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Jun 4, 2001, 1:34:46 PM6/4/01

to Lubos Motl

Hello!

I found the newsgroups using lynx and I am trying to reply via pine for

the first time. :-) BTW have you seen John Baez's paper on octonions? I

hope you find it lovely, too.

> It is important to understand that this is a matter of philosophical opinion

> and not scientific fact. Quantum mechanics violates classical definitions of

> locality. Bell proved it and Eberhard proved it without reference to

This is not the way in which physicists think about the question of

locality. Quantum mechanics does not satisfy the axioms of a classical

theory and therefore the classical definitions of locality are not

relevant.

In order to judge whether a theory is local or not, one must use the

correct physical definitions - i.e. quantum mechanical ones. And by these

definitions, quantum field theories such as the Standard Model are "local

quantum field theories" even though they are fully quantum mechanical

theories that violate Bell's inequalities, for example. Everyone calls

them this way and we know why.

Just formulate a quantum field theory - Klein-Gordon field theory for the

sake of simplicity - in the Heisenberg picture. You have something like

(Box + m^2) Phi = 0. Right, Phi is a quantum mechanical field-operator

satisfying some commutation relations and one can make probabilistic

predictions only (and calculate expectation values of various

observables): the rules of quantum mechanics cannot be broken.

But nevertheless the equation is the same equation as the equation

satisfied by the *classical* Klein-Gordon field - for example it is

Lorentz invariant. Therefore the value of the operator at some point in

spacetime (and various average values, probabilities etc. that one can

construct out of it) is determined purely by its values in the point's

past light cone. Because of this and because the commutators such as

[Phi(x),Phi(y)] vanish for x,y spacelike-separated, all the predictions

what happens at point X in spacetime (probabilities, average values of

something etc.) depend only on the inputs in the past light cone of X.

This is why we say that Quantum Field Theories such as QED are local. This

is also why information cannot be transmitted by superluminal speeds.

> hidden variables. ("Bell's Theorem without Hidden Variables",

> _Nuovo Cimento_, V 30 B, pp 75-89, 1977). Quantum mechanics is

Einstein never accepted the probabilistic nature of Quantum Mechanics.

When I was 17, I was his faithful follower. There have been obviously very

many people like that, many of them much older. John Bell, another

follower, wanted to prove that the question whether the probabilistic

interpretation of QM is plausible or whether we must return to the

"complete" (classical) description of reality can be decided

scientifically (people used to say that such a question could never be

tested). And therefore he finally discovered the inequalities saying that

(if we assume basics of classical logic) in every experiment, the

correlations between certain quantities must be smaller than his bound.

Because QM was predicting generically higher correlations (as was known

already to Einstein, in fact), Bell believed that when such experiments

are performed, they must inevitably give results incompatible with QM and

hidden variables would win the war.

Unfortunately for Bell, the experiments have been done (some of the most

obvious ones have been done recently in the context of "quantum

teleportation") and they showed clearly that predictions of QM worked very

well and Bell's inequalities are really violated in Nature. Bell was very

unhappy till the end of his life that instead of killing QM, he offered a

powerful tool to rule out the theories of hidden variables.

Bell's inequalities are violated in Nature, so what are the wrong

assumptions of Bell's proof? Well, Bell assumed the "classical logic",

just like Einstein. If two photons from a decaying positronium are far

from each other, each of them must be in some "real" state, independent of

the state of his friend. But QM dictates otherwise. The maximum we can say

about the photons is their wave function that can contain correlations

between the two photons, they can be in the state |RR>+|LL>, for example

(both right-handed or both left-handed). Although it is not clear which

polarization of the first photon will be measured (the likelihood is

50:50 for L:R), we can be sure that the result will be the same as for the

second photon.

Such "remote correlations" in the wave function can sound "nonlocal" but

they do not allow to send information faster than light - simply because

none is able to command our photon in which state it should be measured.

If this were possible, because of the correlation we could also command

the remote photon to be measured left-handed (or right-handed) and we

could send information almost immediately. But in the real world, it's not

us who decides about the results of the probabilistic experiments but

rather (undefined) God throwing dice (and ask about his Majesty is beyond

the scope of science). Locality is saved. If we ignore "our" photon and

study only the remote one, the probability for it to be left-handed or

right-handed will be 50:50 regardless of what we do. Forget the

superluminal Internet. In the world of hidden variables this would be

possible, (maybe violating relativity and maybe causality?), in the real

world it is not possible.

Such "remote correlations" exist also in classical physics, in fact. Bell

talks about the Bertlmann's socks. One of them is red, one of them is

blue, and when Mr. Bertlmann sees a red sock on his left foot, he can be

sure that the right foot has a blue sock on it (and vice versa). If

something chaotic happens in the morning, we can still describe the state

of Bertlmann's socks by the classical probabilistic distribution

"50% for left-red and right-blue and 50% for left-blue and right-red".

The only difference in Quantum Mechanics is that the probabilistic

distribution must be derived from a complex wave function (that allows for

the interference, higher correlations etc.) and that there does not exist

a more accurate "classical" description of reality. In fact, the

observation that Bell's inequalities are violated together with requiring

Lorentz invariance IMPLY that the world must be probabilistic as I have

indicated.

The rules of Quantum Mechanics are weird. If thousands of philosophers

tried to invent the strangest thing possible, they would have bever

discovered a thing as strange as Quantum Mechanics (Sidney Coleman).

Nevertheless the current facts are too obvious and the proponents of

hidden variables etc. should finally give up. Dirac, Feynman, von Neumann,

Bohr, Born etc. were sure which interpretation was correct and they did

not need so impressing experimental data which we have today.

Furthermore the Copenhagen interpretation was modernized - we can talk

about the "consistent histories", there is already no conceptual

difference between the micro- and macro- objects. One can derive special

properties of macro-objects from the first principles (decoherence etc.),

see Omnes, Hartle, Gell-Mann, Zurek, Griffiths etc. For me personally, the

question whether we can return to the age of "classical logic" is

certainly closed for many years. And I am sad that such a guru of physics

in the 70s, Gerardus 't Hooft, is spending his time with a similar

deterministic religion.

Another topic is locality in quantum gravity and string theory etc. I

believe that QG inevitably violates some rules of locality, otherwise one

can derive Hawking's loss of information in black holes etc. But this is a

completely different level of thinking which can hardly restore the

paradigms of classical physics, especially because the exotic features of

QG are irrelevant in the realm of atomic physics where the laws of QM work

very well.

Best wishes

Lubos

______________________________________________________________________________

E-mail: lu...@matfyz.cz Web: http://www.matfyz.cz/lumo tel.+1-805/893-5025

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Superstring/M-theory is the language in which God wrote the world.

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