Peter,

If I've said it once, I've said it a hundred times; I'm no mathematician. I do pretty well with integral calculus, but not difEQs, and I don't get tensors, at all. So I'm pretty much handicapped in general relativity. I get the concept of redefining space and time in terms of the path of light. I'm not comfortable thinking in terms of warped space-time, even though I have a conceptual understanding of it.

My intro to special relativity in 1967 used the term "relativistic mass" to mean the mass gained due to velocity; in other words, the difference between a particle's mass in its own frame of reference and its mass in a different inertial frame of reference. I didn't really understand relativity until decades later, when I read some of Einstein's work on my own, without having it "explained" to me by a nutty professor.

I've read discussions of relativity in which "m" represents rest mass, and relativistic mass is "γm", meaning total mass in an observer's reference frame, i.e. rest mass plus the increase due to velocity. In other discussions, rest mass is "m_{0}", and "m" is total mass in the observer's reference frame; m = γm_{0}. So the problem is not disagreements about the science as much as it is about a lack of uniformity in nomenclature.

There are many writings out there, already, using different symbols to represent the same thing, and the same symbols to represent different things. There is also the well-established fact that "m" represents "meter". If an international governing body declares that one set of existing symbols is correct, that will not clear up the confusion until the new convention is universally adopted and the old lack of convention is forgotten. Anyone reading an old unconventional writing will have the responsibility to decipher what system the author used. Publishers will have a duty to annotate those old writings, explaining what the symbols meant to the author.

Perhaps it would be better to invent new symbols, which have not previously been used to mean anything other than what the new convention demands. In particular, the symbol "m" will is likely to be misinterpreted, unless the reader makes an effort to determine whether it is used in the new conventional way or an old unconventional way.

I am comfortable with the symbol "m_{0}" for rest mass. As far as I know, it has no other meaning in literature about relativity. On the other hand, "m = γm_{0}" probably should be changed to something like "m_{t} = γm_{0}". If "m_{t}" means the total mass in an observer's reference frame, and if that symbol has not been used in the past to mean something else, then its meaning would be immediately obvious to the reader.

As for actual scientific disagreements:

· There is the dispute over whether the photon has inertial mass and/or gravitational mass. I accept, without understanding, that a photon has no mass in the context of warped space-time; but in the context of Euclidean space and time, the photon MUST have both inertial and gravitational mass. Defining force as the rate of changing momentum, f = dp/dt, gravity exerts an attractive force on a photon. To conserve momentum, the photon must exert an equal and opposite force on the source of that gravity, so the photon has gravitational mass. Likewise, inertia should be defined in terms of momentum, not velocity; it takes force to alter a photon's momentum, so the photon has inertial mass. Also, a photon does change direction in Euclidean space as it passes near a gravity well. It's velocity (not speed) is different when it emerges on the other side, so it has accelerated. A photon does not accelerate in Minkowski space-time because its path is the definition of a straight line.

· There is also the dispute over whether gravitational mass of a particle is the same in all reference frames or whether it is proportional to relativistic mass. It seems to me that time dilation of a simple two-body gravitational system (e.g. a planet and moon) demands that relativity increases inertial mass but not gravitational mass of the two bodies toward one another. Consider a pair of equal masses orbiting one another due to their mutual gravity. In a recent thread, I took the example of two space ships, each with a mass of 1000 tonne, 100 m apart. In their own inertial reference frame, they orbit once every 107 hours. In a reference frame where gamma = 10, that orbital period becomes 1070 hours because of time dilation. Therefore, they accelerate toward one another ten times slower. If their gravitational mass and inertial mass both increased tenfold, they would accelerate toward one another ten times faster and orbit one another every 10.7 hours. Perhaps the two orbiting bodies do exert ten times as much gravity on a body which is at rest in the observer's reference frame; I haven't figure that one out.