Does the shortest distance exists?

[Harmony]

Is there a shortest possible distance besides zero? Or there's no limitation at all?

 

[koantum]

Is there a shortest possible distance besides zero? Or there's no limitation at all?

Good question. Check out my discussion of it http://thisquantumworld.com/topdown.htm" .

 

[Dense]

Is there a shortest possible distance besides zero? Or there's no limitation at all?

Strictly mathematically, both of your alternatives appear to be incorrect.

There is always a smaller nonzero distance -- just keep dividing by two.

There is also a limit: zero.


But is there a smallest meaningful nonzero distance? That is, some distance that no possible event can occur over a smaller distance, no matter how little time it takes?

Sure. That's called a Planck Length. Planck units are the "smallest meaningful" amounts of anything. Planck time is the smallest meaningful amount of time -- nothing can occur in less time, for example.

The Planck Length is something like 0.0000000000000000000000000000000000016 meters.

That's how far a photon traveling at c will travel in one unit of Planck Time. A proton is about 100,000,000,000,000,000,000 Planck Length units across.

Is there a distance shorter than one Planck Length? Can't you just divide that by two, and so on? Not meaningfully, no. You can conceive of a smaller length philosophically in your head, but that cannot express a valid measurement in the real world.

 

[Harmony]

What will happen when a matter travel for a distance equal to Planck Length? The matter can't travel for any distance between Plack Length and zero, can it?