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4

To be honest, I think that the route you describe (and which is also used in many textbooks) is not physically well motivated at all. You have begun with a theory of a fermion with a global symmetry which maps physical states to different physical states. This theory has the property that specifying initial conditions on a spacelike surface completely ...

6

You are right, it is wrong to think that in gauge theory "gauge transformations are just a redundancy". This becomes true only if one abandons locality, ignores all boundary effects, all instanton effects, hence most of what is interesting about gauge theory. Of course forming gauge equivalence classes (say of observables) is something one wants to do every ...

1

This is how I understand this issue. First, I believe you may agree that imposing gauge invariance is a sensible thing to do. If we want our fields to be invariant under some kind of transformation it better be local, since two separate space-time points shouldn't be related in any unnecessary way, otherwise we may violate causality. A different issue is ...

2

The flaw in your argument is that the claim "entanglement will instantly replicate the photons' paths and such the pattern onto Bob's screen [sic]" is incorrect. The statistics for the measurement outcomes of any experiment performed on one subsystem of a maximally entangled pair is independent of what goes on with the other subsystem. In your case, from ...

4

Your error seems to be the misconception that entanglement will magically make the results of any experiment of photon B exactly mimic those of a similar experiment done on its entangled partner. Entanglement is more subtle than that and must be treated carefully. In particular, there are many different types of entanglement. For example, photons may be ...

2

Some kinds of mutation provide an example of this kind of indeterminacy. UV light can be bad for our health. One of the reasons is that, when we are exposed to sunlight, UVB photons are absorbed by double bonds in pyrimidines, which break open, become reactive, and dimerize (photo-dimerization). This damages the DNA in the same way that it would damage a ...

1

Let's look at a famous, concrete example: Perfectly unpolarized light. Alice creates unpolarized light by randomly (incoherently) mixing left-circular-polarized light with an equal intensity of right-circular-polarized light. Bob creates unpolarized light by randomly (incoherently) mixing vertically-polarized light with an equal intensity of ...

1

I will provide an answer but from a different perspective, and hopefully convince you that there is information in a density matrix which has no classical counterpart. Furthermore this can hence be considered a quantum component, and it can be shown that this information is stored as the eigenvectors of $\rho$. I will give an example of how this manifests. ...

4

Yes, the density matrix reconciles all quantum aspects of the probabilities with the classical aspect of the probabilities so that these two "parts" can no longer be separated in any invariant way. As the OP states in the discussion, the same density matrix may be prepared in numerous ways. One of them may look more "classical" – e.g. the method following ...

0

As far as I am aware, we are only able to speculate about these other "Universes" in the sense that they represent an aggregate of potential (indeterminate) wave functions relating to what events may occur in the time direction known as "future". Or might have occured in the "past" but didn't in this universe. Every time you toss a coin and look at it, that ...

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