Gravity wave paradox

[sylvainlecorne]

Hi, I was thinking of a virtual experiment and found a paradox, hope someone would be able to explain this to me.
Imagine you have 2 objects with identical mass, and moving in the same direction at a speed close to the speed of light.

Since the effects of gravity follow the speed of light, if an object follows another object, both with same very high speed, the object which is behind should "feel" the effect of gravity of the object ahead as if it would be closer, e.g. at the position where the object was a short time before e.g.:

T0: A B --->
T1: A B --->
T2: A B --->
At T2, since the effect of gravity of B propagates "backward" at the speed of light, A would feel the gravity of B as if B is still at the position of T1 (assuming A and B go to a speed close to the speed of light)
The same way, B would never "feel" the effects of gravity of A if both A and B go to a speed close to the speed of light.

Paradox 1: Based on this, it means that the gravitational force of A on B is less than the gravitational force of B on A. This contradicts the principle of action/reaction.

Now if we assume A and B are joint by a cable like this: A----B
Let's make A and B turn around each other very fast. The same way as earlier, A would feel the effect of gravity of B at a "past" position of B. This means that B would be closer to A ahead, than it is from the back (from a gravity effect perspective), and the same way B would "feel" that A is closed ahead than behind. This would mean that A is attracted ahead by B ahead, more than it is attracted backward by B and would thus accelerate. The same way, B would accelerate as well.

Paradox 2: In this scenario, A and B would turn around each other quicker and quicker without any source of energy, which contradicts the principles of conservation of energy

[norman40]

Hi,

This forum is intended for students, parents, and teachers working on K-12 science projects. If you are looking for help with homework or general science discussions there are other sites that should be able to answer your question.

A. Norman