Quantum Physics World

Tuesday, March 21, 2006

Does spooky action at a distance allow faster than light communication?

In my book Quantum Mechanics Demystified, I teach the reader the nuts and bolts of quantum mechanics, in the form of the mathematics necessary to calculate using the theory. While this is a challenging and necessary step for mastering quantum physics, the conceptual results that are born out of this mathematical framework is what makes quantum physics truly interesting. Sometimes, the resutls of quantum theory seem almost mystical, almost to the point of validating new age type thinking. Nowhere is this more true than in the phenomenon of entanglement, an interesting subject put on the map by Albert Einstein in one of his last significant scientific papers.

It is often said that scientists do their best work while young. With Albert Einstein this certainly seems to have been the case. Before the age of 40 he developed special relativity, laid the groundwork for quantum theory by explaining the photoelectric effect and in his greatest achievement, developed his elegant theory of gravity, general relativity. However, it was a paper he wrote with two colleagues in 1935-when Einstein was nearly 56 years old-which stands out as his most cited scientific paper. In fact, it may well turn out to be one of the most significant scientific papers of all time.

This is of course the “EPR” paper, written with his colleagues Boris Podolsky and Nathan Rosen. Following a decade of vehement arguments with the great Neils Bohr about the meaning of quantum theory, this paper stands out as Einstein’s “parting shot” in the debate-his last ditch effort to prove that quantum mechanics could not be a fundamental theory. The paper-titled “Can quantum mechanical description of reality be considered complete?”-uses quantum mechanics to demonstrate that particles which interact in someway become entangled, in a loose sense meaning that their properties become correlated. As we’ll see in a moment, this is not an ordinary correlation in any sense of the word. It implies that there exists a strange connection between the particles that persists even when they are separated by great distances. In some sense, this connection is instantaneous, putting it in direct conflict with the special theory of relativity. It was this strange connection that led Einstein to the phrase “spooky action at a distance”.

Quantum Entanglement

The EPR paper is based on the following thought experiment. Two particles interact and then separate. Furthermore, we imagine that they separate such that they are a great distance apart at a time when measurements on the particles can be made. EPR focused on two properties in particular-the position and momentum of each particle.

These properties or variables were chosen because of the Heisenberg uncertainty principle. The uncertainty principle tells us that the position and momentum of a particle are complimentary, meaning that the more you know about one variable, the less you know about the other. If you have complete knowledge of a particles position, then the particles momentum is completely uncertain. Or if instead you have complete knowledge of the particles momentum, then its position becomes completely uncertain. Intermediate ranges of accuracy are possible, the lesson to take home is that you cannot measure one variable without introducing some uncertainty into the value of the corresponding complimentary variable. The amount of uncertainty is quantified precisely by the uncertainty principle. The uncertainty of quantum mechanics never sat well with Einstein, he felt the theory, which is statistical in nature, is statistical because there exist some unknown or “hidden” variables in the microscopic world we are not yet aware of.

We now imagine that two particles interact and then move off in different directions. Because they have interacted, they become entangled. When two particles are entangled, the state of each particle alone has no real meaning-the state of the system can only be described in terms of the whole. In terms of elementary quantum mechanics, there is a wavefunction which describes the two particles together as a single unit. The wavefunction, being a superposition of different possibilities, exists in a ghostly combination of possible states. The Copenhagen interpretation tells us that the properties of the particle, position or momentum, don’t exist in definite values until a measurement is made.

When a measurement is made, and we can choose to make a measurement on one particle or the other, the wavefunction “collapses” and each particle is found to be in a definite state. The measurement results obtained for entangled particles are correlated. So if we make a measurement result on particle A and find its momentum to be a certain value, we know-without making a measurement on particle B-what its momentum is with absolute certainty. As EPR put it, by making a measurement of momentum on particle A, using momentum conservation tells us that pA + pB is an element of physical reality. In other words the wavefunction has collapsed and the variables have definite values-the ghostly superposition of possibilities is gone. The crucial point is that even though no measurement has been made on the distant particle B, the observer at the location of particle A has learned the value of B’s momentum. Somehow the wavefunction has collapsed instantaneously across a spatial distance-presumably in violation of the speed of light limit set by relativity.

The situation can be made even more interesting by noting that we can choose instead to measure the position of particle A. Again, using conservation principles, we will learn the value of the position of particle B, and the quantity qA - qB assumes physical reality.

Notice that the observer at position A can choose, by making different measurements that he or she desires, which properties of particle B assume definite values-or assume physical reality in the terminology of EPR. They can make this choice at a later time without any prior agreement with an observer in possession of particle B. This is another aspect of spooky action at a distance. The observer at A makes a measurement choice-presumably chosen using the free will of the mind-and forces particle B into a definite value instantaneously.

The interpretation of these results is still in debate, some believe that the wavefunction only represents our state of knowledge about the system. However it seems that it would be difficult for anyone who believes this to examine diffraction images from electron scattering and deny that the wavefunction is a real physical entity.

In summary, it appears that the position or momentum of each member of the EPR pair is determined by measurements performed on the other, distant member of the EPR pair. The effect seems to be instantaneous, leading Einstein and his colleagues to refer to the phenomenon as “spooky action at a distance”. The effect is non-local and appears to be instantaneous, but can anything useful come out of it? Can we exploit this to communicate faster than the speed of light? It turns out that as things are currently understood, the answer is no.

Teleportation

In recent years, it was shown that quantum entanglement could be exploited to transmit the state of a quantum particle from one place to another without having that state propagate through the space that separates the two locations. This certainly sounds magical enough-perhaps like something out of Star Trek-and is the reason that the investigators who discovered this phenomenon denoted it by the term teleportation. As we’ll see in a moment, teleportation demonstrates that despite the spooky action at a distance, special relativity is saved because the ability to communicate is limited in an unexpected way. A fundamental observation that should be made this is true even though teleportation is described using non-relativistic quantum mechanics-a theory where as long as no electromagnetic fields are involved, there is no ultimate speed limit.

We imagine two parties who wish to communicate with each other. In the quantum computing literature they are identified by the overused corny labels of Alice and Bob. It works like this. First, Alice and Bob meet. They create an entangled EPR pair. Then each party takes one member of the pair. Alice stays home, while Bob travels off somewhere, perhaps to Las Vegas.

In teleportation, the quantum particles used can have one of two states, so measurement results can be labeled by a 0 or a 1.

Since Alice and Bob each have in their possession one member of an entangled EPR pair, a spooky action at a distance connection exists between them. Alice can exploit this connection to send Bob the state of a quantum particle. The process is quite simple and Alice just follows these steps.

First, Alice gets the particle she wants to send with Bob, and she allows it to interact with her member of the EPR pair. Then she makes measurements on her member of the EPR pair and the particle that she wants to send to Bob. Since she is making measurements of two particles, her possible measurement results are the two-bit combinations 00, 01, 10, and 11.

Since Alice has allowed her half of the EPR pair to interact with another particle, the state of Bob’s half of the EPR pair must have changed. It’s at this point that special relativity peaks its head in-through the back door. Although the state of Bob’s particle has changed, any measurement results he makes on his half of the EPR pair would be completely random. Bob has no information in his possession about the state of the unknown particle Alice wants to send him. Spooky action at a distance has occurred but at this point it’s completely useless. To get something out of the situation-Alice has to call Bob-on an ordinary telephone say-and tell him her measurement results.

If Alice gets the measurement result 00, Bob doesn’t have to do anything-he now has the state of the particle Alice wanted to send him in his possession. However, that only happens 25% of the time, since Alice can get measurement results 00, 01, 10, and 11. If Alice gets measurement results 01, 10, or 11, Bob must make some measurements of his own on his half of the EPR pair in order to obtain the state of the particle Alice wants to send. We won’t get into the technical details, but in each case a different set of operations must be performed by Bob. Alice has to communicate which set of operations to use-based on the measurement result she obtained in the past-using a classical communications channel. Therefore the “instantaneous” nature of the interaction cannot be exploited until a classical communications channel is used.

The interesting thing about teleportation in my view is that it seems to say that special relativity has a major role to play in the transfer of information. In a way this is a fitting cap off to Einstein’s intellectual legacy. Einstein and Bohr both come out winners. Quantum mechanics stands on its own using the standard theory without hidden variables, yet what you can do with it is constrained by Einstein’s special theory of relativity.

ABOUT THE AUTHOR: David McMahon is a physicist who consults at Sandia National Laboratories and is the author of several math and physics books, including “Quantum Mechanics Demystified”. Information on his books can be found at http://www.davidmcmahonbooks.com/

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