J.C.MacSwell

Just a question. If it has always been then how could we possibly have reached "now"? Another way of looking at this is; if an infinite amount of time had to flow prior to you being born... On the other hand it is easier to imagine a "position" in infinite Euclidean space so if you "see" time the same way then no problem. Just thoughts.

You can. And it's meaningful. For instance if you had an infinite number of planets spread evenly through infinite space and you doubled the infinite planets but not the infinite space you would have doubled the planet density per volume of space.

This is only true for the portion of a constant density sphere that an object is "inside of".

proportional to speed squared

When B receives the signal he will assume/calculate that it was sent by A at 10 minutes on A's clock or after more than 10 minutes of his own time. A will agree that he sent it at 10 minutes but will feel that less than 10 minutes had expired on B's clock when the signal was made.

Can you elaborate? Negative temperature makes me think negative kinetic energy. Would you not need imaginary (square root of negative) velocities?

I made an argument (apparently not convincingly, however noone attempted to refute it) in the more recent thread that translational kinetic energy would effect an additional gravitational force. Without rehashing my argument let me ask this: Is the rest mass of a hydrogen atom, that contains only one proton and one electron, the sum of the rest masses of the electron and proton? Or is there an additional term due to the relativistic mass of the electron wrt the proton?

You would need all the physical data, dimensions of the manifold and surrounding structure, right through to the exhaust etc. Then if you made the right assumptions about the quality of flow (the non laminar part and how it would effect the flow rate) you could make a good calculation. Certainly not likely to be exact though and correct assumptions may require fair bit of experience.

The bold is correct

In the rest frame of the body I think it could be considered its "effective rest mass" or ERM (I am making up a term). I think this ERM would be invariant with changes of reference frame similar to the way a rest mass of a particle is invariant. The particles are in different rest frames and the sum of their invariant masses are less (normally insignificantly) than the ERM of the body they make up but the sum of their relativistic masses are always greater (again normally insignificantly and by the same amout) than the "effective relativistic mass" or ERLVM (another term) of the body. So it all adds up consistently even if different in each frame. To me this "seems" like mass, whatever it is. (and whatever mass is)

Right. You would want to choose your liquid wisely or at least calibrate it for temperature.

Yes, and I think there must be an associated additional gravitational force between objects that are not at rest wrt each other. As for the last bit: you cannot claim you are absolutely at rest, but if you add energy to a body, say heat, then the rest mass of the body increases whereas the rest mass of it's constiuent particles/molecules do not increase but they have a corresponding increase in relativistic mass via their KE. Because it is random it would be considered an increase in the rest mass of the body and not an increase in the relativistic mass or KE of the body as a hole. (I think I have the concept right but as per usual I may be using the terms incorrectly. There may be some increase in rest mass of the particles/molecules, but it will all add up to energy attracting energy gravitationally) In this way I think there must be an increase in gravitational pull with increased relative velocities. Since you don't increase your "velocities of your respective parts" wrt each other when I go off on my near speed of light trip you should feel no need to implode on youself or become a Black hole. So what I am saying is if two particles fly past near light speed on parallel courses, say a meter apart, there will be a greater gravitational force between them if they are going in opposite directions (though obviously not for long)

I think we are assuming you will not. The idea being you could get there by me accelerating to high speed off in the distance where I cannot affect you- you would be near light speed in my reference frame but how could that possibly make you into a blackhole because of your relativistic mass in my reference frame. If this was true we would all implode upon constructing and using particle accelerators. I think that was Swansont's point. All frames might not agree but they must "agree to disagree" in a way consistent with relativity.

I think a ring balances out in the plane of the ring for an inverse linear field and a hypersphere balances out if the field is inverse cubed, etc. etc. (just don't ask me to do the math:D )

A sphere has enough mass opposite to balance things out. Think of the vectors diverging as the wall approaches on the one hand and converging on the other. That and the distance squared rule makes for a balance. A ring does this also but not enough.

If I accelerate to increase my velocity relative to you, I see your time flow slow down and some distances change. I cannot picture how I would expect you to gravitationally implode, but if that was the case would I not expect it to take/approach an infinite time to do so?

I don't know but I would argue yes. Compare two identical planets orbiting a sun. Identical except one is hotter than the other. The energy of the heat, which is really just the additional kinetic energy of the constituent parts, adds inertia to the hotter planet and must therefore increase the gravitational force as well. If not the equivalence principle would not hold exactly. I think this low speed example should hold in principle even though as the constituent particles increased in their velocities the planet would fly apart well below light speed.

This is not required although many designs are done this way.

I checked the link and it says in the first paragraph that it is assuming the escape of a mass that is negligible compared to that of the source. So is the escape velocity of a source mass independant of the mass of the object attempting to escape, but only negligibly small masses escape? (one and only one escape velocity for each source mass) Or is the definition incomplete and they are they only defining escape velocity for the limited (most common) case?

I will check out the link, but how can it not be obvious? It is the same case calculated differently. If the second calculation yields a different answer then the formula cannot be valid for that calculation. I therefore think that the formula only holds for a limited range of mass ratios as an approximation. I agree knowing would be better.

I think this formula assumes the smaller mass is "negligible" compared to the larger mass, but I don't think it completely "cancels out". If it did the escape velocity of the larger mass from the smaller one would be much smaller than the escape velocity of the smaller from the larger... and obviously they must be equal. So I think your point is valid.

Isn't that considered in the average albedo, given that you use frontal area and not surface area?