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David Deutsch recently released a paper titled "The vindication of locality" where he argues that by using the Heisenberg picture rather than the Schroedinger picture, you can "save" locality. The paper is here: http://arxiv.org/abs/1109.6223 Is Deutsch wrong or has he indeed "proven" locality? |
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The notion of locality that Deutsch is trying to establish is his interpretation of Einstein locality, the statement that the "actual physical state of a system" is not modified by the actions one performs on far away systems. The way Einstein meant it, this principle is just plain false in quantum mechanics. Einstein's interpretation of "actual physical state" is called "local hidden variables" nowadays, it tells you the outcome of all measurments on the system. Local hidden variables are ruled out by Bell inequality violations. But Deutsch takes a more liberal view of "actual physical state", identifying it with the best-possible quantum description of a system. Deutsch is saying something well known--- namely that quantum mechanics is compatible with a version of locality, namely that the best-possible quantum description of a system, ignoring other disconnected systems, doesn't change no matter what you do to the disconnected systems. The best possible quantum description of an entangled system is the reduced density matrix, and if you think of this as the "true state of the system", then this true state doesn't change in response to anything you do far away. Deutsch makes this argument more cleanly than usual, by using a quantum computer with two disjoint collections of qubits isolated from each other. This is nice conceptually, but its really no different than the usual version, where you have two regions of space with commuting quantum field operators which correspond to measurements in the separate regions. In both cases, the operators associated to the disjoint sets commute, so that measuring one, or acting using an operator constructed from one set as a Hamiltonian, will do nothing to the density matrix of the other. This type of locality is well known, but it is not completely obvious, because the wavefunction is a global thing--- it describes the whole system, entangling the parts. The existence of local observables guarantees that you can't use this to send signals faster than light, or do anything else nonlocal either. |
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I think the issue was resolved a long time ago in algebraic quantum field theory. There, locality is captured by the structure of a net of algebras, i.e. associating an observable subalgebra to each open subset of spacetime. Locality is captured by the property of isotony, i.e. nested open subsets give rise to nested subalgebras. Causality is often conflated with locality in relativistic theories. Einstein locality is captured by spacelike commutativity. It is essential that fermionic operators are not counted in as observables as they spacelike anticommute. Primitive causality is the property that the subalgebra of the Cauchy development of an open subset is identical to the subalgebra of the open subset itself, i.e. state data on an open subset completely determines the state on its Cauchy development. Combining spacelike commutativity with primitive causality proves what happens far away can't affect what happens here. The correlations can violate the Bell inequalities, but faster than light physical influences are ruled out. |
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Are you thinking of the density matrix as ontic or epistemic? An ontic person will tell you of course it is nonlocal because what happens over there will change what something over here is entangled with over there, and the density matrix is real, damn it, even the values of its entangled components. An epistemic person will tell you what you can know here does not rely upon what happens over there. All you know here only relies on the reduced density matrix here. You only know about what happens over there because information from over there has come to you over here. If the information was tampered with in the process, you will never know any better. Locality is a feature of our world. If you are an ontic, shame on you! |
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