- #1
nuncoop
- 28
- 0
Is it possible to capture photons within a perfectly spherical/reflective ball by aiming a faraday isolator within the ball?
jwalker1196 said:Let us pretend you could. Then the sphere would indeed get more massive. Now, if you were asking could this be done, I would have to say no. You'd have to open the sphere to put them in, allowing for the escape of photons already inside.
But I'll do you one better. Let's say the inside of the sphere is perfectly reflective. Let's also put a hypothetical "photon emitter" in the sphere. This emitter is itself a perfect 1-way reflector, on its outside. Now, requiring power, we run a wire from the emitter through the sphere wall. This wire and its exit point shall also be coated in 100%-reflective material. Now we have an emitter which will continue to do so as long as it has power, filling a sphere ad infinitum.
The sphere becomes more and more massive. The loss is from outside the sphere, so we aren't breaking any Laws of Conservation. The real question is, what happens when the sphere becomes so full of photons that it cannot accept any more?
Singularity?jwalker1196 said:...
.
.
.
The sphere becomes more and more massive. The loss is from outside the sphere, so we aren't breaking any Laws of Conservation. The real question is, what happens when the sphere becomes so full of photons that it cannot accept any more?
jwalker1196 said:The real question is, what happens when the sphere becomes so full of photons that it cannot accept any more?
As others have written, the answer is yes, but at the condition that the sphere remains still: if a still body acquire an energy E, then its mass increases of E/c^2 (this is the correct meaning of Einstein's famous equation E = mc^2), whatever the way it acquires energy (for example, even giving it a spin.)nuncoop said:I forgot to include the second part of my question :P. Would the sphere become more massive if photons were continuously pumped into it?
But two photons traveling in opposite direction have:xArcherx said:There is one problem. Photons have no mass.
E^2 = (mc^2)^2 + (pc)^2
m = 0
lightarrow said:But two photons traveling in opposite direction have:
E^2 = (mc^2)^2 + (pc)^2
p = 0 (because you have to add two equal and opposite momentum) so:
E^2 = (mc^2)^2 --> m = E/c^2
That is: the system of the two photons have mass.
Didn't understood what you said; furthermore, you mean to add energy squared?dst said:Invalid application. Each photon has no rest mass and energy equal to (pc)^2. With 2 photons in opposite directions the energy is (pc)^2 + (-pc)^2 = 2(pc)^2.
(pc)^2 + (-pc)^2 = 2(pc)^2.
And which is the physical meaning of the quantity (pc)^2 + (-pc)^2?xArcherx said:Thanks for this bit of info. It helps with my project. I had to take a second look though, lol. About the adding of a negative but I then clued in with the squares. Just so that I do understand...
you get 2(pc)^2 because (-pc)^2 = (pc)^2 and so...
(pc)^2 + (-pc)^2 = (pc)^2 + (pc)^2 = 2(pc)^2
lightarrow said:Didn't understood what you said; furthermore, you mean to add energy squared?
He's adding energy squared, not because of its physical meaning, but because you calculated the energy squared of a system of two photons incorrectly, (and then took the square root and solved for the mass).lightarrow said:And which is the physical meaning of the quantity (pc)^2 + (-pc)^2?
You can't get the total energy squared by first adding the momenta and then inserting the result into the formula for energy squared. The sum of the squares of the two energies is what he said. The sum of the energies is [itex]\sqrt{m^2c^4+p^2c^2}+\sqrt{m^2c^4+(-p)^2c^2}[/itex]. The contributions from the momenta clearly do not cancel each other.lightarrow said:But two photons traveling in opposite direction have:
E^2 = (mc^2)^2 + (pc)^2
p = 0 (because you have to add two equal and opposite momentum) so:
E^2 = (mc^2)^2 --> m = E/c^2
That is: the system of the two photons have mass.
Sorry Fredrik, (maybe it's the hot) I don't understand where is my mistake.Fredrik said:He's adding energy squared, not because of its physical meaning, but because you calculated the energy squared of a system of two photons incorrectly, (and then took the square root and solved for the mass).You can't get the total energy squared by first adding the momenta and then inserting the result into the formula for energy squared. The sum of the squares of the two energies is what he said. The sum of the energies is [itex]\sqrt{m^2c^4+p^2c^2}+\sqrt{m^2c^4+(-p)^2c^2}[/itex]. The contributions from the momenta clearly do not cancel each other.But two photons traveling in opposite direction have:
E^2 = (mc^2)^2 + (pc)^2
p = 0 (because you have to add two equal and opposite momentum) so:
E^2 = (mc^2)^2 --> m = E/c^2
That is: the system of the two photons have mass.
It looks like you're adding the momenta first, and then inserting the result into a formula that tells us the energy of a particle with a given mass and momentum. You're doing it right in #23.lightarrow said:But two photons traveling in opposite direction have:
E^2 = (mc^2)^2 + (pc)^2
p = 0 (because you have to add two equal and opposite momentum) so:
E^2 = (mc^2)^2 --> m = E/c^2
That is: the system of the two photons have mass.
I thought that what I wrote was such a proof: if you add photons to the box so that it remains still = total momentum acquired from the box is zero = total momentum of the photons injected is zero --> the system of injected photons have mass M = E/c^2 where E is the total energy added with the photons.Fredrik said:Regarding the "relativistic mass" of the combined system: You can assign a relativistic mass to any system with energy simply by writing E=mc2 just because the m defined this way must have dimensions of mass. When the system is a massive particle, this m turns out to be the same as the relativistic mass defined in a more meaningful way, and if the system is something else, like a massless particle or, as in this case, two massive particles, you just take this to be the definition of the relativistic mass.
This is kind of pointless, so I'd rather just talk about the energy of the system instead of its mass. But I guess it makes some sense to do this because a box with a bunch of photons in it is definitely heavier than the same box when it's empty, and I assume that the extra mass we measure when we weigh the box is equal to E/c2. (I haven't seen a proof, but I'd be very surprised if there isn't one).
But two photons traveling in opposite direction have:
E^2 = (mc^2)^2 + (pc)^2
p = 0 (because you have to add two equal and opposite momentum) so:
E^2 = (mc^2)^2 --> m = E/c^2
That is: the system of the two photons have mass.
xArcherx said:For photons, m = 0 so E = pc. Now if you were two have a p + (-p) scenario then you get E = 0
Yes.xArcherx said:So it's |p| + |-p| where |-p| = |p| (of course) and so you get E = (2p)c ?
Also, isn't momentum a vector?
It's p+(-p)=0.xArcherx said:Ball 1 is traveling from Point A to Point B with momentum p. Ball 2 is traveling from Point B to Point A and so it has the momentum -p in relation to Ball 1. The total momentum is...
|p| + |-p| = 2p
This should be E=|p|c. It only tells you the relationship between the energy and the magnitude of the momentum.xArcherx said:...but talking of photons I just can't see it. E = pc but E = hv also, where v = c/λ.
It's p+(-p)=0
This should be E=|p|c. It only tells you the relationship between the energy and the magnitude of the momentum.
Just because you're looking for total momentum. Momentum is a vector (I have written it in bold for this reason) and it's additive.xArcherx said:Even when you are looking for the total momentum?It's p +(-p)=0
If they travel in the same direction; if they travel in opposite directions, the total momentum is the difference.Where if ball 1 is 2 kg and ball 2 is 4 kg, both are traveling 10m/s then...
Momentum of ball 1 is 2 * 10 = 20
Momentum of ball 2 is 4 * 10 = 40
Total momentum should be 60 kg.m/s
It's for this reason that the two momentums have opposite signs.If p means the ball is traveling from point A to point B then -p should simply mean the ball is traveling from point B to point A. Since we wouldn't have a negative mass, then we must have a negative velocity. A negative velocity would simply mean reverse direction just as a negative acceleration means a deceleration.
What do you mean with "stack"?So does this mean that if we had two photons traveling toward each other from opposite directions, at the point of collision their momentums would stack and therefore so would their energy?