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Hi Dustin,

As a preliminary step towards answering your mathematical questions, I’d like to focus on your query about my Eq. (1). In particular, I’d like to point out that this equation is meant to be part of standard quantum mechanics, not just of my model. In this context, hopefully we can agree on the following points:

1. In the relativistic case, it’s possible to have a pair of particles which are in an entangled state, but which have essentially ceased interacting and are now far apart.

2. Once a measurement is performed on one of the particles, the other particle can then be described by its own, single-particle state.

3. This new state can be deduced by combining the original two-particle state and the measurement result together in some way.

4. Even though there is some ambiguity in the time at which the single-particle state becomes available, points 2 and 3 remain valid.

My Eq. (1) was simply my attempt to express point 3 in mathematical form. So my question to you as a mathematician is: How would you describe this piece of standard quantum mechanics in equation form?

It might help here for me to comment on the entangled state psi(x,x’). It’s usual to express the initial boundary conditions of any theory on one particular hyperplane at some initial time ti, so Lorentz invariance is automatically broken in this sense. However, the situation at a later time t should then be Lorentz invariant. My entangled state at time t is defined to be something like:

psi(x,x’) = integral of [K(x,xi)K'(x’,xi’)psi(xi,xi’)] dxi dxi’

where K and K’ are propagators from ti to t and the coordinates xi and xi’ are assumed to be at the same time ti.

And yes, we’ll definitely need to continue after the workshop! I’ll need your email address.

Best wishes,

Rod

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