Re: a question about conservation and photons
- From: Tom Roberts <tjroberts@xxxxxxxxxx>
- Date: Sun, 30 Oct 2005 17:24:52 GMT
bz wrote:
The laws of conservation should(must), of course, apply at all times, during the emission, propagation and absorbtion of a photon.
Reading "light pulse" for "photon", in classical electrodynamics there is no problem -- the fields carry energy and momentum, and the appropriate integrals over all of space are constant (i.e. total energy and momentum are exactly conserved). I believe this can be shown as a general theorem using Maxwell's equations, without making detailed computations for any specific physical situation.
So I assume your question is one of the few instances around here that is truly in the context of quantum field theory (which I will take as QED). This means that the quantum nature of photons becomes important.
In QED the comparable integrals over all of space make no sense. For instance, the "number of photons present" is not a good quantum number, and you cannot count them (in general, such as this discussion). Remember, too, that in the configuration-space representation one must integrate over all possible times for each and every vertex, and then (anti-)symmetrize over all (Fermions)Bosons. This, too, makes the notion of "the configuration of the system at a given instant in time" meaningless. Remember the usual dictum to discuss only MEASURABLE quantities, and you'll realize you cannot measure the "configuration of the system" as would be necessary for this classical notion to apply.
So just as in GR, but for a VERY different reason, the theory has only LOCAL conservation of energy and momentum. In QED this is expressed in the 4-d Dirac Delta function at every vertex that requires total 4-momentum to be conserved.
This would seem to join widely separated (by time and/or distance) items together into a 'system'.
It's not really possible to do that, at least usefully. To be useful such a "system" must have definite quantities "at a given instant in time", and QED does not really permit that (see above).
Just think about it -- you don't really know precisely "when" a given detector detects a photon, because Heisenberg's uncertainty principle applies. Ditto for a source's emission. Ditto for "where" a "given" photon is "located" at a given time (words in quotes are PUNs and are not really well defined -- a consequence of attempting to discuss unmeasurable quantities).
For instance, the question of where does the doppler shift occur? Can it be answered or can we at least be sure that the question is meaningless?
It occurs between source and detector. Remember the usual dictum to discuss only MEASURABLE quantities, and you'll realize you don't need to worry about the more detailed questions you attempt to ask.
I don't imagine that I am the first to ask such questions. Where should I look for answers? What do I need to know to understand where this may go?
Try:
Feynman, _QED_. This is a nonmathematical introduction to QED.
Tom Roberts tjroberts@xxxxxxxxxx .
- Prev by Date: Re: OWLS & Out of Sync Clocks-& By _How Much_ Are They Out of Sync.
- Next by Date: Re: Time dilatation and a space referential
- Previous by thread: Re: a question about conservation and photons
- Next by thread: Re: a question about conservation and photons
- Index(es):
Relevant Pages
|
|
