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Natural Science Forum / Physics / Research / March 2008QM Measurement Problem
More of a mad idea. Some while ago I posted the suggestion that uncertainty in QM might be conserved in some way. The basis for this suggestion was this idea. Suppose we have a system in which a particle is described by some wavefunction. Before a measurement is made there is a level of uncertainty as to its position. What happens a measurement is made? Let us say that the result of that measurement is indicated on an analogue meter. If the original uncertainty were to remain that would result in an uncertainty in the position of the meter needle. In other words a small uncertainty (of the microscopic particle) would be changed into a large one (of the meter needle). So what actually happens is that uncertainty is conserved and a measurement is made. What I am trying to say is that a measurement could be considered as anything which would turn a small uncertainty (however that is quantified) into a larger one. I realise that the situation is more complicated than this in that uncertainty need to be applied to pairs of conjugate variables, but I have picked just one variable to try to illustrate the point. This approach has the great advantage of removing issues about who or what has ability to make the measurement (computer, human, cat). Any thing that would turn the quantum uncertainty into a larger one is a measurement. Does anyone see any value in this approach? How close is it to quantum decoherence? If uncertainty (in some form) is conserved, what kind if symmetry would this imply? -- Martin Hogbin Hello Martin: Unfortunately I see no value in what you wrote. The reason is that the uncertainty principle is about the relationship between two qualitatively different types of measurements. You referred only to position. The conjugate measurement for position is momentum. Position can be measured to an arbitrary degree of precision: spend more money, get a better measure. There is no limit to how precise one can be. Use an electron microscope to watch the needle move. The same can be said for measuring momentum. We can know how much punch a punch has to arbitrary precision. One of the big costs at any atom smasher is measuring the energy and momentum of particles produced. What we cannot know is both the position and the momentum in the same direction. Position in x and momentum in y are not conjugate variables, so they can be measured together to arbitrary precision. This _pair_ of measurements is governed by the uncertainty principle. Although position and momentum are must often used in the popular literature, there are all kinds of other neat pairs of conjugate variables. I bet there is a theorem out there that all measurements have a conjugate. Anyone recall the conjugate for number of photons? It is the light intensity? Doug > Hello Martin: > [quoted text clipped - 21 lines] > have a conjugate. Anyone recall the conjugate for number of photons? > It is the light intensity? Yes, I know about conjugate variables, that is why I mentioned the term, but I cannot see how to deal with this fact so I just ignored it for the moment. I am trying to find an objective definition of 'measurement', one that need not involve physicists, other humans, or cats. I want to be able say that this or that experimental setup constitutes a 'measurement' regardless of whether anybody looks at the results. It seems to me that the basic function of a measurement is to turn a small uncertainty into a large one. The questions I wonder are: How can we quantify the uncertainty? To what system does it apply? As an aside, if Schrodinger's cat is replaced by a physicists, who I guess we must deem able to make a measurement, then the situation gets even more weird. Presumably the physicist knows that he is alive (if that is the case) and the measurement is thus made. If on the other hand he is dead then he cannot make the measurement to that effect and he therefore must remain half-dead/ half-alive, except that we have just said that he is dead. Weird! -- Martin Hogbin Hello Martin: You are not at liberty to ignore the issue of complementarity as it is central to understanding the uncertainty princple. The physics of the uncertainty principle applies to physical systems. A vanishingly small number of these observations are observed by physicists. Whether we look at the position and momentum or not is not relevant - the uncertainty principle governs the relationship between all conjugate variables. The uncertainty principle arises from the properties of complex numbers, which unlike the real numbers, is not a totally ordered set. I was lucky enough to attend a quantum mechanics class where the professor showed that the equation of the uncertainty principle can be derived from properties of complex numbers. The lecture made quite an impression on me. I recreated his talk, but applied it to quaternions which are 3 complex numbers that share the same real, here: http://www.theworld.com/~sweetser/quaternions/quantum/uncertainty/uncertainty.html The notes should make clear: the product of the variation of the measurements of two conjugate variables being greater than their commutator has nothing to do with amplifying a small uncertainty into a large one. I do encourage people to take guesses at new interpretations, and hope they accept that the odds those ideas are correct are vanishingly small. > How can we quantify the uncertainty? > To what system does it apply? Look up the equation and apply to all conjugate variables. As an aside, I avoid all discussions of the cat and work with the details of the equations. The web page referenced above has an impolite number of equations, but that is the way real physics is versus pop physics. The equations are concise, but the word stories are muddled. Doug > Hello Martin: > [quoted text clipped - 6 lines] > not relevant - the uncertainty principle governs the relationship > between all conjugate variables. Yes, I know. > The uncertainty principle arises from the properties of complex > numbers, which unlike the real numbers, is not a totally ordered set. [quoted text clipped - 5 lines] > > http://www.theworld.com/~sweetser/quaternions/quantum/uncertainty/uncertainty.html An interesting page, but it is about the formalism of QM and the application of quaternions it does not address the 'measurement problem'. > The notes should make clear: the product of the variation of the > measurements of two conjugate variables being greater than their > commutator has nothing to do with amplifying a small uncertainty into > a large one. I think you are misunderstanding my suggestion. The large uncertainty that I am referring to is that that the position (and momentum) of the indicating needle would have in my thought experiment, if the position (and momentum) of the measured particle remained uncertain. > I do encourage people to take guesses at new > interpretations, and hope they accept that the odds those ideas are > correct are vanishingly small. Yes, I realise that my chances of coming up with anything new and useful are small but I like to keep trying. -- Martin Hogbin "Martin Hogbin" <goatREMOVETHIS123@hogbin.org> wrote .. >> The uncertainty principle arises from the properties of complex >> numbers, which unlike the real numbers, is not a totally ordered set. What about the possiblity to attribute the idea of having two totally ordered sets at a time on a simple real-valued pair of conjugate exclusively positive quantities x and y=1/x ? Let be F(x) the cosine transform of f(y). > I am trying to find an objective definition of 'measurement', one that > need not involve physicists, other humans, or cats. I want to be able [quoted text clipped - 13 lines] > to that effect and he therefore must remain half-dead/ half-alive, > except that we have just said that he is dead. Weird! But the weirdness comes precisely from your insistence that there must be an "objective" definition of measurement, or, put another way, that state vector resolution is a physical process that occurs at a particular point in spacetime! [The necessity of placing it at a particular point in spacetime, in fact, seems to be another problem with the concept of physical state vector resolution that I haven't seen mentioned before. Since quantum systems are often extended in spacetime, the process of state vector resolution, however we understand it, must be extended also. And this seems to fit very poorly with any simplistic approach to the issue.] Personally I think that Schrodinger's Cat leads naturally to the concept of decoherence. It can perhaps be seen better with another gedanken which I will call the Simplified Schrodinger's Cat. In the Simplified Schrodinger's Cat Experiment, we simply put a cat in a box, close the lid for a period, and open it again. There are a large variety of things we might now observe; the cat may be asleep or awake, it may have scratched or otherwise left its mark in one or more places inside the box. And it's obvious that no meaningful quantum superpositions can be observed between any two distinct states of this kind. The cat has apparently been generating entropy via interactions with itself and anything else on the inside of the box - or at least the portion of the wave function of the universe covering the region of spacetime where the box was closed has evolved in such a way as to produce an equivalent result. Wherever we choose to define measurement - inside the box, or when it is opened - it makes no difference to the physics. And thus, it would appear, state vector resolution is not physical, unless it operates according to some criterion we do not currently recognise. - Gerry Quinn Hello Gerry: I found your "Simplified Schrodinger's Cat Experiment" amusing to think about :-) It opened up a question: why is the system not really like quantum mechanics? My reply is that cats have all kinds of unique identifiable parts. With a group of electrons or a vast pool of photons, one cannot pick out one in particular, and say, the electron left of Ginger is Gilligan. No amount of money can label two electrons. We can tell if they happen to be in different states, but the electrons could swap positions while we were not looking, and we would not be able to tell. In my SSCE, there would be 1000 boxes, each with 1000 Siamese cat clones. In about 500 boxes, the cat has died, in the other 500, the cat clone is alive. Take a picture of all cats in all boxes with your 12.5 mega pixel Nikon D300, import into the Gimp, overlay all the images and average. One thing you notice immediately: the cat looks like a gas! Superimposing this many images makes what was once so solid look very flimsy indeed. I did this for animations of a simple harmonic oscillator which was quite cool (URL at end). You could tell from the ghostly image that many of the states of the cloned cat in a box have a dead cat in it. Now you do the experiment of picking one of these 1000 boxes, which is an act of observation, not of action. You open a box - you cannot number it and say it is box 27 because the boxes are all indistinguishable - and see a dead cat. Repeat 50 times, and about half the time the cat is dead, half the time alive. The observation is NOT killing the cat. The superpositon does look half alive/half dead because that is exactly what goes into the Gimp from the D300. Doug Simple Harmonic Oscillators: Visualizing Classic and Quantum http://www.youtube.com/watch?v=efYhDxm1m-g >...- you cannot > number it and say it is box 27 because the boxes are all > indistinguishable - and see a dead cat. In mathematical terminology we used to say: The reals are uncountable. The perhaps first one who clearly expressed that the relations >, =, and < do not fit infinite quantities was Salviati alias Galileo Galilei when commenting on bijection. In article <b4626a34-2d76-4127-b325- 6aa060aa578e@n75g2000hsh.googlegroups.com>, dougsweetser@gmail.com says... > Hello Gerry: > [quoted text clipped - 7 lines] > the electrons could swap positions while we were not looking, and we > would not be able to tell. Well - even leaving the Pauli Exclusion Principle out of it - that's not really the difference. You could say the same of atoms. Yet a solid structure built out of identical atoms behaves classically, and even individual atoms in such a structure can behave in some ways classically. Suppose you took a flat facet of an iron crystal and used a scanning tuneling microscope to place iron atoms on it so they spelt your name. Those iron atoms will be persistent; they can be imaged repeatedly; they don't do anything crazy at all. They behave classically, at least insofar as their position is concerned. The difference, of course, is that the atoms aren't in a 'cloud'; they are in a solid, and their interaction with their environment is such as to lead to rapid decoherence. They are entangled with each other in such a fashion that the probability of observing a superposition state is infinitesimal. This also, obviously, applies to a cat. And cats also generate entropy, which can be considered a measure of the number of measurements carried out and recorded by the system. So while you might, if you handled the system very carefully, be able to observe some quantum superposition properties of the iron atoms, you have no chance with the cat. > In my SSCE, there would be 1000 boxes, each with 1000 Siamese cat > clones. In about 500 boxes, the cat has died, in the other 500, the [quoted text clipped - 6 lines] > from the ghostly image that many of the states of the cloned cat in a > box have a dead cat in it. I assume you are not actually taking a picture of each cat, which would correspond to an observation, negating the point of the experiment. So your picture corresponds to an ensemble of expected classical results. I don't see where quantum statistics come into it. > Now you do the experiment of picking one of these 1000 boxes, which is > an act of observation, not of action. You open a box - you cannot [quoted text clipped - 3 lines] > is NOT killing the cat. The superpositon does look half alive/half > dead because that is exactly what goes into the Gimp from the D300. I feel you are missing the point here. Your combined image isn't a picture of a quantum superposition state; it is a picture of 1000 classical states, classically superimposed on each other (with additive probability). (And you also can't make the boxes indistinguishable, for reasons similar to those already discussed.) - Gerry Quinn Hello Gerry: > Well - even leaving the Pauli Exclusion Principle out of it The Pauli Exclusion Principle is about states that indistinguishable particles with half integrable spin can occupy. I was addressing the indistinguishable part, not the behavior of half integral spin particles. It is safe to leave Pauli for another discussion. > You could say the same of atoms. I would to be logically consistent. Much about atoms can be described by quantum mechanics, much can be described by classical physics. Nature keeps multiple accounting books open on the same objects. > Yet a solid structure built out of identical atoms behaves classically, and even > individual atoms in such a structure can behave in some ways [quoted text clipped - 3 lines] > repeatedly; they don't do anything crazy at all. They behave > classically, at least insofar as their position is concerned. I don't see the point. It looks like you are alluding to the uncertainty principle, which is not about measuring the certainty of position. Rather the uncertainty is about measuring the position of two conjugate measurements, say position and momentum, and recognizing a constraint on the variation of both measurements. That would apply to this iron crystal. If this is a well ordered crystal, you probably could collect data on the photo electric effect. The same collection of atoms knows how to do both classical and quantum mechanics. > The difference, of course, is that the atoms aren't in a 'cloud'; they > are in a solid, and their interaction with their environment is such as > to lead to rapid decoherence. They are entangled with each other in > such a fashion that the probability of observing a superposition state > is infinitesimal. If I read a little into this (in other words, you did not say this directly, so I apologize in advance if needed), it sounds like the 'cloud' does not have information. In quantum mechanics, the probability distribution represented by the wave function is the best and most complete information one can have about a system. It is the sum of all possible paths. The superposition cannot be seen because it is a composition of data that can be measured. > This also, obviously, applies to a cat. And cats also generate entropy, > which can be considered a measure of the number of measurements carried > out and recorded by the system. So while you might, if you handled the > system very carefully, be able to observe some quantum superposition > properties of the iron atoms, you have no chance with the cat. Entropy is not relevant to this discussion. I created the superposition of a live and dead cat here: http://picasaweb.google.com/dougsweetser/Superposition/photo#5168676570581305906 > I assume you are not actually taking a picture of each cat, which would > correspond to an observation, negating the point of the experiment. No, that is incorrect. We have a system that produces about 50% dead Siamese cats clones every time we have investigated. One time, we make all these observations, collect all the data, and from that data, construct the superposition. We have a system that can repeatably generate indistinguishable collections of dead cats. It appears like you are using the phrase "classical result" for what might also be referred to as the collapse of the wave function. I don't like either term, both sounding to active. > So your picture corresponds to an ensemble of expected classical results. > I don't see where quantum statistics come into it. I am only trying to get at superposition, not even and odd spin statistics. > I feel you are missing the point here. Your combined image isn't a > picture of a quantum superposition state; it is a picture of 1000 [quoted text clipped - 3 lines] > (And you also can't make the boxes indistinguishable, for reasons > similar to those already discussed.) I don't recall in classical physics where folks deal with the information of superpositions of states. That sounds far more like quantum mechanics than classical mechanics, where one has the video of the cat, either live or dead, but certainly not both. In my superposition photo, the cat is unambiguously live and dead, an idea that is suppose to be too odd to understand. I get it. I also understand why you don't accept that I get it, so we can politely disagree. Doug In article <27ad8097-7a65-4dea-be09-866700d5b6b0@ 41g2000hsc.googlegroups.com>, dougsweetser@gmail.com says... > Hello Gerry: > > Yet a solid structure built out of identical atoms behaves classically, and even > > individual atoms in such a structure can behave in some ways [quoted text clipped - 12 lines] > could collect data on the photo electric effect. The same collection > of atoms knows how to do both classical and quantum mechanics. I was responding to your proposal that cats were special because they were made up of non-identical parts which could swap position if we were not looking. As pointed out above, collections of identical parts can behave classically too, so long as the parts are sufficiently entangled with each other or the environment in general. And yes - the uncertainty principle does apply to the crystal. But the interesting thing is that it does not apply, at least naively, to the individual atoms. A particular atom, say the one creating the top serif of the 'D', can consistently be observed to be in the same place, and it is not moving anywhere. There is a real sense in which its position is known exactly, and its momentum is zero. It is living in the classical world, precisely because of its entanglement with the other atoms. > > The difference, of course, is that the atoms aren't in a 'cloud'; they > > are in a solid, and their interaction with their environment is such as [quoted text clipped - 8 lines] > sum of all possible paths. The superposition cannot be seen because > it is a composition of data that can be measured. I didn't say anything like that. I do not know how to phrase what I did say better. The atoms in the solid are strongly entangled with others in their environment - the electrons in your vaguely-described 'cloud', presumably, are not. > > This also, obviously, applies to a cat. And cats also generate entropy, > > which can be considered a measure of the number of measurements carried [quoted text clipped - 3 lines] > > Entropy is not relevant to this discussion. It is, IMO. It is another special feature of cats which brings them further away from the quantum world. > I created the > superposition of a live and dead cat here: > > http://picasaweb.google.com/dougsweetser/Superposition/photo#5168676570581305906 That's not what a quantum superposition state of Schrodinger's cat would look like. That is two possible classical states superimposed. (Two very distinct states, in fact, selected from a myriad possibilities.) You could semi-plausibly have a superposition state that looked like a cat that you could not tell was alive or dead. It would instantly collapse into one or the other, or more likely into a very sick cat. You can make a case that a picture of all classical possibilities superimposed describes the wave function of the cat at a particular time. But this wave function has *already* in the process of its own evolution decohered into an ensemble of non-interfering, effectively classical states. Opening the box just continues this process. > > I assume you are not actually taking a picture of each cat, which would > > correspond to an observation, negating the point of the experiment. [quoted text clipped - 4 lines] > construct the superposition. We have a system that can repeatably > generate indistinguishable collections of dead cats. So you are taking the classical results observed after opening each box, and superimposing them. Just what I said. No picture of an observed superposition state. No indication of interference between dead and alive states. > It appears like you are using the phrase "classical result" for what > might also be referred to as the collapse of the wave function. I > don't like either term, both sounding to active. Classical result = what you get when you open the box and see a dead cat or a live cat. Nothing more. > > So your picture corresponds to an ensemble of expected classical results. > > I don't see where quantum statistics come into it. > > I am only trying to get at superposition, not even and odd spin > statistics. So am I. I am not talking about spin statistics. The point is that quantum superposition states imply interference between the different possible results. Superimposing a lot of non-interfering classical states does not give such a state. > > I feel you are missing the point here. Your combined image isn't a > > picture of a quantum superposition state; it is a picture of 1000 [quoted text clipped - 3 lines] > > (And you also can't make the boxes indistinguishable, for reasons > > similar to those already discussed.) > I don't recall in classical physics where folks deal with the > information of superpositions of states. But everyone who deals with probability produces diagrams similar in a sense to your superimposed diagrams. If you want to analyse a dice game, for example, you start by (notionally) drawing a picture of all the different ways the dice might land. There's nothing non-classical here. Classical thermodynamics involves similar scenarios. > That sounds far more like > quantum mechanics than classical mechanics, where one has the video of [quoted text clipped - 3 lines] > understand why you don't accept that I get it, so we can politely > disagree. "Unambiguously live and dead"? What do you mean by that? You could say that both live and dead cats exist in Everett's 'multiverse', and that your diagram is a picture of the multiverse, I suppose. What it is not is a superposition state in the sense of the word that is normally used. - Gerry Quinn > have a conjugate. Anyone recall the conjugate for number of photons? > It is the light intensity? > > Doug The conjugate to photon number is phase. This brings up a whole bunch of problems associated with the fact that the phase is only defined modulo 2pi so the maximum uncertainty is 2pi. Another one is what the eigenstates are that satisfy the minimum uncertainty condition.  SignatureKeith Blow > The conjugate to photon number is phase. This brings up a whole bunch of > problems associated with the fact that the phase is only defined modulo > 2pi so the maximum uncertainty is 2pi. Another one is what the > eigenstates are that satisfy the minimum uncertainty condition. Phase properties of the quantized single-mode electromagnetic field D. T. Pegg, S. M. Barnett Phys. Rev. A 39, 1665 - 1675 (1989) http://prola.aps.org/abstract/PRA/v39/i4/p1665_1 On the Hermitian optical phase operator S. M. Barnett; D. T. Pegg J. Mod. Opt. 36, 7 (1989) http://www.informaworld.com/smpp/content~content=a713822510 Signature---------------------------------+--------------------------------- Dr. Paul Kinsler Blackett Laboratory (QOLS) (ph) +44-20-759-47520 (fax) 47714 Imperial College London, Dr.Paul.Kinsler@physics.org SW7 2BW, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/ Hello Salviati: I like this quote: > The reals are uncountable. That had deep implications for our description of Nature. What those implications are can be confusing. > What about the possibility to attribute the idea of having two totally > ordered sets at a time on a simple real-valued pair of conjugate exclusively > positive quantities x and y=1/x ? Let be F(x) the cosine transform of f(y). This issue is that you are making up the rule for doing the ordering. If someone else wanted to define F(x) as the sine transform of f(y), the ordering would be different. A simpler approach would be to order by the real value of x, and if there was a tie, order by the imaginary y. An equally valid approach would involve switching the role of x with y. One way to view this from a math perspective is that quantum mechanics uses the norm, z* z, which has a least lower bound of zero. For me, I look at that least lower bound as the vacuum - there can be nothing less than nothing. Take two numbers, z and z', and the product z* z' does not have a least lower bound, but (z* z')* z* z' does. There is nothing difficult about this math, but I appreciate it is a stretch to see a connection to quantum mechanics, since quantum mechanics is about the physical world, and this is a math observation. Doug > Hello Salviati: > [quoted text clipped - 4 lines] > That had deep implications for our description of Nature. What those > implications are can be confusing. Mathematicians would 'correct' me: The set of reals is uncountable. I am arguing: Each single irrational number can be thought to be indefinitely long. And I add: Uncertainty of a pair of conjugate variables originates there. Any analog measurement is uncertain in so far, one can increase acuity at will but one will never reach an absolutely exact value. I consider you correct: Uncertainty relation just makes this obvious. The mistake is as old as are Zeno's turtle and Buridan's donkey. >> What about the possibility to attribute the idea of having two totally >> ordered sets at a time on a simple real-valued pair of conjugate [quoted text clipped - 3 lines] > > This issue is that you are making up the rule for doing the ordering. G. Cantor has shown: There are not two joint but independent dimensions of totally ordered infinite sets. If x is known then y is also known. I disagree with Dedekind and Cantor: We cannot even make up mathematics at will if we expect reasonable results. Ordering of a physical quantity can be arbitrary like the Celsius scale or natural. Elapsed time and radius have an absolute zero. > If someone else wanted to define F(x) as the sine transform of f(y), > the ordering would be different. Of course, this is true if we consider x a relative quantity. >A simpler approach would be to order > by the real value of x, and if there was a tie, order by the imaginary > y. An equally valid approach would involve switching the role of x > with y. Even if we perform complex Fourier transform, only the functions of x and y are not real. Switching the role of x with y was exactly what Heisenberg, Schroedinger, and Dirac did. > One way to view this from a math perspective is that quantum mechanics > uses the norm, z* z, Multiplication by the complex conjugate intended getting rid of 'unphysical' imaginary components. Nobody realized that one-sidedness got lost. Just Weyl worried, and v. Neumann gave up Hilbert space. Hello Salviati: > Mathematicians would 'correct' me: The set of reals is uncountable. I am > arguing: Each single irrational number can be thought to be indefinitely > long. And I add: Uncertainty of a pair of conjugate variables originates > there. The math sounds right, the application to physics does not. The reason is that any single measurement has this property, even measurements made for classical systems. The proof of the uncertainty principle I saw has to do with the properties of complex numbers, not the properties of the reals to which you referred. I recall reading in a book by Stephen Adler that the quantum numbers done over the field of real numbers would be quite dull, no quantum interference. Doug [Mod. note: Please keep replies on topic, i.e. relevant to physics. -ik ] > Hello Salviati: > [quoted text clipped - 4 lines] > That had deep implications for our description of Nature. What those > implications are can be confusing. But our measurements are rationals. The rationals are countable. This too has deep implications for our description of Nature. The reals are formed by some sort of completion of the rationals (Cauchy sequences or Dedekind cuts; I don't care). The idea that such completion is possible assumes we can have arbitrarily small intervals of rational numbers. If we're talking about Nature, this would involve arbitrarily precise measurements, which we know do not exist. The closest we get to real numbers is limits of averages of ever- increasing numbers of measurements. But we can't make infinite numbers of measurements ... -- hendrik > [Mod. note: Please keep replies on topic, i.e. relevant to physics. -ik ] > > Hello Salviati: [quoted text clipped - 15 lines] > increasing numbers of measurements. But we can't make infinite numbers > of measurements ... I don't see that our measurements are necessarily rationals. If we observe that something has rotated exactly once, we can also say it has rotated through 2*pi radians, an irrational number. If we measure a value by determining its square, the quantity itself will be a square root, which is typically irrational. What is correct, I think, is the second point - we cannot make infinite numbers of measurements. That means that our description of any physical quantity - whether it uses rationals, irrationals, or any other sort of number - must be finite. 2*pi is written as an infinitely long non-recurring decimal, but it can be expressed quite briefly in various ways. Does that mean that the quantities *themselves* (as distinct from our descriptions) must be finitely describable? That brings us back on topic... one possible answer, it seems to me, is that classical objects, i.e. objects entangled with an effectively infinite environment, may have a state that cannot be finitely described. - Gerry Quinn >> [Mod. note: Please keep replies on topic, i.e. relevant to physics. -ik ] >> > Hello Salviati: [quoted text clipped - 34 lines] > i.e. objects entangled with an effectively infinite environment, may > have a state that cannot be finitely described. Our measurements are finitely describable. Whether the actual quantities are finitely describable is not something we can determine experimentally. Such infinitude could of course be a nonobservable part of a theory. -- hendrik > - Gerry Quinn Doug Sweetser did not yet get an answer to his question > Anyone recall the conjugate for number of photons? > It is the light intensity? Let me look at the issue by comparison with time and frequency. Both are usually considered continuous quantities. Nonetheless, there are pretty discrete nearly hyperbolic lines linking the pair, cf. http://home.arcor.de/eckard.blumschein.M283.html I will add some new results perhaps as M284 next week. We used to be sure that photons are countable: NoN, one, two, three,... nothing in between. Likewise we could count frequencies. Hello Gerry: You wrote: > A particular atom, say the one creating the top serif > of the 'D', can consistently be observed to be in the same place, and it > is not moving anywhere. There is a real sense in which its position is > known exactly, and its momentum is zero. It is living in the classical > world, precisely because of its entanglement with the other atoms. One certainly can do a series of experiments where the atoms are proven by observation to be sitting right on top of the 'D'. One could do another series of experiments to show that the momentum is zero. One cannot do a single experiment to show that in a measurable sense, "its position is known exactly, and its momentum is zero" without violating the uncertainty principle, the variation of the measurement of the position x times the variation in the measurement of the momentum px must be greater than the super tiny hbar. This was an instructive comment: > The atoms in the solid are strongly entangled with others > in their environment - the electrons in your vaguely-described 'cloud', > presumably, are not. The cloud is both very precise and reproducible. There are many systems that with their superposition of states have a location where there is zero probability to find the atom. An experiment can be set up to measure the probability distribution of the system over space, and we find that there are places with zero probability. We label this quantum interference. Unfortunately, we bring with us the notion of classical interference, where one thing gets together with another thing destructively. That is not the way quantum systems work - everything is independent. > You could semi-plausibly have a superposition state that looked like a > cat that you could not tell was alive or dead. It would instantly > collapse into one or the other, or more likely into a very sick cat. .. > So you are taking the classical results observed after opening each box, > and superimposing them. Just what I said. No picture of an observed > superposition state. No indication of interference between dead and > alive states. This indicates we are not communicating so well on these issues, which is not uncommon. There is no need for a sick cat state. Nor is there a need to show interference between the dead and alive states. As soon as I discuss making a measurement of anything, you slap the label "classical result", a behavior I find mystifying. The CCD camera at the end of a two slit interference experiment would appear to fit this notion of classical result since the signals are either on or off. So here is your definition: > Classical result = what you get when you open the box and see a dead cat > or a live cat. Nothing more. Unfortunately, I don't get what you mean. For me, what classical physics is about is our ability to watch a system, say a live cat, evolve in time. We can watch a cat go from alive to sick to dead over a period of observation. The SSCE I described ("Simplified Schrodinger's Cat Experiment"), there is no observation you can ever do with the cat transitioning in time from live to dead. One gets one or the other. The best we can do to summarize the results is a picture like I provided. Neat, I see a connection to quantum interference. Earlier I had said there is no "sick cat" state. That is a state the classical physicist would expect to see, part of the transition in time from live to dead. In the precise, repeatable system I set up with a thousand cat clones, not a single one was sick. It is the omission of expected states that many find troubling about quantum mechanics. > "Unambiguously live and dead"? What do you mean by that? The cats in the system are never sick. It is also vital to emphasize I am talking about _many_ cats, not a single cat. Issues in quantum theory cannot be understood by reflecting on a solitary cat. One needs a great many of them, all identical. This is not a multiverse. It is a system constructed out of lots of cats, half of them standing, prancing, and playing, the other half stone cold dead. I wish to collect all my data together of what I can expect to find, and that is the superposition of live and dead cats, never sick, unambiguously live and dead. Doug In article <c15007a2-346c-4b96-a0ed- 5678332bb59d@p73g2000hsd.googlegroups.com>, dougsweetser@gmail.com says... > Hello Gerry: > You wrote: [quoted text clipped - 13 lines] > measurement of the position x times the variation in the measurement > of the momentum px must be greater than the super tiny hbar. Indeed. But why would you need to do any measurements when you know exactly where it is at all times? For many purposes, the uncertainty principle is irrelevant when it comes to this atom. As I was saying, for these purposes it's living in the classical world. > This was an instructive comment: > [quoted text clipped - 11 lines] > thing destructively. That is not the way quantum systems work - > everything is independent. I'm not sure what you are getting at here. Our usual model of quantum interference is based on the same equations as the interference of idealised classical waves. (The interactions of classical waves such as ripples in water are never completely linear, of course.) In this model the positions where the probability of finding an atom is zero are those where the wave functions associated with possible states/transitions of the system interfere destructively. > > You could semi-plausibly have a superposition state that looked like a > > cat that you could not tell was alive or dead. It would instantly [quoted text clipped - 12 lines] > the end of a two slit interference experiment would appear to fit this > notion of classical result since the signals are either on or off. Yes - the photograph of an interference pattern in a two-slit experiment is entirely classical. But the picture shows an interference pattern - something that is not present in your picture of Schrodinger's cat. The latter picture could be drawn by somebody who has never heard of quantum mechanics. > So here is your definition: > [quoted text clipped - 5 lines] > evolve in time. We can watch a cat go from alive to sick to dead over > a period of observation. But the period required for decoherence in a cat is so short that the smallest instant you could watch it for is more than long enough! > The SSCE I described ("Simplified Schrodinger's Cat Experiment"), Hey, that was my phrase, describing a different experiment :-) > there is no observation you can ever do with the cat transitioning in > time from live to dead. One gets one or the other. The best we can > do to summarize the results is a picture like I provided. Which means that there is no quantum mechanics to see in the summary of the results. > Neat, I see a connection to quantum interference. Earlier I had said > there is no "sick cat" state. That is a state the classical physicist > would expect to see, part of the transition in time from live to > dead. In the precise, repeatable system I set up with a thousand cat > clones, not a single one was sick. It is the omission of expected > states that many find troubling about quantum mechanics. Again, this omission is purely classical. If you repeat the experiment enough times, the proportion of sick cats will be the (approximately) same as the proportion of (non-poisoned) cats you would classically have expected to fall ill. There is no constructive or destructive interference - just classically additive probabilities. The transition from live to dead in the case of the cats for whom the poison bottle was broken will be observed to have occurred before the box was opened, in all of the boxes where the bottle was broken. Traces of it will be detectable if the cat is autopsied. > > "Unambiguously live and dead"? What do you mean by that? > [quoted text clipped - 4 lines] > It is a system constructed out of lots of cats, half of them standing, > prancing, and playing, the other half stone cold dead. But none exhibiting any real quantum mechanical behaviour. > I wish to > collect all my data together of what I can expect to find, and that is > the superposition of live and dead cats, never sick, unambiguously > live and dead. As I pointed out above, the sick state (a transition state between live and dead) will be observable via autopsy or perhaps other signs in all of the cases where the cat is found dead. It will be observed to have occurred before the box was opened. None of this is in any way surprising, given that the purpose of Scrodinger's thought experiment was to point out the oddness of quantum theory, and ask how we should interpret it - not to demonstrate its truth. For the latter, the two-slit experiment, experiments with entangled photon pairs, etc., are best. A nineteenth-century physicist would have correctly predicted the results that would be obtained from the Schrodinger Cat experiment, because the predictions of quantum theory and classical theory are the same for it. - Gerry Quinn On Feb 23, 2:00pm, "Salviati" <eckard.blumsch...@arcor.de> wrote: > Doug Sweetser did not yet get an answer to his question > > > Anyone recall the conjugate for number of photons? > > It is the light intensity? Isn't it the phase ? k_x * x = phase E * t / hbar = phase (how does it work for spin?) = phase ... N * phase = phase One of the meanings of the Heisenberg relations is that the phase of a quantum system has a total indeterminacy (2*pi). Best regards, Arjen Dijksman |
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