Why do positive and negative charges attract?

[FizixFreak]

These questions, being so basic, were harder to find answers to on the forums (or elsewhere). At least, it was harder to find an answer that satisfied my curiosity. I need a DEEPER, simpler, and more logical understanding of these concepts.:
What does it mean for a particle to have a positive or negative charge?

Why do positive and negative charges attract?

How would this apply to the Quantum model of electrons and protons in an atom?Thanks

*and trust me, deeper and simpler don't contradict each other by my definition. I'm sure most of you will understand.

you have probably gotten the answer but i think that string theory can give a more logical yet complex explanation you must be familiar with the curves in the space time fabric that causes every single object in the universe to attract the any other object causing what we know as gravitational pull.
the electrostatic force is found to be caused by same type of curves in space but since our three dimensions are already covered up by gravitational force there must be other dimensions in the universe in which the curves are caused by charged bodies so the uncharged bodies only create curves in the three dimensional space but charged bodies also create curves in other dimensions and because of these curves the charges attract to each other here is a link. in this video they talk not about the electrostatic force but unified EM force hope you find it helpful
( i might have made some mistakes here some creative criticism will be appreciated)

 

[Kevin_Axion]

you have probably gotten the answer but i think that string theory can give a more logical yet complex explanation you must be familiar with the curves in the space time fabric that causes every single object in the universe to attract the any other object causing what we know as gravitational pull.
the electrostatic force is found to be caused by same type of curves in space but since our three dimensions are already covered up by gravitational force there must be other dimensions in the universe in which the curves are caused by charged bodies so the uncharged bodies only create curves in the three dimensional space but charged bodies also create curves in other dimensions and because of these curves the charges attract to each other here is a link. in this video they talk not about the electrostatic force but unified EM force hope you find it helpful
( i might have made some mistakes here some creative criticism will be appreciated)

Firstly FixiFreak, you're talking about Kaluza-Klein Theory which has been proven incorrect. The curvature of five space-time dimensions produces Maxwell's equations for electromagnetism, Einstein's Field Equations for Gravity and the Radion/Graviscalar. The radion is a hypothetical scalar field which has falsified this theory and also the inconsistency of the theory for producing physical constants has made it inaccurate in describing nature. Also to extend that point, Kaluza-Klein Theory doesn't produce the Quantum Field Theories: Quantum Chromodynamics, and the Electroweak Interactions. So no, Electromagnetism isn't the curvature of five of an extra compactified dimension in Five dimensional space-time and this isn't the correct approach in describing nature. Although the extra dimensions and the geometry of the compactifications into Calabi-Yau Manifolds is etched into the elegance of String Theory.

 

[FizixFreak]

Firstly FixiFreak, you're talking about Kaluza-Klein Theory which has been proven incorrect. The curvature of five space-time dimensions produces Maxwell's equations for electromagnetism, Einstein's Field Equations for Gravity and the Radion/Graviscalar. The radion is a hypothetical scalar field which has falsified this theory and also the inconsistency of the theory for producing physical constants has made it inaccurate in describing nature. Also to extend that point, Kaluza-Klein Theory doesn't produce the Quantum Field Theories: Quantum Chromodynamics, and the Electroweak Interactions. So no, Electromagnetism isn't the curvature of five of an extra compactified dimension in Five dimensional space-time and this isn't the correct approach in describing nature. Although the extra dimensions and the geometry of the compactifications into Calabi-Yau Manifolds is etched into the elegance of String Theory.

so may be you are trying to say that EM force is not caused by warps and curves in the extra dimensions?
but it makes so much sense and it also is the basis of string theory and if kaluza was wrong it proves that string theory is false as well may be it failed on some specific points but the main points of the theory which explain the EM force so beautifully just do not seem to be wrong.

 

[Kevin_Axion]

Warping of five-dimensional space-time to generate Electromagnetism isn't a physical idea established my String Theory. It also isn't a significant basis for the idea of String Theory, I think your perception of the theory is slightly obscured, you should read through this extensively: http://en.wikipedia.org/wiki/Superstring_theory

 

[FizixFreak]

Warping of five-dimensional space-time to generate Electromagnetism isn't a physical idea established my String Theory. It also isn't a significant basis for the idea of String Theory, I think your perception of the theory is slightly obscured, you should read through this extensively: http://en.wikipedia.org/wiki/Superstring_theory

yes i was wrong about that.
but even if we keep string theory out of this the idea of kaluza still seems quite reasonable if this idea does not explain the EM force then what does(is it that CHARGE DUE TO SPIN STUFF)?

 

[Kevin_Axion]

Yes, many theories appear reasonable but Kaluza-Klein theory isn't predictive or is cohesive with experimentally observed quantities: such as the Electron Mass, and the Coupling Strength of the Electromagnetic force. If you find dimensions to be intriguing then Superstring Theory is an idea that will fascinate you. Superstring Theory's extra dimensions (Calabi-Yau Manifolds) are naturally beautiful and are the basis of the theories predictive power and elegance. Spin is a property of particles, you can think of it as quantized angular momentum, so no charge and electromagnetism is derived from spin. Charge is also a quantum property of particles and charged particles interact with the electromagnetic field and with other particles by exchanging virtual photons.

 

[FizixFreak]

Yes, many theories appear reasonable but Kaluza-Klein theory isn't predictive or is cohesive with experimentally observed quantities: such as the Electron Mass, and the Coupling Strength of the Electromagnetic force. If you find dimensions to be intriguing then Superstring Theory is an idea that will fascinate you. Superstring Theory's extra dimensions (Calabi-Yau Manifolds) are naturally beautiful and are the basis of the theories predictive power and elegance. Spin is a property of particles, you can think of it as quantized angular momentum, so no charge and electromagnetism is derived from spin. Charge is also a quantum property of particles and charged particles interact with the electromagnetic field and with other particles by exchanging virtual photons.

alright akward question but how does these exchanges cause attraction or repulsion i mean why do these exchanges cause the charges to accelarate in a field and what are these virtual photons ??

 

[Kevin_Axion]

The sole purpose of this thread was to satsify the question "why do positive and negative charges attract?", many people, including myself included a detailed explanation of how Electromagnetic attraction and repulsion is mediated by virtual photons to charged particles. You ask the question "how do virtual photons cause attraction and repulsion?" Once again there is not one person that knows, it is a property of nature that isn't described through theory, theories such as Quantum Electrodynamics (http://en.wikipedia.org/wiki/Quantum_electrodynamics#Feynman_diagrams) describe how charged particle are effected by virtual photons (http://en.wikipedia.org/wiki/Virtual_particle) and it describes the physical implications but it doesn't ask the question of Why? It doesn't have to, nor should it because nature doesn't ask the question Why? Human's do, it's a quality of our curiosity.

 

[jVincent]

There is a lot of talk in this thread about the nature of your question and whether you should be asking it at all, I think this is unnecessary noise in the discussion.

Why do likes charges attract? Well, let's ask first a more useful question, what is charge? Well charge is a concept we have invented to describe attractive and repulsive forces which we observe between objects. We then went on to describe mathematical formulas which described the nature of these attractions and repulsions.
So the question of why do like charges repel, should really be asked remembering that we ourselves defined the concept of charge based on the repulsion. That is, you are not going to find a question which goes like: "Well, when you have 7 cars in a row, that leads to a charge, and because all cars go the same direction this leads to..."

The reality of the question is that when we do experiments where we transfer a charge to an object, two objects that undergo the exact same charge transfer, be it negative or positive will show a repulsion. Therefor we built the framework with the definitions giving a repulsion for like charges. Later experiments then pinned down the origin of these charges to the subatomic particles.

Of cause a more mathematically complex derivation of a similar result could be given using all the weirdities of quantum mechanics and some would find such an answer more rewarding simply because it contained more equations. However we should remember that QM itself is just a mathematical framework which we built requiring the apparent results of reality to be true, so it doesn't prove anything that it can be used to derive the results it was based on (except that it isn't falsified by those specific experiments).

As Feynman is trying to explain, it is not a case of the answer being unknown, it is a case of the answer being just another level of abstraction invented for the sole purpose of explaining the reality that we find when we cary out experiments. Following down this road your equation becomes.

 

[AJ Bentley]

I can't answer the question as to why (or how) charges come in two varieties, with contrary properties but there is a QM explanation of the interaction of electromagnetic fields with charge. In a way, that answers the question of how the forces arise.
Is that what you are asking about?

 

[Zhabka]

There is a lot of talk in this thread about the nature of your question and whether you should be asking it at all, I think this is unnecessary noise in the discussion.

Agreed! I couldn't believe the stubbornness with which people refused to even consider the question just because it had the word "why" in it. No one even mentioned QED until the second page of posts, shouldn't that have been the very first reply? Obviously no one is expecting a grand-unified-tied-up-in-a-neat-little-package-with-a-nice-looking-bow description of attractive and repulsive forces. But is it really so bad to want something more satisfying than "because that's the way it is", or "its defined that way".

So I send out my respects to Karmic for standing his ground on this! So what if any real discussion on a topic like this will be nothing but conjecture? It never hurts to have a brain storm! After all, before any theory comes into being someone has to first make a guess at a better explanation, only then can you start to see if it holds water.

In my opinion, Faradave gave the best summary of the state of this topic today, hands down. He was a breath of fresh air that made me grin from ear to ear.

***

I wish I had something to add myself, but I don't have much. Although I do remember a few years back when I was in high school. This exact question suddenly started driving me nuts for a few months. At the time I had never heard of Quantum Electrodynamics and I don't think I was even aware of the basics of QM.

One day I decided, "I have to resolve this! I need some paradigm to imagine just to appease my curiosity!". At this point I was no longer concerned so much about being right as I was about just thinking of some way to picture it, just some allegory that made a shred of sense in my own mind.

What I came up with was a lot like the space-time warping some people here have talked about in the context of string theory. At the time the only thing I knew beyond Newtonian mechanics was a qualitative understanding of general relativity. So I just decided to think of the same thing as a mass distorting space-time except that there were two entities which would distort it in "opposite directions".

I thought of it kind of like one distorts the fabric inwards and the other distorts it outwards. To simplify the picture in my head I thought of it like single waves. One was a single crest and the other was a single trough. The crests were space-time ballooning out, the troughs were ballooning in (if that makes sense). If a crest meets a trough then they cancel out and the amount of "fabric" between them decreases, or they attract. If two of the same meet then they amplify each other and the separation grows, or a repulsion.

These days when I imagine that is isn't as satisfying as it was years ago. There are problems like the issue of two crests superimposing. This may separate the entities but it would do so by some specific amount (the sum of their distortions), which would imply that the force would suddenly stop when they were that far apart unless another like charge entered the system. Also, if it is actually space-time that they are distorting then wouldn't any other object, charged or not, be effected and hence appear to to experience the "force" as well?

So clearly it had lots of problems, but that's how ideas in physics work. Wonder, imagine a model, calculate its implications, compare those with reality, repeat.

***

These days, while I have not yet formally studied QED I can somewhat use it to create a little "artists rendition" of the EM interactions in my minds eye which keeps me happy enough for now.

All in all I think you should never tell someone there is no answer. You can't be sure of that anymore than they can be sure that there is an answer, and in the end trying to think of a better explanation will always have a slight chance to actually get you somewhere. If you don't try than you are guaranteed to never make progress.

 

[Zhabka]

But I suppose we shouldn't feel too bad, even the great minds of the Juggalo community are at a loss to explain this phenomenon! Fortunately good old Mr.Feynmann came to their rescue too.

http://www.youtube.com/watch?v=pDN1WYwaJHY&feature=related

 

[JustRosy]

Just a theory. I'm certainly no scientist. I'm sure at least some of what I'm saying here is off in some way or another, but I wanted to take a crack at this anyway.

Do you remember playing a game, probably as a child, where you had a sealed plastic box with a clear top, and inside the box was a plane of holes just above it's bottom, and in one side, were small metal balls which were held away from it, and then released into it? The object of the game was to get all the balls to sit in all the holes. It was harder than it looked, but it could be done, with time and concentration.

I like to look at positive, negative, and neutral charges that way. The charges desiring to be neutral (yet they may at first be either positive or negative) are the holes, the negative and positive charges are the small balls. When you release the balls to roll over the holes, especially at first, most of the balls will be "attracted" to the holes (so long as the box is right side up, of course). The amount of gravity is about the same, regardless of whether there is a hole in the plane or not, but because the balls "fit" into the holes, and because the pull of gravity is inevitably downward, when a ball's path is "disturbed" by the existence of a hole of at least an equal size and shape, with the need for the fit of a particular ball (charge) of at the most an equal size and shape, the ball "falls" into the hole. Gravity can be blamed for this, to some degree, but it would be interesting to see how this game would work in a vacuum. Anyway, the holes themselves do have some influence on the paths of the balls.

This "attraction" is because of a natural need for balance, or neutrality. Balance seems to be almost a requirement of both mother nature and human nature. "Equal and opposite forces..." etc. What do stars do? They try to balance, and spend their lifetimes, even their "after lives" trying to attain it. True balance, of course, means nothingness, from whence nothing can return - and yet nothing is lost, or gained, on any easily measurable level. In the human realm, losses are often converted to gains, the proverbial "lemonade."

Another way to look at it is that every negative charge is in need of another negative charge to be "complete." Negatives "fit" each other, creating positives, and if too many negatives are attracted, this can attract more negatives to fill the holes to create a neutral charge. If no extra negatives are created, some can be lost as positives are "damaged" or split in the process, thus attracting more damaged positives to remove the excess negative charges to fill their own "holes." Positive charges only need to loose a negative charge when split or when introduced to one too many negative charges. They'll do whatever possible to achieve this needed balance, when it's possible. You can also see this in human nature, so it stands to reason that human beings are made up of atomic structures which operate in the same manner, in order to perform varying functions throughout the human body, which give way to processes that create who we are as people.

Here's a question: Does everything, from atoms to galaxies and beyond, spin in the same direction? If so, or if not, why?

 

[Nosh37]

I like where Just Rosy is going with the ball idea. The universe is run on energy I would assume. And because it runs on energy you need to understand ideas of both kinetic and potential energy. Something that is positively charged does not become stable until it is attracted to something negatively charged just like particles in higher densities go to particles in lower densities. The idea of positive and negative charges is almost misleading in this context. It is simply the idea of a property brought on by protons and electrons. Protons and electrons are attracted to each other because it provides stability to the universe. If the universe had no inclination to be stable, I seriously doubt humanity would even be around to answer that question. So be thankful that positive attracts to negative, because it is important.

Just Rosy here is an answer: probably not. Have you heard of the different half spin properties of electrons? You know the property that makes atoms paramagnetic, diamagnetic, and ferromagnetic?

 

[jarekd]

The repulsion/attraction of the same/opposite charges (and quantization) is natural if we see them as being of topological nature - if they are just topological charges. Then we can easily get to Maxwell equations describing their behavior (thread).
The energy of the field grows with its stress. The top picture below shows that the closer opposite topological charges are, the smaller stress of the field (energy) - they attract:
https://dl.dropboxusercontent.com/u/12405967/fig1.jpg

 

[Fiziqs]

At the risk of once again being overly simplistic and stupid, I'm going to suggest a very simple way of explaining the attraction and repulsion of particles. Particles spin. Ta-da!

Like spinning tops, particles spinning in the same direction will violently repel each other, and particles spinning in opposite directions will be drawn together.

Now everybody feel free to point out why this explanation is incorrect. I have found that I can actually learn quite a bit by coming up with a simple way of visualizing something, and then having people much smarter than me tell me why I'm completely wrong. So feel free to point out my error.

Why can't a simple thing like spin, explain the attraction and repulsion of particles?

 

[jarekd]

Fiziqs, you are getting dipole moments this way, while charge is a monopole.
The difference is that while monopoles attract/repel with force proportional to 1/r^2 and it doesn't depend on their orientation ... monopole-dipole (like spin-orbit) interaction is 1/r^3, dipole-dipole 1/r^4 (e.g. making ortho-postronium much more stable than para) and they depend on relative orientation.

 

[Fiziqs]

Fiziqs, you are getting dipole moments this way, while charge is a monopole.
The difference is that while monopoles attract/repel with force proportional to 1/r^2 and it doesn't depend on their orientation ... monopole-dipole (like spin-orbit) interaction is 1/r^3, dipole-dipole 1/r^4 (e.g. making ortho-postronium much more stable than para) and they depend on relative orientation.

Ok, after taking some time read up on the terms in this post I must admit that it is still going over my head. Is there any way to dumb this down? I realize that the post is probably self explanatory to most people here, but unfortunately I'm a little slow.

For example, I'm not sure what you mean when you state that charge is a monopole, or even what dipole moments are really.

Any clarification would be helpful, thanks.

 

[jarekd]

It means that electric field around charge (generally: monopole) is spherically symmetric: arrows direct toward or outward the center.
In contrast, dipoles are asymmetric exactly like bar magnet - emphasize some direction: http://en.wikipedia.org/wiki/Magnetic_dipole
Both spin and rotation/spinning of a charge correspond to magnetic dipole moment - beside being a charge, electron is also a tiny magnet: http://en.wikipedia.org/wiki/Electron_magnetic_dipole_moment

 

[Trenton]

I have often pondered what charge is and how is it able to exert force. The best I could come up with is that charge is some sort of wave function spin or precession. I can't ever remember all the members of the standard model but it seems to me that every particle of matter is either charged or formed of sub-particles that are charged while anything that moves at c is not charged. This is probably not a coincidence. Matter particles or sub-particles seem to be waves structured in such as way as to cancel propagation (string theory?). They move at c but 'run on the spot'. Any precession creates stress or charge with the sign depending on the direction. Attraction or repulsion can then be viewed as a tendency mitigate stress.

All the above comes with a ceveat. I only dreamt it up to stop myself going stark raving mad! I do not claim any of it as valid science. I would welcome comments from people who know QM to clarify the issues raised here and to point to some good papers to read ...

 

[jarekd]

Trenton, as I have tried to explain above - spin and charge are quite different. The former emphasizes some axis (of spin), while pure charge doesn't - is spherically symmetric.
Spinning vortex can be intuition for spin, like Abrikosov vortices in superconductor - carrying quant of magnetic field (spin of particle is also related with magnetic field).
However, for charge we need a different type of topological singularity - not 2D (like vortex), but 3D, like hedgehog. For example we have a field of unit vectors and positive charge is: all vectors outside, negative: all inside.
It is generally called topological index/Conley index: you take a sphere of some dimension, focus on the field only on this sphere and ask how many time it "wraps around it" - so called winding number.
Taking a circle in 2D you get fluxon or spin this way. Taking sphere in 3D you get point singularities - charges this way. It is how it is made in topological soliton models, like Faber's.

 

[Trenton]

Jarekd you are right. A 3D entity such as the hedgehog is required for charge. I googled hedgehog topology. I almost wished I hadn't but only almost. It is a far better model.

Does all this mean though, that all charged particles are indeed EM waves or photons which by means not altogether clear, have become hedgehogs and are radially rather than linearly oscillating - and that this obstructed action (in that the whole no longer propagates at c) is responsible for the charge?

I shall read up your other stuff on the strong/weak interactions and the Higgs but this might take me some time. It seems to me though, that both the strong and weak forces are really the laws of math and are not as fundamental as they are claimed. Hedgehogs appear to like the company of other hedgehogs even if they are the same sex as is proved by the high energy difference between atomc and mollecular hydrogen (covalent electrons). Siamese hedgehogs or particular multi-hedgehog configurations, perhaps forming a single albeit more complex soliton entity, have a lower energy level. In the nucleus where the energy levels are much higher a mix of the sexes is required to smothe the way but the principle is the same. Nobody has ever called covalence a fundamental force as far as I know so why attribute the quark configurations to one?

As for Higgs, is it really true that this long lost boson is the reason why all other particles have mass or is that just the BBC correspondents talking twaddle again? Einstein's GR describes gravity very much better than the BBC and a soliton hedgehog wave would neatly explain inertia - moving the hedgehog would automatically deform space since otherwise part of the wave would go superluminal and the other part subluminal.

It is nice we now have found the Higgs but do we really need it?

 

[Saytrsilenus]

'Why' is not philosophical here. There is a very, very real why! It could be as literal as the nucleus of a particle being slightly distorted to favor a specific direction of acceleration when it was spun, like a hammer throw and the magnetic field lines are just a characteristic of spin. It could be as abstract as a relativistic effect cause by the dilation of time and the resulting probability vector distortion. The reason why is deeply nested in the nature of matter and space/time as well, I think, in the nature of wave motion in the interstices of matter. If you heat a magnet enough it stops being magnetic which might imply that it is a product of the motion in the range of infrared wavelengths, which would be the electrons with a DeBroglie wavelength matching that frequency. The reasons will become clear as did other things, with time and people asking why. The wave nature of matter is the answer to most questions if we look deep enough. Tesla thought that, Schrodinger though that, and so did Planck. Even Einstein came around. Maxwells Equations give a good what and where but the why is mathematically being discovered to be more of a question than one might realize. If probability governs the motion of celestial bodies... then can't intention alter probability on a micro and macroscale? These are not sterile philosophical conjectures, these are mathematical directions of study!

 

[jarekd]

Jarekd you are right. A 3D entity such as the hedgehog is required for charge. I googled hedgehog topology. I almost wished I hadn't but only almost. It is a far better model.

One of places they use this kind of topological singularities are liquid crystals, which can have thermodynamical tendency to form 2D sheets, 1D tubes or 0D hedgehog-like e.g. micelles.
In field theories it is a bit similar (but also different: wave-like instead of diffusion-like) - assume a field which has energetic tendency to locally break symmetry, like choosing a direction.
These directions can form e.g. hedgehog configuration, or generally any singularity of integer topological charge ... or maybe also more complicated topological structures - corresponding to further particles.

Does all this mean though, that all charged particles are indeed EM waves or photons which by means not altogether clear, have become hedgehogs and are radially rather than linearly oscillating - and that this obstructed action (in that the whole no longer propagates at c) is responsible for the charge?

From topological point of view, being charged particle means being hedgehog-like configuration.
Photon is a different story - it does not have charge, but it has angular momentum - it is kind of twist-like wave, like behind marine propeller.

I shall read up your other stuff on the strong/weak interactions and the Higgs but this might take me some time. It seems to me though, that both the strong and weak forces are really the laws of math and are not as fundamental as they are claimed. Hedgehogs appear to like the company of other hedgehogs even if they are the same sex as is proved by the high energy difference between atomc and mollecular hydrogen (covalent electrons). Siamese hedgehogs or particular multi-hedgehog configurations, perhaps forming a single albeit more complex soliton entity, have a lower energy level. In the nucleus where the energy levels are much higher a mix of the sexes is required to smothe the way but the principle is the same. Nobody has ever called covalence a fundamental force as far as I know so why attribute the quark configurations to one?

I don't like the idea of seeing particles as just abstract objects out of the field, while every charge is singularity of electric field - I believe we should search for concrete models for structure of fields near/inside particles.
There are probably different models possible, but we should always have in mind the successes of the Standard model - that while constructing Feynman diagrams for scenarios on these solitons, we should finally get constants in agreement with the current models.

As for Higgs, is it really true that this long lost boson is the reason why all other particles have mass or is that just the BBC correspondents talking twaddle again? Einstein's GR describes gravity very much better than the BBC and a soliton hedgehog wave would neatly explain inertia - moving the hedgehog would automatically deform space since otherwise part of the wave would go superluminal and the other part subluminal.

Soliton particle models also need Higgs-like potential: to handle the situation in the center of singularity, we have to get out of this potential - giving particle rest energy/mass.
But I don't know if it requires/implies a special corresponding "Higgs particle" - which in fact is just one of thousands metastable states.

 

[bahamagreen]

Why questions imply mechanics - the underlying mechanics of the level to which the why question is applied... but the suitable form of the answer for the why question is going to be another level of mechanics. At some level the answers tend to shift from mechanics to math - "why?" questions will ultimately lead all the way down to the fundamental axioms.

A simple attraction dynamics example is gravity. A possible answer to why things attract gravitationally (inverse square and mass relation) could be a geometric answer:

If a four dimensional space in rotation causes a universal three dimensional hyperbolic expansion with positive time, this is the same as if everything was getting larger, and the apparent mechanical result would be that everything seemed to be attracting each other. This expansion would be conveniently unmeasurable because the measuring devices would also be expanding.
This attraction would not require any mediating force and appear to be instantaneous (Newtonian) - because the apparent attraction would be only a geometric mechanical effect of the universal expansion.

You could say that might be the reason, but it can't be proved, so it is exactly as saying, "It just is". But if you want to know why the universe might be a rotating four dimensional entity, that is another why question...

 

[f.wright]

If they didn't, there would be no existence. Atoms could't form. There would be no light. Subhan Allah wa bihamdihi

 

[Khashishi]

While it's meaningless to ask "why" on a fundamental concept, the truth is that we don't know what concepts are fundamental, and what we call fundamental physics gets more esoteric as we learn more. In the case of charges attracting and repelling; I think it's possible to answer that in terms of the stationary action principle. And the stationary action principle can be explained in terms of a Feynman path integral formulation. Beyond that, I don't think there are any good answers.

The problem that Feynman was talking about in the explanation is that the stationary action principle formulation isn't any more intuitive than just stating that charges repel. So you are answering one mystery with another. The more fundamental explanation is better because it matches experiment more precisely, but that doesn't mean it is any more understandable or satisfying to a questioning mind. When you ask why, you probably are searching for something more understandable, not something that gives more precise experimental results. But nothing is understandable below a certain level.

 

[USeptim]

For the moment, there is not a clear why but we can consider this behavior of charges as a "principle" of physics, and it will remain so until a better, unifying principle integrates many of the present "principles".

 

[jarekd]

Great arguments: we can't understand it just because we cannot ... the same as for quantum mechanics ...
Maybe just try changing attitude for a moment and really search for an answer ...

Do we have in mathematics something allowing only constructions of integer "number"?
Yes we have - so called topological singularities and we call this number as winding number or Conley index or ... topological charge.
So what would be dynamics of such topological solitons? Let us look at simple 2D field configuration for "-" and "+" singularities in different distances:
https://dl.dropboxusercontent.com/u/12405967/fig1_cr.jpg
the first observation is that the closer they are, the weaker stress of the field - down to zero when they finally annihilate.
Practically any field theory we would define here, its spatial derivatives correspond to stress of the field - fields have tendency to minimize energy, what means here that opposite charges attract.

And we are very close to Faber's model of electron, where due to using natural Lagrangian, such 3D analogues get dynamics described by Maxwell's equations ...