Order of Kilopi
If you draw a line through space you would pass through matter, in which case it would be either on(ie there) or off(no there) but if matter occupied any real volume, even 1cm^3, then there would be an infinite amount of mass.
There for matter perhaps exists as complex surfaces with zero thickness.
Is this right?
Established Member
I don't quite understand the question.
Why would there be an infinite amount of matter? The universe isn't infinite, for starters.
Administrator
We have no certain idea about what matter is like at or below the Planck scale, which is still much larger than a geometric point. Your notion about infinite density will fall apart when you look that closely.
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Established Member
Quantum uncertainty would throw a spanner in that theory. You can't really pin-point the location of anything on a subatomic level (not twice anyway).
So the answer to the question "Is this point inside a proton/an electron/something else?" is a definite "maybe"!
Order of Kilopi
If I understand your question, it seems that you´re only expressing a paradox (i.e. an apparent absurdity). While it can be treated in an abstract fashion, it has no physical meaning. It´s something like the famous Zenon´s "proof" that motion is impossible.Originally Posted by Frog march
Order of Kilopi
Why?
Administrator
I suspect that Frog march meant infinte density. We frequently see people making this linguistic slip when talking about the impossibility of singularities in the centers of black holes.
If he did mean infinite mass, hopefully he'll correct my misunderstanding.
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Order of Kilopi
If matter is either on or off say 1 or zero, in its presence at a point then a volume of space through which you could draw any line in any orientation and only get 1s would mean that you would have an infinite mass(and you would also have infinite density), if mass was a product of the "amount" of its presence. In the same way that there are an infinite number of numbers between 3 and 4.
Order of Kilopi
Yep, you´re talking bout paradoxes, definitely.In the same way that there are an infinite number of numbers between 3 and 4.
Order of Kilopi
But if each matter "point" occupies some positive volume, then there no longer is an infinite number of matter points in a given volume of space... right?
You can divide the total volume of the shape, say T, by the volume of each point of matter, v, and get the number of points, n=T/v.
Order of Kilopi
I don't think that qualifies as a paradox.
In the OP (and as clarified), Frog march was talking about an infinite number of points of matter, not an infinite mass. Mathematical points are clearly capable of being infinite in number, in a finite segment, so there is no paradox, in that case.
Infinite density is a different question, but, again, mathematically, one can have an infinite density of points in a segment, so there's no paradox there either.
Established Member
Funny things start to happen in mathematics when you add up an infinite number of points along a line...I believe it's called integration. This doesn't work, I think, unless the interval is "dense" enough (I don't think you can integrate over the rational numbers for instance). These are ideas covered in mathematical analysis called "measure theory", and as I recall (vaguelly), it was really complicated
I would guess that matter, however, is discrete, and not continuous. Isn't there also a limit to the size a particle can be (like 10^(-40))?
Pete
Banned
just about...
now imagine spatial tension.... imagine it, as one dimensional lines of force.. which is tension on space..
now take a bunch of tension and curl and roll it up and form it into a ball, and you have mass.... which is still composed of one dimensional lines, formed into a 3d ball.. one dimensional line which are almost not there.
-MT
Established Member
Frog march,
That's assuming matter doesn't have a volume. If matter has volume of it's own...thus taking up more than a geometric point, then there's no problem.
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