What Happens to Acceleration and Spatial Distances Near the Speed of Light?

[PeterDonis]

So two launchers approach each other at relativistic velocity and as they pass one launches forwards and the other backwards parallel. They launch same acceleration?

Same acceleration relative to what?

If you mean the same proper acceleration, which in this scenario is equivalent to the coordinate acceleration in the rest frame of each launcher, if that's the way the launchers are set up, and you have stipulated that they are, then yes. The proper acceleration is determined by the actual thrust felt by the objects being launched, and you have stipulated that that's the same for both launchers. Since each object starts out at rest relative to the launcher that launches it, each object's coordinate acceleration in the rest frame of its launcher will be the same as its proper acceleration.

If you mean coordinate acceleration in a particular frame, then of course the coordinate acceleration of the object launched by launcher #2, in launcher #1's rest frame, will be different than the coordinate acceleration of the object launched by launcher #1, in launcher #1's rest frame. The coordinate acceleration of the two objects will also be different in launcher #2's rest frame. If you work it out, it turns out that the same will be true in any frame.

None of this has anything to do with whether there is such a thing as absolute motion or not, so I'm still not sure why you're asking about it.

 

[russ_watters]

But would the relative motion of the Earth be significant enough to see any difference if it is like .00001c? Wouldn't that also be in the "least significant" stage of acceleration? Up to .1c would be significantly faster than .8-.9c, right?

I don't know what you mean by "least significant stage of acceleration", but particle accelerators get their masses closer than .00001c from c, so it would be noticeable.

 

[TrickyDicky]

Maybe the OP's confusion would diminish by clarifying that the existence of examples of absolute motion like proper acceleration or rotation doesn't imply the existence of an absolute rest.

 

[Jonathan Scott]

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.

There is no such frame in Special Relativity. As I mentioned recently on another thread, when you look at things from a different angle, you see them wider, deeper or whatever, but nothing is different physically. Special relativity extends that to looking at them from another velocity, by extending the mathematics of rotations in space to the Lorentz transformations in space and time, which include "boost" transformations as well as rotations. Other quantities related to time and space are transformed in systematically corresponding ways, including mass and energy.

 

[jerromyjon]

If something is at rest, yeah its always at rest relative to itself, ok. So relative to this "something supposedly at rest" the fastest something can move away in any direction is .99999999c (or c if massless). Now you imagine something approaches then passes at very high velocity, we'll say .5c, and relative to this something in the direction of its travel something else could still appear to accelerate from 0 to .99999999c and this would appear the exactly the same as something accelerating from -.5c, past 0, and to .99999999c in the opposite direction.

 

[mfb]

If something is at rest

This is a meaningless description.

So relative to this "something supposedly at rest" the fastest something can move away in any direction is .99999999c (or c if massless).

Or even closer to c (if not massless) if we put in more energy.

For every observer, physics looks exactly the same, no matter how they move relative to each other.

 

[jerromyjon]

Ok then, Thank you all, I will just have to come to terms with this until I understand the math that explains it. I'm just so close to understanding SR and I'm nit-picking the parts that don't make logical sense to me. Believe it or not I'm actually very good with math I just haven't quite tackled calculus yet.

 

[Nugatory]

On that note, I think we can declare this thread done.