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Since we know the precise velocity of any photon, does that mean it's location is always undeterminable?
We know precise speed(in vacuum), not velocity. And yes we cannot know exactly where the photon is.Since we know the precise velocity of any photon, does that mean it's location is always undeterminable?
explain?The position of photon is more mysterious than the mere uncertainty principle might suggest, however.
Isn't the speed still the same in another medium, just interrupted by electron interaction?We know precise speed(in vacuum), not velocity. And yes we cannot know exactly where the photon is.
AFAIK, the photons of visible light do not have enough energy to excite the electrons of a transparent material. The photons just pass through having lower speed.Isn't the speed still the same in another medium, just interrupted by electron interaction?
Well then I guess Feynman was mistaken.AFAIK, the photons of visible light do not have enough energy to excite the electrons of a transparent material. The photons just pass through having lower speed.
The uncertainty relation is derived from the commutation relation for the position and momentum operators (see this post), but there is no position operator for photons. There are mathematical theorems that tell us that it's impossible to define one.explain?
What did Feynman think about that?Well then I guess Feynman was mistaken.
doesn't matter, my question is about the position of photons as they travel.What did Feynman think about that?
Anyway it is impossible to express transparency as absorption/re-emission, because there will be discrete spectrum of the possible state transitions of the electrons. And we clearly have continuous spectrum.
The uncertainty relation is derived from the commutation relation for the position and momentum operators (see this post), but there is no position operator for photons. There are mathematical theorems that tell us that it's impossible to define one.
I'm not so sure about that. Can you provide a reference?There is actually no guarantee that light moves at the speed of light. It's more LIKELY to do so, but it's not a rule.
That can be said about massive particles too. To be honest I don't fully understand what the result that there's no position operator for massless particles really means.So can it be said photons aren't anywhere until they are absorbed?
If the term "photon" is defined by QED, then they are massless by definition, and the claim that they might have mass doesn't make sense. You can however consider the quantum theory of a massive spin-1 field in Minkowski spacetime, and use it to make predictions about results of experiments. There's one such theory for each value of the mass (and of course for each choice of interactions). Experiments that test those predictions to see which values of the mass gives us the best predictions can be thought of as measurements of the mass of the photon, if the term "photon" is now defined by that class of theories, instead of specifically by QED. I think I've read somewhere that if the mass is small enough, the results are predictions are practically indistinguishable from the predictions of QED. (No, I don't know where). So measurements that tell us that the predictions of QED are "at least this accurate" also give us an upper bound on "photon" mass.I'm not so sure about that. Can you provide a reference?
No, this can not be said.So can it be said photons aren't anywhere until they are absorbed?
No, photon direction is uncertain after position measurement.Since we know the precise velocity of any photon, does that mean it's location is always undeterminable?
Hm, the negation of "isn't anywhere", is "is somewhere", right? So to answer "no" to the question asked, is to answer "yes" to the question of whether the photon "is somewhere" before detection. I would interpret that as having a specific well-defined position, not as being spread out over a smaller region, like the insides of an optical fiber. That's why my answer is "yes".No, this can not be said.
The controlling rule is in fact the Uncertainty Principle. So answering your question with anything else ends up stretching the language in a fashion which leads to either contradiction or confusion. (Which is why Fredrik is correct.)doesn't matter, my question is about the position of photons as they travel.
Actually, I found another more concrete reference on wikipedia: http://en.wikipedia.org/wiki/Propagator#Faster_than_light.3FI'm not so sure about that. Can you provide a reference?
Just to amplify on this: it is not absorbed and re-emitted in the classical sense. There are probabilities that activity occurs. I.e. various paths or histories. The probabilities (paths) then sum (integrate) in a way that has the overall result averaging to a value lower than c.Light gets absorbed and emitted over and over ...
Well:Light gets absorbed and emitted over and over (and over and over). You can think of it like a busy man walking to work from the train station. If a pan-handler asks him for money, it'll slow him down, even though when he's walking, he's always walking as quickly as he can without appearing to be in a hurry :)
What happens with visible light then? it can't have a different explanation.AFAIK, the photons of visible light do not have enough energy to excite the electrons of a transparent material. The photons just pass through having lower speed.Originally Posted by JJRittenhouse
Isn't the speed still the same in another medium, just interrupted by electron interaction?
This is not accurate, and I probably should have commented earlier. The excitation energy of electrons does not determine whether a material is transparent or not. It is more closely related to field effects of the atomic structure. I.e. the arrangement and type of atoms/molecules. They create a virtual field and this leads to the effects of color we see.AFAIK, the photons of visible light do not have enough energy to excite the electrons of a transparent material.
we were getting bogged down in the mechanics of the speed of light through a medium, I was just drawing that to a close where it could be asked in a different topic.The controlling rule is in fact the Uncertainty Principle. So answering your question with anything else ends up stretching the language in a fashion which leads to either contradiction or confusion. (Which is why Fredrik is correct.)
It is probably easiest to say that when a photon has a known velocity (momentum actually), it's position is essentially undefined.