Macro superposition

  • #51
atyy
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I really need help here what do you mean by APPARENT collapse can you be specific are you suggesting your not exactly sure that decoherence collapses wave functions IE superposition. Because this is contradicatry to your earlier posts. This is very confusing for me I dont even know where to begin INVESTIGATING whatever diffrence your talking about. Does decoherance cause wave function collapse or create the illusion that it does and everything is still in superposition. Any help would be greatly appreciated.
Apparent means observationaly its the same - but actual collapse is another matter.

The jig is up here - cant give any more detail without the math - it requires knowledge of the difference between proper and improper mixtures which requires considerably more background than you have. Here is the detail for future reference:
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

Thanks
Bill
I too have had a very hard time too understanding what bhobba means by apparent collapse. In my understanding, from the link he provided, it is the same as collapse. http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf (p38): "Ignorance interpretation: The mixed states we find by taking the partial trace over the environment can be interpreted as a proper mixture. Note that this is essentially a collapse postulate."
 
  • #52
stevendaryl
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I too have had a very hard time too understanding what bhobba means by apparent collapse. In my understanding, from the link he provided, it is the same as collapse. http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf (p38): "Ignorance interpretation: The mixed states we find by taking the partial trace over the environment can be interpreted as a proper mixture. Note that this is essentially a collapse postulate."
I think that all that is meant by "apparent collapse" is that one can use mixtures instead of superpositions to compute expectation values. The use of mixtures is consistent with the claim that the wave function has collapsed into some definite state (but it's unknown which one), but it doesn't actually imply it.
 
  • #53
atyy
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I think that all that is meant by "apparent collapse" is that one can use mixtures instead of superpositions to compute expectation values. The use of mixtures is consistent with the claim that the wave function has collapsed into some definite state (but it's unknown which one), but it doesn't actually imply it.
I'm not sure I understand correctly, but it seems to me that there are two things that require a proper mixture:
1) filtering measurements, used for state preparation
2) unitary evolution of the mixture after the measurement

The reduced density matrix produces an improper mixture. If one uses the post-measurement mixture for state preparation or evolves it unitarily, then the transition from an improper to a proper mixture is collapse.
 
  • #54
463
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Between a sci advisor and some random poster sorry but I prefer to listen to a sci advisor for all I know you might be one of those quantum spiritual types.
good joke !

Beware !

beware of apodictical parrots.


.
 
  • #55
463
7
Between a sci advisor and some random poster sorry but I prefer to listen to a sci advisor for all I know you might be one of those quantum spiritual types.

Anyways please please in lamen terms if you can distinguish or TRY to explain the diffrence between an observational collapse and an actual or mathematical collapse if thats what your implying. Can one mathematiclly determine collapse while at the same time observe collapse experimentally. Please you would help me a great deal see I suffer from obsessive compulsive disorder and the distortion of reality in my own mind created by my own ignorance of how some suggest the quantum world contradicts the macro classical world creates anxiety for me.

THE BASIC QUESTION IN YOUR OPINION CAN ONE THING BE IN TWO PLACES AT THE SAME TIME IN THE MACRO WORLD WITHOUT REMOVING THE EXTERNAL REALITY, PHOTONS BEING THE EXEPTION. I KNOW YOU ALREADY ANSWERED THIS IN YOUR PREVIOUS POSTS BUT NOW I FEEL YOUR TELLING ME THAT WITHOUT MATHEMATICAL CERTIANTY ABSOLUTE COLLAPSE CANT BE DETERMINED. CAN THE MATH HOWEVER BE IN SYNCRONICITY WITH THE OBSERVATIONAL RESULTS. I AM SO CONFUSED AND VERY BUYS IN MY LIFE RIGHT NOW THAT I DONT HAVE THE TIME (HOURS OR WHOLE DAY) TO GO THROUGH COMPLEX DOCUMENTS IN QM. PLEASE HELP ME THE BEST YOU CAN ANY OF THE SCI ADVISORS.

SORRY FOR ALL CAPS AND SPELLING IM USING AN ITALIAN COMPUTER THAT DOESENT HAVE SPELL CHECK.
what is macroscopic for you ?

objects of
1000 atoms
10000 atoms

100 nm or 1000 nm

macroscopic is beyond 10 15 atoms.

the actual experimental limit is 430 atoms.


-------
1.-Mass (in grams) equal to the atomic weight (in amu) is called a molar mass.
2.-The collection of atoms in one molar mass is called a mole.
3.-The exact number of atoms in one mole is Avogadro’s number.

Avogadro number
6.022 x 1023


.
 
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  • #56
stevendaryl
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I'm not sure I understand correctly, but it seems to me that there are two things that require a proper mixture:
1) filtering measurements, used for state preparation
2) unitary evolution of the mixture after the measurement

The reduced density matrix produces an improper mixture. If one uses the post-measurement mixture for state preparation or evolves it unitarily, then the transition from an improper to a proper mixture is collapse.
The miracle of decoherence is that for all practical purposes, there is no difference between using the post-measurement mixture and using a pure state. The only difference is interference terms that are undetectable in practice.
 
  • #57
What is the diffrence between pure and mixed states in lamen terms I reasearched it but Im not exactly sure I understood the concept and how it applies to how the enviorment (decoherance) collapses particles.

Also if someone could explain the density matrix and how it applies to all this it would be much appreciated.
 
  • #58
atyy
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What is the diffrence between pure and mixed states in lamen terms I reasearched it but Im not exactly sure I understood the concept and how it applies to how the enviorment (decoherance) collapses particles.

Also if someone could explain the density matrix and how it applies to all this it would be much appreciated.
If a system is in a pure state, and you know what the pure state is, then your knowledge of the system is complete, and all uncertainty is quantum. If we take a state to apply to an ensemble, this means that every member of the ensemble has been identically prepared and is in the same state.

A proper mixed state means that you do not know exactly what the quantum state is, but only what the state is with some probability, so uncertainty is due to intrinsic quantum uncertainty, as well as your ignorance of the state. In an ensemble, this means that not all members of the ensemble have been identically prepared.

An improper mixed state comes about when the entire system is in a pure state, but you restrict yourself to observing a subsystem. The improper mixed state describes the behaviour of the subsystem.

The density matrix is a way of writing the quantum state so that pure states, proper and improper mixed states can be described in the same mathematical language.

As I understand, decoherence does not collapse the state. In order to have a definite outcome, one must postulate collapse (or use Bohmian or many-worlds formulations). I believe this is also what is said in bhobba's link to Bas Hensen's essay http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf concerning the "Ignorance interpretation" where one postulates "The mixed states we find by taking the partial trace over the environment can be interpreted as a proper mixture. Note that this is essentially a collapse postulate." (p39). For decoherence to give definite outcomes (see Table 3.1 on p39, where "D. Interactions with the environment explain the apparent definiteness of measurement outcomes." needs all 4 assumptions, including assumption 4 that an improper mixture can be interpreted as a proper mixture.

Decoherence does not explain collapse. Decoherence solves the "preferred basis" or "pointer basis" problem. In particular, decoherence says that position is a usually a very good pointer basis, because interactions are usually local in space. From Hensen's p17: "Summarising, the point is that the basis with respect to which decoherence takes place - i.e. superpositions of eigenstates of this basis decohere into a improper mixture of these eigenstates - is determined by the form of the system/apparatusenvironment interaction Hamiltonian. Therefore the'classical' observables, the ones that we perceive as classical, are exactly those determined by this basis. One of the consequences of this is that any interaction described by a potential V(r), is diagonal in position, and therefore position is always the pointer observable measured by the interaction. many interactions in nature are described by such a potential V (R)." See also sections 2.4 and 3.4 of Bas Hensen's essay.
 
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  • #59
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I think that all that is meant by "apparent collapse" is that one can use mixtures instead of superpositions to compute expectation values. The use of mixtures is consistent with the claim that the wave function has collapsed into some definite state (but it's unknown which one), but it doesn't actually imply it.
Apparent collapse is simple. Technically its that an improper mixed state is observationally indistinguishable from a proper one. If it was a proper one then actual collapse would have occurred.

This has been discussed innumerable times by me and others so I do not know why there is any confusion.

Thanks
Bill
 
  • #60
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As I understand, decoherence does not collapse the state.
It transforms a superposition to an improper mixed state - see section 1.2.3 of the paper I constantly post about it:
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

When one applies the measurement postulate (ie Born's rule) to an improper mixed state you get exactly the same result as if it was a proper one. There is zero, no way, nada, of observationally telling if it was not a proper one instead. If it was a proper one collapse would have actually occurred because a proper one is a specific state randomly presented for observation.

That is what is meant by apparent collapse. That is what is meant by solving the measurement problem FAPP.

The paper I link to gives a fair and balanced view of the issue - but I personally think the language it uses in saying it doesn't touch the central issue is too pessimistic. Its true - but so? If solves it FAPP.

Thanks
Bill
 
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  • #61
9,476
2,560
What is the diffrence between pure and mixed states in lamen terms I reasearched it but Im not exactly sure I understood the concept and how it applies to how the enviorment (decoherance) collapses particles. Also if someone could explain the density matrix and how it applies to all this it would be much appreciated.
As mentioned previously on these issues the jig is up. It cant be explained in layman's terms - at least I have no idea how to do it. Its fully explained in the paper I linked to - in particular section 1.2.3 explains exactly the difference between an improper and a mixed state.

You simply need to accept that decoherence, FAPP, results in collapse. If you want to delve deeper you need to learn the technicalities - sorry no out. For example even the term density matrix requires knowledge of what a matrix is which is the subject of college level courses in linear algebra - and that's just one aspect. A layman's explanation is not possible of stuff at that level IMHO. But if anyone wants to have a go then I salute you and hope you succeed. Its beyond me.

Thanks
Bill
 
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  • #62
DevilsAvocado
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Anyways please please in lamen terms if you can distinguish or TRY to explain the diffrence between an observational collapse and an actual or mathematical collapse if thats what your implying. Can one mathematiclly determine collapse while at the same time observe collapse experimentally. Please you would help me a great deal see I suffer from obsessive compulsive disorder and the distortion of reality in my own mind created by my own ignorance of how some suggest the quantum world contradicts the macro classical world creates anxiety for me.

THE BASIC QUESTION IN YOUR OPINION CAN ONE THING BE IN TWO PLACES AT THE SAME TIME IN THE MACRO WORLD WITHOUT REMOVING THE EXTERNAL REALITY, PHOTONS BEING THE EXEPTION. I KNOW YOU ALREADY ANSWERED THIS IN YOUR PREVIOUS POSTS BUT NOW I FEEL YOUR TELLING ME THAT WITHOUT MATHEMATICAL CERTIANTY ABSOLUTE COLLAPSE CANT BE DETERMINED. CAN THE MATH HOWEVER BE IN SYNCRONICITY WITH THE OBSERVATIONAL RESULTS. I AM SO CONFUSED AND VERY BUYS IN MY LIFE RIGHT NOW THAT I DONT HAVE THE TIME (HOURS OR WHOLE DAY) TO GO THROUGH COMPLEX DOCUMENTS IN QM. PLEASE HELP ME THE BEST YOU CAN ANY OF THE SCI ADVISORS.
Take a deep breath batman – and relax – you don't have to worry. Our macroscopic everyday world will continue to work as it always has, with or without mathematical equations.

Science is not religion; it will never give you the final, ultimate, and undisputable TRUTH about the world we live in. Science is about making best possible models on how nature works, to be able to make the best possible predictions about what nature will do next. That's all.

QM makes extremely precise predictions about nature, in fact the best we have, but in the light of history, it will (most probably) not be the final scientific model for the microscopic world.

You can think of it like this; imagine there was a guy in 1687 who got his hands on Newton's personal copy of Philosophiæ Naturalis Principia Mathematica and read about Newton's law of universal gravitation, and went completely nuts: What!? A mysterious force, with infinite speed, that affects the entire world!? HELP! The world will collapse!!

Not that smart, huh?

Newton was a genius, but he – as everybody else – was limited by the time he lived in. His model still works, in most situations, but Einstein expanded the model to get better and more precise predictions, and by this Einstein also "saved us" (:smile:) from becoming a dreadful black hole, that worried the "fictive guy" back in 1687.

Get it? Don't worry!

It's extremely hard to get large objects in that delicate state of coherence, and when we do, it only last for a very short time. And for living organisms (and their thoughts) I stick out my nose and say – impossible – i.e. without killing the organism in the process.

Finally, a statement from one of the brightest in the development of QM:

"I think I can safely say that nobody understands quantum mechanics." – Richard Feynman

... and maybe the Measurement problem (wavefunction collapse) is the greatest contributor to this "perplexity" ...
 
  • #63
DevilsAvocado
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That is what is meant by solving the measurement problem FAPP.
Maybe I’m missing something here, are you saying that the measurement problem is solved? :bugeye:

Who got the Nobel Prize for this?
 
  • #64
stevendaryl
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Apparent collapse is simple. Technically its that an improper mixed state is observationally indistinguishable from a proper one. If it was a proper one then actual collapse would have occurred.

This has been discussed innumerable times by me and others so I do not know why there is any confusion.
Not everyone reads every post.
 
  • #65
atyy
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It transforms a superposition to an improper mixed state - see section 1.2.3 of the paper I constantly post about it:
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

When one applies the measurement postulate (ie Born's rule) to an improper mixed state you get exactly the same result as if it was a proper one. There is zero, no way, nada, of observationally telling if it was not a proper one instead. If it was a proper one collapse would have actually occurred because a proper one is a specific state randomly presented for observation.

That is what is meant by apparent collapse. That is what is meant by solving the measurement problem FAPP.

The paper I link to gives a fair and balanced view of the issue - but I personally think the language it uses in saying it doesn't touch the central issue is too pessimistic. Its true - but so? If solves it FAPP.

Thanks
Bill
I agree with the paper you post. What I don't understand is whether in the "Ignorance interpretation" there is any difference between collapse and apparent collapse. Bas Hensen writes http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf (p37), assumption 4: "Ignorance interpretation: The mixed states we find by taking the partial trace over the environment can be interpreted as a proper mixture. Note that this is essentially a collapse postulate." In Table 3.1 on p38, Hensen lists the 4th assumption as necessary to give definite outcomes.

There is a similar comment in Schlosshauer's http://arxiv.org/abs/quant-ph/0312059 (p9) "The reduced density matrix looks like a mixed state density matrix because, if one actually measured an observable of the system, one would expect to get a definite outcome with a certain probability; in terms of measurement statistics, this is equivalent to the situation in which the system is in one of the states from the set of possible outcomes from the beginning, that is, before the measurement. As Pessoa (1998, p. 432) puts it, "taking a partial trace amounts to the statistical version of the projection postulate.""

So it would seem that in the "Ignorance interpretation" apparent collapse is collapse. (Or are you not using the "Ignorance interpretation"?)
 
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  • #66
DevilsAvocado
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"Ignorance interpretation"
Well, if ignorance is the rigorous solution to the measurement problem, Steven Weinberg's words (2005) still holds:

Steven Weinberg said:
Bohr’s version of quantum mechanics was deeply flawed, but not for the reason Einstein thought. The Copenhagen interpretation describes what happens when an observer makes a measurement, but the observer and the act of measurement are themselves treated classically. This is surely wrong: Physicists and their apparatus must be governed by the same quantum mechanical rules that govern everything else in the universe. But these rules are expressed in terms of a wavefunction (or, more precisely, a state vector) that evolves in a perfectly deterministic way. So where do the probabilistic rules of the Copenhagen interpretation come from?

Considerable progress has been made in recent years toward the resolution of the problem, which I cannot go into here. It is enough to say that neither Bohr nor Einstein had focused on the real problem with quantum mechanics. The Copenhagen rules clearly work, so they have to be accepted. But this leaves the task of explaining them by applying the deterministic equation for the evolution of the wavefunction, the Schrödinger equation, to observers and their apparatus. The difficulty is not that quantum mechanics is probabilistic — that is something we apparently just have to live with. The real difficulty is that it is also deterministic, or more precisely, that it combines a probabilistic interpretation with deterministic dynamics.
= unsolved


Guys, before you drive batman nuts, wouldn’t it be fair to explain the difference between interpretations and a theory, empirically verified?
 
  • #67
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Maybe I’m missing something here, are you saying that the measurement problem is solved? :bugeye:

Who got the Nobel Prize for this?
FAPP - For All Practical Purposes ie APPARENT collapse.

The issue, as has been gone over countess times is, is APPARENT collapse good enough. That is the key, that is the crux.

I have specifically stated many times until I am blue in the face, it does NOT solve the measurement problem - just FAPP. Specific extra interpretive assumptions are required for that. I use the assumption of the ignorance ensemble interpretation, others MW, others decoherent histories. There are tons about - take your pick - its a smorgasbord.

Thanks
Bill
 
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  • #68
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So it would seem that in the "Ignorance interpretation" apparent collapse is collapse. (Or are you not using the "Ignorance interpretation"?)
I hold to the ignorance interpretation but that is not the issue here.

The issue is what decoherehnce does. Its in any interpretation because it follows from the formalism. Decoherence transforms a superposition into an improper mixed state that is observationally indistinguishable from a proper one. If it was a proper one measurement problem solved - collapse has occurred. But its not. But since its observationally indistinguishable from it, it gives the APPEARANCE of collapse that many such as myself say is good enough - or FAPP solves it.

I, on top of that, make an interpretive assumption in my interpretation, the ignorance interpretation, that what an observation does is select from a conceptual ensemble of outcomes that are there prior to observation. In other words I assume it is a proper mixed state and collapse has occurred . You can do this because its observationally indistinguishable so no inconsistency can arise. It is an assumption of my interpretation not implied by the formalism, like the assumption in Many Worlds that each of the outcomes in the mixed state is a world, like the use of histories in decoherent histories, etc etc.

Thanks
Bill
 
  • #69
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Closed for moderation.

EDIT: this thread will remain closed. Everyone has had a chance to say their piece and now the conversation is just going in circles.
 
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