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Idunno
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- TL;DR Summary
- Is it consistent with quantum mechanics to say that quantum objects are instantly reformable, real, wave packets? Also, might collapse be related to energy density of a packet going over threshold?
Hello,
I am a high school physics teacher, and I have been thinking about a way to model quantum mechanics in an intuitive way in order to teach it better, but I don't want to lead my students down the wrong path. I am certainly no expert in quantum theory. In looking at the guidelines, I realize this might not be postable, as it probably comes under the category of a “personal theory”, but I don’t really have any other avenue to ask this. I showed it to some people (experimentalists) at my local university, and they said “you need to talk to a theorist”. Problem is, I don’t know any theorists, and the ones at my university all seem too busy. So I’m hoping to get some help here.
What I have come up with boils down to two questions:
Question (1) Is it consistent with Quantum Mechanics to say that quantum objects (photons, electrons, protons, etc.) are instantly reformable, real, wave packets?
To clarify this as best I can, by "real," I mean that energy exists wherever the wave packet is not cancelling itself out. So that, if a wave packet is split into two, or becomes very big, it can nevertheless instantly reform (shrink (or expand?) upon measurement conditions) and thus instantly move energy about itself? Notice this instantaneous movement of energy is "internal" to the "particle" and not instantaneous movement from particle to particle.
In this view, all the energy of the wave packet is part of "one thing" so that if it reforms to a small spot, all the energy of the quantum object instantly goes to that spot. This would be the main sense that it is a "particle" (it's all together), but, otherwise, the idea of a “particle” doesn't fit too well, as instead of thinking that there is an infinitesimal billiard ball like object moving about that the wavefunction mysteriously influences the path of, you take wavefunctions as real things that are instantly reformable, they can become as small as you want when you measure them and they shrink.
Of course, I am no expert, but to my mind the main issue with this view is that energy moves instantly, which on the surface seems to violate relativity. However, this seems like it would be OK, since it is internal to the "particle" and not instantaneous transmission from particle to particle? It seems like the reasons that make entanglement consistent with relativity would apply to this?
Question (2): Is it possible that the reason why packets instantly reform (wavefunction collapse) is that the energy density goes over some threshold?
To clarify, assuming that the answer to question (1) is yes, I am wondering about what seems like an obvious question (which I've never seen addressed anywhere). In a classical wave, the energy is proportional to the squared amplitude. In QM, the squared amplitude relates to the probability of finding a particle in some region. Might there be a connection? It seems to me that the simplest way that there might be a connection is that if the energy density of a region of the wave packet goes over some threshold (gets "too high") then this might trigger collapse. I don't know what this threshold might be, but if it's true, it seems to explain a lot to my undereducated mind. It's like the wave packet gets out of equilibrium when the energy density gets too high, and this triggers collapse.
Take the example of a wave packet (photon) coming towards a detector. The detector is modeled as a bunch of electron wave packets confined to boxes. Assume all the detector electrons are not in sync, they are all independent with different timing. As the photon wave packet starts to mingle with the detector electrons it interferes constructively and destructively. The idea is that if there is a "good" phase match in some region, then the energy density increases in that region. If the phase match is good enough, then the photon will go over threshold and the wave packet will instantly reform to that region. In the middle of the wave packet the amplitude is intrinsically higher, so the idea is that it is more likely that that region will go over threshold, since an "OK" phase match will take it over threshold, but on the edge of the packet, where the intrinsic amplitude is less, you need a very good phase match to take it over threshold and collapse the packet to that region, so it happens less often on the edge of the packet. I naively imagine that a similar scheme would apply to an electron packet coming towards a detector, where the interaction is mediated by virtual photons, which I know little about.
If the probability of getting a good phase match is the same throughout the packet interfering with the detector, then the probability of collapse (with detector electrons that are not in sync, with a random distribution in their timing) to a region is proportional to the energy density, which, classically is proportional to the squared amplitude. Thus you get a reason for the Born rule with this scheme.
You also get a reason for randomness and unpredictability with this scheme. If you cannot know the relative timing of two wave packets, you cannot predict where and when a packet will go over threshold.
There is more to be said about all this, but I should stop here, as I don't want to make too long of a post. So, please tell me how this sounds. If it is consistent with QM, it seems like an intuitive model for QM to my mind, and you get a reason for randomness, which seems good. To be abundantly clear, I'm far from an expert in QM, just asking.
I am a high school physics teacher, and I have been thinking about a way to model quantum mechanics in an intuitive way in order to teach it better, but I don't want to lead my students down the wrong path. I am certainly no expert in quantum theory. In looking at the guidelines, I realize this might not be postable, as it probably comes under the category of a “personal theory”, but I don’t really have any other avenue to ask this. I showed it to some people (experimentalists) at my local university, and they said “you need to talk to a theorist”. Problem is, I don’t know any theorists, and the ones at my university all seem too busy. So I’m hoping to get some help here.
What I have come up with boils down to two questions:
Question (1) Is it consistent with Quantum Mechanics to say that quantum objects (photons, electrons, protons, etc.) are instantly reformable, real, wave packets?
To clarify this as best I can, by "real," I mean that energy exists wherever the wave packet is not cancelling itself out. So that, if a wave packet is split into two, or becomes very big, it can nevertheless instantly reform (shrink (or expand?) upon measurement conditions) and thus instantly move energy about itself? Notice this instantaneous movement of energy is "internal" to the "particle" and not instantaneous movement from particle to particle.
In this view, all the energy of the wave packet is part of "one thing" so that if it reforms to a small spot, all the energy of the quantum object instantly goes to that spot. This would be the main sense that it is a "particle" (it's all together), but, otherwise, the idea of a “particle” doesn't fit too well, as instead of thinking that there is an infinitesimal billiard ball like object moving about that the wavefunction mysteriously influences the path of, you take wavefunctions as real things that are instantly reformable, they can become as small as you want when you measure them and they shrink.
Of course, I am no expert, but to my mind the main issue with this view is that energy moves instantly, which on the surface seems to violate relativity. However, this seems like it would be OK, since it is internal to the "particle" and not instantaneous transmission from particle to particle? It seems like the reasons that make entanglement consistent with relativity would apply to this?
Question (2): Is it possible that the reason why packets instantly reform (wavefunction collapse) is that the energy density goes over some threshold?
To clarify, assuming that the answer to question (1) is yes, I am wondering about what seems like an obvious question (which I've never seen addressed anywhere). In a classical wave, the energy is proportional to the squared amplitude. In QM, the squared amplitude relates to the probability of finding a particle in some region. Might there be a connection? It seems to me that the simplest way that there might be a connection is that if the energy density of a region of the wave packet goes over some threshold (gets "too high") then this might trigger collapse. I don't know what this threshold might be, but if it's true, it seems to explain a lot to my undereducated mind. It's like the wave packet gets out of equilibrium when the energy density gets too high, and this triggers collapse.
Take the example of a wave packet (photon) coming towards a detector. The detector is modeled as a bunch of electron wave packets confined to boxes. Assume all the detector electrons are not in sync, they are all independent with different timing. As the photon wave packet starts to mingle with the detector electrons it interferes constructively and destructively. The idea is that if there is a "good" phase match in some region, then the energy density increases in that region. If the phase match is good enough, then the photon will go over threshold and the wave packet will instantly reform to that region. In the middle of the wave packet the amplitude is intrinsically higher, so the idea is that it is more likely that that region will go over threshold, since an "OK" phase match will take it over threshold, but on the edge of the packet, where the intrinsic amplitude is less, you need a very good phase match to take it over threshold and collapse the packet to that region, so it happens less often on the edge of the packet. I naively imagine that a similar scheme would apply to an electron packet coming towards a detector, where the interaction is mediated by virtual photons, which I know little about.
If the probability of getting a good phase match is the same throughout the packet interfering with the detector, then the probability of collapse (with detector electrons that are not in sync, with a random distribution in their timing) to a region is proportional to the energy density, which, classically is proportional to the squared amplitude. Thus you get a reason for the Born rule with this scheme.
You also get a reason for randomness and unpredictability with this scheme. If you cannot know the relative timing of two wave packets, you cannot predict where and when a packet will go over threshold.
There is more to be said about all this, but I should stop here, as I don't want to make too long of a post. So, please tell me how this sounds. If it is consistent with QM, it seems like an intuitive model for QM to my mind, and you get a reason for randomness, which seems good. To be abundantly clear, I'm far from an expert in QM, just asking.