SR & GR: Circular Relationship?

[John Anthony]

In Special Relativity, acceleration at high speeds causes time dilation and length contraction. Is it fair to restate this as; Acceleration at high speeds causes curvature of spacetime?
In General Relativity, curvature of spacetime causes acceleration.

Acceleration at high speeds causes increased relativistic mass (which increases gravity).
Gravity causes (or is) acceleration.

I arrived at this conflict when trying to understand how curved spacetime can cause acceleration in GR. I wanted to answer this by changing the relationship between time and length (three spatial dimensions) in curved spacetime, similar to the way it is done in SR, but to increase speed instead. That, in turn, made me wonder about the possible circular relationships that might occur between the two theories.

 

[jedishrfu]

Prof John Wheeler summed it up in his famous quote:

Space tells matter how to move, Matter tells space how to curve.

You might get a better understanding of Relativity here.

http://physicalworld.org/restless_universe/html/ru_4_24.html

and so for your example:

Nearby matter (a sun) tells space how to curve and your rocket ship traveling at high speed will follow the curvature created.

 

[Dale]

Acceleration at high speeds causes curvature of spacetime?

No. Acceleration is the curvature of a worldline, not the curvature of spacetime. You can draw a curved line on a flat piece of paper and the paper remains flat

Acceleration at high speeds causes increased relativistic mass (which increases gravity).

This is not correct. The source of gravity is the stress energy tensor, not only the energy density.

That, in turn, made me wonder about the possible circular relationships that might occur between the two theories.

Special relativity is a special case of general relativity, which is the more general theory

 

[andrewkirk]

Acceleration at high speeds causes increased relativistic mass (which increases gravity).

Given an inertial frame F and an object O moving at a high speed relative to F, it is the high speed of O, not its acceleration, that causes its mass in F ('relativistic mass') to exceed its rest mass.

The increased mass of O in F has no effect on gravity, because gravity (spacetime curvature) is determined by the stress-energy tensor, which is a frame-independent measurement of mass-energy. Since the measurement is frame-independent, the fact that O has a high speed in F has no impact on its stress-energy tensor, and hence on its gravitational effect.

 

[John Anthony]

No. Acceleration is the curvature of a worldline, not the curvature of spacetime. You can draw a curved line on a flat piece of paper and the p

Thanks for your response, Dale. I assumed that acceleration was the curvature of spacetime, because SR was described as having both time dilation and length contraction. Does the worldline involve time as well?

Can you comment on my assumption that curved spacetime can cause acceleration in GR by changing the relationship between time and length in curved spacetime?​

 

[John Anthony]

Given an inertial frame F and an object O moving at a high speed relative to F, it is the high speed of O, not its acceleration, that causes its mass in F ('relativistic mass') to exceed its rest mass.

The increased mass of O in F has no effect on gravity, because gravity (spacetime curvature) is determined by the stress-energy tensor, which is a frame-independent measurement of mass-energy. Since the measurement is frame-independent, the fact that O has a high speed in F has no impact on its stress-energy tensor, and hence on its gravitational effect.

OK. That answers that question. Thanks.

 

[John Anthony]

You might get a better understanding of Relativity here.
http://physicalworld.org/restless_universe/html/ru_4_24.html

Thanks for the reference.

 

[Dale]

Does the worldline involve time as well?

In a spacetime diagram a classical “point particle” is represented by a line which is the location of the particle at each point in time. So, yes, a worldline does involve time

 

[John Anthony]

OK, I guess that resolves the issue of a "circular relationship." Thank you all for your comments.