Seasons
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I said that the wave interacts with the detector in a punctiliar fashion
Well, assuming you mean punctiliar to imply some sort of teleportation effect (because, truth to tell, I've only ever heard the word used linguistically to describe verbal aspect, so I'm not totally sure of its intended application here,) - whereby the photon moves from A to C without passing through B, the problem remains that interference generated by the passage of this quantum through both the slits at B occurs. If it had bypassed this altogether, I cannot see that the recorded interference could occur. Or am I missing something?
Now, as to the photoelectric effect:
My claim is that Einstein's explanation of the photoelectric effect requires only that the energy gained by the electrons be quantized in accord with the Planck-Einstein relations, which in turn follow from the appropriate form of the Schroedinger Equation (postulate 5, which I should also have mentioned in connection with the two-slit experiment, since it is the wave equation - my bad!), with a little help from some of the othe postulates. The problem was, that the ability of light to free electrons seemed to depend on frequency, which Classical Physics claimed to be irrelevant. Einstein's solution was, that according to Planck's hypothesis, E=hf (Energy of a packet = Planck's constant times frequency) , packets of low-frequency light didn't have the energy to free an electron. This is, however, entirely a matter of what goes on at the electrode itself - it says nothing about how the photons get there. In this case the electrons are playing the role of (photon) detectors.
So we have a local, punctiliar interaction - perfectly compatible with my interpretation.
BTW, I want to state that I rather like you, Psimagus, and that I think you are one of the most intelligent people I ever met; I would not be at all surprised to learn that you are in the 99.9 percentile.
Aww! *blush*
Likewise, and you're a pleasure to argue with (I love a good argument - you'd probably noticed
)
I'm sure we're arguing the same position (because I believe that everyone fundamentally is,) but a little dharma combat over the viewpoint is always fun.
Alas, I must away to work now (but I'll come back to the QM tomorrow
Posts 3,774 - 3,785 of 6,170
What I actually said was:
A wave goes through two slits and is diffracted. It interacts with the detector screen in a punctiliar, probabilistic fashion. There is no particle that travels in a continuous trajectory (or several) from the source to the screen.
You write:
All of it goes through both slits simultaneously. No-one knows exactly why or how, but it is evident that it does.
If you disagree with someone, what is the point of saying, "it is evident" that your side is correct? Clearly it is NOT evident to the person you are talking to. Instead, you should give evidence for your position.
I am disappointed. I thought you were going to derive your position from the postulates of Quantum Mechanics. Instead, you are just making dogmatic claims. Can you give me a footnote to some text of Quantum Mechanics, saying that it must be the case that the photon goes through both slits? I can find no such claim in Cohen-Tannoudji et al., nor in the detailed account of the two-slit experiment in Feynmann's Lectures on Physics. Yes, I am prepared to believe that there are some interpretations of QM according to which it is literally true that the photon goes through both slits. The question is, which interpretation (if any) is correct? [The dominant interpretation, last I heard, was the Copenhagen, which would consider the question of whether the particle goes through both slits to be meaningless.]
In the two-slit experiment, we get an interference pattern (when both slits are open) because the wave, Psi (postulate 1) is a wave, and waves diffract when they go through slits, and interfere. We can predict with great accuracy exactly what the resulting interference pattern will look like, given the frequency and velocity of the wave, and this agrees closely with experiment.
On the other hand, how does the assumption that the photon goes through both slits simultaneously predict the interference pattern? Even if a particle could perform the neat trick of going through two distinct slits simultaneously, where would the diffraction/interference pattern come from? You could say that a photon is a special sort of particle that diffracts and interferes. In short, a particle that behaves just like a wave. Why not just call it a wave?
Ok, so the wave diffracts and interferes, and comes to the detector. Then (still postulate 1) the amplitude (modulus) of the wave determines the probability that the particle will appear at a given point on the detector. If we turn the amplitude down sufficiently, we will be able to see individual points of light on the detector. This is the 'particle aspect' of light. I recognized its existence when I said that the wave interacts with the detector in a punctiliar fashion. When you revised my statement to read, "light comes only in waves," you dropped this out (and much else besides. This punctiliar quality manifests at the detector - it does not manifest at the slits.
And this is generally true of quantum mechanics - the wave, Psi, is a continuous phenomenon whose amplitude reflects the probability of a local, punctiliar event. Again, see postulate 1. Now, please tell me which postulates imply that the particle goes through both slits.
A wave goes through two slits and is diffracted. It interacts with the detector screen in a punctiliar, probabilistic fashion. There is no particle that travels in a continuous trajectory (or several) from the source to the screen.
You write:
All of it goes through both slits simultaneously. No-one knows exactly why or how, but it is evident that it does.
If you disagree with someone, what is the point of saying, "it is evident" that your side is correct? Clearly it is NOT evident to the person you are talking to. Instead, you should give evidence for your position.
I am disappointed. I thought you were going to derive your position from the postulates of Quantum Mechanics. Instead, you are just making dogmatic claims. Can you give me a footnote to some text of Quantum Mechanics, saying that it must be the case that the photon goes through both slits? I can find no such claim in Cohen-Tannoudji et al., nor in the detailed account of the two-slit experiment in Feynmann's Lectures on Physics. Yes, I am prepared to believe that there are some interpretations of QM according to which it is literally true that the photon goes through both slits. The question is, which interpretation (if any) is correct? [The dominant interpretation, last I heard, was the Copenhagen, which would consider the question of whether the particle goes through both slits to be meaningless.]
In the two-slit experiment, we get an interference pattern (when both slits are open) because the wave, Psi (postulate 1) is a wave, and waves diffract when they go through slits, and interfere. We can predict with great accuracy exactly what the resulting interference pattern will look like, given the frequency and velocity of the wave, and this agrees closely with experiment.
On the other hand, how does the assumption that the photon goes through both slits simultaneously predict the interference pattern? Even if a particle could perform the neat trick of going through two distinct slits simultaneously, where would the diffraction/interference pattern come from? You could say that a photon is a special sort of particle that diffracts and interferes. In short, a particle that behaves just like a wave. Why not just call it a wave?
Ok, so the wave diffracts and interferes, and comes to the detector. Then (still postulate 1) the amplitude (modulus) of the wave determines the probability that the particle will appear at a given point on the detector. If we turn the amplitude down sufficiently, we will be able to see individual points of light on the detector. This is the 'particle aspect' of light. I recognized its existence when I said that the wave interacts with the detector in a punctiliar fashion. When you revised my statement to read, "light comes only in waves," you dropped this out (and much else besides. This punctiliar quality manifests at the detector - it does not manifest at the slits.
And this is generally true of quantum mechanics - the wave, Psi, is a continuous phenomenon whose amplitude reflects the probability of a local, punctiliar event. Again, see postulate 1. Now, please tell me which postulates imply that the particle goes through both slits.
My apologies, I must have misinterpreted your position. But you did say
"A wave goes through two slits and is diffracted."
And since
A) the integral premise of quantum theory is that stuff comes in indivisible units (quanta), and since
B) photons are such units,
I can't see how you can argue that this unitary "thing" (be it wave, particle, or anything else,) does not pass in its entirety through both slits simultaneously. How else can the interference possibly occur? Or do you disagree with (A) or (B)?
"A wave goes through two slits and is diffracted."
And since
A) the integral premise of quantum theory is that stuff comes in indivisible units (quanta), and since
B) photons are such units,
I can't see how you can argue that this unitary "thing" (be it wave, particle, or anything else,) does not pass in its entirety through both slits simultaneously. How else can the interference possibly occur? Or do you disagree with (A) or (B)?
Well, assuming you mean punctiliar to imply some sort of teleportation effect (because, truth to tell, I've only ever heard the word used linguistically to describe verbal aspect, so I'm not totally sure of its intended application here,) - whereby the photon moves from A to C without passing through B, the problem remains that interference generated by the passage of this quantum through both the slits at B occurs. If it had bypassed this altogether, I cannot see that the recorded interference could occur. Or am I missing something?
Now, as to the photoelectric effect:
My claim is that Einstein's explanation of the photoelectric effect requires only that the energy gained by the electrons be quantized in accord with the Planck-Einstein relations, which in turn follow from the appropriate form of the Schroedinger Equation (postulate 5, which I should also have mentioned in connection with the two-slit experiment, since it is the wave equation - my bad!), with a little help from some of the othe postulates. The problem was, that the ability of light to free electrons seemed to depend on frequency, which Classical Physics claimed to be irrelevant. Einstein's solution was, that according to Planck's hypothesis, E=hf (Energy of a packet = Planck's constant times frequency) , packets of low-frequency light didn't have the energy to free an electron. This is, however, entirely a matter of what goes on at the electrode itself - it says nothing about how the photons get there. In this case the electrons are playing the role of (photon) detectors.
So we have a local, punctiliar interaction - perfectly compatible with my interpretation.
Well, I still don't understand what you mean by punctiliar. The Concise OED doesn't give it at all (it's clearly not related to "punctate" = 'Biol. studded with points' or "punctilio/punctilious" = 'attentive to formality or etiquette',) and I sadly don't have my full OED available (lost the dongle 
) And when I type "define punctiliar" into google, I just get lots about the Greek Aorist tense, and indications that it's some sort of synonym for "momentary", or possibly even "instantaneous". My own conception of its linguistic meaning would be more like "timeless" (or "unfixed in time", or something.) Since the speed of light is neither infinite nor varied by the presence of slitted obstacles in the photon's path, I doubt you mean any of these meanings. Could you elucidate?
) And when I type "define punctiliar" into google, I just get lots about the Greek Aorist tense, and indications that it's some sort of synonym for "momentary", or possibly even "instantaneous". My own conception of its linguistic meaning would be more like "timeless" (or "unfixed in time", or something.) Since the speed of light is neither infinite nor varied by the presence of slitted obstacles in the photon's path, I doubt you mean any of these meanings. Could you elucidate?
Actually, IMCO, the strongest evidence for trajectories comes from scattering, e.g., Compton Scattering.
The strongest evidence against trajectories, IMCO, comes from quantum tunneling. We have a producer of photons, completely surrounded by an unbroken region in which it is impossible for a photon to exist. Outside this barrier, there is a photon detector. There turns out to be a small but non-zero probability that a photon will appear at the detector. How can this be reconciled with the claim that the photon travels in a continuous trajectory?
The term "tunneling" is actually a little misleading, since it suggests that the photon made a hole in the barrier. But this is not so. In quantum tunneling, the barrier remains intact.
The strongest evidence against trajectories, IMCO, comes from quantum tunneling. We have a producer of photons, completely surrounded by an unbroken region in which it is impossible for a photon to exist. Outside this barrier, there is a photon detector. There turns out to be a small but non-zero probability that a photon will appear at the detector. How can this be reconciled with the claim that the photon travels in a continuous trajectory?
The term "tunneling" is actually a little misleading, since it suggests that the photon made a hole in the barrier. But this is not so. In quantum tunneling, the barrier remains intact.
Because the photon is in two places at once. Just as it is when it passes through both slits in the diffraction grating. Doesn't this prove my point?
Ah, I'm sorry about "punctiliar" - it means, "having the form of (or like) a point." (Latin punctum, point) That was poor communication on my part! [Punishes self by swearing off sex for 2 hours.]
It applies to QM in this way: If you have a bright (intense) beam of 'particles', and you pass it through (e.g.) two slits, then the screen behind the slits shows an interference pattern, which is a continuous pattern of varying brightness. This would suggest that you are simply dealing with a wave. BUT if you turn the intensity down, then you see, not just the same pattern at lower intensity, but individual points (as if the screen were being hit by minute particles). However, the individual points appear more often in the areas which were brighter when the beam was high. Otherwise, they appear to be randomly distributed: we cannot predict where the next one is going to be. This gives rise to the following model (postulate 1) : the intensity of the wave at a point on the detector is proportional to the probability of the appearance of a dot. The pattern appears to be continuous at high intensity only because there are so many dots, coming so fast, that we don't see the individual dots.
Because the wave 'carries' the probability, it is often called the 'probability amplitude wave.' Since it is a wave, it diffracts and inteferes.
BTW, I want to state that I rather like you, Psimagus, and that I think you are one of the most intelligent people I ever met; I would not be at all surprised to learn that you are in the 99.9 percentile. If I didn't think you were smart, I wouldn't bother to argue with you. I am also awed by your generous spirit, as manifested by all the help you give to people on the Forge, including me. Please do no misinterpret my opposition to certain of your opinions as an opposition to you personally!!!!!!!!
It applies to QM in this way: If you have a bright (intense) beam of 'particles', and you pass it through (e.g.) two slits, then the screen behind the slits shows an interference pattern, which is a continuous pattern of varying brightness. This would suggest that you are simply dealing with a wave. BUT if you turn the intensity down, then you see, not just the same pattern at lower intensity, but individual points (as if the screen were being hit by minute particles). However, the individual points appear more often in the areas which were brighter when the beam was high. Otherwise, they appear to be randomly distributed: we cannot predict where the next one is going to be. This gives rise to the following model (postulate 1) : the intensity of the wave at a point on the detector is proportional to the probability of the appearance of a dot. The pattern appears to be continuous at high intensity only because there are so many dots, coming so fast, that we don't see the individual dots.
Because the wave 'carries' the probability, it is often called the 'probability amplitude wave.' Since it is a wave, it diffracts and inteferes.
BTW, I want to state that I rather like you, Psimagus, and that I think you are one of the most intelligent people I ever met; I would not be at all surprised to learn that you are in the 99.9 percentile. If I didn't think you were smart, I wouldn't bother to argue with you. I am also awed by your generous spirit, as manifested by all the help you give to people on the Forge, including me. Please do no misinterpret my opposition to certain of your opinions as an opposition to you personally!!!!!!!!
Ah, I'm sorry about "punctiliar" - it means, "having the form of (or like) a point." (Latin punctum, point) That was poor communication on my part! [Punishes self by swearing off sex for 2 hours.]
It applies to QM in this way: If you have a bright (intense) beam of 'particles', and you pass it through (e.g.) two slits, then the screen behind the slits shows an interference pattern, which is a continuous pattern of varying brightness. This would suggest that you are simply dealing with a wave. BUT if you turn the intensity down, then you see, not just the same pattern at lower intensity, but individual points (as if the screen were being hit by minute particles). However, the individual points appear more often in the areas which were brighter when the beam was high. Otherwise, they appear to be randomly distributed: we cannot predict where the next one is going to be. This gives rise to the following model (postulate 1) : the intensity of the wave at a point on the detector is proportional to the probability of the appearance of a dot. The pattern appears to be continuous at high intensity only because there are so many dots, coming so fast, that we don't see the individual dots.
Because the wave 'carries' the probability, it is often called the 'probability amplitude wave.' Since it is a wave, it diffracts and inteferes.
BTW, I want to state that I rather like you, Psimagus, and that I think you are one of the most intelligent people I ever met; I would not be at all surprised to learn that you are in the 99.9 percentile. If I didn't think you were smart, I wouldn't bother to argue with you. I am also awed by your generous spirit, as manifested by all the help you give to people on the Forge, including me. Please do no misinterpret my opposition to certain of your opinions as an opposition to you personally!!!!!!!!
It applies to QM in this way: If you have a bright (intense) beam of 'particles', and you pass it through (e.g.) two slits, then the screen behind the slits shows an interference pattern, which is a continuous pattern of varying brightness. This would suggest that you are simply dealing with a wave. BUT if you turn the intensity down, then you see, not just the same pattern at lower intensity, but individual points (as if the screen were being hit by minute particles). However, the individual points appear more often in the areas which were brighter when the beam was high. Otherwise, they appear to be randomly distributed: we cannot predict where the next one is going to be. This gives rise to the following model (postulate 1) : the intensity of the wave at a point on the detector is proportional to the probability of the appearance of a dot. The pattern appears to be continuous at high intensity only because there are so many dots, coming so fast, that we don't see the individual dots.
Because the wave 'carries' the probability, it is often called the 'probability amplitude wave.' Since it is a wave, it diffracts and inteferes.
BTW, I want to state that I rather like you, Psimagus, and that I think you are one of the most intelligent people I ever met; I would not be at all surprised to learn that you are in the 99.9 percentile. If I didn't think you were smart, I wouldn't bother to argue with you. I am also awed by your generous spirit, as manifested by all the help you give to people on the Forge, including me. Please do no misinterpret my opposition to certain of your opinions as an opposition to you personally!!!!!!!!
You have to remember that if the photon is in several places at once, the "trajectory" is not going to be a neat straight line - it's going to be a probability cone (or cylinder? hmm, I'm not sure,) I certainly don't claim that it moves like a billiard ball along a classical path (obviously if it did, it couldn't be in two places at once,) but it must nonetheless move (I hope we can agree on that!) And it does so at a constant fixed velocity, so that the time taken is exactly proportional to the distance between the two points we locate it. You seem to be implying some sort of arbitrary teleportation/"hopping" from point to point? That would be hard to square with a fixed speed of light, surely?
In quantum tunneling, it can appear on the wrong side of a boundary precisely because the barrier is thin enough to be straddled by the probability cone(/cylinder.) So sometimes you're bound to see the electron on the wrong side of it.
In quantum tunneling, it can appear on the wrong side of a boundary precisely because the barrier is thin enough to be straddled by the probability cone(/cylinder.) So sometimes you're bound to see the electron on the wrong side of it.
Aww! *blush*
Likewise, and you're a pleasure to argue with (I love a good argument - you'd probably noticed
)I'm sure we're arguing the same position (because I believe that everyone fundamentally is,) but a little dharma combat over the viewpoint is always fun.
Alas, I must away to work now (but I'll come back to the QM tomorrow
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