Is There a Fundamental Limit on Acceleration in the Universe?

[mXSCNT]

The universe has a speed limit (speed of light), does it have an acceleration limit?

 

[bcrowell]

In classical general relativity, a particle falling into a black hole has an acceleration that surpasses any finite bound as it approaches the singularity. (This acceleration is only defined in a particular coordinate system, but I don't think any coordinate system exists in which the acceleration doesn't grow without bound.)

In a theory of quantum gravity, you have a natural scale called the Planck scale http://en.wikipedia.org/wiki/Planck_scale , and it does provide a natural acceleration scale: (Planck length)/(Planck time)²=5x10⁵¹ m/s². Since we don't have a theory of quantum gravity, I doubt that anyone can say for sure whether this Planck acceleration sets a maximum on the acceleration of any particle.

 

[pervect]

(This acceleration is only defined in a particular coordinate system, but I don't think any coordinate system exists in which the acceleration doesn't grow without bound.)

Novikov coordinates would be a counterexample - an example in which not only the acceleration, but the velocity, of an infalling (any infalling) particle is zero. In Novikov coordinates a fountain of free falling particles particles and their proper time give the coordinates of any event in space-time. Each particle has a constant value of R* attached to it for the radial coordinate - R*, which is determined by the maximum value of the Schwarzscild R coordinate (though it's not identical to make a horrendous calculation slightly less messy). The proper times are all synchronized to the value zero when the particles are at their maximum Schwarzschild R value.

As far as the OP's question goes, I'm not aware of any fundamental limit on acceleration (which I would think of as proper acceleration, I don't see the need to bring coordinates into it when we can measure acceleration without them).

But I don't have anough knowledge about quantum gravity to say if it would change anything.

 

[bcrowell]

As far as the OP's question goes, I'm not aware of any fundamental limit on acceleration (which I would think of as proper acceleration, I don't see the need to bring coordinates into it when we can measure acceleration without them).

Good point -- and thanks for pointing out the counterexample to my claim about the coordinate-independence of the diverging coordinate acceleration!

-Ben