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American Mathematical Monthly

Unknowable Matters: How Nature's Speed Limit on Communication Relates to Quantum Physics

Stephen McAdam

Published Mar 12, 2012• 1 citation
Publisher

Abstract

It is shown that there is no way of identifying an unknown polarization state of a photon by proving that otherwise faster than light communication would be possible. It is similarly argued that the “no cloning theorem” of quantum physics must be true.
DOI
10.4169/amer.math.monthly.119.04.284

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•Apr 12, 2021•0 citations
If YES, then we can look forward to physical realization of superluminal communication, as the original considerations of the ``no-cloning'' theorem were motivated in part as an explanation of why certain schemes for superluminal signaling cannot work. If NO, then it would seem that some aspects of the ``hidden'' variables must be ``intrinsically hidden'', i.e., ``unknowable'', such that ``hidden-variable'' theories belong more to the ``idealist'' than to the ``realist'' school of thought. I pose this question without proposing a definite answer. I am unaware of any commentary on this topic during these 23 years since the formulation of the ``no-cloning'' theorem, but I would be pleased to be enlightened by more knowledgeable readers.
Physical entities are not truly teleported in so-called quantum teleportation, only their states are. Similarly, physical entities are not truly cloned in so-called quantum cloning, only their states are. The celebrated no-cloning theorem tells us that a universal cloning machine, able to perfectly clone arbitrary states, cannot be built. However, this only applies to discernible quantum entities. For the indiscernible ones, which are already perfect clones of one another, the additional cloning of their state is in fact a natural process, which happens in a spontaneous way, as soon as they are allowed to interact.
Abstract In Quantum Mechanics, two particles are entangled if their physical states depend on one another's so that if we find one of them in state A, for example, we will be sure that the other is in state B. However, until the state of a quantum particle is measured, it will be in a superposition of states, being in neither one nor the other until then, so when an entangled particle is measured, its pair also assumes a state instantly and regardless of how far away it is from the other particle at that time. As promising as it could be to use this fact for instantaneous communication, Quantum Mechanics seems to claim this is impossible, as no method ever invented to do this has worked until today. What we demonstrate here theoretically is that with a protocol and simple optical devices, two people who share polarized entangled pairs of photons can send information to each other faster than light. If this model of communication proves to be experimentally functional, we will have a contradiction to Einstein's theories of relativity, and otherwise, we will have Quantum Mechanics predicting something that does not happen in real life. This result, therefore, shows there is something fundamental about the universe we do not know yet. One of these theories must be mistaken and both deal with fundamental aspects of reality, such as the dynamics of space and time, and the particles that almost all matter around us are made of. Besides, this result is of great relevance also because it has immediate applications in several areas if the model works experimentally, as in space exploration and security, since it will allow the creation of non-interceptable instantaneous communication technologies.