Electron Charge

What happens when you consider it to be a wave rather than a particle?

I'm not a physicst - just wondering

Its position becomes a matter (no pun intended) of probabilities. This raises a secondary question: what happens to the probablities at the point where two electrons would occupy the same space? Pauli Exclusion Principle says they can't, and it's this 'electron degeneracy pressure' that keeps certain, massive stars from collapsing under their own gravity, for instance. But, back to the question:

What happens to the force between two electrons as they become arbitrarily close (say, with the help of a 'gedanken' Penning Trap of shrinking dimensions)? Assume for the moment the electrons' probability waves favour such proximity regardless of HUP's alternatives. :)

Maybe "arbitrarily close" is not allowable; only as close as the Planck length.

An electron and it's antiparticle a positron are the smallest (lowest mass energy) Leptons. It is presently believed that all Leptons are fundamental particles with no sub-components. As such they are considered by observation to be a point charge. Now since these tiny fellows have so little mass energy and are influenced by one of the strongest forces known they only "rest" in a thought experiment.

Oh, I don't let them rest. No, Sir! I'm very generous about what they can do: they're allowed to move one Planck Length per Planck Time, all filmed with a Planck Camera (Craigslist sells the darndest things) and slowed way down so we can single-step it. :)

Now, what happens to the force between two electrons as they become arbitrarily close? No worries - this problem baffled even Lorentz, who figured they were little sort of balls of distributed charge, more or less, basically to avoid numbers approaching infinity - the same problem my simulator has (and with Lorentz' conjecture implemented as a temporary stopgap measure. Neither physicists nor computer programs like infinities all that much).

I'm asking mainly so I can hopefully implement a more physically realistic solution than treating electrons as little balls of uniformly-distributed charge, as I'm doing now. I really do want to know what happens to the force under conditions of extreme proximity.

Speaking as an engineer with curiosity rather than knowledge, I cannot give an answer, but I might be able to point to an area where to look.

As I 'see' it, the electron 'balls' of charge (I imagine to be spherical) have a diameter and are spinning. The speed of rotation is related to the diameter, that itself cannot exceed the space available between the adjacent electrons (atoms, protons, neutrons, molecules, anything).

If energy is conserved, the smaller space means the electron must reduce in diameter, and therefore must spin faster.

Two things arise (there could be a lot more but ignoring them for the moment) First, some electrons (where they 'touch') will spin 100% in phase and some will spin 100% anti-phase, with every other combination of relative spin being possible. Thus imparting energy by 'slowing' down or 'speeding' up adjacent electrons. Possibly with vortex shedding in anti-phase cases - and what is in the vortex? - smaller particles??

Second, how fast can an electron spin?. Is there a limit where the maximum peripheral speed is limited by the speed of light? Thus there seems to be a limit on how much the diameter can be reduced.

Even so, in cases where some sort of balance be reached, assuming electrons stay spherical at all times, what will be in the interstices after matter is at it's densest possible in these circumstances. The densest being related to the maximum number of spherical objects that can be packed into a given volume.

The solution of this type of problem might depend on someone developing maths that deal with multiplying and division by 'near zero' and 'near infinity'. ie, ∞-1)

I believe that you and Lorentz have a fundamental flaw in your premise. I believe that Lorentz was exploring the nature of this flaw when he was considering the force dynamics of two electrons approaching each other. I believe the flaw is that you are trying to characterize the forces between two electrons using Newtonian laws when quantum mechanic laws apply.

To start, there is no implied uncertainty to your premise. Your premise implies a knowledge of the position, trajectory and energy of these two electrons. As Heisenberg pointed out, no more than one attribute can be known to high precision at any one time about a particle.

There is also the unique identity problem of these two electrons. There is nothing on an electron for identification. Electrons have not been observed to have readable bar codes. From a classical perspective it seems that we can just observe the trajectory of a particle and be assured that we are still observing the same particle from the track followed. However, we've since discovered from Lorentz's time of this thought experiment that a flow electrons can and will jump across regions of space without ever entering the intermediate space. This is also not a rare occurrence. Electrons are jumping gaps right now under my fingers.

My point here is that I believe you are observing the modern day equivalent of the flaw in Zeno's paradox. Lewis Carroll gave an amusing demonstration of this flaw. Trying to explain the the motion and forces on sub-atomic particles using a Newtonian, classical physics perspective is just as flawed as applying Aristotelian logic between a tortoise and a warrior.

Yes, I know my understanding is flawed. Hence my question. Thanks for your reply.

Take two beams of electrons, the beams in counter-rotating orbits inside a cyclotron, synchrotron or what have you. Collide them head-on. This has been done, yes? Many times?

Collision implies proximity, yes? You cannot have collisions apart from proximity, however defined. Yes, their position and momentum is subject to HUP, but those probabilities include electrons in very close proximity as well as not. The electrons are not all tunneling through each other, but many are scattering off each other. We've got electrons colliding; at this instant, stop the clock and measure the force between them. Extremely high energy densities result in elevated levels of virtual-particle production, according Feynman, Hawking and others. So, does the force 'level-off' as a result? Does it follow a strictly-Classical pattern of approaching infinity as r-squared approaches zero? What does the force do as the electrons collide - however they do it. That is all I'm asking. The force does *something.* What is that 'something,' and what is its mathematical expression?

Thanks!

GA.

Very, very few of the particles in a colliding beam accelerator actually collide. Most of the particles in each cloud just pass right by each other. I believe that narrowing the discussion down to just two specific particles causes HUP to dominate and virtually nothing else can be predicted. As fissle_mop stated so well in the Physics Forum quantum section:

First of all, there is no end-all analogy for the quantum world. As soon as you understood the first watered down analogy I gave and found the flaw in it, you'd be right back at the doorstep looking for the next one. And so on, and so on, until sooner or later my analogy would be 'electrons act like electrons because electrons act like electrons.' And you would say, "What a douchebag, he just wasted all this time to say nothing." There is no way to completely discuss the quantum world using English, if there was, there would be no Physicists, only English majors (and what a sad world that would be.) That being said, here we go.

Read more: http://www.physicsforums.com

As I was saying, the movement and interaction of small amounts of sub-atomic particles should be viewed with a quantum mechanics perspective and not a Newtonian mechanics. Even in the quantum mechanic world there are contradictory analogies to real and imagined experiments that baffle the scientists in that field. My personal favorite of that is the single electron self interference pattern experiment. How does single particles that presumably travel through one and only one of two slits at a time interfere with the wave function of the not taken path of the other slit? This experiment was performed more than 20 years ago so the explanation to this paradox may now be known but it still baffles me.

So if you can simulate reasonably repeatable electron interaction experiments that agree with observed phenomena down to a proximity of only x units apart, great! Bravo! If things go weird in your simulation when you go to less than x and your measured experimental results are a different weird result, welcome to quantum physics.

I've got one toe in the Quantum World which is basically why I'm here asking these questions, but putting QM aside for a moment, the simulator (which behaves purely Classically) exhibits some surprisingly complex behaviour given the few simple rules of physics which it obeys. For instance, with just slight changes in the 'Coulomb Constant,' the behaviour of the particles (pos and neg in equal numbers, but you change this and about a dozen other parameters) alters radically. Where before they might aggregate into rings, loops or chains, some of which spontaneously fly apart at high speed minutes or even hours into a run, a slight increase to k_e (one part in, say, 10e15), they will no longer stay together for long in any configuration. Makes one wonder what slight changes in the Real Coulomb Constant might have on the behaviour of Real Matter.

And besides being educational (for both author and user), it's just plain fun to watch. :)

I'm sitting on your side of the room on this one, this isn't my strongest area but unless you're talking particles I'm in complete agreement with my limited knowledge

perhaps we can arrange for a get together at CERN sometime and have a couple of beers and smash a few atoms and see what the Quark happens

I believe the electron exceeds the containment of this dimension and dwells on the cusp between two dimensions, as such, it is quite difficult to understand its true nature with our current technology...The energetic quantity that exists in this dimension is an unknown factor, and our measurements can only tell part of the story.....The dimensional boundaries of our reality are unknown, as are the laws that exist in other dimensions and how they interact with our own known reality...The electron's charge is likely to be contained in a field of unknown qualities transcending a single dimension and controlled by unknown forces....at least that's my take

So far your answers are: They are a wave; they are a point particle; they are a probability; they are partly in another dimension.

I have read that atoms don't exist unless they are observed. Since electrons are too small to observe, they must not exist. Besides, many scientists believe that the whole universe is an illusion.

I don't know what you expected here. You won't get answers any better than these. That is the Stark reality.

:)

Well, it's worth a try, yes? I remain optimistic.

Meanwhile, I've done a bit of digging (before and since asking the question here). Evidently it is not an easy question to answer. Resources online either treat the question in a purely Classical, idealised sense (two point charges and the force between them), or don't address it all - esp. not in the QM sense as to what happens to the force as the distance approaches zero. Feynman speculated that the resulting energy density sparks a flurry of virtual-particle production but didn't address what happens to magnitude of the force meanwhile. It does not go to infinity, so what does it do instead, and how does this relate to distance? I would find it a bit farfetched if this simple question has never been asked before.

I agree - I have been poking around online and then pulled out my old textbooks (actually they're not that old - most of the problems have been updated so distances are in leagues rather than furlongs) and I found that this question appears to be studiously avoided.

I would have thought it should come up naturally in discussions of electron traps etc. - just as a thought experiment or even perhaps just to point out "it is meaningless to imagine two electrons approaching the same point because... etc.") But no - not covered. (ah - I smell a conspiracy - I bet they have a couple of co-located electrons in an innocuous looking storage garage at Area 51!)

If you were to ask Steinmetz, he would tell you there are no electrons, only the lines of electric charge that terminate at what is perceived as an electron. This is why the electron appears to be a point charge, or a wave function, depending on the type and circumstances of the observation.

According to Steinmetz, all electric field lines have two terminations, whereas all magnetic field lines close upon themselves. So, for the purposes of your simulation, you should simulate your electrons in pairs. As for the distances, you will have to decide for yourself how close they can become without becoming only one charge and collapsing into a magnetic field!

For those of you not familiar with Steinmetz, the set of equations utilizing this model is the same set of equations where RMS, Inductive reactance, capacitive reactance, i (square root of -1), and a few other textbook equations came from. He is the Ivy-league professor that simplified Maxwell and Faraday. He literally wrote the book on electronics.

How did Steinmetz explain the rest mass of the electron (511 MeV)? Lines of electric charge terminate in something which is different from electric charge, something which has mass and spin, but no size nor internal structure out to the resolution of our best instruments (TeV scales).

Did you just define the mass of the electron as a measure of it's charge? I think you answered your own question!

No, charge is expressed in units of Coulombs, whereas masses of elementary particles are most commonly expressed in units of electron-volts (eV). Particles' energies (including massless particles, such as photons, which have no charge) are *also* expressed in these same units, eV. It comes back to Einstein's famous mass-energy equivalence relation.

Disclaimer - not a particle physicist (and non-US speller of "center"!)...

Surely an electron's charge is distributed throughout the universe - like every other charge and every atomic force. "Where" is the earth's gravity? Well... it's everywhere in the universe, centred at the mass centre of the earth. So where is the charge of an electron... everywhere... I guess centred at the most probable location of the electron.

The electron could be anywhere in the universe - but it is most likely to be in position x,y,z ... trouble is if you define it to be in position x,y,z then you can't know where it will be in one Planck unit of time from now - could be anywhere! Conversely, if you want it to be following a defined path, then you can't know exactly how fast it is going (or, more usually, how much energy it has) nor exactly where on the path it is (or the more you know one the less you know the other).

It's been a while since my last physics lectures, but uncertainty principal tells you something like if it is travelling in a straight line and you want to define its location within, say 100 atomic diameters, then you can only know its speed with less than 1% precision.

And my memory is that the exclusion principal doesn't necessarily say two electrons (for simplicity both moving along the x axis) can't have the same probability of being in the same place along the axis at once, only that if they are then one must be "spin up", the other "spin down". If a third is introduced then one must jump to another energy state.

Ok - I'll shut up now and leave it to a real physicist to correct my dangerously little knowledge. (ps - here's a precisely-located electron)

btw - I didn't make it a big smiley - the internets did that somehow...

I was greatly tempted to somehow work in the word 'esky,' and now I have. :)

(I think the Internets are conspiring to underscore your point. Diffuse smileys are Heisenberg's work, the bastard. :)

Charge can be understood only by its properties and interactions and that defines the limit we can know about the charge. There isn't an electron wearing a coat of charge. Perhaps Physics is not written like story books with pictures and people get falls impressions from interaction images being that of the particle itself. Fields deform the moment something comes closer. If you like those pictures of deformity then be happy in a wrong world.

What the hell are you talking about?