Re: Naive Realism and QM
Hi Serafino, Thanks for your pointers. You obvious know your physics quite well and I think you got my point precisely! Godfrey Kurtz (New Brunswick, NJ) -Original Message- From: scerir [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Sat, 20 Aug 2005 19:22:10 +0200 Subject: Re: Naive Realism and QM Godfrey: There is no energy flux directly associated with wave-functions (like with electomagnetic or mechanical waves) but is a probability density and a probability flux associated with the square of linear functionals of the wave-function. [Scerir] The question, at this point, should be: probability of what? [GK] Exactly! [Scerir] Because, leaving aside those who think (Weinberg, Dyson, etc.) that only fields exist and are real, there are at least a couple of solutions. There are physicists (followers of Bohr [1], more or less) who think [2][3][4] that quantum physics is about 'correlations without correlata', or about 'fotuitousness and clicks'. There are physicists (followers of Einstein, and his idea of Gespensterfeld, etc.) like Born [5], Fock [6], Barut [7], etc., who think that a 'probability' wave, even in 3n-dimensional space, is a real thing, much more than a mathematical tool, and who also think that physics is not just about apparata, or clicks. s. [GK] Maybe I would not divide things exactly that way but, yes, that is basically the choices you have! Either you keep looking for an ultimate ontological category on which quantum information is predicated, or you try and build some understanding of probability as a material of sorts (that was not Bohr, but actually Schrodinger and Madelung on the latter side.) There are however some possible ontological grey areas between these two positions that can be explored and Heiseinberg tried that at some point. Bohr's position (the infamous Copnehagen Interpretations) was a bit more complicated than what the sentence you quote expresses, I would say, so it is hard to know where to place him... -Godfrey [1[ Niels Bohr: 'However, since the discovery of the quantum of action, we know that the classical ideal cannot be attained in the description of atomic phenomena. In particular, any attempt at an ordering in space-time leads to a break in the causal chain, since such an attempt is bound up with an essential exchange of momentum and energy between the individuals and the measuring rods and clocks used for observation; and just this exchange cannot be taken into account if the measuring instruments are to fulfil their purpose. Conversely, any conclusion, based in an unambiguous manner upon the strict conservation of energy and momentum, with regard to the dynamical behaviour of the individual units obviously necessitates a complete renunciation of following their course in space and time.' [2] Carlo Rovelli Relational Quantum Mechanics http://www.arxiv.org/abs/quant-ph/9609002 [3] David Mermin What is quantum mechanics trying to tell us? http://www.arxiv.org/abs/quant-ph/9801057 [4] Aage Bohr http://www.physicstoday.org/vol-57/iss-10/p15.html [5] Max Born: 'Quite generally, how could we rely on probability predictions if by this notion we do not refer to something real and objective?' [6] V.A.Fock 'Disskussija S Nilsom Borom', in 'Voprosy Filosofii', 1964 (a memorandum, about the interpretation of QM and the meaning of wavefunction, he gave to Bohr, in Copenhagen, 1957, who read it and changed his mind about several points, but not all). [7] A.O.Barut http://streaming.ictp.trieste.it/preprints/P/87/157.pdf Check Out the new free AIM(R) Mail -- 2 GB of storage and industry-leading spam and email virus protection.
Re: Naive Realism and QM
Russell Standish wrote: On Wed, Aug 17, 2005 at 04:30:21PM -0700, Lee Corbin wrote: Your point about the squared modulus is well taken. Just why *probabilities* emerge from squared amplitudes, I couldn't tell you. I'm not sure that anyone knows---as I recall, many this is related to the basis problem of the MWI (though Deutsch and others say that decoherence takes care of everything, though). Lee This is simply the Born rule - I give a derivation of the Born rule in my paper Why Occam's Razor. Some other people on this list have asserted prior derivations of the Born rule also, which wouldn't overly surprise me as its not that mysterious. Cheers I've haven't read your derivation, but I've read quant-ph/0505059 by VAn Esch which is a proof that the Born Rule is independent of Everett's MWI and cannot be derived from it. How do you avoid Van Esch's counter example. Brent Meeker
Re: Naive Realism and QM
On Sun, Aug 21, 2005 at 06:12:54PM -0700, Brent Meeker wrote:
I've haven't read your derivation, but I've read quant-ph/0505059 by VAn
Esch which is a proof that the Born Rule is independent of Everett's MWI
and cannot be derived from it.
How do you avoid Van Esch's counter example.
Brent Meeker
I'm not sure its that relevant - I don't derive the Born rule from
Everett MWI per se, but rather from assumption that 1st person
experience should appear as the result of an evolutionary process. I
actually use Lewontin's criteria for evolution - I have an improved
explanation of this in appendix B of my draft book, although
technically it is identical to the FoPL paper.
Another way of viewing this topic is that the Multiverse (or MWI) is a
3rd person description, whereas the Born rule is a 1st person
property. So it is not surprising that the two are independent.
Looking at the paper, Esch proposes an alternative projection postulate
that weights all possible alternatives equally, ie it is equivalent to
the usual PP provided that the state vector is restricted to the set
of vectors \psi such that
\psi|P_i|\psi = 1/n_\psi or 0.
Let \psi' = \sum_i P_i\phi, for any vector \phi, and let
\psi=\psi'/\sqrt{\psi',\psi}, so this set if not empty.
This is a kind of all or nothing approach to \psi - \psi contains only
information about whether x_i is possible, or impossible, but doesn't
contain any shades of gray. It is saying, in other words, that White
Rabbit universes are just as likely as well ordered one - something
that contradicts the previous section on the white rabbit problem.
Instead, I assume that \psi does contain information about the
liklihood of each branch, and once you compute what this is, the usual
Born rule follows.
Cheers
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Re: Naive Realism and QM
Russell Standish wrote:
On Sun, Aug 21, 2005 at 06:12:54PM -0700, Brent Meeker wrote:
I've haven't read your derivation, but I've read quant-ph/0505059 by VAn
Esch which is a proof that the Born Rule is independent of Everett's MWI
and cannot be derived from it.
How do you avoid Van Esch's counter example.
Brent Meeker
I'm not sure its that relevant - I don't derive the Born rule from
Everett MWI per se, but rather from assumption that 1st person
experience should appear as the result of an evolutionary process. I
actually use Lewontin's criteria for evolution - I have an improved
explanation of this in appendix B of my draft book, although
technically it is identical to the FoPL paper.
Another way of viewing this topic is that the Multiverse (or MWI) is a
3rd person description, whereas the Born rule is a 1st person
property. So it is not surprising that the two are independent.
Looking at the paper, Esch proposes an alternative projection postulate
that weights all possible alternatives equally, ie it is equivalent to
the usual PP provided that the state vector is restricted to the set
of vectors \psi such that
\psi|P_i|\psi = 1/n_\psi or 0.
Let \psi' = \sum_i P_i\phi, for any vector \phi, and let
\psi=\psi'/\sqrt{\psi',\psi}, so this set if not empty.
This is a kind of all or nothing approach to \psi - \psi contains only
information about whether x_i is possible, or impossible, but doesn't
contain any shades of gray. It is saying, in other words, that White
Rabbit universes are just as likely as well ordered one - something
that contradicts the previous section on the white rabbit problem.
Instead, I assume that \psi does contain information about the
liklihood of each branch,
That would be one form of the additional postulate which Van Esch says is
necessary to derive the Born Rule - so there is no conflict with his result.
Brent Meeker
Re: Naive Realism and QM
Godfrey: There is no energy flux directly associated with wave-functions (like with electomagnetic or mechanical waves) but is a probability density and a probability flux associated with the square of linear functionals of the wave-function. The question, at this point, should be: probability of what? Because, leaving aside those who think (Weinberg, Dyson, etc.) that only fields exist and are real, there are at least a couple of solutions. There are physicists (followers of Bohr [1], more or less) who think [2][3][4] that quantum physics is about 'correlations without correlata', or about 'fotuitousness and clicks'. There are physicists (followers of Einstein, and his idea of Gespensterfeld, etc.) like Born [5], Fock [6], Barut [7], etc., who think that a 'probability' wave, even in 3n-dimensional space, is a real thing, much more than a mathematical tool, and who also think that physics is not just about apparata, or clicks. s. [1[ Niels Bohr: 'However, since the discovery of the quantum of action, we know that the classical ideal cannot be attained in the description of atomic phenomena. In particular, any attempt at an ordering in space-time leads to a break in the causal chain, since such an attempt is bound up with an essential exchange of momentum and energy between the individuals and the measuring rods and clocks used for observation; and just this exchange cannot be taken into account if the measuring instruments are to fulfil their purpose. Conversely, any conclusion, based in an unambiguous manner upon the strict conservation of energy and momentum, with regard to the dynamical behaviour of the individual units obviously necessitates a complete renunciation of following their course in space and time.' [2] Carlo Rovelli Relational Quantum Mechanics http://www.arxiv.org/abs/quant-ph/9609002 [3] David Mermin What is quantum mechanics trying to tell us? http://www.arxiv.org/abs/quant-ph/9801057 [4] Aage Bohr http://www.physicstoday.org/vol-57/iss-10/p15.html [5] Max Born: 'Quite generally, how could we rely on probability predictions if by this notion we do not refer to something real and objective?' [6] V.A.Fock 'Disskussija S Nilsom Borom', in 'Voprosy Filosofii', 1964 (a memorandum, about the interpretation of QM and the meaning of wavefunction, he gave to Bohr, in Copenhagen, 1957, who read it and changed his mind about several points, but not all). [7] A.O.Barut http://streaming.ictp.trieste.it/preprints/P/87/157.pdf
Re: Naive Realism and QM
Serafino, I think I get the gist of what you are saying but it is not quite the case. There is no energy flux directly associated with wave-functions (like with electomagnetic or mechanical waves) but is a probability density and a probability flux associated with the square of linear functionals of the wave-function. The physical quantities (observables) pertaining to any physical system described by the WF typically do not have fixed values assigned by the theory but only expectation values, i.e. probabilities of being found in one among many of their possible eigenvalues. Quantum Mechanics tells you how to compute these expectation values but only specific experiments assign one among them to a specific system. If I understand what you are trying to say below there is indeed a way of, a posteriori, trying to build a more or less classical picture of a propagation of a beam or even a single particle (represented by a wave packet or something like it). That is what is called a local hidden variable model for QM and it works fairly well for a single isolated degree of freedom. But, as it turns out, none of these clever cartoons can be used to fully interpret the quantum description; this is not merely the result of a theorem but something which has been verified empirically numerous times by now. Come to think of it, even my correction to Lee is in need of correction because QM is not just about amplitudes! The phase relations between wave functions play a very central role in the non local phenomena (i.e. Berry and Aharonov-Bohm effects) so the myth of just amplitudes should be dispelled by now. Best regards, Godfrey Kurtz (New Brunswick, NJ) -Original Message- From: scerir [EMAIL PROTECTED] To: everything-list@eskimo.com Sent: Thu, 18 Aug 2005 22:55:51 +0200 Subject: Re: Naive Realism and QM Godfrey: My point, if I can break it down a bit, is that the amplitudes correspond, not to things but to processes and that what the amplitudes let you compute are relative probabilities for the occurrences of such processes. Maybe. Amplitudes of (whatever) waves satisfy linear equations. So, amplitudes combine linearly when several paths are - in principle - possible. On the contrary, the intensity of waves, that is to say the energy flux, is quadratic in the field amplitudes. So, intensities do not combine linearly. If we imagine there is a relation between the energy flux and the number of particles crossing a given (unit) area (this can be the quantum principle, or the quantum postulate) we also imagine there is a relation between the energy flux - quadratic in the field amplitudes - and the probability for those particles crossing that (unit) area. We can also imagine now there is only one particle flying Regards, serafino Check Out the new free AIM(R) Mail -- 2 GB of storage and industry-leading spam and email virus protection.
Re: Naive Realism and QM
From: Lee Corbin [EMAIL PROTECTED] Godfrey writes As much as I sympathize with your call for preservation of naive realism [LC] Good heavens! How many times must it be said? What is going on with people? There is a *clear* definition of naive realism. Try the almost always extremely reliable wikipedia: http://en.wikipedia.org/wiki/Naive_realism If one is very clear that information about events outside the skin is conveyed to one's brain by layers of intermediate processes, (usually beginning with emissions of photons or by vibrations imparted to air), then you are *not* a naive realist. [GK] My, are prickly today!!! In this is when I was still sympathizing with you! (;-) [LC] Since this has come up so many times before---and not just on this list---I'm really starting to wonder what the explanation is. You can even find links on the web that confuse realism and naive realism. The acid test of what to call something is do the adherents of the view themselves use the term?. Then, in cases like this, we see it for what it is: name calling. [GK] Hold on! I don't believe I have even called you a naive realist! and agree entirely with your opinion on the demerits of introspection. I have to take issue with half of what you say below: [LC] Of course. Anyone who understands and believes in PCR always invites criticism, as least as much as he has time for. I'm not too sure what you mean by to embed. If we are seeking to *explain*---if that is what you mean---then we cannot explain QM by classical physics, but we *can* explain classical physics by QM. (I take our primary activity to be---and the activity I'm most interesting in participating in---*explaining*.) Yes we cannot explain QM by classical physics but NEITHER can we explain from QM the classical world we know and love with its well defined and assigned elements of (naive) physical reality that you so much cherish, I am afraid! If we did there would not be no Measurement Problem, no spooky long-distance correlations, no zombie Schrodinger Cat's around to haunt us... Quantum mechanics' greatest successes have included explanations for what you cite. That is why QM is accepted. [GK] My point is that it does NOT include explanations for any of the items I cite and that is why I cite them and that is why they are called problems. From Bruno's message I take it that you subscribe to the Everett Interpretation which indeed avoids some of these problems but has some more of its own and surely does a number on your naive reality! What is it then: many worlds or one? [LC] But you seem to be saying that the *correct* results of classical physics cannot be obtained from QM. Surely you don't mean that. Of course they can! If they could not, then they'd be wrong! True, classical physics *cannot* explain many phenomena, such as why black bodies radiate the way that they do, and this bothered 19th century physicist a great deal. Planck was *forced* to come up with the concept of the quantum, if he was to be able to explain. [GK] No, I am not saying that QM does not reproduce much of the classical results given the appropriate limits. Indeed it can and it, furthermore, predicts and explains a number of macroscopic (thus part of the world of direct experience) phenomena that Classical Physics does not. What I am saying above (and this is the clincher of the EPR argument as is that of the Everett interpretation) is that QM does not provide you with a picture of a reality where objects naively have their well defined properties associated with assignable elements of physical reality. You see, amplitudes don't just add! They also multiply and square! [LC] Why, of course. Just how innocent of QM do you suppose that I am? I invented the phrase at the basis of things are amplitudes that add after a thorough study of Feynman's volume 3. The multiplication obtains---at the very beginning ---simply from concatenating paths: you multiply amplitudes to get a total amplitude for one path. [GK] If that sentence is any measure of your guilt that you will be doing quantum time, Lee (:-) What you want to say is at the basis of QM there are amplitudes that add, multiply and square. Notice the absence of things! It is the things that ain't there!!! [LC] Your point about the squared modulus is well taken. Just why *probabilities* emerge from squared amplitudes, I couldn't tell you. I'm not sure that anyone knows---as I recall, many this is related to the basis problem of the MWI (though Deutsch and others say that decoherence takes care of everything, though). Lee [GK] Wouldn't that be nice! Unfortunately they are wrong about that. Decoherence is promising but still in need of major patching. Check out the paper by Bassi and Ghiraridi: http://arXiv.org/abs/quant-ph/9912031 There is some newer work on this by Adrian Kent but I don't have the reference handy. As to why the amplitudes square to give probabilities I agree with you
Re: Naive Realism and QM
Godfrey writes: [...] at the basis of QM there are amplitudes that add, multiply and square. Notice the absence of things! It is the things that ain't there!!! Not sure I understand. But the usual rule of addition of probabilities does not apply to quantum probabilities. This does not mean that the usual rule is wrong. It means (or it might mean) that quantum systems evolve via transitions through indeterminate states, which are different from occurrences of events. Regards, serafino
Re: Naive Realism and QM
Hi Serafino, I did not even mention probabilities and you are very right that they do not operate under the same algebraic rules as classical probabilities. My point, if I can break it down a bit, is that the amplitudes correspond, not to things but to processes and that what the amplitudes let you compute are relative probabilities for the occurrences of such processes. QM by itself does not describe the world in terms of things i.e. distinct separable objects such as the ones we see and manipulate with in our everyday. Godfrey Kurtz (New Brunswick, NJ) -Original Message- From: scerir [EMAIL PROTECTED] To: everything-list@eskimo.com Sent: Thu, 18 Aug 2005 22:15:14 +0200 Subject: Re: Naive Realism and QM Godfrey writes: [...] at the basis of QM there are amplitudes that add, multiply and square. Notice the absence of things! It is the things that ain't there!!! Not sure I understand. But the usual rule of addition of probabilities does not apply to quantum probabilities. This does not mean that the usual rule is wrong. It means (or it might mean) that quantum systems evolve via transitions through indeterminate states, which are different from occurrences of events. Regards, serafino Check Out the new free AIM(R) Mail -- 2 GB of storage and industry-leading spam and email virus protection.
Re: Naive Realism and QM
Godfrey: My point, if I can break it down a bit, is that the amplitudes correspond, not to things but to processes and that what the amplitudes let you compute are relative probabilities for the occurrences of such processes. Maybe. Amplitudes of (whatever) waves satisfy linear equations. So, amplitudes combine linearly when several paths are - in principle - possible. On the contrary, the intensity of waves, that is to say the energy flux, is quadratic in the field amplitudes. So, intensities do not combine linearly. If we imagine there is a relation between the energy flux and the number of particles crossing a given (unit) area (this can be the quantum principle, or the quantum postulate) we also imagine there is a relation between the energy flux - quadratic in the field amplitudes - and the probability for those particles crossing that (unit) area. We can also imagine now there is only one particle flying Regards, serafino
Naive Realism and QM
Godfrey writes As much as I sympathise with your call for preservation of naive realism Good heavens! How many times must it be said? What is going on with people? There is a *clear* definition of naive realism. Try the almost always extremely reliable wikipedia: http://en.wikipedia.org/wiki/Naive_realism If one is very clear that information about events outside the skin is conveyed to one's brain by layers of intermediate processes, (usually beginning with emissions of photons or by vibrations imparted to air), then you are *not* a naive realist. Since this has come up so many times before---and not just on this list---I'm really starting to wonder what the explanation is. You can even find links on the web that confuse realism and naive realism. The acid test of what to call something is do the adherents of the view themselves use the term?. Then, in cases like this, we see it for what it is: name calling. and agree entirely with your opinion on the demerits of introspection. I have to take issue with half of what you say below: Of course. Anyone who understands and believes in PCR always invites criticism, as least as much as he has time for. I'm not too sure what you mean by to embed. If we are seeking to *explain*---if that is what you mean---then we cannot explain QM by classical physics, but we *can* explain classical physics by QM. (I take our primary activity to be---and the activity I'm most interesting in participating in---*explaining*.) Yes we cannot explain QM by classical physics but NEITHER can we explain from QM the classical world we know and love with its well defined and assigned elements of (naive) physical reality that you so much cherish, I am afraid! If we did there would not be no Measurement Problem, no spooky long-distance correlations, no zombie Schrodinger Cat's around to haunt us... Quantum mechanics' greatest successes have included explanations for what you cite. That is why QM is accepted. But you seem to be saying that the *correct* results of classical physics cannot be obtained from QM. Surely you don't mean that. Of course they can! If they could not, then they'd be wrong! True, classical physics *cannot* explain many phenomena, such as why black bodies radiate the way that they do, and this bothered 19th century physicist a great deal. Planck was *forced* to come up with the concept of the quantum, if he was to be able to explain. You see, amplitudes don't just add! They also multiply and square! Why, of course. Just how innocent of QM do you suppose that I am? I invented the phrase at the basis of things are amplitudes that add after a thorough study of Feynman's volume 3. The multiplication obtains---at the very beginning ---simply from concatenating paths: you multiply amplitudes to get a total amplitude for one path. Your point about the squared modulus is well taken. Just why *probabilities* emerge from squared amplitudes, I couldn't tell you. I'm not sure that anyone knows---as I recall, many this is related to the basis problem of the MWI (though Deutsch and others say that decoherence takes care of everything, though). Lee
Re: Naive Realism and QM
On Wed, Aug 17, 2005 at 04:30:21PM -0700, Lee Corbin wrote: Your point about the squared modulus is well taken. Just why *probabilities* emerge from squared amplitudes, I couldn't tell you. I'm not sure that anyone knows---as I recall, many this is related to the basis problem of the MWI (though Deutsch and others say that decoherence takes care of everything, though). Lee This is simply the Born rule - I give a derivation of the Born rule in my paper Why Occam's Razor. Some other people on this list have asserted prior derivations of the Born rule also, which wouldn't overly surprise me as its not that mysterious. Cheers -- *PS: A number of people ask me about the attachment to my email, which is of type application/pgp-signature. Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. A/Prof Russell Standish Phone 8308 3119 (mobile) Mathematics0425 253119 () UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 pgpF7VOTnN4h7.pgp Description: PGP signature
RE: Naive Realism and QM
Russel writes why *probabilities* emerge from squared amplitudes, I couldn't tell you. I'm not sure that anyone knows---as I recall, many this is related to the basis problem of the MWI (though Deutsch and others say that decoherence takes care of everything, though). This is simply the Born rule - I give a derivation of the Born rule in my paper Why Occam's Razor. Some other people on this list have asserted prior derivations of the Born rule also, which wouldn't overly surprise me as its not that mysterious. Is it in the part of http://parallel.hpc.unsw.edu.au/rks/docs/occam/occam.html that begins QUANTUM MECHANICS In the previous sections, I demonstrate that formal mathematical systems are the most compressible, and have highest measure amongst all members of the Schmidhuber ensemble. or if not, just where? Lee
