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Natural Science Forum / Physics / Particle Physics / April 2005Settling a bet: is the smallest action h-bar or h-bar/2 ?
My cousin and I are fighting (well, discussing intensely) over an issue which is not often discussed. We now have a bet ongoing; who wins is allowed a trip to the Einstein tower in Berlin paid by the other. (and he lives in Britain ...) This is the issue: There are several textbooks that make the point that there is a smallest action in nature. I also showed my cousin Frank a few original references where Bohr makes this point very clearly. In short, Bohr said; there is a smallest action in nature given by h-bar. This smallest action explains why measurements always disturb the system, and continuing, all the other effects of quantum theory. Therefore, this is my view on the matter: (1) Minimum action = h-bar. - Photons show this clearly. - Even when a spin 1/2 particle changes orientation from +1/2 to -1/2, the difference is 1 h-bar. - Bohr said so - well not really an argument, but I put it down anyway. My cousin Frank disagrees. He says: (2) Minimum action = h-bar/2. He gives several arguments: - There are spin 1/2 particles. - h-bar/2 appears in the modern uncertainty relation. - Bohr wrote all this before spin was discovered. - There is study material telling about h-bar/2. Now we have a deadlock. We both cannot find experimental data for either side that includes spinors. We fight at the interpretation of the Stern-Gerlach experiment (he says it proves 1/2, I say it proves 1). So we decided to put this to sci.physics and ask: Which of the two is correct? We'll send a postcard from Berlin to all those who helped us with the best arguments to settle the question. Cheers Heinz | My cousin and I are fighting (well, discussing intensely) | over an issue which is not often discussed. We now [quoted text clipped - 42 lines] | We'll send a postcard from Berlin to all those who | helped us with the best arguments to settle the question. It takes two to tango so I would say hbar. But if you believe that an electron interacts with itself, then hbar/2. FrediFizzx http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.pdf or postscript http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.ps Planck's constant ( h-bar) is the smallest unit of action, and represents ONE CYCLE of ACTION. Dirac's Constant ( Planck's constant divided by 2 pi ) is an abortion of Planck's constant, and is the amount of ACTION in a radian. Obviously a real number part of the basic unit of a quantum does not exist. In other words, quantum units involve whole numbers. Dirac's Constant came into play because most physical properties are expressed in radian units, rather than cycle units. The bottom line is you can't get a real number part of a quantum unit. For example, go to the bank and try to get pi dollars exactly. You can keep making up quantum sub units such as cents, mils, etc. but you always have to reference the sub unit to some quantum, and in fact the smallest, integer, sub unit, is the actual quantum. For a detailed discussion of this, visit my web site and download the physics tutorial. -- Tom Potter http://home.earthlink.net/~tdp | Planck's constant ( h-bar) is the smallest unit of action, | and represents ONE CYCLE of ACTION. | | Dirac's Constant ( Planck's constant divided by 2 pi ) | is an abortion of Planck's constant, and | is the amount of ACTION in a radian. Do you mean Dirac's constant is h/4pi^2? I am hoping you meant divide by 2 and not divide by 2pi. FrediFizzx http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.pdf or postscript http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.ps Excuse me. I meant to write: Planck's constant ( h ) is the smallest unit of action, and represents ONE CYCLE of ACTION. rather than Planck's constant ( h-bar) is the smallest unit of action, and represents ONE CYCLE of ACTION. ============= Encarta Di·rac con·stant noun constant in quantum mechanics: a constant used in quantum mechanics that is Planck's constant divided by 2p ================= References The CRC Handbook of Chemistry and Physics , 81st edition, 2000-2001 Dirac's constant is equal to Planck's constant divided by 2p. =========== -- Tom Potter http://home.earthlink.net/~tdp http://photos.yahoo.com/tdp1001 > Planck's constant ( h-bar) is the smallest unit of action, > and represents ONE CYCLE of ACTION. Potter left out.... http://www.google.com/search?q=potter+site%3Awww.crank.net http://www.google.com/search?q=potter+fumble+site%3Ausers.pandora.be I suggest that Sam visit the Asperger's Syndrome help group. They might be able to help him. http://home.vicnet.net.au/~asperger Symptoms of Asperger's Syndrome. ================================ There tends to be impairment in two-way social interaction due in the most part to an inability to understand social behaviour. A lack of empathy with others and little or no eye contact may be evident. The person appears to be stuck at the egocentric stage of social and emotional development and therefore perceives the world almost exclusively from their own point of view. -- Tom Potter http://home.earthlink.net/~tdp http://photos.yahoo.com/tdp1001 > Planck's constant ( h-bar) is the smallest unit of action, > and represents ONE CYCLE of ACTION. [quoted text clipped - 27 lines] > visit my web site and download the > physics tutorial. But only of the OP wants to use a crack pot as a source. Tom Potter is a crack pot. > > Planck's constant ( h-bar) is the smallest unit of action, > > and represents ONE CYCLE of ACTION. [quoted text clipped - 30 lines] > But only of the OP wants to use a crack pot as a source. Tom Potter is a > crack pot. I am pleased ( But not surprised.) to see that GR_GR was unable to find a single point in my post to contest. -- Tom Potter http://home.earthlink.net/~tdp http://photos.yahoo.com/tdp1001 >>>Planck's constant ( h-bar) is the smallest unit of action, >>>and represents ONE CYCLE of ACTION. [quoted text clipped - 35 lines] > to see that GR_GR was unable > to find a single point in my post to contest. What Tom was really saying here is that he was glad that I was not to be bothered sorting through his garbage. Tom is glad because he is mentally lazy even about his own theories, and would rather they be taken as the truth without thought than he having to defend them (Which he cannot). > Planck's constant ( h-bar) is the smallest unit of action, Please present evidence for that assertion. > and represents ONE CYCLE of ACTION. And what is a "cycle of action"? > Dirac's Constant ( Planck's constant divided by 2 pi ) > is an abortion of Planck's constant, "abortion"??? > and is the amount of ACTION in a radian. And what is that supposed to mean? How can a radian "contain" action (or anything else)? > Obviously a real number part of the basic unit > of a quantum does not exist. Incomprehensible. > In other words, quantum units involve whole numbers. What exactly do you mean with "quantum units"? > Dirac's Constant came into play > because most physical properties > are expressed in radian units, > rather than cycle units. For example? > The bottom line is > you can't get a real number part of a quantum unit. > > For example, go to the bank > and try to get pi dollars exactly. If you didn't notice: whole numbers and rational numbers are real numbers, too. [snip more like that] Bye, Bjoern So far, only answers from crackpots, so I'll try... > My cousin and I are fighting (well, discussing intensely) > over an issue which is not often discussed. We now [quoted text clipped - 4 lines] > There are several textbooks that make the point that > there is a smallest action in nature. Please give some references. That would be news to me. > I also showed > my cousin Frank a few original references where Bohr makes > this point very clearly. > > In short, Bohr said; there is a smallest action in > nature given by h-bar. Bohr's version of QM has been outdated for 79 years now. So don't rely on what he said. > This smallest action explains > why measurements always disturb the system, > and continuing, all the other effects of quantum theory. Err, you seem to confuse this somehow with Heisenberg's uncertainty principle. > Therefore, this is my view on the matter: > > (1) Minimum action = h-bar. > > - Photons show this clearly. Why do you think so??? > - Even when a spin 1/2 particle changes orientation > from +1/2 to -1/2, the difference is 1 h-bar. That's the difference in the z-component of angular momentum, not in action. > - Bohr said so - well not really an argument, but I > put it down anyway. See above wrt Bohr. > My cousin Frank disagrees. He says: > > (2) Minimum action = h-bar/2. > > He gives several arguments: > - There are spin 1/2 particles. Yes. So what? Again, that is about angular momentum, not about action. > - h-bar/2 appears in the modern uncertainty relation. Yes. So what? The uncertainty relation says nothing about action. > - Bohr wrote all this before spin was discovered. See above wrt Bohr. > - There is study material telling about h-bar/2. About angular momentum or spin, I suspect? > Now we have a deadlock. We both cannot find experimental data > for either side that includes spinors. We fight at the interpretation > of the Stern-Gerlach experiment (he says it proves 1/2, I say it > proves 1). And I say it proves neither, because it's about angular momentum, not about action. > So we decided to put this to sci.physics and ask: > > Which of the two is correct? Neither, as far as I can say. > We'll send a postcard from Berlin to all those who > helped us with the best arguments to settle the question. No, thanks. Bye, Bjoern > > Which of the two is correct? > > Neither, as far as I can say. Oh. If you say that there is no smallest action, you would have to provide an experiment where action (integral of lagr. from t1 to t2) is as small as desired (and in any case smaller that h-bar/2). I guarantee that you will fail. I am so sure that I will pay you (or anybody else) any sum you want in case you find such an experiment. (To make it easy, you do not even have to perform a real experiment, or find a reference to one; you just have to find a suitable Gedanken experiment.) There is no such possibility. Fortunately. So far, quantum theory is still correct. Regards Heinz > > > Which of the two is correct? In my opinion, h-bar is the smallest, by definition. However, I think that this phenomenon is relativistic. And so, (h-bar)/2 certainly exists in an absolute sense, but _not_ relative to you - the observer. So, BOTH of you are RIGHT. You will both go to Berlin. The problem I have is understanding this boundary condition - if it is smooth or catastrophic transition from 4D Minkoski spacetime to 3D. But this really has no bearing on the outcome of your question - you are both right. WK | > > Which of the two is correct? | > [quoted text clipped - 17 lines] | There is no such possibility. Fortunately. | So far, quantum theory is still correct. Bjoern keeps saying that hbar or hbar/2 is not the smallest action but I don't think he has ever presented any experimental evidence or even thought experiment to the contrary. Of course his claim is that it has nothing to do with action even though it has the same units as action. According to this reference it was Planck himself that called h "the quantum of minimum action". http://www.schoolsobservatory.org.uk/study/sci/cosmo/internal/quantum.htm Christoph Schiller who has written a comprehensive free online physics textbook calls hbar/2 the minimum action in nature in the following article. http://www.arxiv.org/abs/physics/0309118 However, he does mention as a footnote that; "In fact, virtual particles can be seen as exceptions to this limit." But does not explain how. And of course virtual particles are not directly observable. So I agree with Schiller that between two different observations of a system there can't be a "change of state" less than hbar/2. FrediFizzx http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.pdf or postscript http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.ps > | > > Which of the two is correct? > | > [quoted text clipped - 21 lines] > don't think he has ever presented any experimental evidence or even > thought experiment to the contrary. Err, why should *I* present an experiment to show that? I would say the burden of proof is on the one who claims that there *is* a smallest action. > Of course his claim is that it has > nothing to do with action even though it has the same units as action. "it"? > According to this reference it was Planck himself that called h "the > quantum of minimum action". > > http://www.schoolsobservatory.org.uk/study/sci/cosmo/internal/quantum.htm Indeed. Hint: that's because in *Bohr's* version of QM, action *was* indeed quantized. You know that Bohr's version of QM is outdated, don't you? > Christoph Schiller who has written a comprehensive free online physics > textbook calls hbar/2 the minimum action in nature in the following [quoted text clipped - 9 lines] > with Schiller that between two different observations of a system > there can't be a "change of state" less than hbar/2. Who is Christoph Schiller? The abstract of this paper sounds as written by a crackpot. According to his address given in the paper, he works at "G & D Research and Development", which seems to be hosted here: http://www.gi-de.com/. So, nothing suggest that Mr. Schiller has the qualifications to make an authorative statement on this subject. [snip] Bye, Bjoern | > | > > Which of the two is correct? | > | > [quoted text clipped - 25 lines] | the burden of proof is on the one who claims that there *is* a | smallest action. I have read many references that call Planck's constant the minimum of action. The burden of proof seems to be with you if you say it is not. | > Of course his claim is that it has | > nothing to do with action even though it has the same units as action. | | "it"? Sigh. Planck's constant. | > According to this reference it was Planck himself that called h "the | > quantum of minimum action". http://www.schoolsobservatory.org.uk/study/sci/cosmo/internal/quantum.htm | Indeed. Hint: that's because in *Bohr's* version of QM, action *was* | indeed | quantized. You know that Bohr's version of QM is outdated, don't you? Why don't you explain to the group why action is not quantized any longer instead of playing these games if you know? I think you are afraid of being shot down. | > Christoph Schiller who has written a comprehensive free online physics | > textbook calls hbar/2 the minimum action in nature in the following [quoted text clipped - 16 lines] | Schiller has the qualifications to make an authorative statement | on this subject. http://www.motionmountain.net/ Schiller has written a free online physics textbook that is highly praised by many physicists. I am sure he knows more about it than you do. Care to take your foot out of your mouth? FrediFizzx > | > | > > Which of the two is correct? > | > | > [quoted text clipped - 29 lines] > I have read many references that call Planck's constant the minimum of > action. Give one. And please one which doesn't talk about *Bohr's* version of QM. [snip] > | > Of course his claim is that it has > | > nothing to do with action even though it has the same units as [quoted text clipped - 3 lines] > > Sigh. Planck's constant. I never said that Planck's constant "has nothing to do with action". > | > According to this reference it was Planck himself that called h "the > | > quantum of minimum action". [quoted text clipped - 6 lines] > Why don't you explain to the group why action is not quantized any > longer instead of playing these games if you know? Err, what on earth is exactly to explain here? Bohr postulated that a certain integral which he called "action integral" is quantized. 10 years later it turned out that Bohr was wrong. I could as well ask you to explain why the Sun does no longer go round the Earth! > I think you are afraid of being shot down. ROTFL! > | > Christoph Schiller who has written a comprehensive free online > physics [quoted text clipped - 23 lines] > Schiller has written a free online physics textbook that is highly > praised by many physicists. There are a lot of praises in his guestbook, indeed. But it's not clear how many of those were really written by physicists. > I am sure he knows more about it than you do. And what makes you so sure about that? > Care to take your foot out of your mouth? Talking to yourself, I see... Bye, Bjoern In sci.physics.particle Bjoern Feuerbacher <feuerbac@thphys.uni-heidelberg.de> wrote: : I could as well ask you to explain why the Sun does no longer go round : the Earth! It doesn't? Uh oh. ----- Richard Schultz schultr@mail.biu.ac.il Department of Chemistry, Bar-Ilan University, Ramat-Gan, Israel Opinions expressed are mine alone, and not those of Bar-Ilan University ----- "Logic is a wreath of pretty flowers which smell bad." | > | > | > > Which of the two is correct? | > | > | > [quoted text clipped - 31 lines] | | Give one. And please one which doesn't talk about *Bohr's* version of QM. I already gave you two. You are a lost cause. I could give you a hundred and you would still not be satisfied. | > | > Of course his claim is that it has | > | > nothing to do with action even though it has the same units as [quoted text clipped - 5 lines] | | I never said that Planck's constant "has nothing to do with action". Well, I am too busy to look up the thread so I will agree that you didn't say it. Comment withdrawn. | > | > According to this reference it was Planck himself that called h "the | > | > quantum of minimum action". http://www.schoolsobservatory.org.uk/study/sci/cosmo/internal/quantum.htm | > | Indeed. Hint: that's because in *Bohr's* version of QM, action *was* | > | indeed quantized. You know that Bohr's version of QM is outdated, don't you? [quoted text clipped - 5 lines] | certain integral which he called "action integral" is quantized. 10 | years later it turned out that Bohr was wrong. Do you have a reference for that statement? | I could as well ask you to explain why the Sun does no longer go round | the Earth! | | > I think you are afraid of being shot down. | | ROTFL! Go for it then. | > | > Christoph Schiller who has written a comprehensive free online | > physics [quoted text clipped - 26 lines] | There are a lot of praises in his guestbook, indeed. But it's not | clear how many of those were really written by physicists. Do a googlegroup search for him. | > I am sure he knows more about it than you do. | | And what makes you so sure about that? I don't haven't seen any 1,000 page physics textbooks that you have written. FrediFizzx > | Give one. And please one which doesn't talk about *Bohr's* version of > QM. > > I already gave you two. You are a lost cause. I could give you a > hundred and you would still not be satisfied. Freddi, Bjoern is an ass-piring proctologist, Don't waste your time, he's a pink pantied button pusher...Mommy bought his degree. Anyway, I'm looking at a ref, authored by, Uvarov, Chapman and Isaacs, in the "Dictionary of Science" and I'll quote ver batim ACTION, "The product of *work* and time, *Planck's constant* of action is measured in the C.G.S. units of *erg*-seconds." The asterisks quote the authors italics. The ref I have is published by Penguin. I've checked that hard and will sign-off on that. Regards Ken S. Tucker | > | Give one. And please one which doesn't talk about *Bohr's* version | of [quoted text clipped - 6 lines] | Don't waste your time, he's a pink pantied | button pusher...Mommy bought his degree. I must be a masochist. ;-) | Anyway, I'm looking at a ref, authored by, | Uvarov, Chapman and Isaacs, in the "Dictionary [quoted text clipped - 9 lines] | I've checked that hard and will sign-off | on that. Well, I don't think that really says anything about hbar being the minimum action but you can see how Bjoern is recanting now about hbar being "action". So he can pack that one up where the moon don't shine (proctology practice?). I still haven't seen anyone come up with actual experimental evidence or a good thought experiment that action can be less than hbar/2. Heck that is ~ 5.27*10^-28 erg sec. Is that even measurable? If Christoph Schiller says it is the minimum action, then that is good enough for me. I certainly trust him more than Bjoern. FrediFizzx out. My work here is done. http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.pdf or postscript http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.ps [snip] > but you can see how Bjoern is recanting now about hbar > being "action". I recanted nowhere here. I only pointed out that I never said that hbar *has nothing to do* with action. I did *not* say that hbar *is* action. Do you have severe reading comprehension problems, or are you deliberately misrepresenting me? > So he can pack that one up where the moon don't shine > (proctology practice?). I still haven't seen anyone come up with actual > experimental evidence or a good thought experiment that action can be > less than hbar/2. I notice you ignored all the processes described in this thread where the action would be lower than that. I wonder why... [snip] > If Christoph Schiller says it is the minimum action, then that is good > enough for me. Argument by authority? > I certainly trust him more than Bjoern. Apparently you trust him so much that you think you can simply ignore the described processes which would contradict him. > FrediFizzx out. My work here is done. Read: "I can't counter the arguments, so I'll flee." Bye, Bjoern >>| Give one. And please one which doesn't talk about *Bohr's* version > [quoted text clipped - 8 lines] > Don't waste your time, he's a pink pantied > button pusher... I see that you have resorted to insults now. Thanks for admitting that you can't answer my arguments. > Mommy bought his degree. My "mommy" died before I even started my PhD studies, a.shole. > Anyway, I'm looking at a ref, authored by, > Uvarov, Chapman and Isaacs, in the "Dictionary [quoted text clipped - 3 lines] > of action is measured in the C.G.S. units of > *erg*-seconds." Your point? That quote doesn't say that action is quantized. [snip] Bye, Bjoern > > Anyway, I'm looking at a ref, authored by, > > Uvarov, Chapman and Isaacs, in the "Dictionary [quoted text clipped - 5 lines] > > Your point? That quote doesn't say that action is quantized. "h" is a constant and invariant. Have you studied the "length" of a photon yet? >>>Anyway, I'm looking at a ref, authored by, >>>Uvarov, Chapman and Isaacs, in the "Dictionary [quoted text clipped - 7 lines] > > "h" is a constant and invariant. Indeed. So what? What has that to do with the statement "action is quantized"? > Have you studied the "length" of a photon yet? No, because photons have no lengths. Your point? Bye, Bjoern > >>>Anyway, I'm looking at a ref, authored by, > >>>Uvarov, Chapman and Isaacs, in the "Dictionary [quoted text clipped - 10 lines] > Indeed. So what? What has that to do with the statement > "action is quantized"? How would you define quantized? > > Have you studied the "length" of a photon yet? > > No, because photons have no lengths. Your point? If you've never studied it, then what qualifies you to make prouncements and predictions? Ken >>>>>Anyway, I'm looking at a ref, authored by, >>>>>Uvarov, Chapman and Isaacs, in the "Dictionary [quoted text clipped - 12 lines] > > How would you define quantized? "can have only discrete values" What has "h is a constant and invariant" to do with "action can have only discrete values"? >>>Have you studied the "length" of a photon yet? >> >>No, because photons have no lengths. Your point? > > If you've never studied it, then what qualifies > you to make prouncements and predictions? How could I study something which doesn't exist? If you asked "Have you ever studied *if* photons have a length", then the answer would be "yes, I studied that, and they have none". Bye, Bjoern > >>>>>Anyway, I'm looking at a ref, authored by, > >>>>>Uvarov, Chapman and Isaacs, in the "Dictionary [quoted text clipped - 16 lines] > What has "h is a constant and invariant" to do with "action > can have only discrete values"? Have you studied the quantization of "charge"? > >>>Have you studied the "length" of a photon yet? > >> > >>No, because photons have no lengths. Your point? > > If you've never studied it, then what qualifies > > you to make prouncements and predictions? > How could I study something which doesn't exist? > If you asked "Have you ever studied *if* photons have > a length", then the answer would be "yes, I studied that, > and they have none". Ah, <sigh> the question was/is clear, repeat, "have you studied the "length of a photon", we're not interested in your results yet, because your methodology is to be judged first. At the risk of confusing you even more, are you able to recall the methodology of the study you maybe did, and would you explain it to us? Regards Ken S. Tucker >>>>>>>Anyway, I'm looking at a ref, authored by, >>>>>>>Uvarov, Chapman and Isaacs, in the "Dictionary [quoted text clipped - 18 lines] > > Have you studied the quantization of "charge"? Yes. And now stop obfuscating and answer my question. >>>>>Have you studied the "length" of a photon yet? >>>> [quoted text clipped - 9 lines] > > Ah, <sigh> the question was/is clear, repeat, The answer was also clear. [snip more trolling] Bye, Bjoern > >>>>>>>Anyway, I'm looking at a ref, authored by, > >>>>>>>Uvarov, Chapman and Isaacs, in the "Dictionary [quoted text clipped - 20 lines] > > Yes. Ok, is "charge" quantized? >And now stop obfuscating and answer my question. When you're qualified. Frankly Bjeorn you delete the uncomfortable, and just throw spit-balls, you monkey with math and waste time. To me mathematics is as pain-staking as scaling a slimy vertical cliff, which I've done. Every single decision is right or wrong, your disrepect for logic and math is why Germany is sinking. ((My Old Boy was a path-finder navigator /debriefer in WW2...mosquitos...every X-mass I got a new gun, I had to buy my own telescope)). Bjeorn you over use the word obfuckulating. Is charge quantized????????????? >>>>>>>>>Anyway, I'm looking at a ref, authored by, >>>>>>>>>Uvarov, Chapman and Isaacs, in the "Dictionary [quoted text clipped - 22 lines] > > Ok, is "charge" quantized? Yes. I said: stop obfuscating and answer my question. I see you don't bother, but simply continue trolling. >>And now stop obfuscating and answer my question. > > When you're qualified. And what makes you think you are in the position to judge if I am qualified or not? > Frankly Bjeorn you delete the uncomfortable, > and just throw spit-balls, you monkey with > math and waste time. I simply point out that I am tired of your obfuscations and your trolling. > To me mathematics is as pain-staking as scaling > a slimy vertical cliff, which I've done. Bad for you. To me, mathematics is something very nice. [snip more trolling] Bye, Bjoern > > Ok, is "charge" quantized? > > Yes. > > When you're qualified. > I am qualified or not? OK, after a week we agree charge is quantitized. Can you express "h" in terms of "q" ? > > To me mathematics is as pain-staking as scaling > > a slimy vertical cliff, which I've done. > > Bad for you. To me, mathematics is something very nice. Egad, you sound like the type who gets giddy, before a 3 hour math exam and wish it was longer afterwards. Math is hard work, results are very nice! >>>Ok, is "charge" quantized? >> [quoted text clipped - 5 lines] > > OK, after a week we agree charge is quantitized. I never disputed that, and that wasn't the original topic. > Can you express "h" in terms of "q" ? No. Why on earth should I? And what sense would that make? Charge "q" is a physical quantity. "h" is a constant of nature. Relating the two doesn't make much sense. And now *finally* answer the question: what has "h is a constant and invariant" to do with "action can have only discrete values"? STOP OBFUSCATING!!!!! [snip] Bye, Bjoern > >>>Ok, is "charge" quantized? > >> [quoted text clipped - 13 lines] > Charge "q" is a physical quantity. "h" is a constant of > nature. Relating the two doesn't make much sense. So the quantized charge q = 4.803*10^-10 esu and h=6.626*10^-27 erg*sec Bjoern is unable to relate? > And now *finally* answer the question: what has > "h is a constant and invariant" to do with "action > can have only discrete values"? Well, if you can't relate "q" and "h" then you should consult another authority, and return with a definite answer. >>>>>Ok, is "charge" quantized? >>>> [quoted text clipped - 17 lines] > > q = 4.803*10^-10 esu So you mean the elementary charge, not charge in general? > and > > h=6.626*10^-27 erg*sec > > Bjoern is unable to relate? There are formulas with which one could connect the *elementary* charge (not charge in general!) with h, but what sense would that make? >>And now *finally* answer the question: what has >>"h is a constant and invariant" to do with "action [quoted text clipped - 3 lines] > you should consult another authority, and > return with a definite answer. STOP OBFUSCATING, TROLL. Bye, Bjoern duh > duh Pathetic troll. > > duh > > Pathetic troll. On the contrary, you were given the numbers and units for two invariants "h" and "q" on April 14, that you *conveniently* deleted. Hard data ain't your bag, me thinks you're a softy in pink panties, pigeon toed, enjoys collecting recipes, arranging flowers, and perhaps has a picture of Tarzan in your bed- room that you continually (um) straighten. That's the truth from what I hear, (and there's nothing wrong with that). Ken S> Tucker >>>duh >> [quoted text clipped - 3 lines] > and units for two invariants "h" and "q" on > April 14, that you *conveniently* deleted. Liar. My post on April 15 still contains these numbers. *You* deleted all my answer (including these numbers) and responded simply with "duh". As I said: pathetic troll. [snip more trolling] Bye, Bjoern [squat] Then answer the question and stop ovulating. (q,h) What's it worth to you to know? > [squat] > > Then answer the question and stop > ovulating. (q,h) > > What's it worth to you to know? Err, originally it was *me* who asked *you* a question (what has ">h is a constant and invariant" to do with "action can have only discrete values"?). Instead of answering it, you came up with lots of obfuscation; and now *you* whine that *I* am not answering *your* question, and am "ovulating"? You are not only a liar and a pathetic troll, you are also a hypocrite. Bye, Bjoern | > [squat] | > [quoted text clipped - 8 lines] | you came up with lots of obfuscation; and now *you* whine | that *I* am not answering *your* question, and am "ovulating"? Hmm... Looks like a Mexican stand-off. Someone came to the gunfight with a knife though. LOL hbar = e^2/alpha*c = E/w and more. FrediFizzx http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.pdf or postscript http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.ps Hi Fredi... > | > [squat] > | > [quoted text clipped - 8 lines] > | you came up with lots of obfuscation; and now *you* whine > | that *I* am not answering *your* question, and am "ovulating"? I haven't yet made any statement (in this thread) about claiming the quantization of action. > Hmm... Looks like a Mexican stand-off. Someone came to the gunfight > with a knife though. LOL > hbar = e^2/alpha*c = E/w and more. Using, the invariants, hbar = e^2/alpha*c = E/w, is a physical law, because it's true in all CS's. If I were to set q1 = n1*e and q2=n2*e, where n1 and n2 are integer charge quantities, and are also invariants, then, it would stand to reason Action = (n1*n2)*hbar = q1*q2/alpha*c = (n1*n2)*E/w which is clearly quantized. BJoern's definition of "quantized" he posted a few days ago is too primitive to be useful, (not worth quoting). The definition IMO that is more common is, d(Action) = 0 but Action =/= constant, (where "d" is a differential). For example, everything on the RHS of the Action equation above has a zero differential. Consider "n1", it has only values like, n1 = 0,1,2,3...N but it can't have 1.333 etc. n1 is a discontinuous function, like a staircase instead of a ramp. All is not lost. Wave Mechanics provides a means to analyze that type of problem. Recall back in E-technician school a blurp about "Complex Waveforms" and "Fourier Series". Well basically, a square wave may be regarded as a sum of sine waves, (I'll the write out the series if you want), and the individual components of that series have non-zero differentials. > FrediFizzx > > http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.pdf > or postscript > http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.ps What do you think Freddi, did I come close? Regards Ken S. Tucker [snip] > | > I have read many references that call Planck's constant the minimum > | > of action. [quoted text clipped - 3 lines] > > I already gave you two. Where? What you gave below was *one* reference where Planck called h "the quantum of minimum action". And I already explained that that quite was about *Bohr's* version of QM. So you have *not* given a reference yet which does *not* talk about *Bohr's* version of QM. [snip] > | > | > According to this reference it was Planck himself that called h > | > | > "the quantum of minimum action". [quoted text clipped - 14 lines] > > Do you have a reference for that statement? For which of my statements above? That Bohr postulated that the "action integral is quantized, or that he was wrong? For the first, see any text which explains in detail Bohr's version of QM. E.g.: <http://www.physics.orst.edu/~henri/Ph314/lect14/lecture_14.html> For the second, simply do a few simple calculations on your own. Several processes were already suggested in this thread which showed that the action can indeed be as small as one likes. [snip] > | > I think you are afraid of being shot down. > | > | ROTFL! > > Go for it then. I already did suggest some processes where the action is smaller than hbar. So far, you have ignored these posts. So, *who* is afraid of being shot down here? [snip] > | > I am sure he knows more about it than you do. > | > | And what makes you so sure about that? > > I don't haven't seen any 1,000 page physics textbooks that you have > written. Why does writing a 1,000 page physics textbook mean that one is qualified to talk about every single thing mentioned in that book? Bye, Bjoern > > | > > Which of the two is correct? > > | > [quoted text clipped - 33 lines] > > According to this reference it was Planck himself that called h "the > > quantum of minimum action". http://www.schoolsobservatory.org.uk/study/sci/cosmo/internal/quantum.htm > Indeed. Hint: that's because in *Bohr's* version of QM, action *was* > indeed quantized. This doesn't add up, unless Planck could see into the future. Planck published his paper on the "quantum of action" in 1900, and Bohr worked on his theories from 1912 on. -- Tom Potter http://home.earthlink.net/~tdp http://photos.yahoo.com/tdp1001 >> > Which of the two is correct? >> [quoted text clipped - 5 lines] >is as small as desired (and in any case smaller >that h-bar/2). You can't even define the action in quantum mechanics. The action is the integral of the Lagrangian with time over a given trajectory. The better the trajectory is defined, the more poorly the Lagrangian is defined since the momentum becomes more poorly defined. It's the uncertainty principle. I could say as a counterpoint that the beginning and ending points of the trajectory can be changed by any arbitrary amount, but the beginning and ending points and the trajectory aren't even well defined. In Feynman's path integral approach, equivalent to wave mechanics, one assumes that the particle follows all possible trajectories. Not just taking off from some starting point with all possible angles, but following paths that loop around in all possible shapes. The trajectory that minimizes the action is the expectation value and the classical limit. hbar has no meaning in the classical limit. >I guarantee that you will fail. I am so sure >that I will pay you (or anybody else) [quoted text clipped - 4 lines] >you just have to find a suitable Gedanken >experiment.) What is the action of the electron of a hydrogen atom that starts in the n=2 S state and transitions to the n=1 S state? What are the beginning and ending points, and what is the trajectory that is followed? >There is no such possibility. Fortunately. >So far, quantum theory is still correct. > >Regards > > Heinz  Signature"Coincidences, in general, are great stumbling blocks in the way of that class of thinkers who have been educated to know nothing of the theory of probabilities." -- Edgar Allen Poe > You can't even define the action in quantum mechanics. The action is the > integral of the Lagrangian with time over a given trajectory. Sorry, but this is wrong. Look up Schwinger's quantum action principle. The action between two endpoints 1 and 2 with states psi_1 and psi_2 is given by < psi_1 | integral L dt | psi_2 > Where L is the Lagrangian operator, defined as in classical physics, but exchanging functions with operators. > What is the action of the electron of a hydrogen atom that starts in the > n=2 S state and transitions to the n=1 S state? What are the beginning > and ending points, and what is the trajectory that is followed? The action value does not depend on the trajectory. That is the essence of Schwinger's quantum principle. It only depends on the end points. (See e.g. Schinger's book.) In summary: the action IS well-defined in quantum theory. The question remains whether the smallest value is h-bar or h-bar/2 ... --- That Schiller pretends that it is h-bar/2 is known; but he gives no good arguments for it. We are not doing things based on authority in physics. Heinz. [snip] | In summary: the action IS well-defined in quantum theory. | The question remains whether the smallest value [quoted text clipped - 5 lines] | gives no good arguments for it. We are not | doing things based on authority in physics. Yes, you are correct. I think Schiller is just being general and trying to be "safe" with hbar/2. The point I was making is that I do think you are correct in that hbar or hbar/2 *is* the minimum action in nature whilst Bjoern says no. Do you think electrons (or fermions) self-interact? FrediFizzx http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.pdf or postscript http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.ps > > You can't even define the action in quantum mechanics. The action is > the [quoted text clipped - 22 lines] > The question remains whether the smallest value > is h-bar or h-bar/2 ... Well the answer is neither, "h" is the smallest action, so both get to go to Berlin, and I'd like you to send me a package of Heinz ketshup. h=6.625*10^-27 ergs*secs = p_0*x^0 = invariant, by definition. > That Schiller pretends that it is h-bar/2 is known; but he > gives no good arguments for it. We are not > doing things based on authority in physics. You mean we have to explain things? Oh darn. Simplify ergs*secs to p*t == p_0 x^0 Let p = mc^2 , ct=r then with c=1, h== mr = m'r' . A balanced balance is independent of the g-field it is in, (that's where invariance enters into that above), so we ask what is the minimum amount of ACTION required to unbalance the balance. Well let's drop a photon on one side, given by p = h*f = h/t , f=1/t = frequency h = p*t = p'*t' The t can be anything you want because w.r.t. another moving CS, t' can be as small as you want and p' will increase making no diff, use a gamma-ray or a radiowave, there's no diff in action, simply because relative motion will shift f to any f' you want, and that can't change the invariant. Let's resurrect our ACTION balance, m1*r1 = m2*r2 as one learns in high school (or teeter-toddering) and find m1*r1 < m2*r2 + h because I dropped a photon onto m2 that was absorbed. What's important to check is that "h" has the same units as m*r. Ok? Regards Ken S. Tucker > Heinz. >>You can't even define the action in quantum mechanics. The action is >>the integral of the Lagrangian with time over a given trajectory. [quoted text clipped - 4 lines] > > < psi_1 | integral L dt | psi_2 > Are these Heisenberg or Schroedinger states? > Where L is the Lagrangian operator, defined as in classical physics, > but exchanging functions with operators. Interesting, I didn't knew this definition. So, let's try a free particle. H = -Laplace/2m, and since there is no potential, L = 0.5 m qdot^2 (where q is the position operator). Insert two eigenstates of momentum or position above and evaluate the expression. [snip] > In summary: the action IS well-defined in quantum theory. > The question remains whether the smallest value > is h-bar or h-bar/2 ... You still have not given an argument *why* there should be a smallest action in nature, and neither a reference to a book which says so. > That Schiller pretends that it is h-bar/2 is known; but he > gives no good arguments for it. We are not > doing things based on authority in physics. Especially in light of the fact that Schiller apparently *is* not even an authority. Bye, Bjoern >> You can't even define the action in quantum mechanics. The action is >the [quoted text clipped - 8 lines] >Where L is the Lagrangian operator, defined as in classical physics, >but exchanging functions with operators. I'm not familiar with Schwinger's quantum action principle, I would have to study it. >> What is the action of the electron of a hydrogen atom that starts in >the [quoted text clipped - 15 lines] >gives no good arguments for it. We are not >doing things based on authority in physics. Why would it have a smallest value at all? <1| \int L dt |2> = \int dx dy <1|x><x|\int L dt|y><y|2> = \int dx dy dt psi1*(x) psi2(y) <x|\int L dt|y> and the action calculation winds up as a sum of actions from every possible starting point to every possible ending point weighted by the wavefunctions. psi1 and psi2 can be anything, t2-t1 can be anything, the Lagrangian contains a potential that can be anything. I don't see anything that limits it to a smallest value or a discrete selection of values. Signature"The average person, during a single day, deposits in his or her underwear an amount of fecal bacteria equal to the weight of a quarter of a peanut." -- Dr. Robert Buckman, Human Wildlife, p119. >>> You can't even define the action in quantum mechanics. The action is >>the [quoted text clipped - 11 lines] >I'm not familiar with Schwinger's quantum action principle, I would have >to study it. Worth looking at. It makes the transition from QM to classical mechanics very natural, formally the same as the transition from wave optics to ray optics. >>> What is the action of the electron of a hydrogen atom that starts in >>the [quoted text clipped - 17 lines] > >Why would it have a smallest value at all? I've never seen anything to the effect that it should. This appears to be a "popular" notion, rather than one firmly anchored in science. > <1| \int L dt |2> > [quoted text clipped - 8 lines] >anything that limits it to a smallest value or a discrete selection of >values. Indeed. Mati Meron | "When you argue with a fool, meron@cars.uchicago.edu | chances are he is doing just the same" [snip] >>>That Schiller pretends that it is h-bar/2 is known; but he >>>gives no good arguments for it. We are not [quoted text clipped - 4 lines] > I've never seen anything to the effect that it should. This appears > to be a "popular" notion, rather than one firmly anchored in science. And I think this is a left-over from Bohr's version of QM, where the "action integral" was indeed quantized. [snip] Bye, Bjoern >[snip] > [quoted text clipped - 9 lines] >And I think this is a left-over from Bohr's version of QM, where the >"action integral" was indeed quantized. That's the most reasonable explanation, indeed. Well, science popularizations tend to be a tad "behind the times", but nearly a century behind the times is a bit much:-) Mati Meron | "When you argue with a fool, meron@cars.uchicago.edu | chances are he is doing just the same" >>>> You can't even define the action in quantum mechanics. The action is >>>the [quoted text clipped - 15 lines] >mechanics very natural, formally the same as the transition from wave >optics to ray optics. Can you help me interpret it? Are |psi1> and |psi2> the same wavefunction at different times, or different states that a system is assumed to have transitioned between? E.g. for a wavefunction |psi> = cos(wt) |a> + sin(wt) |b> do we write <psi(t1)| \int L dt |psi(t2)> or <a| \int L dt |b>? Signature"Outside the camp you shall have a place set aside to be used as a latrine. You shall keep a trowel in your equipment and with it, when you go outside to ease nature, you shall first dig a hole and afterward cover up your excrement." -- Deuteronomy 23:13-14 >>>>> You can't even define the action in quantum mechanics. The action is >>>>the [quoted text clipped - 31 lines] > > <a| \int L dt |b>? It is the first one, as I recall. Has been a while since I looked at this. Mati Meron | "When you argue with a fool, meron@cars.uchicago.edu | chances are he is doing just the same" > Why would it have a smallest value at all? > [quoted text clipped - 10 lines] > anything that limits it to a smallest value or a discrete selection of > values. You might have a point here, but the choice is not that free, and this makes the conclusion not so easy. ps1 and ps2 are related by the evolution equations; so you cannot choose all psi's, t's and potential independently. Heinz >> Why would it have a smallest value at all? >> [quoted text clipped - 18 lines] >ps1 and ps2 are related by the evolution equations; so you >cannot choose all psi's, t's and potential independently. Sure you can. The time evolution operator will evolve the wavefunction for 1 second, for 1/2 second, for a picosecond, for zero seconds, anything you care to put in it, limited only by the regime of your approximation (e.g. if you don't account for a wall). And the wavefunction itself has continuously adjustable parameters. E.g. suppose a Gaussian wavepacket (neglecting pesky constant multipliers...), psi(x,t=0) = exp(ipx)*exp(-x^2/W^2) The momentum p can be given any value, the width W can be given any value. And you can sculpt the evolution of the wavepacket with the potential, which could be time-dependent. You could have a potential like V(x,t) = 0 for t < t0 = V0 (1 - exp(-kt)) which is a reasonable potential if you "suddenly" turn a field on, and t0 and k are free for you to choose. Or pass another charged particle with any impact parameter. Or include the image fields on the walls of your apparatus, which can have virtually any geometry and dimensions and material properties. Even if you wanted to make a comparison with a bound system like the quantum harmonic oscillator, the energy of the bound particle is (n+1/2)hbar*w, and the frequency w can be anything. There you have a system that's quantized and has a lowest energy, but you can't say what the energy step or the lowest value are without more information. Quantization, meaning discrete energy steps and a minimum energy, comes from boundary conditions, as the square well with hard walls or the harmonic oscillator or the hydrogen atom with softer walls. But the actual energies depend on the dimensions, the strength of the potential, the geometry, anything you can think of to throw at it. And a free particle can have any energy. For a free particle, L=H=P^2/2m. Calculate the action over an arbitrary time. Signature"Let us learn to dream, gentlemen, then perhaps we shall find the truth... But let us beware of publishing our dreams before they have been put to the proof by the waking understanding." -- Friedrich August Kekulé The facts of the matter are these: 1. "sh.t happens". (Events occur.) 2. Events are quantum. ( Events don't occur in fractional amounts.) 3. Events are transferred between sources and sinks in units of Planck's Constant. ( The quantum of action.) 4. Planck's Constant is a compound property. It, like area, is a factor of two orthogonal properties. action = energy * time = momentum * distance = mass * diffusity 5. The quantum of action is a single cycle (loop), and counting quanta of action involves counting cycles. ( Not cycles per time, which is frequency, but a direct count of the cycles involved.) 6. As most physical properties as measured as real numbers, it is common express action in radians, rather than cycles. 7. Radians are NOT true quanta, as they force a real number into play. Dirac's constant is an abortion of Planck's Constant that distorts the true nature of quanta. -- Tom Potter http://home.earthlink.net/~tdp http://photos.yahoo.com/tdp1001 > The facts of the matter are these: > [quoted text clipped - 25 lines] > Dirac's constant is an abortion of Planck's Constant > that distorts the true nature of quanta. No wonder you registered at crank dot net, Potter! http://www.google.com/search?q=%22Tom+Potter%22+site%3Awww.crank.net That's got to be embarrassing! It is interesting to observe how threads degenerate when Wormley gets involved in the thread. I suggest that true seekers of wisdom and truth can learn a lot by analyzing this pattern. Note that dichotomies decay exponentially ( A damped oscillation.) and eventually assume a relatively stable back and forth, action/reaction cycle. ( Insult/counter-insult) One could infer that systems degenerate to the **lowest level** that can be sustained by the degenerate partner to an cyclical interaction. In other words exponential probing extends to a finer and finer level, until the limit of the degenerate partner is reached, at which point the cycle becomes a simple, repeating back and forth pattern. This also suggests that the best way to solve problems, is to have competing sides engage in dichotomies, and when the pattern degenerates into a cycle, to substitute new blood for the degenerate component, which reached the limits of its' ability. -- Tom Potter http://home.earthlink.net/~tdp http://photos.yahoo.com/tdp1001 > > You can't even define the action in quantum mechanics. The action is > the [quoted text clipped - 30 lines] > > Heinz. All this silly relativistic/qm terminology when the real substance is back at Newton. "It may also be objected, that if the ultimate ratios of evanescent quantities are given, their ultimate magnitudes will be also given: and so all quantities will consist of indivisibles, which is contrary to what Euclid has demonstrated concerning incommensurables, in the 10th Book of his Elements. But this objection is founded on a false supposition. For those ultimate ratios with which quantities vanish are not truly the ratios of ultimate quantities, but limits towards which the ratios of quantities decreasing without limit do always converge; and to which they approach nearer than by any given difference, but never go beyond, nor in effect attain to, till the quantities are diminished in infinitum. This thing will appear more evident in quantities infinitely great. If two quantities, those difference is given, be augmented in the ultimate ratio of these quantities will be given, to wit, the ratio of equality; but it does not from thence follow, that the ultimate or greatest quantities themselves, whose ratio that is, will be given. Therefore if in what follows, for the sake of being more easily understood, I should happen to mention quantities as least, or evanescent, or ultimate, you are not to suppose that quantities of any determinate magnitude are meant, but such as are conceived to be always diminished without end." [Principia] So you win the bet by disproving the existence of the logical limit for the smallest distance such as the Planck lenght and doing everyone else a favor in determining that a 1 dimensional line does not reduce to a zero dimensional point.You might even have some fun in the process as it is simple enough stuff that I introduced a few years ago. Draw a circumference around a Planck lenght,the circumference being of course 3.141... times greater than the lenght,if you can determine a circumference you can also determine a radius which is half the original lenght and from this discrete lenght you begin again constructing a circumference around this half Planck lenght and so diminishing without end.As long as the relationship between diameter/circumference/ radius and the Pi value holds,pi will always be an irrational number however assume a geometric limit and spend eternity trying to figure out what digit the Pi value ends in. Of course you are all mathematicians and all this stuff is beyond you,sorry. A few points for the discussion. The fact that Bohr's atom model was superseded did not hinder Bohr to embrace quantum theory later on, and to support Schrödinger and Heisenberg. Bohr told about the indivisibilty of the quantum of action in his Como lecture (Thus standard QT was already fully accepted) Niels Bohr, Atomtheorie und Naturbeschreibung, Springer, 1931, p. 16. More: N. Bohr, Atomic Physics and Human Knowledge, Science Editions, New York, 1961. And: M. Jammer, The Philosophy of Quantum Mechanics, Wiley, first edition, 1974, p. 90. ----- Note that any measurement disturbs the system. If action could be as small as possible, the disturbance could be as small as possible and thus be negligible, which it is not. There are no experiments with action values much below h-bar2. That is sure. Photons show this clearly. EVen if the Energy is very large or very small, there is a phase errror, and that gives an actiion error when measuring light action. ----- My explanation of the quantum action principle was only partly correct, I realize now. The action should be the modulus of < psi_1 | integral L dt | psi_2 > I guess. Schwinger also shows that the action is equal to simply h-bar/i < psi_1 | psi_2 > (Only endpoints are involved) . Taking the modulus, this looks to me as if action variation is equal hbar for a one particle system. Is this the result required? Heinz > A few points for the discussion. > > The fact that Bohr's atom model was superseded did not > hinder Bohr to embrace quantum theory later on, and to > support Schrödinger and Heisenberg. Yes. So what? > Bohr told about the indivisibilty of the quantum of action in his > Como lecture (Thus standard QT was already fully accepted) > Niels Bohr, Atomtheorie und Naturbeschreibung, Springer, 1931, > p. 16. That's a quite obscure reference, but I think I can dig it out. > More: N. Bohr, Atomic Physics and Human Knowledge, Science > Editions, New York, 1961. Not available to me. > And: M. Jammer, The Philosophy > of Quantum Mechanics, Wiley, first edition, 1974, p. 90. I think that's a reference I could dig out again. Thanks. > ----- > > Note that any measurement disturbs the system. Yes. > If action could be as small as possible, > the disturbance could be as small as possible Non sequitur. Why on earth do you think so? > and thus be negligible, which it is not. > > There are no experiments with action values much below h-bar2. Several people have already pointed out processes where the action would be smaller. So far, you ignored them. > That is sure. Photons show this clearly. > EVen if the Energy is very large or very small, > there is a phase errror, and that gives an actiion error when measuring > light action. Please tell us how one measures "light action". > My explanation of the quantum action principle was only partly correct, > I realize now. > > The action should be the modulus of < psi_1 | integral L dt | psi_2 > > I guess. You guess? Didn't you say that this is straight from Schwinger's book? > Schwinger also shows that the action is equal to simply > h-bar/i < psi_1 | psi_2 > (Only endpoints are involved) . > > Taking the modulus, this looks to me as if action > variation is equal hbar for a one particle system. Err, why do you think so? Usually |<psi_1 | psi_2>| won't give 1, but something lower, sometimes even zero! > Is this the result required? Would be news to me. Bye, Bjoern > A few points for the discussion. > [quoted text clipped - 6 lines] > Niels Bohr, Atomtheorie und Naturbeschreibung, Springer, 1931, > p. 16. I've dug up that reference. But neither action nor quantization seems to be mentioned on page 16. Did you perhaps mean another page, maybe page 60 or 61? Could you please quote the relevant passages? (in German or English, whatever you like) > More: N. Bohr, Atomic Physics and Human Knowledge, Science > Editions, New York, 1961. And: M. Jammer, The Philosophy > of Quantum Mechanics, Wiley, first edition, 1974, p. 90. I've dug up the second reference, and as far as I can see, Jammer (or Bohr, whom he quotes on that page) says only that when one talks about complementarity, measurement and the like (i.e. about Heisenberg's uncertainty principle), hbar has to be considered the smallest possible value (in the uncertainty relation). He does *not* say that action is quantized there. You should also consider that Bohr used the term "action integral" for oint p dx (integral over a closed orbit), not for int L dt, in his theory. So even if Bohr somewhere says that action is quantized, it doesn't follow automatically that int L dt is quantized. [snip] Bye, Bjoern >>>Which of the two is correct? >> [quoted text clipped - 10 lines] > any sum you want in case you find > such an experiment. Please tell me how one could measure action experimentally. > (To make it easy, > you do not even have to perform a real > experiment, or find a reference to one; > you just have to find a suitable Gedanken > experiment.) Take the motion of a free electron from one point to another. Since the time difference can be as small as you like (if we ignore possible quantization of time...), the action for that process can be as small as you like. > There is no such possibility. Wrong. > Fortunately. Huh? > So far, quantum theory is still correct. But quantum theory does not say that there is a smallest action. Only Bohr's quantum theory said that. And Bohr's theory is outdated since 79 years. Bye, Bjoern Oh, BTW, I asked you for references for your statement "There are several textbooks that make the point that there is a smallest action in nature." Where are they? Bye, Bjoern [snip] > Oh. If you say that there is no smallest action, > you would have to provide an experiment [quoted text clipped - 13 lines] > There is no such possibility. Fortunately. > So far, quantum theory is still correct. Pay up guy. Photons can have arbitrary energy. Thus it is possible for a free electron to transition between any two kinetic energies, arbitrarily close together. You can give the money to your local cancer society. Socks > In Feynman's path integral approach, equivalent to wave mechanics, one > assumes that the particle follows all possible trajectories. Not just > taking off from some starting point with all possible angles, but > following paths that loop around in all possible shapes. This is great stuff - and really sounds alot like trivialities which crop up when delta_t=0. Existence becomes trivial. And if existence is also relative to an observer - Feynman integral makes perfect sense. > > Oh. If you say that there is no smallest action, > > you would have to provide an experiment [quoted text clipped - 8 lines] > > Please tell me how one could measure action experimentally. It has already been done - but the experiments were all misinterpreted because nobody really understands time. Instead of relativism, we have "multiplicities of universes" and mountains of fluff. There is a smallest action - relative to an observer. In an absolute sense, however, it is yet even more impossible to determine that question. [snip] >>Please tell me how one could measure action experimentally. > > It has already been done - but the experiments were all misinterpreted > because nobody really understands time. Please give more details. What experiments, specifically, measured action, how did they do that, and what were the results? [snip] > There is a smallest action - relative to an observer. And what is that supposed to mean? [snip] Bye, Bjoern > [snip] > [quoted text clipped - 5 lines] > Please give more details. What experiments, specifically, measured > action, how did they do that, and what were the results? see- http://www.nyu.edu/classes/neimark/SPOOK1.HTM ======================== The twin-photon experiment by Dr. Nicolas Gisin of the University of Geneva and his colleagues last month was the most spectacular demonstration yet of the mysterious long-range connections that exist between quantum events, connections created from nothing at all, which in theory can reach instantaneously from one end of the universe to the other. In essence, Dr. Gisin sent pairs of photons in opposite directions to villages north and south of Geneva along optical fibers of the kind used to transmit telephone calls. Reaching the ends of these fibers, the two photons were forced to make random choices between alternative, equally possible pathways. Since there was no way for the photons to communicate with each other, "classical" physics would predict that their independent choices would bear no relationship to each other. But when the paths of the two photons were properly adjusted and the results compared, the independent decisions by the paired photons always matched, even though there was no physical way for them to communicate with each other. ======================== This proves alot, but is misinterpreted. > > There is a smallest action - relative to an observer. > > And what is that supposed to mean? On an absolute sense, there is probably no smallest action. But, relative to an observer, there is a limit and it is h-bar. > Bye, > Bjoern >>[snip] >> [quoted text clipped - 26 lines] > them to communicate with each other. > ======================== Please tell me how that experiment measured action. What were the results of the measurement? Please give some numbers. > This proves alot, but is misinterpreted. Feel free to give your own interpretation, and tell me what is proved here in your opinion. >>>There is a smallest action - relative to an observer. >> >>And what is that supposed to mean? > > On an absolute sense, there is probably no smallest action. But, relative to > an observer, there is a limit and it is h-bar. Merely repeating the statement doesn't make it clearer. Bye, Bjoern Just to make it clear: the issue with my cousin is not whether action is quantized - we have no opinion in the matter. The issue is whether the smallest value is h-bar or h-bar/2. For bound systems, the action is surely never smaller that h-bar. The incorrec and simpistic theory by Bohr can be made rigourous and then is called "Einstein-Brillouin-Keller quantization". See the American J. of Physics, 72, 1521-1523, 2004. For unbouns systems, we know of no experiments that allows to measure actions smaller than hbar/2. For example, in a laser beam, where action is given by \int D d phi (D= angular momentum |
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