What are the principal results of the decoherence in QM?

[vanesch]

The books give a partial solution to construct the Hamiltonian operator (the specific time evolution) starting from a classical Hamiltonian. These are the following equations you gave in the post # 38:
a) {A’,B’}_classical= [A,B]_quantum/i hbar.
b) replace the scalar A’ by the operator A, the scalar B’ by the operator B in the scalar Hamiltonian of classical mechanics.

This is just a method to construct the hamiltonian of QM (specific to QM) and not the way to define the Liouville operator of CSM (specific to CSM).

I can understand one wants to mold classical statistical mechanics into a framework using a hilbert space. But that, to me, is not a quantum theory per se. The classical link between momentum, position and energy (h(p,q)) on one hand, and the link between energy and time evolution (Schroedinger equation) on the other hand, are, I think, fundamental. So I don't know if you learn much from this mimickry, even if formally (by forcing the liouville equation to work out) you can make things work. I mean: it is not because we were able to map a classical phase space dynamics, given by the liouville equation, onto a hilbert state mechanism, that we have anything like a quantum theory, do we ? I'm sure that with some effort I'm able to map hydrodynamical problems also on a Hilbert space formulation. But does that give my quantum hydrodynamics then ? Or maybe I'm missing the whole point of this exercise then...

Your error: you assume that the time evolution of the state is given by the hamiltonian obtained by the process to get the quantum hamiltonian starting from the classical hamiltonian. The time evolution operators evolutions are specific to the theories.

I would take that as very very fundamental in a quantum theory... That there is a quantity (energy) which is measurable (and hence a classical function of q and p), and which corresponds to the time evolution.
Of course you can impose just ANY time evolution in a hilbert space, by just any mechanism, and then call the derivative to time the action of an operator, which is called a "hamiltonian". But are we still doing quantum theory here, or just defining mathematical operators in a hilbert space setting ?
In that case, what is this formal game going to learn us about an interpretative issue in quantum theory ?

I am applying quantum probabilities (an observable and a state define a probability law) and not the specificities of the time evolution that are theory dependant.
I have in both theories, expressed with quantum probabilities, the problem of the eingenbasis selection. This is why I think we can use them to understand better decoherence and the preferred basis problems (separation of general problems for theory dependant problems).

I don't understand this. The (p,q) basis is clearly preferred, no ? You have set up everything so that 1) |psi|^2 in that basis is the phase space density and 2) that this density evolves according to the Liouville equation. In what other basis would you ever like to work then ? What does it even MEAN, to be in a |p1,q1> + |p2,q2> state ? To what does this state correspond ?

Do you really think we need a classical “human” (or a machine) to acknowledge the measurement results?

Yes, exactly for the reason you asked in the beginning of this thread. You can consider ALL interactions as given by unitary evolution. So your voltmeter and everything just ends up entangled with whatever it was measuring (that's given by the interaction hamiltonian).

For instance, consider a computer that is counting photoelectric pulses and calculates a correlation. Well, the computer will end up entangled in several terms, and in each of the terms, it will have calculated a different correlation. You will end up with something like:

|computercorr=0.8>|++>|-->|-->|-+>|++> + |computercorr=0.6>|++>|-->|-->|+->|-+> +
|computercorr=0.8>|-->|-+>|++>|-->|++> +
...

That's what you get out of all the interaction hamiltonians between the photonstates and the photodetectors, the counting modules, and the electronics of the computer. The computer has no need to be in only ONE of these states. But clearly, when you LOOK and OBSERVE the computer screen, you only see one answer. That means that the bodystate YOU are consciously aware of, must be in a product state with only ONE state of the computer screen. But as long as you do not look, that computer, its screen and everything else can happily be in an entangled state as above. And to do that, you don't need any preferred basis. The hamiltonians, specifying a unitary evolution operator, are sufficient, and their action is of course independent of the basis in which you apply them.
Computers not being aware of a classical world, they don't mind being in entangled states, so from the point of view of a computer, there's no problem for it to have at the same time a result which is corr = 0.8, corr = 0.2 and 0.1 in different terms. It's just when YOU look at it that you only see one of those results. But that's more something about YOU than about the computer. So the Born rule only applies to YOUR experiences.

(in the sense a voltmeter give a voltage if we, human, are look or not at this voltmeter).

Well, that's not true in a MWI. The voltmeter does not give one voltage on its reading. It gives all possible results, in entangled states. We only seem to observe one of them. But only when we look. Crazy, no ? :-)

This is a matter of words. What is important for the measurement, to acknowledge it or to know if one place a detector (or a question) after the plate, one will see the results implied by the plate (in this case the “measurement”)?

Well, we say that the detector will see the result implied by the plate in one term, and will see another result in another term.

You seem to assume that you need interaction with the environment in order to get a measurement. I do not see why we need such interaction (hence the double slit example with the reflecting plate).
In other words, I can imagine a measurement without any interaction (in the sense negligible during the considered time), just by saying that the detector records the results. The fact that someone may or may not read the results of the detector (now, 10 years later or never) does not change the results.

Well, that's the big difference between a collapse model and a relative state interpretation. In a relative state interpretation, the detector has obtained all the possible results at the same time. In some terms, the detector has clicked, and in other terms, that same detector, at the same time and place, didn't click. It is only when you look at it that you know in what term you are (and not even what "really happened to the detector"). That's the whole point of relative state views.

In a collapse model of course, there IS - as you say - an outcome, whether you look at it or not. And then there needs to be a transistion, through a Born rule. And there needs to be an objective choice of basis. And then, indeed, you have the problem of whatever is an observer, or not, and what is an environment, or not. As long as there is no clear physical dynamics that gives an answer to that, I find these problems so unsurmountable that I prefer a relative-state view in which EVERYTHING HAPPENS, and in which I only consciously experience ONE alternative. And then of course you see the crucial role of me as an observer, and the naturalness of dividing the universe into "my body" and "the rest". This implies (and allows) quantum theory to be valid "all the way up" until I have to make my personal choice as to what term to pick.

And *as long as you do that* and apply the unitary evolution to all interactions, there is no basis problem to be solved (but there is also no definite result obtained) for any interaction that is not a subjective observation by myself. And for THOSE subjective observations, I'd think that using splits that are based upon myself versus the rest of the universe are allowed and rather natural.

Now, I know that this sounds crazy - and probably it is. But it is A POSSIBILITY. And we don't have any clear physical indication of where this unitary evolution fails. Maybe gravity will do so. Maybe not. As long as there is no clear model of how it does so, I take it that what we know of our fundamental laws (unitary evolution) is valid everywhere.

cheers,
Patrick.

 

[vanesch]

I don't see any problem with nonunitarity. In fact nonunitarity is already used in all laboratories of the world. What do you see?

Quantum mechanics is not complete and moreover it is not correct, it need to be complemented.

Ok, but how do you handle Lorentz invariance versus EPR situations ?

cheers,
Patrick.

 

[Juan R.]

Thanks by your comments.

You also said,

"Ok, but how do you handle Lorentz invariance versus EPR situations ?"

I'm sorry vanesch but i don't understand you well. Please can you say me that contradiction you exactly are seing in measuring or collapse:

- violation of invariance by nonrelativistic models of decoherence?

- "Spoky" Action-at-a-distance?

- Correlation of spatially well-separated laboratory experiments?

I prefer that you explain that you are thinking exactly and then i will do a attempt to reply for you best form that i can.

 

[dlgoff]

I can understand one wants to mold classical statistical mechanics into a framework using a hilbert space. But that, to me, is not a quantum theory per se. The classical link between momentum, position and energy (h(p,q)) on one hand, and the link between energy and time evolution (Schroedinger equation) on the other hand, are, I think, fundamental. So I don't know if you learn much from this mimickry, even if formally (by forcing the liouville equation to work out) you can make things work. I mean: it is not because we were able to map a classical phase space dynamics, given by the liouville equation, onto a hilbert state mechanism, that we have anything like a quantum theory, do we ? I'm sure that with some effort I'm able to map hydrodynamical problems also on a Hilbert space formulation. But does that give my quantum hydrodynamics then ? Or maybe I'm missing the whole point of this exercise then...



I would take that as very very fundamental in a quantum theory... That there is a quantity (energy) which is measurable (and hence a classical function of q and p), and which corresponds to the time evolution.
Of course you can impose just ANY time evolution in a hilbert space, by just any mechanism, and then call the derivative to time the action of an operator, which is called a "hamiltonian". But are we still doing quantum theory here, or just defining mathematical operators in a hilbert space setting ?
In that case, what is this formal game going to learn us about an interpretative issue in quantum theory ?



I don't understand this. The (p,q) basis is clearly preferred, no ? You have set up everything so that 1) |psi|^2 in that basis is the phase space density and 2) that this density evolves according to the Liouville equation. In what other basis would you ever like to work then ? What does it even MEAN, to be in a |p1,q1> + |p2,q2> state ? To what does this state correspond ?



Yes, exactly for the reason you asked in the beginning of this thread. You can consider ALL interactions as given by unitary evolution. So your voltmeter and everything just ends up entangled with whatever it was measuring (that's given by the interaction hamiltonian).

For instance, consider a computer that is counting photoelectric pulses and calculates a correlation. Well, the computer will end up entangled in several terms, and in each of the terms, it will have calculated a different correlation. You will end up with something like:

|computercorr=0.8>|++>|-->|-->|-+>|++> + |computercorr=0.6>|++>|-->|-->|+->|-+> +
|computercorr=0.8>|-->|-+>|++>|-->|++> +
...

That's what you get out of all the interaction hamiltonians between the photonstates and the photodetectors, the counting modules, and the electronics of the computer. The computer has no need to be in only ONE of these states. But clearly, when you LOOK and OBSERVE the computer screen, you only see one answer. That means that the bodystate YOU are consciously aware of, must be in a product state with only ONE state of the computer screen. But as long as you do not look, that computer, its screen and everything else can happily be in an entangled state as above. And to do that, you don't need any preferred basis. The hamiltonians, specifying a unitary evolution operator, are sufficient, and their action is of course independent of the basis in which you apply them.
Computers not being aware of a classical world, they don't mind being in entangled states, so from the point of view of a computer, there's no problem for it to have at the same time a result which is corr = 0.8, corr = 0.2 and 0.1 in different terms. It's just when YOU look at it that you only see one of those results. But that's more something about YOU than about the computer. So the Born rule only applies to YOUR experiences.



Well, that's not true in a MWI. The voltmeter does not give one voltage on its reading. It gives all possible results, in entangled states. We only seem to observe one of them. But only when we look. Crazy, no ? :-)



Well, we say that the detector will see the result implied by the plate in one term, and will see another result in another term.



Well, that's the big difference between a collapse model and a relative state interpretation. In a relative state interpretation, the detector has obtained all the possible results at the same time. In some terms, the detector has clicked, and in other terms, that same detector, at the same time and place, didn't click. It is only when you look at it that you know in what term you are (and not even what "really happened to the detector"). That's the whole point of relative state views.

In a collapse model of course, there IS - as you say - an outcome, whether you look at it or not. And then there needs to be a transistion, through a Born rule. And there needs to be an objective choice of basis. And then, indeed, you have the problem of whatever is an observer, or not, and what is an environment, or not. As long as there is no clear physical dynamics that gives an answer to that, I find these problems so unsurmountable that I prefer a relative-state view in which EVERYTHING HAPPENS, and in which I only consciously experience ONE alternative. And then of course you see the crucial role of me as an observer, and the naturalness of dividing the universe into "my body" and "the rest". This implies (and allows) quantum theory to be valid "all the way up" until I have to make my personal choice as to what term to pick.

And *as long as you do that* and apply the unitary evolution to all interactions, there is no basis problem to be solved (but there is also no definite result obtained) for any interaction that is not a subjective observation by myself. And for THOSE subjective observations, I'd think that using splits that are based upon myself versus the rest of the universe are allowed and rather natural.

Now, I know that this sounds crazy - and probably it is. But it is A POSSIBILITY. And we don't have any clear physical indication of where this unitary evolution fails. Maybe gravity will do so. Maybe not. As long as there is no clear model of how it does so, I take it that what we know of our fundamental laws (unitary evolution) is valid everywhere.

cheers,
Patrick.

I've got to say; this post is really, really good. Thanks for being so upfront with your ideas. To me they make perfect since, albeit my mathematical understanding of qm needs lots of updating.

What I don't understand is how gravity might show a non-unitary evolution of the universe.

Regards
Don

 

[vanesch]

Thanks by your comments.

You also said,

"Ok, but how do you handle Lorentz invariance versus EPR situations ?"

I'm sorry vanesch but i don't understand you well. Please can you say me that contradiction you exactly are seing in measuring or collapse:

- violation of invariance by nonrelativistic models of decoherence?

- "Spoky" Action-at-a-distance?

- Correlation of spatially well-separated laboratory experiments?

I prefer that you explain that you are thinking exactly and then i will do a attempt to reply for you best form that i can.

What I mean is: strict unitarity is (to my knowledge) the only way to preserve both explicit locality (and as such possible lorentz invariance) of the theory, while explaining the violations of the Bell inequalities in EPR experiments.
From the moment that you have an objective collapse, this must incorporate automatically an explicitly non-local mechanism which violates locality. (for instance, the "quantum potential" in Bohm's theory, or the projection in von Neumann's approach, are non-local mechanisms and can as such not be made Lorentz invariant).
The only way strict unitarity can weasel out of this non-locality is by stating that there WASN'T any explicit result at spacelike separated points, because the result has to be determined by the observer choosing a term, and clearly the observer cannot be at two spacelike separated events. If he's at one event, the other event doesn't have a result yet. But when you depart from unitarity in one way or another you have clearly an objective non-locality in the theory which is incompatible with lorentz invariance. Ok, this could be true, but then, how does lorentz invariance re-appear in a theory where it was not a fundamental postulate ?

So how is this handled in your view ?

cheers,
Patrick.

 

[Juan R.]

I cannot post more information here

vanesch

The first that I would say is that strict unitarity is imposible.

There is a generalized mistake in QFT of that it is unitary. It is not, usual proofs are full of mathematical mistakes. This is well proven in my article Is this dynamics?, where chapter 3 of Weinberg QFT is revised with very high mathematical detail. (Note: manuscript was sent to a number of expertises including Weinberg for review and mathematical error was not found).

Locality is approximate. This is well-known even at the classical level. For example, in very far from equilibrium situations there are long-range correlations and the field theoretical approach is not longer applicable. People working in far from equlibrium states know that perfectly.

In my recent canonical theory is predicted nonlocality also in "equilibrium" EM. There is a recent Phys Rev (1996, 53, 5, 53-57) article based in rigorous math, that shows that strict locality is impossible in Maxwell EM.

f = F(r, t) + G(R)

locality is only valid when G --> 0.

From usual theories, that recent result is perplexing one, but stric lovcality was the result of the use of elementary math (e.g, in Maxwell EM, QFT, and GR). From my perspective, that result is ok, in fact, my theory already predict that recent result violating locality. There is not surprise from my approach.

This open the door to a consistent interpretation of collapse. Moreover, that PRE work was only valid for EM, my canonical work has been also generalized to gravitation. The result is the failure of GR and its locality postulate. Non locality effects are now measured. In fact, a recent work published in literature introduces several experimental data incompatible with GR but compatible with my approach.

There are many confusion about Lorentz invariance. Many people want not heard about violations of Lorentz because it would imply the introduction of frame dependent effects (that was during decades the main criticism of string theorists to LQG).

Lorentz <=> frame independence.

This is false. Usual proof and math are not correct.

I have already shown that the real relationship is

Lorentz => frame independence.

but

Frame independence does not necesarily imply Lorentz invariance. This is best studied from canonical invariance.

I'm sorry but I cannot offer here details on my theory nor links to my papers on my web page, because some people in this forum this very hungry with me and I don't want personal attack. In fact, in

https://www.physicsforums.com/showthread.php?t=75197&page=3&pp=15

i did an attempt to present my rigorous gravitational theory and people solicited to forum administrators the closing of it because "was not adequate".

It is interesting that Chronos first claim that alternative theories are not adequated for PF and after solicit more information to me! I have not replied his last stupid post about thermodynamics. He simply doesn't know nothing on the topic on advanced gravitation research and post irrelevant posts at level of an undergraduate student.

It is very significative the very low level of replies of people that replied to me in that post. A pair of good rigorous references (I prefer omit here my personal valoration of many Living Reviews in Relativity :-) and a bit of advanced math are sufficient for showing why they are completely wrong. The link to HORIZONS was a joke because i cannot think that anyone intelligent claiming that GR is correct and experimentally proved without doubt can have absolutely no idea of the topic that he is claiming to know.

I think that personal attack is only a sintom of absence of arguments. If one person is wrong, one can say it with educated words.


Your "how does lorentz invariance re-appear in a theory where it was not a fundamental postulate ?" is perfectly answered from canonical invariance.

 

[vanesch]

I've got to say; this post is really, really good. Thanks for being so upfront with your ideas. To me they make perfect since, albeit my mathematical understanding of qm needs lots of updating.

Thanks

What I don't understand is how gravity might show a non-unitary evolution of the universe.

Well, unfortunately my website iknowthesolutiontoallofphysics.com is down for the moment, otherwise you could read my magnificent rigorous theory there

No, seriously, I have no idea ; I have to say I am vaguely seduced by ideas a la Penrose, without knowing exactly what it is about. But the point is the following: or quantum theory is with us for ever (or at least for a few centuries to come), or it isn't. In the first case we will be stuck ethernally with the weird situation of relative states. If we have to, we have to, of course. As I tried to point out, I'm not in favor of relative states for its sake ; simply, if you accept quantum theory as it is today, as a universally valid framework, you cannot escape it. But it is nevertheless weird.

The other option is that quantum theory (strictly unitary) is a limiting case of a more general theory. Now, there are people trying to mess with adding noise to the Schroedinger equation without changing it too much, but that looks to me as some bricolage. We seem to have problems with the following: what happens to quantum theory on macroscopic scales ? And we know already, from EPR situations, that quantum theory DOES something on macroscopic scales, which tends to mess with locality if we leave strict unitarity.

Also, the thing people have troubles with is to incorporate gravity into a strictly unitary quantum theory. Gravity is something which is typically "macroscopic" and moreover, gravity has an intimate relationship with locality. All this makes it a plausible argument that gravity, locality, "classical macroscopic behaviour" and unitarity or not might have something to do with each other ; I had the impression that that was Penrose's viewpoint:
That the troubles with incorporating gravity in a strictly unitary QM, and the interpretational problems of strictly unitary QM on a macroscopic level, together with the link between locality - gravity - strict unitarity - EPR situations, might point to a link between all this. But I don't know *what* link! Just that there is maybe a possibility of a link.

For all other interactions, weak and strong nuclear interactions are clearly microscopic phenomena which don't play a significant role in the macroscopic world, and QED seems to work too well for it to be at the origin of any departure from strict unitarity. But gravity is still the open question: it is (in everyday experiences) "macroscopic".

cheers,
Patrick.

 

[dlgoff]

The other option is that quantum theory (strictly unitary) is a limiting case of a more general theory.

I've alway wondered if maybe "consciousness" (or the thought process) might have some role here. That it might be local yet produce lasting effects (pointer states).

For all other interactions, weak and strong nuclear interactions are clearly microscopic phenomena which don't play a significant role in the macroscopic world, and QED seems to work too well for it to be at the origin of any departure from strict unitarity. But gravity is still the open question: it is (in everyday experiences) "macroscopic".

Oh yes. I see what you mean.

Wish I could be around long enough to see where this goes.

Much thanks

Don