# Spatial Rest

1. Dec 7, 2014

### jerromyjon

I'm wondering, starting with an extreme example, what would happen if two masses accelerate away from each other towards the speed of light. Imagine we could do this very quickly like large hadron separator and the distance is short (in terms of light travel per time) and we compare this to an accelerating frame wouldn't we see a difference in acceleration distance?

2. Dec 7, 2014

### Staff: Mentor

I don't understand what you're asking. What is "acceleration distance"? What does "compare this to an accelerating frame" mean?

3. Dec 7, 2014

### jerromyjon

I have a logical concept in my head that we suppose two objects of equal mass are accelerated in opposite direction simultaneously with the same amount of force. Wouldn't velocity of the launch site in the direction of either mass cause a quicker acceleration in that direction?

4. Dec 7, 2014

### Staff: Mentor

Velocity of the launch site relative to what?
No, as seen by the launch site the setup is completely symmetric.

5. Dec 7, 2014

### jerromyjon

Relative to light speed in either direction, which is the same regardless of motion for EMR but not for matter? I visualize that only in absolute rest could two objects accelerate to as close to c as given propulsion force allows in a calculable distance which progressively contracts. If the launcher is moving .5c and you launch one ahead and one behind you ahead is progressively gaining lead and behind you gladly screeches to a halt and reverses direction?

6. Dec 7, 2014

### Staff: Mentor

Ok so far.

This doesn't make sense; there is no such thing as "velocity relative to light speed". Velocities of objects are relative to other objects. As you have specified the scenario, in the rest frame of the launch site, the two objects accelerate in opposite directions with the same acceleration; therefore their velocities at any instant, in the rest frame of the launch site, will have equal magnitudes but opposite directions. The velocity of the launch site itself relative to something else (like, say, a distant planet or star) is irrelevant to any of that. (I am assuming, btw, that the launch site itself is moving inertially, in free fall.)

If you look at this scenario in a frame in which the launch site is moving, it will no longer look symmetric, true; but that's because different frames give different descriptions of any sequence of events.

7. Dec 7, 2014

### jerromyjon

Doesn't it take more energy to accelerate up to infinity at c so accelerating ahead of launcher moving .9c would take a lot of energy but decelerating from that velocity would also take the same energy?

8. Dec 7, 2014

### Staff: Mentor

Once again, moving relative to what?

Perhaps it would help if you took a step back and explained why you are asking these questions. What are you trying to figure out?

9. Dec 7, 2014

### Staff: Mentor

You cannot "accelerate up to infinity", whatever that might mean.

There is no absolute motion. In the system of the launcher, both objects accelerate exactly in the same way.
In a system that is moving relative to the launcher, things can look different. The object launched "ahead" will gain less velocity (if relativistic effects become relevant), while the object "behind" might reverse its direction (that depends on the numbers).

10. Dec 7, 2014

### jerromyjon

What I was trying to say was the energy or force required to accelerate mass tends to infinity as you approach c.
I think what I might be missing is that we can't measure how close to c we are?

For two objects to accelerate to 300,000 km/s relative to each other would take greater than infinite energy for each. Therefore there is a maximum speed in which the similar energy in similar accelerating masses could accelerate relative to each other, because at some point the energy to accelerate faster is greater than the energy of the propulsion.

11. Dec 7, 2014

### Staff: Mentor

Relative to some fixed inertial frame, yes.

Not in any absolute sense, no. There's no such thing.

I would just say "infinite", or more precisely, I would say that it's impossible to do this with any finite amount of energy. Your phrasing this time is OK because you say "relative to each other" instead of "relative to c".

Let me rephrase what I think you're saying so it actually makes sense. Suppose we have two objects of identical rest mass which start out at rest relative to each other. And suppose that we somehow manage to convert all of the rest mass of each object into energy by means of rocket engines attached to each object that accelerate them in opposite directions. Then, at the end of this process, the two objects will be moving relative to each other at some finite velocity that is less than c. The larger the original rest masses of the objects, the closer their final relative velocity will be to c. (More precisely, what matters is the ratio of original rest mass to final rest mass--the rest mass of the "payload". See below.)

The above is true, but I'm still not sure why you're asking about it.

This, however, is not true; it doesn't even make sense. The point at which the two objects stop accelerating is the point at which there is no more rest mass in either one to convert into energy. (We are idealizing the objects, including their rocket engines, as having negligible rest mass for the "payload", which means anything, like the structure of the rockets or the people aboard the rockets, that can't get converted into energy by the rocket engines.) This has nothing to do with "energy to accelerate" (which doesn't make sense to me either) compared to "energy of the propulsion" (which is frame-dependent anyway).

12. Dec 7, 2014

### jerromyjon

This was what I was trying to avoid with the original example. Suppose we have opposing linear accelerators which accelerate particles up to the maximum velocity their energy can accomplish very quickly, and so in the length of the apparatus both particles reach peak velocity. Would we be able to measure the distance or the time for each particle to achieve this velocity?

13. Dec 7, 2014

### Staff: Mentor

Sure. You can just track where the particle is as function of time.

14. Dec 7, 2014

### jerromyjon

So wouldn't the velocity of the apparatus where the two particles are accelerated away from have an effect on the time to reach max velocity in opposite directions?

15. Dec 7, 2014

### Staff: Mentor

"The velocity of the apparatus" does not exist.

The velocity of the apparatus, as seen by the apparatus, is zero => no.
The velocity of the apparatus, as seen by others, can be non-zero => yes the time and distance can vary.

16. Dec 7, 2014

### jerromyjon

How about two identical launchers moving wrt each other in parallel to the line of acceleration, would all four particles reach max velocity simultaneously?

17. Dec 8, 2014

### Staff: Mentor

Simultaneously in which frame?
No, independent of the frame.

18. Dec 8, 2014

### jerromyjon

Is one frame capable of containing the entire experiment? Ideally we'd want flat space but since that isn't possible could we have a "close enough to flat" and at least perpendicular to gravitational potential? Of course each mass will have a unique path affected differently by surroundings, but would the error be too significant?

I'm just trying to pin down a physical concept that proves an absolute rest frame, something which to my knowledge doesn't exist for light but which I believe could exist for matter. I can't even think of any practical use for this knowledge, I just want to prove or disprove the concept to advance my understanding. If there is no scientific evidence disproving this claim then I would like to devise a test of the hypothesis by the simplest means available. What I don't have is a good understanding of is the accuracy required to obtain definitive results or whether any data from other experiments might provide evidence supporting my hypothesis.

19. Dec 8, 2014

### Staff: Mentor

It doesn't exist for matter either. Repeated experiments have shown this; the best-known is the Michelson-Morley experiment, which has been repeated with much greater accuracy several times.

20. Dec 8, 2014

### jerromyjon

These experiments only measure the relative velocity of light, how does it apply to accelerating masses?