What are the limits of acceleration in special and general relativity?

[Donnie Darko]

hello! days ago I wondered me without finding any answer: if the limit of the speed is c, does exist a limit for acceleration, jerk, joint and the derived following of the move or can these assume endless values? if yes, why? thanks thousand for the answer

 

[Zeit]

Hi,

I've read somewhere that the answer was no, there's no limit to acceleration. I mean that there's no limit to the intensity of acceleration, but there's one to speed : c. So, acceleration would stop if the accelerated body reaches speed of light.

 

[clj4]

hello! days ago I wondered me without finding any answer: if the limit of the speed is c, does exist a limit for acceleration, jerk, joint and the derived following of the move or can these assume endless values? if yes, why? thanks thousand for the answer

Hi, here is a mathematical proof that you can have v=v(t) being a bounded function whereas a=a(t) is unbounded. It can be done by example.

Let a=a(t) be a Dirac impulse, therefore a is unbounded.
Nevertheless, v(t)=Integral(a *dt)=1. End.

 

[Jorrie]

Let a=a(t) be a Dirac impulse, therefore a is unbounded.
Nevertheless, v(t)=Integral(a *dt)=1. End.

Nicely done! In more intuitive language, can one also say that you can have an extreme acceleration for an extremely short time, without affecting the velocity of an object much?

 

[George Jones]

Because there no bound on 4-acceleration, you can have some fun with unbounded 4-acceleration.

See https://www.physicsforums.com/showthread.php?t=110965".

 

[jcsd]

There's no bound imposed by relativity. Obviously extrinsic acceleration must behave in a certain way such that v never exceeds c, but relativity itself can deal with infinite accelerations (i.e. there's nothing to say that dv/dt can't diverge) even if they are unphysical.

 

[Rach3]

Hi, here is a mathematical proof that you can have v=v(t) being a bounded function whereas a=a(t) is unbounded. It can be done by example.

Let a=a(t) be a Dirac impulse, therefore a is unbounded.
Nevertheless, v(t)=Integral(a *dt)=1. End.

This is unphysical.

 

[clj4]

This is unphysical.

While an ideal Dirac impulse is not realistic, in practice it can be approximated with a sinc function that serves the purpose:

http://mathworld.wolfram.com/SincFunction.html

 

[Donnie Darko]

there is a limit from the point of view of the MQ? for example a_max=c/t where t = Planck's time. in this case MQ explains that relativity doesn't

 

[pervect]

there is a limit from the point of view of the MQ? for example a_max=c/t where t = Planck's time. in this case MQ explains that relativity doesn't

What's "MQ"?

GR is a classical theory, so there isn't a smallest unit of time. It's not entirely clear to me that acceleration would have a limit even if time were discreete rather than continuuous.

Going back to SR, what SR winds up saying about acceleration is that

proper acceleration = coordinate acceleration * gamma^3
gamma = 1/sqrt(1-(v/c)^2)

see
http://en.wikipedia.org/wiki/Hyperbolic_motion_(relativity)

Proper acceleration is unlimited, and would correspond to what an accelerometer on the accelerating body measured.

If you imagine some constant proper acceleration, you can see that the coordinate acceleration goes to zero as the velocity approaches infinity.

For any given velocity, you can make coordinate acceleration as well as proper accelration as high as you like at any instant of time. Of course, the velocity increases rapidly, and the coordinate acceleration will quickly "decay" as per the above formulas.