Decoherence does not collapse wavefunc.

[ZPower]

"Decoherence does not generate actual wave function collapse. It only provides an explanation for the appearance of wavefunction collapse. The quantum nature of the system is simply "leaked" into the environment"
http://en.wikipedia.org/wiki/Quantum_decoherence

I have taken a full year of quantum, but this puzzles me. So decoherence does not collapse the wavefunction? but somehow the information leaks to teh enviornment? and it is conserved?
if this is so, then this would be a reversible process, no?
further i though decoherence and wv func collapse are eqivalent?


any thoughts?

 

[cesiumfrog]

They're equivalent because the leak is thermodynamically irreversible: in practice there is no way to recapture all the information after it leaks into the environment.

But it is reversible in principle, and for systems contained in small environments this reversal (as well as intermediate appearance of collapse) is demonstrable.

 

[arkajad]

They are not equivalent because wave function collapses in a finite time and decoherence would need infinite time to collapse anything. Decoherence is an escape mechanism for those who are scared of real collapses

 

[Phrak]

They are not equivalent because wave function collapses in a finite time and decoherence would need infinite time to collapse anything. Decoherence is an escape mechanism for those who are scared of real collapses

There is no such mechanism.

 

[jambaugh]

The quantum nature of the system never ceases to be its quantum nature and that nature in part is that we use a probabilistic description of the system which for a quantum system manifests as a wave function.

What is "leaking into the environment" is the a priori information about the system encoded in an original sharp wave-function.

Remember that nowhere in the decoherence process is one insisting that the quantum system in question be measured, yet it is only when a measurement is made that we collapse the system's wave-function.

Take the classical analogue. Imagine you inject a classical particle into a box with smooth idealized mirror walls. You can in principle trace the trajectory and know the future state of the classical particle. But in a realistic setting the walls are thermal and rough. We can map the original classical state into a singular probability distribution (p=1 for the known state and p=0 for all others). As the particle bounces around the thermal box we see this probability distribution spread out, entropy goes up, and the "sharp" classical description "classically decoheres". If we then look for where the classical particle and measure its classical state we see the probability distribution "collapse" into another singular form, p=1 for the observed state and p=0 for all others.

Quantum systems behave the same except that they have no classical objective state and their probability description is not a distribution over a set of states. It is that uniquely quantum relative distribution over sets of commuting observables which we can express as a diagonal density operator in the corresponding basis.

Instead of a singular description we have a maximal description in the density operator in the form of a unit trace projection operator (projecting onto a 1-dim subspace) which we can discard for the moment and simply refer to a basis element.
\psi : \quad \rho = \psi \otimes \psi^\dagger

That is the closest we get to an actual state of a quantum system. However again with decoherence we must revert to the more general density operator description. This is why we refer to psi (the wave-function) as the "state vector" even though it is not the system's state. It is the square root of its "singular probabilistic description" \rho_\psi.

So keep in mind, even with classical systems we can view our maximal descriptions "object A is in state S" as probabilistic descriptions "object A has probability p=1 of being observed with observable values corresponding to S and p=0 for all others". In both classical and quantum systems decoherence is the spreading of the probabilities due to interaction with inaccessible epistemic elements (the thermal environment), and "collapse" is due to updating the probabilistic description as we again measure the system.

 

[arkajad]

T
Quantum systems behave the same except that they have no classical objective state and their probability description is not a distribution over a set of states.

That is one point of view there are other points of view.

It is that uniquely quantum relative distribution over sets of commuting observables which we can express as a diagonal density operator in the corresponding basis.

That is rather minimalistic and ad hoc point of view.

In both classical and quantum systems decoherence is the spreading of the probabilities due to interaction with inaccessible epistemic elements (the thermal environment), and "collapse" is due to updating the probabilistic description as we again measure the system.

Is this separation between the system and its "epistemic environment" objective or only in the head of a given quantum decoherent physicist. Another physicist will make this separation line perpendicular to the previous one?

 

[cesiumfrog]

Take the classical analogue. Imagine you inject a classical particle into a box with smooth idealized mirror walls. You can in principle trace the trajectory and know the future state of the classical particle. But in a realistic setting the walls are thermal and rough. We can map the original classical state into a singular probability distribution (p=1 for the known state and p=0 for all others). As the particle bounces around the thermal box we see this probability distribution spread out, entropy goes up, and the "sharp" classical description "classically decoheres". If we then look for where the classical particle and measure its classical state we see the probability distribution "collapse" into another singular form, p=1 for the observed state and p=0 for all others.

I've not heard that analogy before, Thankyou.

That is one point of view there are other points of view.

They are not equivalent because wave function collapses in a finite time and decoherence would need infinite time to collapse anything. Decoherence is an escape mechanism for those who are scared of real collapses

The OP is obviously trying to understand how the decoherence program is supposed to work. If you're only interested in soap-boxing your personal evidenceless viewpoint as if it were absolute truth, then how about warning the OP not to be confused by this? But if you're not too scared to then do tell me more about this finite time: in which velocity reference frame is it extremised, and where approximately is its line between microscopic and macroscopic?

 

[arkajad]

But if you're not too scared to then do tell me more about this finite time: in which velocity reference frame is it extremised, and where approximately is its line between microscopic and macroscopic?

There is nothing mysterious about finite time. It is finite in all experiments. Otherwise till now we have no data to compare our theories with. And it has nothing to do with microscopic and macroscopic. SQUIDs are macroscopic. As for the "extremised velocity frame" I have not comments - I do not know what you are referring to. Who is "extremising" what and why?

 

[cesiumfrog]

You say the collapse process (of which you give no details) occurs in some finite period of time. But clearly, different observers will conclude this period of time to have different durations, according to special relativity. So, which observers will be the ones who infer the shortest duration of time for the collapse process? Those in the rest frame of the apparatus? Or the rest frame of the universe?

Also, fine if it has nothing to do with microscopic and macroscopic, but which systems will behave quantum mechanically and which systems will have collapsed into classical behaviour? So far, the decoherence has been very successful in predicting that isolated systems will behave quantum mechanically and systems in greater interaction with their environments will behave as though they have collapsed into classical states. But obviously you must disagree with some part of this, because you argue against decoherence. Are you in Penrose's camp, claiming collapse is mediated by gravitons (and somehow related to consciousness), so mass determines how quickly collapse occurs? Are you in Wigner's camp, claiming collapse depends on whether a chimpanzee mind has contemplated the experimental outcome? What criteria do you propose for predicting which systems will collapse rapidly and which will have long-lasting quantum coherence?

 

[arkajad]

You say the collapse process (of which you give no details) occurs in some finite period of time. But clearly, different observers will conclude this period of time to have different durations, according to special relativity. So, which observers will be the ones who infer the shortest duration of time for the collapse process?

No observers are needed. The process can be fully automatized.

Also, fine if it has nothing to do with microscopic and macroscopic, but which systems will behave quantum mechanically and which systems will have collapsed into classical behaviour.

What is classical behaves classically, what is non-classical needs to be described quantum mechanically. Chairs and tables are classical. Things that happen and events that are recorded are classical.

Are you in Penrose's camp, claiming collapse is mediated by gravitons (and somehow related to consciousness)? Are you in Wigner's camp ...

Neither. But perhaps I am in Niels Bohr's camp:

"All information about atoms expressed in classical concepts
All classical concepts defined through space-time pictures" [Bohr 1927]

 

[Phrak]

You are not in Bohr's camp that I can tell. His philosophy was simply: "This is what you get, and you can't understand my theory any better than what we've given you." A somewhat self serving philosophy, in my opinion.

To posit this superluminal thing called wave function collapse is an addition to the basic postulates of quantum mechanics. Not that there is anything wrong with superluminal connectivity, and I understand the motivation "to make sense" of the underlying postulates--that is, to motivate an empirical equation with elements we are happier to associate with elements of physical reality, but that the mechanisms proposed to obtain this to date are so loopy only indicates to me that no one has yet stumbled upon the right idea.

 

[jambaugh]

That is one point of view there are other points of view.

It is more than a point of view. It is exactly and precisely the assumption that probabilities arise from a distribution over a set of states which leads to Bell inequalities. Probabilities are measures, P(A xor B) + P(B xor C) > or = P(A xor C). Since QM violates Bell inequalities QM probabilities cannot be expressed as distributions over a state space. Hence the occurrence of negative "quasi-probabilities" in Wigner's quasi-distributions.

That is rather minimalistic and ad hoc point of view.

How so? It is the general setting of QM description. The proper representation of a quantum system is a density (co)operator. Only in an idealized Temp=0 limit do we imagine a sharp system wherein we can "square-root" the density matrix to manifest a mode vector (e.g. a wave-function).

Again note that using a language of probabilistic description we can still in principle incorporate certainty via P(X=x)=1, P(X= other) = 0. It is the more general language incorporating the prior "sharp mode" or "classical state" as such a special case. One can still do all of classical physics in this language by restricting the available physically actualizable observables to a commuting subset.

Is this separation between the system and its "epistemic environment" objective or only in the head of a given quantum decoherent physicist. Another physicist will make this separation line perpendicular to the previous one?

It is relative to the definition of the system. Note that relativity is the "gripping hand" of your false alternatives.

You consider an EPR pair and speak of "the left electron" and "the right electron" I consider the same EPR pair and consider "the spin-z = +1/2" and "the spin-z = -1/2" electron. We are partitioning the system into distinct halves (and can thus focus on one half as "the system" and the other as "environment") which are not simply permutations of each other. They are not inseparable but rather hyper-separable.

It is like splitting a position vector (of a classical object) into different coordinates. The coordinates are meaningful relative to a frame but we can choose a continuum of possible frames with a continuum of possible coordinate sets. This doesn't imply that the assertion that this position vector is specifically 3 dimensional, is meaningless.

Likewise in the EPR example we have two "count em! two" electrons. But they ain't objects with an objective fixed separation into components. They are quantum phenomena (a.k.a. quanta) factorable into two component quanta in a continuum of meaningful ways. (Bob looks at spin but using a different axis than mine and his component electrons will be a distinct slicing of the cake.)

And if you look at the logic in interpretations of EPR you'll see in many cases the mistake of thinking that e.g. your L vs R electrons must be a permutation of my spin up vs down electrons prior to a simultaneous measurement of z-spin and position. Until we speak of a measured electron pair we are either speaking about possible outcomes prior to measurement or speaking about the mode of pair production and not a given instance of that pair. Once we make a measurement we are changing what we are referring to and thus collapsing or otherwise discontinuously changing our description.

I bring up the EPR pair because it is a simpler example of this relativity of division. But this applies to the division of system vs episystem as well. Think of this in terms of e.g. Unruh radiation of an accelerating observer. A boosted observer sees a different subdivision of system and episystem and thus his system appears to change "state" increasing in particle number.

 

[jambaugh]

Here's a tip. If one wants to talk about how long it takes for a physical collapse to occur, first define what one means in terms of how you actually observe a collapse e.g. what observables correspond to Non-collapsed and collapsed cases.

Until and unless this is made clear any suppositions about the time it takes or mechanism by which it occurs are no better than the rantings of a medium in a seance.

"You dead husband is wearing a blue coat! He's waving at you lovingly, he says...he says...please deposit $20 to continue your call to the netherworld!"

 

[arkajad]

Here's a tip. If one wants to talk about how long it takes for a physical collapse to occur, first define what one means in terms of how you actually observe a collapse e.g. what observables correspond to Non-collapsed and collapsed cases.

It is a stochastic variable with its distribution determined by the quantum state and the detector. You know quite well that, for instance, radioactive decay is a stochastic process. The same with every other event process controlled by quantum phenomena except that stochastic processes involved are somewhat more complicated than a simple decay.

 

[arkajad]

It is more than a point of view. It is exactly and precisely the assumption that probabilities arise from a distribution over a set of states which leads to Bell inequalities. Probabilities are measures, P(A xor B) + P(B xor C) > or = P(A xor C). Since QM violates Bell inequalities QM probabilities cannot be expressed as distributions over a state space. Hence the occurrence of negative "quasi-probabilities" in Wigner's quasi-distributions.

And why do you make such an assumption? Because, first of all, you have learned from textbooks, second, almost everybody does it, and third, you do not know anything better. But perhaps there are better assumptions? I don't think everybody is happy with such an assumption. In fact I know it.


[QUOTE}How so? It is the general setting of QM description. The proper representation of a quantum system is a density (co)operator. Only in an idealized Temp=0 limit do we imagine a sharp system wherein we can "square-root" the density matrix to manifest a mode vector (e.g. a wave-function). [/QUOTE]

Density operator has been devised for dealing with infinite ensembles of systems. You are not an infinite ensemble. You are a unique, individual system. The same with electrons that leave tracks in cloud chambers. Density matrix is of no use for describing the mechanism of formation of a unique track. And such unique tracks are being formed in the labs each day.

 

[jambaugh]

And why do you make such an assumption? Because, first of all, you have learned from textbooks, second, almost everybody does it, and third, you do not know anything better.

Firstly you are displaying a great deal of hubris to presume to say where I learned anything.

Secondly you are quite wrong as to how I acquired this "assumption".

Thirdly even should we assume I a.) did learn it from a textbook, b.) almost everybody "does it", and c.) that neither I nor these others know anything better...
none of these assumptions make any dent in the validity of my statement but rather would tend to support it.
*When you know the best way you cannot know anything better so failure to know better might be inductive evidence that the way in hand is the best way,
*absent any other information "what everybody does" usually is a pretty good way to do things given everybody has a choice in the matter,
*Textbooks though obviously not infallible are pretty damned good sources of knowledge, (My x-ray diffraction text was an especially good book, chock full of useful and insightful knowledge!).

Fourthly it is quite common to introduce such ad hominem irrelevances when you have no substantive counter to the actual point at hand. So again what makes you think you cannot on your own (as I did) derive Bell's inequalities directly from the simple assumption that your probabilities come from a measure over a state manifold, and in seeing the short and simple form of that derivation see as self evident that violation of Bell inequalities invalidates the assumption of an underlying state of reality. Locality arguments are irrelevant.

This I have done with pen and paper and Bell's book (all I lacked was a candle to complete the excommunication ). You try it and you may see something I didn't.
(start with the "metric" d(A,B) = f(A~B) where ~ is set difference and f is a probability distribution over the set of possible states of your system. Bell's inequality then takes the form of the triangle inequality for this metric assuming f is a measure on the set)
but I'm not interested in your opinion until you do some leg work. (unless of course you agree with me in which case I'll find your opinion wise and fascinating!)

But perhaps there are better assumptions?

and perhaps there are not. Perhaps if I put one more quarter in the slot machine I'll win the Jackpot. Perhaps-ing in the dark gets one nowhere or worse. What evidence or argument have you for supposing a better assumption and by what criteria and value system are you ordering assumptions better to worse? State them and abide by them or remain silent.

I don't think everybody is happy with such an assumption. In fact I know it.

Happiness is irrelevant. Functional meaning and concurrence with experience is all that is meaningful in physics. Like I say when I miss a (pool) shot
"It should have gone in"... and then I say... "and I should have been rich and famous with loads of hot beautiful babes hanging all over me and getting laid every night!"
I say this to emphasize to myself that this sort of "should" is the insistence that things should conform to my dreams instead of my expectations conforming to actuality. In pool it reminds me that I'm responsible for the result and my desire is irrelevant to how things actually behave.

Density operator has been devised for dealing with infinite ensembles of systems. You are not an infinite ensemble. You are a unique, individual system. The same with electrons that leave tracks in cloud chambers. Density matrix is of no use for describing the mechanism of formation of a unique track. And such unique tracks are being formed in the labs each day.

Firstly it is irrelevant why the density operator formal language was first introduced. What is relevant is how it functions. This is why you see me refer to it as a "co-operator" it is a linear functional mapping observables to their expectation values (since it is always used in conjunction with the trace):
rho : X ---> <X> usually expressed as Tr(rho * X).

The density co-operator X-->Tr(rho*X) IS the established set of expectation values for the observables of a system and as such is the most general, all encompassing representation of our knowledge about a physical system. It is the very physical prediction of measurement and as such is the basis for any meaningful statement about a physical system.

So, instead of "the density operator" call this expectation value functional the... expectation value functional if you wish. It is a necessary ingredient in any description of any system be it a singular instance or an ensemble or logically defined class. As it has a previously defined name can we agree to use it?

 

[jambaugh]

It is a stochastic variable with its distribution determined by the quantum state and the detector.

It? You mean collapse is a variable?

An observable is a stochastic variable with distribution determined by the mode of system production and the detector i.e. what observable is to be measured. Is that what you mean?

You know quite well that, for instance, radioactive decay is a stochastic process.

Yes, as is excitation decay. But decay is not the same as collapse. You can express the wave function of a decaying atom + its decay product field and see the nice exponential "decay" in the probability amplitude of the atom being alone and existent vs the growth of the probability amplitude for the decay products to exist and the atom to be absent. All within a perfectly coherent wave-function. It is when you measure for the presence of a decay product (e.g. a gamma detector) that you collapse this composite system description into one where the atom amplitude is 0. To make it easier look at the system of a particle tunneling to a lower energy state for two square wells separated by a finite potential bridge (one square well deeper than the other). A perfectly coherent "decay" description exists without every having to invoke a collapsing wave function.

The same with every other event process controlled by quantum phenomena except that stochastic processes involved are somewhat more complicated than a simple decay.

So again I ask. What is the meaning of a physical decay as opposed to the CI version where one is only considering the paper wave-function which one updates upon a change in knowledge about the system. Where is the observable? It doesn't have to be a direct observable, it can be a quality derived from observables, just so long as you can point to a time and say "Look! Collapse hasn't happened yet" and "Look here! Collapse has occured!" (and be pointing at the system and not at a piece of paper.)

 

[arkajad]

It? You mean collapse is a variable?

An observable is a stochastic variable with distribution determined by the mode of system production and the detector i.e. what observable is to be measured. Is that what you mean?

What I mean is that collapse is governed by a stochastic process. Much like radioactive decay but not that simple.

So again I ask. What is the meaning of a physical decay as opposed to the CI version where one is only considering the paper wave-function which one updates upon a change in knowledge about the system. Where is the observable? It doesn't have to be a direct observable, it can be a quality derived from observables, just so long as you can point to a time and say "Look! Collapse hasn't happened yet" and "Look here! Collapse has occurred!" (and be pointing at the system and not at a piece of paper.)

Observable is what can be observed. For instance a dot on a screen. Then the question is what is the mechanism governing the appearance of such dots in time and space? Because they appear at a certain time and at a certain place. How is the time of appearance and the place of appearance decided? The answer is simple: by a specific stochastic process that is determined by both, the wave function and the screen itself. You do not see the collapse, you do not see the wave function, but you can see the dot. Dots are you data. Wave functions and collapses are the auxiliary concepts that are needed in order to explain the emergence of these data.

 

[arkajad]

So, instead of "the density operator" call this expectation value functional the... expectation value functional if you wish. It is a necessary ingredient in any description of any system be it a singular instance or an ensemble or logically defined class. As it has a previously defined name can we agree to use it?

Being an expectation value functional it is completely irrelevant for the description of an individual quantum system. And nowadays we experiment with individual quantum systems that are being continuously monitored in real time. Density matrix is of no use in such experiments - because it needs infinite ensembles of systems and not just one system. Density matrix is like a probability distribution in a statistical ensemble in classical statistical mechanics. In statistical mechanics we integrate over the phase space, in quantum mechanics we calculate traces. It is good for statistical description of many body systems or infinite ensembles of individual systems. Not for one planet or one electron. For one planet circling around the Sun and one electron leaving track in a cloud chamber something deeper and better is needed.

 

[jambaugh]

What I mean is that collapse is governed by a stochastic process. Much like radioactive decay but not that simple.

Ok I follow you there, but you still avoid the foundational issue. We can speak of the mechanism of decay, and speak of decay times because decay is an observable process.
---"look, the atom is still there at "
---"look, 3 minutes and 18 seconds later my gamma detector went 'ping'!"
With decay you can see the event (or extrapolate back from the speed of the decay products) and you can then do statistics, establish a distribution on decay times, and measure a half-life and from that information postulate a mechanism for decay.

With collapse the physical process is that a measurement is made. You can model the measurement process, express the composite of measuring device and system in a larger context and let it evolve until the description is one of an array of recorded outcomes with corresponding probabilities. Note that you MUST use a density operator formulation here both because of the entanglement between system and measuring device and because the measurement process is thermodynamic in a fundamental way. That is where one sees decoherence. Now you still haven't collapsed the wave-function or rather the density operator until you make a specific assertion: that a specific outcome was made. Collapse is a conceptual process not a physical one and thus the "time it takes" is the time it take one to think it or write it down.

And it should be apparent in this investigation of the measurement process that the things we are writing down are in the end a classical probability distribution and thus at the beginning also was a probability distribution (though by use of a more general method of representation not wholly classical.) It is a representation of our knowledge about how the system or meta-system may behave and not a representation of its physical state.

As far as the time for the decoherence implicit in the measurement process, that is arbitrary. We can make the same measurement (and represent it with the same operator) with many specific laboratory configurations provided each configuration ultimately records the same observable for the system being measured. The decoherence process could be set up to take microseconds or weeks, as we choose, and when and where the decoherence occurs is also relative to how we set up the meta-description of the system + measuring device, e.g. how far out we put our meta-system meta-episystem cut.

As far as measuring the system the details of this meta description is irrelevant. As far as trying to understand measurement and collapse in terms of a model of reality goes, one falls into an infinite regress of measuring devices to observe the measuring devices to observe the measuring devices et cetera ad infinitum.

It is like trying to speak of absolute position. Coordinates only give the position of a system relative to the observer. You can then try to speak of the observers position relative to another observer and you quickly see the futility of it and appreciate the fact that position is always relative. Not meaningless but like electrical potential only meaningful as a difference in values.

Observable is what can be observed. For instance a dot on a screen. Then the question is what is the mechanism governing the appearance of such dots in time and space? Because they appear at a certain time and at a certain place. How is the time of appearance and the place of appearance decided? The answer is simple: by a specific stochastic process that is determined by both, the wave function and the screen itself.

Don't confuse the dynamics of that dot e.g. the mechanism for electron evolution with its collapse. Look at how you use the wave function in describing that dot. Or more precisely since presumably you're speaking of a dot on a CRT screen you have a thermal source (hot cathode) you need to rather use a density matrix.

You do not see the collapse, you do not see the wave function, but you can see the dot. Dots are you data. Wave functions and collapses are the auxiliary concepts that are needed in order to explain the emergence of these data.

They are auxiliary concepts applying to the prediction of outcomes. They "explain" in so far as they do by expressing maximal prediction. Explanation as you seem to want it to mean would involve breaking the phenomenon down into component phenomena, e.g. florescence of the screen, emission of electrons from a hot cathode, propagation through the intermediate e-m field or array of slits and pinholes etc. But in the end each of these component processes must first and foremost be predictably described so that the reductive explanation of the dot makes sense. Then to further explain you must reduce these components. What comes first in this chicken and egg chaise is key. Classically we stop at a large enough scale that we can refer to an idealization of state we call reality. Quantum mechanics begins with the measurement process as an irreducible phenomenon. As such we begin with prediction and predictive description and not with reality representation.

There is a good reason for this and it is that we can express the features of a reality representation within the scope of predictive description but not (as we see in QM) the reverse. Those features are specifically that of an underlying deterministic model. But falsify the hypothesis that such a model is possible and we still have our predictive description. The predictive language of QM is more general than the representative language of CM which is why it can express both quantum and classical phenomena and does so often at the same time as with the decoherence of the system+measuring device.

Within that predictive language the collapse of either psi or rho (on paper) is when you jump from:
"I'm considering a process by which my quantum propagates from a specific source, I use description rho (or psi). It propagates to a measuring device and according to theory the outcomes of my measurements will have the following probabilities P(X=1)=bla, P(X=2) = bla bla,"
to
"I'm now considering the case where we actually observe X=1 so let's update the description so we can calculate future probabilities!"

This is how the wave functions and density operators are actually used in practice, to represent classes of actualized quantum systems. All you have in the lab are a sequence of measurements or similar events, i.e. the recorded data. You cannot be like the zoologist and pull out the preserved specimen to show what you found and double check its features.

The wave-function and density operator both, are analogous to the zoologist's category of species, and not analogous to the DNA record of a single specimen.

When teaching my probability and statistics class I had the students guess the probability that at least two of the class (of 45) had birthdays on the same day. Then I showed them the calculation for that probability and it was much higher than most guessed, (about 94%).
We then went around the room declaring birthdays and sure enough we actually had 2 pairs match up. I then asked the question again... what is the probability that at least two students have the same birthday. One said 90% then quickly corrected himself, 100%!
I asked them then was my calculation wrong? We haven't changed who is in the room?

I did this to emphasize to them the nature of logical classes as opposed to sets. Probabilistic statements are statements about classes of possible outcomes and thus classes of systems, not single instances. By calculating the probability for my room of students I was identifying them as an instance of a particular class and knowing that class I could express a prediction about the actual instance.

Wave-functions are expressions of how a given instance of a quantum system might behave given you know it to be a member of a specific class of systems via the fact that a particular measurement has been made and the value of that measurement is specified.

Thus for example a given momentum eigen-"state" and spin "state" for an electron expresses the class of electrons for which the specified values have been measured. In the momentum-spin representation you have a little dirac delta function centered at the measured momentum in a tensor product with a specific spin "ket". You can write the "wave-function" in that you expand this Hilbert space vector in terms of components of position eigen-states and that representation is useful in that is explicitly gives the (square roots of) the probabilities of subsequent position measurements. Theory tells us how P and X relate and thus that this representation is a sinusoidal curve with a specific wave-length (h/p).

But the electron is not a wave-function. The road is not a line on a map. It is an analogue and to understand the type of analogue you must look at how the map is used. In the road case the map is a direct analogue, a model of the reality of the road. In the wave-function case we look at what we do with the wave function. We use it to calculate probabilities for position measurements, it is a logical analogue not a physical one... or rather it is first and foremost a logical analogue.

You may assert it is also a physical one but you must prove your case for that. I assert that wave-function collapse is a specific indicator that it is not a physical analogue but purely a logical/predictive one since it is the logic of updating our class of systems that instigates our collapsing the wave-function on paper.

I understand the temptation to say "an electron is both wave and particle" but one is mapping the quantum electon's behavior into two distinctly classical phenomena, classical waves and classical particles. It is the spectrum of behaviors one is addressing and we see in this "either or" business the relativity of the actual classical representation. It is the necessary relativity of the "reality" one is trying to paint for the electron. The electron is not the sinusoidal wave nor the dirac delta-function particle... it is a phenomenon of actualizable measurements which we can probabilistically predict using wave functions (and/or density operators) as representations of interrelated probabilities.

 

[arkajad]

Ok I follow you there, but you still avoid the foundational issue. We can speak of the mechanism of decay, and speak of decay times because decay is an observable process.

You can also observe creation of dots. In the real time (like in Tonomura's lab) or post factum.

---"look, the atom is still there at "
---"look, 3 minutes and 18 seconds later my gamma detector went 'ping'!"
With decay you can see the event (or extrapolate back from the speed of the decay products) and you can then do statistics, establish a distribution on decay times, and measure a half-life and from that information postulate a mechanism for decay.

I was in Tonomura's lab I was watching creation of dots from interference experiments.

With collapse the physical process is that a measurement is made. You can model the measurement process, express the composite of measuring device and system in a larger context and let it evolve until the description is one of an array of recorded outcomes with corresponding probabilities. Note that you MUST use a density operator formulation here both because of the entanglement between system and measuring device and because the measurement process is thermodynamic in a fundamental way.

Perahaps you MUST. I don't.

That is where one sees decoherence. Now you still haven't collapsed the wave-function or rather the density operator until you make a specific assertion: that a specific outcome was made. Collapse is a conceptual process not a physical one and thus the "time it takes" is the time it take one to think it or write it down.

WEll, you have your way of looking at things, I have mine way.

And it should be apparent in this investigation of the measurement process that the things we are writing down are in the end a classical probability distribution and thus at the beginning also was a probability distribution (though by use of a more general method of representation not wholly classical.) It is a representation of our knowledge about how the system or meta-system may behave and not a representation of its physical state.

And our knowledge is a representation of the reality. So, what we are writing is a representation of the reality.

As far as the time for the decoherence implicit in the measurement process, that is arbitrary. We can make the same measurement (and represent it with the same operator) with many specific laboratory configurations provided each configuration ultimately records the same observable for the system being measured. The decoherence process could be set up to take microseconds or weeks, as we choose, and when and where the decoherence occurs is also relative to how we set up the meta-description of the system + measuring device, e.g. how far out we put our meta-system meta-episystem cut.

Someone would have to define decoherence precisely. I never seen such a definition. It is always defined in such a way that you must become a believer and stop asking questions.

As far as measuring the system the details of this meta description is irrelevant. As far as trying to understand measurement and collapse in terms of a model of reality goes, one falls into an infinite regress of measuring devices to observe the measuring devices to observe the measuring devices et cetera ad infinitum.

I think the point is not to understand "collapse" but to understand the mechanism by which a single electron creates dots on the screen or in a cloud chamber in real time.

It is like trying to speak of absolute position. Coordinates only give the position of a system relative to the observer. You can then try to speak of the observers position relative to another observer and you quickly see the futility of it and appreciate the fact that position is always relative. Not meaningless but like electrical potential only meaningful as a difference in values.

Who needs an "observer". Tracks are being formed without any observer. A photographic emulsion is needed or something equivalent like a cloud chamber or electron microscope and CCD. Observers are just to enjoy what has been created without their participation.

Don't confuse the dynamics of that dot e.g. the mechanism for electron evolution with its collapse. Look at how you use the wave function in describing that dot. Or more precisely since presumably you're speaking of a dot on a CRT screen you have a thermal source (hot cathode) you need to rather use a density matrix.

I am not confusing. Events happen, they are irreversible, and they are accompanied by wave function collapses. A finite number of them. They do occur in real time. This time and place depends on the wave function, external fields and whatever is causing the collapse - for instance the presence of the screen at a certain location. Density matrix is of no use for describing such an mechanism. I am talking about an individual process, perhaps one event that will never occur again. Of course you can always smear out such an event with additional uncertainties caused by noise, temperature etc. But they are just obscuring the phenomenon that takes place - creating a classically existing, real, dot on a real photographic plate. The dot and the plate are real. They are actualities and not only wavy possibilities. And what we need is a mechanism of how potentialities become actualities in real time.

But the electron is not a wave-function. The road is not a line on a map. It is an analogue and to understand the type of analogue you must look at how the map is used. In the road case the map is a direct analogue, a model of the reality of the road. In the wave-function case we look at what we do with the wave function. We use it to calculate probabilities for position measurements, it is a logical analogue not a physical one... or rather it is first and foremost a logical analogue.

Yes, but we can use them also to extract more than just probabilities. We can use them for the purpose of describing the track formation in real time. Except texbooks are telling you how to do that.

You may assert it is also a physical one but you must prove your case for that. I assert that wave-function collapse is a specific indicator that it is not a physical analogue but purely a logical/predictive one since it is the logic of updating our class of systems that instigates our collapsing the wave-function on paper.

Well, that is your point of view, and I am not surprised.

I understand the temptation to say "an electron is both wave and particle" but one is mapping the quantum electon's behavior into two distinctly classical phenomena, classical waves and classical particles. It is the spectrum of behaviors one is addressing and we see in this "either or" business the relativity of the actual classical representation. It is the necessary relativity of the "reality" one is trying to paint for the electron. The electron is not the sinusoidal wave nor the dirac delta-function particle... it is a phenomenon of actualizable measurements which we can probabilistically predict using wave functions (and/or density operators) as representations of interrelated probabilities.

One thing is sure: dots are dots, tables are tables, chairs are chairs, data are date. We need to explain the data and guess what is the mechanism of their formation and their organization.

Data are not wavy. They are classical and Boolean within a reasonable approximation. Their appearance, their characteristics are caused by something real and by something wavy. When you want to explain some statistical averages seen in the data - then density matrix can be handy. But when you want to understand the mechanism of creation of a single finite data set - density matrix is useless. It is much like with tossing a coin. You may be interested in finding whether the coin is biased or not by tossing the coin a large number of times or you may want to know what is the mechanism by which such an average results - that is you want to discover a stochastic process that reproduces these averages. Usually knowing the stochastic process let's you to be able to calculate more and to predict more than just the knowledge of a some of the expectation values of some random variables.

 

[jambaugh]

The text that you have entered is too long (22531 characters). Please shorten it to 20000 characters long.

OK Gotta trim it.

 

[StevieTNZ]

Sorry if this sounds silly but:
what is the purpose of decoherence? Why would it make macroscopic objects behave classically if QM applies to the macroscopic level? I'm a bit confused...

I've read in different books it doesn't collapse the wavefunction, and was even told that even though some particle may look like its not in a superposition, it still is - because the way I see it is if a theory is meant to hold all the time, then no collapse occurs because QM does not allow it.

 

[jambaugh]

Sorry if this sounds silly but:
what is the purpose of decoherence?

Who's purpose? Purpose presupposes a holder of purpose.

Why would it make macroscopic objects behave classically if QM applies to the macroscopic level? I'm a bit confused...

It helps to first understand what it means to behave classically vs quantum mechanically and there are different ways to see this.

One could say that the decoherence destroys interference effects but that is not always true, a classical wave e.g. radio waves from a transmitter will interfere quite nicely.

I've read in different books it doesn't collapse the wavefunction, and was even told that even though some particle may look like its not in a superposition, it still is - because the way I see it is if a theory is meant to hold all the time, then no collapse occurs because QM does not allow it.

As I've come to understand QM, you shouldn't think of the collapse of the wavefunction as a physical process but a conceptual process we apply after the physical act of measurement when we update our information about the system. (Just as you update the value of a Lotto ticket after the drawing, or your suppositions of the likely location of your keys after you see them on the coffee table.)

Likewise superposition is not a physical property of the system but a property of how you are resolving the system in terms of potential observables. A vertically polarized photon "is not in a superposition" of Vert vs Horiz. modes but "is in a superposition" of left circular and right circular polarization modes. It is the modes (of measurement) which superpose not the photon.

Now to understand decoherence you have to go to a richer description using density operators. The sharp density operator of a system which can also be described as a wavefunction:
\rho = \psi\otimes \psi^\dag \simeq |\psi\rangle \langle \psi |
will under decoherence become a "mixed state" density operator

\rho = p_1 \rho_1 + p_2 \rho_2 + \cdots
where the p's are "classical" probabilities and the "rho's" are distinct sharp modes. (I think it is a mistake to distinguish classical vs quantum probabilities. Probabilities are probabilities. Rather one should distinguish a classical probability distribution from a quantum probability "distribution" since the latter is not a density of probabilities over the observable states.)

Its entropy has increased from 0 to some positive value.

So as a system decoheres its description looks more like a classical probability distribution over a set of objective states instead of as a quantum superposition.

One of the principle subjects of interest for decoherence is in considering entangled pairs or other forms of correlated measurements. Decoherence eases the degree of correlation to something we can describe in terms of classical probability distributions.

Physical manifestations are the loss of superconductivity or superfluidity above the critical temperatures. The quantum correlations which make these effects manifest is lost due to too much random interaction with the environment.

 

[yoda jedi]

What I mean is that collapse is governed by a stochastic process.

like CSL models.

 

[7th bardo]

So,should we think of decoherence as being a mathematical abstraction rather than a physical process?

 

[Zarqon]

As I've come to understand QM, you shouldn't think of the collapse of the wavefunction as a physical process but a conceptual process we apply after the physical act of measurement when we update our information about the system. (Just as you update the value of a Lotto ticket after the drawing, or your suppositions of the likely location of your keys after you see them on the coffee table.)

Likewise superposition is not a physical property of the system but a property of how you are resolving the system in terms of potential observables. A vertically polarized photon "is not in a superposition" of Vert vs Horiz. modes but "is in a superposition" of left circular and right circular polarization modes. It is the modes (of measurement) which superpose not the photon.

I'm not sure if I just didn't understand your meaning properly, but I don't quite agree with that description.

In my view, the superposition state is in fact the "real" state of the system as long as it's in it. For example, take the state |+> = |0> + |1>. If you measure in the computational basis you would find for example |1>, but this does not mean that the measurement is simpy an update of information or that the state was in |1> all the time, like your keys on the table analogy suggests. In the key case they really were on the table all the time, even before the measurement, but in the |+> case this is not true because experiments done to the state before the collapse would yield quite different results between |+> and |1>, in particular measurements in the |+>,|-> basis would find the state |+> 100% of the time.

I tend to think of it more like asking a grey square whether it's black or white, you're bound to get non determined answer, and it's not just a matter of updating the information, the state after the collapse is actually different in a real and measurable way.

 

[jambaugh]

So,should we think of decoherence as being a mathematical abstraction rather than a physical process?

No more so than we should think of entropy as a mathematical abstraction. Entropy has physical meaning but is not an observable of a system. It is rather a quantitative measure of our knowledge about a given system in so far as it is a property of a maximally restrictive class of systems to which we can say a given system belongs as an instance.

[By maximally restrictive, I mean we use all the existant knowledge about the system, not necessarily all simultaneously possible knowledge about the system. In short I'm not talking about necessarily sharp descriptions and in fact the lack of sharpness is what entropy is quantifying. One may refer to a sharp mode too as a maximally restricted class but in this case maximal in the sense of using all possible information not just what is actually known.]

Since decoherence involves an increase in entropy of a system it too is a description of a (maximally restrictive) system class associated with that system.

A class of systems is a mathematical abstraction with perfectly concrete physical meaning when the class is defined in terms of observables. E.g. the class of electrons (specifying mass and charge) for which the z component of spin has been measured at +1/2 and momentum at say some vector value p.

We express that class of systems by writing a wave-function (if it is sharply described as above) or a density operator (which is more general allowing for cases of non-zero entropy). In a laboratory we may instantiate that class (actualize an instance of an electron) which requires physical constraints and measurements.

 

[arkajad]

like CSL models.

This is the simplest possibility, with an extremely simple stochastic process. I don't think it is general enough to describe all physical experiments that are being done in the labs. CSL is simple to explain, simple to apply, but it assumes one homogeneous mechanism for all collapses. This is not what we see looking at particle tracks. The collapses are evidently (at least for me) due to the presence of the detectors and there is no need (and not much use) of collapsing the wave function in a vacuum.

 

[jambaugh]

I'm not sure if I just didn't understand your meaning properly, but I don't quite agree with that description.

In my view, the superposition state is in fact the "real" state of the system as long as it's in it. For example, take the state |+> = |0> + |1>.

There are multiple issues here. Letting the "real" issue sit for the moment. The "state" |+> is not in a superposition w.r.t. the |+> vs |-> basis but of course is w.r.t. the |0> vs |1> basis. Hence superposition is not "a property of the system" in an absolute sense but rather a relationship between a given ket and our choice of basis.

If you measure in the computational basis you would find for example |1>,

You might so find. Prior to adding this additional physical assumption you only know the probabilities which is to say you don't know. It is when you actualize the assumption that you "collapse" your knowledge of how the system will subsequently behave. In this sense the quantum collapse is no different from the classical collapse in the case of the glasses...

but this does not mean that the measurement is simpy an update of information or that the state was in |1> all the time, like your keys on the table analogy suggests.

The collapse component is simply an update of information. Since the subsequent measurement is not compatible with the implied previous measurement (|+> vs |->) you simultaneously loose any dependence on that previous measurement for future predictions.

Going back to the glasses analogy for a moment. If I last recall seeing my glasses in my car then my probability distribution for where I most likely will find them will take that into account. But once I see them on the coffee table that old assumption is removed.

In the key case they really were on the table all the time, even before the measurement,

Of course and this is where the "glasses" differ from the quantum system but it doesn't detract from the fact that my knowledge about where the glasses might be has been changed by my observing where they are.

but in the |+> case this is not true because experiments done to the state before the collapse would yield quite different results between |+> and |1>,

You can't have your cake and eat it too. Either you did measure |1> or you didn't. You can't go back in time and undo this. So you are talking cases and not a given system. Once you change the assumption that you did measure |1> vs |0> and that you observed the value |1> you are "uncollapsing" the wave-function... and so you have the prior prediction...

in particular measurements in the |+>,|-> basis would find the state |+> 100% of the time.

Consider it this way. Suppose you did make the [1] measurement but did so to a given system after I had measured it (but haven't yet told you what observable I measured nor what value I got.)

You would still write the |1> wave-function, even to describe the system prior to your measurement. If I then told you I measured a specific observable you would use that |1> wave function to predict the probability of the value I measured and finally if I said I measured |+> you would collapse the wave-function to |+> prior to my measurement to see what "alice" measured before me.

By reversing the sequence of assumptions made, I have totally change where you write the |+> description and where you write the |1> description. Can you still then say these are states of reality? Or are they not truly representations of our knowledge about the system in question?

 

[StevieTNZ]

Qunatum Mechanics doesn't state a collapse will occur - and if the theory holds then a collapse never occurs - correct? When we say the wavefunction has collapsed, it really hasn't?

 

[arkajad]

Qunatum Mechanics doesn't state a collapse will occur - and if the theory holds then a collapse never occurs - correct? When we say the wavefunction has collapsed, it really hasn't?

Quantum mechanics, when it was being consceaved was unsure about the collapse. Schrodinger himself was unsure. Then there came applications and QM concentrated on applications that doo not need collapse. The mechanism of forming tracks in cloud chambers was never explained by QM. http://en.wikipedia.org/wiki/Mott_problem" discussed probabilities of different tracks but did not say anything about the mechanism itself and about the timing of the events. So physicists decided that one is not supposed to ask about "mechanisms". Why? Because no one (except of Schrodinger, but who cares?) asks such questions.

The model of Belavkin and Melsheimer "http://arxiv.org/abs/quant-ph/0512192" " is just one possibility, but it is not completely satisfactory. There are other options available. But this is not the mainstream physics, so the territory is left to the "decoherence teams" - which form the mainstream approach these days.

 

[Zarqon]

Consider it this way. Suppose you did make the [1] measurement but did so to a given system after I had measured it (but haven't yet told you what observable I measured nor what value I got.)

You would still write the |1> wave-function, even to describe the system prior to your measurement. If I then told you I measured a specific observable you would use that |1> wave function to predict the probability of the value I measured and finally if I said I measured |+> you would collapse the wave-function to |+> prior to my measurement to see what "alice" measured before me.

By reversing the sequence of assumptions made, I have totally change where you write the |+> description and where you write the |1> description. Can you still then say these are states of reality? Or are they not truly representations of our knowledge about the system in question?

When I think of an example where you measure on the state without telling me I get the opposite conclusion, explained by the following:

Consider that I start with the state |+>. If I measure in the |+>,|-> basis I would now find the state |+> with 100% probability. Let's now consider what happens if you did a measurement in the |0>,|1> basis without telling me. You would "collapse" the state to one of them, let's just say it happened to be |1>.

Now, without you telling me anything, i.e. my knowledge about the system does not change, I now have a non-zero probability of measuring |-> (50%) if I again measure in my basis. The probability of measuring |-> has thus changed without my knowledge being changed at all.

I can only interpret this as the fact that the physical state has actually changed, which is completely different from any classical analogy, where no amount of information update can ever change the location of neither keys nor glasses.

 

[yoda jedi]

Qunatum Mechanics doesn't state a collapse will occur - and if the theory holds then a collapse never occurs - correct? When we say the wavefunction has collapsed, it really hasn't?

Nonlinear Quantum Mechanics states that collapses occur itself.

 

[StevieTNZ]

What is the difference between linear and nonlinear quantum mechanics? Which one is correct?

 

[arkajad]

Fuly linear quantum mechanics does not allow for collapse. A mild non-linearity allows you to have collapses.
In fact the description of an individual system that involves a wave function may be nonlinear, but the evolution of statistical ensembles of systems, described by a density matrix, may still be linear.

 

[jambaugh]

Qunatum Mechanics doesn't state a collapse will occur - and if the theory holds then a collapse never occurs - correct? When we say the wavefunction has collapsed, it really hasn't?

As you see there are "interpretational differences". If you hold that "collapse" is a conceptual process then it is meaningless to say "it occurs" but rather one says the theorist "collapses" his description upon new information (my position).

But taking the other side for arguments sake, Quantum mechanics describes the evolution of the system between measurements (or post preparation or pre destructive detection) via unitary operators. The unitarity conserves probability (or in the relativistic setting probability current). The problem with describing a collapse is (whether it be "real" or not) there is in the language of it an assumed update of assumptions from what we can predict for the outcome of a measurement vs what we know when we assume a specific measured value. Even if "collapse has been realized" we will still, until integrating that assumption describe the system as via the equivalent of a density operator. In this setting "collapse" is represented by decoherence. There is a change in the entropy of the representation. This implies a non-unitary (though still linear?) evolution of the system itself during the measurement process.

Basic QM doesn't describe the evolution during measurement, only between measurements and thus doesn't say anything about linearity vs non-linearity of the measurement process nor about the reality of collapse vs virtuality of collapse. It says that after measurement we can update our wave-function to represent the known measured value. If we don't know it but it is still recorded somewhere, we can use a "classically" probabilistic description (density operator) until we access the record.

Now theorists trying to push the envelope have considered non-linear perturbations of QM to see if they can "explain" collapse or measurement. From my position (which is pretty close to the orthodox CI interpretation) this is not an issue. The distinction between classical and quantum physics is one of fundamental format of description. One does not "explain" a change of description. One can express classical physics in the same format as QM and one gets the same "collapses" when one integrates new measurement values. In so doing one sees collapse as being non-physical.

 

[jambaugh]

When I think of an example where you measure on the state without telling me I get the opposite conclusion, explained by the following:

Consider that I start with the state |+>. If I measure in the |+>,|-> basis I would now find the state |+> with 100% probability. Let's now consider what happens if you did a measurement in the |0>,|1> basis without telling me. You would "collapse" the state to one of them, let's just say it happened to be |1>.

Now, without you telling me anything, i.e. my knowledge about the system does not change, I now have a non-zero probability of measuring |-> (50%) if I again measure in my basis. The probability of measuring |-> has thus changed without my knowledge being changed at all.

I can only interpret this as the fact that the physical state has actually changed, which is completely different from any classical analogy, where no amount of information update can ever change the location of neither keys nor glasses.

Yes this is quite correct. Measurement is a physical act and it will sometimes change the physical system. If you think of it being in a state then you must say the state has changed (provided it was not already in an eigen-state).

Take your example again and let me tell you what I did physically w.r.t. placing an intervening measuring device but not tell you the recorded outcome and you will get the correct probabilistic predictions of outcomes for your subsequent measurements if we repeat the process over and over to see the relative frequencies.

You will use a density matrix to describe my act of measurement without knowing the measured outcomes. It will give you the same probabilities for your subsequent measurements as you observe.

Now If we take the cases where I measured values, (supposing the predictions of your subsequent measurement were not 50%-50%.) I could make more precise predictions of the probabilities of outcomes for those subsequent to |1> measurements, and likewise for those subsequent to |0> measurements. I will in short see a correlation between your subsequent measurements and my hidden 1 vs 0 records. This means I can better predict individual outcomes than you since I have more information, however it does not invalidate the probability distribution you see. My sharp |1> vs |0> is no less nor more valid than your rho at predicting given the information we individually have available.

I further assert there is no foundational difference between how the kets and the density operators are used. They are neither of them "states" and both representations of probable behavior.

You still didn't address my reversed application of the "mode vectors" ("state vectors" as you'd say). The example shows the time symmetry of the QM and the appropriate time reversed parsing of the experimental predictions and it shows the "kets" changing to different "states" between a given pair of measurements purely because we are reversing our conditional probabilities. It shows to my mind the kets are not referring to states of the system but rather to states of our knowledge about the system.

 

[arkajad]

Even if "collapse has been realized" we will still, until integrating that assumption describe the system as via the equivalent of a density operator. In this setting "collapse" is represented by decoherence. There is a change in the entropy of the representation. This implies a non-unitary (though still linear?) evolution of the system itself during the measurement process.

If the collapse would be described mathematically in this way - then we would certainly have a problem. But it can be described in a different way. Collapse happens objectively - as it leaves an objective "track", the wave function changes in a mildly nonlinear way, then it continues its non-unitary evolution until the next collapse etc. The nonunitarity is negligible far from the detectors, the evolution is the standard and unitary in an empty space without detectors.

This completely describes the evolution of a single quantum system under a continuous monitoring.

Yet, if we are not interested in a single quantum system, but care only about averages over an infinite ensemble of similarly prepared systems, only then, if we wish, we do the averaging and get the perfect linear Liouville master equation for the density matrix.

In short:

Single systems are described by collapsing wave functions, ensembles are described by non-collapsing, continuous in time, linear master equation for the density matrix. That's all.

 

[yoda jedi]

linear and nonlinear quantum mechanics? Which one is correct?

we don't know yet...


http://www.fqxi.org/data/articles/Schwab_Asp_Zeil.pdf

 

[chafelix]

Another question on decoherence: Take stat mechanics. There we have an atomic system and an environment(consisting of atomic subsystems that will be traced over) plus an interaction between them, V(t). The atomic system could be for example an atom and the environment could reprsent collisions with other atoms or particles and the result of the interaction would be a broadening and shifting of its levels, e.g. creating a finite lifetime for the atomic states.
To get a finite lifetime one ABSOLUTELY NEEDS to trace over.

Now take decoherence. We again have an atomic system and an environment. The collapse we get is again triggered by the interaction and again the many degrees of freedom(=huge number of "environmental" particles). What is not so clear is the "tracing over" mechanism in decoherence. What are we tracing over?

 

[jambaugh]

If the collapse would be described mathematically in this way - then we would certainly have a problem. But it can be described in a different way. Collapse happens objectively - as it leaves an objective "track", the wave function changes in a mildly nonlinear way, then it continues its non-unitary evolution until the next collapse etc. The nonunitarity is negligible far from the detectors, the evolution is the standard and unitary in an empty space without detectors.

You're speaking of a particle track in a cloud chamber. We can describe that track as a sequence of position measurements and indeed speak of the idealized limit of continuous measurement. But the reality is that the track is a discrete sequence of position measurements. This has nothing to say as to the discussions. Yes we can measure the position of a quantum. Yes we can measure it twice, three times, 10^14 times.

Now this non-linearity which you assert. Where is that required and to what level are you applying it? If you want to describe a quantum system with position observable, observed every 10^-5 seconds or so. You have 1 description for the future measurements sans incorporation of the intermediate measurements. You get for that last measurement a nice classical probability distribution. You get for adjacent measurements nice conditional probabilities which incorporate the dynamics and the uncertainties of momenta.

You update your description by inputting say the first or say the 108th position measurement value and you get a different description because you input more information. The description has "collapsed". Input more actualized values and you collapse it more. Eventually you have something which looks very close to a classical particle trajectory but it is still an expression of where you saw bubbles i.e. records of measurements. You still express the measurement within the linear algebra over the Hilbert space. There is no need for nor empirical evidence supporting the introduction of non-linearity in the dynamics at the level of the operator algebra. We already have the non-linearity of the positional dependence we see in all mechanics.

This completely describes the evolution of a single quantum system under a continuous monitoring.

But of course. The description is that of a sequence of measured values (of position). That is all we ever see, measurements. This is why I harp on the fact that assertions of "what goes on" between measurement are meaningless. Rather we can predict outcomes of measurement and evolve our prediction based on known dynamics. The dynamically evolving wave-function (or equivalent density op) are mathematical representations of that array of predictions.

Yet, if we are not interested in a single quantum system, but care only about averages over an infinite ensemble of similarly prepared systems, only then, if we wish, we do the averaging and get the perfect linear Liouville master equation for the density matrix.

So you declare. But why ignore the equivalence of representation, even for single quantum systems? Why are you so opposed to using the mathematical tools best equipped to express both the quality and degree of knowledge we have about how a single system will behave in subsequent measurements?

Here is our fundamental difference. You acknowledge that the density operator is a probabilistic description and thus expresses behavior of an ensemble. Let me use a different word, class instead of ensemble. We should be general enough to not presuppose the prior objective existence of the "ensemble" but rather allow "on the fly" instantiation of members. I can speak of the probability of outcomes of a single die throw because I can instantiate an arbitrary number of throws of that single die. There is no fixed number of outcomes and so I speak of the class of throws and not the set or ensemble.

(For other readers let me refresh memories with the definition: A class is a collection of things defined by common attributes as opposed to sets which are defined purely in terms of membership. i.e. sets must have their elements defined prior to the set definition while classes are defined by the criterion by which an instance is identified as being a member of that class. Thus we cannot prior to measurement say an given electron is an element of the set of electrons with spin z up. After measurement we have used the property of its spin to define its membership in the class of electrons whose spin has been measured as up. The act of measurement and value defines the class and defines the electron as an instance of it.)

Now getting back to quantum theory. How can you define a probability for a single quantum? It will either be measured with one value or another, not an ensemble of values so one cannot speak of the probability of a single quantum's behavior as an intrinsic property of that one reality. Similarly we cannot observer say an interference pattern for a single quantum. It just goes "blip" leaving a single position record. Rather one speaks of the class of equivalent quanta and the frequency of outcomes for that class which we can repeatedly instantiate by virtue of a source of such quanta to which we may affix a symbol \psi_0. The "ket" or Hilbert space vector or wave-function from which we calculate various transition probabilities or measurement probabilities is a symbol attached to a source of individual quanta. The wave-function is as much an representation of an "ensemble" as is a density operator. The interference pattern of the wave-function like the probability of any outcome can only be confirmed by an ensemble of experiments, not a single instance.

This I assert is the only interpretation consistent with operational usage. That the wave-function and density operator both, are the quantum mechanical analogue of a classical probability distribution.

In short:

Single systems are described by collapsing wave functions, ensembles are described by non-collapsing, continuous in time, linear master equation for the density matrix. That's all.

In short, single systems are prepared in such a way that we know they are members of a class of systems which we represent by a wave-function. Under measurement, given the fact that an act of measurement is a physical interaction, we update the class of system to which we assign the single system being described. Sometimes with less than maximal information the most accurate available class description is not a wave-function but a density operator. That is all.

Now my description is less assertive than yours, do you agree? We both agree we can speak of a class of systems "with the same wave-function" right?

If you can bring yourself to acknowledge that it is possible, and useful to sometimes... upon occasion, speak of a class of quantum systems with the same set of values for a given complete observable, and hence the same wave-function, then can you explain to me, other for personal spiritual reasons, how you can say this is ever not the case?

 

[arkajad]

If you want to describe a quantum system with position observable, observed every 10^-5 seconds or so. [/tex]
In a cloud chamber it is not you who decides how often the the records are being made. It is decided by the coupling. The timing is random is part of the random process.

You update your description by inputting say the first or say the 108th position measurement value and you get a different description because you input more information. The description has "collapsed". Input more actualized values and you collapse it more.

I am not imputing anything. All is done through the coupling. What I do is - at the end I may have a look at the track.

Eventually you have something which looks very close to a classical particle trajectory but it is still an expression of where you saw bubbles i.e. records of measurements. You still express the measurement within the linear algebra over the Hilbert space. There is no need for nor empirical evidence supporting the introduction of non-linearity in the dynamics at the level of the operator algebra.

Try to accomplish the above with a linear process and show me the result.


[QUOTE}Now getting back to quantum theory. How can you define a probability for a single quantum?

I am describing the stochastic process that reproduces what we see, including the timing of the events. You can compare my simulation with experiment. And how you compare two results of an experiments? You have two photographs of an interfence pattern with 10000 electrons each time. One done on Monday and one on Tuesday. Of course the dots are in different places. And yet you notice that both describe the same phenomenon. How? Because you neglect the exact places and compare statistical distributions computed usin statistical procedures applied to your photographs each with 10000 dots.
Is there a probability involved? Somehow is, but it is hidden.
The same when you compare two tracks in an external field. They are not the same. And yet they have similar "features". For instance the average distance between dots, approximately the same curvature, when you average etc. Is probability involved? Somehow is, but it is hidden in the application of statistics to finite samples.

If you can bring yourself to acknowledge that it is possible, and useful to sometimes... upon occasion, speak of a class of quantum systems with the same set of values for a given complete observable, and hence the same wave-function, then can you explain to me, other for personal spiritual reasons, how you can say this is ever not the case?

I prefer down to Earth approach - comparing simulations based on a theory with real data coming from rel experiments. I have nothing against classes. But for me the success of any theory is in being able to simulate processes that we observe in our labs.

I am stressing the importance of timing - which is usually dynamical and not by "instantaneous measurement at chosen time" from the textbooks. Textbooks do not know how to deal with the dynamical timing - which a standard in the labs.

 

[jambaugh]

I am describing the stochastic process that reproduces what we see, including the timing of the events. You can compare my simulation with experiment. And how you compare two results of an experiments? You have two photographs of an interfence pattern with 10000 electrons each time. One done on Monday and one on Tuesday. Of course the dots are in different places. And yet you notice that both describe the same phenomenon. How? Because you neglect the exact places and compare statistical distributions computed using statistical procedures applied to your photographs each with 10000 dots.
Is there a probability involved? Somehow is, but it is hidden.
The same when you compare two tracks in an external field. They are not the same. And yet they have similar "features". For instance the average distance between dots, approximately the same curvature, when you average etc. Is probability involved? Somehow is, but it is hidden in the application of statistics to finite samples.

Your simulation matches experiments only in the aggregate, (same relative frequencies, same lines of cloud chamber bubbles but not identical individual outcomes) thus your inference is again about classes of individual quanta. I'm sure you're doing good work but my objections are to how you use the term "collapse". If you are simulating entanglement then you are positively not simulating the physical states of the quantum systems since you would necessarily satisfy Bell's inequality and/or failing to get the proper correlations). You would need to be simulating the (probability) distributions of outcomes directly which would involve nothing more than doing the QM calculations.

I prefer down to Earth approach - comparing simulations based on a theory with real data coming from rel experiments. I have nothing against classes. But for me the success of any theory is in being able to simulate processes that we observe in our labs.

The issue is what the theory says, the semantics of the language you use. Words mean things. I can simulate a given probability distribution but that won't mean the internals of my simulation correspond to a physical process which upon repetition match that distribution. My point is that the theory matches what goes on in the lab only in so far as it makes probabilistic predictions, quite accurate ones, but only for aggregates of (and hence classes of) experiments.

I am stressing the importance of timing - which is usually dynamical and not by "instantaneous measurement at chosen time" from the textbooks. Textbooks do not know how to deal with the dynamical timing - which a standard in the labs.

The fact that you think the measurement is an instantaneous process as represented in the textbooks is where I see you misinterpreting. The mathematics is instantaneous because it represents something one level of abstraction above the the physical process, namely the logic of the inferences we make about predictions. (There is no "timing" in mathematics 2+2=4 eternally.) The "collapse problem" is not with the theory but with the mind misunderstanding to what a specific component of the theory is referring.

The representation of measurement goes beyond "instantaneous" as I pointed out in the (logically) reversed representation of an experiment. I'll repeat in more detail:

Consider a single experimental setup. A quantum is produced from a random source, a sequence of measurements are made, A then B then C, (which take time and room on the lab's optical bench or whatever) and then final system detector registers the system to assure a valid experiment. If you like you can consider intermediate dynamics as well but for now let's keep it simple.

What does theory tell us about the sequence of measurements? Firstly there is randomness in outcomes. Secondly there is correlation of measured values. How are they correlated? QM says...

Prob(B=b |A=a) = |\langle b|a\rangle |^2=Tr(\rho_b \rho_a)
Prob(C=c |B=b) = |\langle c|b\rangle |^2=Tr(\rho_c \rho_b)
But then only if the measurements are complete i.e. non-degenerate (unless you're using density operators in which case everything works fine.)

We can reverse the conditional probabilities:
Prob(A=a|B=b) = |\langle a|b\rangle |^2=|\langle b|a\rangle |^2
et cetera.

When we point to the lab bench at the region between measuring device A and measuring device B we might say "state |a\rangle" but that's just saying that over at measuring device A we registered "a" and so that is the condition on subsequent measurements (whether they be B, or C or D). We can similarly point to that same region and say "state \langle b|" but we'd mean that a subsequent measurement "b" is made and so this is the condition on prior measurements (be they A, or C or D). Whether we are "forward tracking" or "back tracking" the causal correlation between measurements, we are expressing these correlations via the "bras" and "kets", not modeling a physical state of the system, and we can only confirm we are using the correct ones by carrying out many measurements thus they represent at best classes of systems.

e.g. |a\rangle is the class of systems for which A has been measured with value 'a'.

Now the business with collapse is a matter of transitioning from the point where we make a measurement and acknowledge a particular value that was measured. You can say it this way:

"We consider an ensemble of systems for which A was observed and consider the subset for which A=a" Here we "collapse" to the subset of a fixed ensemble.

Or we can speak in the singular.
"We consider a single quantum for which A is observed, and then..." wait for it ... "we consider the case of an actual measured value of A=a." Now we know the quantum is, for the purposes of subsequent measurements, in the class of those for which a measured value A=a has occurred.

We collapse the class to which we assign the single quantum for our purposes of making subsequent predictions. The collapse is not itself a physical act it is a conceptual step we make corresponding to the physical act of measurement. That measurement may be delayed, may take a very short time or may take an arbitrarily long time. The details are unimportant to the conceptual process of incorporating that information (or as is more typical considering a hypothetical possibility.)

Your humble stochastic simulations are fine research --I am sure-- but please refer to the physical processes by their rightful name, "interaction", not "collapse".

 

[arkajad]

Your simulation matches experiments only in the aggregate, (same relative frequencies, same lines of cloud chamber bubbles but not identical individual outcomes) thus your inference is again about classes of individual quanta. I'm sure you're doing good work but my objections are to how you use the term "collapse". If you are simulating entanglement then you are positively not simulating the physical states of the quantum systems since you would necessarily satisfy Bell's inequality and/or failing to get the proper correlations). You would need to be simulating the (probability) distributions of outcomes directly which would involve nothing more than doing the QM calculations.

I am sure I am getting all the correlations that are seen in experiments. I do not care about Bell inequalities which do not even address the continuous monitoring of single quantum systems.

The issue is what the theory says, the semantics of the language you use. Words mean things. I can simulate a given probability distribution but that won't mean the internals of my simulation correspond to a physical process which upon repetition match that distribution. My point is that the theory matches what goes on in the lab only in so far as it makes probabilistic predictions, quite accurate ones, but only for aggregates of (and hence classes of) experiments.

I am not talking about simulating of probability distributions. I am talking about stochastic processes and their trajectories in time.

The fact that you think the measurement is an instantaneous process as represented in the textbooks is where I see you misinterpreting. The mathematics is instantaneous because it represents something one level of abstraction above the the physical process, namely the logic of the inferences we make about predictions. (There is no "timing" in mathematics 2+2=4 eternally.) The "collapse problem" is not with the theory but with the mind misunderstanding to what a specific component of the theory is referring.

The collapse is a part of a stochastic process. Sometimes we have one collapse - the time of the collapse is always a random variable. That is what the standard approach to QM does not takes into account - because of the historical reasons and because of the inertia of human thought.

The representation of measurement goes beyond "instantaneous" as I pointed out in the (logically) reversed representation of an experiment. I'll repeat in more detail:

Consider a single experimental setup. A quantum is produced from a random source, a sequence of measurements are made, A then B then C, (which take time and room on the lab's optical bench or whatever) and then final system detector registers the system to assure a valid experiment. If you like you can consider intermediate dynamics as well but for now let's keep it simple.

What does theory tell us about the sequence of measurements?

It tells us absolutely nothing about the timing. You are consistently neglecting this issues.

Your humble stochastic simulations are fine research --I am sure-- but please refer to the physical processes by their rightful name, "interaction", not "collapse".

In fact, I do not the term "interaction", because interaction is usually understood as a "Hamiltonian interaction". I prefer the term "non-Hamiltonian coupling".

 

[jambaugh]

I am sure I am getting all the correlations that are seen in experiments. I do not care about Bell inequalities which do not even address the continuous monitoring of single quantum systems.

Bell's inequalities (and their violation) are about correlations, if you don't care then you don't care.

I am not talking about simulating of probability distributions. I am talking about stochastic processes and their trajectories in time.

I know you are not talking about it but that is what you are doing. You are saying your computer model stochastic process matches the probability distributions for physical systems. There and only there can you compare with experiment. You speak of "collapse" but there's no reason to believe the "collapses" in your stochastic model matches anything "out there in actuality". It is the old classic phenomenologist's barrier. "We can only know what we experience." Yes it is too restrictive for science in general. At the classical scale we can infer beyond the pure experience but QM specifically pushes us to the level where that barrier is relevant and we must be more the positivist or devolve into arguments over "how many angels can dance on the head of a pin".

The collapse is a part of a stochastic process. Sometimes we have one collapse - the time of the collapse is always a random variable. That is what the standard approach to QM does not takes into account - because of the historical reasons and because of the inertia of human thought.

Yes the collapse is a part of a stochastic process, but that process is a conceptual process, (your model or mine) not a physical process (actual electrons). Again you speak of "the time of the collapse" as if you can observe physical collapse and again I ask "HOW?" Until then the "why QM does not take this into account" question lacks foundation.

I think you misuse the term "collapse" where you should be speaking of "decoherence" which is the physical process (of external random physical variables i.e. "noise" being introduced into the physical system.)

It tells us absolutely nothing about the timing. You are consistently neglecting this issues.

And I'm explaining why it not only can be neglected but should be. The timing of "collapse" is not a physically meaningful phrase. I can collapse the wave-function (on paper) at any time I choose after the measurement is made. If you'd like to discuss the physical process of measurement itself then let's but in a different thread as that is quite a topic in itself.

In fact, I do not the term "interaction", because interaction is usually understood as a "Hamiltonian interaction". I prefer the term "non-Hamiltonian coupling".

"Coupling" is "interaction", Hamiltonians are how we represent the evolution of the whole composite of the two systems being coupled. When you focus on part of that whole you loose the Hamiltonian format but it is still an interaction. You can still work nicely with this focused case using ... pardon my bringing this up again... density matrices and a higher order algebra. The density operators can still be "evolved" linearly but no longer with a adjoint action of Hamiltonian within the original operator algebra. You see then decoherence occur (the entropy of the DO increases over time, representing this random stochastic process you're modeling). I think you'd find it of value to determine exactly how your computer models of stochastic processes differs from or is equivalent to this sort of representation.

I think your prejudice against DO's (describing a single system) is what is keeping you from understanding this fully. The dynamics of the coupling of system to episystem can be expressed via a hamiltonian on the composite system + episys. and then tracing over the "epi" part yields a non-sharp and "decohering" system description...but again only expressible as a density operator.

Again I submit when you speak of a "wave function valued random variable" (which it seems to me you are using) you are effectively describing a density operator.

Consider a random distribution of Hilbert space vectors with corresponding probabilities:
\{(\psi_1,p_1),(\psi_2,p_2),\cdots\}
it is equivalently realized as a density operator:
\rho = \sum_k p_k \rho_k
where
\rho_k = \psi_k\otimes\psi^\dagger_k.

That IS what the density operator represents pragmatically and within the modern literature. Yes when we speak of a (random) ensemble of systems we must use density operators but that isn't the D.O.'s definition. A probability can be associated with a single system in that it expresses our knowledge about that system in the format of: to what class of systems that one belongs. In expressing this we understand the definition of the value of a probability comes from the class not from the singular system. A D.O. is a probability distribution over a set of Hilbert space vectors e.g. wave-functions.

 

[arkajad]

Bell's inequalities (and their violation) are about correlations, if you don't care then you don't care.

I know you are not talking about it but that is what you are doing. You are saying your computer model stochastic process matches the probability distributions for physical systems.

It matches more than that. It matches in also the fact that in real words probabilities are calculated out of the counting and averaging of characteristics of single events and not out of the calculating of integrals. Those who neglect that fact are deliberately blind to a part of the reality. They say: "we need just tools for calculating numbers". Well, that's their choice.

You speak of "collapse" but there's no reason to believe the "collapses" in your stochastic model matches anything "out there in actuality".

There are no reasons to believe anything. Each believe is just a personal choice. Like choosing "we only need to know how to calculate numbers and nothing more".

It is the old classic phenomenologist's barrier. "We can only know what we experience." Yes it is too restrictive for science in general. At the classical scale we can infer beyond the pure experience but QM specifically pushes us to the level where that barrier is relevant and we must be more the positivist or devolve into arguments over "how many angels can dance on the head of a pin".

QM "pushes" some physicists and some philosphers into what you call "positivism", but some are more resistant than others. But even so, the "event" based model can calculate more than the posivitistic "don't ask questions, just calculate" model. So, also with a positivistic attitude you are behind.

Yes the collapse is a part of a stochastic process, but that process is a conceptual process, (your model or mine) not a physical process (actual electrons).

Well, Hilbert spaces, wave functions, operators, spacetime metrics, are also conceptual. So what?

Again you speak of "the time of the collapse" as if you can observe physical collapse and again I ask "HOW?" Until then the "why QM does not take this into account" question lacks foundation.

They always come in pairs: collapse, event). We observe events. Collapses are in the Platonic part of the world. Nevertheless if you want to simulate events you need the collapses. Like in order to calculate orbits of planets you need to solve differential equations. Differential equations are in the Platonic world as well.

I think you misuse the term "collapse" where you should be speaking of "decoherence" which is the physical process (of external random physical variables i.e. "noise" being introduced into the physical system.)

"Random variables"? "External"? "noise"? Are these better or sharper terms? I strongly doubt.

And I'm explaining why it not only can be neglected but should be. The timing of "collapse" is not a physically meaningful phrase.

It is not a physical phrase. "Timing of the event" is such. But they alsways come in pairs.

I can collapse the wave-function (on paper) at any time I choose after the measurement is made. If you'd like to discuss the physical process of measurement itself then let's but in a different thread as that is quite a topic in itself.

Right. You can collapse wave-function on paper and you can erase diffrential equation on paper. This will not destroy the planet's orbit.

"Coupling" is "interaction", Hamiltonians are how we represent the evolution of the whole composite of the two systems being coupled. When you focus on part of that whole you loose the Hamiltonian format but it is still an interaction. You can still work nicely with this focused case using ... pardon my bringing this up again... density matrices and a higher order algebra. The density operators can still be "evolved" linearly but no longer with a adjoint action of Hamiltonian within the original operator algebra. You see then decoherence occur (the entropy of the DO increases over time, representing this random stochastic process you're modeling). I think you'd find it of value to determine exactly how your computer models of stochastic processes differs from or is equivalent to this sort of representation.

You can play with density matrices, but they will not let you to understand and to simulate the observed behavior of a unique physical system. You may deliberately abandon that, you may decide "I don't need it, I don't care", but even in this case I am pretty sure that is a forced choice. You choose it because you do not know anything better than that. You even convince yourself that there can't be anything better. But what if there can be?

I think your prejudice against DO's (describing a single system) is what is keeping you from understanding this fully. The dynamics of the coupling of system to episystem can be expressed via a hamiltonian on the composite system + episys. and then tracing over the "epi" part yields a non-sharp and "decohering" system description...but again only expressible as a density operator.

It is not so much my prejudice. It's my conscious choice.

Again I submit when you speak of a "wave function valued random variable" (which it seems to me you are using) you are effectively describing a density operator.

Well, it is like saying: when you speak of a function, you effectively speak about its integral. In a sense you are right, but knowing a function you can do with more than just computing one of its characteristics.

Consider a random distribution of Hilbert space vectors with corresponding probabilities:
\{(\psi_1,p_1),(\psi_2,p_2),\cdots\}
it is equivalently realized as a density operator:
\rho = \sum_k p_k \rho_k
where
\rho_k = \psi_k\otimes\psi^\dagger_k.

This is one way. Now, try to go uniquely from your density matrix to the particular realization of the stochastic process. You know it can't be done. Therefore there is more potential information in the process than in the Markov semi-group equation.

That IS what the density operator represents pragmatically and within the modern literature. Yes when we speak of a (random) ensemble of systems we must use density operators but that isn't the D.O.'s definition.

No, I don't have to. Like having a function I don't have to calculate it's integral. I can be more interested in its derivative, for example. Or I can modify its values on some interval.

A probability can be associated with a single system in that it expresses our knowledge about that system in the format of: to what class of systems that one belongs. In expressing this we understand the definition of the value of a probability comes from the class not from the singular system. A D.O. is a probability distribution over a set of Hilbert space vectors e.g. wave-functions.

Well, you are speaking about "our knowledge" while I am speaking about our attempts to understand the mechanism of formation of events. A mechanism that can lead us to another, perhaps even better mechanism, without random numbers at the start.

 

[jambaugh]

Pardon the long delay in reply, I've been tied up with the holidays and family...

...
There are no reasons to believe anything. Each believe is just a personal choice. Like choosing "we only need to know how to calculate numbers and nothing more".

Then you see no distinction between belief in voodoo and belief in atoms. There is so much wrong with this statement I don't know where to begin.

QM "pushes" some physicists and some philosphers into what you call "positivism", but some are more resistant than others. But even so, the "event" based model can calculate more than the posivitistic "don't ask questions, just calculate" model. So, also with a positivistic attitude you are behind.

Resistant or not, what you can calculate doesn't validate the identification of your calculus with "reality", especially when there exists multiple methods of calculation. Reality is not the mathematics it is the empirical assumptions which cannot be ignored. I can ignore your stochastic processes without any loss in the fidelity of the predictions of QM.

Well, Hilbert spaces, wave functions, operators, spacetime metrics, are also conceptual. So what?

So they are not "the reality" but our tools for calculating what does or may happen... and we err in forgetting this fact. (e.g. when we wonder about collapse (and the timing thereof) as if it were happening other than on paper or in the mind of the holder of the concept.)

They always come in pairs: collapse, event). We observe events. Collapses are in the Platonic part of the world. Nevertheless if you want to simulate events you need the collapses. Like in order to calculate orbits of planets you need to solve differential equations. Differential equations are in the Platonic world as well.

OMG you are a Platonist? No wonder...
You say "Platonic part of the world" I say "on paper". Are we just arguing semantics or do you actually believe there is a real universe of mathematical forms?

BTW we could calculate orbits prior to the development of differential calculus. We simply extended into the future the epicycle series matching prior observations. Of course the differential calculus is superior as it relates the behavior to e.g. the masses of the bodies and thus eliminating the infinite series of variables which must be determined empirically...

and yet again, when you speak of "the time of the collapse" as if you can observe physical collapse, I ask "HOW?" Until then the "why QM does not take this into account" question lacks foundation.

"Random variables"? "External"? "noise"? Are these better or sharper terms? I strongly doubt.

I placed some of these terms in quotes, because they were common usage synonyms for the sharper ones. But YES "Random variable" has a specific sharp meaning, the symbol representing outcomes of a class of empirical events, specifically outcomes to which we can assign probabilities. And "External" has a perfectly well defined operational meaning. We can isolate a system from external effects without changing the system itself (as a class, i.e. defined by its spectrum of observables and degrees of freedom).

What is more important "external" and "noise" have distinct operational meanings. You can "externally" inject "noise" into a system and see the effect. What meaning is there for "collapse" except as a calculation procedure?

Right. You can collapse wave-function on paper and you can erase diffrential equation on paper. This will not destroy the planet's orbit.

Very good. That's progress. Now then you agree there is a "collapse on paper" but you seem to be saying there is also a "collapse in reality" which the paper process is representing. Correct?

You can play with density matrices, but they will not let you to understand and to simulate the observed behavior of a unique physical system. You may deliberately abandon that, you may decide "I don't need it, I don't care", but even in this case I am pretty sure that is a forced choice. You choose it because you do not know anything better than that. You even convince yourself that there can't be anything better. But what if there can be?

"anything better" is a value judgment. Let us establish the value judgment within which we work as physicists. I say "there can't be anything better" specifically in the context of the prediction of physical outcomes of experiments and observables. By what value system do you claim something that is "better"?

It is not so much my prejudice. It's my conscious choice.

A prejudice may or may not be a conscious choice. The point is that it is an a priori judgment. Revisit it, and ask instead what is the justification for that judgment. I know a man who consciously ignores the evidence of evolution because it might undermine his faith in the literal "truth" of the bible. Are you doing the same w.r.t. density operators?

I keep bringing these up because, like using differential equations instead of epicycles, they provide more insight into what is mathematically necessary to predict physical events. What is excised by their use vs wave functions, must not necessarily be a component of physical "reality". Most importantly one finds there is no distinction between a "quantum probability" vs a "classical probability" and so no distinction in the interpetation of their "collapse (on paper)". (which recall was the reason I brought them up to begin with.)

Well, it is like saying: when you speak of a function, you effectively speak about its integral. In a sense you are right, but knowing a function you can do with more than just computing one of its characteristics.

Yes you have more components to play with (like with epicycles you have more variables to tweak). The important point is that with the DO's you have less yet no loss of predictive information. Thus the "more" you refer to is not linked or linkable to any empirical phenomena. Does it then still have physical meaning in your considered opinion?

This is one way. Now, try to go uniquely from your density matrix to the particular realization of the stochastic process. You know it can't be done. Therefore there is more potential information in the process than in the Markov semi-group equation.

Again see my point above... what utility does this procedure have if it does not change what one can empirically predict? (I do not deny it might have some utility but I call your attention to the nature of that utility if it does manifest.)

No, I don't have to. Like having a function I don't have to calculate it's integral. I can be more interested in its derivative, for example. Or I can modify its values on some interval.

Yes you can do what you like as a person but are you then doing physics or astrology? To express the maximal known information about a system in terms of usage common to the physics community you really really should use density operators as they are understood in that community.

Well, you are speaking about "our knowledge" while I am speaking about our attempts to understand the mechanism of formation of events. A mechanism that can lead us to another, perhaps even better mechanism, without random numbers at the start.

Then you are on a speculative quest. That is fine and good. But acknowledge that you speculate instead of declaring the orthodox to be "wrong". When you find that mechanism and can justify the superiority of believing the reality of it then come back.

Let me recall for you the thousands of amateur "theoriests" which post on the various blogs and forums about how "Einstein is wrong because I can predict what he predicts by invoking an aether". They justify their noisy insistent proclamations by saying they're "seeking a mechanism to explain"... an explanation is always in terms of other phenomena and when someone seeks to explain in terms of fundamentally unobservable phenomena there is no merit in it.

Yes I am a positivist when it comes to physics. Pure deduction can only link between prepositions, it cannot generate knowledge on its own. However too many times we find implicit hidden axioms in the logic of arguments about nature. Under further scrutiny we find those implicit axioms are chosen out of wish fulfillment to justify the desired conclusions. The only way to avoid this is to adhere to a positivistic discipline, stick to terms which either have operational meaning or explicitly mathematical meaning.

If one does not grant "reality status" to wave function in the form e.g. of Bhomian pilot waves then there is no need to explain collapse, it is explained already in the paper version in a simple trivially obvious way.

The chain of explanation must stop somewhere. it isn't "http://en.wikipedia.org/wiki/Turtles_all_the_way_down" ". I see that quantum mechanics is as it is because it is the limit of our ability to explain in terms of more fundamental empirical phenomena. As the mathematician must eventually stop the chain of formal definition at the point of fundamental undefined terms so too the physicist must stop the chain of explanation at the point of fundamental unexplained phenomena. At that level physics must remain positivistic.

 

[arkajad]

So they are not "the reality" but our tools for calculating what does or may happen... and we err in forgetting this fact. (e.g. when we wonder about collapse (and the timing thereof) as if it were happening other than on paper or in the mind of the holder of the concept.)

You are missing the point. Everybody is calculating lot of things. And you too. There is nothing wrong with calculations. There is nothing wrong with solving differential equations - they are on paper or in the mind.

The point is whether at the end of your calculation you get something that you can compare with observations. In this respect there is no difference between solving differential equations and models with collapses. In each case at the end you get numbers or graphs that you can compare with experimental data.

So, your war is misdirected.

 

[jambaugh]

You are missing the point. Everybody is calculating lot of things. And you too. There is nothing wrong with calculations. There is nothing wrong with solving differential equations - they are on paper or in the mind.

The point is whether at the end of your calculation you get something that you can compare with observations. In this respect there is no difference between solving differential equations and models with collapses. In each case at the end you get numbers or graphs that you can compare with experimental data.

So, your war is misdirected.

What you say here is correct w.r.t. calculations yielding observable predictions. But the validity of a calculation does not imply the reality of the mathematical objects or processes used.

Specifically the calculation step "collapse the wave-function" does not, just by virtue of giving correct empirical predictions, imply there is a physical collapse occurring. It is thus incorrect to speak of "when the collapse occurs" or "cause of a collapse" as if it were physical.

That is what I have been consistently attacking and the issue you keep sidestepping.

There is a distinct physical process of decoherence which one can express easily in the density operator language (which you resist accepting) which is not the same as collapse and indeed shows that classical and quantum collapse are indistinguishable. (Classical collapse being the baysian updating of probabilities given subsequent observations.)