On Fri, Nov 29, 2019 at 5:12 AM 'Brent Meeker' via Everything List <
everything-list@googlegroups.com> wrote:
> On 11/27/2019 11:51 PM, Philip Thrift wrote:
>
>
> This was the issue about mass raised weeks ago when Sean Carroll's book
> came out.
>
> There has never been an answer.
>
>
> If you think in terms of the wf of the multiverse, it's just a ray in
> Hilbert space and moves around. It doesn't split. What "splits" is the
> subspace we're on. So when we measure a spin as UP or DOWN, our subspace
> splits into two orthogonal subspaces on which the ray projects. But they
> are only orthogonal on that one dimension (the spin of that particle), so
> any other variable encoded in the ray gets projected with the same value as
> before, e.g. the energy or the particle.
>
Right. The subsystem we are considering (an electron fired at a screen or
through an S-G magnet) is just a subspace of the full Hilbert space. We can
take the tensor product of this subspace with the rest of the universe to
recover the full Hilbert space:
|universe> = |system>{\otimes}|environment>
We can then analyse the system in some basis:
|system> = Sum_i c_i |basis_i>,
where c_i are complex coefficients, and |basis_i> are the basis vectors for
(i = 1, ...,, N), N being the dimension of the subspace.
It is assumed that the normal distributive law of vector algebra acts over
the tensor product, so each basis vector then gets convoluted with the same
'environment' in each case, we have
|universe> = Sum_i c_i (|basis_i>|environment>).
Each basis vector is a solution of the original Schrodinger equation, so it
carries the full energy, moment, change etc, of the original state. The
environment is just the rest of the universe minus the quantum quantities
associated with the system of interest. So each term in this sum has the
full energy, charge, and so on of the original state.
If we take each component of the above sum to represent a self-contained
separate world, then all quantum numbers are conserved in each world.
Whether there is global conservation depends on how we treat the
coefficients c_i. But, on the face of it, there are N copies of the
basis+environment in the above sum, so everything is copied in each
individual world. Exactly how you treat the weights in this situation is
not clear to me -- if they are treated as probabilities, it seems that you
just have a stochastic single-world model.
Bruce
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