Apparatus
Imagine two devices separated by a large distance (any distance large enough to nullify quantum mechanical effects). These are devices that receive inputs and yield results. There are two modes in which an input may be received: classical and quantum-mechanical. Moreover, the input is generated by the same source and is delivered simultaneously.
Procedure
- A set of inputs is generated at the source.
- Each input may instruct the device to yield a result ‘x’ or ‘y’.
- Device A reads the instructions and yields a result, A’
- Device B reads the instructions and yields a result, B’
(A’ and B’ are now the states of the instructions after they have been measured by A and B, respectively)
Observations
- If A’ and B’ are in the same state – i.e., if they are the result {x, x} or {y, y} – then they may be said to be entangled. To have achieved this, A and B must have communicated in some way to yield the same results arising from the input or must be in possession of some information that enabled them to yield the same result.
- If it so happened that A and B communicated instantaneously – i.e., at faster than the speed of light – then they may be said to be quantum entangled. (Note that, in a quantum mechanical context, the results are found to be identical only upon observation, which means the act of observing the result is also a participant in the measurement process.)
Inferences
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John Stewart Bell[/caption]#1 If we assume the observations are being made on particles instead of some arbitrary “inputs”, then Heisenberg’s uncertainty principle kicks in. When we make the measurement, we are changing the value of some state variable of the particle, and it is the final state that we end up observing. John Stewart Bell, a Scottish physicist, was the first to make this observation, and added that the act of observation was somehow tied in with quantum entanglement (i.e., that the results were quantum-entangled in some way owed itself in part to the act of observing).
#2 The act of observing is a classical phenomenon because the devices A and B that enable the measurement are classical devices. That said, J.S. Bell argued that this is where the line between classical mechanics and quantum mechanics blurred.
Theoretical physicists live in a classical world, looking out into a quantum-mechanical world. The latter we describe only subjectively, in terms of procedures and results in our classical domain. (…) Now nobody knows just where the boundary between the classical and the quantum domain is situated. (…) More plausible to me is that we will find that there is no boundary. The wave functions would prove to be a provisional or incomplete description of the quantum-mechanical part. It is this possibility, of a homogeneous account of the world, which is for me the chief motivation of the study of the so-called "hidden variable" possibility.
- J.S. Bell
#3 The EPR (Einstein-Podolsky-Rosen) paradox is aimed at refuting quantum mechanics by leveling itself against the possibility of quantum entanglement. Since entanglement occurred only on conjugate entities – particles that are somehow but definitely paired – then the measurement of one of the A’-state variables should render indeterminate that state variable in B’ (Heisenberg uncertainty prin.). However, entanglement has already been observed. This means that either the two particles should have communicated or that the information necessary to generate the same outcome was already present in the two particles.
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The physicists preferred the latter explanation, asserting that some “hidden local variable” was responsible for controlling the outcome of the act of observing. Of course, they made two assumptions in reaching this conclusion: locality and realism. (Note that this is a classical explanation of a perceived quantum mechanical effect.)
#4 In 1964, Bell came out with his famous theorem that refuted EPR’s preferred explanation. He observed that any local realist theories are incompatible with quantum mechanics. Essentially, this means that since a great number of experiments agree with the predictions of quantum mechanical theory, and since many of the results are greater than to be explicable by local hidden variables, either locality or realism is in conflict with quantum mechanics.
The principle of locality states that an object is affected directly only by its immediate surroundings, not by an event that is occurring simultaneously a large distance away. Realism, or counterfactual definiteness (CFD), is the ability to assume the existence of objects and parameters even when they have not been observed – or, to believe that constitutionally present particles shape the properties of the object at all levels. Bell posited that locality had been violated, and that superluminal communication was happening.
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David Bohm[/caption]#5 Bell’s hypothesis was based on the de Broglie-Bohm theory, which interpreted quantum mechanical effects as being caused by an encoding function (called the wave function) that did not let the particles that it guided feedback into itself. The interpretation also assumed that the velocities of the particles depended solely on the wave function, and that the wave function depended on the whole configuration of the universe. That's a contradiction of locality right there.
What does this have to do with teleportation?
Teleportation, by definition, is an instance of non-locality because it implies instantaneous communication. If two particles can communicate faster than at the speed of light to replicate quantum mechanical effects, then perhaps complex objects can someday be replicated instantaneously across large distances by simultaneously reproducing the quantum states of the particles associated with the object.
Of course, such a possibility is hinged on Bell’s theorem being true, on the EPR paradox’s implied existence of locality being false. To date, numerous experiments have been conducted that have neither conclusively validated nor invalidated Bell’s theorem. The difficulty lies in what Bell's theorem implied for the real world: it made quantum mechanics and local realism mutually exclusive. Either quantum mechanics fell short of explaining some physical parameters, or superluminal information communication was occurring (see Lorentz covariance).
[youtube http://www.youtube.com/watch?v=V0zQHNmz0gU]
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