Is Space Discrete or Continuous in a Planck World?

[dst]

On a ruler, you could move from the 1cm marking on a ruler to the 2cm marking, or you could move from the 0.5cm marking to the 1.5cm marking - both are 1cm movements but you cannot go from 1.5cm to 1cm in a 1cm movement. If we had Planck co-ordinates, could you move from 1 => 2 and also 1.5 => 2.5, and from 1 => 1.5?

Also, in a hypothetical world where all movement occurs by contact alone, suppose we have two perfectly smooth flat planes, and no "action at a distance" in any way, separated exactly by 1 Planck length. Could these plates collide?

In other words - is space continuous but appears discrete when probed, or is it absolutely discrete?

 

[rbj]

the Planck scale is pretty ridiculously tiny (10^-25 the size of atoms). i don't think any human being knows exactly what movement could be happening down at that scale. i don't think it is widely accepted physics, but i think some physicists (maybe they were physicist wannabees, i can't remember who it was) have hypothesized that reality might be discrete in position and time (kinda like cellular automata) and that the Planck Length is the unit of discrete length and the Planck Time is the unit of discrete time. but nobody knows if that is true. if it happens to be true, then movement could only be in discrete amounts (equal to either one Planck Length in any direction or zero movement) and would happen at discrete times (separated by the Planck Time). there would be no halfway between adjacent Planck length positions. i dunno. it's "highly speculative".

 

[Mephisto]

it all depends on your coordinate axis. I think the answer to your question is yes. You can move one cm to right, or you can move one Planck distance to the right. Don't think of it in terms of 0.5 -> 1.5 or something. The physical part is only the difference (1), not the actual coordinate representation, because that depends where you set your origin.
However, you can't travel half a Planck length as far as i know. Planck length is the lowest meaningful distance. But I'm not an expert on this so take that with a grain of salt.

when i heard of spacetime being quantized this way, one idea crept into mind immediately: Matrix :)

 

[dst]

it all depends on your coordinate axis. I think the answer to your question is yes. You can move one cm to right, or you can move one Planck distance to the right. Don't think of it in terms of 0.5 -> 1.5 or something. The physical part is only the difference (1), not the actual coordinate representation, because that depends where you set your origin.
However, you can't travel half a Planck length as far as i know. Planck length is the lowest meaningful distance. But I'm not an expert on this so take that with a grain of salt.

when i heard of spacetime being quantized this way, one idea crept into mind immediately: Matrix :)

Well, here's a better example. Two infinitely large planes (1 Planck length thick, no EM fields or anything that can act with no contact) are accelerating towards each other, such that there's 1 Planck length between them. Both are accelerating at the same rate. Can they collide? If one suddenly stops then the other plane can go the Planck length between them and contact, but if neither stops, they have to move half a Planck length to collide.

As for the co-ordinates, of course that depends on your origin, but if an object is half a Planck length away from another, it doesn't matter. If we have the aforementioned two planes split apart such that they are half-integered distances apart, then one has to go through the other or what?

Of course there's an inherent fallacy in assuming you could even have a solid object at this scale, but Planet Hypothetia has to be weird.

 

[ZLBilley]

In a discrete system, a distance of 1 would be the same thing as two objects touching, being the closest two objects can possibly get two each other. So basically if two things were one Planck length apart in a discrete universe they would be colliding.