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Many formulas in Special relativity have v - velocity. And theory says there is no absolute velocity only relative and it cannot be greater than speed of light.

Consider this thought experiment: Empty space, two asteroids A and B, are stationary relative to each other at very close distance. There is an astronaut on asteroid A, he kicks asteroid B and distance between asteroids begin to increase. Then astronaut takes a rock from his asteroid A and throw it in the direction of B, this gives some acceleration (momentum), he notice the distance between asteroids increase more rapidly now. So he continue to repeat this process...

Does astronauts (A) velocity relative to B = change of distance between A and B per tick in special relativity?

Will astronauts (A) velocity relative to B exceed speed of light?

Special relativity states that objects with mass cannot have velocity greater that speed of light, so does it mean there are no such 2 reference frames in universe which move faster than C ? I'm pretty sure there are lots of rocks in universe whose distance change much faster than C.

Alex Burtsev
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    Relative velocities, as viewed by a third observer, are allowed to go past $c$. It's the velocity of B as measured by A that cannot exceed $c$. – Chris Feb 04 '18 at 01:45
  • @Chris Does this mean astronaut will not be able to throw more rocks? or he will throw them but they will not give acceleration? – Alex Burtsev Feb 04 '18 at 01:52
  • No. You can keep throwing rocks as long as you like. You just can't accelerate anything past $c$. You can keep getting closer and closer without limit. – Chris Feb 04 '18 at 01:56
  • @Chris But if he can't accelerate past c, the rock he throws will just float before his nose, it will not accelerate him, so it will not fly away from him, that looks strange -) – Alex Burtsev Feb 04 '18 at 02:01
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    No. From his point of view, the rock he throws will just fly away, nothing special about it. He feels the full accleration, but his time is dilated, so that acceleration is smaller in his original reference frame. – Chris Feb 04 '18 at 02:04
  • @Chris in his original frame? Its if viewed from B? But from astronauts view everything is as usual? Suppose he sends a radio signal to B, will it get to B from his reference frame? and from B frame? and from third observer who view A and B distance increase faster than light. – Alex Burtsev Feb 04 '18 at 02:32
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    You should probably just crack open a SR textbook. Those are all pretty elementary questions in relativity. – Chris Feb 04 '18 at 06:46
  • Be careful about having questions that receive negative votes. Of alllllll my questions, I had only 2 that received negative votes. Despite that, the physics.stackexchange.com response was to ban me from being able to ask anymore questions. Quote: "Sorry, we are no longer accepting questions from this account.", meaning my account. It is about the same as being banned from driving after receiving 2 parking tickets. – Sean Feb 04 '18 at 19:12
  • @Sean Thanks pal, you know Quora banned Walter Lewin, sometimes those Corps do crazy thing, no one cares, people will always find a way to collaborate. – Alex Burtsev Feb 04 '18 at 20:09

1 Answers1

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There is no absolute velocity only relative.

This is not something new that comes out of Special Relativity. It has existed since Galileo. Inertial frames are relatively moving with respect to each other at constant velocity.

Does astronaut A's velocity relative to B = change of distance between A and B per tick in special relativity?

Yes, Special Relativity does not change the definition of velocity as change in distance per tick. But, "distance" and "tick" is observer-dependent. So, I guess the better way to phrase this is "Astronaut A's velocity relative to B = change of distance between A and B (as seen from B) per tick (as measured by B).

Will astronaut A's velocity relative to B exceed speed of light?

Never. That is a result from Relativity.

I'm pretty sure there are lots of rocks in universe whose distance change much faster than C.

It's not about how many rocks you have. The inertia of astronaut A increases as he approaches the speed of light. As astronaut A's speed gets closer to the speed of light, the same force causes less and less acceleration, so that you never reach the speed of light.

PhyEnthusiast
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  • "The inertia of astronaut A increases" so he can measure his inertia and determine his absolute speed? "the same force causes less and less acceleration" so he can measure how much acceleration he gets per force and determine his absolute speed? – Alex Burtsev Feb 04 '18 at 10:18
  • The inertia of an object depends on the velocity of the object as seen from a frame. You see, even inertia of an object is dependent on which frame you are watching the object from, so you can't. – PhyEnthusiast Feb 04 '18 at 11:00
  • Forces and accelerations are always frame-dependent in relativity. – PhyEnthusiast Feb 04 '18 at 11:01
  • https://en.wikipedia.org/wiki/Acceleration_(special_relativity) is helpful in understanding this I think. – PhyEnthusiast Feb 04 '18 at 11:03
  • @AlexBurtsev It seems like you don't want to learn Relativity. Instead, you want to expose some error or inconsistency in it (that's how it seems to me). Do you really think you can expose some kind of a mathematical inconsistency in STR, when experts in mathematics and physics have worked it out in detail and are still working with it? – PhyEnthusiast Feb 04 '18 at 11:12
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    Just learn about it first and then ask about something you want clarification about here at StackExchange – PhyEnthusiast Feb 04 '18 at 11:13
  • "The inertia of astronaut A increases" This is not wrong, but it risks giving a beginner a false impression of what's going on. For instance you can't say that the inertial mass is $\gamma m$ because that is only correct for forces applied transverse to the direction of relative motion. For forces (anti-)parallel to the relative motion the coordinate inertia is $\gamma^3 m$, and at other angle it takes on a more complicated form. – dmckee --- ex-moderator kitten Feb 15 '18 at 17:46
  • @dmckee I am not saying anything about how much or by what factor inertia increases. I am just saying it increases, that's all. – PhyEnthusiast Feb 16 '18 at 02:22