# Acceleration in special theory of relativity

• I
• LagrangeEuler
In summary, according to the principles of both special and non-relativistic mechanics, it is not possible for an inertial frame of reference ##S'## to exist in which a body does not accelerate if it accelerates in the original frame ##S##. This is due to the constant velocity transformation between frames, which would result in another constant velocity and contradict the body's acceleration. Additionally, in Newtonian mechanics, the acceleration would not be constant if the velocity is changing in the transformed frame.

#### LagrangeEuler

In a inertial frame of reference ##S## body accelerate with constant acceleration ##a##. Can then exist inertial frame of reference ##S'## which moves with speed ##u## relative to ##S## in which body does not accelerate? And why?

No. If it does not accelerate in S' then it moves with constant velocity with respect to that frame. Transforming that velocity to S yields another constant velocity. And that is in contradiction with body being accelerated.
That is true in both SR and non-relativistic mechanics.

Demystifier, vanhees71 and Ibix
Can such a thing hgappen in Newtonian mechanics? If not, what does Relativity change?

LagrangeEuler and vanhees71
Thanks. And can exist inertial frame of reference ##S'## in which acceleration is not constant if in the system ##S## acceleration is constant?

LagrangeEuler said:
Thanks. And can exist inertial frame of reference ##S'## in which acceleration is not constant if in the system ##S## acceleration is constant?
Is that something you could work out for yourself? Using the transformation of acceleration from one frame to another, perhaps.

I think that if one system acceleration is constant in the system that moves with velocity ##u## relative to this one acceleration will not be constant, because in formula for acceleration is velocity of moving object that changes from point to point.

LagrangeEuler said:
I think that if one system acceleration is constant in the system that moves with velocity ##u## relative to this one acceleration will not be constant, because in formula for acceleration is velocity of moving object that changes from point to point.
Yes, exactly.