Which Concepts Are Employed in General Relativity Calculations?

[Rapier]

Homework Statement

I'm staring down a concept homework assignment that is giving me fits. We are just moving into relativity.

6) The quantity γmc^2 represents...
a) the rest mass energy.
b) relativistic kinetic energy.
c) total relativistic energy.
d) relativistic momentum.
e) None of the above.

I can't find this in my textbook, but mc^2 is the rest energy. So I thought that must be a. But γ is the symbol for a photon, and a couple of other things. I might be second guessing myself with e.

11) Which of the following (if any) is/are is NOT relativistically invariant?
a) Mass.
b) Speed of light.
c) Momentum.
d) Space-time interval.
e) All of the above are relativistic invariants.
f) None of the above are relativistic invariants.

Relativistic variants are the stuff that changes at relativistic speeds. So relativistic invariants are the stuff that DOESN'T change at relativistic speeds. The stuff that is NOT relativistic invariants are relativistic variants. So I am looking for stuff that changes at relativistic speeds. The speed of light can't ever change so it can't be B, which also eliminates E. Mass doesn't change, but there is a relativistic mass...I'm not sure if that means mass changes or perhaps just the effect of mass changes. Whatever happens to mass, so happens momentum. Space-time travel definitely changes at relativistic speeds (time dilation and length contraction).

So, relativistic variants (A, C, D) and relativistic invariants (B). I thought the answer would be A C and D but that isn't an option. So I think I've either misunderstood my relativity chapter or I'm argued myself into a loop somewhere along the way.

12) Which of the following do NOT use general relativity in calculations?
a) Describing black holes.
b) Global positioning.
c) Gravitational lensing.
d) Describing neutron stars.
e) All of the above employ general relativity calcultions.

The chapter discusses that GPS is an application of the special theory of relativity. But I thought that the special theory was more specific than general. But none of the others are in my text, but I know that general relativity talks about gravity and stuff which is relative (get it...relative...HAH!) to A C and D. So I really think that it's E and that general relativity actually does describe GPS.

Help? I've been working on this for far too long and my brain is just fried! Thanks!

 

[217 MeV]

Hi Rapier!

In question 6, $\gamma$ denotes the Lorentz factor, $\gamma=\frac{1}{\sqrt{1-\frac{v{^2}}{c^{2}}}}$. Does this help you determine the correct answer?

For question 11, as you correctly said, we have the idea of a relativistic mass. This is the "actual" mass of an object traveling at speeds comparable to the speed of light; this implies that the mass of an object depends on its velocity, does this make mass relativistically variant or invariant?

You are right in saying that GPS uses special relativity (SR) in its application. SR describes processes that involve velocities comparable to that of the speed of light (or just generally where light is involved). General relativity (GR) is used to describe gravity as a geometrical entity, the warping of space-time. This warping is significant around large masses (i.e. areas of high gravitational field strength). Applying GR to GPS would definitely increase its precision, but often this is not necessary.

I hope I've helped!

 

[Rapier]

Hi Rapier!

In question 6, $\gamma$ denotes the Lorentz factor, $\gamma=\frac{1}{\sqrt{1-\frac{v{^2}}{c^{2}}}}$. Does this help you determine the correct answer?

For question 11, as you correctly said, we have the idea of a relativistic mass. This is the "actual" mass of an object traveling at speeds comparable to the speed of light; this implies that the mass of an object depends on its velocity, does this make mass relativistically variant or invariant?

You are right in saying that GPS uses special relativity (SR) in its application. SR describes processes that involve velocities comparable to that of the speed of light (or just generally where light is involved). General relativity (GR) is used to describe gravity as a geometrical entity, the warping of space-time. This warping is significant around large masses (i.e. areas of high gravitational field strength). Applying GR to GPS would definitely increase its precision, but often this is not necessary.

I hope I've helped!

The lorentz transformations are used to describe the changes that happen during relativistic travel. If I replace the gamma with the 1/sqrt(1-(v^2/c^2) that looks like the equation for total relativistic energy. C.

Mass is relativistic variant. :) Obviously the number of moles of material won't change (which I think is what we really mean non-relativisticly when we say mass is constant), just because you're moving forward doesn't mean atoms just pop into existence. So relativistic mass is more about the effect a mass has on it's surroundings. If I'm understanding correctly. Oh, this means they are all relativistic except the Speed of Light so my answer is C.

Your description for general vs special relativity was very clear. The text seemed to muddle it for me. Using your description it is easy to see that B is the answer because it uses the shift in relativistic time to calculate distance.

Thank you so much for your help.

 

[vela]

Mass is relativistic variant. :) Obviously the number of moles of material won't change (which I think is what we really mean non-relativisticly when we say mass is constant), just because you're moving forward doesn't mean atoms just pop into existence. So relativistic mass is more about the effect a mass has on it's surroundings. If I'm understanding correctly. Oh, this means they are all relativistic except the Speed of Light so my answer is C.

You should rid yourself of the notion of relativistic mass. When physicists refer to mass of an object, they're talking about its rest mass.

Your description for general vs special relativity was very clear. The text seemed to muddle it for me. Using your description it is easy to see that B is the answer because it uses the shift in relativistic time to calculate distance.

This is incorrect. GPS is actually one of the rare instances where general relativity has an impact in everyday life. See, for example, http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html.

 

[217 MeV]

This is incorrect. GPS is actually one of the rare instances where general relativity has an impact in everyday life. See, for example, http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html.

Yeah, perhaps I should have clarified that slightly, GPS does use both GR and SR in order to attain the precision that we expect nowadays.