[Richard777 (OP)]

Length contraction is well documented in the literature. Assume two general types of contraction; one type is associated with straight motion and straight lengths, and one type is associated with curved motion and wavelengths. Plank length and Plank wavelength are equal.

Both types of contraction may be combined, giving a vector of acceleration. If vector components are suitably defined a “Schwarzschild acceleration vector” is represented. The Schwarzschild metric is simply obtained from the Schwarzschild acceleration vector.

Is the limit of contraction Plank length?

[jeffreyH]

For that to be true the speed of an object would have to be indistinguishable from the speed of light due to the uncertainty principle. I am trying to imagine the situation and can't at the moment.

[Kryptid]

I have wondered (and still do wonder) if the true length contraction equation does not asymptotically approach zero as you near the speed of light, but asymptotically approaches the Planck length instead. I don't think existing experimental techniques are anywhere near sensitive enough to tell the difference, given how extremely tiny the Planck length is.

[jeffreyH]

Think of this in terms of an object orbiting a black hole very near to the photon sphere so that its angular velocity is very close to c. Angular momentum has been shown to be quantised. Refer to Stern and Gerlach. If so then it should be true that the Planck length should be a limit. This is the only situation I can envisage where an object can have acquired the necessary orbital velocity without input of energy from other sources. The question is what would the value of the Lorentz factor be at this limit. It can't be infinite since the Planck length is not zero.

[Bill S]

It can't be infinite since the Planck length is not zero.

Now, there's a thought to savour!  Can a "length" be zero, and still be a length?