JWT Kottekoe relativistic mass isn’t absolutely wrong, it just isn’t necessary, and it can cause a lot of confusion. For instance a lot of folk think an increase in relativistic mass would cause gravity to increase, and therefore if the object is going fast enough it would turn into a black hole. Also, if relativistic mass were real mass then some pretty weird things would be true:
A single particle traveling close to c could collapse stellar objects into black holes.
An object would have different masses in different directions, so
Mass would wind up being some kind of a matrix function.
The only “advantage” I know of to defining “mass” as “total energy” is that a lot of people have heard that as your velocity approaches c, your mass increases, and telling them that’s wrong might confuse them. But then, whenever you’re teaching relativity, you’re always going to have to deal with telling people that things they thought were true are actually wrong, so I don’t see that as a very compelling reason. It’s much easier to say that m is m, and that the formula for momentum is p = mu, where u is a quantity very much like velocity, rather than associating the relativistic effects with the mass, and then explaining why this “change in mass” doesn’t show up in some other formulae.
Chronos and Ring, Thanks for explaining this. I understand your point and appreciate learning something new. It is not new physics, but superior nomenclature. When I took GR many years ago, I don’t think this was the common terminology, but who knows, perhaps I have forgotten. Once you start throwing around four vectors and stress energy tensors, it is clear how to proceed. I’ll have to look it up in my copy of Misner, Thorne, and Wheeler.
I had never seen the quote from the letter to Lincoln Barnett, but I bow down to Einstein’s view of the best way to describe and think about it. (Actually, Lincoln Barnett’s book, “The Universe and Dr. Einstein” was my first encounter with relativity as a teen ager).
Blue shifting doesn’t make a photon travel faster. Photons of all frequencies travel at c in a vacuum.
Perhaps a confusion arose we’re mixing in talk of the OMG particle, which was likely a proton, which has mass, and requires increasing energy to accelerate it close to c.
wrt the maximum frequency, I kinda thought the Planck length would be a limit: that photons with a wavelength less than the Planck length could not exist. But from googling it seems there’s no reason to think this. There’s no reason to suppose, for example, that the universe is quantised into Planck cubes.
Not if it’s just a single photon all by itself. You could, so far as we know, have a photon with so much energy that it would collapse into a black hole if it ever hit an electron, or even one so energetic that it would collapse into a black hole from a collision with a cosmic microwave photon. I include the “so far as we know” there because such a photon would be in a regime where quantum gravity would presumably be relevant, and since we don’t know how quantum gravity works, we can’t say for sure that the rules wouldn’t have changed on us to prevent that.
I doubt physicists waste much breath arguing over whether “mass” means rest-mass, m-naught-times-gamma, or energy-equivalent-mass, or whatever. The sense of the term is going to be clear from context. If someone says electrons have mass X, photons have zero mass, or some cosmic ray has the mass of a bagel with cream cheese, we know what he means.