The Bell theorem.pdf

PHYSICS TODAY / APRIL 1985 PAG. 38-47

Is the moon there when nobody looks?

Reality and the quantum theory

Einstein maintained that quantum metaphysics entails spooky actions at a distance ;

experiments have now shown that what bothered Einstein is not a debatable point

but the observed behaviour of the real world.

N. David Mermin

[David Mermin is director of the Laboratory of Atomic and Solid State Physics at Cornell University. A

solid-state theorist, he has recently come up with some quasithoughts about quasicrystals. He is known to

PHYSICS TODAY readers as the person who made “boojum” an internationally accepted scientific term.

With N.W.Ashcroft, he is about to start updating the world’s funniest solid-state physics text.

He says he is bothered by Bell’s theorem, but may have rocks in his head anyway.]

Quantum mechanics is magic 1

In May 1935, Albert Einstein, Boris Podolsky and Nathan Rosen published 2 an argument that quantum

mechanics fails to provide a complete description of physical reality. Today, 50 years later, the EPR paper

and the theoretical and experimental work it inspired remain remarkable for the vivid illustration they

provide of one of the most bizarre aspects of the world revealed to us by the quantum theory.

Einstein’s talent for saying memorable things did him a disservice when he declared “God does not play

dice.” for it has been held ever since the basis for his opposition to quantum mechanics was the claim that a

fundamental understanding of the world can only be statistical.

But the EPR paper, his most powerful attack on the quantum theory, focuses on quite a different aspect: the

doctrine that physical properties have in general no objective reality independent of the act of observation.

As Pascual Jordan put it 3 :

“Observations not only disturb what has to be measured, they produce it….We compel [the electron]

to assume a definite position…. We ourselves produce the results of measurements.”

Jordan’s statement is something of a truism for contemporary physicists. Underlying it, we have all been

taught, is the disruption of what is being measured by the act of measurement, made unavoidable by the

existence of the quantum of action, which generally makes it impossible even in principle to construct probes

that can yield the information classical intuition expects to be there.

Einstein didn’t like this. He wanted things out there to have properties, whether or not they were measured 4 :

“We often discussed his notions on objective reality. I recall that during one walk Einstein suddenly

stopped, turned to me and asked whether I really believed that the moon exists only when I look at it.”

The EPR paper describes a situation ingeniously contrived to force the quantum theory into asserting that

properties in a space-time region B are the result of an act of measurement in another space-time region A ,

so far from B that there is no possibility of the measurement in A exerting an influence on region B by any

known dynamical mechanism. Under these conditions, Einstein maintained that the properties in A must

have existed all along.

Spooky actions at a distance

Many of his simplest and most explicit statements of this position can be found in Einstein’s

correspondence with Max Born. 5 Throughout the book (which sometimes reads like a Nabokov novel),

Born, pained by Einstein’s distaste for the statistical character of the quantum theory, repeatedly fails, both in

his letters and in his later commentary on the correspondence, to understand what is really bothering

Einstein. Einstein tries over and over again, without success, to make himself clear. In March 1948, for

example, he writes:

“That which really exists in B should …not depend on what kind of measurement is carried out in part

of space A; it should also be independent of whether or not any measurement at all is carried out in

space A. If one adheres to this program, one can hardly consider the quantum-theoretical description

as a complete representation of the physically real. If one tries to do so in spite of this, one has to

assume that the physically real in B suffers a sudden change as a result of a measurement in A.

My instinct for physics bristles at this.”

Or, in March 1947:

“I cannot seriously believe in [the quantum theory] because it cannot be reconciled with the idea that

physics should represent a reality in time and space, free from spooky actions at a distance.”

The “spooky actions at a distance” (spukhafte Fernwirkungen) are the acquisition of a definite value of a

property by the system in region B by virtue of the measurement carried out in region A . The EPR paper

presents a wavefunction that describes two correlated particles, localized in regions A and B , far apart.

In this particular two-particle state one can learn (in the sense of being able to predict with certainty the

result of a subsequent measurement) either the position or the momentum of the particle in region B as a

result of measuring the corresponding property of the particle in region A . If “that which really exists” in

region B does not depend on what kind of measurement is carried out in region A , then the particle in region

B must have had both a definite position and a definite momentum all along.

Because the quantum theory is intrinsically incapable of assigning values to both quantities at once, it must

provide an incomplete description of the physically real. Unless, of couse, one asserts that it is only by virtue

of the position (or momentum) measurement in A that the particle in B acquires its position (or momentum):

spooky actions at a distance.

At a dramatic moment Pauli appears in the Born-Einstein Letters , writing Born from Princeton in 1954 with

his famous tact on display:

“Einstein gave me your manuscript to read; he was not at all annoyed with you, but only said you were

a person who will not listen. This agrees with the impression I have formed myself insofar as I was

unable to recognize Einstein whenever you talked about him in either your letter or your manuscript.

It seemed to me as if you had erected some dummy Einstein for yourself, which you then knocked

down with great pomp. In particular, Einstein does not consider the concept of ‘determinism’ to be as

fundamental as it is frequently held to be (as he told me emphatically many times)… In the same way,

he disputes that he uses as criterion for the admissibility of a theory the question: Is it rigorously

deterministic? “

Pauli goes on to state the real nature of Einstein’s “philosophical prejudice” to Born, emphasizing that

“Einstein’s point of departure is ‘realistic’ rather than ‘deterministic’.” According to Pauli the proper

grounds for challenging Einstein’s view are simply that:

“One should no more rack one’s brain about the problem of whether something one cannot know

anything about exists all the same, than about the ancient question of how many angels are able to sit

on the point of a needle. But it seems to me that Einstein’s questions are ultimately always of this

kind.”

Faced with spooky actions at a distance, Einstein preferred to believe that things one cannot know anything

about (such as the momentum of a particle with a definite position) do exist all the same.

In April 1948 he wrote to Born:

“Those physicists who regard the descriptive methods of quantum mechanics as definitive in principle

would…drop the requirement for the independent existence of the physical reality present in different

parts of space; they would be justified in pointing out that the quantum theory nowhere makes explicit

use of this requirement. I admit this, but would point out: when I consider the the physical

phenomena known to me, and especially those which are being so successfully encompassed by

quantum mechanics, I still cannot find any fact anywhere which would make it appear likey that [the]

requirement will have to be abandoned. I am therefore inclined to believe that the description of

quantum mechanics…has to be regarded as an incomplete and indirect description of reality…”

A fact is found

The theoretical answer to this challenge to provide “any fact anywhere” was given in 1964 by John S.Bell,

in a famous paper 6 in the short-lived journal Physics. Using a gedanken experiment invented 7 by David

Bohm, in which “properties one cannot know anything about” (the simultaneous values of the spin of a

particle along several distinct directions) are required to exist by EPR line of reasoning, Bell showed (“Bell’s

theorem”) that the nonexistence of these properties is a direct consequence of the quantitative numerical

predictions of the quantum theory. The conclusion is quite independent of whether or not one believes that

the quantum theory offers a complete description of physical reality.

If the data in such an experiment are in agreement with the numerical predictions of the quantum theory,

then Einstein’s philosophical position has to be wrong.

In the last few years, in a beautiful series of experiments, Alain Aspect and his collaborators at the

University of Paris’s Institute of Theoretical and Applied Optics in Orsay provided 8 the experimental answer

to Einstein’s challenge by performing a version of the EPR experiment under conditions in which Bell’s type

of analysis applied.

They showed that the quantum-theoretic predictions were indeed obeyed. Thirty years after Einstein’s

challenge, a fact -not a metaphysical doctrine- was provided to refute him.

Attitudes toward this particular 50-year sequence of intellectual history and scientific discovery vary

widely. 9 From the very start Bohr certainly took it seriously. Leon Rosenfeld describes 10 the impact of the

EPR argument:

“This onslaught came down upon us as a bolt from the blue. Its effect on Bohr was remarkable….A

new worry could not have come at a less propitious time. Yet, as soon as Bohr had heard my report of

Einstein’s argument, everything else was abandoned.”

Bell’s contribution has become celebrated in what might be called semi-popular culture. We read, for

example, in The Dancing Wu Li Masters that 11 :

“Some physicists are convinced that [Bell’s theorem] is the most important single work, perhaps, in

the history of physics.”

And indeed, Henry Stapp, a particle theorist at Berkeley, writes that 12 :

“Bell’s theorem is the most profound discovery of science.”

At the other end of the spectrum, Abraham Pais, in his recent biography of Einstein, writes 13 of the EPR

article that “bolt from the blue” the basis for “the most profound discovery of science” :

“The only part of this article which will ultimately survive, I believe, is…a phrase [‘No reasonable

definition of reality could be expected to permit this’] which so poignantly summarizes Einstein’s

views on quantum mechanics in his later years.”

I think it is fair to say that more physicists would side with Pais than with Stapp, but between the majority

position of near indifference and the minority position of wild extravagance is an attitude I would

characterize as balanced. This was expressed to me most succintly by a distinguished Princeton physicist on

the occasion of my asking how he thought Einstein would have reacted to Bell’s theorem.

He said that Einstein would have gone home and thought about it hard for several weeks that he couldn’t

guess what he would then have said, except that it would have been extremely interesting. He was sure that

Einstein would have been very bothered by Bell’s theorem.

Then he added:

“Anybody who’s not bothered by Bell’s theorem has to have rocks in his head.”

To this moderate point of view I would only add the observation that contemporary physicists come in two

varieties.

Type 1 physicists are bothered by EPR and Bell’s theorem.

Type 2 (the majority) are not, but one has to distinguish two subvarieties.

Type 2a physicists explain why they are not bothered. Their explanations tend either to miss the point

entirely (like Born’s to Einstein) or to contain physical assertions that can be shown to be false.

Type 2b are not bothered and refuse to explain why. Their position is unassailable. (There is a variant of

type 2b who say that Bohr straightened out 14 the whole business, but refuse to explain how.)

A gedanken demonstration

To enable you to test which category you belong to, I shall describe, in black-box terms, a very simple

version of Bell’s gedanken experiment, deferring to the very end any reference whatever either to the

underlying mechanism that makes the gadget work or to the quantum-theoretic analysis that accounts for the

data. Perhaps this backwards way of proceeding will make it easier for you to lay aside your quantum

theoretic prejudices and decide afresh whether what I describe is or is not strange. 15

What I have in mind is a simple gedanken demonstration. The apparatus comes in three pieces. Two of

them ( A and B ) function as detectors.

They are far apart from each other (in the analogous Aspect experiments over 10 meters apart). Each

detector has a switch that can be set to one of three positions; each detector responds to an event by flashing

either a red light or a green one. The third piece ( C ), midway between A and B , functions as a source.

(See figure 1 .)

There are no connections between the pieces, no mechanical connections, no electromagnetic connections,

nor any other known kinds of relevant connections. (I promise that when you learn what is inside the black

boxes you will agree that there are no connections.)

The detectors are thus incapable of signaling to each other or to the source via any known mechanism, and

with the exception of the “particles” described below, the source has no way of signaling to the detectors.

The demonstration proceeds as follows:

The switch of each detector is independently and randomly set to one of its three positions, and a button is

pushed on the source; a little after that, each detector flashes either red or green. The settings of the switches

and the colors that flash are recorded, and then the whole thing is repeated over and over again.

The data consist of a pair of numbers and a pair of colors for each run. A run, for example, in which A was

set to 3, B was set to 2, A flashed red, and B flashed green, would be recorded as “ 32RG ”, as shown in

figure 2 .

Because there are no built-in connections between the source C and the detectors A and B , the link between

the pressing of the button and the flashing of the light on a detector can only be provided by the passage of

something (which we shall call a “particle”, though you can call it anything you like) between the source and

that detector. This can easily be tested; for example, by putting a brick between the source and a detector.

In subsequent runs, that detector will not flash. When the brick is removed, everything works as before.

Figure 1 - An EPR apparatus .

The experimental setup consist of two detector, A and B , and a source of something (“particles” or whatever) C . To

start a run, the experimenter pushes the button on C ; something passes from C to both detectors. Shortly after the button

is pushed each detector flashes one of its lights. Putting a brick between the source and one of the detectors prevents

that detectors from flashing, and moving the detectors farther away from the source increases the delay between when

the button is pushed and when the lights flash. The switch settings on the detectors vary randomly from one run to

another. Note that there are no connections between the three parts of the apparatus, other than via whatever it is that

passes from C to A and B .

The photo below shows a realization of such an experiment in the laboratory of Alain Aspect in Orsay, France. In the

center of the lab is a vacuum chamber where individual calcium atoms are excited by the two lasers visible in the

picture. The re-emitted photons travel 6 meters through the pipes to be detected by a two-channel polarizer.

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