How Many Unique Points Exist in a Region of Space?

[Chase]

As far as I know a point in space is shown by it's t,x,y and z coordinates? Anyway it isn't so much how it's defined that I'm interested in, it's more about what a point of space is.

Let's say we took a 1cm^2 region of space, how many unique points of space does this region have? What distinguishes one point in space to another point? Is there a fundamental limit as to how small the distance can be from point a to point b?

I heard Planck length being thrown around a bit but I don't really understand it, is this the smallest physical distance that can exist or just the smallest physical distance we can measure? Basically what I want to know is if you take two points on a straight line, how many unique points exist between them?

 

[phinds]

The term "point" refers to a dimensionless quantity, so it is not meaningful to ask how many you can get in a shoebox.

Point in space is defined only to the extent you can reference it to some relatively fixed coordinates. Something centered on the Earth, for example, would be constantly changing position, so you would have to say "a point relative to the Earth" in some way. That is, there is no absolute position in space, only positions relative to something else.

 

[DennisN]

Basically what I want to know is if you take two points on a straight line, how many unique points exist between them?

A point is actually a rather abstract concept, since mathematically it has no extent.
So the answer to your question depends on if you ask from a mathematical point of view, or a physical, so:
Mathematically: There are infinitely many points between two points.
Physics: I can't say the question makes any sense to me, since we do not know (yet) if there is any smallest fundamental unit of length.

 

[phinds]

To add to what Dennis said, you may have heard that the Plank length is the smallest length possible, but that's not known. What is surmised is that the Plank length is the smallest we will ever be able to MEASURE, even theoretically. We are currently something like 15 or 20 orders of magnitude away from being able to measure a Plank length in practice.

 

[adianamonet]

There are infinitive points between point A and B on a line. Planck length is 1.616199×10^−35 meters, it's just a unit of measure. But, Dennis is right we don't currently know the smallest fundamental unit of length. I'm honestly not sure if we ever will. But, to answer your question the answer is infinitive, but you can also argue Planck length if you want.

 

[Chase]

There are infinitive points between point A and B on a line. Planck length is 1.616199×10^−35 meters, it's just a unit of measure. But, Dennis is right we don't currently know the smallest fundamental unit of length. I'm honestly not sure if we ever will. But, to answer your question the answer is infinitive, but you can also argue Planck length if you want.

It doesn't seem accurate to just say "if I want..." What I want is irrelevant, I just wanted to know what science says it is. I think I got my answer though.

 

[adianamonet]

It's all still a debate. Some people say infinitive and others use Planck length. But the "more scientific" answer is infinitive.

 

[phinds]

It's all still a debate. Some people say infinitive and others use Planck length. But the "more scientific" answer is infinitive.

No, you misunderstand. It is not a debate. The Plank length has nothing to do with this question and was brought in by the OP through a misunderstanding.


And by the way, "infinitive" is a term describing a grammatical form and has nothing to do with math. You want either infinite (the big one) or infinitesimal (the small one)

 

[adianamonet]

Oh ok, sorry about that. Yeah I misunderstood your question.