einstein simply refused to accept a straightforward consequence of quantum mechanics: non-locality.

Now, if you have no reason to believe something, and you don’t believe it, but it happens to be true, then, in one sense, you’re wrong in your belief.  But you can’t be accused of being unreasonable or irrational.  So, in an uninteresting sense, Einstein was wrong, in not having beliefs that scientists would later provide good evidence for.  But the same could be said of everybody, ever.

Einstein didn’t believe that nonlocality was a feature of the world. But should he have? Was he wrong not to believe in nonlocality?  What reason did anyone have, in 1935, or in the late ‘40s, when he wrote his fullest discussions of his attitude towards quantum mechanics, for thinking that nonlocality was a feature of physical reality?

We can’t fault Einstein for not having read Bell’s 1964 paper, or for not having read the December 20, 1982 issue of Physical Review Letters—after all, he was no longer alive by the time Doc Brown and Marty McFly arrived in 1955, and, besides, as far as we know, they didn’t bring literature of that sort with them. We can't fault him, either, for not having read this week's issue of Nature.  Hindsight is 20-20, and we now know two things that, as far as I know, nobody really knew during Einstein’s lifetime.

1. Some quantum correlations are not locally explicable.
2. Quantum correlations persist when the systems are separated by a large distance.

The first, of course, is Bell's theorem, and the second we know through a series of increasingly impressive experimental demonstrations of violations of Bell inequalities.  Re 1:  As Bell himself emphasized, the mere fact that outcomes of spatially separated experiments are correlated is no indication of any sort of nonlocality.  As you're reading this, someone else on the other side of the world might be reading the same words.  No spooky action-at-a-distance is needed to explain this; nor is there any need for direct influence between the two of you, as there's a common source for what's displayed on your computer screen, and what is being displayed on the other side of the world.

 

As I’ve emphasized in earlier blog posts (here and here),  Einstein was not nearly as dogmatic about locality as he is sometimes painted to be.  He did not regard the assumptions of locality and separability as non-negotiable; his attitude was that one could, indeed, drop them as requirements on a physical theory, given good reason.  But he saw no reason to do so.  He wrote, in 1948,

if I consider the physical phenomena with which I am acquainted, and especially those which are so successfully comprehended by means of quantum-mechanics, then, nevertheless, I nowhere find a fact which makes it appear to me probable that one has to give up requirement II [of locality and separability]. For that reason I am inclined to believe that the description afforded by quantum-mechanics is to be viewed … as an incomplete and indirect description of reality, that will again be replaced later by a complete and direct description (Einstein 1948; translation in Howard 1985).

Systems that are interacting or have interacted, and whose quantum-mechanical state is entangled, have probabilistically correlated behaviour.  That by itself isn’t enough to answer Einstein’s challenge to point to a phenomenon that would count as evidence for a breakdown of locality. Correlations are already familiar in classical probability theory: for example, if two classical  systems interact, a probability distribution that represents thermal equilibrium will involve correlations between the two.  An answer to Einstein’s challenge would have to give us some reason to think that quantum correlations aren’t like that.

My question for historians: did anyone even attempt to provide an argument of that kind, during Einstein’s lifetime?

References

Aspect, A., J. Dalibard, and G. Roger (1982). Experimental test of Bell’s inequalities using time-varying analyzers. Physical Review Letters 49, 1804-1807.

Bell, John S.,  (1964). On the Einstein-Podolsky-Rosen Paradox. Physics 1, 195-200.

Einstein, Albert (1948). Quanten-mechanik und wirklichkeit. Dialectica 2, 320–324.

Hensen, B. et al. (2015).  Loophole-free Bell inequality violation using electron spinsseparated by 1.3 kilometres. Nature, online 21 October 2015.

Howard, Don (1985). “Einstein on Locality and Separability.” Studies in History and Philosophy of Science 16, 171-201.

Bohr's reply to EPR (Part III)

Did Bohr find a flaw in the EPR argument?

He says he did.  In a brief note (Bohr 1935a) published soon after the publication of the EPR paper, in his fuller reply to EPR (1935b), and in his later (1949) recap of his discussions with Einstein about QM, Bohr claims to have discovered an ambiguity in the EPR reality criterion.

The EPR reality criterion reads:

If, without in any way disturbing a system, we can predict with certainty (i.e. with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity (EPR 1935, p. 777).

Here’s what Bohr says about the alleged ambiguity:

the wording of the above-mentioned criterion of physical reality proposed by Einstein, Podolsky and Rosen contains an ambiguity as regards the expression “without in any way disturbing a system.” Of course there is in a case like that just considered no question of a mechanical disturbance of the system under investigation during the last critical stage of the measuring procedure. But even at this stage there is essentially the question of an influence on the very conditions which define the possible types of predictions regarding the future behavior of the system.  Since these conditions constitute an inherent element of the description of any phenomenon to which the term “physical reality” can be properly attached, we see that the argumentation of the mentioned authors does not justify their conclusion that quantum-mechanical description is essentially incomplete (Bohr 1935b, p. 700; 1949, p. 324).

EPR consider two systems that interact for a while, and then, after a certain time, no longer interact.  On the basis of this absence of interaction, they conclude that what is done to the first system produces no change in the state of the second system.  According to Bohr, this is ambiguous between two readings.

1. They could mean that an experiment performed on the first system produces no mechanical disturbance of the other.
2. On the other hand, they could mean that an experiment performed on the first system has no effect on the types of predictions that can be made about the other.

I submit that there is no ambiguity, because (2) is not a possible reading of what EPR meant.  Of course the choice of experiment done on one particle has an effect on the sorts of predictions that can be made about the other; that’s the whole point of the argument!  And EPR do note that, since the choices are mutually exclusive, to make a choice means losing the opportunity to make the other sort of prediction about the other particle:

one would not arrive at our conclusion if one insisted that two or more physical quantities can be regarded as simultaneous elements of reality only when they can be simultaneously measured or predicted. On this point of' view, since either one or the other, but not both simultaneously, of the quantities P and Q can be predicted, they are not simultaneously real (p. 780).

Bohr says that that the conditions that define the possible types of prediction that can be made about a system constitute an inherent element of the description of any phenomenon to which the term “physical reality” can be properly attached.  This sounds to me as if he saying that being able to predict the outcome of a position “measurement” is a condition for applying the concept of position, and being able to predict the outcome a momentum “measurement” is a condition for applying the concept of momentum. But, if that’s what he’s saying, he’s simply taking the out that EPR offer at the end of their paper.  They note that this way out has the consequence that the reality of properties of one system depends on what is done to the other.  If that is, indeed, what Bohr is saying, then one wishes he had said so straightforwardly!

References

Bohr, Niels (1935a).  Quantum Mechanics and Physical Reality. Nature 136, 65.

——— (1935b). Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Physical Review 48, 696-702.

——— (1949).  Discussions with Einstein on Epistemological Problems in Atomic Physics, in P.A. Schilpp, ed., Albert Einstein: Philosopher-Scientist (Chicago: Open Court Press), 199–241.

Einstein, Albert, Boris Podolsky, and Nathan Rosen (1935), Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Physical Review 47, 777-780.

           

Bohr's Reply to EPR (Part II)

In Part I, I claimed that Bohr simply took for granted the conclusion that EPR argue for, namely, that quantum mechanics does not yield a complete description of physical reality,  and that where they part ways is the unargued-for suggestion that a more complete theory is possible.

If this is right, why isn't it clear to every reader of Bohr's reply to EPR?

The reason, I think, is that it wasn't clear in Bohr's own mind.  When I read Bohr, it often seems to me that he is conflating two distinct questions.  One is the question of whether there could be a theory whose state-descriptions go beyond what is allowed by quantum mechanics.  The other is whether we might ever be in a position to know more about the state of a quantum system than is allowed by the uncertainty relations.

They aren't the same question. Think of classical mechanics.  In classical mechanics, a complete state-description is a specification of precise values of all the system's dynamical variables.  For systems composed of many molecules, it would be hopeless to even come close to knowing the precise state of the system, and so we resort to probability distributions over the set of precise states.  It is irrelevant, for the way the theory is used, whether these limitations on knowledge of the precise state are pragmatic limitations, or limitations in principle.

Einstein's view was that quantum wave functions had a status similar to the probability distributions used in classical statistical mechanics; they represented incomplete knowledge of a precise state that would occur in some other theory (not necessarily classical).   If anyone, prior to Einstein's death, presented a good argument for why one shouldn't think of quantum states in this way, I haven't seen it.  No such argument is found in Bohr's reply to EPR.

Though I don't understand Bohr's response to Einstein, I do understand what Einstein attributes to Bohr as a reply, in his Replies to Critics in the Schilpp volume.  There are two ways to reject the conclusion of an argument. One is to find a flaw in the reasoning; the other is to accept the reasoning that leads from premises to conclusion, and to reject one or more of the premises.  Bohr's reply to EPR reads as if he thinks he's found a flaw in the reasoning; he says he's detected an ambiguity in the EPR reality criterion, an ambiguity fatal to the argument.  But in the Replies, Einstein has Bohr reject a premise of the argument.

Of the "orthodox" quantum theoreticians whose positions I know, Niels Bohr's seems to me to come nearest to doing justice to the problem.  Translated into my own way of putting it, he argues as follows:

If the partial systems A and B form a total system which is described by its ψ-function ψ/(AB), there is no reason why any mutually independent existence (state of reality) should be ascribed to the partial systems A and B viewed separately, not even if the partial systems are spatially separated from each other at the particular time under consideration.

So: I understand that as a potential reply to EPR, though I also think that it would be incumbent on someone who replied that way to answer Einstein's challenge, at the end of the Dialectica article, to point to some phenomenon that suggests that we should reject the premise.

As it appears to me, there can be no doubt that the physicists who hold the quantum mechanical manner of description to be, in principle, definitive, will react to these considerations as follows: They will drop requirement II of the independent existence of the physical realities which are present in different portions of space; they can rightly appeal to the fact that the quantum-theory nowhere makes explicit use of this requirement.

I grant this, but note: if I consider the physical phenomena with which I am acquainted, and especially those which are so successfully comprehended by means of quantum-mechanics, then, nevertheless, I nowhere find a fact which makes it appear to me probable that one has to give up requirement II. (Einstein 1948, translation in Howard 1985)

I don't think that Bohr, or anyone else, answered that challenge in Einstein's lifetime.

References

Einstein, Albert (1948). Quanten-mechanik und wirklichkeit. Dialectica 2, 320–324

Einstein, Albert (1949).  Remarks concerning the essays brought together in this co-operative volume, in P.A. Schilpp, ed., Albert Einstein: Philosopher-Scientist (Chicago: Open Court Press), 665–688.

Howard, Don (1985). “Einstein on Locality and Separability.” Studies in History and Philosophy of Science  16, 171–201.