Is MWI Self-Contradictory and Does Time Travel Need a New Approach?

[Dmitry67]

1. I need to think about Demystifier's argument before I reply.
2. Yes, it is obvious that I like MWI, like it is obvious that you hate it. But how does it change the facts and observations?

I talk about observations (post #69, item B), I ask you about wha is not in agreement with the observations? You reply in emotional manner about 'love' and 'hatred'. If your statement is refuted on page N, you simply repeat it on page N+1!

Right now science is telling us MWI can't make sense of Born Rule, thus must be wrong!

It was show in this thread that this logic is WRONG! There are many things science can't explain, but it does not make it "wrong". Demystifier had provided an example in post #20. Did it help?

 

[Fyzix]

No it was shown that his argument only works if you assume that consciousness is something special...
Your impossible to argue with...

 

[Dmitry67]

Shown by whom? Where?
Anyway, I am happy that at least you had abandoned the stuff with the 'picture of spacetime unzipping', 'clean and complete separation', 'problems with SR', so now your critics is focused solely on the Born rule.

 

[Dmitry67]

According to MWI, reality does not exist in the 4-dimensional spacetime, but in the infinite dimensional Hilbert space, or as a special case, in the many-dimensional configuration space of particle positions. It is this "weird" highly dimensional space on which MWI is local. But on this space, Bohmian mechanics is also local. Therefore, Bohmian mechanics is not less local than MWI.

Well, let's say it differently. In MWI, "reality" exist in Hilbert space, but it can be also 'mapped' into our physical 4D space (in a given basis). Such mapping can create multiple (almost) non-interacting 'branches', occupying the same physical space. If we can create a transformation from one to another, based on MUCH you can't say what is 'more' real. I hope you agree.

So while what you said is true in Hilbert space, in physical space all 'influences' are limited to the light cones. So MWI provides 'stronger' locality then BM, where 'particles' affect each other FTL in physical space.

Am I right?

 

[Hurkyl]

No, this doesn't work.
Remember it's the SAME person getting both balls.

No, it's the same person getting one ball. And the physical state is a probability distribution over two colors, rather than a definite choice of color.

(For reference, a probability distribution, in this case, means nothing beyond assigning a non-negative number to each color so that the numbers add to 1)

This is what the negation of definite outcomes means. (Well, technically, asserting the existence of a probability distribution over the outcomes is stronger than merely asserting there isn't a definite outcome)

 

[Hurkyl]

According to MWI, reality does not exist in the 4-dimensional spacetime, but in the infinite dimensional Hilbert space, or as a special case, in the many-dimensional configuration space of particle positions. It is this "weird" highly dimensional space on which MWI is local. But on this space, Bohmian mechanics is also local. Therefore, Bohmian mechanics is not less local than MWI.

No, he really meant local in the usual sense of Minkowski space. One can identify space-time by operators that relate to position in space-time, and the time-evolution really is locally realistic^*, at least assuming something resembling these axioms.

*: Defining "realistic" to mean that any physically meaningful calculation is completely determined by the quantum state. (Indefiniteness is a key here -- assuming definite outcomes would require a hidden variable to decide how to collapse)

 

[Demystifier]

Well, let's say it differently. In MWI, "reality" exist in Hilbert space, but it can be also 'mapped' into our physical 4D space (in a given basis). Such mapping can create multiple (almost) non-interacting 'branches', occupying the same physical space. If we can create a transformation from one to another, based on MUCH you can't say what is 'more' real. I hope you agree.

So while what you said is true in Hilbert space, in physical space all 'influences' are limited to the light cones. So MWI provides 'stronger' locality then BM, where 'particles' affect each other FTL in physical space.

Am I right?

I think you are only partially right. The crucial question is whether reality in the Hilbert space can be mapped into the 4D spacetime. It can, but only on the macroscopic level when decoherence takes place. In a more general context, there is nothing "physical" about the 4D spacetime that our intuition is used to. Thus, at the fundamental level, the 4D world does not exist in any meaningful sense, so the world cannot be local on that space.

By the way, when decoherence takes place, at the macroscopic level Bohmian mechanics can also be well approximated by classical local laws of motion. Thus, I can conclude again that BM is not less local than MWI.

 

[Demystifier]

No, he really meant local in the usual sense of Minkowski space. One can identify space-time by operators that relate to position in space-time, and the time-evolution really is locally realistic^*, at least assuming something resembling these axioms.

*: Defining "realistic" to mean that any physically meaningful calculation is completely determined by the quantum state. (Indefiniteness is a key here -- assuming definite outcomes would require a hidden variable to decide how to collapse)

I would say that this (more or less standard) view of quantum theory is NOT the many-world view of quantum theory. In particular, your definition of reality above, which may be fine by itself, is NOT the many-world definition of reality. In MWI spacetime is NOT identified with operators that relate to position in space-time. In MWI, operators do not exist in an ontological sense. Only wave functions do.

 

[Varon]

Something I don't quite get. When do branches get separated. Is it after what is equivalent to Collapse.. where instead of Collapse the branches split off and all real?

But before Collapse, the particles are in superposition, so what happens during superposition? Like are the branches active before collapse? If only after, then superposition prior to collapse is as mysterious as Copenhagen?

 

[Demystifier]

Varon, in MWI there is no collapse. The split is described by the Schrodinger equation itself, or more precisely by the theory of decoherence emerging from the Schrodinger equation.

 

[Varon]

Varon, in MWI there is no collapse. The split is described by the Schrodinger equation itself, or more precisely by the theory of decoherence emerging from the Schrodinger equation.

I know. But before split or decoherence, the system is in superposition.. What happens inside this superposition?

 

[Hurkyl]

Something I don't quite get. When do branches get separated. Is it after what is equivalent to Collapse.. where instead of Collapse the branches split off and all real?

But before Collapse, the particles are in superposition, so what happens during superposition? Like are the branches active before collapse? If only after, then superposition prior to collapse is as mysterious as Copenhagen?

Maybe it would help to see a mathematical example of how relative state works?

The simplest example, I think, is the quantum state of a qubit and the relative state of its "spin around the z axis".


The state space of a qubit can be described geometrically as the unit ball. The surface, called the Bloch sphere, is the space of pure states -- the ones you're most familiar with as being described by kets in a Hilbert space. For any unit vector v, the point on the sphere it describes represents the qubit state "spin-up along the v-axis".

In this geometric picture, (convex) linear combinations are interpreted in the sense of classical statistics. If P,Q are two points in the unit ball, then aP + bQ is the state that represents a statistical distribution of being in state P with probability a, and state Q with probability b.



The relative state "spin around the z axis" can also be represented geometrically as the interval [-1, 1]. The two endpoints 1 and -1 (the "surface" of the interval) represent "spin up" and "spin down" respectively.

The relationship between the two is the straightforward one: if (x,y,z) is the state of a qubit, then the state of its subsystem "spin around the z axis" is simply z.



Now, "spin around the z axis" is actually really, really simplistic -- it's actually a classical system, and even with a unique choice of 'basis' states! It's a particle that's in a statistical distribution over the possibilities "up" and "down". If we're studying this subsystem, it makes sense to call these two possibilities worlds.




Now, suppose the qubit starts at the North pole -- the state (0,0,1). Let's assume the qubit is a closed system. Time evolution, according to Schrödinger's equation, will move this state around the surface of the sphere -- the state is always a pure state! There are no worlds or anything, there is simply "which axis am I oriented around now?"

But, we might be interested in looking how the "spin around the z axis" subsystem behaves while all of this is happening. It starts off in the "up" state. But as time progresses, it slides back and forth in the interval. The state of this subsystem is (completely) described as being a weighted mixture of the two worlds "up" and "down", the specific weights depending on just where in the interval it is.


Other relevant things are that any operator (acting on the Hilbert space) in the {|z+>, |z->} basis can also be interpreted as acting on the "spin around the z axis" subsystem. e.g. any measurement operation can be described in terms of having some value on the "up" state, and some value on the "down" state, and that's all there is to it. If time evolution was diagonal in that basis, then the state of the "spin around the z axis" subsystem would evolve in a purely classical fashion. In this case it's a rather boring fashion, since "up" can only evolve to "up" and "down" can only evolve to "down", but in general it would be more interesting.

 

[Demystifier]

But before split or decoherence, the system is in superposition.. What happens inside this superposition?

Nothing which could be understood in classical terms. The cat is neither dead nor alive, etc. Fortunately, for macroscopic stuff decoherence is very very fast, so in practice such weird superpositions can never be seen. That's why it is hard to imagine the cat which is neither dead nor alive.

 

[Varon]

Nothing which could be understood in classical terms. The cat is neither dead nor alive, etc. Fortunately, for macroscopic stuff decoherence is very very fast, so in practice such weird superpositions can never be seen. That's why it is hard to imagine the cat which is neither dead nor alive.

So in Many worlds, superposition in one world still exist (before split or decoherence). So Many World Interpretation doesn't make it simplier. It only explains what happens after split or decoherence when branches become separate worlds, but not before. So you still have the mysterious superposition state in one world just like Copenhagen.

 

[Demystifier]

So in Many worlds, superposition in one world still exist (before split or decoherence). So Many World Interpretation doesn't make it simplier. It only explains what happens after split or decoherence when branches become separate worlds, but not before.

No, it describes very well what happens before in mathematical terms, but not in classical terms such as cats.

So you still have the mysterious superposition state in one world just like Copenhagen.

I don't think that superposition is mysterious for Copenhagen. What is mysterious for Copenhagen is how the superposition suddenly ceases to be a superposition. It says - by a measurement - but it does not specify what the measurement is.

 

[Varon]

No, it describes very well what happens before in mathematical terms, but not in classical terms such as cats.


I don't think that superposition is mysterious for Copenhagen. What is mysterious for Copenhagen is how the superposition suddenly ceases to be a superposition. It says - by a measurement - but it does not specify what the measurement is.

Superposition in Copenhagen is not mysterious? It is. Explain how one electron at a time double slit experiment can still interfere with itself. Somehow it becomes a wave in between emission and detection. Let's just focus on Copenhagen whose superposition I assume is similar to the superposition in Many worlds before split or decoherence. Let's avoid Bohmian, your specialization for now.

 

[Varon]

Maybe it would help to see a mathematical example of how relative state works?

The simplest example, I think, is the quantum state of a qubit and the relative state of its "spin around the z axis".


The state space of a qubit can be described geometrically as the unit ball. The surface, called the Bloch sphere, is the space of pure states -- the ones you're most familiar with as being described by kets in a Hilbert space. For any unit vector v, the point on the sphere it describes represents the qubit state "spin-up along the v-axis".

In this geometric picture, (convex) linear combinations are interpreted in the sense of classical statistics. If P,Q are two points in the unit ball, then aP + bQ is the state that represents a statistical distribution of being in state P with probability a, and state Q with probability b.



The relative state "spin around the z axis" can also be represented geometrically as the interval [-1, 1]. The two endpoints 1 and -1 (the "surface" of the interval) represent "spin up" and "spin down" respectively.

The relationship between the two is the straightforward one: if (x,y,z) is the state of a qubit, then the state of its subsystem "spin around the z axis" is simply z.



Now, "spin around the z axis" is actually really, really simplistic -- it's actually a classical system, and even with a unique choice of 'basis' states! It's a particle that's in a statistical distribution over the possibilities "up" and "down". If we're studying this subsystem, it makes sense to call these two possibilities worlds.




Now, suppose the qubit starts at the North pole -- the state (0,0,1). Let's assume the qubit is a closed system. Time evolution, according to Schrödinger's equation, will move this state around the surface of the sphere -- the state is always a pure state! There are no worlds or anything, there is simply "which axis am I oriented around now?"

But, we might be interested in looking how the "spin around the z axis" subsystem behaves while all of this is happening. It starts off in the "up" state. But as time progresses, it slides back and forth in the interval. The state of this subsystem is (completely) described as being a weighted mixture of the two worlds "up" and "down", the specific weights depending on just where in the interval it is.


Other relevant things are that any operator (acting on the Hilbert space) in the {|z+>, |z->} basis can also be interpreted as acting on the "spin around the z axis" subsystem. e.g. any measurement operation can be described in terms of having some value on the "up" state, and some value on the "down" state, and that's all there is to it. If time evolution was diagonal in that basis, then the state of the "spin around the z axis" subsystem would evolve in a purely classical fashion. In this case it's a rather boring fashion, since "up" can only evolve to "up" and "down" can only evolve to "down", but in general it would be more interesting.

Thanks. I'll analyse it sometime after I learned all the maths (so don't make it quite complicated). For now. I just wanted to know if the superposition before split or decoherence in Many Worlds has the same ontology as the superposition of Copenhagen before collapse. I'll explain. Bohr stated that in the absence of measurement to determine position, there is no position. In Many worlds before split or decoherence, does a particle also has no position or does the wave function contain multiple copies of the particles (prior to split or decoherence)?

 

[Demystifier]

Superposition in Copenhagen is not mysterious? It is. Explain how one electron at a time double slit experiment can still interfere with itself. Somehow it becomes a wave in between emission and detection. Let's just focus on Copenhagen whose superposition I assume is similar to the superposition in Many worlds before split or decoherence. Let's avoid Bohmian, your specialization for now.

That's easy. Electron is a wave, so nothing is easier than to interfere with itself. Nothing mysterious.

 

[Demystifier]

In Many worlds before split or decoherence, does a particle also has no position or does the wave function contain multiple copies of the particles (prior to split or decoherence)?

In MWI there are no particles at all. Only waves.

 

[Varon]

In MWI there are no particles at all. Only waves.

If that's true. How come the detector can detect particles if only waves exist?

Anyway. I just read that in a doublet slit experiment in Many Worlds. When an electron is emitted, the electron splits immediately where one goes to the upper slit in one world, the second goes to the lower slit in the other world. And interferences is due to superposition of universes (whatever this means). So when you said only waves are present, this is what propel the electron to their respective places in each universe that can interfere in the screen, isn't it.

I wonder if what I just mentioned is a Dewitt version or original Everett version (not likely). How do you create an Everett version out of the double slit experiment?

 

[Demystifier]

If that's true. How come the detector can detect particles if only waves exist?

According to MWI, detector does not detect particles. It detects localized waves, which people like to call "particles". The localization itself is described and explained by decoherence.

 

[Varon]

According to MWI, detector does not detect particles. It detects localized waves, which people like to call "particles". The localization itself is described and explained by decoherence.

You are kidding right?

In Many worlds. I have never heard it stated that particles are localized waves (shades of Schroedinger). In MWI. Particles exist at all times.. only duplicated during split or after decoherence. What version MWI are you talking about anyway?

 

[Demystifier]

You are kidding right?

In Many worlds. I have never heard it stated that particles are localized waves (shades of Schroedinger). In MWI. Particles exist at all times.. only duplicated during split or after decoherence. What version MWI are you talking about anyway?

I believe you have seriously misunderstood something about MWI.

 

[Varon]

I believe you have seriously misunderstood something about MWI.

Ok. I'll re-read the books about it. Maybe it is because it's called a Universal
Wavefunction... but we clearly have particles... so what happened to the particles inside the wavefunction. If the wavefunction is the particle. So I am a wave function? I'll consider you not kidding. Anyway. I'll look into it.

 

[Dmitry67]

Absolutely serious.
Photon wave hits 10 megapixel digital camera matrix. It decoheres into 10 millions of states where only one cell is affected. This is what we call a 'photon'

 

[Varon]

According to MWI, detector does not detect particles. It detects localized waves, which people like to call "particles". The localization itself is described and explained by decoherence.

Ok. After preferred basis chosen, one of the eigenvalues corresponds to our world. Here an electron is a wave. We are told an electron is a point particle. So in the MWI counterpart, what is the length of the Universal Wavefunction wavelength corresponding to the electron?

 

[Varon]

Absolutely serious.
Photon wave hits 10 megapixel digital camera matrix. It decoheres into 10 millions of states where only one cell is affected. This is what we call a 'photon'

In Copenhagen, collapse chooses one of the eigenvalues which becomes a particle.

In Many worlds, after decoherence and basis chosen, one of the eigenvalues correspond to our world.

In both cases, one of the eigenvalues is chosen.

This means Copenhagen and Many worlds are equivalent in one of the eigenvalues chosen. So how come is one call a particle, the other a wave. Maybe a particle in Copenhagen is also a localize wave just like in Many Worlds?

Anyway. What is the length of the wavelenth corresponding to one of the eigenvalues in Many worlds and Copenhagen?

 

[Dmitry67]

In both cases, one of the eigenvalues is chosen.

No.
In MWI, there is a symmery between all outcomes (ignoring their probability or, how it is better to be called in MWI, "intensity of existence")
ALL outcomes exist.
This is very important.
No specific outcome is "chosen"

However, as observers remember only the past, not the future, and as they effectively lose an ability to 'communicate' with the 'other branches', all observers (in every branch) have an illusion, they 'their' outcome is the only one which exist.

 

[Dmitry67]

Ok. After preferred basis chosen, one of the eigenvalues corresponds to our world. Here an electron is a wave. We are told an electron is a point particle. So in the MWI counterpart, what is the length of the Universal Wavefunction wavelength corresponding to the electron?

The same as in QM.
MWI is a 'pure' QM - MWI does not have any additional assumptions, on the contrary, it is a claim that no additional assumptions are needed.

 

[Varon]

No.
In MWI, there is a symmery between all outcomes (ignoring their probability or, how it is better to be called in MWI, "intensity of existence")
ALL outcomes exist.
This is very important.
No specific outcome is "chosen"

However, as observers remember only the past, not the future, and as they effectively lose an ability to 'communicate' with the 'other branches', all observers (in every branch) have an illusion, they 'their' outcome is the only one which exist.

I know. It's just a bad choice of words when I said one of the eigenvalues is chosen. What I meant was our branch only experience one of the eigenvalues and all outcomes exist. Since all are wave, I'm asking what is the wavelength of the particle in this sense. So it's the same de Broglie wavelength? But this is based on wavelengh = h/momentum. Is there another formula that only inputs the particle existence without regards to momentum?

 

[Varon]

If Many worlds has only wave function and no particles. Why didn't Schroedinger discovered it? He spent a lifetime believing only wavefunction exist, what makes him fail to propose the Many worlds where there are only waves?

Back in the 1920s when Schroedinger thought it's all waves and no particles. Henrik Lorentz made him realized that wavepacket spreads. Lorentz told Schroedinger "Wave packet will spread with time and your idea of representing particles completely in terms of the superposition of waves is invalid"

Now what I want to know is how is this wave packet spreading related to one of the eigenvalues (let's avoid Many worlds in this question to avoid complication).

 

[Dmitry67]

I know. It's just a bad choice of words when I said one of the eigenvalues is chosen. What I meant was our branch only experience one of the eigenvalues and all outcomes exist. Since all are wave, I'm asking what is the wavelength of the particle in this sense. So it's the same de Broglie wavelength? But this is based on wavelengh = h/momentum. Is there another formula that only inputs the particle existence without regards to momentum?

Why do you think that it should be different in MWI from what QM tells us? Note that the wavelength of particle has nothing to do with how small detector can be. For example, famous 21cm hydrogen line can excite hydgogen atoms which are 10-8cm in size. If we have a 'matrix' with step of 0.001cm, made of such atoms, we would see a 0.000001cm^2 'dot', created by 21cm lightwave (these results will be true in any Int, of course).

 

[Dmitry67]

If Many worlds has only wave function and no particles. Why didn't Schroedinger discovered it? He spent a lifetime believing only wavefunction exist, what makes him fail to propose the Many worlds where there are only waves?

Back in the 1920s when Schroedinger thought it's all waves and no particles. Henrik Lorentz made him realized that wavepacket spreads. Lorentz told Schroedinger "Wave packet will spread with time and your idea of representing particles completely in terms of the superposition of waves is invalid"

Now what I want to know is how is this wave packet spreading related to one of the eigenvalues (let's avoid Many worlds in this question to avoid complication).

I think there were 2 major reasons.
1. The idea was too crazy - they already had enough crazyness to deal with;
2. In the beginning of 20th century, there was a gap separating macro and micro, huge gap separating 'measurement devices' from QM. So there was a hope that QM weirdness would somehow 'fade' when approaching the macroscopic scale. Like how Bohr showed earlier in his model how Qm levels in atom transform into continuum of states on bigger scales.

 

[Varon]

I think there were 2 major reasons.
1. The idea was too crazy - they already had enough crazyness to deal with;
2. In the beginning of 20th century, there was a gap separating macro and micro, huge gap separating 'measurement devices' from QM. So there was a hope that QM weirdness would somehow 'fade' when approaching the macroscopic scale. Like how Bohr showed earlier in his model how Qm levels in atom transform into continuum of states on bigger scales.

You prefer MWI because of the collapse postulate seems to make the deterministic wave function inconsistent. It is not. Here comes the magic of the observers (either particles sensing other particles or bigger environment or system). It has got to do with Information Theory and information exchange between the quantum. This is actually quite elegant. Fra has even formulated almost a complete theory of it. Try it before delving into the MWI schizophenia. What's your criticism of Fra appraoch? (Note: Fra is the one without the Wolverine icon)

 

[Demystifier]

Maybe a particle in Copenhagen is also a localize wave just like in Many Worlds?

Yes. In fact, the only (relatively well-known) interpretation of QM in which "particles" really are particles - is the Bohmian interpretation.