> On 30 Nov 2019, at 02:35, 'Brent Meeker' via Everything List 
> <everything-list@googlegroups.com> wrote:
> On 11/28/2019 4:17 PM, Bruce Kellett wrote:
>> On Fri, Nov 29, 2019 at 5:12 AM 'Brent Meeker' via Everything List 
>> <everything-list@googlegroups.com <mailto: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 basis just defines a coordinate system for the Hilbert space.  It 
> doesn't mean that the wf ray has any component along a basis vector.  The c_i 
> can be zero; in which case that basis vector doesn't carry anything.  No 
> every Schrodinger equation solution is realized because initial conditions 
> may make it zero.
>> 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.
> Yes, I think that's right.  Which is the attraction of the epistemic 
> interpretation: you treat them as probabilities so you renormalize after the 
> measurement.  And one problem with the ontic interpretation is saying what 
> probability means.  But it seems that the epistemic interpretation leaves the 
> wf to be a personal belief.

It is a first person plural belief, sharable by vast collection of interacting 
universal entities whose existence can be proved in weak theory of arithmetic. 
It is a view from inside any model of arithmetic, but unprovable in any theory 
of arithmetic.


> Brent
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