Theory of Acceleration: Is There a Limit?

[ObjectivelyRational]

Is anyone aware of any theory which includes a theoretical limit on acceleration in the same way C is the universal speed limit?

[[By this I do not mean some sort of practical limit set by energy density and known systems of propulsion.]]

 

[Ibix]

This has been discussed a few times on here. The answer is no.

 

[ObjectivelyRational]

Physicists are always coming up with new theories all the time, whose central tenets and or side effects introduce new consequences. I asked my question in the OP just in case some new outlier theory might include such a thing.

Thank you for informing me that, as of now, and to your knowledge, no such theory has been proposed.

 

[Sorcerer]

What about jerk, da/dt? In fact while we’re at it, what about dⁿx/dtⁿ? It is only when n=1 that there is a limit?

 

[Nugatory]

What about jerk, da/dt? In fact while we’re at it, what about dⁿx/dtⁿ? It is only when n=1 that there is a limit?

Yes, and that's actually somewhat intuitively reasonable if you think of the rule as "the slope of the worldline must be greater that 45 degrees".

 

[Ibix]

What about jerk, da/dt? In fact while we’re at it, what about dⁿx/dtⁿ? It is only when n=1 that there is a limit?

Kind of. There ate no limits on ##d^2x/d\tau^2##, proper acceleration, nor on higher derivatives so far as I am aware. There are soft limits on ##d^2x/dt^2## and higher derivatives, because you can't sustain an arbitrary coordinate acceleration forever. You can make it as high as you like, but never for long enough to exceed c. This is what the ##\gamma## does in ##p=\gamma mv## when you start differentiating.

The restriction on ##dx/dt## means that a worldline that is timelike somewhere is timelike everywhere, or "causality exists".

 

[Sorcerer]

Kind of. There ate no limits on ##d^2x/d\tau^2##, proper acceleration, nor on higher derivatives so far as I am aware. There are soft limits on ##d^2x/dt^2## and higher derivatives, because you can't sustain an arbitrary coordinate acceleration forever. You can make it as high as you like, but never for long enough to exceed c. This is what the ##\gamma## does in ##p=\gamma mv## when you start differentiating.

The restriction on ##dx/dt## means that a worldline that is timelike somewhere is timelike everywhere, or "causality exists".

Ah, yes. You should always have a factor of 1 - (v/c)² in every derivative in there somewhere, shouldn't you? Because of the chain rule. The first derivative of ##\gamma## changes the exponent from -1/2 to -3/2, the second to -5/2. and so on. So the restriction is always on the v/c factor. If that is greater than 1, then since the exponent will eternally be negative, you'd be dividing by zero or have an imaginary number.

 

[TeethWhitener]

Naively, if your acceleration is ~3.5×10⁵² m s^-2, then the Unruh temperature equals the Planck temperature. Not really a theoretical limit, though. More of a curiosity.

 

[Sorcerer]

Naively, if your acceleration is ~3.5×10⁵² m s^-2, then the Unruh temperature equals the Planck temperature. Not really a theoretical limit, though. More of a curiosity.

This is interesting. Gonna have to look this up.