# Several Questions About Mass (Physics)

I actually have more than one question about mass in physics. So why not just put it in one thread?

Einstein proved time and space are relative. Is mass relative too? Because I never hear people say that. Yet it is still affected by velocity, isn’t it? And if mass is relative, then how do you measure it accurately (or consistently, in any event)?

Also how do you measure mass in a weightless environment? I’ve heard of the astronauts doing this. But how? Please describe this in detail.

And lastly, gravity slows down time. What effect does it have on mass? Yes, I know it gives mass weight. But mass and weight are two separate things. Does it have any effect on the actual mass of an object?

A particle will have an invariant mass, which you can measure, theoretically, by being in a co-moving frame in which it is at rest and has no momentum. This is essentially (up to the speed of light) equal to the particle’s energy in that frame; in other frames of reference it will have greater energy.

ETA

Push on the object, and see how much inertia it has.

I suppose you could say that when you apply a force to an object, the resulting acceleration will depend on the “relativistic mass”.

Einstein determined that space-time interval is invariant - and that mass (what used to be called “rest mass”) is also invariant.

One way to measure mass in space is by shaking the object - the more massive it is, the more effort it takes to shake it.

Yes. The faster an object moves, the more mass it will have. At infinite velocity (obviously impossible) it will have infinite mass (also impossible, but it illustrates the correlation.)

Gravity is indistinguishable from acceleration. (That’s one of the fundamental concepts of Einstein’s relativity. If you’re standing on the floor of a windowless elevator, there’s no way to tell whether you’re unmoving in a place of gravity, or whether the elevator is zooming upwards and you feel like gravity is pulling you down.)

Therefore, yes, whatever effects high velocity has, high gravity will do the same, and time will slow down.

My apologies to everyone. I’m sure I confused “velocity” and “acceleration” in those posts. If anyone wants to straighten me out on which is right, please go ahead.

Relativistic mass is a very seductive concept. It makes sense in a couple of contexts and makes a mess in all others and has been declared undesirable by many physicists from Einstein and on (including Einstein). For instance you end up with having to deal with a different mass concept in the direction of travel and all other directions.

Yeah, the basic idea behind “relativistic mass” is that you’ve got this equation for momentum that works in Newtonian physics, p = m*v (and no, I don’t know why the letter “p” is used for momentum). Well, if you take the Newtonian definitions of p, m, and v, you find that in relativity, the actual equation is p = gamma*m*v, where gamma is a number that depends on the velocity: At velocities much less than the speed of light, like we’re used to, it’s very close to 1, but as v approaches c, gamma increases without bound.

Some physicists got a bee in their bonnet about this, and declared that, no, the equation for momentum absolutely must still look like the Newtonian equation we’re used to, and so decided to absorb the gamma into the mass: Relativistic mass is gamma times the Newtonian mass, and so now, using this “relativistic mass”, we’re back to p = m*v.

Which is of course silly: There’s no fundamental reason why the new equations must look like the old equations. But even if you insist that they do, the folks who came up with relativistic mass did it the wrong way: They should instead have absorbed the gamma into v, which makes something called “proper velocity” (denoted by the letter u). And so then we have p = m*u , where m is still the good old familiar Newtonian mass, and u is a concept that turns out to actually be useful in a wide variety of applications in relativity.

It seems like it often takes a while to figure out convenient ways to express a new concept - Maxwell’s original equations were a confusing mess, as I recall, so I guess it’s not that surprising that people initially combined gamma with m. And, of course, even after physicists got out of the habit of using “relativistic mass,” the term had firmly lodged itself into popular-science books, so it’s as immortal as the solar system atom now.

And the 9-planet solar system. Oh well.

The solar system isn’t that immortal. If relativistic mass exists then there must be a frame of reference where the Sun is so massive it collapses into a black hole.

There was a “Probability Zero” (i.e. spoof story making a deliberate science error) in Analog with that idea in the 1980s I think.

“Escape Velocity” by Don Sakers - Title: Escape Velocity

Thanks. I’d like to say I invented the idea independently but I just stole it from someone. Maybe someone on this board.