Photons in a Box Contribute Weight

[cbd1]

So how does this "mass equivalence" actually affect anything if it does not have inertia nor is it gravitationally attracted? How do you measure such
"mass equivalence"?

Free light, while in flight, only has mass equivalence, and no rest mass. The photons, while in flight, only interact with the environment by their mass equivalence having effect on the curvature of spacetime to a degree of which is equal to their energy's *mass equivalence*. Light only exhibits qualities of inertial and gravitational mass when it collides with something or is absorbed/emitted by a system. It is not gravitationally attracted; rather, it follows geodesics in its flight path, which is always straight in spacetime, but appears to be deviated to us by gravity, because we see the universe in a Euclidean way, though it is not Euclidean.

For instance, my ideation involves that during inflation there was only free energy, having only mass equivalence, in the universe. Nothing interacted, though there was all the energy and mass equivalence then as there is today. It was only when particles (fermions) materialized that interaction began--and inflation ended, due to things then having the characteristic required to be gravitationally attracted (i.e. rest mass).

 

[Dale]

I would say that matter is energy which is confined into particles (fermions). ... However, be there no particles, there is no mass, only *mass equivalence*. When energy is composed into particles, allowing for rest mass, the energy can then be gravitationally accelerated and have inertia. However, were this energy not bound into particles (fermions), it will not be.

In addition to the excellent replies you have already received I would just like to point out that the W and Z bosons have mass also. So even if we are speaking of isolated fundamental particles (and not systems of 2 or more) then mass is not always associated with matter.

Also, you can easily see that EM fields have inertia from the fact that their Lagrangian is symmetric wrt spatial translations.

 

[DaTario]

I would say that if you have a ball bouncing inside a box, its mass (ball's mass) will contribute to the box' mass in a way which takes into account the specific shape of trajectory of the ball inside de box. Its collisions with the walls and so forth. But when ball and box are not touching, we could say that the box, at least during a small time interval, would behave as if it was empty (no mass contribution). Very similar must be the situation with light inside.

Best Regards

DaTario

 

[JesseM]

The gif brought a question to mind: A gravitational field accelerates all objects in it at the same rate. Does this also apply to light? It seems it could be considered as such if the light is traveling tangent to the gravitational field, for on Earth it would accelerate the ray towards the ground at 9.8m/s^2, like all other objects in free fall. However, if it is traveling straight towards the gravitational field, it cannot be as such.

Actually it does apply to light traveling vertically as seen in the accelerating reference frame where the box (or either of the rockets in the gif) is considered to be at rest. The idea that light always moves at c only applies to inertial frames, which in the context of gravity would mean a free-falling frame. In the accelerating frame, the speed of a vertical light ray does change, with the ray accelerating towards the "floor" at 9.8 m/s^2.

If you haven't read about the equivalence principle yet I'd definitely recommend doing so...

Further, could this box (assuming the walls are weightless) theoretically be accelerated to the speed of light?

You can't assume the walls are literally massless, just that the mass is so small it can be treated as negligible for the sake of the problem. But as long as the mass is not exactly zero, it's impossible to accelerate it to the speed of light (and I'm pretty sure there aren't any massless particles such that, if a group of them were traveling together and formed a closed shape like a box, they would reflect photons that hit the 'walls' and keep them inside)

 

[Passionflower]

So it's not that the light is being accelerated toward the ground in the sense that the light is getting faster or increasing in magnitude, but its direction can be changed, at least.

The (proper, e,g, measured locally) speed of light does not change in a gravitational field. The Schwarzschild coordinate speed of light decreases while for massive particles this coordinate speed depends on a critical speed which is c/\sqrt{3}, above this speed a test particle's coordinate speed will slow down, below it it will speed up.

 

[George Jones]

for massive particles this coordinate speed depends on a critical speed which is c/\sqrt{3}, above this speed a test particle's coordinate speed will slow down, below it it will speed up. Massive particles also have a critical proper speed which is c/\sqrt{2}.

I became interested in this type of stuff a few months ago, and I did a bunch of calculations in Schwarzschild and Rindler spacetimes. There is some confusion in the literature, but a couple of interesting references are:

http://arxiv.org/abs/gr-qc/0310020;

http://arxiv.org/abs/gr-qc/0310020.

For accelerated motion in special relativity, see Figure 1 of the second reference.

 

[Passionflower]

Both references are identical, I suppose you meant http://arxiv.org/abs/gr-qc/0111103v2 for the second one.

 

[George Jones]

Both references are identical,

Oops; thanks.

I suppose you meant http://arxiv.org/abs/gr-qc/0111103v2 for the second one.

Actually, I meant

http://arxiv.org/abs/gr-qc/0406118.

 

[Passionflower]

http://arxiv.org/abs/gr-qc/0406118

For accelerated motion in special relativity, see Figure 1 of the second reference.

How fascinating!
Fermi coordinates are truly enlightening in relativity!

The famous elevator with a twist: