What are the principal results of the decoherence in QM?

[Terra Incognita]

B
I didn't look yet at that paper ; however I've been playing myself also with H_q x H_p stuff for fun (not thinking any serious scientist would do something like that :-). What I found was that the dynamics is trivial: each |p0,q0> state is an eigenstate of the hamiltonian and hence nothing ever happens. P and Q commute with each other, and with the hamiltonian, so in the Heisenberg picture, because [P,H] = [Q,H] = 0, dP/dt = 0 = dQ/dt. Because all variables are supposed to be functions of P and Q, all variables are constants of motion. Nothing moves.

I even think it stays at [q0,p0,t]...

Oh dark side of the force, what are you saying to the little padawan!

Master, I think you have to review the problem .

In the Koopman-von Neumann approach, we have rho(q,p,t)= <psi||q,p><q,p|psi>= |psi(q,p,t)|^2. There is a lot of papers studying this formulation, you just have to search through arxiv (very instructive).

rho is the probability density that obeys the plain old classical Liouville equation.
if you have the initial state [q0,p0,to] with certainty=> rho(q,p,to)= delta(q-qo)deltal(p-po)
And at time t: rho(q,p,to)= delta(q-q(t))delta(p-p(t)) where q(t) and p(t) is the path of the particle (plain old Newton equation). => the particle moves on the phase space.

TI.

 

[Terra Incognita]

Snip the first part of the post, by the humble padawan as the master has done an error .

Master, does the dark side of the force have weaknesses? :shy:

I don't think so if you illuminate the slit plate with a light beam that also covers the plate outside of the holes! There is clearly an interaction between the beam and the plate in that case, which will lead us to an entangled state.

Just replace the photons by electrons and the plate by an infinite quantum wall potential with holes at the 2 slits location => we have no entanglement.
The effective interaction on photons due to the plate is just more difficult to calculate (absorption + emission of the photons by the plate: metal with slits as an example), but you will recover the same thing as for electron hitting an infinite quantum wall potential with 2 slit holes.

Consider the EM modes to be resolved in 3 (orthogonal) eigenspaces of position: E1 (modes that go through hole 1), E2 (modes that go through hole 2), E3 (modes that are completely absorbed by the plate).

I think that the E3 mode is reflection of the photons by the plate (like electrons). This is the main difference between your approach and mine: I am assuming in this toy model energy conservation (first order idealisation): what we observe in the double slit experiment results.

If you do not assume energy conservation, you are describing an experiment somewhat different: your transformation of the state |cold> into |hot>.

Believe me master, the interference pattern observed on the screen assumes the energy conservation (energy transfer negligible between photons and plate).

Master Yoda, where are you? Save me from the dark side of the force.

T.I.

EDIT: and bingo, the energy conservation requirement inferes [H_plate, H_int]=0 if I am right

 

[vanesch]

In the Koopman-von Neumann approach, we have rho(q,p,t)= <psi||q,p><q,p|psi>= |psi(q,p,t)|^2. There is a lot of papers studying this formulation, you just have to search through arxiv (very instructive).

I looked quickly at it, and should look deeper...

But the way I did my stuff (not knowing this KvN approach) is "according to the book", if you want to build a quantum theory.

1) first step: enumerate a basis ; this is done by POSTULATING a complete set of commuting observables, and postulating their different (combined) outcomes. For the scalar point particle, for instance, this is usually done by saying that X, Y and Z are a complete set of commuting observables, and all the different outcomes are all possible 3-tuples (x,y,z) with x,y and z a real number.

2) associate to each of the sets of outcomes ONE basis vector of the Hilbert space of states ; define the operators associated to the commuting set of observables such that these basis vectors are eigenvectors of the operators, with eigenvalue the corresponding value in the tuple.
So to each 3-tuple (x,y,z) corresponds ONE basis vector |x,y,z> ;
To the X-position corresponds an operator X such that X |x,y,z> = x |x,y,z> etc...

3) define all other quantities with respect to these observables and states, in one way or another ; especially, define the hamiltonian in such a way.
A special case are the quantum theories associated to classical systems (but not all quantum systems need to be constructed upon a classical system !).
Here, we use the famous correspondence principle {A,B} <-> [A,B]/i hbar, which leads us to find out what the momentum operators Px, Py, Pz are, together with the hamiltonian.

4) the dynamics is given by the Schroedinger equation i hbar d/dt |psi> = H |psi>

Now, clearly if we are going to use commuting Q and P, we cannot use the classical correspondence, but we can use the first principle.
This means, that now, a complete set of commuting observables is X,Y,Z,Px,Py,Pz, so we have basis states |x,y,z,px,py,pz>

In order to have a dynamics, if we take the classical hamiltonian h(p,q) and we define the operator H(P,Q) by the same functional relationship, then we simply have that:

i hbar d/dt |x,y,z,px,py,pz> = H |x,y,z,px,py,pz> = h(p,q) |x,y,z,px,py,pz> which means that the only time evolution of |x,y,z,px,py,pz> is an exponential phase factor (the |x,y,z,px,py,pz> are stationary states).

Because all observables of a system which have a classical correspondence are functions of p and q, say, a(p,q), we then have that all states |x,y,z,px,py,pz> are eigenstates of the associated operator A (with same functional relationship to P and Q as a(p,q)).

As such, nothing moves in this quantum system !

Now of course, you can define ANOTHER dynamics, with a hamiltonian that is not the corresponding classical hamiltonian (I take that that's what is done in the KvN approach, but didn't study it enough).

But then you're not applying quantum theory according to the book, IMHO.

cheers,
Patrick.

 

[Juan R.]

Interesting questions "Terra"

1)What are the principal results of the decoherence in QM?

Posibly the main result derived from decoherence is that in some situations the role played with the environment is much more important that the role played with the own system, obligating to break the old phylosphy of physics of modelling nature spliting always the universe into two parts, system and environment, and ignoring the latter. Preciselly that was the main criticism of Feynman to usual QM for closed systems. Decoherence, therefore is a "recovering of environments".

2) Is there a general theorem we can use to determinate the states of macroscopic bodies (huge number of particles)?

If you refer to determinate "prefered basis", the clear emergence of classicality, and all of that, still there is no. However, in a more broad sense, the states of macroscopic bodies can be directly obtained from statistics.

Moreover, there are some mathematical theorems that proving that the decoherence approach, even being really important is not the key to the solving of the problem of measure and the link with the classical word.

One would be also skeptic of some assumed rigorous mathematical proofs that one can read in literature. The main mistakes often are non-rigorous mathematical manipulations around the group character of the unitary evolutor asociated to Schrödinger dynamics.

Gell-Mann & Hartle histories formalism has basically the same problems.

 

[vanesch]

Just replace the photons by electrons and the plate by an infinite quantum wall potential with holes at the 2 slits location => we have no entanglement.

There is no entanglement because there is nothing there, just an "abstract potential" :-)

But ok, that was not my point. My point was that such an interaction is not a measurement! There is no paper coming out of a computer with a printed result.

I think that the E3 mode is reflection of the photons by the plate (like electrons). This is the main difference between your approach and mine: I am assuming in this toy model energy conservation (first order idealisation): what we observe in the double slit experiment results.

Ok, granted. But that was not so much the point in fact. The point was that no measurement (= observation, potentially by a human being) was performed by shining light on a heavy mirror with holes in it (I thought a black screen, but if you prefer a mirror, then that's what we will take).

Believe me master, the interference pattern observed on the screen assumes the energy conservation (energy transfer negligible between photons and plate).

Well, there is of course much less energy that gets through the holes than what was in the beam, given the fact that a big part ( |e3> ) is reflected.

But all this is not the point. The point is that this evolution of the EM field state by a potential is not a measurement !
The measurement is the interaction with the photomultiplier and the amplification to macroscopic levels of the photo-electric emission, followed by an observation of the result, in one way or another, by a human being. It is this system which cannot be considered separate from the environment. All the unitary evolution (such as the interaction with the screen, and even the photo-electric interaction) can be done in ANY basis. It is the final application of the Born rule that needs to be done in a special basis.

cheers,
Patrick.

 

[Terra Incognita]

Interesting questions "Terra"

Thanks juan and welcome to this interesting debate/learning of the humble padawan I am .

1)What are the principal results of the decoherence in QM?

Posibly the main result derived from decoherence is that in some situations the role played with the environment is much more important that the role played with the own system, obligating to break the old phylosphy of physics of modelling nature spliting always the universe into two parts, system and environment, and ignoring the latter. Preciselly that was the main criticism of Feynman to usual QM for closed systems. Decoherence, therefore is a "recovering of environments".

We have the same behaviour for classical systems: strong interaction or not of the system with the environment. May or may no we neglect the influence of the environment in the system?
This is why I am using the “double slit interference” toy model in this thread. We can add or remove (by thought), the interaction with the environment (e.g. what Master Patrick has proposed for the slit plate - strong interaction and what I have proposed - negligible interaction).

If the decoherence is just of matter of quantifying the interaction hamiltonian between the system and the environment why not saying it at the very beginning?
We can say the same thing for a classical statistical system (interaction with the environment). This property is not the exclusive domain of QM.

What extra properties do we have? (Of the strong correlation of QM systems with the environment compared with the classical systems)

2) Is there a general theorem we can use to determinate the states of macroscopic bodies (huge number of particles)?

If you refer to determinate "prefered basis", the clear emergence of classicality, and all of that, still there is no. However, in a more broad sense, the states of macroscopic bodies can be directly obtained from statistics.

You mean classical probability? If this is the case, I call this a preferred basis (the basis where we collect the statistics of the system).

Moreover, there are some mathematical theorems that proving that the decoherence approach, even being really important is not the key to the solving of the problem of measure and the link with the classical word.

It is what I begin to understand. Do you have a pointer to some of these theorems?

One would be also skeptic of some assumed rigorous mathematical proofs that one can read in literature. The main mistakes often are non-rigorous mathematical manipulations around the group character of the unitary evolutor asociated to Schrödinger dynamics.

Gell-Mann & Hartle histories formalism has basically the same problems.

I do not know the Gell-Mann & Hartle histories formalism. However, I agree perfectly concerning the lack of rigorous mathematical proofs in physics and their result extrapolations.

TI.

 

[Juan R.]

Thanks,

Yes we have similar behaviour for classical systems. However, in general, the effect of the environment in a small quantum system is much more important that for large systems. This is seen in the so-called scale of decoherence.

I do not think that decoherence is just "quantifying the interaction hamiltonian between the system and the environment", because i think that one does very important asumptions regardins the statistics and correlations of the systems. For example, one basic element for decoherence is choosing at least a quantum state mixed. But basically you may are right in your basic thinking about the parafernalia around decoherence.

The ultra rapid scale of the effects is one important question, but the important question is that decoherence implies the erasing of the coherences bewteen quantum states. Whereas in classical systems this is not posible (there is not coherences) and basically the effect of environment is changing the populations of levels.

I mean that in both classical and quantum systems we habe a well defined form for know the quantum or classicla state and compute observables. We need a method for obtain the states of decoherent systems!

I will cite them including new material mine in a paper that I posted in my web, but if you need literature "urgently", please contact with me at mail and I attempt to send you some material.

This follow is not very rigorous, of course, but basically GMH approach is to standard decoherence approach like Feynman formulation is to Schrödinger one. GMH approach emphasizes processes instead of states and interferences between histories instead of nondiagonal components of density matrices, etc. It is an integral method inspired in Feynman path integral.

 

[vanesch]

2) Is there a general theorem we can use to determinate the states of macroscopic bodies (huge number of particles)?

If you refer to determinate "prefered basis", the clear emergence of classicality, and all of that, still there is no. However, in a more broad sense, the states of macroscopic bodies can be directly obtained from statistics.

I agree with you up to a point, in that decoherence doesn't solve the measurement problem, which consists of several steps:

1) the final wavefunction, containing the observer, must be written in a certain basis ;

2) we have to pick out ONE of these terms

3) we do this with a probability given by the Born rule

Clearly, decoherence doesn't solve 2) and 3). It doesn't even completely solve 1). But it makes an important step in 1), namely it shows that if that final wavefunction, containing the observer (so at least a human brain!), also contains enough "thermal bath" which counts as the environment, then there are special ways of writing that final wavefunction, in such a way that, on a coarse level, it consists of terms of the kind

|environment> x|observer> x|observed_pointers_of_macroscopic_measurement_apparatus>

such that the individual components are essentially orthogonal, and that the terms are "robust" against time evolution, in that they keep their form on a scale which is compatible with macroscopic, classical observation, such as: the dial of that am-meter is near the indication "4 A".

As 2) and 3) are not solved, the importance of this part in the solution of 1) depends on how one takes on 2) and 3), but it is at least highly suggestive that this way of writing the final wavefunction (this basis) can be a starting point of introducing solutions to 2) and 3). I am personally convinced that you cannot solve 2) and 3) "from within" quantum theory, so that you need extra postulates to do so ; that extra postulate can then use the special decomposition obtained by decoherence as a starting point.

My personal view on things goes like this:
The simplest postulate to solve issues 2) and 3), assuming full unitary quantum theory is universally valid on all levels, is: USE this decoherence basis, and apply the Born rule in it. The ambiguity of HOW to split the universe in two pieces (stuff, and the environment) is simply that the physical implementation of the observer (his body) is the stuff, and the rest is the "environment". You cannot have an observer which is not associated with a part of the universe (you need a body). But of course the physical construction (the body) itself cannot be the observer, because it simply occurs in a superposition, and it won't select out 1 of the terms. So that's where my 'consciousness' thing comes in: the observer is the consciousness, and it is, by postulate, associated to a body state which occurs in a product state with the rest of the universe ; the choice is made by the Born rule.

You can of course try to make more elegant postulates, which have in the end, the same effect. You could also use less elegant postulates, saying that a consciousness is always associated to a classical body state. That's then more in the Copenhagen spirit. But then you put in classicity by hand ; so if decoherence gives us a "natural" way of decomposing the state in "classically looking" terms, why not use it ?

That's a deus ex machina, I agree with it. The only OTHER way out is to use a physical collapse: a physical process which induces the selection of one of the terms in an objective way. That means that quantum theory is not universally valid (no unitary evolution for all physical processes). We already know from EPR stuff that this physical process will incorporate weird non-locality, and as of now, we don't know of any non-local dynamical process. I still think that gravity *might* be a solution there. But as long as we don't have anything really working on that side, I stick to my first view.

cheers,
Patrick.

 

[dlgoff]

So that's where my 'consciousness' thing comes in: the observer is the consciousness, and it is, by postulate, associated to a body state which occurs in a product state with the rest of the universe

I think this is very interesting. Does this mean that "consciousness" would have been around in the early universe? I mean, since there was physics before we were ever around.

Regards

 

[vanesch]

I think this is very interesting. Does this mean that "consciousness" would have been around in the early universe? I mean, since there was physics before we were ever around.

You can freely make any hypothesis there

But you didn't necessarily have to have a Born rule application before we were around ! Everything could nicely have been evolving unitarily (and still is)... After all, you only need a Born rule to explain a classical experience (the picking out of one term). If you weren't around, you don't need to explain an experience that wasn't there. You only need to pick out one term once you're there to observe it.

cheers,
Patrick.

 

[dlgoff]

You can freely make any hypothesis there

Yes

After all, you only need a Born rule to explain a classical experience (the picking out of one term). If you weren't around, you don't need to explain an experience that wasn't there. You only need to pick out one term once you're there to observe it.

Point taken.

Thanks

 

[Juan R.]

vanesch

The outcome of measurement or the emergence of classicality precisely are not representable by wavefunctions. Another problem of QM is unitarity. All models minimally realistic are always non-unitary ones. These flaws are the basis of problem of why QM is incompatible with classical reality.

Since that most part of approaches to "solve" the measurement problem begin assuming the standard postulates of QM, they all fail in the correct rigorous derivation of classical properties.

The Born rule is just approximated one.

And of course, Penrose and other, are correct in that for solving the measurement problem one needs to go outside of standard QM. There are several attempts to do this. One of more interesting one is that from my own called thermomaster formulation of canonical science.

It is a nonlinear formulation using generalized state vectors (mixed and pures) and random contributions from "foam" spacetime.

All usual equations of decoherence (e.g. Caldeira-Leggett) are recovered like special cases valid in determined situations. Novel QM generalizations like the generalized Ito-Schrödinger equations are alos special limits.

Even highly mathematical formulations like the Brushels-School model of collapse of wavefunctions for LPS can be improved also from this method (especially in the mathematical formulation of the inadequacy of the Hilbert space for the description of large systems).

The ambiguity of HOW to split the universe in two pieces (stuff, and the environment) is much more difficult that you say. Take an elementary particle and the rest. QM work perffectly and you have particle physics. Split the universe now in benzene more the rest. Now QM does not work. Split on a cat more the rest and the failure of QM is still higher.

 

[vanesch]

The outcome of measurement or the emergence of classicality precisely are not representable by wavefunctions.

I do not agree with that statement. Coherent states are good quantum descriptions of classical states.

Another problem of QM is unitarity. All models minimally realistic are always non-unitary ones. These flaws are the basis of problem of why QM is incompatible with classical reality.

Yes, that's of course essential: it is the strict unitarity that forbids any objective selection of a classical state ; and as I pointed out myself, the only solution to that problem is to depart from unitarity (and hence from quantum theory as such) ; I also pointed out that gravity might be our hope there.

Nevertheless, there is a huge problem to solve when you do that: how do you account for EPR situations ? Do you sacrifice Lorentz invariance and locality on a macroscopic scale ? I have never seen a satisfactory solution to that problem. What I said was: as long as I haven't seen any WORKING solution that explains me how we need Lorentz invariance and locality on macroscopic scales, and nevertheless can introduce a mechanism that can account for EPR situations, I presume that quantum mechanics is correct (and unitary evolution also).

Since that most part of approaches to "solve" the measurement problem begin assuming the standard postulates of QM, they all fail in the correct rigorous derivation of classical properties.

The Born rule is just approximated one.

Well, that should then be observable, no ?

And of course, Penrose and other, are correct in that for solving the measurement problem one needs to go outside of standard QM. There are several attempts to do this. One of more interesting one is that from my own called thermomaster formulation of canonical science.

It is a nonlinear formulation using generalized state vectors (mixed and pures) and random contributions from "foam" spacetime.

All usual equations of decoherence (e.g. Caldeira-Leggett) are recovered like special cases valid in determined situations. Novel QM generalizations like the generalized Ito-Schrödinger equations are alos special limits.

Even highly mathematical formulations like the Brushels-School model of collapse of wavefunctions for LPS can be improved also from this method (especially in the mathematical formulation of the inadequacy of the Hilbert space for the description of large systems).

Can you give us a succinct account of the basic ideas in these approaches ?
I want to see how each of them handles the EPR problem.

The ambiguity of HOW to split the universe in two pieces (stuff, and the environment) is much more difficult that you say. Take an elementary particle and the rest. QM work perffectly and you have particle physics. Split the universe now in benzene more the rest. Now QM does not work. Split on a cat more the rest and the failure of QM is still higher.

I don't understand why you say this. I don't see where quantum mechanics fails for a benzene molecule. You do not need to apply any Born rule from the standpoint of a benzene molecule. When you do unitary calculations with benzene it works very well. There's a branch, called quantum chemistry, which has nice results doing exactly such things...

But maybe you didn't get what I wanted to state. I stated the following: in order to even be able to talk about an observation (which can be confronted to a theory), you need AN OBSERVER. The whole purpose of physics is to explain our subjective experiences (which are usually taken to be derived DIRECTLY from an objective world, but that's just a working hypothesis, which might, or might not, be true). That means then that to that observer belongs a certain part of the universe, (the stuff). And that's a natural split.
If there is no observer, there are no subjective observations, there are no physical theories that can be falsified and there is no physics. Within the working hypothesis of an existing objective world, corresponding to the subjective observations (which was the viewpoint of classical physics), you can do away with that observer. In quantum theory, that gives problems ; and one way to deal with them is to do away with our working hypothesis of an objective reality DIRECTLY corresponding to our subjective experiences, and to postulate how our subjective observations are derived from ANOTHER objective reality (the wavefunction of the universe). For instance through the Born rule.

This explanation does not have to be correct. But it is not necessarily false either, and it allows for quantum theory to be correct "all the way up", on the condition of an extra description of how the subjective experiences are related to an objective reality.

The main problem I have in letting go quantum theory "all the way up" is that I have never seen anything else that works as well, without introducing ad hoc stuff made up for the purpose, and which solves the EPR riddle. Now, maybe you have such solutions in sight. In that case, I'm more than happy to learn about them.

cheers,
Patrick.

 

[Terra Incognita]

There has been a lot of discussion since my previous posts and my study of Master Vanesh and Juan R. posts! The padawan I am is happy to see some interest on this subject by the members of this community. I hope this will continue. Please contribute to this thread!
I am taking now more time before replying as the subject is now more developed, especially with some of the posts of Master Vanesh and Juan R.!). As a padawan, I would like to understand this exciting subject :shy: .

But the way I did my stuff (not knowing this KvN approach) is "according to the book", if you want to build a quantum theory.

KvN is interesting because it is just mathematical way to express classical statistical mechanics (CSM) in a Hilbert space formulation. It allows understanding better the correspondence principle and compares the 2 theories in the same plane (like Special relativity motion equation and Newton equation motion).

We use the formalism of QM that allows one to compute probability from the specificities of the theories (the specific time evolution) as a general mathematical tool.

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).

However, how do we construct the evolution operator in CSM from the classical Hamiltonian? Thanks to the Liouville equation.
Once one get this equation, one can build a new way to define the quantum observables (the Hamiltonian) with respect to the CSM observables (the liouville operator and the q and p operators). The paper arXiv:quant-ph/0305063 v1 is one example to propose such a process (rather than using the orthodox way). Choosing this method or the one of the books is just a matter of taste.

In order to have a dynamics, if we take the classical hamiltonian h(p,q) and we define the operator H(P,Q) by the same functional relationship, ...
i hbar d/dt |x,y,z,px,py,pz> = H |x,y,z,px,py,pz> = h(p,q) |x,y,z,px,py,pz> which means that the only time evolution of |x,y,z,px,py,pz> is an exponential phase factor (the |x,y,z,px,py,pz> are stationary states)

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.

But then you're not applying quantum theory according to the book, IMHO.

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).

But all this is not the point. The point is that this evolution of the EM field state by a potential is not a measurement !
The measurement is the interaction with the photomultiplier and the amplification to macroscopic levels of the photo-electric emission, followed by an observation of the result, in one way or another, by a human being. It is this system which cannot be considered separate from the environment. All the unitary evolution (such as the interaction with the screen, and even the photo-electric interaction) can be done in ANY basis. It is the final application of the Born rule that needs to be done in a special basis.

Do you really think we need a classical “human” (or a machine) to acknowledge the measurement results?
I have tried to show that we may not need to in the post # 34 (or at least it is not so evident). A given system with a given interaction Hamiltonian is a measurement apparatus as long as we can say if we look (but we have not to) at the right place (in this case after the slits), we have the results of the measurement.
In other words we cannot distinguish this system from a measurement apparatus (in the sense a voltmeter give a voltage if we, human, are look or not at this voltmeter).

Using this system, we can connect other systems: the screen to see the arrival of photons (a local interaction). The screen may be described by another Hamiltonian (for example one that focuses the photons in the screen). However, this screen has no impact in the measurement of the photons performed by the double slit plate, just because the state of the screen is locate with certainty behind the plate.

But all this is not the point. The point is that this evolution of the EM field state by a potential is not a measurement !
The measurement is the interaction with the photomultiplier and the amplification to macroscopic levels of the photo-electric emission, followed by an observation of the result, in one way or another, by a human being. It is this system which cannot be considered separate from the environment. All the unitary evolution (such as the interaction with the screen, and even the photo-electric interaction) can be done in ANY basis. It is the final application of the Born rule that needs to be done in a special basis.

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”)?

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.


Working on the other posts, or may be loosing my mind,

TI the Padawan .

 

[Juan R.]

vanesch

Coherent states are NOT good quantum descriptions of classical states. Precisely any classical system is one violating superposition principle.

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.


All of those approaches are well-known:

Penrose based in "quantum gravity".

Caldeira-Leggett is a standard in computation of classical states in molecular systems.

Ito-Schrödinger equations are standard modifications of usual law with nonunitary terms allowing collapse.

Prigogine theory is based in the idea (standard) of that instable states cannot be represented like vectors in a Hilbert space. That and the collapse of Hilbert space structure due to Poincare resonances is used as a basis for obtaining a new formulation of QM, with generalized states on an RHS mathematical space, and nonunitarity leaded by the lambda transformation. It is not very standard but is well-known.

My formulation is novel, and permit us to obtain the formulas already used in literature (and that work perfectly) and correct some mistakes of others like that of Prigogine for LPS.

The paper will be published in my web.

I don't see significant problems on them. Why do you see problems?

Quantum mechanics fails for ANY molecule more heavy that H2 or NH3.

Precisely it is THE problem of quantum chemistry. How to define a molecule in QM! Imposible!

The problem for taking account the observer is a problem of all science, it is overemphasized in QM due to strang role of collapse in Copenhagen, Everett, and others interpretations.

The role of the "observer" is rather relative. Its impact on a QM measurement in "insignificant".

Reality doesn't DIRECTLY corresponding to our "subjective" experiences. A molecule of bencene exists independiently of I was observing it or not.

There is no such one thing like the wavefunction of the universe. Universe cannot be represented by a wavefunction. It is in a mixed state. A cat has no wavefunction.

Regarding news generalizations of QM (including mine own) I cannot see more problems with the new aproaches that with the usual formulation of quantum mechanics which of course is internally inconsistent (e.g. unitary and nonunitary, based in wavefunctions and not, reversible and irreversible, etc.).

In fact, at large part of practice with standard QM is purely ad hoc. For example, ad hoc, electrons have wavefunction, but cats no. Ad hoc, some superpositions are permited (electron here/there) but others no (electron/quark), such one is forced to lot of empirical rules and ad hoc arguments. On N one asumes ad hoc that nuclear framework is described by a quantum wavepacket. Still if one want study the N in the DNA, one is forced to ignore its, etc, etc, etc.

I think that have not the last word of course, but my work could open a new line of attack to a problem already too old.

 

[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