I hope I'm not bothering anybody here

[Lars]

I have a question which has been bugging me for the last day or so. The problem is that I am a complete physics novice, and while I studied Mathematics a long time ago, I haven't used it in years and have forgotten most of it since. Which is why I hope that I'm not bugging you with this question. My questions is probably about something that is really trivial in quantum physics, but I can’t stop thinking about it.

If this is a stupid question just tell me so and it won’t bother me at all. And actually, I think this may actually be more of a philosophy question then a physics question.

Okay start here it is:

Imagine an object about a centimeter long up against a ruler. The end of the object is positioned at the 1 cm mark, the start of the object is at the 2 cm mark. Now push the object a little bit, say half the distance of the object. Now the object is at the 1.5 cm to 2.5 cm. I am probably not saying this well, but at a certain intellectual level the simple fact that I can move my object into a sort of space half again the size of my object implies that I can chop it at least in half.

Okay now imagine, hypothetically, that I can shrink in size, dwindling down and down into the sub-atomic level of size. I am now so tiny that right in front of me is a Quark, or if a Quark is not the smallest division of something matter-like or energy-like then whatever is. It is here that my question becomes relevant. I reach out my finger and nudge this Quark half the distance of itself in a direction.

This would seem to me to imply four possibilities.

1) I shrink in size again. Dwindling down and down and down again, and look up at the quark which is now growing like a meteor, like a planet above me, which would imply that the quark was again divisible. After all there is open space to put bits of it in.

2) That space and matter have absolutely no relationship to one another. One is just the thing, the other is just the empty space to put the thing into.

3) That at some level there is a smallest unit of space that is roughly approximately in size to the smallest unit of matter. And that my hypothetical pushing is more like moving pixels across a computer screen than true motion. One unit of charge, charging a nearby unit of space, and the unit of space that it has just vacated becoming uncharged.

4) That something else entirely is going on and that I am too caught up in my rather vague memories of classical physics.

So I guess my question is this. Is there a smallest unit of space?
Lars Townsend

 

[Lars]

I emailed this question to a friend too, and this is his reply, which makes sense, so sorry for bugging you guys.

I am not a physics researcher but in my opinion, the
jury is still out on whether or not space-time is
quantized. Energy definitely seems to be and since
matter and energy are the same, one can say that
matter is also quantized. Many say that the Planck's
time is the shortest quantized time and Planck's
length is the smallest unit and if so, then like
quantized electon energy levels, objects actually jump
between the discrete positions instead of moving
continuously between them. I think some recent
experiments have shown that time is NOT quantized
which implies that space isn't either but as I said, I
don't believe the question has been settled.

 

[Careful]

We don't know
You might want to look into the literature for trans-Planckian particles.
Cheers,

Careful

 

[masudr]

Firstly, note that the most fundamental particles are assumed to be of no size, in the standard model, at least. Electrons, for example, are assumed to be point particles. Introducing a size for electrons would involve lots of complications in it's description under the Dirac equation, or Quantum Electrodynamics.

Secondly, we don't really know if spacetime is quantized, we have not yet many instruments that can probe nature on the scale we expect the quantization to become apparent. And there are a few contending theories that describe what happens to the nature of spacetime on such a scale.

Finally, space (or more correctly, spacetime) and matter do have a relationship with each other. In fact, the relationship is very strong. Einstein's field equations literally equate (with some proportionality constant) ten numbers made out of space time curvature with ten numbers made out of the energy and momentum of matter.