Many-worlds true quantum event generator

[rodsika]

No, the point is that some observables like position and momentum don't commute, so you have to decide whether the position basis or the momentum basis is to be "preferred" in order to break down the universal state vector into a set of eigenstates which you call "worlds" in DeWitt's version of the MWI.

You could take a look at this thread, and there's some discussion of the preferred basis problem starting on p. 9 of this paper. But you can find more references just by typing the words "preferred basis everett" (not in quotes) into google scholar or google books.

Hi JesseM, I'm reading old archive about the preferred basis problem and I came across the following post by Fredrik/wolverine in 2009. He said:
"There are always infinitely many bases to choose from. What decoherence does is (among other things) to single out one of them as "special"."
He said "infinite many bases". You mentioned only position and momentum. What others, how can it reach infinite? what weird combination is possible that can make it so numerous? pls give 10 examples of other bases beside our usual observables. Thanks

The following is from A. Neumaier site, one of the critique of Many Worlds. He wrote (what do
you think?):
"
Q8 When does Schrodinger's cat split?
******** As the cyanide/no-cyanide interacts with the cat the cat
******** is split into two states (dead or alive). From the surviving
******** cat's point of view it occupies a different world from its
******** deceased copy. The onlooker is split into two copies only
******** when the box is opened and they are altered by the states
******** of the cat.
Indeed, this confirms that splitting is a subjective process not
affecting the world at large. Otherwise the number of worlds could not
depend on the point of view? Or is it to be understood as follows:
As the cyanide/no-cyanide interacts with the cat the world is split
into two, one containig a dead cat and the other one that is alive?
And each of these two worlds splits again as the onlooker opens the box?
But then we have 4 worlds, two of which corresponding to nonexistent
possibilities (e.g., the world with the dead cat which is found alive
on opening the box). Thus only one split should have occured, and the
`explanation' is nonsense."

 

[JesseM]

Hi JesseM, I'm reading old archive about the preferred basis problem and I came across the following post by Fredrik/wolverine in 2009. He said:
"There are always infinitely many bases to choose from. What decoherence does is (among other things) to single out one of them as "special"."
He said "infinite many bases". You mentioned only position and momentum. What others, how can it reach infinite? what weird combination is possible that can make it so numerous? pls give 10 examples of other bases beside our usual observables. Thanks

'
Basis vectors need not be eigenstates of any observables, the basis vectors could each involve a superposition of multiple positions and multiple momenta for example. To have a basis for a given space (like Hilbert space in QM) just means you have a set of vectors such that every possible vector in the space can be expressed as a weighted sum of the basis vectors, but the basis vectors themselves are "linearly independent" so one basis vector cannot be a weighted sum of other basis vectors.

The following is from A. Neumaier site, one of the critique of Many Worlds. He wrote (what do
you think?):
"
Q8 When does Schrodinger's cat split?
******** As the cyanide/no-cyanide interacts with the cat the cat
******** is split into two states (dead or alive). From the surviving
******** cat's point of view it occupies a different world from its
******** deceased copy. The onlooker is split into two copies only
******** when the box is opened and they are altered by the states
******** of the cat.
Indeed, this confirms that splitting is a subjective process not
affecting the world at large. Otherwise the number of worlds could not
depend on the point of view? Or is it to be understood as follows:
As the cyanide/no-cyanide interacts with the cat the world is split
into two, one containig a dead cat and the other one that is alive?
And each of these two worlds splits again as the onlooker opens the box?
But then we have 4 worlds, two of which corresponding to nonexistent
possibilities (e.g., the world with the dead cat which is found alive
on opening the box). Thus only one split should have occured, and the
`explanation' is nonsense."

I think a more mathematical analysis than I know how to do would be required to address this. If you think in terms of my comments on the other thread about macrostates vs. microstates, it might for example be that if you just consider the macrostates of the cat they have already decohered before the box is opened (interference between live cat macrostate and dead cat macrostate has become negligible), but that if you considered the macrostates of the cat + experimenter system than interference would still be significant until the box was opened, so that this could be the basis for talking about an initial split in the cat and a later split in the experimenter when he opens the box. But I can't definitely say that this is how it works since I don't know enough about how to do the math.

 

[rodsika]

'
Basis vectors need not be eigenstates of any observables, the basis vectors could each involve a superposition of multiple positions and multiple momenta for example. To have a basis for a given space (like Hilbert space in QM) just means you have a set of vectors such that every possible vector in the space can be expressed as a weighted sum of the basis vectors, but the basis vectors themselves are "linearly independent" so one basis vector cannot be a weighted sum of other basis vectors.

I think a more mathematical analysis than I know how to do would be required to address this. If you think in terms of my comments on the other thread about macrostates vs. microstates, it might for example be that if you just consider the macrostates of the cat they have already decohered before the box is opened (interference between live cat macrostate and dead cat macrostate has become negligible), but that if you considered the macrostates of the cat + experimenter system than interference would still be significant until the box was opened, so that this could be the basis for talking about an initial split in the cat and a later split in the experimenter when he opens the box. But I can't definitely say that this is how it works since I don't know enough about how to do the math.

Let's talk about Hilbert Space.
Let's say you have w,x,y,z axis.
You make axis w as momentum, x as position, y as spin, z as charge. Then you only need one vector to characterize the whole system.
I think you refer to the w, x, y, z axis as basis vector. But you said "the basis vectors could each involve a superposition of multiple positions and multiple momenta for example". You are saying we need to put more axis like u and v to Hilbert Space and make it a superposition of multiple momentum? I thought the 4 axis for example can characterize a system based on its position, momentum, spin and charge. But by adjusting the main vector, one can change the value of the momentum.* Is it standard practice to put more axis to Hilbert Space to character superposition of momentum for example?

 

[JesseM]

Let's talk about Hilbert Space.
Let's say you have w,x,y,z axis.
You make axis w as momentum, x as position, y as spin, z as charge. Then you only need one vector to characterize the whole system.

No, each possible momentum eigenstate is a separate vector orthogonal to all the others, same with position etc. So if you want use basis where the vectors are each position eigenstates, you need a separate basis vector for positions x1, x2, x3, etc. Since some observables like position and momentum have a continuous range of possible values, the full Hilbert space must be infinite-dimensional.

 

[bg032]

Let $$\Psi(t)=U(t)\Psi_0$$ be the universal wave function. According to de Witt, at every $$t$$ there is a (approximately defined) preferred decomposition of $$\Psi(t)$$ into the sum of orthogonal vectors (worlds):

$$\Psi(t)=\Psi_1 + \ldots + \Psi_{n_t}.$$​

The problem of how to define this decomposition is referred to as the preferred basis problem. However I find this term misleasing, because, in order to define the above decomposition there is no need to define a basis for the whole Hilbert space of the universe. The name preferred decomposition would be more appropriate.

 

[Dmitry67]

Why should there be a preferred decomposition? Such claim is equivalent to a claim that cat is *not* in a superposition before opening a box. Also, in other 'alternatives' the very number of objects (an elements of decomposition) might be different (say, there is no life on Earth).

It does not make any sense to me. "Preferred" to who? Based on what criteria? It is an attempt to drag into MWI framework some "objective" view of the Universe. The only 'objective' view is universe wavefunction itself. Like in relativity we can't ask 'does it move' without specifying 'relative to what', in 'pure' MWI we can't ask 'what happens' without specifying 'relative to what basis/observer'.

When such 'preferred' stuff is forced into MWI, we get such weird artefacts like 'preferred basis problem' or 'splitting is not lorentz-invariant, because preferred basic exists in preferred frame' etc

 

[JesseM]

Well, the preferred basis issue is part of DeWitt's version of the MWI. The advantage is that it allows you to state precisely what the different "worlds" are at any given moment (and their respective probabilities if you also assume the Born rule). The disadvantage, as you say, is that it seems a bit arbitrary and sort of messes with the elegance of the "the wavefunction is all there is" version of the MWI. That "wavefunction is all there is" version is probably more popular, with the "worlds" just being distinguished by decoherence, but the disadvantage of that version is that there is no precise and rigorous definition of what the worlds or branches are, when there has been "enough" decoherence for worlds to become differentiated, etc. See John Bell's criticisms of the non-precise "for all practical purposes" (FAPP) definition of worlds in http://duende.uoregon.edu/~hsu/blogfiles/bell.pdf.

 

[bg032]

Why should there be a preferred decomposition? ...

My position is that the universal wave function has a pattern which strongly suggests a preferred decomposition. Suppose for example that $$\Psi(t)$$ is the sum of spatially well separated (in 3N configuration space) wave packets which remains separated under time evolution. Bohm has extensively studied this situation. For me it is obvious that such a pattern strongly suggests the preferred decomposition in which every element is a single wave packet. This decomposition is evident even though it cannot be exactly defined, because the boundaries between the wave packets cannot be exactly defined.

Of course, the fact that the universal wave function posseses such a pattern has to be proved. Note however that the presence of such a pattern is not matter of interpretation or of taste. At least in principle, it can be proved or disproved by calculating Schroedinger's evolution of a wave function with reasonable (not conspirative) initial conditions.

Another example: the clouds in the sky derive from a pattern of the density $$\rho(x)$$ of water vapor. We cannot exactly define the boundary of a cloud. Nevertheless for us clouds are existing objects, and if the pattern of $$\rho(x)$$ is appropriate, you can distinguish and count the clouds.

Why should there be a preferred decomposition? Such claim is equivalent to a claim that cat is *not* in a superposition before opening a box. Also, in other 'alternatives' the very number of objects (an elements of decomposition) might be different (say, there is no life on Earth).

I am not sure to understand this. Assuming that the wave functions |cat alive> and |cat dead> are spatially separated in configuration space, the wave function of the cat (and therefore of the universe) is already decomposable according the above criterion before opening the box.

 

[Dmitry67]

bg032, ok, slightly different version.

Say, I have an emitter of 'wave packets'. When it emits a wave packet, it becomes 'spacially separated' from it. It is programmed to emit it when radioactive atom decays. There are 100 atoms.

After a while, there is a superposition of emitter plus from 0 to 100 wavepackets. From 1 to 101 spacially separated subsystems. How do you decompose such system?

I agree with you: in *some* cases the pattern is clear, but it is not a universal rule.

 

[bg032]

Well, the preferred basis issue is part of DeWitt's version of the MWI. The advantage is that it allows you to state precisely what the different "worlds" are at any given moment (and their respective probabilities if you also assume the Born rule). The disadvantage, as you say, is that it seems a bit arbitrary and sort of messes with the elegance of the "the wavefunction is all there is" version of the MWI. That "wavefunction is all there is" version is probably more popular, with the "worlds" just being distinguished by decoherence, but the disadvantage of that version is that there is no precise and rigorous definition of what the worlds or branches are, when there has been "enough" decoherence for worlds to become differentiated, etc. See John Bell's criticisms of the non-precise "for all practical purposes" (FAPP) definition of worlds in http://duende.uoregon.edu/~hsu/blogfiles/bell.pdf.

JesseM, in my previous post (posted I think at the same time of yours) is explained why I have no problem with approximately defined branches. For me branches are patterns of the wave function, and patterns may be evident even though vaguely defined. Branches are like clouds in a sky with well defined clouds: they cannot be exactly defined but nevertheless they exist and are evident.
On the contrary, I am totally unsatisfied by the mechanism based on decoherence for giving rise to the branches, which I find confused and elusive. In the paper of Wallace you cited you can read:

“Worlds” are mutually dynamically isolated structures instantiated within the quantum state, which are structurally and dynamically “quasiclassical”.

What does this mean? What are mutually dynamically isolated structures? I do not understand...


Dmitry67: certainly you can built situations in which the decomposition into separated wavepackets is not possible. However my opinion is that at the macroscopic level the universal wave function has a strong tendency to decompose into permanently non-overlapping wave packets. The reason of this is basically the form of the potential of the hamiltonian + the process of macroscopic amplification and the interaction with the environment. The splitting into non-overlapping parts arises at the microscopic level in the scattering processes, and than it is amplified and made permament by the interaction with the environment. See for example chapters 5 and 6 in the book of Bohm: The Undivided Universe.
However I know that this opinion would have to be better proved, and it is largely minority in the physics community, which is mainly oriented towards the decoherence mechanism.

 

[JesseM]

In the paper of Wallace you cited you can read:

“Worlds” are mutually dynamically isolated structures instantiated within the quantum state, which are structurally and dynamically “quasiclassical”.

What does this mean? What are mutually dynamically isolated structures? I do not understand...

I think he probably means that if you consider the reduced density matrix for "the structure" (whether the structure refers to a subsystem of some larger system, or to a set of coarse-grained macrostates of a given system which omit a lot of microscopic detail), then decoherence has dynamically caused the off-diagonal interference terms to have a very tiny amplitude, so that it is approximately correct to just see it as a classical statistical ensemble of the diagonal terms in the density matrix, each of which could be seen as a version of the structure in a different "world".

 

[rodsika]

No, each possible momentum eigenstate is a separate vector orthogonal to all the others, same with position etc. So if you want use basis where the vectors are each position eigenstates, you need a separate basis vector for positions x1, x2, x3, etc. Since some observables like position and momentum have a continuous range of possible values, the full Hilbert space must be infinite-dimensional.

Let's take the case of an electron. The projection of the state vector on each axis is a measure of the possibility of an electron being at a particular position. That's why one has, as you said, to use separate vector orthogonal to all the others for each value. However, earlier you said:

"Basis vectors need not be eigenstates of any observables, the basis vectors could each involve a superposition of multiple positions and multiple momenta for example."

I thought each basis (meaning located in the axis) vector represent one value. But you said it could involve superposition of multiple positions? How could one value becomes a superposition of values?

Second let's take the case of Hydrogen atom with nucleus composed of 3 quarks and electron around it. When putting it in Hilbert Space. Do you use an axis or basis vector for each value of each position, momentum, etc. of the up quark, down quark and electron?

 

[JesseM]

Let's take the case of an electron. The projection of the state vector on each axis is a measure of the possibility of an electron being at a particular position.

Only if you use a basis where the basis vectors are position eigenstates. If the basis vectors are momentum eigenstates, each basis vector represents a quantum state that's a superposition of different possible positions. And you are free to pick a set of basis vectors that aren't eigenstates of position or momentum or any other observable, each of which is a distinct quantum state that represents a different superposition of positions/momenta/etc.

I thought each basis (meaning located in the axis) vector represent one value.

No, that's only true if the basis vectors are eigenstates of an observable, but the definition of "basis" has nothing to do with the notion that each vector should be a value of some observable. Reread what I said in post #72:

To have a basis for a given space (like Hilbert space in QM) just means you have a set of vectors such that every possible vector in the space can be expressed as a weighted sum of the basis vectors, but the basis vectors themselves are "linearly independent" so one basis vector cannot be a weighted sum of other basis vectors.

So if you have some set S of quantum state vectors, such that any possible new state vector you could come up with can be expressed as a weighted some of the vectors in S, and such that none of the vectors in S can be expressed as a weighted some of the other vectors in S, then S is a valid basis.

 

[rodsika]

Only if you use a basis where the basis vectors are position eigenstates. If the basis vectors are momentum eigenstates, each basis vector represents a quantum state that's a superposition of different possible positions. And you are free to pick a set of basis vectors that aren't eigenstates of position or momentum or any other observable, each of which is a distinct quantum state that represents a different superposition of positions/momenta/etc.

No, that's only true if the basis vectors are eigenstates of an observable, but the definition of "basis" has nothing to do with the notion that each vector should be a value of some observable. Reread what I said in post #72:

So if you have some set S of quantum state vectors, such that any possible new state vector you could come up with can be expressed as a weighted some of the vectors in S, and such that none of the vectors in S can be expressed as a weighted some of the other vectors in S, then S is a valid basis.

Ok.

Earlier in the thread you said "the point is that some observables like position and momentum don't commute, so you have to decide whether the position basis or the momentum basis is to be "preferred" in order to break down the universal state vector into a set of eigenstates which you call "worlds" in DeWitt's version of the MWI."

Why.. what would it looks like if other MWI branches only have momentum basis? Can you please describe what that world would be like? For example. A ball rolling on the floor. If momentum basis only is chosen, what would happen. Or since preferred basis in other branches can be any basis in Hilbert space, (right?) Let's say the preferred basis chosen is charge. What would happen if a ball is rolling on the floor in that branch.. or do you mean to say the branch where charge is the preferred basis won't have moving objects but everything static?

 

[JesseM]

Ok.

Earlier in the thread you said "the point is that some observables like position and momentum don't commute, so you have to decide whether the position basis or the momentum basis is to be "preferred" in order to break down the universal state vector into a set of eigenstates which you call "worlds" in DeWitt's version of the MWI."

Why.. what would it looks like if other MWI branches only have momentum basis?

What do you mean "other MWI branches"? The idea of DeWitt's version is that you pick a single set of basis vectors for the whole universal wavefunction, not that each branch has its own basis. I don't know what the worlds would "look like" if you used a momentum basis, would it even make sense to talk about distinct brain states of observers if each particle's position was maximally uncertain? It seems to me that this is another aspect of the preferred basis problem, that it's hard to make sense of what it would even mean to choose a basis where the positions of particles weren't confined to a sufficiently narrow range to be able to talk about brain structures, measurement records etc.

 

[rodsika]

What do you mean "other MWI branches"? The idea of DeWitt's version is that you pick a single set of basis vectors for the whole universal wavefunction, not that each branch has its own basis. I don't know what the worlds would "look like" if you used a momentum basis, would it even make sense to talk about distinct brain states of observers if each particle's position was maximally uncertain? It seems to me that this is another aspect of the preferred basis problem, that it's hard to make sense of what it would even mean to choose a basis where the positions of particles weren't confined to a sufficiently narrow range to be able to talk about brain structures, measurement records etc.

I thought it was like the concept of Inflationary Bubble Universes where there are different constants of nature in each parallel universe, or the concept of Superstring Landscape where there are different laws of physics in each landscape universe. Similary. I thought different Many Worlds or Branches have different Preferred Basis chosen such that we can have one branch where charge or spin is the preferred basis. But is this impossible. So if one basis is chosen in the Universal Wavefunction, all the billions of worlds or branches would choose the same basis. Is this a definite certainty or can Hilbert Spaces be doctored to produce different Preferred Basis for each branch? What's the proof it can't? Remember decoherence divide the worlds.. so if our world has position as preferred basis. What would stop other branches to have spin as preferred basis? Why does the mathematics of Hilbert Space prevent that?

Btw just curious. Are you a physicist? What is your specialization?

 

[JesseM]

I thought it was like the concept of Inflationary Bubble Universes where there are different constants of nature in each parallel universe, or the concept of Superstring Landscape where there are different laws of physics in each landscape universe. Similary. I thought different Many Worlds or Branches have different Preferred Basis chosen such that we can have one branch where charge or spin is the preferred basis. But is this impossible. So if one basis is chosen in the Universal Wavefunction, all the billions of worlds or branches would choose the same basis. Is this a definite certainty or can Hilbert Spaces be doctored to produce different Preferred Basis for each branch? What's the proof it can't? Remember decoherence divide the worlds.. so if our world has position as preferred basis. What would stop other branches to have spin as preferred basis? Why does the mathematics of Hilbert Space prevent that?

Are we still talking about DeWitt's version? The "preferred basis" is a basis for splitting the entire universal wavefunction into a set of different "worlds", I don't even understand what it would mean for different branches to have their own basis. I will say that since there is no requirement that the basis vectors all be eigenvectors of the same observable, I think you could probably have a single basis where some of the basis vectors were position eigenvectors, some were momentum eigenvector, etc. (by the way spin commutes with both position and momentum, see [post=2676394]here[/post], so you could have a basis where every vector was both a position eigenvector and a spin eigenvector, meaning every particle would have both a precise position and a precise spin, or a basis where every vector was both a momentum eigenvector and a spin eigenvector).

Btw just curious. Are you a physicist? What is your specialization?

No, I got my undergraduate degree in physics and still read about physics-related stuff a fair amount on my own, but that's the extent of my training.

 

[rodsika]

Are we still talking about DeWitt's version? The "preferred basis" is a basis for splitting the entire universal wavefunction into a set of different "worlds", I don't even understand what it would mean for different branches to have their own basis. I will say that since there is no requirement that the basis vectors all be eigenvectors of the same observable, I think you could probably have a single basis where some of the basis vectors were position eigenvectors, some were momentum eigenvector, etc. (by the way spin commutes with both position and momentum, see [post=2676394]here[/post], so you could have a basis where every vector was both a position eigenvector and a spin eigenvector, meaning every particle would have both a precise position and a precise spin, or a basis where every vector was both a momentum eigenvector and a spin eigenvector).

No, I got my undergraduate degree in physics and still read about physics-related stuff a fair amount on my own, but that's the extent of my training.

I'm not referring to any particular version. You mean the idea of Preferred basis is different in different versions of quantum interpretations like Bohmian, etc.?

Also you mean Preferred Basis can change? Or is it fixed. If fixed. What Prefered basis is chosen to explain our classical world? How many set of preferred basis are there. Like...

1st Preferred Basis is: Position

2nd Preferred Basis: Position + Spin,

3rd Preferred Basis: Position not commuted with Momentum, etc.

I mean. What are the exact Preferred Basis chosen for our universe?

Hmm.. I thought anyone who has undergraduate degree in physics is automatically a physicist? why not?

 

[JesseM]

I'm not referring to any particular version. You mean the idea of Preferred basis is different in different versions of quantum interpretations like Bohmian, etc.?

The function of the preferred basis in DeWitt's version is to define the set of worlds, what would you need a preferred basis for in Bohmian mechanics? There aren't multiple worlds there, and every particle has a hidden position variable at all times. And in non-DeWitt MWI decoherence is supposed to define what observable the environment is effectively "measuring", I think one of the papers linked on this thread said it normally be position but for small systems interacting more slowly/weakly with the environment it could be energy.

Also you mean Preferred Basis can change? Or is it fixed.

Change over time, you mean? I don't know what DeWitt's version would say about that.

If fixed. What Prefered basis is chosen to explain our classical world? How many set of preferred basis are there. Like...

1st Preferred Basis is: Position

2nd Preferred Basis: Position + Spin,

3rd Preferred Basis: Position not commuted with Momentum, etc.

How is "position not commuted with momentum" different than "position"? There's no such thing as position that does commute with momentum, it's an inherent property of the two observables that they don't commute. And I don't think position alone would suffice as a basis, if you want a basis made up of eigenvectors of observables I think you need a complete set of commuting observables to span the Hilbert space. Anyway, as I said the arbitrariness of choosing the basis is exactly why the preferred basis issue is a problem for DeWitt's version of the MWI.

 

[rodsika]

The function of the preferred basis in DeWitt's version is to define the set of worlds, what would you need a preferred basis for in Bohmian mechanics? There aren't multiple worlds there, and every particle has a hidden position variable at all times. And in non-DeWitt MWI decoherence is supposed to define what observable the environment is effectively "measuring", I think one of the papers linked on this thread said it normally be position but for small systems interacting more slowly/weakly with the environment it could be energy.

Change over time, you mean? I don't know what DeWitt's version would say about that.

How is "position not commuted with momentum" different than "position"? There's no such thing as position that does commute with momentum, it's an inherent property of the two observables that they don't commute. And I don't think position alone would suffice as a basis, if you want a basis made up of eigenvectors of observables I think you need a complete set of commuting observables to span the Hilbert space. Anyway, as I said the arbitrariness of choosing the basis is exactly why the preferred basis issue is a problem for DeWitt's version of the MWI.

Why do you put so much weight on DeWitt. Maybe we should just reject DeWitt version because he didn't give any explanation why or how the Preferred Basis is chosen at all.. just a priori... In Everett original formula, he used the concept of "Relative state" as shown in the Stanford website which was incomplete. Therefore why can't we just accept the Decoherence version of MWI as it needs the environment to define the Preferred basis. Now in pure Decoherence version (without DeWitt Adhoc ness), is it possible other branches would have other environments (akin to parallel worlds with different laws of nature) such that the environment there with constants of nature that don't admit positions to have charge as the preferred basis? Or do you mean Many Worlds only work within our Spacetime with our given Constants of Nature??

 

[JesseM]

Why do you put so much weight on DeWitt.

I don't, but the problem of needing to find a preferred basis seems specific to DeWitt's version, so since you were asking questions about how to pick it I figured you were asking about that version.

Therefore why can't we just accept the Decoherence version of MWI as it needs the environment to define the Preferred basis.

Right, but with the decoherence version there is no precise definition of "worlds" and decoherence only approximately forces various subsystems into a mix of eigenstates of some observable like position, the interference terms don't entirely disappear and the whole business also depends on how you divide "subsystem" and "environment".

Now in pure Decoherence version (without DeWitt Adhoc ness), is it possible other branches would have other environments (akin to parallel worlds with different laws of nature) such that the environment there with constants of nature that don't admit positions to have charge as the preferred basis?

We have to assume the same basic laws apply to all "worlds" in the MWI because you have to be able to represent the wavefunction of the universe as a single state vector evolving according to the Schroedinger equation. The paper you linked to earlier by Schlosshauer says that decoherence tends to drive subsystems towards an ensemble of position eigenstates, though in some cases it can be energy eigenstates instead, see page 14:

In general, three different cases have typically been
distinguished (for example, in Paz and Zurek, 1999) for
the kind of pointer observable emerging from an interaction
with the environment, depending on the relative
strengths of the system’s self-Hamiltonian bHS and of the
system-environment interaction Hamiltonian bHSE :

(1) When the dynamics of the system are dominated
by bHSE , i.e., the interaction with the environment,
the pointer states will be eigenstates of bHSE (and
thus typically eigenstates of position). This case
corresponds to the typical quantum measurement
setting; see, for example, the model of Zurek (1981,
1982), which is outlined in Sec. III.D.2 above.

(2) When the interaction with the environment is weak
and bHS dominates the evolution of the system (that
is, when the environment is “slow” in the above
sense), a case that frequently occurs in the microscopic
domain, pointer states will arise that are energy
eigenstates of bHS (Paz and Zurek, 1999).

(3) In the intermediate case, when the evolution of
the system is governed by bHSE and bHS in roughly
equal strength, the resulting preferred states will
represent a “compromise” between the first two
cases; for instance, the frequently studied model
of quantum Brownian motion has shown the emergence
of pointer states localized in phase space,
i.e., in both position and momentum (Eisert, 2004;
Joos et al., 2003; Unruh and Zurek, 1989; Zurek,
2003b; Zurek et al., 1993).

(again, look at the actual paper to see the notation rendered correctly, I didn't feel like translating the various Hamiltonian symbols into LaTeX)

 

[Dmitry67]

However my opinion is that at the macroscopic level the universal wave function has a strong tendency to decompose into permanently non-overlapping wave packets. The reason of this is basically the form of the potential of the hamiltonian + the process of macroscopic amplification and the interaction with the environment.

This is true only when Universe had cooled enough. In early Universe (quagma state) or even just an ordinary plasma matter was too hot, so no separate structures existed, and even more, no structures with any sort of "memory" were possible.

Of course, we are free to pick any basis, including "this area of quagma", but the result does not have a lot of sense, like the famous "photon perspective" question.

 

[bg032]

This is true only when Universe had cooled enough. In early Universe (quagma state) or even just an ordinary plasma matter was too hot, so no separate structures existed, and even more, no structures with any sort of "memory" were possible.

Of course, we are free to pick any basis, including "this area of quagma", but the result does not have a lot of sense, like the famous "photon perspective" question.

I agree, but I do not see problems; now the universe is cooled and now we observe a quasi-classical realm.

 

[woolyhead]

Hi. Can I say it seems to me that none of the standard or non standard explanations are very true. I think they are the best theories we can come up with in the hope that they will somehow spawn a better predictive capability but in another sense they are all just attempts to cover the fact that we just don't know, while giving us some sort of picture of what happens, based on our experience of the world around us and how she works. I agree that what "makes sense" to us may not be any sort of reality in the "absolute sense" Our mathematical analyses are based on having some sort of image in our minds about how maths should work, but although it seems to work out in practice most of the time, we shouldn't start to believe too much in the maths either. At root nature is a mystery.

 

[Fyzix]

Hi. Can I say it seems to me that none of the standard or non standard explanations are very true. I think they are the best theories we can come up with in the hope that they will somehow spawn a better predictive capability but in another sense they are all just attempts to cover the fact that we just don't know, while giving us some sort of picture of what happens, based on our experience of the world around us and how she works. I agree that what "makes sense" to us may not be any sort of reality in the "absolute sense" Our mathematical analyses are based on having some sort of image in our minds about how maths should work, but although it seems to work out in practice most of the time, we shouldn't start to believe too much in the maths either. At root nature is a mystery.

I agree with you about this.
It seems a lot of people who are MWI proponents value math over observed reality.



Dmitry67,

So you are admitting that the Dewitt Many Worlds with real splitting of worlds are in violation with relativity, correct?
So you are also agreeing that since that MWI version cannot make sense of probability and has problems with relativity, it's basically worse than Bohm which can atleast get probability right?

So you are a proponent of the "pure wave mechanics" which has no relativity problem, but still can't make sense of probability without additional postulates?

 

[Fyzix]

JesseM, you seem to be pretty knowledgeable in this subject.
Are you a proponent of MWI or just playing Devil's Advocate?

 

[JesseM]

JesseM, you seem to be pretty knowledgeable in this subject.
Are you a proponent of MWI or just playing Devil's Advocate?

Insofar as there's any "real truth" about what's going on with QM my hunch is that the truth would a) not involve anything special happening during "measurement", since measuring devices are just large collections of particles which should follow the same laws as smaller collections, and b) not involve any violation of relativistic locality. So given Bell's theorem I think something along the lines of the MWI is the best option, but I hold out hope that in the future someone may find a new formulation of a "many-worlds-like" interpretation that doesn't have the preferred basis problem of DeWitt's version or the ambiguity about how to derive probabilities of the "pure wavefunction" version.

 

[Fyzix]

Well the thing is, DeWitt MWI got problems with relativity, Bohm got problems with relativity, Bohm derive Born Rule.

So Bohm is the obvious choice between the two, but personally I struggle with accepting problems with relativity.

If we discard both of those and move onto the "pure wavemechanics", we are still stuck with the Probability problem.
It seems that a lot of people don't really recognize the severity of the probability problem, it's flat out disproving MWI at this point.
It's saying "MWI DOES NOT FIT REALITY", so how may one go about solving it?

Well one is definitely forced to add postulates, which most MWI adherents are now starting to slowly accept... Such as either particles (Many Bohmian Worlds) or some other selection process, either way, "PURE" MWI is disproved.
(Unless you manage to fool yourself into believing that consciousness somehow solves it all...)

By the way, there seems to be some problems with decoherence too, that it alone isn't enough to account for our experience in "pure wave mechanics"

See here:
http://arxiv.org/PS_cache/arxiv/pdf/1001/1001.1926v1.pdf


Not to mention that others such as Tim Maudlin also has critized this "pure wave mechanics decoherence approach).

I think it's safe to conclude that these 2 approaches (in their current forms) have been thoroughly refuted.

 

[JesseM]

If we discard both of those and move onto the "pure wavemechanics", we are still stuck with the Probability problem.
It seems that a lot of people don't really recognize the severity of the probability problem, it's flat out disproving MWI at this point.

How does it "disprove" it? It's not that the "pure wavemechanics" version gives incorrect probabilities, it's just that it's not clear how to get any probabilities from it (some MWI advocates claim that arguments from decision theory are sufficient), but I don't see why we can't hope that new insights might appear in the future. For example, one interesting suggestion I saw here was that one might describe the evolution of the universal wavefunction in computational terms, and somehow treat classical observers as sub-computations, so the computation required to compute the evolution of the universal wavefunction might naturally lead to a probability measure on different possible sub-computations. Another speculation I've seen is mangled worlds though I don't really understand this proposal very well. And there's the interesting result of http://www.lps.uci.edu/barrett/publications/SuggestiveProperties.pdf showing that if you model the state vector of an idealized observer performing an infinite series of measurements in some quantum experiment, as the number of experiments go to infinity the state will approach "an eigenstate of reporting that their measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts", even with no assumption of anything like the Born rule.

By the way, there seems to be some problems with decoherence too, that it alone isn't enough to account for our experience in "pure wave mechanics"

See here:
http://arxiv.org/PS_cache/arxiv/pdf/1001/1001.1926v1.pdf

But it depends what you mean by "account for our experience", for example the author of that problem has some philosophical (not technical) objections to the idea of using coarse-graining to define macroscopic "worlds", but if you define the range of possible "experiences" we could have as some collection of coarse-grained descriptions of our lab equipment or brain states, then decoherence could (I think) explain why we don't see interference between different possible coarse-grained macrostates. So it becomes a philosophical question of whether you think this is a good enough way of accounting for the apparent classical macro-world or whether you're bothered by the lack of any totally well-defined formula for what the most "natural" choice of coarse-graining would be, there's no debate about the technical details of what decoherence says or doesn't say. Personally I find such an approach unsatisfying, but to make definitive statements like this:

I think it's safe to conclude that these 2 approaches (in their current forms) have been thoroughly refuted.

...is just silly. For something to be "thoroughly refuted" in physics there needs to be some undeniable technical critique that causes the approach to fall apart, not just verbal philosophical objections.

 

[Fyzix]

First let's take the standard DeWitt MWI approach, I would say that YES, unless we are willing to let go of relativity, this approach is refuted by relativity...

How does it "disprove" it? It's not that the "pure wavemechanics" version gives incorrect probabilities

Well, it sort of does...
Take a simple experiment where QM predicts 0.1% chance of X occurring and 0.9% of Y occurring.
We repeat this ten times and always get 1 X and 9 Y's, according to MWI this "probability" would always go to 50/50 as the universe branch into 2 branches.
So infact it does give us probabilities that are in direct conflict with reality...

(some MWI advocates claim that arguments from decision theory are sufficient)

Yes a few people do, but these are a minority of people who has just decided that they believe in MWI and therefore do not really care too much.
There are quite a few papers that adresses this decision theory approach and shows why it's wrong... I guess you are aware of these papers.

but I don't see why we can't hope that new insights might appear in the future.

Sure we can hope, but hoping isn't science, then we might as well hope for a interpretation that doesn't have any of these problems resulting from progress in ToE...

For example, one interesting suggestion I saw here was that one might describe the evolution of the universal wavefunction in computational terms, and somehow treat classical observers as sub-computations, so the computation required to compute the evolution of the universal wavefunction might naturally lead to a probability measure on different possible sub-computations.

Yes, I've been in contact with the author of this paper discussing MWI before.
He himself doesn't seem overly enthusiastic about it, giving MWI without modification less than 25% of being correct in the end...
That says a lot when the author of the paper admits it's in serious problems (which I admire him for).

Another speculation I've seen is mangled worlds though I don't really understand this proposal very well.

I'm aware of this approach, interestingly enough the previous author you mentioned has given a clear and simple critique of the Mangled Worlds theme right here:

http://onqm.blogspot.com/2009/09/decision-theory-other-approaches-to-mwi.html

And there's the interesting result of http://www.lps.uci.edu/barrett/publications/SuggestiveProperties.pdf

I haven't checked this out yet, but I've been in contact with Jeff Barrett and while he has faith in pure wave mechanics, it's not done like he said.
Bohmian Mechanics is also something he considers "pure wave mechanics" (although he is not particulary fond of Bohmian mechanics), but in his view Pure wave mechanics does not have to imply all outcomes, which changes the game quite a bit...

As for the problems with decoherence, I will try to dig up Tim Maudlin's objections too so you can see that there are infact technical and philosophical reasons for not being satisfied with this approach at all.

 

[Dmitry67]

1 So you are admitting that the Dewitt Many Worlds with real splitting of worlds are in violation with relativity, correct?
2 So you are also agreeing that since that MWI version cannot make sense of probability and has problems with relativity, it's basically worse than Bohm which can at least get probability right?
3 So you are a proponent of the "pure wave mechanics" which has no relativity problem, but still can't make sense of probability without additional postulates?

1 Dewitt's point of view is not about 'real' splitting of worlds, but about the 'preferred' splitting 'in most cases' as I understand. As this description is non-mathematical and fuzzy. So as I understand, Dewitt does not suggest a NEW interpretation, but rather an interpretation over an interpretation :)

Even, as I suspect, he was trying to bring a false notion of 'objectiveness of splitting', we all agree that as unitary evolution of the universe wavefunction don't violate relativity, then all 'subproducts' of it are in agreement with relativity.

I don’t want to say that he is WRONG: It is like saying that 'world consists of separate stars, planets and gas clouds'. True as some approximation, but not on a fundamental level.

2 Issues with Born rule are well known, but let’s put them aside for now.
Regarding Bohmian mechanics, do you know the current status of the BM? AFAIK, what is called BM is not even relativistic. There are some *different* versions, compatible with relativity, one with hidden preferred frame (so the theory is 'secretly' Lorentz-non-invariant), another (Demystifier’s) does not have it, but his work is controversial (there was a discussion here, people did not agree on math). In any case, BM *is struggling with relativity issues right now*.
Regarding BM, I don’t see why an assumption of having extra particles is ‘weaker’ than the assumption of the Born rule it should ‘explain’. As you know, the laws of motion of these ‘particles’ as made just to satisfy the Born rule, working back. BM requires additional ‘curve fitting’ to explain new phenomena like Hawking radiation, Unruh effect etc (not sure if it is applicable to the Demystifier’s version: I know that his version handles these issues, but not sure if he had made any special assumptions to explain these phenomena). Finally, I expect BM to ‘break’ at the TOE level.

3 Yes. I even think that situation is much more complicated: at first, what is an observer? What basis I should use – my body, my head with my hair, my head without my hair, my brain, distinct ‘computational’ states of my brain? There are many microscopically different states of the brain mapped to the same ‘computational’ state (it is like microprocessor takes input value of +4.9V, +5.0V, +5.1V as ‘true’, ignoring the difference on the computational level). Then, we even haven’t started to address the continuous observation, when splitting of an observer constantly occurs, redefining the basis, and to make it more complicated, doing it in a basis-dependent manner!

It is soooo interesting and we are only in the beginning of our way. Ultimately, I believe only theory of consciousness would be able to answer why Born rule is observed Note: MWI (on frogs level) is not about what happens, it is about what is observed (Einstein would be happy!)

 

[Fyzix]

As soon as you bring splitting in, relativity is violated, like I showed you with the quote from Jeff Barrett.
According to this, even Deutsch's version actually requires splitting and hence violates relativity...

I know there are some attempts to solve dBB's problems with relativity, I'm not sure if they have been successful yet.
However my point is that give nthe fact that the splitting MWI violates relativity AND can't make sense of Born Rule, dBB only violates relativity, and is thus favoured over the splitting MWI.

I understand that you are very fond of MWI, like you said, very much because you also subscribe to the hypothesis that the universe is made of math.
But seriously, I doubt your consciousness dream will ever yield anything.
The way I see it ( and most others ) is that if MWI is on the right path, it's still missing sometihng essential, like particles or something else.

By the way, Einstein would infact not be happy.
You have to think that this MWI view was obviously thought about by the founders, without making a full theory of it.
But was rejected due to it's many problems.

 

[Dmitry67]

As soon as you bring splitting in, relativity is violated, like I showed you with the quote from Jeff Barrett.
According to this, even Deutsch's version actually requires splitting and hence violates relativity...

Fyzix, repeating the same argument twice does not make it valid. It was shown that the argument you are repeating over and over again does not make any sense. Do you need an exact quote?

Dmitry67's comment seems accurate to me, Schlosshauer's main criticism is that he personally finds it counterintuitive that systems would constantly be "copied" (and I think he's taking 'copying' too literally, it's just a metaphor for the different elements in the superposition), not that this would be incompatible with any known physical principles: "there is a problem in imagining that such a splitting process somehow physically copies the systems involved." His other criticism is that "A strong picture of spacetime somehow unzipping into connected spacetime regions along the forward light cone of the measurement event, would not be compatible with special relativity insofar as relativity presupposes that all events occur on the stage of Minkowski spacetime", but this is a strawman since the MWI does not offer such a "strong picture" picture of spacetime "unzipping", it says that there are superpositions of different macroscopic states in the same spacetime (though this would become trickier if we tried to incorporate different curvatures of spacetime in general relativity...without a theory of quantum gravity, what the MWI says about spacetime curvature is bound to be speculative though)

 

[bg032]

As soon as you bring splitting in, relativity is violated, like I showed you with the quote from Jeff Barrett.
According to this, even Deutsch's version actually requires splitting and hence violates relativity...

If splitting is considered the representation of a pattern of the universal wave function, (like clouds are the representation of a pattern of the density of water vapor), I don't see any problem with relativity. Suppose that the two vectors $$\Psi(t)$$ and $$\Psi'(t)$$ represent the same universal wave function as seen by two diferent reference frames. Their patterns determine two different (time -dependent) decompositions:

$$\Psi(t)=\Psi_1(t) + \ldots + \Psi_{n_t}(t)$$ and $$\Psi'(t)=\Psi'_1(t) + \ldots + \Psi'_{n'_t}(t).$$​

There is no direct law for transforming the first decomposition into the second one, and therefore there is no violation of relativity.

 

[Fyzix]

Don't mind Dmitry67, he likes to see past things that doesn't fit his hypothesis.

Check out the link to the stanford entry I gave earlier in the paper explaining them problem.