# Why is acceleration independent of reference frames?

I want to know why is the measurement of acceleration independent of inertial reference frames?
I mean if displacement, velocity varies with change of inertial reference frames, acceleration should vary.
And, one more question: When we say that displacement or velocity varies with change in reference(inertial) reference frames, are we talking about variation in magnitude only or both magnitude and direction. I think it should be both magnitude and direction.

## Answers and Replies

Orodruin
Staff Emeritus
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You can derive this directly from the velocity addition formula. Just differentiate it with respect to time.

Dale
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2020 Award
I want to know why is the measurement of acceleration independent of inertial reference frames?
I mean if displacement, velocity varies with change of inertial reference frames, acceleration should vary.
Hi randomgamernerd, welcome to PF!

In relativity there are two different acceleration concepts and it is important to distinguish between the two of them.

One of them is coordinate acceleration, this seems to be the kind of acceleration you are thinking about. You are correct, length contraction and time dilation make it so that different frames disagree on coordinate acceleration.

The other kind is called proper acceleration. This is the acceleration that you physically feel, the acceleration measured by an accelerometer. This acceleration is invariant, and becomes very important as you transition from SR to GR.

nasu
Gold Member
I want to know why is the measurement of acceleration independent of inertial reference frames?
I mean if displacement, velocity varies with change of inertial reference frames, acceleration should vary.
And, one more question: When we say that displacement or velocity varies with change in reference(inertial) reference frames, are we talking about variation in magnitude only or both magnitude and direction. I think it should be both magnitude and direction.
I suppose that you mean the classical (non-relativistic) case.
In this case, even though the velocity depends on the frame, the change in velocities is frame independent.
This is so because in the non-relativistic limit the transformations between inertial frames are just adding some constant ( velocity) which cancel out when you take the difference.

The relativistic case is a little more complex, as already mentioned (Dale's post).

Dale
Dale
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2020 Award
My apologies for my answer. For some reason I thought this was in the relativity section. My response was probably overboard for a basic general physics question.

i forgot to give a reply.