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Author Topic: What does this relativistic thought experiment indicate?  (Read 4800 times)

Offline Supercryptid

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Let's say that you have a universe which has two spaceships in it and no other frames of reference. The spaceships fly past one-another at high speed. They are not accelerating but are keeping a constant velocity. According to relativity, the captain on Ship A might think that his ship is standing still, and that Ship B is flying past his stationary ship. The captain on Ship B would think that he was standing still and that the other ship was moving.

Now let's move them really quickly.

As an object goes faster and faster, kinetic energy is converted into mass. Near the speed of light, an object can grow to many times its rest mass. Eventually, if it goes fast enough, the mass of an object will be so great that it will reside inside of its own Schwarzchild radius. In essence, it will become a black hole.

So now the captain in Ship A sees Ship B going by so fast that he sees it collapse into a black hole. However, the captain on Ship B still thinks that he is standing still and therefore does not observe any such change in his ship. The captain on Ship B, of course, sees Ship A become a black hole instead. How can this be the case?

Can one observer see an object as a black hole and a different observer see the same object as normal? If Ship B used its thrusters to slow down relative to Ship A so that it was no longer in its own Schwarzchild radius, would the captain of Ship A watch the black hole "uncollapse" back into a spaceship?


 

Offline lightarrow

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What does this relativistic thought experiment indicate?
« Reply #1 on: 20/03/2009 18:38:33 »
Let's say that you have a universe which has two spaceships in it and no other frames of reference. The spaceships fly past one-another at high speed. They are not accelerating but are keeping a constant velocity. According to relativity, the captain on Ship A might think that his ship is standing still, and that Ship B is flying past his stationary ship. The captain on Ship B would think that he was standing still and that the other ship was moving.

Now let's move them really quickly.

As an object goes faster and faster, kinetic energy is converted into mass. Near the speed of light, an object can grow to many times its rest mass. Eventually, if it goes fast enough, the mass of an object will be so great that it will reside inside of its own Schwarzchild radius. In essence, it will become a black hole.

So now the captain in Ship A sees Ship B going by so fast that he sees it collapse into a black hole. However, the captain on Ship B still thinks that he is standing still and therefore does not observe any such change in his ship. The captain on Ship B, of course, sees Ship A become a black hole instead. How can this be the case?

Can one observer see an object as a black hole and a different observer see the same object as normal? If Ship B used its thrusters to slow down relative to Ship A so that it was no longer in its own Schwarzchild radius, would the captain of Ship A watch the black hole "uncollapse" back into a spaceship?
This could be a good example of why the concept of "relativistic mass" is useless. A body's mass doesn't vary with speed. That's all.
 

lyner

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What does this relativistic thought experiment indicate?
« Reply #2 on: 20/03/2009 19:28:10 »
You often make similar points, lightarrow, and I sometimes see what you are getting at. But how do you account for the fact that faster moving particles are more difficult to accelerate? (This is a fact, is it not?)
 

Offline yor_on

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What does this relativistic thought experiment indicate?
« Reply #3 on: 20/03/2009 19:48:18 »
Are you referring to 'invariant mass' Lightarrow? What are you thinking here? To me any particle accelerating will 'collect' more energy, and as you say energy is mass? - Explain yourself Sir, in as succinct and crisp manner as you please Sir. (sounds like something from a cornflakes packet that one:) . And if you really need to draw those shy scared mathematic symbols into this enlightened discussion , feel free to do so, but please, keep them simple :)
 

Offline lightarrow

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What does this relativistic thought experiment indicate?
« Reply #4 on: 20/03/2009 19:58:37 »
You often make similar points, lightarrow, and I sometimes see what you are getting at. But how do you account for the fact that faster moving particles are more difficult to accelerate? (This is a fact, is it not?)
F = ma doesn't hold in relativity.
The correct equation is:

F = dp/dt = γma + γ3mv(va)/c2

Characters in bold means vectors.
« Last Edit: 20/03/2009 20:18:24 by lightarrow »
 

Offline lightarrow

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What does this relativistic thought experiment indicate?
« Reply #5 on: 20/03/2009 20:06:24 »
Are you referring to 'invariant mass' Lightarrow? What are you thinking here? To me any particle accelerating will 'collect' more energy, and as you say energy is mass? - Explain yourself Sir, in as succinct and crisp manner as you please Sir. (sounds like something from a cornflakes packet that one:) . And if you really need to draw those shy scared mathematic symbols into this enlightened discussion , feel free to do so, but please, keep them simple :)
Invariant mass, of course. About energy = mass that's not correct. If you remember, I wrote that mass is "energy confined in a fixed region of space" so if your system is the moving body, then its kinetic energy doesn't belong to the system, and the system's mass is just its rest mass (you are in the body's frame of reference so the body is still). So, or you consider the entire region of space where the object is moving, and then the mass *of this* system increases with the body's speed (but then you have others problems, for example that the energy of that system disappears when the body exit the system), or you consider the body only, and then its mass doesn't vary .
 

Offline Vern

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What does this relativistic thought experiment indicate?
« Reply #6 on: 20/03/2009 20:46:20 »
Quote from: lightarrow
So, or you consider the entire region of space where the object is moving, and then the mass *of this* system increases with the body's speed (but then you have others problems, for example that the energy of that system disappears when the body exit the system), or you consider the body only, and then its mass doesn't vary.
That is a very enlightening way of thinking about relativistic mass. It makes it easier to grasp why photons trapped in matter increase the mass of the matter.
 

Offline yor_on

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What does this relativistic thought experiment indicate?
« Reply #7 on: 21/03/2009 10:36:37 »
If I get this right Lightarrow :) you are both discussing the idea of a system, and where the divisional lines should be drawn defining a system, as well as states that there is no objective reality to that a object can be defined as having both 'invariant mass' and 'relative mass'? That as 'relative mass' will be something disposed on the system by 'outer circumstances'? And that the 'reality' then will be its invariant mass?
 

Offline yor_on

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What does this relativistic thought experiment indicate?
« Reply #8 on: 21/03/2009 13:13:25 »
Supercryptid it is a nice question, and it seems to follow logically as when a object accelerates, the momentum and so also its 'relative mass' grows. but the mass referred to for a 'Black Hole'  is it's 'invariant mass' non-changing, no matter what frame of reference you place it in, be it a spaceshutle or Earth. The relative mass is as Lightarrow points out something 'transfered' through acceleration and even though acceleration do create its own gravity well concentrated to the aft outside of your spaceship, it won't be able to transform that 'immaterial point' of moving into a black hole.
 

Offline lightarrow

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What does this relativistic thought experiment indicate?
« Reply #9 on: 21/03/2009 13:32:50 »
If I get this right Lightarrow :) you are both discussing the idea of a system, and where the divisional lines should be drawn defining a system, as well as states that there is no objective reality to that a object can be defined as having both 'invariant mass' and 'relative mass'? That as 'relative mass' will be something disposed on the system by 'outer circumstances'? And that the 'reality' then will be its invariant mass?
You are getting the idea  :)
 

Offline lightarrow

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What does this relativistic thought experiment indicate?
« Reply #10 on: 21/03/2009 13:34:27 »
Supercryptid it is a nice question, and it seems to follow logically as when a object accelerates, the momentum and so also its 'relative mass' grows. but the mass referred to for a 'Black Hole'  is it's 'invariant mass' non-changing, no matter what frame of reference you place it in, be it a spaceshutle or Earth.
 The relative mass is as Lightarrow points out something 'transfered' through acceleration and even though acceleration do create its own gravity well concentrated to the aft outside of your spaceship, it won't be able to transform that 'immaterial point' of moving into a black hole.
Exactly.
 

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What does this relativistic thought experiment indicate?
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