# Re: Energy conservation in many-worlds

> On 3 Dec 2019, at 05:21, 'Brent Meeker' via Everything List
>
>
>
> On 12/2/2019 5:39 PM, smitra 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.
>
> That's true.  But it waaay under estimating the number of brain states
> consistent with a thought.  The reason is that many different quasi-classical
> brain states will be consistent with that thought...not only different
> quantum superpositions.

Yes, that is the real problem. Too much states, a priori, many leading to
aberrant histories. But then Mechanism put a structure allowing reasonable
(quantum) measure. This means Mechanism is not refuted, and rather confirmed by
the introduction of statistics at the core of the physical reality.

>
>>
>> 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.
>
> I don't see the difference.  The computer will also have many different
> microscopic states and particles in superpositions (depending on how bases
> states are defined).  You are simply begging the question by calling it a
> "dumb device".  Dumb or smart are not states or sequences of states, they are
> relations to an external environment and internal purposes.

They are relations in between universal entities. First person plurality
suggest we share some of them, in some degrees.

>
>>
>> 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,
>
> It's not clear to me.  How can there be a response to an input ("input" to
> what) that doesn't occur?  And why would such a response be anything but
> crazy?

Why necessarily crazy? If you can prove this, you refute Mechanism.

Bruno

>
> Brent
>
>> 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.
>>
>> Saibal
>>
>
>
> --
> You received this message because you are subscribed to the Google Groups
> "Everything List" group.
> To unsubscribe from this group and stop receiving emails from it, send an