Re: Does Bell's Interconnectedness Therom take everything into account?

There are many pages on the internet related to Bell's inequalities and the EPR (Einstein-Podolsky-Rosen) Paradox (which is, like all Paradoxes in physics, not a paradox at all). Some of which are very good. Some are not. There are many books on the subject. Some of which are very good... you get the idea. The problem is that quantum mechanics is seen as being very mystical. It is really not. The essence of quantum mechanics is a set of mathematical rules which are very well understood and have, so far, held firm to all experimental tests that have been performed on them. Quantum mechanics is, however, not intuitive. This is where people think that it is very mysterious. I am not one of those people, but that is philosophy and not physics.

Let us start with some clarification that, although Bell's theorem (or inequalities) and the EPR paradox are related, they are not the same thing.

Bell's theorem is concerned with determining whether there are hidden variables in quantum theory. I.e. parameters of the system which are not observed, but which ultimately control the outcome of experiments. Violation of Bell's inequalities shows that quantum mechanics does not have any hidden variables. The description that one has of a system is all there is. This is widely accepted, but like all of physics, should not be taken for granted. Information about Bell's Theorem and inequalities can be found all over the web, for example:

http://www.upscale.utoronto.ca/GeneralInterest/Harrison/BellsTheorem/BellsTheorem.html

http://scienceworld.wolfram.com/physics/BellsInequalities.html

The EPR paradox is, on the other hand, concerned with two things. The first of which is the possibility of hidden variables and the second, and the one that is most often discussed, something called non-locality. Non-locality is also referred to as "spooky action at a distance" or can be thought of as a wavefunction of one particle collapsing the wavefunction of another where there is a large spatial separation of the two particles.

Just in case you are getting bored and don't end up reading to the end of this article I want to stress right now that nowhere in quantum mechanics does information travel faster than the speed of light. This is fundamental to physics. A wavefunction may collapse "instantanously", but there is no such thing as superluminal travel. Sorry. :)

Now to the specifics:

It is true that Alain Aspect, when he tested the Bell inequalities and, at the same time, was able to show that the so-called EPR paradox was not a paradox, but reality, did his experiments with particles of light. These light particles, or photons as we usually call them, travel at the speed of light, which confuses things slightly since people want to mix things up with the theory of special relativity. This adds to the confusion, but in fact there is no mystery. Photons travel at the speed of light. There is no need to get confused with time dilation or Lorentz contraction - a photon travels about 30 cm in one nanosecond, and two photons will travel away from each other. I know this since I have measured their relative motion quite frequently. I will come back to this later since it is not really relevent to our current discussion. More information about Alain Aspect and his experiments can be found on the following web pages:

http://atomoptic.iota.u-psud.fr/EnMain.htm

http://perso.wanadoo.fr/eric.chopin/epr/aspect.htm

Anyway, to get away from relativity I can tell you about three experiments which were performed on other particles, which are not photons and don't travel at the speed of light. These experiments also show a violation of Bell's inequalities giving us evidence that the lack of hidden variables is a property of all quantum particles, and not just photons. The first involves two trapped Beryllium ions, which are large atoms. David Wineland's group at the National Institute of Standards and Technology in Colorado, USA, showed that two of these atoms can be entangled (share a quantum state) and violate the inequality:

M.A. Rowe, D. Kielpinski, V. Meyer, C.A. Sackett, W.M. Itano, C. Monroe, and D.J. Wineland,
"Experimental violation of a Bell's inequality with efficient detection,"
Nature 409, 791-794 (2001). http://www.boulder.nist.gov/timefreq/ion/qucomp/papers.htm

David Wineland's group

A second experiment which showed violation of the inequalty was performed by Helmut Rauch and co-workers at the Atomic Institute of Austrian Universities in Vienna. Here, instead of an atom, they took just neutrons (one atomic constituent) and performed single-neutron intereference. Their article was published in the journal Nature. You might not be able to look at the following link if your institution doesn't have a subscription to the journal, but you will find it in a library:

Violation of a Bell-like inequality in single-neutron interferometry
YUJI HASEGAWA, RUDOLF LOIDL, GERALD BADUREK, MATTHIAS BARON & HELMUT RAUCH
Nature, volume 425, number 6953, page 45.

Another test of Bell's inequality was performed in Japan on a somewhat exotic particle called a B-meson. B-mesons are sub-atomic particles generated in particle accelarators. However, I am no expert on B-mesons so I am not even going to go into what they are. Let us just take them as another example of a particle, which is not a photon, which violates the Bell inquality. There is a brief article on this experiment at:

Bell inequality with B-mesons:

http://physicsweb.org/articles/news/7/11/3

So, I hope that I have convinced you that you don't need photons to test the Bell inequality. You also don't need photons to test the EPR paradox, however, I am not aware that non-locality has been convincingly tested yet - the atom people are working on it.

Let me just finish by talking about information. I said above that information cannot travel faster than the speed of light. That is not to say that some things in physics do not travel superluminally. One thing that often causes confusion is something called the phase of a light pulse (remember that light is a wave and waves have a certain phase). This often travels faster than the pulse itself, but it is the pulse itself that contains the information and this never travels faster than c. The implication for the EPR paradox is that, even if you know that the state of the particle B changes instantaneously, you cannot check that it is correlated with the particle A in a time faster than it takes for light to travel at least from A to B. That is the beauty of physics.

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aside:

Since the question was asked by an undergraduate physics student, I want to finish this with suggesting a little problem. If we go back to special relativity, which I was keen on dropping earlier on in the article, you can start to think about the timing of when the wavefunction was collapsed in the EPR paradox. If you assume that there are two particles A and B and an observer O, you can start drawing the light cones for each of these three objects. See if you can figure out whether the position of the observer matters in determining who made the measurement first. Did the person at A measure the state of A before B, or vice versa? I am sure you have already guessed that the answer is confusing. However, it is interesting and all well described by mathematics.

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