# Where does acceleration play a role in special relativity?

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1. Feb 21, 2015

### delsaber8

So my question arises from the whole time dilation thought experiment where one person stays on earth the other speeds off in a rocket at near light speed. Upon return of course the one in the rocket is younger, etc. The reason I bring this up is how do we determine who is actually moving, without an acceleration. I thought you need a force to determine the relative motion and since all the SR equations seem to only focus on velocity how do we know it isn't simply the earth moving away from the rocket ship. I mean I'm sure something explains this, but I'm just slightly confused where and how it is incorporated. I also figure that I should add, my knowledge of special relativity is very elementary as I have never studied the theory in-depth.

2. Feb 21, 2015

### Staff: Mentor

Someone had to turn around in order for them to compare times. The one turning around performed an acceleration.

3. Feb 21, 2015

### Staff: Mentor

Special Relativity does include consideration of acceleration. And the way you know you are accelerating is if there is a net force acting on you. So the guy in the rocket is the one who experiences the acceleration, while the guy back on earth does not experience acceleration.

Chet

4. Feb 21, 2015

### pervect

Staff Emeritus
Special relativity, like Newtonian mechanics, works only in inertial frames. Inertial frames, by definition, do not accelerate. A non-exhaustive but hopefully illuminating requirement for a frame to be inertial is that an accelerometer, placed at constant coordinates within the frame, reads zero.

The relative acceleration of any two inertial frames will be zero.

Acceleration does not enter directly into the Lorentz transform, length contraction, or time dilation, only the velocity is important.

So - the requirements for special relativity to work are basically similar to the requirements for Newtonian mechanics, except that if you want to take into account gravitational effects, you need to use General Relativity rather than special relativity. It is difficult to say when you can neglect GR effects unless you're able to compute them - as a rule of thumb, I'd suggest looking at some of the GR effects with simple formula (like Gravitational Time Dilation) to see if they are significant in the problem.

Acceleration isn't really an issue for SR, except for the part where SR requires that inertial frames do not accelerate.

5. Feb 22, 2015

### Orodruin

Staff Emeritus
Just like you can do Newtonian mechanics by introducing time dependent coordinate systems by introduction of fictitious forces, you can do SR in coordinates that are not inertial. This is essentially equivalent to being able to describe a Euclidean space with curvilinear coordinates. The space is still Euclidean regardless of the coordinate representation, some things might be obscured by the non-linear coordinate system, but others may appear more tractable. If I use Rindler coordinates in Minkowski space, I am still doing SR. However, this goes beyond what you would typically encounter when studying SR.