I lookd through those wikipedia articles last night too and what you wrote here sounds accurate to them. I was confused by at least one thing though–in one relevant article, it is claimed that momentum is one of several components that goes into the calculation of an object’s gravitational field. This suggests to me that relativistic mass does affect the gravitational field around an object having that relativistic mass. If this is the case, then my question is, does it affect the gravitational field in the same way rest mass would affect that field? And if that’s a yes, then my next question is how do we avoid the implication that accelerating an object to an extremely high speed will in and of itself cause the object to make stellar objects around it collapse into black holes?
Nothing personal here. I approached him, he didn’t approach me.
No, what actually happened was someone pissed in my cheerios that morning.
Why would anyone do that? It’s so gross.
But… I do think it’s true that it is bad (impolite or something) to, as someone else put it, “have the knowledge to give an answer like si blakely’s but refuse to even when asked to expand” assuming no exculpating factors.
Sorry guys I see this alot on the Dope and it aggravates me. People confuse “fighting ignorance” with “being unkind to the unknowledgable.” But anyway, I won’t bring it up again (in this thread).
To help me understand whether this mass is real or not, let’s talk about another quality of mass. According to special relativity does a high velocity particle have a greater gravitational pull than a resting particle?
According to special relativity, no. Velocity is just a relative quantity, and gravity is a force that is invariant across different inertial frames (an inertial frame is one that is not accelerating). So if you observe an object standing still, then observe it going at some relativistic speed, it will have the same gravity.
In general relativity, that changes. Gravity is no longer a force, but a result of the warping of spacetime by mass-energy. This is another instance where the mass-energy equivalence (E=mc[sup]2[/sup]) comes in, as gravity is not just a result of mass, but a result of energy as well, as they are just different forms of the same thing. In the Einstein field equations, you have the Einstein tensor, which describes curvature, and the stress-energy tensor, which describes the source. A source of curvature can be a simple point mass, but it can also be the energy of motion. In other words, an object in motion will warp spacetime more than an object standing still, and therefore will have a different sort of gravitational field associated with it. This isn’t the same thing as the object’s mass increasing with its speed, because the whole field shape changes. For example, an object that is not moving but is simply rotating in place will also have a different gravity than one that is not rotating, as the energy of its rotation also warps spacetime. This might seem to contradict SR at first, but in GR, the gravitational field is not invariant in all frames, it depends explicitly on what frame you’re in.
Thanks for the response. I meant to say “general relativity”:smack:. So this somewhat bolster’s the formulation of a moving particle having more mass.
No, you really can’t look at as anything to do with increased mass. The field changes but not in a manner that has any relation to relativistic mass.
Good call si_blakely. this is also true for photons, which obviously have no mass at all. A system of photons with parallel velocity vectors has no mass whereas a system with a zero momentum frame does. Of course since photons have energy they do attract via the gravitoelectric force but they also have momentum which generates an equal and opposite gravitomagnetic force.
The reason for the concept of relativistic momentum in the first place is that some folks wanted to make the equations look the way they liked them, instead of the simplest way, and did a poor job of it, to boot. In Newtonian physics, the formula for momentum is P = mv. In relativistic physics, however, the formula is P = gammamv, where gamma = 1/sqrt(1-v[sup]2[/sup]/c[sup]2[/sup]) is a quantity that shows up in a lot of the relativity equations. Now, if you want to make this formula look like the familiar Newtonian formula, one way you could do it is by saying that there’s something called relativistic mass (which I’ll denote by a capital M) and say that M = gammam, and therefore in relativity, P = M*v. This makes that particular equation look nice, but then you really ought to ask if this “relativistic mass” behaves like we think mass ought to, in other ways. And the answer is, no, it doesn’t really (for instance, something won’t collapse into a black hole from having a “relativistic mass” that’s too high). You are, of course, free to define a quantity like that (you can define whatever you want), but it turns out it isn’t very useful at all.
Now, on the other hand, you could also decide to “clean up” the equation by absorbing the gamma into the velocity, instead of absorbing it into the mass. So you could define something called “relativistic speed”, or “proper speed” as it’s more commonly known, denoted by u. Then you’d have that u = gammav, and P = mu. This makes the equation just as pretty as in the relativistic mass version, but it has the benefit that proper speed really does behave like we’d expect speeds to behave in many different contexts, and many different sorts of equations get simpler when you use proper speed rather than regular speed in them.
The thing that has always bothered me about proper velocity is that, unlike other properties with the word proper attached, it can’t be measured directly by the traveler.
And since it’s observer distance divided by traveler or proper time, no one could actually measure it.
It cleans up a lot of equations, but do you have any suggestions on intuiting it?