Hypothetical scenario 1:
There's a planet. Two rockets sit together on a launchpad on the planet. Their relative velocity is zero. They then launch at the same time on parallel trajectories at identical speeds. Because the rockets have mass, they are gravitationally attracted to one another. And with friction from the launchpad no longer holding them in place, this causes them to now (slowly) accelerate towards each other.
The rockets now both accelerate to arbitrarily large, but identical fractions of the speed of light.
* Does this change in velocity relative to the planet cause their gravitational attraction to each other to increase?
No it doesn't. The source of gravity in GR is not just (relativistic) mass, but the stress-energy tensor. One way of putting it, is that velocity and acceleration also play a role in determining the strength of gravity (and their contributions are not attractive). It's important not to try and carry over Newtonian concepts to GR.
One rule of thumb to remember this particular situation by, is that a black hole in one frame is a black hole in any frame. That is, you can't change the dynamics of the system by changing reference frames.
Another way to think of it (but a grossly oversimplified one), is that the relativistic mass increase is offset by the relativistic effects on time and length.
Hypothetical scenario 2:
An object accelerates away from a reference point at 99% of the speed of light. We now measure the mass of the object. The object then comes to a complete stop, and then accelerates to 99% of the speed of light back towards our reference point. We again measure the mass of the object.
* Will the two measurements be equal?
Yes. The two are symmetrical.
Hypothetical scenario 3:
The entire universe consists of two objects. They are at rest. Object 1 accelerates to 50% of the speed of light in a direct line away from object 2. Call the amount of energy required for this acceleration, Energy A. Object 2 now accelerates to 50% of the speed of light in a direct line towards object 1. This causes them to now be at rest. Object 1 now accelerates to 50% of the speed of light in a direct line away from object 2. Call the amount of energy required for this acceleration, Energy B.
* Are Energy A and Energy B equal?
* Is A+B equal to, or less than infinity?
Yes, A and B are equal. You've basically changed the reference frame half way through the thought experiment (when you said they're at rest again). From that moment on it's exactly the same experiment again. If I were to guess, the confusion probably arose from still thinking as if the reference frame was the original one, in which case the two objects are never at rest apart from the initial setup, so you can't treat them as if they were (e.g., you can't accelerate an object moving at 0.5c by another 0.5c).
No reason why they should sum to infinity.
Hypothetical scenario 4:
There sits in space an indestructible platform. Sitting on the platform is a spaceship with a reactionless drive. Due to the reactionless drive, it will not be pushing against the platform as a consequence of its launch. The ship then accelerates to a sufficiently large fraction of c that its mass becomes arbitrarily large.
* What happens? The ship, by virtue of its gravitational force upon the platform, will tend to pull it along. But the fact of it being pulled along means its speed relative to the platform is reduced...which reduces the relative mass and therefore the force of gravity exerted by the ship upon the platform. How is this resolved?
This looks like a much more complicated problem than it seems at a first glance. I'd take it to somewhere like physicsforums rather than ask here.
Why are you asking about such things on B12 anyway? You might get a few informed answers as long as it's SR, but these questions dip into GR, and that's a something you'll need more than just geeks for.
If physicists stopped using relativistic mass, it probably means that the relativistic mass is not an actual physical concept. Hence, in all these examples the mass doesn't actually increase, it just gets harder to accelerate things when their velocity is close to c.
No, it's not exactly that. It's a useful concept, as long as you know what you're doing.
Have a read through these:
http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.htmlhttps://www.physicsforums.com/threads/what-is-relativistic-mass-and-why-is-it-not-used-much.783220/#post-4919337The problem with relativistic mass is that it's actually different for if you want to move along or perpendicular to your velocity vector.
That seems to be true for the relativistic equivalent of the inertial mass, not for the source of gravity. The first link above has some discussion on the subject.
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Topic: Physics questions: Consequence of relative velocity in relativity (Read 1212 times)