Why is the pilot-wave theory controversial ? Is it?

[Demystifier]

Drew, pilot-wave theory requires actually less assumptions than the orthodox interpretation! Sure you need an extra assumption of point particles, but you get two other assumptions for free: Born's rule (i.e. that the modulus squared gives the probability) is a consequence, as is collapse! Both of these are extra assumptions in the orthodox interpretation.

However, something tells me that even though you now know this you still won't adhere to the pilot-wave interpretation (although according to your last post you should). People are weird like that.

Simplicity is a subjective concept. There is no objective measure of simplicity of a theory.

For PRACTICAL physicists, which most physicists are, the standard interpretation is still simpler because it requires a smaller amount of CALCULATION. It is simpler to calculate psi and probability density |psi|^2 then to calculate psi and a large ensemble of trajectories. Practical physicists are more interested in ability to efficiently calculate than in ability to intuitively explain.

But still, there are even situations in which it is PRACTICALLY SIMPLER to calculate the trajectories and the probability density than to calculate psi. See e.g.
Phys. Rev. Lett. 82, 5190–5193 (1999) [http://prl.aps.org/abstract/PRL/v82/i26/p5190_1]
In such situations, even for practical physicists Bohmian QM is really simpler than standard QM.

Other practical uses of Bohmian particle trajectories are discussed in a recent book
https://www.amazon.com/dp/9814316393/?tag=pfamazon01-20

 

[DrewD]

There are more physical assumptions. You need an unmeasurable pilot wave that controls the trajectories of real particles that have a physical position and momentum but, despite these being well defined, they cannot be simultaneously measured. I don't like that. I didn't say it was wrong.

You are right, I will not start using Bohmian mechanics because my research is in quantum information and nobody uses this interpretation because it provides nothing new (that's actually not true, but there has been no experimental confirmation of the one new prediction that I know of). It might be a nice way to think about things, and I often do imagine quantum particles to be somewhat like the Bohm interpretation, but until there is a reason to follow a less common interpretation that would make reading QM papers more difficult, you are correct.

You will probably continue to adhere to the pilot-wave interpretation, which is equally valid but provides nothing new, despite the fact that the rest of the physics community uses a different formality. This will make your research in anything except re-deriving QM difficult, but people are weird like that. Maybe you will make a breakthrough. Good luck.

 

[Demystifier]

There are more physical assumptions. You need an unmeasurable pilot wave ...

But standard QM also needs THE SAME unmeasurable wave (which is not called "pilot", but is mathematically the same anyway).

 

[nonequilibrium]

Simplicity is a subjective concept. There is no objective measure of simplicity of a theory.

For PRACTICAL physicists, which most physicists are, the standard interpretation is still simpler because it requires a smaller amount of CALCULATION. It is simpler to calculate psi and probability density |psi|^2 then to calculate psi and a large ensemble of trajectories. Practical physicists are more interested in ability to efficiently calculate than in ability to intuitively explain.

But still, there are even situations in which it is PRACTICALLY SIMPLER to calculate the trajectories and the probability density than to calculate psi. See e.g.
Phys. Rev. Lett. 82, 5190–5193 (1999) [http://prl.aps.org/abstract/PRL/v82/i26/p5190_1]
In such situations, even for practical physicists Bohmian QM is really simpler than standard QM.

Other practical uses of Bohmian particle trajectories are discussed in a recent book
https://www.amazon.com/dp/9814316393/?tag=pfamazon01-20

But when simply calculating the wavefunction suffices (due to only being interested in averaged behaviour), why can't the pilot-wave theorist also be satisfied with just calculating the wavefuntion in those cases? Why would he go through the trouble of the extra calculations? Concerning practical issues, I see the explicit trajectories more like an add-on which can be helpful in numerical simulations but are not important for predicting observations (of course they're important for understanding observations). Am I missing your point? More succinctly: can you think of a case where a pilot-wave theorist is obliged to go through more trouble than, say, someone adhering to the Copenhagen interpretation?

By the way, interesting book! I didn't know there was one like that out there.

There are more physical assumptions. You need an unmeasurable pilot wave that controls the trajectories of real particles that have a physical position and momentum but, despite these being well defined, they cannot be simultaneously measured. I don't like that. I didn't say it was wrong.

You are right, I will not start using Bohmian mechanics because my research is in quantum information and nobody uses this interpretation because it provides nothing new (that's actually not true, but there has been no experimental confirmation of the one new prediction that I know of). It might be a nice way to think about things, and I often do imagine quantum particles to be somewhat like the Bohm interpretation, but until there is a reason to follow a less common interpretation that would make reading QM papers more difficult, you are correct.

You will probably continue to adhere to the pilot-wave interpretation, which is equally valid but provides nothing new, despite the fact that the rest of the physics community uses a different formality. This will make your research in anything except re-deriving QM difficult, but people are weird like that. Maybe you will make a breakthrough. Good luck.

I don't follow you when you say "there are more physical assumptions" or "it adds nothing new". These words are probably too subjective in a sense. In my view, for example, the pilot-wave theory requires less physical assumptions, since collapse and Born's rule are physical. Unless you don't call them physical, in which case you're thinking in an interpretation where hardly anything is physical, and I've never quite understood that reasoning, but maybe that's my bad. As for providing "nothing new": surely we all agree it adds a lot on the theoretical level? In the sense that: it explains collapse, it explains Born's rule, it explains the time-dependent Schrödinger equation form the time-independent one etc. Most importantly, in my case, it is clear about what it's talking about, but it seems like most people don't have that problem with other interpretations, so it seems to be an iffy topic. In case you're talking about practical issues: even there it adds some new things. As you may have heard of, there is the concept of quantum non-equilibrium. Indeed, this has not been confirmed, so it's not an argument pro the pilot-wave theory, but it is an argument against the statement that it brings nothing new. More importantly, for real pratical issues, it leads to new methods of numerical simulations (I can provide links if you're truly interested) which seem to improve on the older methods. Maybe there are more such new practical effects in pilot-wave theory, but I'm not an expert on it.

As concerning your statement that pilot-wave theory works with an undetectable pilot-wave: I've encountered this statement before, even in this thread (and responded to it then in more depth). But as Demystifier just posted: I don't understand why you have such problems with it since it's the same wavefunction you're used to.

 

[Demystifier]

... it explains the time-dependent Schrödinger equation form the time-independent one etc. ...

Are you sure about that? Can you explain it or give a reference?

 

[nonequilibrium]

Are you sure about that? Can you explain it or give a reference?

Sure, it's really a nice little idea. From the little I know of quantum gravity, it seems the interest originates from there, in an attempt to derive the time-dependent Schrödinger equation from a time-independent universal wavefunction, this by treating spacetime as a macroscopic quantity.

Let's keep it simple, keeping the idea clear: the set-up is a two-particle system, the first with coordinates q, the latter with coordinates Q. The "universal" wavefunction is the time-independent \Psi(Q,q) satisfying E \Psi = \hat H \Psi. We now suppose that the Q-particle is macroscopic, such that we know its (Bohmian) position Q(t) at all times. We now want to treat the subsystem q quantum-mechanically. To do this, it is logical to define the conditional wavefunction \psi(q,t) := \Psi(Q(t),q). Note that the conditional wavefunction is now time-dependent since we've evaluated the universal wavefunction in the Bohmian trajectory for the macroscopic particle. It's not hard to prove/see that this conditional wavefunction and the universal wavefunction predict the same physics for the small particle.

Now due to the postulates of pilot-wave theory we know \dot Q(t) in terms of \Psi. Consequently, using the chain rule, we can calculate i\partial_t \psi(q,t). One gets that in highest order of M, being the mass of the macroscopic particle Q, we get that i\partial_t \psi = \hat H' \psi where \hat H' denotes the appropriate Hamiltonian for the subsystem. The math is a bit cumbersome, however I worked it out in a bachelor (i.e. undergraduate) project I made; I will PM it to you.

Summarizing, in the case of a time-independent Schrödinger equation, we can derive the time-dependent Schrödinger equation for a subsystem in case the environment is macroscopic.

Another, in my view less compelling, approach is taken by Goldstein in e.g. http://arxiv.org/pdf/quant-ph/0308039v1.pdf (page 21). The above approach, the one I outlined, I haven't seen as such in print. I think perhaps Kittel talks about it in his quantum gravity book, but I'm really not sure, this is more of a guess. Anyway I don't claim priority on this one, the suggestion mainly came from my advisor for the project (Ward Struyve), and I don't know where he got his juice, although there is a link with Tejinder Pal Singh as I outline in my project. I'll send the PM in a moment. (Anyone else interested is free to PM me, of course.)

NB: you are of course aware, Demystifier, but for other readers of this post I might note that the concept of conditional wavefunction is not new at all and can be read about in many papers/books about pilot-wave theory, e.g. Bohmian Mechanics by Dürr and Teufel. It's a nice new concept that pilot-wave theory brings in and seems to be fertile.

 

[nonequilibrium]

EDIT: the post I replied to seems to have been snipped

 

[bhobba]

But standard QM also needs THE SAME unmeasurable wave (which is not called "pilot", but is mathematically the same anyway).

Yea, but its ontological status is different. In most other interpretations (not all but most) of QM its purely a device for calculating probabilities, in BM it is supposed to actually exist out there and have physical effects that guide the actual particle that also exists - is like the aether in LET - and most physicists reject it for the same reason the aether is rejected. Like I say all interpretations suck in their own special way and the existence of the pilot wave that can not be detected is one way BM sucks.

Thanks
Bill

 

[nonequilibrium]

Bhobba, what is it then, according to you, that one measures, as viewed from the orthodox interpretation (or whatever interpretation you feel comfortable with). Apparently it cannot be the wavefunction, since you say that those interpretations treat it as unphysical. It can't be a point particle since then you'd have the pilot-wave theory, since any theory with point particles and wavefunctions can be shown to be the usual de Broglie-Bohm theory. Unless, of course, you deny the physical reality of anything in between measurements, "measurements" just being blips on a machine meaning nothing else, in which case I wonder why you would use the word "measurement" at all. This question is probably too philosophical, but I feel as though without your answer on it, I can't understand the other things you say (at least I can't understand your view on the matter so far, although I'd like to).

 

[bhobba]

Bhobba, what is it then, according to you, that one measures, as viewed from the orthodox interpretation (or whatever interpretation you feel comfortable with).

One doesn't 'measure' anything because that tacitly assumes what is being measured and what is doing the measurement is independent. What interpretations such as the Ensemble interpretation, Copenhagen, Consistent Histories etc provide is a prediction of the probabilities of what the outcome of a system and measurement apparatus is. Specifically the basis vectors one expands a state into varies from experimental, measurement, observational - whatever words you want to use - setup, apparatus etc etc - it's inherently contextually dependent.

That is why decoherence is so important because it gives a physical explanation for this state of affairs - exactly how the state is decohered by interaction with the environment depends on the environment - ie the overall observational situation.

In such a view a state doesn't physically exist out there - it simply codifies in a mathematical entity what the outcome of a system and observational apparatus is ie its purely a theoretical device.

Thanks
Bill

 

[nonequilibrium]

I've often heard decoherence explains collapse, but I've never seen it done (without some invalid argument along the road). Can you give me a reference? (Specifically I understand how decoherence leads to non-interfering components, but I don't understand how one specific component is selected out in such interpretations as you mention.)

Anyway you seem to be implying that every element of a theory is directly observable seems like a necessary part of a good theory/interpretation? Wouldn't you say "understanding" is equally important as "predicting"? Anyway, more importantly, do you have a clear notion of what you mean by "directly observable"? Indirectly, everything is observable in a theory, otherwise it wouldn't be in the theory.

 

[bohm2]

Anyway you seem to be implying that every element of a theory is directly observable seems like a necessary part of a good theory/interpretation? Wouldn't you say "understanding" is equally important as "predicting"?

I'm sympathetic to this view and I'm guessing this is the reason why I find Valentini's and Bohm's/Hiley's Bohmian approach more "understandable"/"explanatory" than DGZs minimalist Bohmian interpretation. Now we have sub-interpretations within interpretations. Belousak writes it like this:

On the DGZ view, then, the guidance equation allows for only the prediction of particle trajectories. And while correct numerical prediction via mathematical deduction is constitutive of a good physical explanation, it is not by itself exhaustive thereof, for equations are themselves 'causes' (in some sense) of only their mathematical-logical consequences and not of the phenomena they predict. So we are left with just particles and their trajectories as the basis within the DGZ view of Bohmian mechanics. But, again, are particle trajectories by themselves sufficient to explain quantum phenomena? Or, rather are particle trajectories, considered from the point of view of Bohmian mechanics itself, as much a part of the quantum phenomena that needs to be explained?...the mere existence of those trajectories is by itself insufficient for explanation. For example, to simply specify correctly the motion of a body with a certain mass and distance from the sun in terms of elliptical space-time orbit is not to explain the Earth's revolving around the sun but rather to redescribe that state of affairs in a mathematically precise way. What remains to be explained is how it is that the Earth revolves around the sun in that way, and within classical mechanics, Newton's law of universal gravitation and second law provide that explanation.

The author then goes on to argue for favouring the non-minimalist Bohmian model (e.g. quantum potential, etc.). I found that argument kind of persuasive for the same reason I found your argument above persuasive.

 

[nonequilibrium]

Bohm2, thank you for your posts (incl #22). They are certainly interesting remarks. I have two questions:

* One minor one: you seem to imply Valentini favours interpreting the quantum potential as a causal agent (instead of just a handy mathematical similarity with the Hamilton-Jacobi formalism of classical mechanics). However, I remember reading some passages of his work where he definitely implies the reverse, more in the line of what you seem to call the minimalist Bohmian interpretation. Does this claim seem odd to you? (if so I'll dig up the exact reference) If not, in what way did I misunderstand you?

* More importantly: although I'm in principle not against the kind of argument you bring forth (regarding explaining the trajectories) I can't find it very convincing. If I understand correctly, you're not satisfied with predicting the trajectories, but also want to find a causal agent. Indeed this is in line with my own comment regarding "understanding". But I'm having trouble with how one determines what does not need to be explained, trajectory-wise. In Newtonian mechanics, linear motion at constant speed needs not be explained (first law of Newton). How is it obvious that in the dBB case we still regard this as the case that needs no further explanation?

I'm trying to understand your point of view. Which is it that you want to interpret physically: the wavefunction, or the quantum potential? Perhaps the quantum force? Or all of them? And for any: how do you circumvent the seemingly fundamental problem concerning them being functions on configuration space? Actually, I suppose this only a problem if one tries to interpret the wavefunction physically; it's less of a problem for the quantum potential, say. After all, that case is reminiscent of electrodynamics. Do point out of I'm being inconsistent with this view.

 

[bhobba]

I've often heard decoherence explains collapse, but I've never seen it done (without some invalid argument along the road). Can you give me a reference? (Specifically I understand how decoherence leads to non-interfering components, but I don't understand how one specific component is selected out in such interpretations as you mention.)

Anyway you seem to be implying that every element of a theory is directly observable seems like a necessary part of a good theory/interpretation? Wouldn't you say "understanding" is equally important as "predicting"? Anyway, more importantly, do you have a clear notion of what you mean by "directly observable"? Indirectly, everything is observable in a theory, otherwise it wouldn't be in the theory.

The reason you have not seen decoherence explaining the measurement problem is because it strictly speaking doesn't - it explains it only for all practical purposes. It explains how a superposition is transformed into a mixed state but where each pure state of the mixed state is an eigenstate of what is being measured. This means the usual rules of probability apply where you can consider it in an actual state that the measurement reveals rather than some kind of weird superposition where it is literally in a number of states simultaneously eg literally being in two positions at the same time. The ensembles of the ensemble interpretation then actually exist and you simply pick out one of them. Here is the textbook I am studying right now about it:
https://www.amazon.com/dp/3642071422/?tag=pfamazon01-20

Why do you want to use terminology like directly observable for a situation when it is the system AND observational apparatus that the theory describes?

Sure understanding is important and I think I understand the interpretations I mentioned better than an inherently unobservable pilot wave that strongly reminds me of an aether.

Don't be fooled by statements of guys like Feynman who say no one understands QM - in the context of what he was writing about it is 100% true - but that context is in terms of everyday pictures where you simply can not picture a particle taking two paths simultaneously. If you refuse to think in terms like that - no problem. If you try to then you will as he said go down a hole that no one has ever escaped from. You can also ascribe to BM if you like - but I personally think this unobservable pilot wave is a crock of crap - but to each his/her own. I personally have no problem with viewing the world in ways different from everyday experience. I recently heard an audiobook on entanglement where they talked about a discussion Feynman and Bohm had while they were in Brazil. Dave was really proud of BM claiming it solves all sorts of problems but, Dick explained - basically - it only solved those problems if you think they are problems - he had zero issues with interpretations that refused to think in terms of ordinary everyday pictures - it worked perfectly OK for him that way - as it does for me.

Thanks
Bill

 

[Demystifier]

Bhobba, I could appreciate your quite orthodox view of QM, provided that you give me straight answers to the following questions:
1. Does anything exist before we observe it?
2. If yes, then what it is?
3. If you don't know what it is, then do you think physics should try to find it out?

 

[bhobba]

Bhobba, I could appreciate your quite orthodox view of QM, provided that you give me straight answers to the following questions:
1. Does anything exist before we observe it?
2. If yes, then what it is?
3. If you don't know what it is, then do you think physics should try to find it out?

Without decoherence then it does not exist before you observe it - the act of observation causes it to exist. With the ensemble interpretation the naive view is it really does exist in that state prior to observation but the Kocken-Sprecker theorem says - no way. Ballentine was fouled up by this and resorted to the belief some sub quantum process meant it really did exist - and this was Einsteins view - QM was incomplete. However since it is really a theory about the results of observation ie information - there is nothing physically going on so the act of observation causing it to exist is not really a problem. But it does whisper in your ear - something else is going on here.

I believe that something else is decoherence. It causes a superposition to become a mixed state where each pure state of a mixed state is an eigenvector of what is being observed so no collapse occurs - observation does not change a state - it reveals what is really there. A mixed state is in one of its pure states - we simply do not know which one. This is completely different from a superposition. It does not solve the measurement problem because it does not say how a particular eigenstate is selected (there are other issues such as what can we say before the environment quickly decoheres it - but that is the main one) - what it does however is explain how it is in an eigenstate before observation - it really is in a definite eigenstate before observation. Schrodinger's cat really is alive or dead - not some weird state where it is both alive and dead.

To be 100% sure my answers to your questions are:

1. Yes
2. We don't know - but it is a definite outcome 100% for sure - we simply do not know which one.
3. I have zero problems with a system being in a definite state and not knowing what it is and physicists should not worry about it. But if they want to - well as one wag once said - free scientific inquiry - the first part is redundant.

Thanks
Bill

 

[Demystifier]

For bhobba, mr. vodka, and bohm2:
I don't think that wave function in BM is more real than in standard QM.

In standard QM, one may (or may not) think of psi merely as a mathematical tool to compute the probability.
Likewise, in BM one may (or may not) think of psi merely as a mathematical tool to compute the particle trajectories.

Both in standard-QM camp and in BM camp there are people who disagree on how "real" the wave function is. But in both camps, this question is NOT considered to be a crucial one.

 

[Demystifier]

Without decoherence then it does not exist before you observe it - the act of observation causes it to exist.

1. Yes
2. We don't know - but it is a definite outcome 100% for sure - we simply do not know which one.
3. I have zero problems with a system being in a definite state and not knowing what it is and physicists should not worry about it. But if they want to - well as one wag once said - free scientific inquiry - the first part is redundant.

I would like to remind you that questions 1. 2. and 3. were referring to reality BEFORE observation. So perhaps you would like to rewrite your answers to 1. 2. and 3., because in the present form it doesn't make sense.

 

[bhobba]

For bhobba, mr. vodka, and bohm2:
Both in standard-QM camp and in BM camp there are people who disagree on how "real" the wave function is. But in both camps, this question is NOT considered to be a crucial one.

I agree that there is disagreement on how real the potential that determines the position of the particle is is in BM. But I do not agree this issue is not crucial - I believe you really must consider it real or how else does it determine the position of the particle. I think there was a post earlier on in this thread that explained the issue.

Thanks
Bill

 

[bhobba]

I would like to remind you that questions 1. 2. and 3. were referring to reality BEFORE observation. So perhaps you would like to rewrite your answers to 1. 2. and 3., because in the present form it doesn't make sense.

I would like to remind you that a mixed state is in a particular pure state prior to observation - we simply do not know which one. Schrodengers cat is definitely alive or dead prior to observation with decoherence.

Thanks
Bill

 

[Demystifier]

I agree that there is disagreement on how real the potential that determines the position of the particle is is in BM. But I do not agree this issue is not crucial - I believe you really must consider it real or how else does it determine the position of the particle.

First, the quantum potential determines acceleration, not position. But that's not important here.

What is important is to understand some analogies with classical mechanics. Is Hamiltonian H(p,x) real, for if not then how else it determines the motion of the particle? Is Newton potential V(x) real, for if not then how else it determines the motion of the particle? Is the solution S(x,t) of the Hamilton-Jacobi equation real, for if not then how else it determines the motion of the particle?

Well, if all these things in classical mechanics are real, then so is psi(x,t) in BM. In fact, psi(x,t) in BM is the most similar to S(x,t) in classical mechanics.

 

[Demystifier]

I would like to remind you that a mixed state is in a particular pure state prior to observation - we simply do not know which one. Schrodengers cat is definitely alive or dead prior to observation with decoherence.

I think you misunderstood something about decoherence. (Which is surprising for someone who is reading the excellent Schlosshauer's book.)

 

[bhobba]

What is important is to understand some analogies with classical mechanics. Is Hamiltonian H(p,x) real, for if not then how else it determines the motion of the particle? Is Newton potential V(x) real, for if not then how else it determines the motion of the particle? Is the solution S(x,t) of the Hamilton-Jacobi equation real, for if not then how else it determines the motion of the particle?

The Hamiltonian is not real - however from it you can derive a force that is presumably caused by some real agency - after all that is the meaning behind Newtons first law - as it stands it follows from the definition of force which being a definition says nothing. The physics is the assumption the force is caused by something real.

I was a bit confused about this myself at one time where I thought Newtons laws were basically tautological rubbish but I had a long discussion with John Baez about it and he explained what was really going on which is it is basically a prescription that says get to the forces where the forces are actually caused by something REAL. The same with the potential of BM - it codifies something REAL.

Thanks
Bill

 

[bhobba]

I think you misunderstood something about decoherence. (Which is surprising for someone who is reading the excellent Schlosshauer's book.)

I don't think I do - but hey anything is possible - I am not perfect - far from it.

Decoherence results from considering the system, environment and measurement apparatus as a whole and is in a mixed state. Due to decoherence the off diagonal elements of the state and apparatus quickly go to zero by the leaking of the phase to the environment which means the pure states are now eigenstates of the measurement apparatus. An eigenstate is a state that gives that particular outcome - no ifs - no buts. A mixed state is in one of it's pure states 100% for sure - we simply do not know which pure state it is.

If there is any error with the above feel free to correct it.

Thanks
Bill

 

[martinbn]

Yea, but its ontological status is different. In most other interpretations (not all but most) of QM its purely a device for calculating probabilities, in BM it is supposed to actually exist out there and have physical effects that guide the actual particle that also exists - is like the aether in LET - and most physicists reject it for the same reason the aether is rejected. Like I say all interpretations suck in their own special way and the existence of the pilot wave that can not be detected is one way BM sucks.

Thanks
Bill

What does it mean to actually exists out there ... in phase space?

 

[Demystifier]

Decoherence results from considering the system, environment and measurement apparatus as a whole and is in a mixed state.

By "system", I guess you mean the measured subsystem, am I right? Then these three together as whole are in the pure state, not mixed state.

Due to decoherence the off diagonal elements of the state and apparatus

You probably mean: system and apparatus?

quickly go to zero by the leaking of the phase to the environment which means the pure states

Pure states of what? Of system? Of apparatus? Of environment? Of everything together?

are now eigenstates of the measurement apparatus.

I don't even understand what it means. I know what is eigenstate of an operator, but I never heard about an "eigenstate of measurement apparatus".

An eigenstate is a state that gives that has that particular outcome - no ifs - no buts.

Perhaps by "eigenstate" you mean one of macroscopically distinct states of the apparatus?

A mixed state is in one of it's pure states

This is an oximoron. A mixed state cannot be in a pure state.

If there is any error with the above feel free to correct it.

Is the above enough?

 

[bhobba]

What does it mean to actually exists out there ... in phase space?

First I am not an expert on BM - I only know the basics. But the the particle is guided by a quantum potential which determines its acceleration. Its reality (or as a codification of something real) follows from Newtons first law that some agency must be responsible for a force acting on a particle. I suppose you can claim its not real and nothing causes the particles acceleration - it simply happens because that's how nature works - but to me that is simply unacceptably weird - but hey QM is pretty weird to begin with - but I don't think that weird.

Thanks
Bill

 

[bhobba]

By "system", I guess you mean the measured subsystem, am I right? Then these three together as whole are in the pure state, not mixed state.

By system I mean the system being measured.

Pure states of what? Of system? Of apparatus? Of environment? Of everything together?

The outcome of the observation is the quantum state of the tensor product of the system and apparatus. If you are for example measuring position its is in an eigenstate of position

I don't even understand what it means. I know what is eigenstate of an operator, but I never heard about an "eigenstate of measurement apparatus".

Whoa - let's stop here. In every discussion of quantum decoherence I have read (as far as measurements are concerned) the measuring apparatus is itself considered a quantum system and what it indicates is considered a state of the apparatus. For example in Schrodinger's cat the cat (once observed) is considered to be in a quantum state that is either alive or dead. These are the measurement outcomes and are referred to as eigenstates, being the eigenstates of the operator corresponding to the measurement - also called the pointer basis. The tensor product of the system being measured and the apparatus is considered as a state represented by a density operator. The density operator is represented by a matrix using the possible states of the measurement apparatus (after observation ie the pointer basis) as the basis of that representation. Now what decoherence says is the off diagonal elements very quickly goes to zero so that the state of the system being measured is a mixed state of states that definitely give a specific measurement outcome. The interpretation of a mixed state is it is in a specific state - in this case a state that gives a definite measurement outcome - but we only know the probabilities of what state that is.

Do you agree or disagree?

Thanks
Bill

 

[Demystifier]

By system I mean the system being measured.

Then, as I said, the system, apparatus, and environment together are in a PURE state, not mixed.

The outcome of the observation is the quantum state of the tensor product of the system and apparatus.

OK, now it's clear.

Whoa - let's stop here. In every discussion of quantum decoherence I have read (as far as measurements are concerned) the measuring apparatus is itself considered a quantum system and what it indicates is considered a state of the apparatus.

I agree, a state of the apparatus is a well-defined concept. But the EIGEN-state of the apparatus is not.

For example in Schrodinger's cat the cat (once observed) is considered to be in a quantum state that is either alive or dead. These are the measurement outcomes and are referred to as eigenstates, being the eigenstates of the operator corresponding to the measurement.

That's not wrong, but is not precise enough. In particular, if you determine whether the cat is dead or alive, it is not obvious what is the corresponding OPERATOR which is being measured. And without an operator, the word "eigenstate" does not have a meaning.

The tensor product of the system being measured and the apparatus is considered as a state represented by a density operator. The density operator is represented by a matrix using the possible states of the measurement apparatus (after observation) as the basis of that representation. Now what decoherence says is the off diagonal elements very quickly goes to zero so that the state of the system being measured is a mixed state of states that definitely give a specific measurement outcome.

That's OK, but ...

The interpretation of a mixed state is it is in a specific state - in this case a state that gives a definite measurement outcome - but we only know the probabilities of what state that is.

... is not OK. Even Schlosshauer explains that such an interpretation is not appropriate. One reason is because the TOTAL system (measured system, apparatus AND environment together) is not in a mixed state. There are other reasons as well.

Do you agree or disagree?

I agree that measured system and apparatus are in a mixed state, but as I said, I disagree that this fact alone is sufficient to conclude that "they are in a definite pure state but we only don't know which one".

 

[bhobba]

... is not OK. Even Schlosshauer explains that such an interpretation is not appropriate. One reason is because the TOTAL system (measured system, apparatus AND environment together) is not in a mixed state. There are other reasons as well.

But the measured system and apparatus together are in a mixed state with diagonal elements in the pointer basis and off diagonal elements zero. The total system including environment continues to evolve unitarily - the measured system and apparatus does not - it has become entangled with the environment.

I agree that measured system and apparatus are in a mixed state, but as I said, I disagree that this fact alone is sufficient to conclude that "they are in a definite pure state but we only don't know which one".

I am scratching my head about that one. By definition a mixed state is an ensemble of states. A mixed state is exactly the same as randomly selecting one of the pure states from this ensemble of states. This is exactly the same as the system being in one of the pure states and only knowing a probability of which one it is - observationally it is indistinguishable. Every singe book I have ever read on QM, and believe me I have read a few, has defined mixed states that way.

Just to ensure I am not going crazy I did an internet search and easily found a previous thread:
https://www.physicsforums.com/showthread.php?t=260622
'Seriously, a mixed state is an ensemble description. In fact, one of the peculiar things about the interplay between mixed state statistics and quantum statistics is that considering particles in a "mixed state" is indistinguishable from considering them in a randomly drawn pure state if that random drawing gives a statistically equivalent description as the mixed state.'

What exactly with the above do you not agree with?

Thanks
Bill