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I am imagining two bodies flying through empty space near the speed of light relative to their (distant) surroundings. Let’s say they are a bowling ball and a tennis ball. They are not moving with respect to one another, so their kinetic energy should be zero, yes? And their potential energy would be small. I realize that they have a lot of energy in relation to a wall that gets in their way, but without the wall, there is no kinetic energy in the system, no? But I am told that bodies approaching the speed of light gain huge kinetic energy, and that kinetic energy exerts a gravitational force. If so, wouldn’t the two bodies be able to determine an absolute speed by measuring their gravitational pull? If it is larger than expected, then they have an absolute speedometer. But if their mutual pull appears normal to them, then how can their gravitational pull on each other simultaneously appear extraordinarily high to an observer moving in the opposite direction? (Please understand I am not asking whether a speeding object turns into a black hole.)

Qless
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    Related: If a mass moves close to the speed of light, does it turn into a black hole?. – PM 2Ring Nov 27 '21 at 17:26
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    BTW, this is a classic example of how the (now deprecated) concept of relativistic mass is misleading. – PM 2Ring Nov 27 '21 at 17:27
  • Right. I’m trying to figure out how substituting in large kinetic energy is an improvement. – Qless Nov 28 '21 at 04:11
  • "how can their gravitational pull on each other simultaneously appear extraordinarily high to an observer moving in the opposite direction?" It doesn't. To calculate the gravity between the two balls, you work in the rest frame of their centre of mass. However, the time it takes for the balls to collide will be dilated for the observer moving at high speed relative to the balls. – PM 2Ring Nov 28 '21 at 04:48
  • I see. So relative to the frame moving with the balls, there is not a huge amount of kinetic energy to gravitate. But to an observer moving in the opposite direction, the balls will appear to have huge kinetic energy, which gravitates, but they won’t appear to quickly slam into each other because of time dilation. So… do the balls exert a large gravitational pull on the observer, larger than if at rest relative to him or her? – Qless Nov 28 '21 at 18:09
  • This question has no answer? – Qless Nov 29 '21 at 01:22
  • Yes, the kinetic energy in a system contributes to the gravity. But special relativity is oblivious to gravity, you need general relativity for that. Spacetime curvature (i.e., gravity) is determined by the stress-energy-momentum tensor, which includes momentum and pressure components. – PM 2Ring Nov 29 '21 at 03:49
  • I figured as much. I suppose another way to put my question is: Does an observer in the same frame as the balls calculate a different stress-energy tensor for the balls compared to what a moving observer would calculate for them? – Qless Nov 30 '21 at 04:42
  • Would this (above) be a better question for me to post? – Qless Dec 01 '21 at 03:30
  • Yes, the stress-energy is frame-dependent. See https://physics.stackexchange.com/q/494078/123208 – PM 2Ring Dec 01 '21 at 09:16
  • Wow, now THAT is cool! And it answers my question much more directly. And I learned something new: quasi-local quantities and psuedotensors. Thanks! – Qless Dec 02 '21 at 17:40

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