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If we know the velocity exactly then the light must be everywhere at the same time right?

- Thread starter duffbeerforme
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- #1

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If we know the velocity exactly then the light must be everywhere at the same time right?

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To be precise the uncertainty principle which you're referrring to relates the uncertainty between position and momentum. It seems to me (although I'm not 100% sure) that since its quite possible to measure the momentum p of the photon and its energy E to arbitrary precision (i.e. the energy operator commutes with the position operator) then one can deduce the precise value of the momentum. The relation is p = (E/c^2)c = E/c and therefore c = E/p.

If we know the velocity exactly then the light must be everywhere at the same time right?

Pete

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As the person above me said, the uncertainty relation doesn't apply to any two observables you can think of. It only applies to observables that don't "commute". So it would apply to position and momentum, but not to position and velocity.

If you consider the position and momentum of a photon, you will see that neither variable is known precisely. The momentum of any given photon is actually a cloud of momenta. So, let's say you think you have photons of a given wavelength (and therefore, a given momentum). It turns out that what you actually have is a bunch of different wavelengths that differ slightly from each other. Think of the photon as a bunch of waves with different wavelengths grouped together in a "wave packet" like here:

http://www.st-andrews.ac.uk/~bds2/ltsn/Edinburgh/wave/index.html

Likewise, the point where the photon contacts the detector is not a precise point but is a small cloud of points.

The smaller the position cloud is, the bigger the momentum cloud will be, and vice-versa.

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There is no such thing as aI'm not an expert, but I think I can answer this one.

As the person above me said, the uncertainty relation doesn't apply to any two observables you can think of. It only applies to observables that don't "commute". So it would apply to position and momentum, but not to position and velocity.

As far as measuring position as a function of time and deducing the speed from those measurements then I don't see how that is possible since detecting the position of a photon involves destroying the photon. Two successive measurements of position would then seem to be impossible.

Pete

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