Postulates of many worlds interpretation of QM

[Dmitry67]

Ilja,

1. Sure, there are as many different decompositions as observers.
2. You should define what means 'physically different'. And this part is slippery. I don't find it in your paper. What I mean, it is not enough to say that 'physics is different'. Of course it is different

An it is not something new: as I learned, the number of gluons in proton depends on the scale, and Unruh effects shows that even the particle content of macroscopic events is different in different frames.

What you need to show is that the 'different physics' are different macroscopically in the same branch. Note that the very notion of a 'branch' is decomposition-dependent, so it is absolutely not clear how you can 'compare' different physics.

Again, it is not enough to show that physics is 'different'. You need to show that it is INCONSISTENT. For example, looking the same same object from different angles you see a different picture but it is ok.

Here is a well-known example: http://en.wikipedia.org/wiki/Wigner's_friend
In 2 different basis (inner and outer observer) the events are different. Inner observer is decoherenced immediately, so for the inner observer cat is dead OR alive, while for the outer observer (in his basis) the cat (and the inner observer) are in the superposition.

 

[Ilja]

1. Sure, there are as many different decompositions as observers.

If there is some equivalence, explain. For every observer a decomposition? How, in this case, is the observer defined? For every decomposition an observer? In this case, is the Earth an observer?

As I understand the situation, it is completely different. One postulates that there is some decomposition of the universe into systems. Then one starts with this decomposition, applies decoherence, and after this we obtain some decoherence-preferred basis which allows to define everything else, in particular observers.

2. You should define what means 'physically different'. And this part is slippery. I don't find it in your paper. What I mean, it is not enough to say that 'physics is different'. Of course it is different

For defining what is physically different I simply rely on the standard shut up and calculate interpretation, and I have presented an experiment which gives, in this interpretation, different physical predictions.

An it is not something new: as I learned, the number of gluons in proton depends on the scale, and Unruh effects shows that even the particle content of macroscopic events is different in different frames.

Of course the theory of the KdV equation is nothing new, it is already quite old. But what do your examples have to do with my argument? I have not got the point. In relativity, the effects for different observers follow the same physical laws. This is the content of various equivalence principles. In my situation, where is no such equivalence principle. The physical Hamiltonian (as expressed in terms of p and q) for different decompositions is different.

What you need to show is that the 'different physics' are different macroscopically in the same branch. Note that the very notion of a 'branch' is decomposition-dependent, so it is absolutely not clear how you can 'compare' different physics.

I don't have to care about branches. To show that the physics is different for different decompositions, different physics in the shut up and calculate interpretation is sufficient. You can choose: Or MWI agrees with shut up and calculate or not. That choice is not my problem. As well, it is not my problem how to prove which choice is correct. In the first case, my consideration is sufficient, in the second, MWI will be ruled out empirically, because it is shut up and calculate which is used in calculations, and which is empirically successful.

Again, it is not enough to show that physics is 'different'. You need to show that it is INCONSISTENT. For example, looking the same same object from different angles you see a different picture but it is ok.

In standard quantum theory, the p and q operators are part of the definition of the theory. They are not observer-dependent. Using different operators H=H(p,q) means different physics.

I have given an argument in the paper why the "many worlds solution" of this does not work. The alternative Hamilton operators do not have the symmetries of the operators we postulate, like p_i^2+\sum 1/|q_i-q_j|. If we would be in a typical of the many physically different worlds, our world would be less symmetric.

Here is a well-known example: http://en.wikipedia.org/wiki/Wigner's_friend
In 2 different basis (inner and outer observer) the events are different. Inner observer is decoherenced immediately, so for the inner observer cat is dead OR alive, while for the outer observer (in his basis) the cat (and the inner observer) are in the superposition.

It seems this difference is on a completely different level.

 

[Dmitry67]

1
If there is some equivalence, explain. For every observer a decomposition? How, in this case, is the observer defined? For every decomposition an observer? In this case, is the Earth an observer?

2
As I understand the situation, it is completely different. One postulates that there is some decomposition of the universe into systems. Then one starts with this decomposition, applies decoherence, and after this we obtain some decoherence-preferred basis which allows to define everything else, in particular observers.

3
For defining what is physically different I simply rely on the standard shut up and calculate interpretation, and I have presented an experiment which gives, in this interpretation, different physical predictions.

4
I don't have to care about branches.

1
An observer is defined based on the question asked.
"I am going to see a dead or alive cat?" defines YOU as an observer, and a CAT
The very need for a Decoherence starts from the question. You can not ask any question bout physics without already making some sorts of decompositions - into you, cat, moon, earth, accelerator etc.

2
Correct, we get some results for the given basis. But this basis is not special in any way. We can chose any other basis based on our needs.

3
But of course it gives! It is like in CI where wavefunction is just a 'knowledge' so different observers can get different values for all operators. In the example with Wigners friend, there are different results: for multiple copies of the already-decoherenced observer and for the distant not-decoherenced observer.

4
You can't talk about MWI ignoring the branches.
As events in different branches are different then of course they MUST have different physics, and of course before an observer is decoherenced with an observable his pre-calculated (based on his previous knowledge) values of p, r etc should not agree with the values observed by the decoherenced observer!

However note that p, r are not observables until you get decoherenced with a system. If I pre-calculate them in advance based on the system setup (the system itself can be in Andromeda) is a one thing, but MEASURE a position (hence beging decoherenced = forced to 'chose' one branch) is another thing.

In that sense pre-calculated values based on the knowledge in MWI is almost CI-like - a non-physical thing, calculated based on the 'knowledge'. So different observers should not automatically agree on it.

 

[Fra]

Fra, I am trying to understand your question.

I knew that guy would eventually get someone to confuse the two of us by ending all his posts with "/Fredrik".

Sorry for the confusion here :) My actual first name is Fredrik which is the simple reason I have it as my sig. [ Why I do that? I guess I've always done that. I do it it emails and in general, it's a long story that began way back (before my time on this forum). It's just an old habit I have, that I rarely think about. Some people have long quotes or links to their fave website in their signatures - I simply use a slash followed by my actual first name as s sort of code for "end of message". ]

Given that I had some slight discussions with Dmitry67 in some other threads, I could imagine the resulted confusion :)

/Fredrik

 

[Fra]

Not to mention that user=Fredrik is a superhero, user=Fra is a yeast cell :)

/Fredrik

 

[Dmitry67]

Yes, sorry for the confusion :)

 

[Count Iblis]

About Fredrik/Fra, see also here:

https://www.physicsforums.com/showthread.php?t=310098

 

[Fredrik]

Sorry for the confusion here :) My actual first name is Fredrik which is the simple reason I have it as my sig.

No problem. It's a common name (in Sweden). By the way, I didn't mean to sound upset about it. (I'm not).

Back on topic... I read Hartle's paper. It contains some good stuff, and is definitely an interesting read, but he's assuming that if the states of a system are represented by the rays of a Hilbert space H, and you combine several such systems into a larger system, then the Hilbert space of the larger system is the tensor product H¤...¤H. He offers no justification for this. So his derivation of the Born rule has the same problem as everyone else's. (See #27).

Also, he doesn't mention the MWI at all. In fact, he spends half the paper arguing that states are not objective properties of systems. This is of course less relevant. If he had been able to derive the Born rule without assuming that we should use tensor products, it would have been very relevant for the MWI, regardless of whether he says it is.

Not to mention that user=Fredrik is a superhero,...

You just made me picture myself in spandex and a cape...it wasn't pretty.

 

[Ilja]

1
An observer is defined based on the question asked.
"I am going to see a dead or alive cat?" defines YOU as an observer, and a CAT
The very need for a Decoherence starts from the question. You can not ask any question bout physics without already making some sorts of decompositions - into you, cat, moon, earth, accelerator etc.

Sorry, but I don't follow. I exist independent of the questions I ask. I can ask a lot of different questions, but these questions do not define me. Not even metaphorically. If your point of view would be true, it would be one more reason to object against its use of various notions as confusing, but in this case MWI seems innocent, and it seems to be your personal confusion.

2
Correct, we get some results for the given basis. But this basis is not special in any way. We can chose any other basis based on our needs.

That's also not the standard understanding of MWI. Instead, MWI people have tried a lot to get some preferred basis (this problem is known as the preferred basis problem, and they were very happy finding that decoherence can give them a preferred basis. Unfortunately, it cannot give a preferred basis, because it depends on the decomposition into systems.

3
But of course it gives! It is like in CI where wavefunction is just a 'knowledge' so different observers can get different values for all operators. In the example with Wigners friend, there are different results: for multiple copies of the already-decoherenced observer and for the distant not-decoherenced observer.

The question is not if different observers see different things. This is so even in classical physics and was known already in Ancient Greece. Different physics means that for the same experiment, observed by the same observer, we obtain different statistics of measurement results. That means different Born rule distributions.

4
You can't talk about MWI ignoring the branches.
As events in different branches are different then of course they MUST have different physics, and of course before an observer is decoherenced with an observable his pre-calculated (based on his previous knowledge) values of p, r etc should not agree with the values observed by the decoherenced observer!

Different physics means different laws of physics, leading to different predictions about probabilities of measurement outcomes. And, again, regarding the probabilistic measurement outcomes I'm talking about the shut up and calculate interpretation. I don't see that talking about branches and MWI gives in any way the Born distributions, therefore I'm not talking about branches. But because I don't plan to prove that it is really impossible in MWI to obtain somehow the Born rule, I can accept, for the purpose of the argument, that MWI can recover somehow the shut up and calculate predictions based on the Born rule.

However note that p, r are not observables until you get decoherenced with a system. If I pre-calculate them in advance based on the system setup (the system itself can be in Andromeda) is a one thing, but MEASURE a position (hence beging decoherenced = forced to 'chose' one branch) is another thing.

I disagree. The observables are (and have to be) well-defined without decoherence - they are self-adjoint operators, and such self-adjoint operators are defined once the Hilbert space is defined. In particular, the Hamilton operator is well-defined without any decoherence. What decoherence can do (given the decomposition into systems) is to make a choice among the preexisting observables - it prefers some subset of observables as especially easy to measure - the decoherence-preferred observables. The other observables remain observable, but measuring them does not give much, because interaction of the measured system with the environment changes the state in short time, and after this the information you have obtained during your measurement is of not much value.

Then, decoherence has nothing to do with some force to choose a branch. There is no such force, and decoherence does not lead to such a force. All what decoherence does is to define, for a given decomposition into systems, a preferred q-like basis, something which is a necessary prerequisite for the definition of the branches.

 

[atyy]

You just made me picture myself in spandex and a cape...it wasn't pretty.

Wolverine has a cape

 

[Dmitry67]

1
That's also not the standard understanding of MWI. Instead, MWI people have tried a lot to get some preferred basis (this problem is known as the preferred basis problem, and they were very happy finding that decoherence can give them a preferred basis. Unfortunately, it cannot give a preferred basis, because it depends on the decomposition into systems.

2
The question is not if different observers see different things. Different physics means that for the same experiment, observed by the same observer, we obtain different statistics of measurement results. That means different Born rule distributions.

3
I disagree. The observables are (and have to be) well-defined without decoherence - they are self-adjoint operators, and such self-adjoint operators are defined once the Hilbert space is defined. In particular, the Hamilton operator is well-defined without any decoherence.

1,2
Well, may be I am really believe in a slightly different flavor or MWI?
For me it was absolutely obvious that you can't discuss 'what X is observing' without using X as 'preferred basis'. And you can't use any other basis if you are discussing X's impressions of the world. Hence your argument is valid for those whole believe in some 'preferred basis' (for me it is a nonsense) but in my flavor of MWI there is no paradox, because you are not free in chosing the basis.

Wiki article states that the choice of basis is arbitrary. Do you have any links about 'how standard MWI defines a preferred basis'?

3
This is what was called an observable in good old QM which did not include measurement. But you can't 'observe' it, it is just a mathematical operatior. You can observe an arrow of a voltmeter. The only true observables are the macroscopic events. Only thermodynamically irreversible events can be remembered (as memory is irreversible by definition) and hence be a part of your consciousness, hence, a particle must be irreversibly absorbed in order to say something about p, r etc.

But of course, you can calculate the result of these operators based on your knowledge about the wavefunction, but you don't know exactly your branch and wavefunction, so you should not be surprised that different observers get different results.

 

[Ilja]

1,2
Well, may be I am really believe in a slightly different flavor or MWI?
For me it was absolutely obvious that you can't discuss 'what X is observing' without using X as 'preferred basis'. And you can't use any other basis if you are discussing X's impressions of the world. Hence your argument is valid for those whole believe in some 'preferred basis' (for me it is a nonsense) but in my flavor of MWI there is no paradox, because you are not free in chosing the basis.

Wiki article states that the choice of basis is arbitrary. Do you have any links about 'how standard MWI defines a preferred basis'?

I take Wallace and Zurek as the writers which explain MWI in the best way. I have no links, but use arxiv.org search for Zurek or Wallace on quant-ph, and you will find among them what are the IMHO best articles about MWI.

But this is only a personal opinion, and, as you can judge from the style of my papers, I try to avoid mentioning details of MWI. The reason is that my picture of MWI does not really make sense, at least I'm unable to understand how one can take MWI (given in my understanding) seriously. Because this may be the flaw of my understanding of MWI, I prefer to be careful. Here I can be a little less careful, I think.

About the preferred basis: If there exists a preferred basis, one is, of course, not free to choose one, but has to use the preferred one. If you don't want a preferred basis, you end up with (in)consistent histories, which is even worse, because it is a rejection of classical logic without necessity.

The main problem with your scheme - an observer defining a decomposition of the universe, and, then, consequently a preferred basis by decoherence - is that no such standard decomposition exists, because there are states of the universe without me, but no states of a decomposition of the universe without a state of all the subsystems. Such a decomposition makes sense only in some environment of the actual state of universe, described not by the state vector, but by some branch in MWI jargon. Thus, all this looks heavily circular.

This is what was called an observable in good old QM which did not include measurement. But you can't 'observe' it, it is just a mathematical operatior. You can observe an arrow of a voltmeter. The only true observables are the macroscopic events. Only thermodynamically irreversible events can be remembered (as memory is irreversible by definition) and hence be a part of your consciousness, hence, a particle must be irreversibly absorbed in order to say something about p, r etc.

I disagree that only decoherence-preferred observables are observable. There may be operators which are not observable - those with macroscopic superpositions as eigenstates. But in pure quantum theory we can measure lot's of different operators, for sufficiently small ones you can even measure every operator, not only the decoherence-preferred ones (as far as this notion makes sense for small pure quantum systems), because decoherence needs some time, is only an approximate mechanism.

 

[Fredrik]

The main problem with your scheme - an observer defining a decomposition of the universe,

That choice of words makes the problem with that scheme pretty clear. A "decomposition of the universe" is a way to express the Hilbert space of states of the universe as a tensor product: \mathcal H=\mathcal H_1\otimes\mathcal H_2. But the "observer" here is the physical system with Hilbert space \mathcal H_2. So to say that the observer defines the decomposition is essentially the same thing as saying that \mathcal H_2 defines \mathcal H_2, and that doesn't really say anything.

 

[Dmitry67]

1
If you don't want a preferred basis, you end up with (in)consistent histories, which is even worse, because it is a rejection of classical logic without necessity.

2
The main problem with your scheme - an observer defining a decomposition of the universe, and, then, consequently a preferred basis by decoherence - is that no such standard decomposition exists, because there are states of the universe without me, but no states of a decomposition of the universe without a state of all the subsystems.

3
I disagree that only decoherence-preferred observables are observable. There may be operators which are not observable - those with macroscopic superpositions as eigenstates. But in pure quantum theory we can measure lot's of different operators, for sufficiently small ones you can even measure every operator, not only the decoherence-preferred ones (as far as this notion makes sense for small pure quantum systems), because decoherence needs some time, is only an approximate mechanism.

1
Again, it is possible (and very likely) that in act different observers do not agree on what you call an 'observables', and even on the number of the elementary particles, but they Do agree ont he microscopic events. Unruh effect is a good example

2
in the Universe without YOU there is no need to calculate a decoherence in some basis at all: you can be satisfied with a unitary evolution of the 'universe' wavefunction.

3
Note the words I highlighted
So, you do not get the values of these 'observables' directly.
At first, you must decoherence your system (or a particle) with some macroscopic device, right?

 

[Ilja]

That choice of words makes the problem with that scheme pretty clear. A "decomposition of the universe" is a way to express the Hilbert space of states of the universe as a tensor product: \mathcal H=\mathcal H_1\otimes\mathcal H_2. But the "observer" here is the physical system with Hilbert space \mathcal H_2. So to say that the observer defines the decomposition is essentially the same thing as saying that \mathcal H_2 defines \mathcal H_2, and that doesn't really say anything.

My problem with this is not that it is in some sense tautological. In \mathcal H=\mathcal H_1\otimes\mathcal H_2 the "observer" is always in some state. But what is my state if the wave function is localized around a state of the universe where the Earth does not exist? It could be, at best, something like the state of my immortal soul or so.

 

[Ilja]

Again, it is possible (and very likely) that in act different observers do not agree on what you call an 'observables', and even on the number of the elementary particles, but they Do agree on the microscopic events. Unruh effect is a good example

In standard semiclassical gravity they can agree about the observables as well as in classical relativity, where everybody agrees about the showings of a traveling clock from A to B along a given trajectory.

One can associate some observables with some observers, but this association is quite arbitrary. If one considers a particle detector in some state of movement, say, along a given trajectory, the prediction about the resulting average particle numbers measured by this detector is unique, well-defined.

in the Universe without YOU there is no need to calculate a decoherence in some basis at all: you can be satisfied with a unitary evolution of the 'universe' wavefunction.

You have not got the point. The wave function is a function on the space of all possible universes. From this birds view there are only particular branches with or without me, the multiverse is not with or without me.

Now I have a wave function, and want to know what I can expect to observe. How does this work? You would like to look at branches which contain me. But the branches are simply not defined before decoherence has finished its job. You need decoherence to define the branches. To define decoherence, you need a decomposition into systems. This decomposition into systems has to be defined on the full Hilbert space, the one which contains all these superpositions of something close to our own branch (better, what becomes our own branch, everything else appropriately defined) to something where Earth does not exist.

The "decomposition into systems" means some H=H_{rest}\otimes H_{obs}. Then, every basic state (branch) is a product \psi=\psi_{rest}\psi_{obs}. What is \psi_{obs} supposed to describe if the Earth does not exist? H_{obs} is always the same, independent of the question if \psi_{rest} describes a state where the Earth exists or not.

Note the words I highlighted
So, you do not get the values of these 'observables' directly.
At first, you must decoherence your system (or a particle) with some macroscopic device, right?

If you want to talk about the standard applications of decoherence outside many worlds, no problem. You have some classical Copenhagen part of the world, and this part defines nicely a decomposition into various systems, in part classical, in part quantum. The observer is, in this case, classical, thus, fixed at every moment of time. States where the Earth does not exist are simply not part of such considerations.

MWI has the problem how to obtain all this background in a consistent way. It cannot start with me or some other systems here on Earth to define a decomposition into systems to start decoherence, because these systems are only defined in some small subset of the small part of the multiverse which contains our Earth.

Now about the usual way to apply decoherence: I measure what I like, by rotating variouos devices in various ways. If the measurement device is rotated in one way, the decoherence-preferred observable is, say, S₁, if it is rotated in another way it may be something different, S₂. Thus, for small quantum systems all quantum observables may appear observable, one simply has to use some appropriate environment, with appropriately rotated devices, where it appears decoherence-preferred.

 

[Count Iblis]

I don't understand the arguments about decoherence being necessary to define observers. Suppose you have a quantum computer that can implement internal observers. I.e. observers are computer programs that can observe their virtual world. Then one can always project out the sectors of the individual programs to compute the probabilities of what they observe.

Here you do have a definiton of each program in some standard basis and you can argue that you could map arbitrary states to computational states of any program. This problem also exist in purely classical models. You can always invent a mapping from the states of one physical system (say a gas) to another system (say a brain). Then the reason why a gas in a container is not conscious is presumably because what matters is the program the brain is running. The mapping from the gas to the brain would contain all the nontrivial aspects of that program.

This then suggests that observers would always have to be defined as algorithms.

 

[Dmitry67]

Ilja,
I understand what you are saying now and I agree - yes, it is a little bit recursive. While I am thinking about "what is a probability in MWI" I can give you a short answer. Just to explain, why I am not worrying about that recursion.

Yes, you exist only in some subset of branches. We don't have a formal definition of a human, or an observer, that notion is fuzzy. Hence, we can't define what branches you 'occupy' precisely. It is even possible that some deep things like 'what is an observation?' can be explained only it very high level terms which require a definition of consciousness. Yes, I have to admit that everything fuzzy, recursive and observer-dependent. The way Fra likes it :)

Why I am still optimistic?

In MWI the only and ultimate reality is the global wavefunction. And our 'sense of reality' is just an illusion. There is no classical behavior at all, it is one of the biggest illusions we have.

For that reason I do not really care about the problem with the 'preferred basis', because basis and decoherence are not needed to define physical laws or reality - they are just needed to explain the illusion a particular frog has.

For that very reason I am sure that all frogs impressions are consistent - because frogs impression is just a mapping of the bird's view using some basis. And when we map the same thing we always get the consistent partial views. To repeat, decoherence does not explain the reality, it explains an illusion

Even may be MWI requires a definition of an observer and may be even consiousness to explain all the observations, it is much much better then CI because CI uses these high level things (like 'knowledge of an observer') to explain the microscopic world, while MWI uses it to explain only high level things, so it might require a definition of consciousness to explain, what we 'feel', but we don't need all that stuff in the microscopic world.

But I have to agree with you, there are some deep questions in MWI which are not clear right now.

 

[Ilja]

I don't understand the arguments about decoherence being necessary to define observers. Suppose you have a quantum computer that can implement internal observers. I.e. observers are computer programs that can observe their virtual world. Then one can always project out the sectors of the individual programs to compute the probabilities of what they observe.

Here you do have a definiton of each program in some standard basis and you can argue that you could map arbitrary states to computational states of any program. This problem also exist in purely classical models. You can always invent a mapping from the states of one physical system (say a gas) to another system (say a brain). Then the reason why a gas in a container is not conscious is presumably because what matters is the program the brain is running. The mapping from the gas to the brain would contain all the nontrivial aspects of that program.

This then suggests that observers would always have to be defined as algorithms.

That's the way Wallace explains how MWI works. There are no observers in general, but the notion of an observer is derived, follows from decoeherence, appear only in the classical limit, as some emergent subjects. It's not me who has invented this, it is the (IMHO wrong) idea of the many worlders that they can derive everything from the wave function taken alone.

About quantum programs able to observe something none-classical I don't even want to speculate in a forum. I don't know enough about them.

 

[Ilja]

Yes, I have to admit that everything fuzzy, recursive and observer-dependent. The way Fra likes it :)

Why I am still optimistic?

In MWI the only and ultimate reality is the global wavefunction. And our 'sense of reality' is just an illusion. There is no classical behavior at all, it is one of the biggest illusions we have.

For that reason I do not really care about the problem with the 'preferred basis', because basis and decoherence are not needed to define physical laws or reality - they are just needed to explain the illusion a particular frog has.

Sorry, but I could not resist to transform this argument into a theological one:

Yes, I have to admit that everything fuzzy.

Why I am still optimistic?

In religion the only and ultimate reality is God. And our 'sense of reality' is just an illusion. There is no classical behavior at all, it is one of the biggest illusions we have.

For that reason I do not really care about the problem with human reality, because human reality is not needed to define Gods laws or Gods reality - they are just needed to explain the illusion a particular frog has.

For that very reason I am sure that all frogs impressions are consistent - because frogs impression is just a mapping of the bird's view using some basis.

They are inconsistent with each other - the inconsistent histories interpretation uses an explicit consistency condition to define consistent parts of it. For some given preferred basis, they become consistent, this is why MWI needs one preferred, and not some.

And when we map the same thing we always get the consistent partial views. To repeat, decoherence does not explain the reality, it explains an illusion

The shadows on the wall seen by Plato's prisoners are real shadows. Because they follow from the really existing objects, the really existing source of light, and the really existing wall. Naming them illusion explains nothing. An explanation has to describe how the illusion emerges, in a logically consistent way.

Even may be MWI requires a definition of an observer and may be even consiousness to explain all the observations, it is much much better then CI because CI uses these high level things (like 'knowledge of an observer') to explain the microscopic world, while MWI uses it to explain only high level things, so it might require a definition of consciousness to explain, what we 'feel', but we don't need all that stuff in the microscopic world.

CI uses high level things, but gets the real answers. MWI has yet to show that it gets them. With my counterexample, the job of the many worlders becomes (I think) much harder. I think I have shown that MWI needs some additional structure to fix the physics, thus, to become equivalent as a physical theory to QM.

I have today received the journal ref:

Found Phys (2009) 39: 486–498
DOI 10.1007/s10701-009-9299-4
Why the Hamilton Operator Alone Is not Enough
I. Schmelzer

 

[Dmitry67]

The shadows on the wall seen by Plato's prisoners are real shadows. Because they follow from the really existing objects, the really existing source of light, and the really existing wall. Naming them illusion explains nothing. An explanation has to describe how the illusion emerges, in a logically consistent way.

This is a good example. Yes, shadows on the wall. And it is not well defined what is a wall. And these walls are not flat. And to analyze their shape, we use the shadows.

BTW, returning to the 'observables' which are not obserables at all: can you see elementary particles with your naked eye? You do you use some devices to get values of these 'observables'?

 

[Ilja]

BTW, returning to the 'observables' which are not obserables at all: can you see elementary particles with your naked eye? You do you use some devices to get values of these 'observables'?

I don't - I'm a pure theorists. Your point being? Of course one has to use devices. My argument was that for pure quantum systems one can use very different devices measuring very different observables, in simple cases all of them. Without any contradiction with decoherence.

 

[Dmitry67]

I don't - I'm a pure theorists. Your point being? Of course one has to use devices. My argument was that for pure quantum systems one can use very different devices measuring very different observables, in simple cases all of them. Without any contradiction with decoherence.

My point is that you can't observe them. You can read some numbers from your device. Hence you never get the true value of your 'observable', but just a result of a decoherence of a particle or other QM system with a measurement device. Again, you can never get values of p, r DIRECTLY.

 

[Ilja]

My point is that you can't observe them. You can read some numbers from your device. Hence you never get the true value of your 'observable', but just a result of a decoherence of a particle or other QM system with a measurement device. Again, you can never get values of p, r DIRECTLY.

I can never get even the color of the tomato I like to eat DIRECTLY. So I don't see a point. All measurement results are indirect, depend in their interpretation on our theories.

 

[Dmitry67]

My point isthat in your article you have proven the tautology (you call it a "different physics"). The culmination of your proof is the point what you say that p, r have different values based on the basis, so it mean "different physics". But it is predicted by MWI!

1. In Wigners friend experiment, p,r of the cat is different in the basis of the Wigner and in the basis of his friend inside the box. This is how this experiment is explained in MWI
2. Different 'branches' of the same observer might have different values of 'observables', for example, the same observer have have different values for the cat (dead and alive version/branch).

 

[Ilja]

My point isthat in your article you have proven the tautology (you call it a "different physics"). The culmination of your proof is the point what you say that p, r have different values based on the basis, so it mean "different physics". But it is predicted by MWI!

1. In Wigners friend experiment, p,r of the cat is different in the basis of the Wigner and in the basis of his friend inside the box. This is how this experiment is explained in MWI
2. Different 'branches' of the same observer might have different values of 'observables', for example, the same observer have have different values for the cat (dead and alive version/branch).

No. In Wigners friend, the basis is the same: the positions (or something close to it which is decoherence-preferred) of Wigner, his friend, and the remaining part of the universe. And all their observations are compatible with standard QM laws of physics, with the standard Hamiton operator.

And different branches see different results, but all results are results compatible with the same laws of physics. Instead, the different phyisics related with my non-uniqueness examples means different laws of physics, where Hamilton operators are different, even if they have a similar form in the canonical variables.

 

[Dmitry67]

I am trying to understand, are you talking about 'different laws' relative to different decoherence basis or relative to the different 'branches'?

Different basis and bracnhes form 2 levels of hierarchy: we can have different decoherence basis and for each basis we can have different branches. For example, in Wigners friend experiment we have:

*** Before the box is opened:

1. Wigners friend basis
1.1 Wigners friend branch - observing a dead cat
1.1 Wigners friend branch - observing a cat which is alive
2. Wigner's basis (not decoherenced yet with the inside of the box)

*** After the box is opened:

1. Wigners friend basis
1.1 Wigners friend branch - observing a dead cat
1.1 Wigners friend branch - observing a cat which is alive
2. Wigner's basis
2.1 (in sync with 1.1) Dead cat
2.2 (in sync with 1.2) Alive cat

 

[Ilja]

I am trying to understand, are you talking about 'different laws' relative to different decoherence basis or relative to the different 'branches'?

Different basis and branches form 2 levels of hierarchy: we can have different decoherence basis and for each basis we can have different branches. For example, in Wigners friend experiment we have:

*** Before the box is opened:

1. Wigners friend basis
1.1 Wigners friend branch - observing a dead cat
1.1 Wigners friend branch - observing a cat which is alive
2. Wigner's basis (not decoherenced yet with the inside of the box)

*** After the box is opened:

1. Wigners friend basis
1.1 Wigners friend branch - observing a dead cat
1.1 Wigners friend branch - observing a cat which is alive
2. Wigner's basis
2.1 (in sync with 1.1) Dead cat
2.2 (in sync with 1.2) Alive cat

First, again, there is no difference between "Wigner's basis" and "Wigner's friends basis". The preferred basis is for everything, and it is uniquely defined given a decomposition of the whole universe into different subsystems. Now, in Wigner's case we have three different subsystems - Wigner, his friend, and the rest of the world - and the decomposition into these three subsystems is the same, therefore the preferred decoherence basis is the same.

The non-uniqueness has nothing to do with different branches. Branches depend already in their definition on the choice of a decoherence-preferred basis.

The non-uniqueness is below that level. There are different decompositions into systems, which lead to different choices of the decoherence-preferred basis, and, as a consequence, to different definitions what it means to be a "branch".

 

[cstromeyer]

Hi, this paper by S. Dolev and A.C. Elitzur shows that the results of their experiment are not compatible with a "collapse" (or "wave guide" interpretation of QM such as Bohmian mechanics) on pages 3-4:

http://arxiv.org/abs/quant-ph/0102109

Additionally, this paper by G. Castagnoli et al. also argues against a MWI of QM:

http://arxiv.org/abs/quant-ph/0005069

 

[Ilja]

Hi, this paper by S. Dolev and A.C. Elitzur shows that the results of their experiment are not compatible with a "collapse" (or "wave guide" interpretation of QM such as Bohmian mechanics) on pages 3-4:

http://arxiv.org/abs/quant-ph/0102109

As an argument against pilot waves this is clearly not conclusive. Pilot wave trajectories are known to behave strangely (which is sometimes used as an argument against them).