Can you connect 'gravity' to energy? Depends on how you look at it, energy is transformations. But what is it that 'transforms'? Gravity? Not as I know, 'gravity's slope' stays the same, no matter how many photons, or mass, that 'travels' it, loosely speaking here. The transformations we see either involves particles of mass, or massless. 'Gravity' is more of a roadsign for those, directing them.

But there is no denying that gravity's potential have a effect on what 'energy' something will express. But that is also a expression between 'frames of reference'. So, can you define 'gravity' as a frame of reference? I'm not sure, once again we find it has to do with definitions. If gravity either radiates or, at least, have a origin in mass and motion, then I would say no as we might have to define it from a source. But it's tricky and I'm not sure if I agree with myself here

The reason why I don't mention 'energy' is just that, for what we can observe today, only are defined from transformations, as far as I know. Seen another way you very well can define gravity as 'frames of reference'. That as gravity exist in all 'points' of this universe (as I presume), and that you nowhere will find points near to each other of the same 'gravitational potential'. Add to that, that we live in a universe defined by 'relative motion', meaning that there is a constant dynamic change of each points 'gravitational potential' inside times arrow.

I don't know really, the idea of some 'walls of the universe' seems pretty meaningless to me, to define it as such we first would have to agree on a 'distance' and even though you can Lorentz transform distances, and clocks, that doesn't give you a 'absolute frame', just a way of comparing them. And a universe without walls becomes a universe where you no longer can define 'energy' jumping from them to 'space', as the inflation seems to do, for the moment.

I like 'magnifying and contracting' better. It, to me, seems to be a better general description of change in SpaceTime, and it also seem to be observer dependent.

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Can we define 'energy' as being on one invariable kind in a 'inertial frame'? Nope, we can't, that photon may give you one relation on Earth, but another on Jupiter. The 'energy' it express in your measurement/its annihilation will differ. But we still can define mass that way, can't we? Invariant (rest) mass is defined as being of the 'exact same' in all inertial, as well as accelerated, frames. There is one crucial difference between mass and radiation though. Radiation has no rest frame, it's always of one invariant 'speed' in all frames, and from all frames as measured locally. 'c'.

Rest/invariant mass can be 'at rest', if we by that define it such as in a uniform motion (geodesic) on its own, or relative something else. But different uniform motions, relative some agreed on origin, will give you a different outcome, in a impact. So how can we expect a 'invariant mass' to be the same? And actually, we do the same with 'quanta' of radiation, as a photon. We expect it too to be of one invariant 'energy'.

What is invariant mass and how do we define it?

"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.. .

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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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"So the custom is to assign to each object the "invariant" mass which is the inertia it WOULD have if it were sitting still." And 'sitting still' I here define as being in a uniform motion, then being, as I understands it, impossible to differ from being 'still', inside a 'black room scenario', as in your rocket. And then you have planets, etc, too, where your 'invariant mass' also can be said to be 'at rest' relative the planet. Which in its turn are uniformly traveling a geodesic, as I see it being at rest with 'gravity', excepting its own gravitational potential.

So, ignoring the 'warping' a invariant mass 'influences' on the space around it, we may define a invariant mass 'rest frame' as being a uniform motion in where it will be at rest with 'gravity', 'weightless' if you like, following a geodesic. And the mass itself is measured from the 'inertia' created at a course change (acceleration). So, if this is right it then automatically assume all uniform motions (geodesics) to be the same, no matter what speed you have relative a origin. At least it assumes that the inertia created must be the same at a course change (acceleration). Is that correct? That no matter my 'speed' the inertia will be constant in a uniform motion?

What exactly is 'invariant' in a uniform motion. As I see it the only invariance you will find is relative the gravitational potential of the space surrounding you, allowing you a geodesic at any 'speed' relative some origin. I most definitely expect your inertia to change with your uniform 'relative motion'. So is 'inertia' a well chosen standard for this? (Also it seems to me that the 'inertia' will differ depending on how you choose to deflect that uniformly moving object. You will get one energy colliding head on, another if hitting it at a right angle to its motion.)

"Longitudinal" inertia, versus a sideways, or "transverse" inertia as Marcus expressed it. But there are no frames of reference in this universe that are 'still', except as defined as I did, against '(Space) gravity's potential' uniformly moving, and/or as defined against another object in your geodesic. Then again, mass should be of one invariant type, ideally. That as we relate it to a invariant 'energy'.

So, a question of locality maybe?