It also have to do with how you define relativistic mass. Something moving in a circular motion around a center has a relativistic mass, even if uniformly moving (keeping a same speed). That's because it 'breaks' its natural velocity (speed and direction combined) at all times, constantly changing its direction. To change direction involves a acceleration as I think of it.

(Ahem, better expressed, breaking a geodesic always involves a acceleration. My reasoning holds if you define a uniform paths 'velocity' as following a geodesic, which can be seen as the 'straightest path' in a non-euclidean universe. And let this be a lesson to you, never reread what you once wrote, or you will find yourself changing almost all, of what you once thought of as 'self-explanatory'

But uniformly moving objects in geodesics, do they have a relativistic mass? If you can't decide their motion, how can you decide their velocity? and without a velocity there should be no increase in relativistic mass, as I gather it? It's a important point to make I think.

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I better rewrite that one

It's not about velocities really. What I mean is that all uniform motions must become equivalent in form of describing a relativistic mass. But as all uniform motion only are uniform until you change course, using velocity to describe it seems appropriate to me.

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And looking at it that way 'motion' becomes suspect, don't you think? We seem to have two definitions of it. One we call 'relative motion' in where you are free to define 'what moves', relative some other object, not involving any added 'forces' as 'gravity', due to whatever velocity you define. Then we have all sorts of accelerations, not only uniform, that must be considered adding a relativistic mass, and a 'gravity', if I'm thinking right here.

But then we have the fact that we can define different uniform velocities, giving 'motion' as a concept a existence outside those two definitions. Only a acceleration can create that local 'gravity well' though.

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And, by the way, it also makes me think about momentum and how we define that as having a direction?

Does it?

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I'm not sure about this though, as a acceleration create a relativistic mass, equivalent to its speed (kinetic energy) in the end becoming infinite limiting the speed to just under 'c'. Can't you assume that this will hold true for a uniform motion too? But then it comes back to uniform motion, and there we have no proofs I know for local changes due to your increased velocity, as long as we're talking measuring uniform motion?

It once again comes down to how you expect the universe to be/act for me. As a whole expression? Then it should exist in a uniform motion too as I suspect, as it should be a redistribution of a 'defined total energy' of the universe. But if it is a strictly local definition that holds then it's not you that change, but your relation to the universe around you. If one trust measurements to define what is 'real', that is?

(The point I'm trying to see, and understand, myself here

is that it's easy to define a energy to something, as long as you do it relative something else. But when it comes to locally measuring a difference, due to a uniform motion, all such 'change' disappear, as I understands it. Relativity is indeed about needing two frames of reference, and then measure.)

If I was to put it into a context I would define two identical systems (closed particle chambers), uniformly moving relative some third part, defined as 'inertial' and so being 'still'. Then you accelerate a electron inside each identical particle chamber, using identical 'force', and measure as it hits the detector.

Now, the particles relativistic mass will increase due to what velocity you give the electron, but if we now also measure the chambers uniform motion relative that third part, defined as 'unmoving', would different uniform motions of the chambers themselves also give us different detector results (locally measured)? If they would, then the chambers uniform motion must play a part in defining the electrons 'energy', assuming identical setups.

But if it doesn't have any influence?

And I don't expect it to have any.