# Re: Energy conservation in many-worlds

> On 30 Nov 2019, at 02:35, 'Brent Meeker' via Everything List
>
>
>
> On 11/28/2019 4:17 PM, Bruce Kellett wrote:
>> On Fri, Nov 29, 2019 at 5:12 AM 'Brent Meeker' via Everything List
>> 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.

Bruno

>
> Brent
>
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