Does Planck Time Imply an Acceleration Limit?

[Battlemage!]

Mods, I wasn't sure whether to put this in quantum physics or relativity, but since the speed of light is the limiting factor I chose here. Move wherever you think is best.

Okay so the speed of light is the asymptote for the speed that objects can accelerate to, and the Planck time is the smallest unit of time, right?

So shouldn't this put a cap on how large an acceleration an object can have? I.e., the asymptote for acceleration would have to be the speed of light divided by the Planck time, right?

Or am I missing something crucial here?

Acceleration is basically velocity divided by time, so if there is a speed limit of c and a minimum time, then doesn't there have to be an acceleration limit too?Thanks for any responses!

 

[jtbell]

and the Planck time is the smallest unit of time, right?

No. Just like the Planck length is not the smallest unit of length (see our Insights article about this), the Planck time is not the smallest unit of time. (both "as far as we know", of course)

 

[Battlemage!]

Thanks for the info jtbell! Reading the Insights article right now.

EDIT- I see it's just more unit choices. While useful, not necessarily fundamental to the universe (although some of those ratios seem really important).

Anyway, this pretty much answered the question for me:

"
The simplest reason that Planck-pixels don’t make up the universe is special relativity and the idea that all inertial reference frames are equally valid. If there is a rest frame in which the matrix of these Planck-pixels is isotropic, in other frames they would be length contracted in one direction, and moving diagonally with respect to his matrix might impart angle-dependence on how you experience the universe. If an electromagnetic wave with the wavelength of one Planck length were propagating through space, its wavelength could be made even smaller by transforming to a reference frame in which the wavelength is even smaller, so the idea of rest-frame equivalence and a minimal length are inconsistent with one-another.

Reference https://www.physicsforums.com/insights/hand-wavy-discussion-planck-length/"

Obviously the same thing applies to time dilation and the Planck time, I would imagine.