Re: Schrodinger's Cat vs Decoherence Theory

[Bruce Kellett]

From: *Lawrence Crowell* >



On Thursday, June 14, 2018 at 7:29:50 AM UTC-5, Bruce wrote:

From: *Lawrence Crowell* 

I can't make a measurement of energy that is something other than
the eigenstates or the diagonal form of the Hamiltonian. Energy
is the physical quantity which defines the einselected basis that
is stable in a classical-(like) outcome or for the emergence of
classicality.


That is incorrect. If you are making a position measurement,
energy does not come into it. Certainly, for many physical system,
such as atoms and molecules, the energy eigenstates are what one
measures. But one measures these in the  preferred energy basis,
which is quite similar to the preferred position basis. We are
used to a position basis with eigenstates as position delta
functions along the real line. The preferred energy basis is
similar, energy delta functions along the real line (remember that
we can get any real value as the result of a generic energy
measurement. Energies are quantized only for specific physical
systems.)


I was wondering if you might catch this. I needed more time to reflect 
on this and left this open. It is true that the position measurement 
does not involve a kinetic energy E = p^2/2m or E = sqrt(p^2 + m^2) 
term. Things are not too mysterious with momentum measurements. Is 
energy completely out of the loop? Remember that potential energy V = 
V(x) in most cases. So in the double slit experiment what happens? The 
photon or electron wave reaches the screen and interacts with it. This 
interaction is going to be position dependent and I would argue this 
potential energy is much larger than the kinetic energy V(x) >> 
p^2/2m, and so in a decent approximation E = E(x). Again, this is not 
the energy of the free particle, but what happens with the particle 
interaction with the screen.


There can be more. In particular if the interaction is of the form V = 
ipx, constants ignored. Since px = i/4[(a^†)^2 - a^2 + ħ] this is a 
parametric amplification operator and it squeezes the state into the 
position basis.


As a result I still think, though have not worked through anything, 
that energy is somehow deeply involved with the einselection of states 
and the emergence of a large scale classical world. As for below it is 
not the case that we make spectral measurements of atoms or other 
systems that are in a basis other than the diagonalization basis for 
the eigenvalues measured.


I don't know why you think that energy is central to einselection. The 
idea is that the einselected basis vectors correspond to an operator 
that commutes with the interaction Hamiltonian. But that is just the 
interaction Hamiltonian, not the full Hamiltonian which could be seen as 
the energy operator. So this criterion applies independently for any 
measured quantity, be it position, momentum, energy, or anything else. 
These einselected bases are not related in any other way. As I have 
pointed out, this criterion does not, of itself, tell us what the 
einselected basis is -- we have to go to something else for this.


Bruce

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Re: Is the "bubble multi-verse" and "qm many-worlds" the same thing?

[agrayson2000]

On Thursday, June 14, 2018 at 8:15:59 PM UTC, agrays...@gmail.com wrote:
>
>
>
> On Wednesday, June 13, 2018 at 11:30:27 PM UTC, Jason wrote:
>>
>>
>> Physical Theories, Eternal Inflation, and Quantum Universe 
>> , Yasunori Nomura
>>
>> We conclude that the eternally inflating multiverse and many worlds in
>> quantum mechanics are the same. Other important implications include: 
>> global spacetime
>> can be viewed as a derived concept; the multiverse is a transient 
>> phenomenon during the
>> world relaxing into a supersymmetric Minkowski state. We also present a 
>> theory of “initial
>> conditions” for the multiverse. By extrapolating our framework to the 
>> extreme, we arrive at a
>> picture that the entire multiverse is a fluctuation in the stationary, 
>> fractal “mega-multiverse,”
>> in which an infinite sequence of multiverse productions occurs.
>>
>> "Therefore, we conclude that the multiverse is the same as (or a specific 
>> manifestation
>> of ) many worlds in quantum mechanics."
>>
>> "In eternal inflation, however, one first picks a causal patch; then one 
>> looks for observers in it.” Our framework does not follow this approach. We 
>> instead pick an observer first, and then construct the relevant spacetime 
>> regions associated with it.
>>
>> Instead of admitting the existence of the “beginning,” we may require 
>> that the quantum observer principle is respected for the whole history of 
>> spacetime. In this case, the beginning of our multiverse is a fluctuation 
>> of a larger structure, whose beginning is also a fluctuation of an even 
>> larger structure, and this series goes on forever. This leads to the 
>> picture that our multiverse arises as a fluctuation in a huge, stationary 
>> “megamultiverse,” which has a fractal structure."
>>
>>
>> The Multiverse Interpretation of Quantum Mechanics 
>> , Raphael Bousso and Leonard Susskind
>>
>> In both the many-worlds interpretation of quantum mechanics and the 
>> multiverse
>> of eternal inflation the world is viewed as an unbounded collection of 
>> parallel universes.
>> A view that has been expressed in the past by both of us is that there is 
>> no need to
>> add an additional layer of parallelism to the multiverse in order to 
>> interpret quantum
>> mechanics. To put it succinctly, the many-worlds and the multiverse are 
>> the same
>> thing [1].
>>
>>
>> Jason
>>
>
> *Not right. Not even wrong. AG. *
>

Eternal inflation and string theory imply universes created by natural 
processes. The jury is out on those. OTOH, the MWI has human beings 
creating universes by going into a lab and doing trivial quantum 
experiments. Of course they're they same (for idiots). AG 

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Re: Is the "bubble multi-verse" and "qm many-worlds" the same thing?

[agrayson2000]

On Wednesday, June 13, 2018 at 11:30:27 PM UTC, Jason wrote:
>
>
> Physical Theories, Eternal Inflation, and Quantum Universe 
> , Yasunori Nomura
>
> We conclude that the eternally inflating multiverse and many worlds in
> quantum mechanics are the same. Other important implications include: 
> global spacetime
> can be viewed as a derived concept; the multiverse is a transient 
> phenomenon during the
> world relaxing into a supersymmetric Minkowski state. We also present a 
> theory of “initial
> conditions” for the multiverse. By extrapolating our framework to the 
> extreme, we arrive at a
> picture that the entire multiverse is a fluctuation in the stationary, 
> fractal “mega-multiverse,”
> in which an infinite sequence of multiverse productions occurs.
>
> "Therefore, we conclude that the multiverse is the same as (or a specific 
> manifestation
> of ) many worlds in quantum mechanics."
>
> "In eternal inflation, however, one first picks a causal patch; then one 
> looks for observers in it.” Our framework does not follow this approach. We 
> instead pick an observer first, and then construct the relevant spacetime 
> regions associated with it.
>
> Instead of admitting the existence of the “beginning,” we may require that 
> the quantum observer principle is respected for the whole history of 
> spacetime. In this case, the beginning of our multiverse is a fluctuation 
> of a larger structure, whose beginning is also a fluctuation of an even 
> larger structure, and this series goes on forever. This leads to the 
> picture that our multiverse arises as a fluctuation in a huge, stationary 
> “megamultiverse,” which has a fractal structure."
>
>
> The Multiverse Interpretation of Quantum Mechanics 
> , Raphael Bousso and Leonard Susskind
>
> In both the many-worlds interpretation of quantum mechanics and the 
> multiverse
> of eternal inflation the world is viewed as an unbounded collection of 
> parallel universes.
> A view that has been expressed in the past by both of us is that there is 
> no need to
> add an additional layer of parallelism to the multiverse in order to 
> interpret quantum
> mechanics. To put it succinctly, the many-worlds and the multiverse are 
> the same
> thing [1].
>
>
> Jason
>

*Not right. Not even wrong. AG. * 

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Re: Schrodinger's Cat vs Decoherence Theory

[Lawrence Crowell]

On Thursday, June 14, 2018 at 7:29:50 AM UTC-5, Bruce wrote:
>
> From: Lawrence Crowell >
>
> On Wednesday, June 13, 2018 at 11:18:10 PM UTC-5, Bruce wrote: 
>>
>> From: Brent Meeker 
>>
>>
>> No.  There's a preferred basis in which this "world" and it's spots on 
>> the screen, is spanned by basis vectors which are orthogonal to the basis 
>> vectors of the "worlds" in which the spots are in different places on the 
>> screen.  But in each world there are different (not necessarily position) 
>> bases, but they describe the same physics.
>>
>>
>> I don't think that is correct. The preferred basis is selected as the 
>> eigenvectors of the operator that commutes with the interaction 
>> Hamiltonian. If you choose a different basis for the Hilbert space, even by 
>> a simple rotation of your present basis, you are going to get eigenvectors 
>> (and eigenvalues) of a different operator. Since this operator must also be 
>> dominant in the interaction Hamiltonian, the physics is necessarily going 
>> to be different. A different position basis is going to result in more than 
>> different places on the screen for the spots.
>>
>> Bruce
>>
>
> I would agree, and that you are invoking the Hamiltonian segues into what 
> I wrote yesterday. I can set an apparatus to measure the spin of an 
> electron in any orientation.
>
>
> That is true; but that is just making a choice about what to measure -- 
> equivalent to the choice of whether to measure the position or momentum of 
> a free particle. These measurements are mutually exclusive, but they do not 
> set the measurement basis. When you use a S-G magnet to measure the spin 
> projection of a spin-half particle you chose an orientation, but the actual 
> measurement that gives you the required result is a position measurement -- 
> whether the particle emerges in the up or down channel. That is why this 
> was originally referred to as "space quantization".
>
> I can't make a measurement of energy that is something other than the 
> eigenstates or the diagonal form of the Hamiltonian. Energy is the physical 
> quantity which defines the einselected basis that is stable in a 
> classical-(like) outcome or for the emergence of classicality.
>
>
> That is incorrect. If you are making a position measurement, energy does 
> not come into it. Certainly, for many physical system, such as atoms and 
> molecules, the energy eigenstates are what one measures. But one measures 
> these in the  preferred energy basis, which is quite similar to the 
> preferred position basis. We are used to a position basis with eigenstates 
> as position delta functions along the real line. The preferred energy basis 
> is similar, energy delta functions along the real line (remember that we 
> can get any real value as the result of a generic energy measurement. 
> Energies are quantized only for specific physical systems.)
>
>
I was wondering if you might catch this. I needed more time to reflect on 
this and left this open. It is true that the position measurement does not 
involve a kinetic energy E = p^2/2m or E = sqrt(p^2 + m^2) term. Things are 
not too mysterious with momentum measurements. Is energy completely out of 
the loop? Remember that potential energy V = V(x) in most cases. So in the 
double slit experiment what happens? The photon or electron wave reaches 
the screen and interacts with it. This interaction is going to be position 
dependent and I would argue this potential energy is much larger than the 
kinetic energy V(x) >> p^2/2m, and so in a decent approximation E = E(x). 
Again, this is not the energy of the free particle, but what happens with 
the particle interaction with the screen.

There can be more. In particular if the interaction is of the form V = ipx, 
constants ignored. Since px = i/4[(a^†)^2 - a^2 + ħ] this is a parametric 
amplification operator and it squeezes the state into the position basis. 

As a result I still think, though have not worked through anything, that 
energy is somehow deeply involved with the einselection of states and the 
emergence of a large scale classical world. As for below it is not the case 
that we make spectral measurements of atoms or other systems that are in a 
basis other than the diagonalization basis for the eigenvalues measured.

LC
 

> I think people get trapped into thinking that our usual delta-function 
> basis for either position or energy is the only possible basis, because 
> that is the only basis in which we are able to measure anything. But that 
> itself is just a consequence of einselection to a preferred basis -- 
> attempting to measure in some other basis is not a position or energy 
> measurement as we know it, and the eigenfunctions of the alternative 
> operators decohere into our known basis extremely rapidly. But the fact 
> that the usual basis is ubiquitous, made so by decoherence, does not 
> explain why it is that basis, rather than some other basis, which is stable 
> against decoherence. 

Re: Is the "bubble multi-verse" and "qm many-worlds" the same thing?

[Jason Resch]

I found this write up by Sean Carroll that provides a better picture (for
me at least) about what the two papers are describing:

http://www.preposterousuniverse.com/blog/2011/05/26/are-many-worlds-and-the-multiverse-the-same-idea/

Jason

On Wed, Jun 13, 2018 at 6:30 PM, Jason Resch  wrote:

>
> Physical Theories, Eternal Inflation, and Quantum Universe
> , Yasunori Nomura
>
> We conclude that the eternally inflating multiverse and many worlds in
> quantum mechanics are the same. Other important implications include:
> global spacetime
> can be viewed as a derived concept; the multiverse is a transient
> phenomenon during the
> world relaxing into a supersymmetric Minkowski state. We also present a
> theory of “initial
> conditions” for the multiverse. By extrapolating our framework to the
> extreme, we arrive at a
> picture that the entire multiverse is a fluctuation in the stationary,
> fractal “mega-multiverse,”
> in which an infinite sequence of multiverse productions occurs.
>
> "Therefore, we conclude that the multiverse is the same as (or a specific
> manifestation
> of ) many worlds in quantum mechanics."
>
> "In eternal inflation, however, one first picks a causal patch; then one
> looks for observers in it.” Our framework does not follow this approach. We
> instead pick an observer first, and then construct the relevant spacetime
> regions associated with it.
>
> Instead of admitting the existence of the “beginning,” we may require that
> the quantum observer principle is respected for the whole history of
> spacetime. In this case, the beginning of our multiverse is a fluctuation
> of a larger structure, whose beginning is also a fluctuation of an even
> larger structure, and this series goes on forever. This leads to the
> picture that our multiverse arises as a fluctuation in a huge, stationary
> “megamultiverse,” which has a fractal structure."
>
>
> The Multiverse Interpretation of Quantum Mechanics
> , Raphael Bousso and Leonard Susskind
>
> In both the many-worlds interpretation of quantum mechanics and the
> multiverse
> of eternal inflation the world is viewed as an unbounded collection of
> parallel universes.
> A view that has been expressed in the past by both of us is that there is
> no need to
> add an additional layer of parallelism to the multiverse in order to
> interpret quantum
> mechanics. To put it succinctly, the many-worlds and the multiverse are
> the same
> thing [1].
>
>
> Jason
>

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Re: Schrodinger's Cat vs Decoherence Theory

[Bruce Kellett]

From: *Lawrence Crowell* >

On Wednesday, June 13, 2018 at 11:18:10 PM UTC-5, Bruce wrote:

From: *Brent Meeker* 


No.  There's a preferred basis in which this "world" and it's
spots on the screen, is spanned by basis vectors which are
orthogonal to the basis vectors of the "worlds" in which the
spots are in different places on the screen.  But in each world
there are different (not necessarily position) bases, but they
describe the same physics.


I don't think that is correct. The preferred basis is selected as
the eigenvectors of the operator that commutes with the
interaction Hamiltonian. If you choose a different basis for the
Hilbert space, even by a simple rotation of your present basis,
you are going to get eigenvectors (and eigenvalues) of a different
operator. Since this operator must also be dominant in the
interaction Hamiltonian, the physics is necessarily going to be
different. A different position basis is going to result in more
than different places on the screen for the spots.

Bruce


I would agree, and that you are invoking the Hamiltonian segues into 
what I wrote yesterday. I can set an apparatus to measure the spin of 
an electron in any orientation.


That is true; but that is just making a choice about what to measure -- 
equivalent to the choice of whether to measure the position or momentum 
of a free particle. These measurements are mutually exclusive, but they 
do not set the measurement basis. When you use a S-G magnet to measure 
the spin projection of a spin-half particle you chose an orientation, 
but the actual measurement that gives you the required result is a 
position measurement -- whether the particle emerges in the up or down 
channel. That is why this was originally referred to as "space 
quantization".


I can't make a measurement of energy that is something other than the 
eigenstates or the diagonal form of the Hamiltonian. Energy is the 
physical quantity which defines the einselected basis that is stable 
in a classical-(like) outcome or for the emergence of classicality.


That is incorrect. If you are making a position measurement, energy does 
not come into it. Certainly, for many physical system, such as atoms and 
molecules, the energy eigenstates are what one measures. But one 
measures these in the  preferred energy basis, which is quite similar to 
the preferred position basis. We are used to a position basis with 
eigenstates as position delta functions along the real line. The 
preferred energy basis is similar, energy delta functions along the real 
line (remember that we can get any real value as the result of a generic 
energy measurement. Energies are quantized only for specific physical 
systems.)


I think people get trapped into thinking that our usual delta-function 
basis for either position or energy is the only possible basis, because 
that is the only basis in which we are able to measure anything. But 
that itself is just a consequence of einselection to a preferred basis 
-- attempting to measure in some other basis is not a position or energy 
measurement as we know it, and the eigenfunctions of the alternative 
operators decohere into our known basis extremely rapidly. But the fact 
that the usual basis is ubiquitous, made so by decoherence, does not 
explain why it is that basis, rather than some other basis, which is 
stable against decoherence. We could easily choose another basis, and as 
I pointed out to Brent, the split into separate branches on the MWI 
would be very different in a different basis. Eigenfunctions and 
probabilities would be different with a different basis, so the physics 
would be different. The real question is "Why is physics the way it is? 
It could easily have been different."


Bruce

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Re: Is the "bubble multi-verse" and "qm many-worlds" the same thing?

[Lawrence Crowell]

On Wednesday, June 13, 2018 at 6:30:27 PM UTC-5, Jason wrote:
>
>
> Physical Theories, Eternal Inflation, and Quantum Universe 
> , Yasunori Nomura
>
> We conclude that the eternally inflating multiverse and many worlds in
> quantum mechanics are the same. Other important implications include: 
> global spacetime
> can be viewed as a derived concept; the multiverse is a transient 
> phenomenon during the
> world relaxing into a supersymmetric Minkowski state. We also present a 
> theory of “initial
> conditions” for the multiverse. By extrapolating our framework to the 
> extreme, we arrive at a
> picture that the entire multiverse is a fluctuation in the stationary, 
> fractal “mega-multiverse,”
> in which an infinite sequence of multiverse productions occurs.
>
> "Therefore, we conclude that the multiverse is the same as (or a specific 
> manifestation
> of ) many worlds in quantum mechanics."
>
> "In eternal inflation, however, one first picks a causal patch; then one 
> looks for observers in it.” Our framework does not follow this approach. We 
> instead pick an observer first, and then construct the relevant spacetime 
> regions associated with it.
>
> Instead of admitting the existence of the “beginning,” we may require that 
> the quantum observer principle is respected for the whole history of 
> spacetime. In this case, the beginning of our multiverse is a fluctuation 
> of a larger structure, whose beginning is also a fluctuation of an even 
> larger structure, and this series goes on forever. This leads to the 
> picture that our multiverse arises as a fluctuation in a huge, stationary 
> “megamultiverse,” which has a fractal structure."
>
>
> The Multiverse Interpretation of Quantum Mechanics 
> , Raphael Bousso and Leonard Susskind
>
> In both the many-worlds interpretation of quantum mechanics and the 
> multiverse
> of eternal inflation the world is viewed as an unbounded collection of 
> parallel universes.
> A view that has been expressed in the past by both of us is that there is 
> no need to
> add an additional layer of parallelism to the multiverse in order to 
> interpret quantum
> mechanics. To put it succinctly, the many-worlds and the multiverse are 
> the same
> thing [1].
>
>
> Jason
>

My tendency is to say no. The type II multiverse, Vilenkin bubbles etc, I 
tend not to think is somehow equivalent to the MWI. I dislike the prospect 
that cosmology is somehow equivalent to a particular quantum 
interpretation. Quantum interpretations are not empirically verifiable and 
tend in some ways to be more metaphysics meant to make quantum nonlocal 
strangeness somehow sensible within our intuitive grasp on reality. This 
might however have something to do with type I multiverse. I will discuss 
the type II multiverse first.

The Speaker of the House of Representatives in the 1980s Tip O'Neil said 
that all politics is local. In physics we may have a similar situation; all 
physics is local. Maybe it is better to put this as all causal principles 
are local. There are  reasons to suspect this might be the case. General 
relativity itself has a funny relationship with energy; it is not 
localizable in general. 

The Hamiltonian constraint in general relativity H = 0 leads to a 
Schrödinger-like equation HΨ[g] = 0 for quantum gravity  where the term 
i∂Ψ[g] /∂t is absent or zero. We may write this as K_tΨ[g] = 0 for K_t a 
Killing vector. This says the Killing vector along timelike directions is 
in general zero or does not exist. This means there is no Noetherian 
principle for a conservation law of energy. In general relativity 
conservation laws are due to the imposition of symmetries on the structure 
of spacetime that are in addition to the local Lorentz symmetry. 

This may also be seen with a Gauss' law argument. If you have a spacetime 
with an even distribution of mass-energy or galaxies it is not possible to 
establish a Gaussian surface to evaluate the mass-energy content of the 
manifold. For solutions such as type D solutions for black holes the 
solution has an asymptotically flat region where such an evaluation may be 
made. 

This carries over to a multiverse situation. The eternal inflation of 
Vilenkin et al posits a manifold with a large vacuum energy density on any 
local frame, where the vacuum collapses into low energy configuration and 
there is a bubble in this inflationary region. It is possible to think of 
this bubble percolating into its own spacetime manifold, but from the 
perspective of any observer in this bubble it does not matter if this 
bubble is Swiss cheese bubble in the inflationary manifold or if it is a 
closed spacetime region that pops off the inflationary manifold. This may 
happen if the physical vacuum in the bubble is sufficiently small that 
there can't be any causal interaction across it. In this setting the 
boundary of the Swiss cheese bubble propagates no information to 

Re: Schrodinger's Cat vs Decoherence Theory

[Lawrence Crowell]

On Wednesday, June 13, 2018 at 11:18:10 PM UTC-5, Bruce wrote:
>
> From: Brent Meeker < meek...@verizon.net >
>
> On 6/13/2018 3:53 PM, Bruce Kellett wrote:
>
> From: Brent Meeker > 
>
> On 6/12/2018 10:26 PM, Bruce Kellett wrote:
>
> From: Brent Meeker < meek...@verizon.net >
>
>
> On 6/12/2018 8:25 PM, Bruce Kellett wrote:
>
> From: Brent Meeker < meek...@verizon.net >
>
>
> An isolated system has energy eigenvalues.  But any realistic macroscopic 
> system is only going to conserve energy approximately.  I think energy 
> eigenvalues are found in atoms and maybe molecules.  But larger systems 
> (C60 Bucky balls?) tend to emit and absorb photons that localize them in a 
> position basis.
>
>
> I am glad you said "a position basis" and not "the position basis" -- a 
> mistake that is frequently made. Position is an operator in a high 
> dimensional Hilbert space, and there are an infinite number of possible 
> bases for this space, each corresponding to a different operator in the 
> space. Which one of these operators (and bases) is "the" position basis? 
> The answer from decoherence theory is that it is the basis that is stable 
> against environmental decoherence. But, as I pointed out in a post on the 
> 'Entanglement' thread, this is defined by the operator that commutes with 
> the interaction Hamiltonian. However, the interaction Hamiltonian is 
> usually defined in terms of point particle interactions, so commutes with 
> the position operator because it contains that operator itself. So that 
> particular definition of the stable basis is circular -- any chosen 
> operator in the position Hilbert space would fit the bill provided it was 
> used for both the position measurement and the interaction Hamiltonian. 
>
>
> But is it a vicious circle? Aren't all the position bases going to be 
> physically equivalent?
>
>
> Well, yes. Insofar as you can describe any vector in a linear space in 
> terms of any of the possible bases. But no. Not all of these descriptions 
> are the same -- what is given by the eigenvalues of one operator will be a 
> superposition of the eigenvalues of another operator. In terms of position 
> measurements, we get single dots on the screen in the basis consisting of 
> delta functions for positions along the line. 
>
>
> I don't see that.  Suppose I did a Fourier transform of the basis 
> consisting little bins across the screen. The indeed each spot on the 
> screen will be represented by a superposition of Fourier components, but it 
> will still be a spot in that representation.  And the Schroedinger eqn 
> solution for the interference pattern on the screen will also be a 
> superposition of Fourier components.
>
>
> So you are saying that there is no preferred basis problem? What do you 
> think the problem is?
>
>
> No.  There's a preferred basis in which this "world" and it's spots on the 
> screen, is spanned by basis vectors which are orthogonal to the basis 
> vectors of the "worlds" in which the spots are in different places on the 
> screen.  But in each world there are different (not necessarily position) 
> bases, but they describe the same physics.
>
>
> I don't think that is correct. The preferred basis is selected as the 
> eigenvectors of the operator that commutes with the interaction 
> Hamiltonian. If you choose a different basis for the Hilbert space, even by 
> a simple rotation of your present basis, you are going to get eigenvectors 
> (and eigenvalues) of a different operator. Since this operator must also be 
> dominant in the interaction Hamiltonian, the physics is necessarily going 
> to be different. A different position basis is going to result in more than 
> different places on the screen for the spots.
>
> Bruce
>

I would agree, and that you are invoking the Hamiltonian segues into what I 
wrote yesterday. I can set an apparatus to measure the spin of an electron 
in any orientation. I can't make a measurement of energy that is something 
other than the eigenstates or the diagonal form of the Hamiltonian. Energy 
is the physical quantity which defines the einselected basis that is stable 
in a classical-(like) outcome or for the emergence of classicality.

LC 

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Re: Schrodinger's Cat vs Decoherence Theory

[Bruce Kellett]

From: *Brent Meeker* mailto:meeke...@verizon.net>>

On 6/13/2018 9:18 PM, Bruce Kellett wrote:

From: *Brent Meeker* mailto:meeke...@verizon.net>>



No.  There's a preferred basis in which this "world" and it's spots 
on the screen, is spanned by basis vectors which are orthogonal to 
the basis vectors of the "worlds" in which the spots are in 
different places on the screen. But in each world there are 
different (not necessarily position) bases, but they describe the 
same physics.


I don't think that is correct. The preferred basis is selected as the 
eigenvectors of the operator that commutes with the interaction 
Hamiltonian. If you choose a different basis for the Hilbert space, 
even by a simple rotation of your present basis, you are going to get 
eigenvectors (and eigenvalues) of a different operator. Since this 
operator must also be dominant in the interaction Hamiltonian, the 
physics is necessarily going to be different. A different position 
basis is going to result in more than different places on the screen 
for the spots.


But what about my example of taking the Hilbert space of Fourier 
components of the distribution of spots on the screen?  It doesn't 
have delta functions as the basis vectors, but it spans the same 
physical results.


How do you know that this gives the same physical results? The position 
operator is different, so the interaction Hamiltonian is no longer given 
by interactions between point particles, obeying a separation force law 
depending on the distance. If you are right and the physics is unchanged 
by a basis change, then there is no preferred basis problem because all 
bases would give the same physics. But that is manifestly false. Just 
consider the expansion of some state in two different bases for the same 
measurement space (different operators, mind):


 }psi> = Sum_i c_i |a_i> = Sum_j d_j |b_j>.

the c_i =/= d_j in general. So the worlds are split into different 
branches, with different weights, depending on which basis is chosen. 
This does not seem like the same physics to me.


Sure, it is the same initial vector, so we can related the bases by a 
simple linear transformation. But decoherence will operate on different 
sets of states in the two cases; the branching worlds will be different. 
So there is no way this could be said to represent the same physics in 
general.


Bruce.

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