Transformation Of Line To A Point

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#1 petrushkagoogol

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Posted 04 February 2019 - 07:32 AM

If I apply a finite number of transformations to a line of finite length (where a transformation is the division of the line into half) can I ever get a point ?

IMHO it is not possible.

To reach a point the number of transformations tends to infinity, which is not achievable practically, although the inverse is possible, by finitely extending a point to a line, in one dimension.

Is this correct or not ? 🤔

#2 Dubbelosix

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Posted 04 February 2019 - 09:13 AM

Taking the limit of

$ds \rightarrow 0$

Then the line element $ds$ has no dimensions (which means) you are in the space of pointlike physics. Be clear, the pointlike dynamics are only used for particles with a mass - an electron is shown from classical mechanics that it makes no sense to speak of it as a point - not only this, but classical mechanics predicted that particles would behave pointlike anyway, so we tend to think of it as a scaling phenomenon. If an electron radius was truly made to go to zero, then infinities would arise in the theory; and this means physics is no good. So the idea has to be abandoned, at least in principle.

#3 petrushkagoogol

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Posted 04 February 2019 - 07:36 PM

Taking the limit of

$ds \rightarrow 0$

Then the line element $ds$ has no dimensions (which means) you are in the space of pointlike physics. Be clear, the pointlike dynamics are only used for particles with a mass - an electron is shown from classical mechanics that it makes no sense to speak of it as a point - not only this, but classical mechanics predicted that particles would behave pointlike anyway, so we tend to think of it as a scaling phenomenon. If an electron radius was truly made to go to zero, then infinities would arise in the theory; and this means physics is no good. So the idea has to be abandoned, at least in principle.

Edited by petrushkagoogol, 04 February 2019 - 07:38 PM.

#4 devin553344

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Posted 05 February 2019 - 03:38 AM

If I apply a finite number of transformations to a line of finite length (where a transformation is the division of the line into half) can I ever get a point ?

IMHO it is not possible.

To reach a point the number of transformations tends to infinity, which is not achievable practically, although the inverse is possible, by finitely extending a point to a line, in one dimension.

Is this correct or not ?

As represented by a computer with a given precision they will reach the same position at some point. And physics suggest that measuring space breaks down at some super-tiny distance, the Planck length. So yes you could turn a line into a point theoretically for all intents and purposes.

Edited by devin553344, 05 February 2019 - 03:49 AM.

#5 devin553344

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Posted 05 February 2019 - 03:51 AM

Taking the limit of

$ds \rightarrow 0$

Then the line element $ds$ has no dimensions (which means) you are in the space of pointlike physics. Be clear, the pointlike dynamics are only used for particles with a mass - an electron is shown from classical mechanics that it makes no sense to speak of it as a point - not only this, but classical mechanics predicted that particles would behave pointlike anyway, so we tend to think of it as a scaling phenomenon. If an electron radius was truly made to go to zero, then infinities would arise in the theory; and this means physics is no good. So the idea has to be abandoned, at least in principle.

One can use Riemann zeta operations to describe infinities depending on the physics. The Casimir effect is an example of that.

Edited by devin553344, 05 February 2019 - 03:55 AM.

#6 Dubbelosix

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Posted 05 February 2019 - 05:42 AM

What do you mean? I just showed you the limit of a line, going to zero, which is now a point.

What more do you want?

#7 Dubbelosix

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Posted 05 February 2019 - 05:44 AM

One can use Riemann zeta operations to describe infinities depending on the physics. The Casimir effect is an example of that.

No, this is not true. We do not accept as science minded people, that a system displays any infinities - infinity is a mathematical abstraction, not a physical situation. Devin, are you also Petru?

I have a strong feeling the two of you are the same people, its not fashionable to answer your own posts.

#8 Dubbelosix

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Posted 05 February 2019 - 05:46 AM

In fact, infinities are not embraced in physics, because they are not a science. You cannot observe or measure an infinity so such topics are classed as rubbish. Scientists hate the idea of infinities so much, they created them by accident then tried to find ways to make a patchwork of the situation, called renormalization.

#9 devin553344

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Posted 05 February 2019 - 08:24 AM

No, this is not true. We do not accept as science minded people, that a system displays any infinities - infinity is a mathematical abstraction, not a physical situation. Devin, are you also Petru?

I have a strong feeling the two of you are the same people, its not fashionable to answer your own posts.

Probably paranoia about Petru, Strange clearly you have not studied Riemann zeta operations which also include photon gas and the use of Riemann zeta 3 and 4 which clearly represents infinity. It is a standard summation with infinite iterations, do you not know calculus? I've ran the Riemann zeta calculations on my computer using c# programming language, and I calculated it to 300,000,000 iterations, although it's true nature is infinity. https://en.wikipedia...wiki/Photon_gas

Edited by devin553344, 05 February 2019 - 08:42 AM.

#10 devin553344

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Posted 05 February 2019 - 08:27 AM

In fact, infinities are not embraced in physics, because they are not a science. You cannot observe or measure an infinity so such topics are classed as rubbish. Scientists hate the idea of infinities so much, they created them by accident then tried to find ways to make a patchwork of the situation, called renormalization.

Renormalization works for negative Riemann zeta operations but one only needs to calculate a certain number of iterations for positive Riemann zeta operations. You should try simulating it with computer programming language, you could learn something.

#11 petrushkagoogol

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Posted 05 February 2019 - 08:49 AM

Renormalization works for negative Riemann zeta operations but one only needs to calculate a certain number of iterations for positive Riemann zeta operations. You should try simulating it with computer programming language, you could learn something.

Brilliant

PS : Thanks Anders Heljberg for the C# programming language
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#12 Dubbelosix

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Posted 05 February 2019 - 09:11 AM

Renormalization works for negative Riemann zeta operations but one only needs to calculate a certain number of iterations for positive Riemann zeta operations. You should try simulating it with computer programming language, you could learn something.

I can now see you are the same people... anyway...

you totally missed the point, and the issue with dealing with singularities. An example is a case in which we ''and we really don't need to'' make the radius of systems like an electron go to zero and this creates a singularity problem with the self energy. Then renormalization is used to reconfigure so that these singularities are blotted out. But there was an issue from the word ''go'' as not all fundamental particles are of the same size, classical mechanics already told us that a sufficiently small system with a ''quantum radius'' would appear to act pointlike in experiments, and so truly calling them pointlike could be wrong in the fundamental sense, as an approximation though, it works perfectly fine.

So the real question is, why do we accept the nonsense of a radius going to zero? The fact is we don't accept it, but physicists in an attempt to correct it, did it the wrong way around, resulting in a renormalization instead of asking why these unacceptable physics were not taken to the root, to find what the problem was that created it.

#13 devin553344

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Posted 05 February 2019 - 10:58 AM

I can now see you are the same people... anyway...

you totally missed the point, and the issue with dealing with singularities. An example is a case in which we ''and we really don't need to'' make the radius of systems like an electron go to zero and this creates a singularity problem with the self energy. Then renormalization is used to reconfigure so that these singularities are blotted out. But there was an issue from the word ''go'' as not all fundamental particles are of the same size, classical mechanics already told us that a sufficiently small system with a ''quantum radius'' would appear to act pointlike in experiments, and so truly calling them pointlike could be wrong in the fundamental sense, as an approximation though, it works perfectly fine.

So the real question is, why do we accept the nonsense of a radius going to zero? The fact is we don't accept it, but physicists in an attempt to correct it, did it the wrong way around, resulting in a renormalization instead of asking why these unacceptable physics were not taken to the root, to find what the problem was that created it.

Not to mention a singularity, and I am assuming you're talking about a black hole collapse, will never reach a zero radius. It will always have some value however small while it's collapsing. Zero is an infinity in the radius area which can't be reached by a collapsing system.

#14 Dubbelosix

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Posted 05 February 2019 - 12:20 PM

Not to mention a singularity, and I am assuming you're talking about a black hole collapse, will never reach a zero radius. It will always have some value however small while it's collapsing. Zero is an infinity in the radius area which can't be reached by a collapsing system.

Then you assume wrong because I am talking about the classical electron radius.

It's like talking to a brick wall.

#15 Moronium

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Posted 05 February 2019 - 02:37 PM

infinity is a mathematical abstraction, not a physical situation.

I agree with this, and the same is true of a "point."  A point is merely an abstract theoretical construct which cannot exist in "reality."  You can go back centuries, to Euclid, and see this.

Euclid defined a point as having no dimensions: no length, no width, no breadth.  In other words, it's something that could not possibly "really" exist.  It exists only in theory.

The original post makes the same basic point that Zeno was trying to make, millennia ago, to "prove" that motion is impossible.  The "paradox" he created was based on the premise that any distance can be infinitely divided, and could never reach zero.  Hence, he reasoned, the fastest sprinter could never catch up to a tortoise that was 3 feet in front of him.

Edited by Moronium, 05 February 2019 - 02:51 PM.

#16 devin553344

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Posted 05 February 2019 - 04:31 PM

Then you assume wrong because I am talking about the classical electron radius.

It's like talking to a brick wall.

Brick Wall Said: You mentioned singularity. Which is why I naturally was thinking this: https://en.wikipedia...nal_singularity

Please: There is no proof that an electron could be a singularity or a point, you'd be better off using the black hole idea and making it a gravitational singularity.  How could an electron collapse or even hold onto its energy with that charge repulsion? It wouldn't silly

There's clearly something going on with the electron that physicists don't understand, and maybe never will. Unless you embrace my theory. :End Brick Wall Said.

Edited by devin553344, 05 February 2019 - 05:21 PM.