Hypothetical situation of planck length object and lightspeed

[Curtis15]

Initially known theories:

1. General consensus: Planck length is smallest measurable unit of length

2. Objects approacing light speed contract in length

Scenario: Some hypothetical mass measured to be a Planck length is accelerated infinitely close to light speed.

Questions: Can a length contraction be detected? Does the length contraction actually occur?

 

[Uglybb]

The problem gets a little stickier than that if the universe is divided up into a spacetime mesh at plank distance.

A light beam or particle moving at some angle to the mesh must do the old computer graphics jaggie (http://en.wikipedia.org/wiki/Jaggies) because you have a grid.

Try get your head around conservation of energy and momentum around that ... or is that why we have Quantum mechanics to take it off grid for the jumps :-).

 

[danR]

1. There is no absolute length contraction. The idea has no physical meaning. There is the appearance of length change to an external observer with a relatively different velocity.

2. Classical relativistic length-appearance change was modified with the introduction of Penrose and/or Terrell effect/rotation (1959).

3. Due to the Penrose-Terrell effect, objects observed transversely to the objects' directions do not contract in appearance. Scientific American made this error a few years ago when they showed colliding heavy ions as shortened into oblate spheroids.

4. We are presumably talking about spherical geometry concerning sub-atomic particles.

5. At quantum scales well above Planck lengths anyway, it's hard to think about length distortion for objects that only have a defined wave-function.

6. At quantum scales, measuring rods lose their meaning. They have meaning only for the classical macroscopic (trains, spaceships, etc.) relativistic textbook discussions. Where are the 'end points' of 'measuring rods' when the end-points have only wave-function 'locations' in space? However, clock-metrics are retained as far as (relative!) time-dilation is concerned.