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Offline lightarrow

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What is electric charge ?
« Reply #25 on: 07/10/2007 11:43:45 »
The question is: What is an electric charge? It can be described in terms of it's properties. For example, as the smallest unit of force that can be obtained by the interaction between two such charges, but that's not very satisfying, but neither is describing it as a cloud of certain photons.

Lest you think I'm about to tell you what it is, however, I don't know either, but let me perhaps provide some food for thought. There is a wonderful theorem by W.V.D. Hodge that says on a closed manifold, and here I begin to speak loosely, a differential form can be expressed as the sum of the curl of a form or one lower dimension, the gradient of one higher dimension, and one of the same dimension whose gradient and curl are both zero. In even looser words, this means everything can be expressed as either a rotation or source, that is, as either a squirt or an eddy.

In a Minkowski space there are six kinds of eddy with one associated with each plane. Three such planes have both coordinates whose square is positive, and three have coordinates with one dimension whose square is negative. Let us associate the first three of these with the magnetic field and the others with the electric. Charge is then the fourth component of the vector core of the electric field and the field is itself the eddy associated with the charge.

Does this tell you what elecrtomagnetic field or the electric charge is? I don't think so, but perhaps it's food for thought. Incidentally. thank you McQueen for a delightful question.

Now, ask him to explain what you've written (but don't ask me)  ;)
 

Offline gamburch

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What is electric charge ?
« Reply #26 on: 07/10/2007 12:03:02 »
I guess it is a little weird, but let me give it a try. In two-space (a plane) there are only two types of field that are solutions of the laplaces equation. One is circles around a point, the other is radii emitted from a point.

The same is true in the four-space of relativity. Maxwell's equations say the electromagnetic field is the eddy part. What I'm trying to say is charge is the core of the eddy for the electric field, that is the eye of the hurricane.

All this means is maybe there is a way of looking at four-space to make all this make sense and explain what an electron is. Let me know if this helps
 

Offline lightarrow

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What is electric charge ?
« Reply #27 on: 07/10/2007 12:25:20 »
lightarrow, I thought that the article you posted provided a fairly convincing argument for the statement that it is time that bends and not space.  Of course by time bending I mean in relation to space (thus the concept of spacetime), not by itself.  Time alone is time but considered as part of spacetime it is bent relative to space.  That is at least what I got from the article (before it became unscientific).
Sincerely, I still have to understand what that article says about it. If I'll manage, I'll tell you.

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What is Noether's theorem?
One of the most interesting and useful matematical theorems applied to physics.
Everything starts from a function called "lagrangian" L which is T - V, T = kinetic energy and V = potential energy. The theorem put in relation physics symmetries with conserved quantities, starting from the lagrangian L. Examples:

The physical system (its lagrangian) is invariant under space translations --> momentum is conserved.

The physical system is invariant under space rotations --> angular momentum is conserved.

The physical system is invariant under time translations --> energy is conserved.

Invariance under space translations is called "space homogeneity", under space rotations "space isotropy", under time translation "time homogeneity".

In simple terms: space homogeneity means that every point of space is equivalent; example: you are inside a starship in the void, far from stars or planets and you conduct an experiment. Then you move the starship some kilometres and you repeat the experiment. Space homogeneity implies that you will find the same results. Well, from this very obvious and intuitive fact (that, however, must be proved experimentally) comes momentum conservation. Isnt'it fascinating?

Space isotropy means that after rotation of your spaceship (in the same place) the experiment's results are unchanged as well...

Time homogeneity means that, in the same place and with the same spaceship's orientation, if you make the experiment now or after 1 year, it'll give the same results. From this fact, comes energy conservation!

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Isn't density a dimension, and surface area and all of those sort of things?  A dimension in the sense that they describe a property of an object?  That being true, I think it is a very logical deduction that charge and mass should be dimensions of an object.  The only difference bewteen surface area and charge or mass is that surface area doesn't produce an acceleration while charge and mass do.  Therefore, on the subatomic scale, shouldn't an object be merely a wave which has dimensions q and m (and one for the strong and maybe weak force too)?  Come to think of it, I have never heard of a subatomic particle being described by size, only mass and charge (and spin, color, etc...).  Macro objects (atomic nuclei and up for this case) are given a size by the distances their constituent particles are held apart then.  Is space unaltered then by mass/charge/etc... and it is merely the time component of spacetime which changes (this having a component dimension for each interaction property of matter)?  Does this make sense?
Sorry but I don't follow you. Explain better.
 

Offline lightarrow

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What is electric charge ?
« Reply #28 on: 07/10/2007 12:36:36 »
I guess it is a little weird, but let me give it a try. In two-space (a plane) there are only two types of field that are solutions of the laplaces equation. One is circles around a point, the other is radii emitted from a point.

The same is true in the four-space of relativity. Maxwell's equations say the electromagnetic field is the eddy part. What I'm trying to say is charge is the core of the eddy for the electric field, that is the eye of the hurricane.
Shouldn't charge be the source, and so the divergence, not the curl, of the electric field? divE = -ρ/ε0 where ρ = charge density.
 

Offline gamburch

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« Reply #29 on: 07/10/2007 13:46:39 »
What you say is very true in three dimensions. Let me show why. When one writes something up in four dimensions things change. Hodge's theorem states that ω = dα + δβ + γ. In this equation, by the theorems of differential forms ddα = dγ = 0. δδβ = δγ = 0.
On the other hand we can set δβ = A where A is the electromagnetic potential and A a one-form. The electromagnetic field is then defined by ω = dA and Maxwell's equation by δω = j and dω = 0. Where I was sloppy was to use the terms curl and divergence instead of derivative operator and Hodge Star operator. The equation δω = j does define (more accurately, a component of it defines) ΔE = ρ. I hope this clears up the matter.
 

Offline McQueen

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What is electric charge ?
« Reply #30 on: 07/10/2007 15:26:49 »
Quote
One of the most interesting and useful matematical theorems applied to physics.
Everything starts from a function called "lagrangian" L which is T - V, T = kinetic energy and V = potential energy. The theorem put in relation physics symmetries with conserved quantities, starting from the lagrangian L. Examples:

The physical system (its lagrangian) is invariant under space translations --> momentum is conserved.

The physical system is invariant under space rotations --> angular momentum is conserved.

The physical system is invariant under time translations --> energy is conserved.


I am the last person to say that mathematics is not beautiful, but that does not make it any different from an abstract piece of art. Look at this site on ‘renormalisation’ not by one author but by many authors, http://www.secamlocal.ex.ac.uk/people/staff/mrwatkin/zeta/renormalisation.htm  and the funny thing is that they all say the same thing, namely that QM came up with infinities that were rationalized (read normalized) by replacing those infinities with finite values taken from actual observation . (Read: these beautiful mathematical concepts were framed around what was being observed and did not lead to them ….. by any means) Does this make sense, if it does, you are way ahead of me. N.B: It is important to note that all these people also think that ‘renormalisation’ (i.e., rationalizing a 10^^12 discrepancy) actually works. So there you have it , who is right in all this?
« Last Edit: 07/10/2007 15:28:39 by McQueen »
 

Offline lightarrow

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« Reply #31 on: 07/10/2007 18:12:08 »
Quote
One of the most interesting and useful matematical theorems applied to physics.
Everything starts from a function called "lagrangian" L which is T - V, T = kinetic energy and V = potential energy. The theorem put in relation physics symmetries with conserved quantities, starting from the lagrangian L. Examples:

The physical system (its lagrangian) is invariant under space translations --> momentum is conserved.

The physical system is invariant under space rotations --> angular momentum is conserved.

The physical system is invariant under time translations --> energy is conserved.


I am the last person to say that mathematics is not beautiful, but that does not make it any different from an abstract piece of art. Look at this site on ‘renormalisation’ not by one author but by many authors, http://www.secamlocal.ex.ac.uk/people/staff/mrwatkin/zeta/renormalisation.htm  and the funny thing is that they all say the same thing, namely that QM came up with infinities that were rationalized (read normalized) by replacing those infinities with finite values taken from actual observation . (Read: these beautiful mathematical concepts were framed around what was being observed and did not lead to them ….. by any means) Does this make sense, if it does, you are way ahead of me. N.B: It is important to note that all these people also think that ‘renormalisation’ (i.e., rationalizing a 10^^12 discrepancy) actually works. So there you have it , who is right in all this?

I haven't read those site, but, concerning renormalization, of which I know only very little, some physicists would agree with you that it's a nonsense. If you asked me, I would say that not even photons (as moving particles) exists, so you are talking to someone who believes in very solid-real things in physics, and that sometimes people don't understand exactly where physics ends and mathematics begins.
 

Offline McQueen

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What is electric charge ?
« Reply #32 on: 07/10/2007 22:30:24 »
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I haven't read those site, but, concerning renormalization, of which I know only very little, some physicists would agree with you that it's a nonsense. If you asked me, I would say that not even photons (as moving particles) exists, so you are talking to someone who believes in very solid-real things in physics, and that sometimes people don't understand exactly where physics ends and mathematics begins.
I am thinking of starting a 'Week of the photon Thread' in which the photn will be discussed one aspect or property at a time, since many people don't seem to know much about photons.
 

Offline Mr Andrew

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What is electric charge ?
« Reply #33 on: 09/10/2007 01:55:18 »
lightarrow, in regards to the paragraph on density and dimensions and what not, I was only trying to prove that charge is a dimension of matter like mass and so it's effects should be considered similarly (such as in the bending of spactime).  The article you had posted early in the thread discussed the Kaluza-Klien modification to GR in which charge interacted with a fifth dimension and only other charged particles felt the effects of the bending of this dimension.  This seems all too logical but it has not become a major component of relativity theory...why is that?  It seems so very obvious (and I would toy with the idea quantitatively if only I had the mathematical background).
 

Offline lightarrow

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« Reply #34 on: 09/10/2007 21:05:06 »
lightarrow, in regards to the paragraph on density and dimensions and what not, I was only trying to prove that charge is a dimension of matter like mass and so it's effects should be considered similarly (such as in the bending of spactime).  The article you had posted early in the thread discussed the Kaluza-Klien modification to GR in which charge interacted with a fifth dimension and only other charged particles felt the effects of the bending of this dimension.  This seems all too logical but it has not become a major component of relativity theory...why is that?  It seems so very obvious (and I would toy with the idea quantitatively if only I had the mathematical background).
I don't know the answer to your question. I would like to know your idea.
 

Offline Mr Andrew

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« Reply #35 on: 11/10/2007 17:16:54 »
What if charge interacted with this fifth dimension of spacetime in the same manner as mass interacts with the first four dimensions?  Many of the predictions of GR could be made for charges instead of masses.  Light would bend in an electric field...etc.  Like I said, I don't have enough math to play around with this, someday though....
 

Offline lightarrow

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« Reply #36 on: 11/10/2007 19:10:30 »
What if charge interacted with this fifth dimension of spacetime in the same manner as mass interacts with the first four dimensions?  Many of the predictions of GR could be made for charges instead of masses.  Light would bend in an electric field...etc.  Like I said, I don't have enough math to play around with this, someday though....
I think Einstein did try to incorporate this idea in a unified fields theory, but he didn't succeed.
 

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What is electric charge ?
« Reply #36 on: 11/10/2007 19:10:30 »

 

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