# Teleportation by quantum isolation

This is a thought experiment, so please don't treat it too harsh :-)

Short: If we could isolate two places A and B in the universe from all and any interaction with the surroundings, is there a physical law which states "if something is dropped in place A, it has to stay there"?

Long version: Let's assume that the energy of the whole universe is fixed. Let's further assume that it is (by some trick) possible to completely isolate a box of 1m^3, say in the center of a planet (all gravitational and centrifugal forces cancel themselves out), the mass of the planet shields against radiation and we use a trick to shield against neutrinos or we ignore them since the rarely interact with matter).

How does an object behave when it has no interaction with the rest of the universe whatsoever? If I put an object in a box described above and I have several such boxes, would it matter in which box the object is?

Is there a law which says "even if no one knows, the object has to stay where it is"? Or is that just our expectation based on everyday experience?

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Classically Sklivvz's answer would be correct. But in quantum world the story is not quite over. In the following I'll talk about particles (because for them quantum effects are more apparent) but it would also be true for bigger objects (although the bigger the object the more improbable the "teleportation" would be).

First, from the point of view of Quantum Mechanics and for a while assuming that you can really cancel all forces on the particle you are essentially investigating a double-well potential. There will always be some tunelling between two boxes. If the boxes are too far away then it will be very improbable (where this improbability increases exponentially with distance) but surely possible that if you look into second box after some time, you'll find your particle there.

Now, in reality the picture is complicated by Quantum Field Theory. First, it stops to make sense to talk about particles because they are indistinguishable and also they can be created out of nothing. Related to this is the fact that you can't ever dispose of all interaction because vacuum itself is very lively place! There are particles created and annihilated all the time and this has observable effects on any object (see Casimir effect).

So you would need you object to be big enough so that it becomes distinguishable (with high probability). But as already stated the bigger the object, the lower the probability that it leaves the box.

The conclusion, as you might have guessed beforehand, is that with extremely high probability nothing interesting will happen at all.

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correct - by "object" I have assumed a classical-sized test object. – Sklivvz Nov 28 '10 at 15:45
I missed vacuum fluctuations; thanks for pointing that out. – Aaron Digulla Nov 28 '10 at 18:02
Interestingly, if the two boxes were close together, a particle-antiparticle pair could be spontaneously created between the two, and the antiparticle annihilate with the original particle. The result would be that the particle has disappeared from one box and appeared in the other - in other words, the teleportation mentioned in the question title. – Phil H Nov 30 '10 at 13:24

Of course: Newton's first law!

Every body remains in a state of rest or uniform motion (constant velocity) unless it is acted upon by an external unbalanced force. This means that in the absence of a non-zero net force, the center of mass of a body either remains at rest, or moves at a constant speed in a straight line.

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I agree for classical physics. But I don't change it's state of motion, I just change its space-time coordinate in an instant. So the first law doesn't really apply. – Aaron Digulla Nov 28 '10 at 18:04
@Aaron: you can't just change an object's spacetime coordinate by a finite amount instantaneously, unless you have something which can exert an infinite force at your disposal (this doesn't exist in the real world). Doing so would be a violation of Newton's second law in classical physics, or of the Schrödinger equation in quantum mechanics. – David Z Nov 28 '10 at 22:19
@David: So how does an electron tunnel? As I understand it, the same rules could apply to macroscopic objects (only the probability is way too low to experience it). – Aaron Digulla Nov 29 '10 at 14:17

How does an object behave when is has no interaction with the rest of the universe whatsoever? Like every object you ever studied in a physics class. Interaction with the rest of the universe is the hard part that we always abstract away so we can isolate some particular interaction of interest. A perfectly isolated system would always behave in perfect accordance with the rules governing whatever sort of object it was.

In quantum terms (since you've got "quantum" in the question title), what you're describing is an infinite square well. That is, the potential barrier for the system in question is of infinite height, perfectly isolating the system from everything else. The wavefunction at the edges of the box would be exactly zero, and the wavefunction everywhere outside the box would be zero. This is the only system in quantum physics that does not have some probability (however infinitesimal) of turning up at some different location. This is, of course, a textbook idealization and not anything you could actually make in reality.

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