I've read that a particle at absolute zero cannot be completely without motion, because then we would simultaneously know about its position and velocity at the same time. I'm wondering about a particle, such as a photon, travelling at the speed of light. Since we know everything about its velocity, wouldn't it follow that the photon could be anywhere in the universe? Also, we exactly know its momentum since its mass is zero. Wouldn't we run into the same issue?

Question

I've read that a particle at absolute zero cannot be completely without motion, because then we would simultaneously know about its position and velocity at the same time.  I'm wondering about a particle, such as a photon, travelling at the speed of light.  Since we know everything about its velocity, wouldn't it follow that the photon could be anywhere in the universe?  Also, we exactly know its momentum since its mass is zero.  Wouldn't we run into the same issue?

anonymous · Answer

are you asking that a photon having velocity of light @ absolute zero temparature?

anonymous · Answer

Not at absolute zero.  Just a photon in general.  Wouldn't we run into problems with the Uncertainty Principle?

festinger · Answer

thing is... for a photon the momentum is:
$$p=\frac{h}{\lambda}$$

and not the classical p=mv

So what if we know speed? we still couldn't tell whether it's frequency exactly.
Besides, a more practical problem would be we know that the lightbulb emits light with speed c. but this light spreads out in a sphere, we don't know which photon strikes where.

anonymous · Answer

actually you can pretend it has rest mass,because,$$M=m/\sqrt{?}(\mu \epsilon)$$ yes we have take its rest mass.

anonymous · Answer

Thanks for the momentum response!  That makes more sense.

As for the other one, are you saying that we're not really concerned with the speed of the particle, but more with the frequency of light?

anonymous · Answer

here mew and epsilon are respective absolute permitty of that medium,where we will take consider the experiment.

festinger · Answer

I know the speed of light, but it is not that useful, because momentum for photons is usually expressed different.

So knowing the speed of light does not tell me anything about momentum.

To find momentum, I have to find the wavelength/frequency of the photon, which is a rather difficult task!

anonymous · Answer

@festinger,the equation is right,DeBroglie equation.

anonymous · Answer

Ah, alright, I think I see now.  The usual problem with the Uncertainty Principle is either momentum and position or velocity and position, but you're saying that the velocity and position problem is derivative from the momentum and position problem?

anonymous · Answer

*And since we look at momentum differently, we worry about something different like frequency?

festinger · Answer

De broglie proposed that since light can behave as a particle, could particles than behave as waves? Thus, it should be no surprise that the expressions are the same.

From special relativity, total Energy, E is:
$$E^{2}=(pc)^{2}+(mc^{2})^{2}$$
Since photons have zero mass, and from E=hf for right, it reduces to the de broglie form.

I am not sure about the equation you wrote, it may be of something that is of higher level physics.

I am not saying that we worry about something different. All I am trying to say is momentum isn't as clearly defined as knowing speed of light is c and mass is 0...

anonymous · Answer

or we can take that Heisenbergs uncertainty principle,where,$$deltaxX deltap=h/4\pi$$
whwre x=uncertainty in position,and p=uncertainty of momentum.

anonymous · Answer

Great, thanks guys!

anonymous · Answer

you are welcome.:)