Is there a maximum acceleration limit?

[polaris12]

in other words, if c is the maximum velocity possible, then is there a number that gives the maximum acceleration possible? Would it be something like c divided by the Planck time?

 

[bcrowell]

Classically, there definitely isn't. In units where G=c=1, there is only one unit, which you can say is the meter. If you had a frame-independent maximum acceleration, that would fix a scale. There is no such fixed scale in classical relativity.

If a theory of quantum gravity were to share the same fundamental principles as GR, it would have coordinate-independence and the equivalence principle. By the equivalence principle, any acceleration whatsoever can be made to be zero by a choice of coordinates. Of course it's possible that coordinate-independence or the equivalence principle fails in quantum gravity. We don't have a theory of quantum gravity, so we don't know.

 

[MihaiM]

Classically, there definitely isn't. In units where G=c=1, there is only one unit, which you can say is the meter. If you had a frame-independent maximum acceleration, that would fix a scale. There is no such fixed scale in classical relativity.

Can't the same thing be said about the maximum speed, $c$?

Strictly speaking about acceleration and SR, I'm asking the same question again: isn't there a requirement for a theoretical maximum limit of acceleration? There is an intuitive contradiction between acknowledging $c$, $l_p$ and $t_p$, but no limitation in acceleration. It doesn't sound conceptually possible to admit accelerating a particle with an acceleration, relative to a static observer, greater than the one required to reach $c$ in less than Planck time (in the same frame of reference).

 

[kcdodd]

His point is that if there were such a thing as a maximum acceleration, then it would have to be a new fundamental constant, and thus be independent of the observation frame due to the principle of relativity. However, we know how accelerations transform between frames based in SR. Just work it out and there is no way to choose an acceleration to be the same in two different frames. Which is completely different then the constancy of c.

 

[Frogeyedpeas]

Just kind of came across this thread (don't mean to troll and bring back a dead thread really) but just a comment on the idea

If Quantum Mechanics were to define a discrete unit of measure for the universe (I don't know if Planck's constant is that unit of measure) of which it is impossible to make a smaller unit of movement (we'll call it R)

Then the acceleration that gives you a velocity of (C-R)/R over a period of time R (Keep in mind that constant acceleration does not equal constant change in velocity due to finite value of velocity) would be the maximum acceleration possible and should be frame invariant because in terms of distance based on quantum mechanics C-R is the closest thing to C that is not C and there is no such thing as C-R/2. It simply cannot be attained and should it be attained it would (once again looking at this discretely) would suggest that an object accelerated to a velocity of C in a finite time. Not possible.

But suppose you had an initial velocity of (with respect to the observer and axis of observation) -c/2 and you accelerated to C-R over a period of R. There is nothing that says that cannot happen and yet if this same amount of acceleration were performed from Rest then it would mean you accelerated to a velocty beyond C in finite time. So now depending on your initial velocity the maximum possible acceleration changes... So we can define the maximum possible acceleration of a particle as a function rather than a constant and this function is equal to:$\frac{C-R-V}{R}$ Where V is the velocity of the particle at the given moment, C is the speed of light, and R is the smallest discrete unit of distance physically possible (I don't believe we have confirmed any value of R or whether it exists yet but we have made that Planck's constant/4*pi is our closest value to R so far.

This value is now dependent on your frame so C and V must be made into vector quantities to denote not only their magnitude (C's magnitude is obviously C) but also their direction as the acceleration constant varies depending on where your accelerating to. I suppose that means the maximum value that this expression can take on is therefore,

$\frac{2C-2R}{R}$ and that is acceleration from C-R in one direction to C-R in the opposite direction over a length of time R... But once again this is just one case...

Atleast that's my idea on it, but as stated earlier it doesn't really create a numerical maximum but rather a functional maximum unless that's the trend.

 

[TheEtherWind]

c is never assumed to be the maximum speed limit. It is only assumed to be invariant. As far as it being the speed limit, it is seen that, by assuming invariance, there arise equations that make it seem to take an infinite amount of energy to accelerate to c. As for a maximum acceleration, there are no contradictions to any particular instantaneous magnitude of acceleration that aren't physically achievable. If you want an invariant acceleration, try formulating an interval like this

x²+y²+z²=(V_ot+(1/2)at²)²

which is silly... but... you know.