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atyy
Science Advisor
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Here's an an attempt to construct an argument against a change in the "potential to know" due to a known unitary operation. The basic idea is that a known unitary operation preserves information.
If the interference disappears due to a known unitary operation, then the interference can be made to appear by reversing the operation. It may be thought that this involves "doing something" as opposed to "doing nothing". However, "doing nothing" is also "doing something", because "doing nothing" is unitary evolution by a known Hamiltonian which happens to be free. To illustrate that that is doing something, consider the case where an atom is used and high vacuum is needed. The creation of the high vacuum is the creation of the known Hamiltonian, which happens to be chosen to be free, so it is not "doing nothing".
If the interference disappears due to a known unitary operation, then the interference can be made to appear by reversing the operation. It may be thought that this involves "doing something" as opposed to "doing nothing". However, "doing nothing" is also "doing something", because "doing nothing" is unitary evolution by a known Hamiltonian which happens to be free. To illustrate that that is doing something, consider the case where an atom is used and high vacuum is needed. The creation of the high vacuum is the creation of the known Hamiltonian, which happens to be chosen to be free, so it is not "doing nothing".