Can We Talk of Points of Space?

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The discussion centers on the existence of points in space and their implications for physics and mathematics. Participants debate whether points are merely conceptual tools rather than physical entities, suggesting that if points do not exist, then positions in space (x,y,z) are also not absolute realities. The conversation highlights the distinction between mathematical models and physical reality, with some arguing that space itself may be a conceptual framework rather than a tangible structure. The idea of diffeomorphism invariance is introduced to support the notion that physical laws do not rely on fixed points. Ultimately, the discussion raises fundamental questions about the definitions and roles of points and space in both physics and mathematics.
misster y
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Hello, I'm new here, excuse my english...
Are there points in our space?
If there are not, as it seems obviously if space was (is) created since big-bang (can points be created?), the consecuences are strong.
For example, we deduce inmediately the uncertainty of positions --if there are not points, there are not (x,y,z)--, every function f(x,y,z) is aproximate, the space is not continuos, we are not in R^3 but in Q^n, etc...
What do you think?

Llorenç Balsach
http://www.webcom.com/musics/escrits.htm

"The matter-energy is not inside a space-time, but the space-time is a manifestation of the matter-energy"
 
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"Points" are not physical objects- they are concepts.

As far as saying "every function f(x,y,z) is aproximate", well of course that's true.

You seem to be confusing physics with mathematics!
 
misster y said:
the consecuences are strong...

Meh...

Math are tools, models, you use the ones that serve your purpose. In my case, f(x,y,z) is just fine.
 
HallsofIvy said:
"Points" are not physical objects- they are concepts.
Is space also a concept?
We see the matter but also feel the space!
I points are a concept then the position (x,y,z) of matter is another concept not a reality.
But I can do the question with other words: Can we talk of points of space? Can we apply this absolute concept in physics?
This is an axioma that never appears in the books of physics!
 
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Points are basically a tool for our bookkeeping. They do not correspond to any physical structure. The fact that laws of nature seem to be diffeomorphism invariant strongly supports this position.
 
ahrkron said:
Points are basically a tool for our bookkeeping. They do not correspond to any physical structure.
Yes, I agree.
But, let me insist: if points are a tool for our bookkeeping, what is a punctual position of a particle? It is also a tool?, have a particle a position?, my idea is that there is not an exact-punctual position but not due to the uncertainly principle nor to our medition instruments but because there are not points, there are not a point to assign a position --nor instants--. There are not (conceptual) points in our space as in maths. In the fundaments of physics, what is the definition of the position of matter?
For me all this is due that the matter-energy is not inside a space-time, but is the space-time that is a manifestation of a matter-energy!
 
There are no points in noncommutative geometry and it still works quite good.
 
misster y said:
Is space also a concept?
We see the matter but also feel the space!

A "space" is a geometric concept. It is usually considered a plenum (which should answer your original question).

You say we can "feel the space"...I disagree. I know that we can conceive of space -- indeed, of many spaces -- but I don't think perception of space is anything more than relating yourself to some other "observer" (IOW, without two reference points, would you still "feel the space"?).
 
ahrkron said:
Points are basically a tool for our bookkeeping. They do not correspond to any physical structure. The fact that laws of nature seem to be diffeomorphism invariant strongly supports this position.
Could you explain a bit about what 'diffeomorphism invariant' means?
 
  • #10
This link takes you to a section of Carlo Rovelli's "living review" on Loop Quantum Gravity exactly on that issue:
http://relativity.livingreviews.org/Articles/lrr-1998-1/node11.html
 
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  • #11
misster y said:
Is space also a concept?
We see the matter but also feel the space!
I points are a concept then the position (x,y,z) of matter is another concept not a reality.
But I can do the question with other words: Can we talk of points of space? Can we apply this absolute concept in physics?
This is an axioma that never appears in the books of physics!

If you are going to talk about "points" and "space" in this way, then I have to ask "what is YOUR definition of 'point' or 'space'". The fact is that physics and mathematics often use the same terms with DIFFERENT definitions. Which are you using?
 

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