# What is intuitively the source of the gravitational field?

Quantum:
Does this mean it is just better to "shut the heck up and calculate"? That is, to forget about trying to "intuit" these things and just learn how to apply them mechanically to solve problems and generate predictions for experiments?
Not according to Richard Feynman:

"A physical understanding is a completely unmathematical, imprecise, and inexact thing, but absolutely necessary for a physicist."
On the other hand such an understanding is not easy to come by.... he also says:

“Do not keep saying to yourself, if you can possible avoid it, "But how can it be like that?" because you will go 'down the drain', into a blind alley from which nobody has escaped. Nobody knows how it can be like that.

pervect:
I can also add that tensors have a long history of use before GR, particularly in fluid mechanics. Of course, the classical tensors transform via the Gallilean transformation - the relativistic tensors transform via the Lorentz transform.
Interesting!: Einstein was guided in part via Lorentz, Fitzgerald and the 'ether' controversy of the early 1920's. I spent some time, unsuccessfully, trying to find out how the development of tensors in fluid mechanics may have influenced Einstein, how he might have gained insights from that work. I know there is documentation of Einstein's work because [I think it may have been Brian Greene who commented on it.] Einstein's original notes and his errors,false starts,corrections and alternative formulations were noted.

Quantum Immortal:
Is it correct to say...... The tensor represents, 'invariant energy'? I really want an answer to this one.
I wanted to emphasize the following because I often forget.

pervect:
There are several ways of talking about the stress energy tensor. One way of looking at it is this - the stress energy tensor, when multiplied by the 4-velocity of an observer, gives the purely spatial energy momentum density (which is a 4-vector) measured by an observer moving at that four velocity. This is the approach used by MTW in "Gravitation", basically
This is a good way to 'intuit' that different observers see componets of the SET differently.

The components of any tensor field, like the SET, only have meaning relative to a choice of frame. But the overall SET is a covariant object regardless of the fact that relative to a given frame field its components are not. That's the whole point of using tensors. Their components relative to a frame field correspond to frame dependent [say, varying observer velocity] locally measurable quantities but the tensors themselves are frame independent, geometric objects.

A single fast electron has the same 'gravitational spacetime curvature' as a slow one. But it follows a different trajectory. A moving object does not curve space-time any differently from a stationary object. [We take the SET gravitational source term in the frame of the object, or system.] So a 'hot' plasma has more 'gravity' than a cooler one because the faster moving mor energetic ions exert more pressure in the frame of the system. The overall KE may remain constant but the pressure does not.

The gravitational spacetime curvature is an intrinsic geometric quantity, and invariant under coordinate transformations. Moving objects do generate different apparent forces on test particles through the source term (stress-energy tensor) in the Einstein equation...so different trajectories result.

As an example of some of this, the [idealized] symmetrical collapse of a star does not change the external gravitational spacetime curvature unless one assumes radiation carries away some energy. The components of the SET varying in such as way as to maintain over all gravitational uniformity.

Quantum:
There is a nice complementary forum discussion here with some good physical insights:
Energy gravitates?

You should have read my last post instaid.
Now i think that the tensor, its just all of mechanics.....
The divergence of it is the continuity equation of all mater....
It describes how matter "flow".... thats just all of mechanics....
Its just presented in an

The electric charge, has no other property, then that you need to keep track of how much you have.
Raw abstract charge, has no mass, no energy, no nothing. That why its an invariant. Its like how many grains of sand you have....

Yes, i don't over do it with philosophical questions......

The link, doesn't really say if gravitational energy is already included in the equations
On the issue about GR and the energy of the field, does it mean, that ultimately, its inconsistent???
Not knowing how much energy you have, is not exactly a small problem....
The equivalence of inertial mass and gravitational is part of GR???

PeterDonis
Mentor
2019 Award
The divergence of it is the continuity equation of all mater....
This is true, but note that it's only true if "energy of the gravitational field" is *not* included in the SET.

On the issue about GR and the energy of the field, does it mean, that ultimately, its inconsistent???
No, it means that there's no way to describe "the energy of the field" as a tensor.

Not knowing how much energy you have, is not exactly a small problem....
Why? I understand why it's counterintuitive to not be able to describe "the energy in the field" as a tensor; but our intuitions didn't evolve to comprehend relativity in the first place. GR, as a theory, makes accurate predictions without having to describe "the energy in the field" as a tensor, so it can be done; the fact that it's counterintuitive just means you need to recalibrate your intuitions if you want to understand how GR does it.

The equivalence of inertial mass and gravitational is part of GR???
Yes.

Not knowing how much energy you have, is not exactly a small problem...
Peter hit a key point here:

GR, as a theory, makes accurate predictions without having to describe "the energy in the field" as a tensor, so it can be done.....
In addition, we have gotten by without anyone having experimentally detected [observed] a 'field'. Fields can be said to be abstract mathematical models; what we actually observe experimentally are the local quanta of these abstractions, that is, particles of finite, actually pointlike, size....say, like in a photomultiplier or cloud chamber.

Also, 'problems' could be considered having no absolute distance or time, no single measure of gravitational curvature nor an absolute inertial frame of reference in this universe.....that's just the way things are....so far as we currently understand.

But also keep in mind that for slow moving Newtonian environments, like planets, a gravitational potential energy and even energy conservation seems pretty robust. For many fast moving particle interactions, gravity is so weak it can be pretty well ignored. It would be nice, of course, if we could integrate relativistic gravity into the standard model of particle physics.

Quantum: You might find the few paragraphs here of interest:

http://en.wikipedia.org/wiki/Charge_invariance

and here:

http://en.wikipedia.org/wiki/Gravitational_energy