Accelerating Particles > c: Special Relativity Considerations

[Tigersharkmks]

consider a circular loop (a particle accelator). Suppose any particle moves their with speed ≈ c. Now let the radius be such that it completes loop in 1 sec. Therfore velocity at any postion in the loop is c with direction tangent to it. So consider two point A & B where they are at 90 degree to each other. So Δv = √2*c. Therfore acceleration in Δv/Δt = √2*c/0.25 (Since it had only traveled one-quatar of loop). Therfore acceleration is 4*1.44*c > c. So is it a violation of special relativity or such process is not possible or special relativity allows acceleration to be greater than c. Time & radius is given from electron's frame.
Thank you!

 

[mathman]

Acceleration is rate of change in velocity as a function of time. It is dimensionally different from velocity, so comparing with c is meaningless. You can make it numerically as large as you want by changing the time dimension, say from seconds to nanoseconds.

 

[HallsofIvy]

consider a circular loop (a particle accelator). Suppose any particle moves their with speed ≈ c. Now let the radius be such that it completes loop in 1 sec. Therfore velocity at any postion in the loop is c with direction tangent to it. So consider two point A & B where they are at 90 degree to each other. So Δv = √2*c. Therfore acceleration in Δv/Δt = √2*c/0.25 (Since it had only traveled one-quatar of loop). Therfore acceleration is 4*1.44*c > c. So is it a violation of special relativity or such process is not possible or special relativity allows acceleration to be greater than c.

There is no such restriction on acceleration. It is speed that cannot be greater than c.
In fact, as mathman said, acceleration and speed have different units so it makes no sense to compare acceleration and c. That would be like saying an object "cannot be longer than c".

Time & radius is given from electron's frame.
Thank you!

 

[georgir]

Is a crocodile more green than long?