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Old Jul 16th 2015, 06:25 AM   #1
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Can anyone answer this relativity paradox?

Two astronauts in space compress a lightweight spring. After using it to fling themselves apart, they measure and agree their relative speed. Using special relativity, each astronaut calculates that the other's mass has increased by a millionth. But the rest mass of one was twice that of the other, so he gained twice the energy. How do they agree how much energy they put into the spring?

Observers remaining at rest would measure two relative speeds, not one, and would disagree even with the sum of the astronauts' estimates (special relativity's mass equation being non-linear).


Here is a slightly shorter paradox: www.freephysics.uk/Strobe-paradox-01.pdf

Last edited by AndrewS; Jul 21st 2015 at 04:01 AM. Reason: To reflect more recent replies.
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Old Jul 16th 2015, 12:14 PM   #2
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I have a couple of questions. Why do we say one astronaut or the other put more energy *into* the spring? Was the spring not already compressed?

If I remember correctly the force of an idealized spring is F = k*x where k is a spring constant and x is the the distance the spring has been moved (compressed) from its uncompressed position. The force doesn't change because of what its acting on.

My thinking is that even with general relativity objects, with different mass, in a uniform gravity fall at the same speed. On earth a feather falls slower than a billiard ball but on the moon their respective acceleration to the ground would be almost identical. I think the same reasoning would apply with the spring.

Anyway, thats my only-did-first-year-university-physics-papers view. Maybe the physics gurus on this site can enlighten you better.
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Old Jul 16th 2015, 04:15 PM   #3
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Two astronauts in space compress a lightweight spring.
How do they do this?

And if they are in space away from gravity, the spring is not lightweight, it has no weight.
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Old Jul 17th 2015, 12:43 AM   #4
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Originally Posted by studiot View Post
How do they do this?

And if they are in space away from gravity, the spring is not lightweight, it has no weight.
They compress it with a spring compressing device. If you prefer, its a lightmass spring.
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Old Jul 17th 2015, 01:04 AM   #5
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Relativity paradox

In reply to kiwiheretic, yes the spring was already compressed. Everyone agreed how much energy was put into the spring. This is why it makes no sense that they can't agree how much came out.

I am not referring to any acceleration. I am comparing the inertial frames before and after the acceleration.

I can see why there may be some confusion. The link to the pdf documents where I seek to explain this and all other paradoxes of special relativity has been removed. I have asked for it to be reinstated.
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Old Jul 17th 2015, 03:31 AM   #6
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They compress it with a spring compressing device.
Normally if you compress a spring on earth your reaction is eventually connected to a large massive body, namely the planet.

So how will the compression device obtain its activating reaction?
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Old Jul 17th 2015, 04:03 AM   #7
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Originally Posted by studiot View Post
Normally if you compress a spring on earth your reaction is eventually connected to a large massive body, namely the planet.

So how will the compression device obtain its activating reaction?
They could use a lever, such as when compressing the spring in an air rifle.
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Old Jul 17th 2015, 04:29 AM   #8
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Try and draw a diagram for yourself.

Let us say they have lazy togs that compress eagainst each end og the spring..

On Earth you could simply lift the arrangement and the weight of the object provides the clamping action.

But the lifting device is then pulling against the Earth in some way.

Now suppose that they are in space and you try to pull the lever on top of the tongs.

What will happen?

Answer you will rotate.

It's the same with your air rifle.

So think about this statement 'the astronauts compress the spring' and describe how they accomplish this.
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Old Jul 17th 2015, 05:17 AM   #9
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Originally Posted by studiot View Post
Try and draw a diagram for yourself.

So think about this statement 'the astronauts compress the spring' and describe how they accomplish this.
I could compress a spring in an air rifle even if I were in space. I would use one arm acting against another. It would be similar to using nutcrackers to compress a nut. But this isn't really about how the energy is stored, it's about the energy difference between the inertial frames before and after it's released.

Imagine instead they bring a cylinder of compressed air from Earth and then they allow some of this into a device with a piston. They measure the volume and pressure of the contents and make allowance for the frictional loss when it's released.
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Old Jul 17th 2015, 05:25 AM   #10
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I could compress a spring in an air rifle even if I were in space.
But you didn't specify one body, you specified two astronauts.

And just how much energy could you impart to a spring with your two arms?
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