It is a difference Pete, between defining gravity as paths of 'minimal resistance', or none, to say that there is a force defining those paths. If I look at what we can derive from gravity in form of usable energy then? Did Einstein have any thoughts on from what his force originate? I can define it to energy and mass, but it does not tell me why it exist?

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What I mean is that I find gravity a mystery. I don't find it explained by referring to tension, pressure, energy density and stress, etc, although it may make it calculable. If we use our planet to define it it becomes easy to think of it as a force of sorts, driving waterwheels (as from a waterfall) and all sorts of things. But does that really make it a force? What is a force, something you can't transform away, or something you can transform away?

You can point out that in a uniform motion nothing will be locally measurable, as being in a closed room, measuring a light bulb at rest with the room and the uniformly moving rocket. And it doesn't matter for this what speed one defines to the geodesic (rockets path). There is no extra local energy as far as I know, due to different uniform speeds. Then again, is there a way to be at rest with electrical charges, and what would happen to it if so? Quantum mechanically it becomes really weird as a electrons momentum is related to its 'cloudyness', if I may. The larger the 'electron cloud' the less momentum, the smaller the electron cloud the greater its kinetic energy, and momentum as I gather. the electron doesn't really 'move' at all, it's smeared out inside that cloud, although you can locate it by probing, so forcing a definition of a position. So how can one be 'at rest' with such an idea?

Anyway, The Higgs field should be a suggestion toward some explanation making sense from a older semi classical perspective to me. As it presumes a common space in where a field can exist, that's almost a classical description, isn't it? The one I got from Einsteins description, not that I've read that extensively about gravity, my main interest have been time so far, is one where gravity isn't a force at all? It may come down to what you mean by affine connections there Pete, and you need to explain that without the mathematics, if possible, to let us see how you think.

The way I've thought of it so far is one in where gravity becomes some sort of 'holes' :) with mass acting as 'stops' gravitationally, 'accelerating' us, as on earth one constant G. It's like there is an idea of directions, those gets their definitions from mass, uniform constant accelerations, and possibly pure 'energy', if such a thing can be described? Then again, Einsten refer to gravity as a equivalence to inertia if I read him right, and all types of accelerations have inertia, not only uniform accelerations. I find this one nice describing that equivalence. Maybe one should avoid using gravity at all? Just refer to the inertia observed in matter, caused by accelerated motion and mass, and as I mentioned before, possibly 'pure energy', whatever that is? Another concept I find hard to handle, because energy that exist to me is the one created in transformations, interactions of all sorts, resulting in radiation etc.

By Marcus;

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"When something is moving it has a "longitudinal" inertia and a sideways or "transverse" inertia. But it no longer has a mass, because mass is a directionless quantity. So the custom is to assign to each object the "invariant" mass which is the inertia it WOULD have if it were sitting still. Lorentz discovered this ambiguity of inertia of a moving object back in 1904 even before Einstein.. .

The equations (GR) that model gravity do not have mass in them they have *energy density* and related pressures. Energy is what causes gravity in GR. Energy tells space how to curve and curved space tells energy how to move...

When something is moving it has a different "longitudinal" inertia from its sideways or "transverse" inertia. It takes more force (measured in the lab frame) to produce a given acceleration vector in the direction of motion than the same acceleration sideways. It is harder to speed a moving body up than it is to deflect it---even if the observer at rest can see that the size of the acceleration vectors are the same. People used sometimes to talk about the "transverse mass" (gamma m) as opposed to the "longitudinal mass" (gamma3 m). But nowadays most physicists when they say mass just mean "rest mass"----there is no other kind. But if you google with keywords "longitudinal mass" and "transverse mass" you can still find these gamma formulas and some discussion of these things.

The factor gamma = (1 - beta2 )-1/2 can be quite large for beta near one. So there can be a big difference between gamma and (gamma3 ! The difference between forwards inertia and sideways inertia can be very large. Like, if gamma is 2, then the thing is 4 times more resistant to speeding up than it is to deflection (where the same size acceleration is to be produced) Or if gamma is 10, the thing is 100 times more resistant to speeding up than to deflection. Nowadays the use of the term "relativistic mass" is more of an endearing eccentricity than anything else. Like wearing a sword, or having suits of armor in one's livingroom. For a moving body, the "relativistic mass" is essentially the same as transverse"------inertia measured as resistance to deflection-----and the formula for it is gamma m."

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And yes, we have relative motion defining those paths too, even though a relative motion is one without inertia locally, and in any 'two way description' equivalent to being 'still'.