Which is the difference between matter and energy?

[dapifo]

As Strange says. An object has one rest mass, it may have many measured masses. One of those measured masses may correspond to the rest mass if the conditions under which it is measured are such that the mass you measure is the rest mass. You appear to be assuming that if there are two quantities, one invariant and one not, that they can never be equal to each other. Which is patently false. Just because one is an invariant and one is not does not mean that they can never be equal.

This looks like the Uncertainty Principle of Mass .....(!!!)...We can open an ATM thread (!!!)

[Strange]

This looks like the Uncertainty Principle of Mass

No, its just a standard part of relativity theory. There is no "uncertainty" at all.

[dapifo]

No, its just a standard part of relativity theory. There is no "uncertainty" at all.

Only the "uncertainty" (difficulty) of messuring the mass of an object considering all the ...stress-energy tensor concepts !!!!

[Strange]

Only the "uncertainty" (difficulty) of messuring the mass of an object considering all the ...stress-energy tensor concepts !!!!

I don't think there is any particular problem measuring mass.

The stress-energy tensor is part of the Einstein Field Equations that describe space time. Solving these equations for real examples, in order to calculate the effects of mass, energy, etc can be complicated. In many cases there is no analytical solution so you have to use an approximation or a simulation. For some cases there are exact solutions: black holes of various types, a universe with homogeneous distribution of mass, and others.

[Shaula]

Only the "uncertainty" (difficulty) of messuring the mass of an object considering all the ...stress-energy tensor concepts !!!!

The QM uncertainty principle is to do with the non-zero value of the commutation of some pairs of variables. It actually has nothing to do with experimental difficulties in measuring a quantity. It is far deeper than that. It relates instead to the ability of certain eigenstates to coexist and is a fundamental limit to strong measurements in QM. It is certainly not just experimental difficulty.

[Reality Check]

As is often the case, I am merely disagreeing with what
was said, not with what was meant.

What were you disagreeing with in the statement that "The source of the curvature of spacetime and thus gravity in General Relativity is the stress-energy tensor"?
Your next post says that you wrer okay with my longer explanation..

[Strange]

What were you disagreeing with in the statement that "The source of the curvature of spacetime and thus gravity in General Relativity is the stress-energy tensor"?

I think he is drawing a distinction between the mathematical "tool" used to represent the physical factors which curve space time and the actual physical factors themselves.

[caveman1917]

I think so. In principle, anyway. You can have a solution of the Einstein Field Equations with no matter and energy, e.g. the Milne model. But now I am out of my depth ...

A more simple one would be minkowski space, ie the SR stuff.

[caveman1917]

A beam of light, with all the light travelling in one
direction, also has zero mass. The photons within
the beam are not attracted to each other by gravity.
Two beams of light side-by-side, travelling in the
same direction, are not attracted to each other by
gravity. Unfortunately I forget exactly what the case
is with two beams of light travelling side-by-side in
opposite directions. I think they *are* attracted to
each other by their mutual gravity.

Indeed.

The point is whether we can find a center-of-momentum frame or not, which is an inertial frame in which the energy of the system is minimized, which provides us with an invariant notion of "mass". So for a lump of matter, the center-of-momentum frame is the one attached to its center of mass, and the mass equals its rest mass. For a bottle filled with a hot gas, and thus consisting of many molecules bouncing around chaotically, the mass is not the sum of the rest masses of the molecules, but the total energy (rest mass + kinetic energy) in the frame in which that quantity is minimized (which will usually be the frame in which the bottle is stationary).

Going to the photon arrangements, for a single photon (or many such photons) all travelling in a single direction, it is obvious that no center-of-momentum frame exists. The energy of the photon in any frame is proportional to its frequency. So suppose we randomly pick a frame and it has a certain frequency. We can then choose a frame that's moving in the direction of the photon relative to our first frame, and due to the doppler shift the frequency (and thus energy) will be lower. But we can keep doing that ad infinitum, so there doesn't exist a center-of-momentum frame (and if we'd define it as the limit of our frame-shifting process, the limit would be zero energy anyway). This is of course also true for two or more beams of light all going in the same direction. If we have at least one photon that is going in another direction (such as two opposite directional beams), we can define a center-of-momentum frame in which the system will have non-zero energy. And that energy is then the invariant mass of our system of photons and a source for their mutual gravitational attraction. We should note that the source of gravity is the stress-energy, not the invariant mass per se, but it does work out that way in this case.

[Strange]

A more simple one would be minkowski space, ie the SR stuff.

Of course it would. Why didn't I think of that? Oh yes, because I don't understand this stuff!