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Glom
2004-Apr-27, 07:40 PM
I know SR applies to activities in inertial frames, but if a spacecraft is accelerating to relativistic speed in a straight line, will using variable velocity derivations of the SR equations suffice? At what point do you need to go SR?

NB this is not an invitation to discuss what is wrong with relativity.

tlbs101
2004-Apr-27, 08:51 PM
As I understand it, the moment the "spacecraft" is accelerating, and not at a constant (relativistic) velocity, GR must be used, and SR does not apply.

That is my understanding, anyway. I could be wrong.

.

SeanF
2004-Apr-27, 08:59 PM
If you're observing from a non-accelerating reference frame, I believe you can use SR-derived equations - key word is "believe." :)

If you're observing from the accelerating reference frame itself, you would definitely need to use GR - of that much I'm certain.

I'm going to take that back. It actually may be possible to use SR-derived equations even when viewing from the accelerating reference frame - but I'm not sure about that, now, either. :-?

If so, though, it would basically boil down to just deriving the GR equations, wouldn't it?

Grey
2004-Apr-28, 12:01 AM
I know SR applies to activities in inertial frames, but if a spacecraft is accelerating to relativistic speed in a straight line, will using variable velocity derivations of the SR equations suffice? At what point do you need to go SR?
If the acceleration is small, then the effects from GR are fairly small. In this case, you can approximate the situation with an infinite number of reference frames ranging in velocity from zero to the ending velocity, and your results will be pretty close. If your acceleration was constant, you could probably get a good first-order correction just by adding in the GR effects of an equivalent gravitational field.

daver
2004-Apr-28, 04:27 PM
I derived the equations for a relativistic rocket under constant acceleration using just SR; these matched some other equations posted on the net, so I was relatively certain I'd done it correctly. It's of course entirely possible that the other equations were derived using only SR as well, so the agreement might not have particularly significant.

Eroica
2004-Apr-28, 04:57 PM
My understanding is that gravity is the only thing SR can't handle. So long as you can ignore gravitational effects, SR should suffice.

But I've been wrong about these things before .... :-\$

SeanF
2004-Apr-28, 04:58 PM
My understanding is that gravity is the only thing SR can't handle. So long as you can ignore gravitational effects, SR should suffice.

But I've been wrong about these things before .... :-\$

Ah, but GR says that gravity and acceleration are identical - or, at least, indistinguishable. So, if SR can handle acceleration, it should be able to handle gravity, too, no?

daver
2004-Apr-28, 08:51 PM
Ah, but GR says that gravity and acceleration are identical - or, at least, indistinguishable. So, if SR can handle acceleration, it should be able to handle gravity, too, no?
I should let someone who knows more about GR than how to spell it in, but the situations obviously aren't identical. Three observers, A, B, and C. A is in a 1 g gravity field, but otherwise motionless with respect to C. B is in a rocket accelerating at 1 g, who starts out motionless with respect to C. After a year, C predicts radically different results as to A and B's perceptions.

SeanF
2004-Apr-28, 09:03 PM
Ah, but GR says that gravity and acceleration are identical - or, at least, indistinguishable. So, if SR can handle acceleration, it should be able to handle gravity, too, no?
I should let someone who knows more about GR than how to spell it in, but the situations obviously aren't identical. Three observers, A, B, and C. A is in a 1 g gravity field, but otherwise motionless with respect to C. B is in a rocket accelerating at 1 g, who starts out motionless with respect to C. After a year, C predicts radically different results as to A and B's perceptions.

In the A-C situation, how are you keeping C from falling if it's in a gravitational field?

milli360
2004-Apr-30, 02:13 PM
After a year, C predicts radically different results as to A and B's perceptions.
Predicts using GR?

daver
2004-Apr-30, 04:13 PM
After a year, C predicts radically different results as to A and B's perceptions.
Predicts using GR?

No, GR of course gives the correct answer. If you were misapplying the equivalence principle you might say that C would think A and B were in the same boat, as one was accelerating at 1 g while the other was in a 1 g field; hence after one year C would think that both would be extremely time dilated.

SeanF
2004-Apr-30, 04:32 PM
Three observers, A, B, and C. A is in a 1 g gravity field, but otherwise motionless with respect to C. B is in a rocket accelerating at 1 g, who starts out motionless with respect to C. After a year, C predicts radically different results as to A and B's perceptions.

Daver, you didn't answer my question. The implication is that A's distance to C doesn't change. How do A and C maintain a constant distance if there's a gravitational field present?

daver
2004-Apr-30, 10:26 PM
Three observers, A, B, and C. A is in a 1 g gravity field, but otherwise motionless with respect to C. B is in a rocket accelerating at 1 g, who starts out motionless with respect to C. After a year, C predicts radically different results as to A and B's perceptions.

Daver, you didn't answer my question. The implication is that A's distance to C doesn't change. How do A and C maintain a constant distance if there's a gravitational field present?

Keep C a bit away from A--10 AU ought to be good enough for this example.

Tensor
2004-May-01, 02:41 AM
My understanding is that gravity is the only thing SR can't handle. So long as you can ignore gravitational effects, SR should suffice.

But I've been wrong about these things before .... :-\$

Ah, but GR says that gravity and acceleration are identical - or, at least, indistinguishable. So, if SR can handle acceleration, it should be able to handle gravity, too, no?

It's my understanding SR can handle gravity too, although it gets ugly. You have to chop the problem into inertial frame pieces, solve those pieces applying the equivalence principle (acceleration, instead of gravity), and then put it all back together again. Like I said, ugly, and not something I would want to try.

Taibak
2004-May-01, 04:49 AM
My understanding is that gravity is the only thing SR can't handle. So long as you can ignore gravitational effects, SR should suffice.

But I've been wrong about these things before .... :-\$

Ah, but GR says that gravity and acceleration are identical - or, at least, indistinguishable. So, if SR can handle acceleration, it should be able to handle gravity, too, no?

It's my understanding SR can handle gravity too, although it gets ugly. You have to chop the problem into inertial frame pieces, solve those pieces applying the equivalence principle (acceleration, instead of gravity), and then put it all back together again. Like I said, ugly, and not something I would want to try.

Ugh... that's a bunch of integrals I just don't want to do....

I'll stick with GR, thank you very much. 8-[

Tensor
2004-May-01, 06:25 AM
It's my understanding SR can handle gravity too, although it gets ugly. You have to chop the problem into inertial frame pieces, solve those pieces applying the equivalence principle (acceleration, instead of gravity), and then put it all back together again. Like I said, ugly, and not something I would want to try.

Ugh... that's a bunch of integrals I just don't want to do....

Hey, I said it would be ugly. #-o

I'll stick with GR, thank you very much. 8-[

Well, on the bright side, you wouldn't have to learn Differential Geometry. 8-[

Chip
2004-May-01, 08:56 AM
Ah, but GR says that gravity and acceleration are identical - or, at least, indistinguishable. So, if SR can handle acceleration, it should be able to handle gravity, too, no?

Let's also keep in mind that Newtonian physics does not disappear within the realms and reference frames of SR and GR. Its effects are present, though integrated in new as well as familiar ways.

milli360
2004-May-01, 03:19 PM
After a year, C predicts radically different results as to A and B's perceptions.
Predicts using GR?

No, GR of course gives the correct answer. If you were misapplying the equivalence principle you might say that C would think A and B were in the same boat, as one was accelerating at 1 g while the other was in a 1 g field; hence after one year C would think that both would be extremely time dilated.
Ah. But whose fault is that? I don't see why one would insist on misapplying the equivalence principle.

Taibak
2004-May-01, 03:23 PM
It's my understanding SR can handle gravity too, although it gets ugly. You have to chop the problem into inertial frame pieces, solve those pieces applying the equivalence principle (acceleration, instead of gravity), and then put it all back together again. Like I said, ugly, and not something I would want to try.

Ugh... that's a bunch of integrals I just don't want to do....

Hey, I said it would be ugly. #-o

I'll stick with GR, thank you very much. 8-[

Well, on the bright side, you wouldn't have to learn Differential Geometry. 8-[

I like differential geometry.... :wink:

Diamond
2004-May-01, 04:59 PM
If you're observing from a non-accelerating reference frame, I believe you can use SR-derived equations - key word is "believe." :)

If you're observing from the accelerating reference frame itself, you would definitely need to use GR - of that much I'm certain.

I'm going to take that back. It actually may be possible to use SR-derived equations even when viewing from the accelerating reference frame - but I'm not sure about that, now, either. :-?

If so, though, it would basically boil down to just deriving the GR equations, wouldn't it?

Yes, you can have acclerations in SR. See http://www.math.ucr.edu/home/baez/physics/Relativity/SR/acceleration.html