I’ll DEFINITELY check it out. When I took this stuff in college it was just a requirement I needed for my engineering major. I slogged through it (mostly on a strong math background), but I didn’t really pay that much attention to be honest. I want to at least get a good grasp of the concepts from a laymans perspective, so I can at least discuss the subject rationally without looking TOO stupid.
From John Mace
You’ll have to let me know what you think. When you get to the book (I think its the 5th or 6th book in the series) that is nearly pure Ayn Rand…you’ll know instantly why people were comparing them.
Very simply, mass is the energy of a system that cannot be transformed away.
Plus mass and energy are not things they’re properties of a system, and the mass and energy of any closed system cannot change. The reason they can’t change is because momentum must be conserved. The relativisticly correct equation that describes this is:
m2 = E2 - p2
E = energy
m = mass
p = momentum
c = 1
So if the momentum can’t change then neither can the mass.
A moving object does not gain mass and its gravitational attraction does not increase. This must be true because all of its kinetic energy can be transformed away. If this weren’t true then any relativistic object would collapse most stellar objects into black holes.
Gardner updated Relativity for the Million in 1976 and renamed it The Relativity Explosion. That’s out of print, too, but you can get it used. In 1997 he wrote Relativity Simply Explained, but I haven’t read it.
Just when I’m thinking I’m getting a handle on things… Ok, what does this mean? A moving object does NOT gain mass at relativistic speeds? What happens to it then? If it doesn’t GAIN mass, does it CHANGE mass? Same with the gravitation…it doesn’t increase attraction?
Is the Universe considered a closed system? I suppose it might be at that, but a very large one.
If you plug in the formulas for E and p and simplify you get m = m. So mass is not dependent on velocity and it is an invariant quantity.
The above equation represents the “energy-momentum four-vector” which is one of the most basic concepts in SR. The time component of this vector equals the energy, the space component equals the momentum and its magnitude is the mass.
Relativistic mass is an outmoded concept which can cause a lot of confusion and the vast majority of physicists do not use it, and it certainly does not enter in energy stress tensor which is the source of gravitation.
Agreed that relativistic mass is an outmoded concept, but it’s not completely irrelevant to the stress-energy tensor, i.e. objects travelling at relativistic speeds weigh more.
At a given time the gravitaional forces between two objects would be greater when they are moving in different inertial frames than if they were in the same inertial frame.
That’s true but its very different from saying that a moving object weighs more than a stationarly object. In the above case the system has a zero monentum frame and so the kinetic energy is part of the systems mass. In other words the energy can’t be transformed away.
Actually let me rethink this. The system of two moving masses would definitely exert an increased gravitational attraction on a third body but I’m not so sure their mutual attraction would increase.
The field would be different because the mass, momentum and energy densities would be different but I don’t think the attraction would be any greater.
Does this mean that energy and mass are the same thing, if the object in question is not moving (i.e. has zero kinetic energy)? Is there any intuitive way to understand what the math is saying here? How can energy EQUAL mass, if the mass is not moving?? Is this just one of those things you take on ‘faith’ because the math says its so, or is there a way to explain this that a dope like me can understand it?
Mass and energy are not the same thing. In fact they’re not things at all they’re properties of a system. Energy is the time component of the momentum four-vector and mass is the magnitude of the four-vector. However in the rest frame, and only the rest frame, E does equal mc[sup]2[/sup].
Two photons moving parallel have energy but no mass. If they’re moving anti-parallel then they have both mass and energy.
Because any system that has mass also has energy.
E = mc[sup]2[/sup] / (1 - v[sup]2[/sup]/c[sup]2[/sup] ) [sup]1/2[/sup]
When you get to the book (I think its the 5th or 6th book in the series) that is nearly pure Ayn Rand…you’ll know instantly why people were comparing them.