What does the Uncertainty Principle say about the location of photons?

Since we know the precise velocity of any photon, does that mean it's location is always undeterminable?
 
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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.
 
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Uncertainty principle deals with position and momentum, not with position and velocity. Quantum mechanical particles have probability distribution for momentum, and its variance is the relevant quantity for uncertainty principle.

The position of photon is more mysterious than the mere uncertainty principle might suggest, however.
 
We know precise speed(in vacuum), not velocity. And yes we cannot know exactly where the photon is.
Isn't the speed still the same in another medium, just interrupted by electron interaction?
 
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Isn't the speed still the same in another medium, just interrupted by electron interaction?
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.
 
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.
Well then I guess Feynman was mistaken.
 

Fredrik

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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.
 
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.

If you measure the position of a photon with 100% precision, suddenly, you have no idea which direction it's moving. Think of a lightbulb. A single photon coming out of a light bulb might be sent in any random direction. Thus, you don't know its momentum.

On the other hand, try to measure the momentum. Paint the light bulb black except for one tiny hole at the top. For every photon that comes out, you can be pretty sure about what direction it's going. But if you make the hole small enough (and thus, the direction certain enough), the light ends up diffracting! It spreads out all over the place, and the result is you have no idea where it will end up when you measure it!
 
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Well then I guess Feynman was mistaken.
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.
 
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.
doesn't matter, my question is about the position of photons as they travel.
 
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.

So can it be said photons aren't anywhere until they are absorbed?
 

diazona

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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.
I'm not so sure about that. Can you provide a reference?
 

Fredrik

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So can it be said photons aren't anywhere until they are absorbed?
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.

I'm not so sure about that. Can you provide a reference?
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.
 
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zonde

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So can it be said photons aren't anywhere until they are absorbed?
No, this can not be said.
For example, if you connect your source and detector with optical fiber then considering travel time of photon it can be said that it is in fiber before detection.
However if you consider wavefunction then it can be more tricky. As operators acts on wavefunction considerations about problems with some operator should be related to wavefunction not particles.
 

zonde

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Since we know the precise velocity of any photon, does that mean it's location is always undeterminable?
No, photon direction is uncertain after position measurement.
Before position measurement photon trajectory can be described classically.
See for example http://en.wikipedia.org/wiki/Ghost_imaging" [Broken]. Wikipedia article seems quite short about this so you probably would need to google a bit.
 
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What is the reason for lower light speed in medium? They suddenly gain mass or something?
 

Fredrik

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No, this can not be said.
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".

Of course, it can also be interpreted the way you did, which is why "no" is also a valid answer.
 

DrChinese

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doesn't matter, my question is about the position of photons as they travel.
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.
 

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