Is There a Solution to the Faster-than-Light Problem in General Relativity?

[romesh97]

hello
I am facing a conceptual problem in general relativity. I realized that according to einstein's theory of gravity, if I start rotating, I can say myself to be stationary and the entire cosmos revolving around me making me feel the outward force(centrefugal force in earlier view).
But according to my view, I will be viewing distant parts of the cosmos rotating faster than the speed of light.
I know that in gravitational fields light slows down making it not fixed or absolute. But in this case mass is moving faster which I am not able to grasp.
Help me and correct me if I have made wrong assumptions.

 

[ZapperZ]

hello
I am facing a conceptual problem in general relativity. I realized that according to einstein's theory of gravity, if I start rotating, I can say myself to be stationary and the entire cosmos revolving around me making me feel the outward force(centrefugal force in earlier view).

This is incorrect. There are no equivalence here. I can show you a very simple experiment where you can tell if you are spinning, or it is the universe that's spinning. Use a Faucault pendulum. If you are not spinning, the pendulum stays oscillating in one plane in your frame. If you are the one spinning, the pendulum will precess.

Zz.

 

[romesh97]

This is incorrect. There are no equivalence here. I can show you a very simple experiment where you can tell if you are spinning, or it is the universe that's spinning. Use a Faucault pendulum. If you are not spinning, the pendulum stays oscillating in one plane in your frame. If you are the one spinning, the pendulum will precess.

Zz.

But can I not say the precessing of the pendulum a gravitational influence of the ratating cosmos rather than the influence of my rotation.

 

[phinds]

But can I not say the precessing of the pendulum a gravitational influence of the ratating cosmos rather than the influence of my rotation.

Use a small one and hold it in your hand. For that matter, just hold a weight on a string.

 

[ZapperZ]

But can I not say the precessing of the pendulum a gravitational influence of the ratating cosmos rather than the influence of my rotation.

There's no "gravity" here. I am saying your understanding of relativity is incorrect.

In relativity, the validity of a frame and its equivalence means that you have no means to know if you're in one frame or another. 2 inertial references frame have the same footing in everything, and there's no experiment that you can do that tells you that you are in one frame or another, without looking at each other.

Here, I've shown an example where your statement that "... if I start rotating, I can say myself to be stationary and the entire cosmos revolving around me making me feel the outward force(centrefugal force in earlier view)... " is wrong. You CANNOT say that it is equivalent to being stationary and that it is the rest of the universe that's spinning. It is NOT equivalent because I've just shown you an experiment that can DISTINGUISH one from the other.

Zz.

 

[bcrowell]

Welcome to PF!

The prohibition on motion faster than c is local. Globally, GR doesn't even have a well-defined notion of the velocity of a distant object. For example, suppose A says that distant galaxies are moving away from us, but B says those galaxies are at rest and the space in between is expanding. GR doesn't offer any way of deciding who is right. According to A, the velocities may very well be greater than c: http://arxiv.org/abs/astro-ph/0310808

Although it's true that rotation is absolute, not relative, in GR, I don't think that fact has anything to do with resolving your actual question. There are other theories, such as Brans-Dicke gravity, in which rotation is relative, and in those theories the answer to your question would be the same.

 

[romesh97]

There's no "gravity" here. I am saying your understanding of relativity is incorrect.

In relativity, the validity of a frame and its equivalence means that you have no means to know if you're in one frame or another. 2 inertial references frame have the same footing in everything, and there's no experiment that you can do that tells you that you are in one frame or another, without looking at each other.

Zz.

But i am NOT in an inertial frame. Since i am rotating, i am in a non inertial frame.

 

[romesh97]

Welcome to PF!

The prohibition on motion faster than c is local. Globally, GR doesn't even have a well-defined notion of the velocity of a distant object. For example, suppose A says that distant galaxies are moving away from us, but B says those galaxies are at rest and the space in between is expanding. GR doesn't offer any way of deciding who is right. According to A, the velocities may very well be greater than c: http://arxiv.org/abs/astro-ph/0310808

Although it's true that rotation is absolute, not relative, in GR, I don't think that fact has anything to do with resolving your actual question. There are other theories, such as Brans-Dicke gravity, in which rotation is relative, and in those theories the answer to your question would be the same.

so what you are saying is that GR proves the mach's principle wrong.

 

[ZapperZ]

But i am NOT in an inertial frame. Since i am rotating, i am in a non inertial frame.

Exactly! And if you are NOT spinning while the rest of the universe is rotating, then you are in an inertial frame! The two situations you cited are NOT equivalent, i.e. you CANNOT say "... if I start rotating, I can say myself to be stationary and the entire cosmos revolving around me... "! That's my whole point!

Zz.

 

[romesh97]

Exactly! And if you are NOT spinning while the rest of the universe is rotating, then you are in an inertial frame! The two situations you cited are NOT equivalent, i.e. you CANNOT say "... if I start rotating, I can say myself to be stationary and the entire cosmos revolving around me... "! That's my whole point!

Zz.

But if i am not spinning and the rest of the universe is rotating, won't its gravitational influence make me feel the outward force.
How can i distinguish whether i am spinning which is making me feel the force due to my acceleration or it is the universe spinning which is making me feel the outward force due to its gravitational influence.
I can say my frame to be inertial when i feel no force AND can compare my motion with other bodies of the cosmos.
But i was, in my original question, trying to say that there is a relative motion between me and the universe.Then how to distinguish between the two.
And hence show some solution to my problem.
Correct me if i am wrong.

 

[PAllen]

so what you are saying is that GR proves the mach's principle wrong.

Yes. Einstein hoped it might be included, but GR does not include Mach's principle in the sense you mean; it rejects it.

 

[bcrowell]

Yes. Einstein hoped it might be included, but GR does not include Mach's principle in the sense you mean; it rejects it.

But Brans-Dicke gravity salvages it: http://www.lightandmatter.com/html_books/genrel/ch08/ch08.html#Section8.3

 

[romesh97]

But Brans-Dicke gravity salvages it: http://www.lightandmatter.com/html_books/genrel/ch08/ch08.html#Section8.3

so what it means is that we must consider the average distribution of mass in rotational motion.

correct me if i am wrong.

 

[romesh97]

Yes. Einstein hoped it might be included, but GR does not include Mach's principle in the sense you mean; it rejects it.

so does GR rejects the Mach's principle in its entirity or only in rotational motion?

I have read its use in the twin paradox where the away twin experiences acceleration (which slows its clock or time) due to its movement relative to the universe while the home twin, according to the away twin, accelerates, but not relative to the universe.

Does this mean that mach's principle is true for linear acceleration and not for rotational acceleration?

correct me if i am wrong.

 

[chill_factor]

you are wrong.

you can distinguish between universal rotation and yourself being stationary by being in deep space holding a pole with a donut on it. the donut will move slide outwards if you were spinning.

if the universe was spinning and you were stationary, the donut would not slide outwards. if it was gravity, why is only the donut being pulled outwards, and not you?

now you have been corrected.

 

[romesh97]

if the universe was spinning and you were stationary, the donut would not slide outwards. if it was gravity, why is only the donut being pulled outwards, and not you?

now you have been corrected.

i WILL be pulled outward along with the pole if it was universe spinning - cause gravity is universal. how can i say that i won't? gravity WOULD act on me.

Tell me if I am wrong and correct me......

 

[romesh97]

Guys,i know that einstein denounced the mach's principle in the later years of his life. i just want to know the logical reason, according to GR, why it is wrong. (simply because it is so appealing and satisfactory.It is hard for me to accept it to be wrong in one go!).I am not able to work out a logical reason which can prove it wrong.

Please help me out.

 

[chill_factor]

i WILL be pulled outward along with the pole if it was universe spinning - cause gravity is universal. how can i say that i won't? gravity WOULD act on me.

Tell me if I am wrong and correct me......

if you were pulled outwards by gravity along with the pole how can you see the donut move though? you'll be accelerating at the same rate as the donut.

but if you were spinning, you'll note the radial distance of the donut increasing, and the donut moving away from you.

now you can distinguish whether you are spinning or not. again, you are wrong, and you have been corrected.

 

[romesh97]

if you were pulled outwards by gravity along with the pole how can you see the donut move though? you'll be accelerating at the same rate as the donut.

but if you were spinning, you'll note the radial distance of the donut increasing, and the donut moving away from you.

now you can distinguish whether you are spinning or not. again, you are wrong, and you have been corrected.

i am trying to say that i will feel my arms pulled outwards.
but since I'm concidering the universe to be spinning AROUND me, the gravity would increase as one moves farther from me. if the donut rotates along my axis of rotation,it won't move outward(since it would experience equal force at equal distances from the centre or the axis). but it is, as you said, not along the axis of my rotation but further from the axis.

please correct me if i am wrong....

 

[PAllen]

so does GR rejects the Mach's principle in its entirity or only in rotational motion?

I have read its use in the twin paradox where the away twin experiences acceleration (which slows its clock or time) due to its movement relative to the universe while the home twin, according to the away twin, accelerates, but not relative to the universe.

Does this mean that mach's principle is true for linear acceleration and not for rotational acceleration?

correct me if i am wrong.

Pretty much in its entirety in the sense you mean (some people, e.g. Julian Barbour, have proposed a variant of Mach's principle that can represented in GR).

The problem with explaining the twin paradox as you propose is that the equations of GR say that the the twin differential would come out the same way even if there were only two clocks of near vanishing mass in the entire, otherwise empty, universe.

You are free to try to construct a theory that matches GR for verified predictions, while differing in empty universe predictions (but you can't discuss it here unless you get it published in a peer reviewed journal). It is hard to do. As bcrowell pointed out, one attempt at formulating such a theory (that is not GR: Brans-Dicke theory), made testable predictions that have been disproven. Julian Barbour's 'shape dynamics' implements a different interpretation of Mach's principle than what you are describing.

 

[Thinkor]

Pretty much in its entirety in the sense you mean (some people, e.g. Julian Barbour, have proposed a variant of Mach's principle that can represented in GR).

The problem with explaining the twin paradox as you propose is that the equations of GR say that the the twin differential would come out the same way even if there were only two clocks of near vanishing mass in the entire, otherwise empty, universe.

You are free to try to construct a theory that matches GR for verified predictions, while differing in empty universe predictions (but you can't discuss it here unless you get it published in a peer reviewed journal). It is hard to do. As bcrowell pointed out, one attempt at formulating such a theory (that is not GR: Brans-Dicke theory), made testable predictions that have been disproven. Julian Barbour's 'shape dynamics' implements a different interpretation of Mach's principle than what you are describing.

What do you mean by an "empty universe prediction"? A prediction that in an empty universe G_\mu\nu ≠ 0?

 

[PAllen]

What do you mean by an "empty universe prediction"? A prediction that in an empty universe G_\mu\nu ≠ 0?

Empty except for a couple of test observers. A literal Machian would say that if there are no distant stars to provide reference, there is no distinguishability between inertial and non-inertial motions. So for universe of nothing but twin clocks with thrusters, one of whom uses theirs to move away and return to the other, there should be no differential aging. GR and SR both predict that is nonsense. However, we will never be able to perform such an experiment.

 

[Naty1]

bcrowell posts:

For example, suppose A says that distant galaxies are moving away from us, but B says those galaxies are at rest and the space in between is expanding. GR doesn't offer any way of deciding who is right. According to A, the velocities may very well be greater than c,,,

isn't that also true for B?