# Re: Energy conservation in many-worlds


> On 3 Dec 2019, at 02:39, smitra <smi...@zonnet.nl> wrote:
>
> On 02-12-2019 09:39, Bruce Kellett wrote:
>> 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
>>> 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
>
> Your subjective state (everything that you're aware at some instant), doesn't
> fully specify the exact physical state of your brain. The number of distinct
> physical brain states is so astronomically large that your mindset and how
> you are feeling about everything isn't going to be consistent with only one
> physical brain state. This means that given your subjective state, the
> physical state of your MWI sector should be described as a very complex
> superposition involving a large number of brain states that are entangled
> with the environment.
>
> If we assume that we can bypass this problem and that we can locate ourselves
> in one single branch, then this leads to the following paradox. Consider
> simulating such a conscious entity on a computer. At all moments in time, the
> physical state of the computer is just transitioning from one particular
> state to another state. Since consciousness is related to the actual physical
> state of the computer, replacing the computer by a dumb device that doesn't
> compute anything, which simply cycles through physical states that the
> computer would move through given some particular set of inputs, will render
> exactly the same consciousness.
>
> This absurd conclusion depends only on the single world assumption, it's a
> consequence of the non-existence of counterfactuals. Clearly actions as a
> response to counterfactual inputs must be relevant for consciousness, but
> there is no room to do that within classical single World physics. But as I
> pointed out above the generic state of a conscious involves being located not
> in a single branch, but being distributed over an astronomically large number
> of different branches.

Yes, at least aleph_0 “branches”. But there is no real branch, just
differentiating first person experiences. The linearity of the tensor product
makes the histories partially sharable among different universal machines. In
fact Hardegree did show that quantum logic is a sort of logic of
counterfactuals. I think the quantum can be said to come from the existence of
counterfactuals and our (discrete machine) inability to make low grained
distinctions (due to our digitalness).

Bruno

>
> Saibal
>
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