On Mon, Dec 2, 2019 at 7:19 PM Philip Thrift <cloudver...@gmail.com> wrote:
> On Sunday, December 1, 2019 at 6:24:08 PM UTC-6, Bruce wrote:
>>
>> On Sat, Nov 30, 2019 at 12:35 PM 'Brent Meeker' via Everything List <
>> everyth...@googlegroups.com> wrote:
>>
>>> On 11/28/2019 4:17 PM, Bruce Kellett wrote:
>>>
>>>
>>> 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 formalism supposes that the state represented by each basis vector
>> becomes entangled with the environment to leave a record of the result of
>> the measurement. Coordinate systems do not become entangled with anything.
>> So the schematic above must represent the particle or whatever that is
>> being measured (considered of interest, if you wish to avoid the "M" word.)
>>
>>
>>
>>> 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.
>>>
>>
>> Irrelevant to the main point.
>>
>>> 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.
>>>
>>
>> Yes, I find this easier to understand in a single-world situation. In
>> either case, you have to renormalise the state -- energy, charge and
>> everything -- for each branch in many-worlds as much as in a single-world.
>> In fact, as Zurek points out, even in many-worlds you end up on only one
>> branch (stochastically). So the other branches do no work, and might as
>> well be discarded. If you are really worried about the possibility of fully
>> decohered branches recombining, take out life insurance......
>>
>> Bruce
>>
>
>
> "even in many-worlds you end up on only one branch (stochastically)"
>
>
> Sean Carroll himself has said (in a tweet) that if you let probabilities
> (stochasticity) in - like the camel's nose under the tent - you might as
> well have a one world - not many worlds - theory.
>
We do have only one world. Do you know of anyone who lives in more than one
branch of the multiverse?
Bruce
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