![]() |
| If this is your first visit, be sure to check out the FAQ by clicking the link above. You may have to register before you can post: click the register link above to proceed. To start viewing messages, select the forum that you want to visit from the selection below. |
|
|||||||
| Tags: incompatibility, particle, properties, question, system |
|
|
Thread Tools | Display Modes |
|
#11
|
|||
|
|||
|
bernard.chaverondier:
"Bilge" a écrit dans le message de ue-al.net... Chaverondier The uncertainty principle applies to so called conjugate observables as for instance position R and momentum P of a given particle. Such observables are said to be conjugate because their commutator [R, P] writes [R, P] = i hbar Now, the question of Heisenberg uncertainty principle is more tricky than it is generally believed. The commutation relations should not be mistaken for an intrinsic cause of Heisenberg uncertainties relations. Bilge The uncertainty relations are defined by the commutation relations. That's why the uncertainty relations quantize quantum mechanics. Chaverondier Heisenberg uncertainties show up because of the commutations relation _and_ because of the uncertainties of quantum measurements. The two conditions are needed to provide these observed uncertainties. Wrong. The uncertainty, \delta A\Delta B = hbar/2, occurs for any pair of hermitian operators with a commutator equal to i\hbar. Indeed, when you know perfectly the sate of the observed system in representation position (or in momentum position, that's equivalent), that's not enough to know perfectly the position measurement outcome you will get. You can only predict the satistics of such position measurement outcomes according to Born rules statistics. Representation is irrelevant. You don't need to choose a representation in which either p or x is diagonal. That's because the quantum measurement outcomes depend not only on the quantum state of the observed system. They depend also on the unknown quantum state of the measuring apparatus and that of the environment that interact with them. You are reading too much into quantum mechanics. The uncertainty in your apparatus also obeys quantum mechanics, unless you got the equipment from a different universe. Quantum mechanics might be weirdm but it's not that weird. Chaverondier Indeed, when you know a given quantum wave in position representation, you know its representation in momentum representation too without any quantum indeterminacy. The transformation between the two representations is the unitary and deterministic Fourier transform. There is no possibility to find any uncertainty there. Bilge That makes no sense. The wavefunction is not an hermitian operator, Chaverondier The wave function has nothing to do with an hermitian operator of course. Why should it be otherwise ? It shouldn't but I was responding to your paragraph above in which you were talking about indeterminacy and various representations for a wavefunction, which makes no sense. I was just pointing out that it makes no sense. (the Fourier transform is an unitary, deterministic process, that has nothing to do with the unitary, deterministic evolution operator Ut = exp(-iHt/hbar)) None of those has anything to do with a ``deterministic'' anything. All those do is change repersentations. Bilge so it's non-sensical to talk about uncertainty in a representation. Chaverondier That's what I said. There is no intrinsic uncertainty to find in the commutation relation (which rules the shift from momentum to position representation). Then why bring it up at all? You're using apples to explain oranges. [...] Bilge It has everything to do with the conjugate nature of the observables. Chaverondier This conjugate nature is necessary but not sufficient to give rise to the impossibility of simultaneous measurements. What's impossible about simultaneous measurements? Any two events with a spacelike separation can be made simultaneous, by definition of simultaneous. It would be impossible for any two events to _not_ be able to be made simultaneous if the events were spacelike. Measurement uncertainties, following the Born rules, are necessary too. Without these measurements uncertainties the conjugate nature of the observables wouldn't be enough to give rise to the uncertainties relations. Nonsense. The uncertainty relations are defined by the commutation relations. The uncertainty is defined as the rms deviation from the expectation value of an operator, \Delta A^2 = A - A^2 = A^2 - A^2 Find \Delta A\Delta B for any pair of hermitian operators which have a commutator [A,B] = i. [...] Chaverondier The explanation seems so simple that it is somewhat puzzling. This comes from our ignorance of the quantum state of the measuring apparatus and that of the environment that interacts with the measuring apparatus and the observed system. Bilge No, it doesn't otherwise that would be apparent in the entropy. Chaverondier And it is. When decoherence shows up, the system evolves from a pure state rho = |psipsi| to a so called mixed state rhô' (a weighed sum of rank 1 projectors connected to the preferred Hilbert basis of the measuring apparatus) The choice of basis is irrelevant to the entropy. The entropy is the entropy. The entropy of the observed quantum system S = -k ln(rhô) increases to S' = -k ln(rhô') The entropy is S = k tr (\rho ln \rho). The trace is invariant under a change of basis. This entropy increase models the loss of information of the local observer. He ignores the EPR correlations that are propagating from the system to the measuring apparatus, then from the measuring apparatus to the environnement according to the unitary, deterministic and reversible propagation of the infinite Von Neumann Chain. EPR correlations don't constitute information. When you actually perform an experiment demonstrating otherwise, then you can say that. Until then, you're trying to pass off your idea on how to fix something that isn't broken as fact. As in classical physics, this apparent irreversibility and indeterminacy is a consequence of the loss of information of the local observer and (in my opinion) should not be interpreted as a fundamental indeterminacy. That's your opinion. On the other hand, what quantum mechanics does say is that indeterminacy is fundamental. If it weren't, it would be classical mechanics. |
| Ads |
|
#12
|
|||
|
|||
|
"Bill Hobba" a écrit dans le message de
... Bilge The uncertainty relations are defined by the commutation relations. That's why the uncertainty relations quantize quantum mechanics. Chaverondier Heisenberg uncertainties show up because of the commutations relation _and_ because of the uncertainties of quantum measurements. The two conditions are needed to provide these observed uncertainties. Indeed, when you know perfectly the sate of the observed system in representation position (or in momentum position, that's equivalent), that's not enough to know perfectly the position measurement outcome you will get. You can only predict the satistics of such position measurement outcomes according to Born rules statistics. Bill Yea - but the state represents all that can be known. Chaverondier And in my opinion there is no more to know as far as the system is in a shear state. Some information is unknown from the local observer only if the reduced density operator of the observed system indicates that "the system is in a mixed state". Actually, the mixed nature of the quantum state of the system should not be mistaken for an intrinsic property of the observed system. Indeed, it is mainly a property of the lack of knowlegde of the local observer. It indicates that the system is, or has been, EPR correlated with its surrounding so that the knowledge of the local observer (which is encapsulated in the reduced density operator of the observed system) has been somewhat deteriorated and is now incomplete. A part of the information that would be necessary to predict deteministically future evolutions of the observed system is lies in the EPR correlations of the system with its surrounding. These EPR correlations are not modeled in the reduced density operator. The reduced density operator represents the best knowledge the local observer can have as far as he knows only this quantum part of the inseparable quantum whole comprising the observed system and the surrounding it is EPR correlated with. The entropy encrease that follows a quantum measurement of a system which is not in a pure state of the measuring apparatus (as a measurement of position of a system which is nearly in a shear quantum state of momentum for instance) indicates this deterioration of the knowlege of the local observer when the quantum collapse process occurs. S = -k lnRhô increases when the density operator Rhô shifts from a known shear state to a mixed state (ie a weighed sum of shear states) providing the obsever whith only probabilities that the system be in such or such shear state. That's analog to a classical statistical physics situation when the increase of the Boltzmann entropy is not and has not to be interpreted as a fundamental irreversibility, but on the contrary as a loss of knowledge of the macroscopic observer. Chaverondier That's because the quantum measurement outcomes depend not only on the quantum state of the observed system. Bill Why that is no one really knows - different interpretations different reasons. Chaverondier Here I provide my one. The hypothesis that there would be some unknown fundamental irreversibility and indeterminism in quantum measurement is (in my opinion) both superfluous and incompatible with the unitary, deterministic and reversible propagation of the infinite Von Neumann chain. Chaverondier They depend also on the unknown quantum state of the measuring apparatus and that of the environment that interact with them. Bill In the Copenhagen interpretation the QM state of the measuring apparatus is irrelevant because it is considered to operate along classical lines. Chaverondier In my opinion, there is no classical behaviour. This should be considered only as a convenient macroscopic approximation. This additional hypothesis has to be considered as an efficient manner to calculate, not as an additional postulate that would be required in order to complete quantum mechanics basics at a fundamental level. That's as if one mistook the Biot and Savard law for an additional law that would have to be added to the Maxwell equations to complete the description of electromagnetism at a fundamental level. Bill One of the central issues with QM, if not the central issue, is the point where we can draw that boundary is not defined in the theory - leading to ideas such as it can be made at chemical processes in the brain of a human observer. Chaverondier In my opioinion, there is no such boundary. All the world is a quantum world and the classical boundary is only a convenient approximation. Chaverondier This conjugate nature is necessary but not sufficient to give rise to the impossibility of simultaneous measurements. Measurement uncertainties, following the Born rules, are necessary too. Bill Nope - only one rule is necessary. Namely if a system is in state p and we conduct an experiment to see if it is in state q then if will give a true result with a probability of |q|p|^2 and the system will then be in state q Chaverondier Which is the Borne rule providing the statistics of quantum measurements outcomes given the quantum state of the system and the preferred basis of the measuring apparatus, ie the eigen-vectors of the observable associated with this measuring apparatus. Bill This is called the collapse of the wave function and is probably the central issue with QM. Different interpretations have different takes on exactly what this means eg in the consistent histories interpretation they try to do away with the idea of observation entirely so the collapse is just something a theorist calculates - not something that actually occurs. All the rest follows from this one assertion as was shown by Von Neumann in Mathematical Foundations of QM. Chaverondier The collapse causes off-diagonal terms of the reduced density operator of the observed system to vanish (when expressed in the preferred Hilbert basis of the measuring apparatus). This is a real phenomenon that stems from a progressive (though very fast) entanglement of the observed system with the measuring apparatus followed by the entanglement of the measuring apparatus with its environment. That is not any more a working hypothesis. It has been observed experimentally and it is now studied by numerous physics laboratories. Chaverondier Without these measurements uncertainties the conjugate nature of the observables wouldn't be enough to give rise to the uncertainties relations. Bill I have no idea what you are trying to say. Chaverondier You just answered this question above. The uncertainties that link conjugate observables stems from the uncertainties of the measuring process (which statistics are given by the Born rules). In my opinion, there is no fundamental indeterminacy here. There is only a lack of knowlege of the local observer on the quantum state of the apparatus and the environnement that prevent the observer to know what outcome will be found out of the quantum measurement process. Except in the special case when the system is in an eigen state of the measured observable, the knowledge of the quantum state of the system isn't enough to predict the outcome that will stem from the deterministic quantum evolution of the inseparable quantum whole comprising the observed system the measuring apparatus and the environmement that interact with them. Bernard Chaverondier http://perso.wanadoo.fr/lebigbang/transformation.htm Derivation of Lorentz transforms and definition of inertial systems of coordinates in the framework of Aristotle space-time. http://perso.wanadoo.fr/lebigbang/epr.htm Quantum determinism or Relativist locality ? |
|
#13
|
|||
|
|||
|
"Bilge" a écrit dans le message de
... Bilge The uncertainty, \delta A\Delta B = hbar/2, occurs for any pair of hermitian operators with a commutator equal to i\hbar. Chaverondier Yes and the issue we are discussing about is that the interpretation of this result in terms of uncertainties relies on the interpretation of quantum measurement uncertainties. The question is to know if such measurement induced uncertainties are fundamental or result from the lack of knowlege ot the observer about the quantum state of the measuring apparatus and that of the environement. I believe into this second interpretation which is a deterministic, contextual hidden variables, explicitly non local interpretation of quantum mechanics and I provide in this post some of the reasons why I favor this deterministic interpretation of QM. (see also the sub-quantum (deterministic) theory of Micho Durdevich, Universidad Nacional Autonoma de Mexico, "Physics Beyond the Limits of Uncertainty Relations". A picture of physical reality which is based on individual physical systems, completely causal, and statistically compatible with quantum mechanics. http://www.matem.unam.mx/~micho/subq.html) Bilge Representation is irrelevant. You don't need to choose a representation in which either p or x is diagonal. Chaverondier Of course. That is not the issue. The issue is about Heisenberg uncertainties and the fact that these uncertainties pertains actually to the uncertainties showing up in the quantum measurement process Now, the manner you transform a position representation into a momentum one stems from the commutation relation. This relation amounts to indicate that the two representations are Fourier transforms one of each other. The fact that the two representation are Fourier transform of each other (ie the commutation relation) is not intrinsically the cause of Heisenberg uncertainties. Indeed, the fact that two observables cannot be diagonalized in the same Hilbert basis wouldn't give rise two the indeterminacy of the measurement of one of them just after the other one has been measured if the quantum measurement uncertainties were not to show up. Bilge You are reading too much into quantum mechanics. The uncertainty in your apparatus also obeys quantum mechanics, unless you got the equipment from a different universe. Chaverondier In don't believe that there were any uncertainty in quantum mechanics itself. The uncertainty is a property indicating the lack of knowledge of the observer, not a lack of cause deterministically ruling quantum dynamics of isolated quantum systems. One of the idea that plague the understanding of quantum mechanics is the idea that the state of a given particle for instance would be ill known if we are not up to provide one unique value of position and one unique value of momentum at the same time for instance. That's because of this classical belief that the Heisenberg uncertainties are misleadingly named uncertainties relations. This stems from a classical interpretation of what should be a complete knowledge of the state of the particle. This classical point of view cannot fit quantum world. In quantum world, the state of a particle is perfectly known as soon as its wave function is known. Its being in a superposition state should not to be considered as a lack of knowledge of the state of the system, but a lack of knowledge of the result of a quantum measurement. This lack of knowledge is a consequence of the lack of knowledge of the quantum state of the measuring apparatus and its environment and should not be mistaken for a lack of knowledge of the quantum state of the observed system itself. Chaverondier (the Fourier transform is an unitary, deterministic process, that has nothing to do with the unitary, deterministic evolution operator Ut = exp(-iHt/hbar)) Bilge None of those has anything to do with a ``deterministic'' anything. All those do is change representations. Chaverondier The best knowledge of the momentum of a quantum system you can have is, for instance, its momentum representation. Now, you have absolutely no uncertainty or incomplete knowledge of this momentum representation if you know the position representation. Chaverondier This conjugate nature is necessary but not sufficient to give rise to the impossibility of simultaneous measurements. Bilge What's impossible about simultaneous measurements? Chaverondier It's impossible to know with certainty the position measurement outcome of a quantum particle (for instance) even if a momentum measurement has provided a precise representation of its quantum state (in momentum representation). The uncertainty that shows up is because the outcome of a given measurement doesn't depend only on the quantum state of the system. It depends also on the quantum state of the measuring apparatus and that of the environment. Chaverondier Measurement uncertainties, following the Born rules, are necessary too. Without these measurements uncertainties the conjugate nature of the observables wouldn't be enough to give rise to the uncertainties relations. Bilge Nonsense. The uncertainty relations are defined by the commutation relations. Chaverondier No. Not only and you provide the reason. Bilge The uncertainty is defined as the rms deviation from the expectation value of an operator, \Delta A^2 = A - A^2 = A^2 - A^2 Find \Delta A\Delta B for any pair of hermitian operators which have a commutator [A,B] = i. Chaverondier Yes, and the statistical interpretation of what is \Delta A^2 as well as the interpretation of the inequalities between rms of conjugate observables as uncertainty relations rely on the Born rule devoted to predict the statistics of quantum measurements uncertainties. Chaverondier And it is. When decoherence shows up, the system evolves from a pure state rho = |psipsi| to a so called mixed state rhô' (a weighed sum of rank 1 projectors connected to the preferred Hilbert basis of the measuring apparatus) The entropy of the observed quantum system S = -k ln(rhô) increases to S' = -k ln(rhô') Bilge The choice of basis is irrelevant to the entropy. The entropy is the entropy. The entropy is S = k tr (\rho ln \rho). The trace is invariant under a change of basis. Chaverondier Why should it be otherwise ? Bilge EPR correlations don't constitute information. When you actually perform an experiment demonstrating otherwise, then you can say that. Until then, you're trying to pass off your idea on how to fix something that isn't broken as fact. Chaverondier The proof of the impossibility to transfer information thanks to EPR effect relies on the interpretation of quantum indeterminacy as a fundamental one. This interpretation conflicts (in my opinion) with the unitary, deterministic and reversible propagation of the infinite Von Neumann chain, but let us come back to the issue under discussion (which is not about FTL but about quantum mechanics determinism). The knowledge about EPR correlations of the system with its surrounding is encapsulated in the knowledge of the quantum state of the quantum whole comprising the observed system, the measuring appararus and the environmement. The reduced density operator of the observed system lacks the information about EPR correlations that are modeled in the quantum state of the quantum whole comprising the observed system, the measuring apparatus and its environement. Chaverondier As in classical physics, this apparent irreversibility and indeterminacy is a consequence of the loss of information of the local observer and (in my opinion) should not be interpreted as a fundamental indeterminacy. Bilge That's your opinion. On the other hand, what quantum mechanics does say is that indeterminacy is fundamental. If it weren't, it would be classical mechanics. Chaverondier No. There is no superposition of state in classical mechanics. There is no quantification of the energy spectrum in classical systems. There are no refraction and interference effects of classical particles. There is no quantum inseparability in classical mechanics and there is no indistinguishability of particles in classical mechanics The quantum measurement indeterminacy is a consequence of quantum inseparability that prevents the observer to predict deterministically the evolution of the observed system knowing only the reduced density operator modeling the system alone (instead of the quantum state of the quantum whole comprising the observed system, the measuring apparatus and its environement). Bernard Chaverondier http://perso.wanadoo.fr/lebigbang/transformation.htm Derivation of Lorentz transforms and definition of inertial systems of coordinates in the framework of Aristotle space-time. http://perso.wanadoo.fr/lebigbang/epr.htm Quantum determinism or Relativist locality ? |
|
#14
|
|||
|
|||
|
Sorry about threadlet.
"bernard.chaverondier" wrote in message ... "Bilge" a écrit dans le message de ... Bilge The uncertainty, \delta A\Delta B = hbar/2, occurs for any pair of hermitian operators with a commutator equal to i\hbar. Chaverondier Yes and the issue we are discussing about is that the interpretation of this result in terms of uncertainties relies on the interpretation of quantum measurement uncertainties. The question is to know if such measurement induced uncertainties are fundamental or result from the lack of knowlege ot the observer about the quantum state of the measuring apparatus and that of the environement. I believe into this second interpretation which is a deterministic, contextual hidden variables, explicitly non local interpretation of quantum mechanics and I provide in this post some of the reasons why I favor this deterministic interpretation of QM. (see also the sub-quantum (deterministic) theory of Micho Durdevich, Universidad Nacional Autonoma de Mexico, "Physics Beyond the Limits of Uncertainty Relations". A picture of physical reality which is based on individual physical systems, completely causal, and statistically compatible with quantum mechanics. http://www.matem.unam.mx/~micho/subq.html) Bilge Representation is irrelevant. You don't need to choose a representation in which either p or x is diagonal. Chaverondier Of course. That is not the issue. The issue is about Heisenberg uncertainties and the fact that these uncertainties pertains actually to the uncertainties showing up in the quantum measurement process Now, the manner you transform a position representation into a momentum one stems from the commutation relation. This relation amounts to indicate that the two representations are Fourier transforms one of each other. The fact that the two representation are Fourier transform of each other (ie the commutation relation) is not intrinsically the cause of Heisenberg uncertainties. Indeed, the fact that two observables cannot be diagonalized in the same Hilbert basis wouldn't give rise two the indeterminacy of the measurement of one of them just after the other one has been measured if the quantum measurement uncertainties were not to show up. Bilge You are reading too much into quantum mechanics. The uncertainty in your apparatus also obeys quantum mechanics, unless you got the equipment from a different universe. Chaverondier In don't believe that there were any uncertainty in quantum mechanics itself. The uncertainty is a property indicating the lack of knowledge of the observer, not a lack of cause deterministically ruling quantum dynamics of isolated quantum systems. One of the idea that plague the understanding of quantum mechanics is the idea that the state of a given particle for instance would be ill known if we are not up to provide one unique value of position and one unique value of momentum at the same time for instance. That's because of this classical belief that the Heisenberg uncertainties are misleadingly named uncertainties relations. This stems from a classical interpretation of what should be a complete knowledge of the state of the particle. This classical point of view cannot fit quantum world. In quantum world, the state of a particle is perfectly known as soon as its wave function is known. Its being in a superposition state should not to be considered as a lack of knowledge of the state of the system, but a lack of knowledge of the result of a quantum measurement. This lack of knowledge is a consequence of the lack of knowledge of the quantum state of the measuring apparatus and its environment and should not be mistaken for a lack of knowledge of the quantum state of the observed system itself. Chaverondier (the Fourier transform is an unitary, deterministic process, that has nothing to do with the unitary, deterministic evolution operator Ut = exp(-iHt/hbar)) Bilge None of those has anything to do with a ``deterministic'' anything. All those do is change representations. Chaverondier The best knowledge of the momentum of a quantum system you can have is, for instance, its momentum representation. Now, you have absolutely no uncertainty or incomplete knowledge of this momentum representation if you know the position representation. Chaverondier This conjugate nature is necessary but not sufficient to give rise to the impossibility of simultaneous measurements. Bilge What's impossible about simultaneous measurements? Chaverondier It's impossible to know with certainty the position measurement outcome of a quantum particle (for instance) even if a momentum measurement has provided a precise representation of its quantum state (in momentum representation). The uncertainty that shows up is because the outcome of a given measurement doesn't depend only on the quantum state of the system. It depends also on the quantum state of the measuring apparatus and that of the environment. Chaverondier Measurement uncertainties, following the Born rules, are necessary too. Without these measurements uncertainties the conjugate nature of the observables wouldn't be enough to give rise to the uncertainties relations. Bilge Nonsense. The uncertainty relations are defined by the commutation relations. Chaverondier No. Not only and you provide the reason. Bilge The uncertainty is defined as the rms deviation from the expectation value of an operator, \Delta A^2 = A - A^2 = A^2 - A^2 Find \Delta A\Delta B for any pair of hermitian operators which have a commutator [A,B] = i. Chaverondier Yes, and the statistical interpretation of what is \Delta A^2 as well as the interpretation of the inequalities between rms of conjugate observables as uncertainty relations rely on the Born rule devoted to predict the statistics of quantum measurements uncertainties. Chaverondier And it is. When decoherence shows up, the system evolves from a pure state rho = |psipsi| to a so called mixed state rhô' (a weighed sum of rank 1 projectors connected to the preferred Hilbert basis of the measuring apparatus) The entropy of the observed quantum system S = -k ln(rhô) increases to S' = -k ln(rhô') Bilge The choice of basis is irrelevant to the entropy. The entropy is the entropy. The entropy is S = k tr (\rho ln \rho). The trace is invariant under a change of basis. Chaverondier Why should it be otherwise ? Bilge EPR correlations don't constitute information. When you actually perform an experiment demonstrating otherwise, then you can say that. Until then, you're trying to pass off your idea on how to fix something that isn't broken as fact. Chaverondier The proof of the impossibility to transfer information thanks to EPR effect relies on the interpretation of quantum indeterminacy as a fundamental one. This interpretation conflicts (in my opinion) with the unitary, deterministic and reversible propagation of the infinite Von Neumann chain, but let us come back to the issue under discussion (which is not about FTL but about quantum mechanics determinism). The knowledge about EPR correlations of the system with its surrounding is encapsulated in the knowledge of the quantum state of the quantum whole comprising the observed system, the measuring appararus and the environmement. The reduced density operator of the observed system lacks the information about EPR correlations that are modeled in the quantum state of the quantum whole comprising the observed system, the measuring apparatus and its environement. Chaverondier As in classical physics, this apparent irreversibility and indeterminacy is a consequence of the loss of information of the local observer and (in my opinion) should not be interpreted as a fundamental indeterminacy. Bilge That's your opinion. On the other hand, what quantum mechanics does say is that indeterminacy is fundamental. If it weren't, it would be classical mechanics. Chaverondier No. There is no superposition of state in classical mechanics. There is no quantification of the energy spectrum in classical systems. There are no refraction and interference effects of classical particles. There is no quantum inseparability in classical mechanics and there is no indistinguishability of particles in classical mechanics The quantum measurement indeterminacy is a consequence of quantum inseparability that prevents the observer to predict deterministically the evolution of the observed system knowing only the reduced density operator modeling the system alone (instead of the quantum state of the quantum whole comprising the observed system, the measuring apparatus and its environement). Bernard Chaverondier http://perso.wanadoo.fr/lebigbang/transformation.htm Derivation of Lorentz transforms and definition of inertial systems of coordinates in the framework of Aristotle space-time. http://perso.wanadoo.fr/lebigbang/epr.htm Quantum determinism or Relativist locality ? Suggestion: Consider dropping the term "deterministic" and use "effectuationist" instead. om... Peter Kinane http://www.effectuationism.com/ |
|
#15
|
|||
|
|||
|
"bernard.chaverondier" wrote in message ... "Bill Hobba" a écrit dans le message de ... Bilge The uncertainty relations are defined by the commutation relations. That's why the uncertainty relations quantize quantum mechanics. Chaverondier Heisenberg uncertainties show up because of the commutations relation _and_ because of the uncertainties of quantum measurements. The two conditions are needed to provide these observed uncertainties. Indeed, when you know perfectly the sate of the observed system in representation position (or in momentum position, that's equivalent), that's not enough to know perfectly the position measurement outcome you will get. You can only predict the satistics of such position measurement outcomes according to Born rules statistics. Bill Yea - but the state represents all that can be known. Chaverondier And in my opinion there is no more to know as far as the system is in a shear state. Shear state? Do you mean pure state? If so see below. Some information is unknown from the local observer only if the reduced density operator of the observed system indicates that "the system is in a mixed state". Actually, the mixed nature of the quantum state of the system should not be mistaken for an intrinsic property of the observed system. Indeed, it is mainly a property of the lack of knowlegde of the local observer. Mixed state means a state that is a superposition of states of definite position say. But such only has a meaning in regard to a predefined experimental setup. In principle any state is 'pure' in the sense it is assumed some experiment can be designed to detect it. I am having trouble understanding the context of some of the terminology you use. Can you confi rm you accept the terminology of the following presentation http://www.physics.utoronto.ca/~stei...enna_Lect2.ppt. If not please let me know because that details my understanding of it eg we have no idea whether a collapse really occurs as demonstrated by the fact that interpretations that demand it exist and other that do not also exist - and they are all perfectly compatible with QM. What I find difficult in your writing is you seem to be taking a certain predetermined view of things that is known to yourself but is not spelt out clearly from the start and mixing it up with concepts that we simply do not know for sure. The same for non locality - we simply do not know if QM has non locality or not - it is entirely interpretation dependant. Nothing a-priori demands that QM is determined by hidden variables as assumed in a bell type analysis. It indicates that the system is, or has been, EPR correlated with its surrounding so that the knowledge of the local observer (which is encapsulated in the reduced density operator of the observed system) has been somewhat deteriorated and is now incomplete. A part of the information that would be necessary to predict deteministically future evolutions of the observed system is lies in the EPR correlations of the system with its surrounding. I have no idea what your are trying to say. In QM the state tells us everything we can know about a system - EPR or no EPR (which is just and example of strange correlations inherent in the idea that two particles are described by the one state in certain circumstances). These EPR correlations are not modeled in the reduced density operator. The reduced density operator represents the best knowledge the local observer can have as far as he knows only this quantum part of the inseparable quantum whole comprising the observed system and the surrounding it is EPR correlated with. EPR correlations are modeled completely in QM and totally consistent with it. The entropy encrease that follows a quantum measurement of a system which is not in a pure state of the measuring apparatus (as a measurement of position of a system which is nearly in a shear quantum state of momentum for instance) indicates this deterioration of the knowlege of the local observer when the quantum collapse process occurs. Again I have no idea what you are trying to say. S = -k lnRhô increases when the density operator Rhô shifts from a known shear state to a mixed state (ie a weighed sum of shear states) providing the obsever whith only probabilities that the system be in such or such shear state. That's analog to a classical statistical physics situation when the increase of the Boltzmann entropy is not and has not to be interpreted as a fundamental irreversibility, but on the contrary as a loss of knowledge of the macroscopic observer. Chaverondier That's because the quantum measurement outcomes depend not only on the quantum state of the observed system. Bill Why that is no one really knows - different interpretations different reasons. Chaverondier Here I provide my one. The hypothesis that there would be some unknown fundamental irreversibility and indeterminism in quantum measurement is (in my opinion) both superfluous and incompatible with the unitary, deterministic and reversible propagation of the infinite Von Neumann chain. Then please provide the full mathematical details of the interpretation. An example of such would be primary state diffusion as proposed by Ian Percival - http://arxiv.org/abs/quant-ph/9508021. I would appreciate it if your ideas were expressed in a similar way because I have great difficulty understanding what you are on about. Please do not take what am about to say next in a bad way - it is not meant to be. But what I see from you writing is ideas jumbled together - what I would like to see in then coherently presented such as what Griffith has done in the Consistent Histories interpretation. Chaverondier They depend also on the unknown quantum state of the measuring apparatus and that of the environment that interact with them. Bill In the Copenhagen interpretation the QM state of the measuring apparatus is irrelevant because it is considered to operate along classical lines. Chaverondier In my opinion, there is no classical behaviour. What we need is less opinion and more fact. The fact is interpretations exist in which classical behavior is assumed to exist eg the Copenhagen interpretation. The problem with the idea of no classical behavior is what is to count as an observation. One possibility is the consistent histories interpretation that does not require the concept from the outset. This should be considered only as a convenient macroscopic approximation. This additional hypothesis has to be considered as an efficient manner to calculate, not as an additional postulate that would be required in order to complete quantum mechanics basics at a fundamental level. That's as if one mistook the Biot and Savard law for an additional law that would have to be added to the Maxwell equations to complete the description of electromagnetism at a fundamental level. Ok when you have the full detail of such worked out repost. Bill One of the central issues with QM, if not the central issue, is the point where we can draw that boundary is not defined in the theory - leading to ideas such as it can be made at chemical processes in the brain of a human observer. Chaverondier In my opioinion, there is no such boundary. All the world is a quantum world and the classical boundary is only a convenient approximation. Then what is an observation? PSD solves it by introducing random processes at about the plank time and that is what collapses the wave function. Consistant histories resolves it by not introducing it into the description in the first place. What you need to do is detail your ideas, including exactly what you mean by terms like 'shear state' so we can see how it all fits together. Chaverondier This conjugate nature is necessary but not sufficient to give rise to the impossibility of simultaneous measurements. Measurement uncertainties, following the Born rules, are necessary too. Bill Nope - only one rule is necessary. Namely if a system is in state p and we conduct an experiment to see if it is in state q then if will give a true result with a probability of |q|p|^2 and the system will then be in state q Chaverondier Which is the Borne rule providing the statistics of quantum measurements outcomes given the quantum state of the system and the preferred basis of the measuring apparatus, ie the eigen-vectors of the observable associated with this measuring apparatus. If you call the above the Born rule then nothing else is required - indeterminacy of momentum and position follows immediately from it. Bill This is called the collapse of the wave function and is probably the central issue with QM. Different interpretations have different takes on exactly what this means eg in the consistent histories interpretation they try to do away with the idea of observation entirely so the collapse is just something a theorist calculates - not something that actually occurs. All the rest follows from this one assertion as was shown by Von Neumann in Mathematical Foundations of QM. Chaverondier The collapse causes off-diagonal terms of the reduced density operator of the observed system to vanish (when expressed in the preferred Hilbert basis of the measuring apparatus). This is a real phenomenon that stems from a progressive (though very fast) entanglement of the observed system with the measuring apparatus followed by the entanglement of the measuring apparatus with its environment. That is not any more a working hypothesis. It has been observed experimentally and it is now studied by numerous physics laboratories. Correct - Quantum State Diffusion and entanglement are now well known phenomena associated with wave function collapse. But they in no way resolve the fundamental issue - what causes the collapse or even is such really exists. Different interpretations handle it differently. The above sounds a lot like the consistent histories interpretation. Chaverondier Without these measurements uncertainties the conjugate nature of the observables wouldn't be enough to give rise to the uncertainties relations. Bill I have no idea what you are trying to say. Chaverondier You just answered this question above. The uncertainties that link conjugate observables stems from the uncertainties of the measuring process (which statistics are given by the Born rules). I do not know what you mean by 'Born rules'. There is one and only one statistical assertion of QM - the Von Neumann statistical assertion that I detailed above from which all statistical assertions of QM follow. If that is what you mean by 'Born rules' please use the singular form - Born rule because only one rule is necessary. In my opinion, there is no fundamental indeterminacy here. There is only a lack of knowlege of the local observer on the quantum state of the apparatus and the environnement that prevent the observer to know what outcome will be found out of the quantum measurement process. Fine - then write up the detail of your interpretation similar to the paper I gave on PSD and the book by Griffith on Consistent histories. Except in the special case when the system is in an eigen state of the measured observable, the knowledge of the quantum state of the system isn't enough to predict the outcome that will stem from the deterministic quantum evolution of the inseparable quantum whole comprising the observed system the measuring apparatus and the environmement that interact with them. Thanks Bill Bernard Chaverondier http://perso.wanadoo.fr/lebigbang/transformation.htm Derivation of Lorentz transforms and definition of inertial systems of coordinates in the framework of Aristotle space-time. http://perso.wanadoo.fr/lebigbang/epr.htm Quantum determinism or Relativist locality ? |
|
#16
|
|||
|
|||
|
bernard.chaverondier:
"Bilge" a écrit dans le message de ue-al.net... Bilge The uncertainty, \delta A\Delta B = hbar/2, occurs for any pair of hermitian operators with a commutator equal to i\hbar. Chaverondier Yes and the issue we are discussing about is that the interpretation of this result in terms of uncertainties relies on the interpretation of quantum measurement uncertainties. The question is to know if such measurement induced uncertainties are fundamental or result from the lack of knowlege ot the observer about the quantum state of the measuring apparatus and that of the environement. I think it's fairly straight forward to determine. In order to construct an experiment, you have to choose in advance what it is you plan to measure so that you don't try to measure two incommensurate quantities. This doesn't happen in classical physics and in scattering experiments, the actual interactions in the detectors is irrelevant. Measuring an anguar distribution that distinguishes between spin observables almost never is done by analyzing the spin of the scattered particles. That is too hard. What is usually done is just a simple measurement of an asymmetry in the direction of the scattered particles or a difference in total cross section using a polarized beam or polarized target or possibly both. A tyipical analyzing power measurement does nothing but count particles in two detectors which are located symmetrically about the target. You get counts in the right side and left side detectors and take the analyzing power to be something like A = (L-R)/(L+R). There's no mysterious epr correlations involved. You seem to forget that quantum mechanics gets the most use in situations that require quantum mechanics, but have nothing at all to do with epr measurements. You still don't have a classical experiment, since something like a tensor polarized deuteron beam is not classical. What you're doing is attempting to explain a particular experiment with an unnecessary and elaborate interpretation and completely ignoring the zillions of other, more mundane examples of commutation relations and the uncertainty principle appear for exactly the same reason. I believe into this second interpretation which is a deterministic, contextual hidden variables, explicitly non local interpretation of quantum mechanics and I provide in this post some of the reasons why I favor this deterministic interpretation of QM. You can believe whatever you wish, but unless you can find an experiment that gives what you believe some additional reality, all you're doing is adding philosophical baggage that at best serves no purpose and at worst is ligically incompatible with what you are trying to explain with it. (see also the sub-quantum (deterministic) theory of Micho Durdevich, Universidad Nacional Autonoma de Mexico, "Physics Beyond the Limits of Uncertainty Relations". A picture of physical reality which is based on individual physical systems, completely causal, and statistically compatible with quantum mechanics. http://www.matem.unam.mx/~micho/subq.html) OK, what that boils down to is yet another attempt to attribute the uncertainty principle to something else in order to say some even more abstract quantity is deterministic (in a weird sort of way), but for some rather nebulous reason, we can't observe a particle such that it doesm't appear to behave just like quantum mechanics. Sorry, I don't buy it without an example of an experiment which can distinguish between the interpretations. Attributing reality to something with no real existence is silly. Bilge Representation is irrelevant. You don't need to choose a representation in which either p or x is diagonal. Chaverondier Of course. That is not the issue. The issue is about Heisenberg uncertainties and the fact that these uncertainties pertains actually to the uncertainties showing up in the quantum measurement process So far, they show up just like the standard theory says they will. As far as I know, the epr experiment did not require any novel explanations to construct. It was constructed from standard quantum theory, in part, because einstein thought what quantum mechanics predicted was ridiculous on its face. Now, the manner you transform a position representation into a momentum one stems from the commutation relation. That's a rather content-free statement. What you just said is equivalent to saying the manner in which you perform a canonical transforms stems from the poisson bracket. Well, that's only true because a canonical transformation preserves poisson brackets by definition. The reason canonical transformations are important is because they preserve possoin brackets. All that means is that the poisson brackets are important to the theory and the particular choice of variables that preserve them is irrelevant to any physics, apart from what it happens to be convenient to measure. This relation amounts to indicate that the two representations are Fourier transforms one of each other. So what? How you transform between representations is irrelevant. What's relevant is that the commutator bracket isn't changed in fundamental way. What's the commutator [p,x] in the number basis, |n? It's simple. It's -i\hbar. You can check it by performing a canonical transformation and obtaining x = a + a(+), p = i(a - a(+)). That quantizes the harmonic oscillator, which is quantized in whatever basis you choose. The fact that the two representation are Fourier transform of each other (ie the commutation relation) is not intrinsically the cause of Heisenberg uncertainties. Indeed, the fact that two observables cannot be diagonalized in the same Hilbert basis wouldn't give rise two the indeterminacy of the measurement of one of them just after the other one has been measured if the quantum measurement uncertainties were not to show up. Buy a quantum mechanics book. What you are saying is complete non-sense. [...] Bilge What's impossible about simultaneous measurements? Chaverondier It's impossible to know with certainty the position measurement outcome of a quantum particle (for instance) even if a momentum measurement has provided a precise representation of its quantum state (in momentum representation). Again, you demonstrate that you don't know what you are talking about. Even conjugate operators commute on spacelike intervals. [*snip*] |
|
#17
|
|||
|
|||
|
"Bill Hobba" a écrit dans le message de
... "bernard.chaverondier" wrote in message ... Bill Mixed state means a state that is a superposition of states of definite position say. Chaverondier No. Mixed states should not be mistaken for superposition states. A superposition state is still a pure state because the interference between the components of the state of the system is possible. Bill In principle any state is 'pure' Chaverondier No. If a system S1 is entangled with a system S2, then even if S=S1US2 is in a pure state |psi, you cannot separate system S1 from system S2 without loss of information. This is explained on the slide "What happens if you don't look at part of your system" of the link you provided in this thread http://www.physics.utoronto.ca/~stei...enna_Lect2.ppt. ) When you look only the part S1 of a system S = S1US2 in a pure but entangled state |psi, the part S1 of S is not any more in a pure state. It is in a mixed state that is obtained by the so called partial trace operation rhô1 = somme_k psi2_k| rhô |psi2_k * where rhô denotes the density operator of system S = S1US2, rhô = |psipsi| * where rhô1 denotes the reduced density operator of system S1 * where the |psi2_k denote an Hilbert basis of the Hilbert space state of system S2 You loose information when you try to define an entangled part S1 of an inseparable quantum whole S=S1US2 separately from the rest of this quantum whole. See for instance, the slides "decoherence arises from throwing away information" and "decoherence party line" of the link http://www.physics.utoronto.ca/~stei...enna_Lect2.ppt you provided to me. I quote the slide "decoherence party line" because it's very important "coherence is never lost, as _unitary_ evolution preserves the purity of states. In principle, the measurement interaction is _reversible_. In practice, once the system interacts with the environment, ie anything with too many degrees of freedom for us to handle, we cannot reverse it. Just as in classical mechanics, it is the _approximation_ of an open system which leads to effective _irreversibility_ and _loss of information_ (increase in entropy) loss of information = loss of coherence" Bill I am having trouble understanding the context of some of the terminology you use. Can you confirm you accept the terminology of the following presentation http://www.physics.utoronto.ca/~stei...enna_Lect2.ppt Chaverondier First "shear state" is a translation error of mine. I wanted to say pure state. Second, what I call the statistics Born rule is what you call the Von Neumann statistical assertion. Now, I read your link and I didn't notice any point of disagreement except on the slide "what are the effect of measurement ?" where there is a big mistake about the explanation of the collapse of a system S1US2 in the state (|+-+|-+)/2^(1/2) when measuring one of the two entangled parts. The explanation which is provided on this slide amounts to a _local_ hidden variable interpretation which has been discarded by the experimental verification of Bells inequalities violations. Otherwise, your link is OK. Bill What I find difficult in your writing is you seem to be taking a certain predetermined view of things that is known to yourself but is not spelt out clearly from the start and mixing it up with concepts that we simply do not know for sure. Chaverondier Presently; the only thing where my point of view seems to differ from the most widely accepted one is that I don't believe in the hypothesis that the so called collapse would be something different from the unitary, deterministic and reversible evolution of the quantum whole comprising all parts involved in the measurement process, ie * the observed system * the measuring apparatus * the environment interacting with them. As in classical statistical mechanics, when an apparent irreversibility and an apparent indeterminacy show up, that's (in my opinion) a consequence of a loss of information of the observer. Surprisingly, your link seems to agree with this point of view (which suggests that the views on that topic may be changing). Bill The same for non locality - we simply do not know if QM has non locality or not - it is entirely interpretation dependant. Chaverondier You know that the result of a measurement on one part S2 depends on the measurement that has been performed on The part S1 of an entangled system S=S1US2 (ie the state of the measuring apparatus of S1 when the measurement on S1 has been performed) The best illustration is the Greenberg Horn Zeilinger thought experiment that is even more striking that the EPR experiment because only equalities are involved. (see "do we really understand quantum mechanics ?" by Frank Laloe http://www.phys.ens.fr/cours/notes-d...mq-anglais.pdf 8 Mo unhappily, chapter 4.3 GHZ equality ) Now, the interpretation of EPR effect as an action at a distance depends on the interpretation of quantum measurement indeterminacy. The principle of relativity of motion is preserved if quantum measurement indeterminacy is assumed to be fundamental. In the case when quantum indeterminacy is interpreted as a loss of knowledge of the local observer, then the principle of relativity of motion is lost. Bill Nothing a-priori demands that QM is determined by hidden variables as assumed in a Bell type analysis. Chaverondier The Bell experiment and the Bell's inequalities violation that have been proven don't demand hidden variables. They are incompatible with _local_ hidden variables and are compatible with _contextual_ hidden variables. If we stick to the idea that the unitary, deterministic, reversible quantum formalism that applies to isolated quantum systems works fine and that no strange and unknown process breaking this reversibility would show up, I don't see how it is possible to escape the interpretation according to which the quantum measurement indeterminacy stems from a loss of knowledge of the contextual hidden variables (forgotten variables instead of hidden would be better in my opinion) ie (in my opinion) the quantum state of the measuring apparatus and its environment (see "Hidden Variables and Nonlocality in Quantum Mechanics" Douglas Hemmick" http://www.intercom.net/~tarababe/DissertPage.html ) and The sub-quantum (deterministic) theory of Micho Durdevich, Universidad Nacional Autonoma de Mexico, "Physics Beyond the Limits of Uncertainty Relations". A picture of physical reality which is based on individual physical systems, completely causal, and statistically compatible with quantum mechanics. http://www.matem.unam.mx/~micho/subq.html Incidentally, the deterministic interpretation of the measurement process seems to be shared by the author of the link you have provided. Chaverondier A mixed state indicates that the system is, or has been, EPR correlated with its surrounding so that the knowledge of the local observer (which is encapsulated in the reduced density operator of the observed system) has been somewhat deteriorated and is now incomplete. A part of the information that would be necessary to predict deterministically future evolutions of the observed system is lies in the EPR correlations of the system with its surrounding. Bill I have no idea what your are trying to say. Chaverondier It is explained in the link you have provided. I quote the last slide "summary" "the reduced density matrix of an entangled sub-system appears mixed because the discarded part of the system carry away information. This is the origin of decoherence of the measured subsystem." Bill In QM the state tells us everything we can know about a system - EPR or no EPR Chaverondier When you consider the measurement process, the system becomes EPR correlated with the measuring apparatus. The whole comprising the system + the measuring apparatus can still be represented by a pure state (as far as it is not entangled with the environment) but the observed system cannot be anymore modeled by a pure state. It is modeled by a mixed state, ie by its reduced density operator (which doesn't provide information about the EPR correlation of the observed system with the environment). This is explained on the link you have provided. Chaverondier The entropy increase that follows a quantum measurement of a system which is not in a pure state of the measuring apparatus (as a measurement of position of a system which is nearly in a shear quantum state of momentum for instance) indicates this deterioration of the knowledge of the local observer when the quantum collapse process occurs. Bill Again I have no idea what you are trying to say. Chaverondier See the slide "decoherence party line" of the link you have provided for instance. Chaverondier Here I provide my one. The hypothesis that there would be some unknown fundamental irreversibility and indeterminism in quantum measurement is (in my opinion) both superfluous and incompatible with the unitary, deterministic and reversible propagation of the infinite Von Neumann chain. Bill Then please provide the full mathematical details of the interpretation. An example of such would be primary state diffusion as proposed by Ian Percival http://arxiv.org/abs/quant-ph/9508021 I would appreciate it if your ideas were expressed in a similar way because I have great difficulty understanding what you are on about. Chaverondier I am still working the bibliography and what you are asking amounts to a work of several years (at least). Presently, I am working about all that and use the net as a mean to get a lot of valuable hints and links on the topic. The point where I am presently is that one. 1/ I have stated the compatibility of faster than light propagating interactions with an appropriate formulation of relativist invariance of phenomena that actually satisfy this symmetry in the framework of Aristotle space-time see http://perso.wanadoo.fr/lebigbang/epr.htm (unhappily written in French. Up to now, I have not taken the time to translate it in English) and in English http://perso.wanadoo.fr/lebigbang/transformation.htm derivation of the Lorentz transforms and definition of inertial frames in the framework of Aristotle space-time. 2/ I have pointed out that the proof on the no communication theorem relies on the dubious hypothesis that quantum measurement indeterminacy would be of fundamental nature. see http://perso.wanadoo.fr/lebigbang/no_communication.htm Now, I cannot see how this assumed fundamental indeterminacy could be interpreted as compatible with the unitary, reversible and determinist propagation of the Von Neumann chain. So, I rather interpret the Copenhagen interpretation to be an efficient tool as for instance is the Biot and Savart law of electromagnetism. I believe the quantum measurement process to be a deterministic process as soon as the quantum whole encompassing the observed system, the measuring apparatus and the environment apparatus are accounted for. Bill Then what is an observation? Chaverondier Of course, a model of quantum measurement is needed to support a deterministic, explicitly non local interpretation of quantum measurement and that's where I would like to go. Presently, I just want to discuss these ideas to get all the objections that can oppose this point of view and get valuable hints and links on the topic. Indeed, I think it would not be a good idea to do a lot of work without knowing in the first place all the objections that have to be considered and the present "state of the art" on the topic. Bernard Chaverondier http://perso.wanadoo.fr/lebigbang/transformation.htm Derivation of Lorentz transforms and definition of inertial systems of coordinates in the framework of Aristotle space-time. http://perso.wanadoo.fr/lebigbang/epr.htm Quantum determinism or Relativist locality ? |
|
#18
|
|||
|
|||
|
"Bilge" a écrit dans le message de
... Chaverondier I believe into this second interpretation which is a deterministic, contextual hidden variables, explicitly non local interpretation of quantum mechanics. (see "Hidden Variables and Nonlocality in Quantum Mechanics" by Douglas Hemmick http://www.intercom.net/~tarababe/DissertPage.html ) Bilge You can believe whatever you wish, but unless you can find an experiment that gives what you believe some additional reality, all you're doing is adding philosophical baggage that at best serves no purpose and at worst is logically incompatible with what you are trying to explain with it. Chaverondier Agreed. That's what I am interested in. |
|
#19
|