Relativity Baking My Noodle

Zillah

I have two conflicting beliefs in my head, each of which I was independently sure of, but that now I realise seem to clash. These are:

- The faster an object moves the greater its mass, which becomes a problem as you approach the speed of light, because it would take infinite energy to reach the speed of light.
- Motion is relative, there is no such thing as objective position or motion, we can only describe these things in relation to other things.

So we have Spaceship A and Spaceship B, they're identical, they each weight 10 tons. Let's say A sees B approaching at 90% the speed of light. We know that we can't describe one as moving or not, all we know is that they are getting closer to each other. A could be traveling towards B at 90%C, or vice versa, or each could be approaching the other at 45%C.

However, surely, according to the first rule above, they should each be able to use their engines to accelerate so that their closing speed is +1%C,and whichever one had to use more energy to accelerate is the one that is 'really' moving?

I'm having trouble reconciling the idea that motion is relative with the assertion that velocity has an objective effect on mass.

ScumLord

Zillah wrote: »

- Motion is relative, there is no such thing as objective position or motion, we can only describe these things in relation to other things.

There's always something in our universe to relate to when we're moving. I always thought the thing about motion was just a thought experiment, where you imagine an empty universe and then the idea of objects moving breaks down because you're not moving towards or away from anything, so you seem like you're stuck in the one spot even though you could technically be moving away from the point you started in. You just wouldn't know unless you left a marker behind.

The two ships are moving in relation to the rest of the stuff in the universe, not just each other. So both are moving. Even if they tried to stop in relation to the other ship they'd still be moving as part of the galaxy they're in.

Morbert

Zillah wrote: »

I'm having trouble reconciling the idea that motion is relative with the assertion that velocity has an objective effect on mass.

You are correct. These two ideas cannot be reconciled.

The solution: Velocity does not have an objective effect on mass. Instead, velocity and relativistic mass are quantities that depend on a particular choice of reference frame.

Assume both spaceship A and B have the same mass m when they are at rest beside each other.

In your scenario spaceship A will measure their own mass to be m, and spaceship B (travelling at .9c)'s mass to be 2.3 m. Spaceship B, on the other hand, will measure their own mass to be m, and measure spaceship A's mass to be 2.3m. Neither frame of reference is incorrect. Each just employs a different description.

However, surely, according to the first rule above, they should each be able to use their engines to accelerate so that their closing speed is +1%C,and whichever one had to use more energy to accelerate is the one that is 'really' moving?

So let's say both A and B turn on their (identical) engines. They both agree about how much force their engines generating, but they will disagree about who is acceleratng. They will never be able to run their engines long enough, no matter how powerful the engine, such that they measure the other ship's acceleration to be greater than c, even though there might be a third party that observes the distance between them receding at 1.1c.

This website has a nice interactive explanation of the scenario you're asking about.
http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/einvel2.html#c2