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lyner

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Chaos
« on: 28/12/2007 16:39:23 »
Chaos was introduced not many decades ago and it is applied to topics like the weather, these days.
It was very fashionable at one time and there were many books written about it. Fractal patterns, generated by simple chaotic maths models were all over the poster shops.
I haven't come across anything about it on TNS; I wonder why.
Chaotic and random behaviour are often difficult to tell apart.
How do we feel about Quantum Physics being governed by chaos theory, rather than random statistics?
Remember, not all chaotic fluctuations are particularly wild and can appear as noise on top of larger signals.
Accepting that the basis of quantum things was chaotic and not random would imply that Einsteins assertion that "God does not play dice" could be right.
Any random thoughts?


 

another_someone

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Chaos
« Reply #1 on: 28/12/2007 16:56:28 »
I think the counter argument would be Bell's theorem.

http://en.wikipedia.org/wiki/Bell%27s_theorem
Quote
Bell's theorem is the most famous legacy of the late physicist John S. Bell. It is famous for showing that the predictions of quantum mechanics (QM) are not intuitive, and touches upon fundamental philosophical issues that relate to modern physics. Bell's theorem states:
    “No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics.”

Einstein, beginning with the EPR paper, was critical of the standard interpretation of quantum mechanics because it postulated "spooky action-at-a-distance" and suggested a theory that postulated "local hidden variables." Bell's theorem, published nine years after Einstein's death in 1955, is considered to prove that any efforts to construct a local physical theory are bound to fail to accurately predict the quantum facts.

http://en.wikipedia.org/wiki/Bell%27s_theorem#Practical_experiments_testing_Bell.27s_theorem
Quote
Experimental tests can determine whether the Bell inequalities required by local realism hold up to the empirical evidence.

Bell's inequalities are tested by "coincidence counts" from a Bell test experiment such as the optical one shown in the diagram. Pairs of particles are emitted as a result of a quantum process, analysed with respect to some key property such as polarisation direction, then detected. The setting (orientations) of the analysers are selected by the experimenter.

Bell test experiments to date overwhelmingly violates Bell's inequality. Indeed, a table of Bell test experiments performed prior to 1986 is given in 4.5 of Redhead, 1987. Of the thirteen experiments listed, only two reached results contradictory to quantum mechanics; moreover, according to the same source, when the experiments were repeated, "the discrepancies with QM could not be reproduced".

Nevertheless, the issue is not conclusively settled. According to Shimony's 2004 Stanford Encyclopedia overview article[6]

    "Most of the dozens of experiments performed so far have favored Quantum Mechanics, but not decisively because of the 'detection loopholes' or the 'communication loophole.' The latter has been nearly decisively blocked by a recent experiment and there is a good prospect for blocking the former."

To explore the 'detection loophole', one must distinguish the classes of homogeneous and inhomogeneous Bell inequality.


The standard assumption in Quantum Optics is that "all photons of given frequency, direction and polarization are identical" so that photodetectors treat all incident photons on an equal basis. Such a fair sampling assumption generally goes unacknowledged, yet it effectively limits the range of local theories to those which conceive of the light field as corpuscular. The assumption excludes a large family of local realist theories, in particular, Max Planck's description. We must remember the cautionary words of Albert Einstein[7] shortly before he died: "Nowadays every Tom, Dick and Harry ('jeder Kerl' in German original) thinks he knows what a photon is, but he is mistaken".

Objective physical properties for Bell’s analysis (local realist theories) include the wave amplitude of a light signal. Those who maintain the concept of duality, or simply of light being a wave, recognize the possibility or actuality that the emitted atomic light signals have a range of amplitudes and, furthermore, that the amplitudes are modified when the signal passes through analyzing devices such as polarizers and beam splitters. It follows that not all signals have the same detection probability (Marshall and Santos 2002).
 

Offline lightarrow

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« Reply #2 on: 28/12/2007 17:20:42 »
Chaos was introduced not many decades ago and it is applied to topics like the weather, these days.
It was very fashionable at one time and there were many books written about it. Fractal patterns, generated by simple chaotic maths models were all over the poster shops.
I haven't come across anything about it on TNS; I wonder why.
Chaotic and random behaviour are often difficult to tell apart.
How do we feel about Quantum Physics being governed by chaos theory, rather than random statistics?
Remember, not all chaotic fluctuations are particularly wild and can appear as noise on top of larger signals.
Accepting that the basis of quantum things was chaotic and not random would imply that Einsteins assertion that "God does not play dice" could be right.
Any random thoughts?
Decoherence:
http://arxiv.org/abs/quant-ph/0306072
http://en.wikipedia.org/wiki/Quantum_decoherence
claims that non-linear effects of the interaction between quantum system - environment can be responsible for some of the quantum systems's strange behaviours.
Non-linearity is a first condition for chaothic behaviour.
I'm not sure that Bell's theorem could disprove the existence of a form of determinism in this case because I think that theorem applies to the quantum system only (the particle, to be clear) and not to the set "quantum system + environment".
 

another_someone

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Chaos
« Reply #3 on: 28/12/2007 20:05:09 »
I'm not sure that Bell's theorem could disprove the existence of a form of determinism in this case because I think that theorem applies to the quantum system only (the particle, to be clear) and not to the set "quantum system + environment".

I have to say that this is one of those areas of quantum physics (as if there were not enough other such areas) where I get a bit confused.

If all is quantum physics, then how can there be a separation of quantum system and environment, since is not the quantum system its own environment, for to imply otherwise would be to imply there is something in the universe that is not encompassed by quantum physics?

I understand that from a pragmatic perspective, sometimes it is convenient to regard large parts of the universe as an approximate collective entity that is non-quantum in nature; but is this not merely an approximation for the purpose of simplification, rather than a real statement that the environment is not really quantum in nature?
 

Offline lightarrow

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« Reply #4 on: 28/12/2007 20:30:54 »
I'm not sure that Bell's theorem could disprove the existence of a form of determinism in this case because I think that theorem applies to the quantum system only (the particle, to be clear) and not to the set "quantum system + environment".

I have to say that this is one of those areas of quantum physics (as if there were not enough other such areas) where I get a bit confused.

If all is quantum physics, then how can there be a separation of quantum system and environment, since is not the quantum system its own environment, for to imply otherwise would be to imply there is something in the universe that is not encompassed by quantum physics?

I understand that from a pragmatic perspective, sometimes it is convenient to regard large parts of the universe as an approximate collective entity that is non-quantum in nature; but is this not merely an approximation for the purpose of simplification, rather than a real statement that the environment is not really quantum in nature?

Clearly I expressed things...unclearly. You have, let's say, an electron, an experimental apparatus and a detector. Standard QM describes the results of the experiment on the electron in terms of the "electron's properties". So it says that the "quantum system" under measurement is "the electron" and the rest is "the environment" = the detector and all the other objects in the apparatus or anything else that can influence our electron. Here the locution "quantum system" is just another way to say that we are studying the electron and doesn't mean to imply that the rest doesn't have a quantum description.

With this (standard) description, you discover that these "properties" of the electrons, behave in a strange way: Heisenberg Uncertainty Principle, superposition, entanglement, ecc.

Now the question is: is it really possible to separate the electron's properties from the experimental setting? Maybe not. This last point of view (=  it's not possible to separate them) certainly requires a deep modification in our way to describe things: you are George independently of the fact that you are talking with me or with another person, e.g., but the electron instead could be somewhat "different" according to the experimental setting, so that what we are actually measuring are not "the electron's properties" but "all the system's properties" where "all the system" means electron + apparatus + detector.
« Last Edit: 28/12/2007 20:40:55 by lightarrow »
 

another_someone

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« Reply #5 on: 28/12/2007 20:48:25 »
Now the question is: is it really possible to separate the electron's properties from the experimental setting? Maybe not. This last point of view (=  it's not possible to separate them) certainly requires a deep modification in our way to describe things: you are George independently of the fact that you are talking with me or with another person, e.g., but the electron instead could be somewhat "different" according to the experimental setting, so that what we are actually measuring are not "the electron's properties" but "all the system's properties" where "all the system" means electron + apparatus + detector.

OK - this I understand, and in a way concur with, but does it not break the basic underlying premise of science (whether that premise be right or wrong) that in any way one can regard the observer as separate from the observed - it also follows from that that we must remove the notion of free will, since free will implicitly implies that the person acting under free will is somehow separate from the environment in which he acts.  All of these may be truths, but how can science continue to function in these circumstances?
 

Offline lightarrow

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« Reply #6 on: 29/12/2007 10:31:09 »
OK - this I understand, and in a way concur with, but does it not break the basic underlying premise of science (whether that premise be right or wrong) that in any way one can regard the observer as separate from the observed - it also follows from that that we must remove the notion of free will, since free will implicitly implies that the person acting under free will is somehow separate from the environment in which he acts.  All of these may be truths, but how can science continue to function in these circumstances?
A possible answer can come from here:
http://arxiv.org/PS_cache/quant-ph/pdf/9609/9609002v2.pdf

Anyway it's not necessary to dismantle all physics to follow that approach; even simple concepts as velocity are actually observer-dependent:
Quote
...For instance, I say that my hand moves at a velocity v with respect to the lamp on my table. Velocity is a relational notion (in Galilean as well as in special relativistic physics), and thus it is always (explicitly or implicitly) referred to something.
« Last Edit: 29/12/2007 11:08:01 by lightarrow »
 

another_someone

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Chaos
« Reply #7 on: 29/12/2007 13:13:47 »
A possible answer can come from here:
http://arxiv.org/PS_cache/quant-ph/pdf/9609/9609002v2.pdf

I am not sure that this really is an answer to Bell's theorem (although I don't claim to understand the issues enough to be certain of the facts here).  As I understand it, all this is suggesting is a pre-Copenhagen interpretation, which simply says that the uncertainty of quantum physics is a manifestation of of the energy used to probe the system, but this is, as I understand it, exactly what Bell's theorem was designed to address.

What I understood your earlier statement to suggest was not that simply we cannot view a system without disturbing it, but it does not address that which I thought you might be referring to, that we ourselves might be preprogrammed only to be able to view certain events, because we ourselves are limited by the system we are a part of.

Anyway it's not necessary to dismantle all physics to follow that approach; even simple concepts as velocity are actually observer-dependent:
Quote
...For instance, I say that my hand moves at a velocity v with respect to the lamp on my table. Velocity is a relational notion (in Galilean as well as in special relativistic physics), and thus it is always (explicitly or implicitly) referred to something.

Yes, velocity is observer dependent, but it still allows that two observers can both put themselves in the same position, and see the same outcome.

What it does not suggest (and, as I indicated above) is the possibility that the observer is constrained to see only certain events, and has no ability but to see that which they are constrained to see (i.e. that the observer is not a passive entity merely seeing the event from a particular viewpoint, but that the observer is an active component that is also acted upon, and constrained by, the system as a whole).
 

Offline lightarrow

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« Reply #8 on: 29/12/2007 16:41:11 »
A possible answer can come from here:
http://arxiv.org/PS_cache/quant-ph/pdf/9609/9609002v2.pdf
I am not sure that this really is an answer to Bell's theorem (although I don't claim to understand the issues enough to be certain of the facts here).  As I understand it, all this is suggesting is a pre-Copenhagen interpretation, which simply says that the uncertainty of quantum physics is a manifestation of of the energy used to probe the system
From what did you understand that in the paper?
Quote
, but this is, as I understand it, exactly what Bell's theorem was designed to address.
What I understood your earlier statement to suggest was not that simply we cannot view a system without disturbing it, but it does not address that which I thought you might be referring to, that we ourselves might be preprogrammed only to be able to view certain events, because we ourselves are limited by the system we are a part of.
I've lost you here.
Quote
Yes, velocity is observer dependent, but it still allows that two observers can both put themselves in the same position, and see the same outcome.

What it does not suggest (and, as I indicated above) is the possibility that the observer is constrained to see only certain events, and has no ability but to see that which they are constrained to see (i.e. that the observer is not a passive entity merely seeing the event from a particular viewpoint, but that the observer is an active component that is also acted upon, and constrained by, the system as a whole).
Even here I don't know what you want to say.
 

another_someone

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« Reply #9 on: 30/12/2007 11:28:15 »
OK, maybe we are talking at cross purposes, so I will try and explain what I am saying with an analogy.

Bell's theorem does not give us deterministic answers of the kind that says if there are local hidden variables that behave in a classical manner then you will get result X, but if none exist then you get result Y; but rather it gives statistical answers that say if you have a device that sits and counts how often an event happens, you will have the event happen X times if the classical hidden variable exists, but Y times if no such variable exists.

So lets draw an analogy here.  Suppose a politician wants to know that on a certain stretch of road, how many women drivers use that road and how many men drivers use that road.  The politician then hires a private contractor to count the drivers who use that road, and pays the private contractor a certain sum of money to give him the answers he desires.

The private contractor then realises he does not have enough money to pay for full time staff to sit there and count every single vehicle that passes along the road, so he hires some part time women who will count how many men and women use that road, and allows them to use whatever time suits them to count the vehicles, and will then assume what is true for that sample will be true for the whole.

In fact, the women choose to count vehicles at times when they are not doing other things (such as going shopping, or taking their children to school), so at the times when most women would be using the stretch of road (e.g. taking their children to school, or going shopping) they will not actually be measuring what is travelling along the road.  Thus, not surprisingly, the contractor will report back to the politician that far more men use that road than women use that road.  This is not a true indication of who actually uses the road, but is a manifestation of the fact that tools used to measure who used the road (the women hired to do the count) were subject to similar distortions to that which effected the traffic use itself, and so they preferentially counted one group of users and ignored another group of users.

To verify Bell's inequality we need to make similar statistical measurements, but we too have to use the tools at our disposal, which are themselves the same type of thing that we are measuring (i.e. we have to use the same type of elementary particles to measure what is happening to other elementary particles).  Even if we were use our own eyes, so our eyes are themselves made up of electrons, protons, etc., and in fact most of what we measure is only a measure of how it effects electrons (whether within electronic devices, or within chemical reactions).
 

Offline lightarrow

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« Reply #10 on: 30/12/2007 12:29:33 »
OK, maybe we are talking at cross purposes, so I will try and explain what I am saying with an analogy.

Bell's theorem does not give us deterministic answers of the kind that says if there are local hidden variables that behave in a classical manner then you will get result X, but if none exist then you get result Y; but rather it gives statistical answers that say if you have a device that sits and counts how often an event happens, you will have the event happen X times if the classical hidden variable exists, but Y times if no such variable exists.

So lets draw an analogy here.  Suppose a politician wants to know that on a certain stretch of road, how many women drivers use that road and how many men drivers use that road.  The politician then hires a private contractor to count the drivers who use that road, and pays the private contractor a certain sum of money to give him the answers he desires.

The private contractor then realises he does not have enough money to pay for full time staff to sit there and count every single vehicle that passes along the road, so he hires some part time women who will count how many men and women use that road, and allows them to use whatever time suits them to count the vehicles, and will then assume what is true for that sample will be true for the whole.

In fact, the women choose to count vehicles at times when they are not doing other things (such as going shopping, or taking their children to school), so at the times when most women would be using the stretch of road (e.g. taking their children to school, or going shopping) they will not actually be measuring what is travelling along the road.  Thus, not surprisingly, the contractor will report back to the politician that far more men use that road than women use that road.  This is not a true indication of who actually uses the road, but is a manifestation of the fact that tools used to measure who used the road (the women hired to do the count) were subject to similar distortions to that which effected the traffic use itself, and so they preferentially counted one group of users and ignored another group of users.

...and so it's explained the strange correlations of EPR paradox that hidden variables hypothesis cannot explain.  :)
 

Offline McQueen

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« Reply #11 on: 30/12/2007 13:53:52 »
May I  once and for all state that if Bell's theorem were true there would be a completely new and fool-proof encryption system on the net. Ergo , it is not true! So forget about EPR, Einstein was right! There is no non-locality in the Universe as we know it.
 

Offline lightarrow

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« Reply #12 on: 30/12/2007 20:33:22 »
May I  once and for all state that if Bell's theorem were true there would be a completely new and fool-proof encryption system on the net. Ergo , it is not true! So forget about EPR, Einstein was right! There is no non-locality in the Universe as we know it.
But Bell's theorem doesn't state there is non-locality.
 

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« Reply #12 on: 30/12/2007 20:33:22 »

 

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