# Limit of the speed is c

1. Aug 17, 2006

### 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

Last edited: Aug 17, 2006
2. Aug 17, 2006

### 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.

3. Aug 17, 2006

### clj4

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.

4. Aug 17, 2006

### Jorrie

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?

5. Aug 17, 2006

### George Jones

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

See here.

6. Aug 17, 2006

### jcsd

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

7. Aug 17, 2006

### Rach3

This is unphysical.

8. Aug 17, 2006

### clj4

9. Aug 20, 2006

### 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

10. Aug 20, 2006

### pervect

Staff Emeritus
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.