The dE/dt of QM

  • #1
Ivan Seeking
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Main Question or Discussion Point

Perhaps this is an easy one for you experts our there. When we consider an electron that occupies some local and small region of space, and then we assume that this electron [if it means anything to talk about a particular one] is un-measured - back in an unknown state- but that by the laws of physics it must still exist with some radius of our local space Ct, where t is the time since our last measurement of the position of charge q, and that this electron then disappears from this local space due to some quantum fluctuation, or by some other acceptable mechanism allowed by Quantum Theory [I don't claim to understand what I'm into here]. Then what about the dE/dt of local space - E being the electric field of local space? Do we require that time is quantized here, or can dE/dt become infinite? Am I way off track here? It seems to me - based on my limited understanding of such strange stuff - that this situation is allowed. But it also seems that if it ever did happen and we would all go to infinitely magnetic...which would seem to be a problem. But I also understand that quantized time is still considered an unresolved proposition. Enlightenment please?
 
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Answers and Replies

  • #2
damgo
Plain old quantum mechanics is not relativistic -- an electron measured to be at a particular position is not constrained to be within its light-cone in QM, which gives you some tiny probability of it being anywhere at finite time (nothing goes infinite.)

Of course this is incorrect. If you want to really talk about the electric field, you need to quantize that, and switch to quantum field theory (QFT.) This is usually required for highly relativistic systems, too, because those often create/destroy particles which is not allowed in regular QM.
 
  • #3
Ivan Seeking
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OK. But given QFT or whatever proper option to address this issue, how do we avoid infinities due to the quantum nature of charge. Is the explanation quantized time, or is this a matter of properly interpreting the collapse of the wave function of the charge.... I can't get past the problem that if charge is here and then not, i.e. if the wave function for the charge that was just here suddenly collapses at some distant location, which I think is allowed by some quantum processes, then it seems that something must save us from infinities. What? Time is the only thing that comes to mind
 
  • #4
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I consider, that your problem needs to be connected with moving of electron in magnetic field and to consider an electron, as one electromagnetic wave, which is closed as a ring.
In figure is shown frame with the current, which creates inwardly of frame homogeneous magnetic field. Shall conditionally consider, that this is so. Inwardly of frame there is moving ring with current J.
I can think that in the left part of ring a velocity of positive charges vj is totalized to the speed of moving of ring v. In this case, the ring will be move to the left.
I can think that in the right part of ring a velocity of electrons is totalized to the speed of moving of ring v. In this case, the ring will be move to the right.
I can think that both processes go simultaneously. In this case, the ring will not be move, nor to the left, nor to the right.
By the way, answer to this technical question till now is absent.
http://www.sibnet.ru/~polytron/mag_2.gif [Broken]
 
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  • #5
damgo
I can't get past the problem that if charge is here and then not, i.e. if the wave function for the charge that was just here suddenly collapses at some distant location, which I think is allowed by some quantum processes, then it seems that something must save us from infinities.
Nope, if I understand your question correctly. Supposedly when a measurement is done, collapse is instantaneous, so you would have infinite derivatives of some quantities. The idea of measurement is sort of an abstraction/idealization, so you might be able to argue that there are no real infinities -- but that's beyond my knowledge.

However, if an electron were to be instantaneously annihilated, it's not like the EM field around it would just disappear -- it would decay, but not instantaneously. I think you could figure out exactly how just by playing with Maxwell's equations and boundary conditions, but I'm not sure.
 
  • #6
Ivan Seeking
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Originally posted by damgo
Nope, if I understand your question correctly. Supposedly when a measurement is done, collapse is instantaneous, so you would have infinite derivatives of some quantities. The idea of measurement is sort of an abstraction/idealization, so you might be able to argue that there are no real infinities -- but that's beyond my knowledge.

However, if an electron were to be instantaneously annihilated, it's not like the EM field around it would just disappear -- it would decay, but not instantaneously. I think you could figure out exactly how just by playing with Maxwell's equations and boundary conditions, but I'm not sure.
Yes. As soon as you mentioned decay I wondered why this was not immediately obvious to me. Then I realized that I am recalling a statement by an undergrad prof who commented that if a charge was to simply disappear, the entire universe would be annihilated. [I think this is also supposed to happen with the intersection of two perfect EM plane waves...luckily nothings perfect]. Perhaps this comes from an outdated idea? I have no idea where he got this. Any ideas?
 

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