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I read that the reason that macroscopic superpositions decohere is because it’s difficult/impossible to isolate macroscopic objects from the environment. Why is this so difficult/impossible and why isn’t this the case for microscopic objects?

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Two reasons I can think of:

1) Because macroscopic objects have mass and are affected by the surrounding eletromagnetic field. This field is external and sort of 'steals away' the information stored in the object, making it lose coherence. This way, coherence is lost to the environment. Even if you don't have a significant magnetic or electric field applied to the object, there is always microwave radiation (like heat) getting in and, if you object has non zero temperature, getting out. Photons don't affect each other, so they can be isolated from this field.

You could try and decrease the temperature to near absolute zero and then you could get some small objects (like a few atoms) to behave coherently. But once you start to size up your object to something macroscopic another problem arises.

2) Since your object is big, its constituent parts are being affected by different parts of the environment, and these environment parts don't behave coherently. Because of this, and even though this interaction is small because of the low temperature and all, it can be shown that this model predicts that the object will decohere fast, with an exponential dependancy on its size.

This, in my opinion is one of the most beautiful achievements of quantum information theories because it explains in some way why Schrödinger's cat can't remain in a superposition of dead/alive states for any significant amount of time.

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Decoherence of an object $O$ is caused by how $O$ influences its environment, not by how the environment influences $O$. The degree of decoherence corresponds to the degree to which information about $O$ can be inferred from what it did to its environment.

An apple influences its environment in practically unavoidable ways. Air molecules bouncing off its surface causes continual decoherence of the apple's location, keeping both $\Delta x$ and $\Delta p$ negligibly small by macroscopic standards (but without violating the uncertainty principle $\Delta x\Delta p\gtrsim\hbar$). Even in a vacuum, cosmic background radiation scattering from the apple is more than enough to cause continual decoherence of its location. In principle, we can easily infer the apple's location from how it affects the motion of air molecules or the cosmic background radiation, so decoherence is very effective.

In contrast, a photon can travel a significant distance without disturbing its environment enough to cause decoherence. The photon may slightly perturb the state of its environment, but the degree of decoherence is small as long as the perturbed state-vector of the environment is nearly parallel (as a vector in the Hilbert space) to the original state-vector of the environment.

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  • $\begingroup$ Cosmic background radiation can't go through metal containers unless it is a very high energy gamma-ray which is rare. But you will still have thermal radiation from the container which presumably causes decoherence of the apple. $\endgroup$ – Virgo Sep 7 at 2:38

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