Can space be partitioned infinitely many times?

Question

Can you keep cutting space up into smaller and smaller 'parts' so to speak, does this go on forever?

Answer 1

No! If you combine Heisenberg's uncertainty principle and the energy available within a vacuum according to the Casimir effect, you come up with a very small minimal time interval. dE*dT=h/2pi
So obviously the minimum possible functional length would be L=c*dt
I make it about 10^-35m..below this size is just a quantum blur.. I even suspect that this is the operational dimension of the singularity at the heart of a black hole.
Incidentally string theoristas have speculated that the other 8 missing dimensions of space are curled up with this radius and that their modes of vibration give rise to all the particles including their mass, charge, spin etc

Answer 2

Seriously....... you can not cut up empty space. ;)

But lets consider that you are asking if we can "divide" space.

I might be in the minority in this............ but I'm going to argue no. Infinity does not completely exist in the real measured universe. theres just so big it might as well be infinite and so small it might as well be infinitesimal.

If we divide space, we have introduced a difference with a defined border. We are cutting it closer and closer, until it reaches an infinite closeness. At some point, no further difference in the two areas are possible.

This is, not true in logic. Mathematically, you can keep on adding an extra digit but in the real world, that infinitesimal number just wont matter nor even exist at some point.

Time it is argued similarly has an infinitesimal value of duration taken as the planks constant. I don't see why one could not exist for space.

Answer 3

If it is infinite then why not? LOL But not so fast.

If you are referring to matter, as we know it, then the finite size would be the smallest amount of 'quantum' energy or the smallest elementary particle.

On the other hand

Mathematically however you can divide space of a finite interval between 0 and 1 to infinity.

Answer 4

I would imagine yes. The partitions' size would only approach zero but never reach it no matter how infinitessmal the partition would become. This would be graphically represented by a standard calculus limit curve.

Answer 5

Physics can make no predictions at distances smaller than the Planck length, [(h-bar)(G)/c^3]^(1/2) = 1.616x10^(-35) meter. The energy at such a wavelength would be mass equivalent to being inside its Schwarzschild radius, creating a black hole. Information does not exit the interior of a black hole.

Answer 6

You'd need a pretty sharp knife to cut trough space, especially when your smaller parts gets really small!

Answer 7

Infinite divided by half is Infinite

Answer 8

It like ever thing else must end somewhere, once it reaches the atom stage its time to worry.

Answer 9

I bet I could use the words "wormhole" or "fractals" in an answer if only I were clever enough to know exactly what they mean.

Answer 10

Yes, it's called calculus and we do it all the time.