# Re: Energy conservation in many-worlds

On 03-12-2019 05:21, 'Brent Meeker' via Everything List wrote:

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.




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.




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?




I agree that also in classical computing there will be a huge number of different states corresponding to the same conscious awareness. The point is then that the generic state of the (classical) device rendering the conscious thought plus environment will be an entangled state that contains information about the algorithm. If we consider a classical computer computing the square of numbers and the input is 2 then the output will be 4. Another algorithm that multiples the number by 2 will also have an output of 4, and there is also an algorithm that always outputs 4 no matter what the input is.


The output for an input of 2 + u for very small u is for the first algorithm approximately 4 + 4 u, for the second it is 4 + 2 u, for the third it is 4. If the computer where to process data from the environment that are in a small range near 2, then the environment would be in some random superposition that would yield such inputs, the state of the computer plus environment would evolve to an entangled state that tells you how the output is related to the input for small variations around the input of 2. The entangled state at any instant tells you which algorithm is running, you don't need to refer to a sequence of inputs over some period of time.


Now the computer computing the square of a number won't be conscious, but our consciousness won't be able to specify the exact micro-state we're in. This means that our consciousness corresponds to an entangled superposition of input and output states. This then defines the algorithm that generates our consciousness. There are then counterfactuals within the range of precision of our awareness.

Saibal


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



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