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Nicholas_Bostaph
2003-May-23, 03:55 PM
I have what could be a stupid question related to the speed of light (since I never did have a physics class in HS). I'm just starting to take interest in astronomy again (haven't really thought about it since I was very young) and hope to pick up my first telescope soon :). I've been reading over this board the past few days and find it very educational. Anyway, I started thinking about this scenario the other day and I can't seem to resolve it so it's been really bothering me. Here it is, any thoughts would be appreciated.

If I understand relativity correctly (which I may not) the energy required to accelerate any matter increases exponentially as you approach the speed of light, because relativistic speeds increase the mass of that matter. That's why particles without mass (like photons) can travel at exactly c.

Now, assume that you have two massive bodies, lets say neutron stars for instance, that for some reason are speeding at each other. As they approach, they will begin to exert gravity on one another, which will accelerate them. Now, as they accelerate, they will require more energy to continue the acceleration, but will require that simply because they have more mass due to their velocity. Since the energy accelerating them (gravity) should increase directly proportionally to mass, shouldn't their acceleration continue without end...past the speed of light? Couldn't this also happen if massive binary stars began a decaying orbit of one another?

I've no doubt that I did something wrong in this reasoning, but could someone please tell me what before it drives me crazy :P. Thanks!

Carv
2003-May-23, 04:37 PM
I'm not sure I'm reading this right--Are you saying objects accelerate indefinitely as they fall down?

Russ
2003-May-23, 09:06 PM
You have an interesting postulate but you're leaving out many of the factors you need to make your determination. Most obvious is the rate of closure at the start of the cycle. For the sake of argument we'll say 100 kilometers/sec. Then you need to know the Roche limit for each neutron star and the tangent for the impact, we'll say 500 klicks for the Roche limit and zero for the tangent so they hit head on.

Without going into all of the math, the answer is, they can't accelerate fast enough into each others gravity well, such that their rate of clusure is equal to, or in excess of, C. Once they have merged, they will form a black hole (BH) and then all bets are off. What happens inside the event horizon of a BH is pure speculation at this stage of the game.

Confussion to Brooks of Sheffield! :) :D :lol:[/quote]

Avatar28
2003-May-23, 09:45 PM
Also, you're confusing inertal mass with gravitational mass. As you approach C, INERTIAL mass increases. Gravitational mass does not, so you won't get any further acceleration due to the increase in mass.

If I read the question right, his thought is that as you approach C, mass increases so therefore the gravity exerted by the object would increase which would, in turn, further increase the rate of acceleration which would increase the mass faster and so on.

Carv
2003-May-24, 12:37 AM
I see. Well, that's an interesting question. But in any event, if the objects were close enough to pull each other toward each other, they won't have enough collision distance between them to accelerate anything up to relativistic speed, so it's kind of a moot point.

Klausnh
2003-May-26, 03:36 PM
Also, you're confusing inertal mass with gravitational mass. As you approach C, INERTIAL mass increases. Gravitational mass does not, so you won't get any further acceleration due to the increase in mass.

there is no difference between gravitational and inertial mass as far as we know.

kilopi
2003-May-26, 05:50 PM
From the World of Physics (http://scienceworld.wolfram.com/physics/BlackHole.html), it says "The two body problem of general relativity (Einstein and Rosen 1935) is still unsolved. It cannot be treated analytically. The first numerical solution of the head-on collision of two black holes of equal mass was obtained by Smarr (1979), and Matzner et al. (1995) determined the details of the coalescence." That seems relevant to the OP.

Nicholas_Bostaph
2003-May-28, 01:55 PM
I figured I was missing something but couldn't figure out what...so I was hoping someone here would set me straight. Thanks guys ;).

And yeah, I was assuming that inertial mass and gravitational mass were the same thing. I'll have to research that...

Grey
2003-May-28, 02:35 PM
And yeah, I was assuming that inertial mass and gravitational mass were the same thing. I'll have to research that...
To the best of our knowledge (and it's one of the axioms of general relativity), inertial mass and gravitational mass are the same thing. It's tricky to test because gravity is such a weak force. The most accurate experiment that I know of has verified the principal of equivalence to 1 part in 100 billion (10^11), and there continue to be experiments to compare the two at greater levels of precision.

kurtisw
2003-May-28, 03:02 PM
And yeah, I was assuming that inertial mass and gravitational mass were the same thing. I'll have to research that...
To the best of our knowledge (and it's one of the axioms of general relativity), inertial mass and gravitational mass are the same thing.

Yes, this is true.

For this point, a subtle but important point needs to be made. As velocity increases, it is not the *mass* that increases, but actually the *momentum*. In Newtonian physics, momentum is mass times velocity. And since we know that the velocity cannot go faster than the speed of light, most people take that to mean that the mass is increasing. But that's not technically true.

For the gravitational pull and acceleration measurements, I believe it is the "rest mass" that comes into the equations, not the effective mass (the momentum divided by the velocity).

kilopi
2003-May-28, 03:11 PM
For the gravitational pull and acceleration measurements, I believe it is the "rest mass" that comes into the equations, not the effective mass (the momentum divided by the velocity).
Energy has "gravitational pull," so no, that would not be right. It's the "effective" mass.

rsa
2003-May-28, 05:26 PM
What I think that is being missed here (although alluded to) is that as the relativistic mass increases the inertial mass increases as well making the neutron stars harder and harder to accelerate. Discounting the problem of having enough time for the netron stars to acelerate to c, as the gravitational mass approached infinity the inertia would approach infinity as well. Hence, you would never quite get to the speed of light.

Eric Carlson
2003-May-28, 06:48 PM
If two neutron stars collide, they would not exceed the speed of light. However, it's a lot more complicated than that.

Let's start with a much simpler problem. Take an electron, and put it in a constant electric field. The electron will accelerate, increasing its kinetic energy without bound. So eventually, it must be moving faster than the speed of light. Right?

Wrong. The formula for kinetic energy is not the Newtonian E=mv^2/2. The relativistic formula is a bit more complicated, but the point is, as the electron approaches the speed of light, its kinetic energy approaches infinity. So you can get arbitrarily high energies without ever reaching c.

Naively, you might think this solves the colliding neutron star problem. If we had a nice simple theory of gravity, I suppose it would. But general relativity is very tricky. In particular, gravity is not a simple scalar theory. Gravitational attraction depends not only on the mass of the objects creating it, but also on their velocity. So we can't simply jump to any conclusions based on the previous argument.

If you start getting into the details of general relativity, you'll realize that the question as asked is ill formed. Neutron stars are definitely not points, so which point in the neutron star are you going to use to measure the velocity of it? It won't even be spherically symmetric,so you can't just say "the center." Also, how are you going to measure velocity? Any hypothetical measurement of velocity would involve something like bouncing light signals from one place to another. Since the neutrons stars are about to combine to make a black hole, light from any point you are trying to measure might not even make it out of the black hole! So, you see, it isn't easy to answer the question about the velocity of the two neutron stars. It turns out these questions are incredibly ill posed in general relativity. And, oh yeah, the problem is also too hard to solve, given current technology, so even if you make the question well-posed, the answer might well be "we don't know."

kurtisw
2003-May-28, 09:04 PM
For the gravitational pull and acceleration measurements, I believe it is the "rest mass" that comes into the equations, not the effective mass (the momentum divided by the velocity).
Energy has "gravitational pull," so no, that would not be right. It's the "effective" mass.

Here's (http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html) a site that discusses this.