do the particles ever collide in QED

[Farsight]

Which is the first time to my knowledge you have used these terms in this thread

Yes, on this thread. I've referred to curl before, saying it's also known as rot which is short for rotor, and that you can get a handle on curl as opposed to curvature by thinking of a wire: you bend it into a Fibonacci spiral, it's curved. But if you also bend it orthogonally too, it's curled, like a hair. I tend not to talk much about divergence because fluid analogies and sources and sinks can be misleading. In no sense does an electric or electromagnetic field flow out of a positron into an electron. Nor does wind flow out of an anticyclone into an cyclone. The Falaco soliton is a vortex, but it isn't like the vortex when you empty your bath.

As for your "proof" using (once again) your silly graphics, please explain what they mean. What is the differential operator on the RHS of the equality? Why are you "adding" differential operators? I can tell you this, though. From elementary operator theory, the divergence of the curl is zero. Want to see the proof? Or better, provide a (non-graphical) one of your own? I await your reply with high expectations...

It's not a proof . It's an explanation of why electrons and positrons move linearly and rotationally the way they do . You couldn't explain it, remember? And now you're carping about adding differential operators? How many times do I have to show you how to combine electric field lines and magnetic field lines to depict the electromagnetic field. Which has a screw nature, and isn't totally unlike the gravitomagnetic field. It ain't magic you know.

 

[Arlich Vomalites]

A cyclone has intrinsic spin. It's intrinsic because it makes it what it is. If you take the rotation away from a cyclone, it's just wind. An electron has intrinsic spin too.

Do you think that because electron is a fermion, also a spin-1/2 particle, that it means that the electron rotates, that spin-1/2 means a rotating particle?

I think that in order to get a rotation of 360 degrees, a full circle, you need a spin-1 particle, that is a boson. I think that you are conflating magnetic fields and electric fields. It is the magnetic field which is rotating. You don't have a magnetic field that does only half a circle, a 180 degrees of rotation.

What is the quantum of the magnetic field?

The electron has a charge even if it is not rotating. Charge is a fundamental property that particles have, it is not at all a consequence of rotation, or movement. A moving charge produces the magnetic field which is rotating, and a rotating charge produces the magnetic field which is rotating too. Magnetic field is always rotating. But it is wrong to say that rotation or movement causes the charge of the particles. In fact, I think no-one knows where the charge comes from as far as I know.
The world is just made of positivity and negativity, without that duality the world would not exist. The duality
that appears as the electron and the positron.
Where does goodness and evilness come from?

If you take the rotation away from an electron, it's just light.

No. It is still an electron. But it is just not rotating. It has charge, mass, its spin is 1/2, those are the properties of the electron.

What's the difference between the wind and a cyclone? The rotation. What's the difference between a 511keV photon and an electron? The rotation. What's the difference between a cyclone and an anticyclone? The rotation. What's the difference between an electron and a positron? The rotation. Don't ask me why this isn't common knowledge. It ought to be.

What do you get if the cyclone does only half a circle, a 180 degrees rotation? Do you have a wind or a cyclone?

The difference between an electron and a positron is the same as the difference between negativity and positivity.

What is the difference between goodness and evilness? The rotation?

 

[QuarkHead]

And now you're carping about adding differential operators

Carping? Want a little lesson in operator theory? Good, here goes....
Operators act on vector spaces by definition. If and only if 2 (or more) such operators act on the same vector space (the domain) and have the same image set (the codomain) then they can be added. With this (and a few extra bits and pieces) one says that the space of all such operators is a vector space

I explained that the set of all vector fields on a given manifold is itself a vector space. But since a vector field is thus a vector, and since the curl operator maps vector fields onto vector fields, and since the divergence operator maps vector fields onto scalar fields, they have different codomains and therefore adding the curl operator to the divergence operator makes no sense

How many times do I have to show you how to combine electric field lines and magnetic field lines to depict the electromagnetic field.

Leaving aside the fact that we do not know what is meant by a "field line", did you not earlier claim that there exists no electric field, no magnetic field, only the electromagnetic field?

Did not James R and I explain how the Faraday field strength tensor (at a point) is derived from the electric vector field and the magnetic vector field (both at the same point)?

And did you not poo-poo our efforts at the time?

 

[tashja]

Prof. Lincoln:

Thank you tashja, thank you Prof. Wilczek.

My idea of an electron-electron collision is based on a finite size electron model. I gave an example of such an model on my link, it is in G. Poeltz's article. I think that this model is a classical model based on classical ideas, and the collision is a direct impact, and it happens when the distance between colliding electrons becomes zero. So there is nothing like that in QED according to Prof. Wilczek. I also thought the same way , that QED does not describe what happens when the distance of the colliding particles becomes zero. I think Feynman himself also said so in his book QED, The Strange Theory of Light and Matter.

A direct impact between two electrons is impossible according to contemporary measurements. For example, we have probed the size of electrons and have concluded that they act like pointlike objects. Experimentally, this means that the size is less that about 10^-19 meters, or about 1/10,000 the size of a proton. They may have a discrete size, but it is smaller than that.

Anyway, I became interested in thinking about the possibility if two electrons had enough kinetic energy to collide, and cause a fusion reaction, and where would it lead to. If during the Big Bang the electrons has enough kinetic energy to collide into each others, could it have led into a formation of an anti-matter nucleus, an anti-proton?

If two electrons collided and fused, they would create a particle with charge = -2, which is inconsistent with an antiproton (charge = -1). In addition, there is the problem that electrons don’t feel the strong nuclear force, which is what generally creates quarks. So this seems to be an unproductive train of thought.

An anti-matter nucleus is negative, as opposed to a normal matter nucleus, the proton, which is positive. Where does the negativity of an anti-proton come from? My guess is that it comes from electrons.

The charge of an antiproton comes from the antiquarks contained within it. On this there is no credible dissension.

Arlich Vomalites:

Forget the details of what happens in the collision for a moment. Think of a collision as a black box. Things go in; things come out. My question to you is: if you think two electrons can collide, what comes out of the collision?

That is a good question. Normally electrons are not supposed to able to fuse into each others.
But what if it could happen, what do you get? A fusion reaction with electrons?

There is no credible possibility for electrons to fuse. They experience electrostatic repulsion and thus fusion is impossible. If it turns out that electrons are composite objects (for which there is no evidence), then it is likely that the constituents will experience some other binding force, so if this is true, all bets are off. On the other hand, if electrons are composed of tiny subatomic cacti, maybe they will emit quantum prickly things. My point is not to take that seriously, but to remind everyone that without data, one can imagine all sorts of things. And, sad to say, to first order, every theoretical idea is wrong. Correct theoretical ideas are exceedingly rare, but wrong ones are generated all the time. Thus one can speculate, but one should never take those speculations seriously without confirmation. The odds simply aren’t in your favor.

I am asking that we should be able to quantize the electric field, so that we could understand what the electron is and what are its properties. If we understand the electron, we can answer what is going to happen when electrons fuse. QED does not quantize the electric field. QED quantizes the electro-magnetic field whose quantum is the photon. I am asking correspodingly, what is the quantum of the electric field which is obtained by quantizing of the electric field?

QED does quantize the electromagnetic field. However distinguishing between the electric and electromagnetic field is silly. They are one and the same. In essence, electricity >>is<< magnetism and vice versa. There is, of course, a lot more to that statement, but it might help convince the author that this train of thought is also unproductive.

Hope this helps.

D

 

[Arlich Vomalites]

thanks again tashja and Prof. Lincoln


Prof. Lincoln:

If two electrons collided and fused, they would create a particle with charge = -2, which is inconsistent with an antiproton (charge = -1). In addition, there is the problem that electrons don’t feel the strong nuclear force, which is what generally creates quarks. So this seems to be an unproductive train of thought.

Gordon Kane writes in his book Supersymmetry, Squarks, Photinos and the Unveiling of the Ultimate Laws of Nature about the decay of the proton. He writes that it is possible in some GUTs that a proton decays into two positrons and an electron. Correspondingly, an anti-proton could decay into two electrons and a positron,
now you have an antiproton with a charge= -1 -1 + 1 = -1

What kind of a reaction could fuse two electrons and a positron, is quite another question.
But it is possible to imagine some possible reactions which can do that.

Prof. Lincoln:
The charge of an antiproton comes from the antiquarks contained within it. On this there is no credible dissension.

Yes. But we may continue and ask: where does the charge of the antiquarks come from?
It is possible that the fundamental particles are the electron and the positron, from which the charge comes.
I am not sure if anyone really knows the origin of the charge, so I can't so more than that.

Prof. Lincoln:
There is no credible possibility for electrons to fuse. They experience electrostatic repulsion and thus fusion is impossible. If it turns out that electrons are composite objects (for which there is no evidence), then it is likely that the constituents will experience some other binding force, so if this is true, all bets are off. On the other hand, if electrons are composed of tiny subatomic cacti, maybe they will emit quantum prickly things. My point is not to take that seriously, but to remind everyone that without data, one can imagine all sorts of things. And, sad to say, to first order, every theoretical idea is wrong. Correct theoretical ideas are exceedingly rare, but wrong ones are generated all the time. Thus one can speculate, but one should never take those speculations seriously without confirmation. The odds simply aren’t in your favor.

I said that it is possible to think that electrons are capable of fusing although they have no inner structure
similar to protons.

If you could divide the proton, the nucleus of the hydrogen atom, into two halves, you don't end up having
hydrogen. By definition the atom is the smallest piece that matter can be divided. The smallest piece of gold is one atom of gold.
Half of a nucleus of a hydrogen atom is not hydrogen anymore.

On the other hand, a half of an electron is a half of an electron. Half of an electron does not change into something else. This is because the electron is the most fundamental particle, alongside with the positron.
Yes, it is true that we can imagine all sorts of things, but I imagine what I said, although to a first order every
theoretical idea is wrong.

QED does quantize the electromagnetic field. However distinguishing between the electric and electromagnetic field is silly. They are one and the same. In essence, electricity >>is<< magnetism and vice versa. There is, of course, a lot more to that statement, but it might help convince the author that this train of thought is also unproductive.

Hope this helps.

D

QED quantizes the electromagnetic field, whose quantum is the photon. The photon is a boson, a massless boson. Correspondingly, one may ask what is the quantum of the electric field. Again it is possible to
imagine all sorts of things, and I imagine that the quantum of the electric field is a massless fermion.

 

[Farsight]

Do you think that because electron is a fermion, also a spin-1/2 particle, that it means that the electron rotates, that spin-1/2 means a rotating particle?

Yes. See The Discovery of Electron Spin by S A Goudsmit:

"When the day came I had to tell Uhlenbeck about the Pauli principle - of course using my own quantum numbers - then he said to me: "But don't you see what this implies? It means that there is a fourth degree of freedom for the electron. It means that the electron has a spin, that it rotates".

Note though that the electron isn't some spinning ball. It has intrinsic spin. So does a tornado. It's a tornado because air is rotating. The rotation makes it what it is.

I think that in order to get a rotation of 360 degrees, a full circle, you need a spin-1 particle, that is a boson. I think that you are conflating magnetic fields and electric fields. It is the magnetic field which is rotating. You don't have a magnetic field that does only half a circle, a 180 degrees of rotation.

I'm not conflating anything. Really. And note that the electron is a spin ½ particle. The rotation is different.

What is the quantum of the magnetic field?

The magnetic field is just one "aspect" of the electromagnetic field, and the quantum of that is the virtual photon. But note that there are no real photons flying back and forth between two magnets.

The electron has a charge even if it is not rotating.

No it doesn't. If it isn't rotating, the electron isn't an electron, it's a photon.

Charge is a fundamental property that particles have, it is not at all a consequence of rotation, or movement.

It is. It isn't fundamental. You can create charged particles in pair production. And you can destroy that charge in annihilation.

A moving charge produces the magnetic field which is rotating, and a rotating charge produces the magnetic field which is rotating too. Magnetic field is always rotating.

Yes, it's a "turn field". It's how you see the electromagnetic field, which is a "twist field", when you're moving through it. Or when it's moving through you.

But it is wrong to say that rotation or movement causes the charge of the particles. In fact, I think no-one knows where the charge comes from as far as I know.

I know.

The world is just made of positivity and negativity, without that duality the world would not exist. The duality that appears as the electron and the positron.

I think the duality is down to bispinor rotations like this:

Where does goodness and evilness come from?

People doing unto others as they would have others do unto them. Or not, as the case may be.

No. It is still an electron. But it is just not rotating. It has charge, mass, its spin is 1/2, those are the properties of the electron.

Yes. And we create the electron and the positron out of light in pair production. We had something that was moving linearly at c, and then we've got something with spin ½. And a magnetic moment. Which we can diffract. Then after electron-positron annihilation we've got photons again. You don't have to be the brain of Britain to work out that the electron is a wave in a closed path.

What do you get if the cyclone does only half a circle, a 180 degrees rotation? Do you have a wind or a cyclone?

A wind.

The difference between an electron and a positron is the same as the difference between negativity and positivity.
What is the difference between goodness and evilness? The rotation?

No. But that is the difference between the electron and the positron.

 

[Farsight]

Carping? Want a little lesson in operator theory? Good, here goes....
Operators act on vector spaces by definition. If and only if 2 (or more) such operators act on the same vector space (the domain) and have the same image set (the codomain) then they can be added. With this (and a few extra bits and pieces) one says that the space of all such operators is a vector space

I explained that the set of all vector fields on a given manifold is itself a vector space. But since a vector field is thus a vector, and since the curl operator maps vector fields onto vector fields, and since the divergence operator maps vector fields onto scalar fields, they have different codomains and therefore adding the curl operator to the divergence operator makes no sense.

I think it makes sense. Here's a depiction of it. Actually it's convergence rather than divergence, but nevermind. We've got convergence then curl then both.

Leaving aside the fact that we do not know what is meant by a "field line", did you not earlier claim that there exists no electric field, no magnetic field, only the electromagnetic field?

I said a charged particle has an electromagnetic field rather than an electric field or a magnetic field. When you combine charged particles in some particular fashion you then see what we call a magnetic field. In that sense a magnetic field exists. Ditto for an electric field.

Did not James R and I explain how the Faraday field strength tensor (at a point) is derived from the electric vector field and the magnetic vector field (both at the same point)?

You explained nothing.

And did you not poo-poo our efforts at the time?

I'm still doing it. All you did was put up a mathematical expression with no list of what the various terms meant. It was merely a restatement of an assertion. The explanatory content was nil.

 

[tashja]

You don't have to be the brain of Britain to work out that the electron is a wave in a closed path. Then after electron-positron annihilation we've got photons again.

No, it's not. The electron is a cacti, and the annihilation products are quantum prickly things.

Sorry, Farsight. But I couldn't resist. That comment by Prof. Lincoln was hilarious lol.

 

[PhysBang]

Yes. See The Discovery of Electron Spin by S A Goudsmit:

"When the day came I had to tell Uhlenbeck about the Pauli principle - of course using my own quantum numbers - then he said to me: "But don't you see what this implies? It means that there is a fourth degree of freedom for the electron. It means that the electron has a spin, that it rotates".

I suppose that's fine if one wants to keep physics to all the results before, say, 1930, but what do we do with all the observations that we have after that point?

Can you produce an equation for a rotating electron that will reproduce the behavior of quantum mechanical spin?

Note though that the electron isn't some spinning ball. It has intrinsic spin. So does a tornado. It's a tornado because air is rotating. The rotation makes it what it is.

This is a nice fantasy, but can you produce the equation that governs a tornado electron that reproduces the behavior of quantum mechanical spin?

 

[PhysBang]

I think it makes sense.

That, and your response with pictures, is simply crazy talk.

You are either really too stupid to follow the very simple mathematics QuarkHead laid out for you or you have some serious mental illness that is keeping you from reading and comprehending properly. It's really worrying; for your own health, please see a doctor.

I'm still doing it. All you did was put up a mathematical expression with no list of what the various terms meant. It was merely a restatement of an assertion. The explanatory content was nil.

No, you have stolen mathematical terms that you have picked up from different sources and you throw them around, trying to borrow the weight of authority from them. You can try to run from the meanings of those terms, but it doesn't look good for you.

 

[Farsight]

No, it's not. The electron is a cacti, and the annihilation products are quantum prickly things.

Sorry, Farsight. But I couldn't resist. That comment by Prof. Lincoln was hilarious lol.

I don't like his answers tashja. They're condescending. The sort of answers you might give to a five-year-old. Hydrogen atoms don't twinkle. Magnets don't shine. We can diffract electrons. It's quantum field theory, not quantum point-particle theory. In QED the electron is an excitation of the electron field. The electron's field is what it is. Those scattering experiments are like hanging out of a helicopter and probing a whirlpool with a bargepole, then when you can't feel anything solid, saying whatever's in the middle of this thing must be really really small. I don't know if you've watched any of the Fermilab videos. Some aren't bad, but by and large they're pitched very low.

 

[QuarkHead]

I think it makes sense.{ to add the div operator to the curl operator}

Then there's nothing more to say except that you are WRONG

We've got convergence then curl then both

Leaving aside what you are calling "curl" in your silly picture seems not have a source, there is is far deeper confusion on your part. I have absolutely no doubt that you will welcome the following enlightenment.

Suppose 2 functions $$f(x)=2x$$ and $$g(x)=x^2$$. Then if I say "first f then g" I mean to say "apply the function g to the image of x under f" and write $$g(f(x)) = (2x)^2$$. which is easily seen to e different from $$f(g(x)) = 2(x^2)$$

Note the common notation $$f(g(x)) \equiv (f \circ g)x$$

This is called "function (or operator, if you prefer) composition". Not addition not multiplication

So suppose you are willing to drop your assertion that your diagrams refer to operator addition but rather to operator composition, then what your words (but not your silly diagram) seem to say is curl(div). Noting that every student knows that div(curl) = 0, and using the above simple example, tell what is curl(div) for some field of your own choosing

 

[Farsight]

Then there's nothing more to say except that you are WRONG

Leaving aside what you are calling "curl" in your silly picture seems not have a source...

My silly picture? But Quarkhead, that isn't my picture. Have a look at page 7 of this paper.

It's Maxwell's picture.

Gotcha!

 

[OnlyMe]

I don't like his answers tashja. They're condescending. The sort of answers you might give to a five-year-old.

When you post things like the following,

Hydrogen atoms don't twinkle. Magnets don't shine.

Seems like,

The electron is a cacti, and the annihilation products are quantum prickly things.

Is an answer that fits right in with your statement/description.

 

[krash661]

 

[QuarkHead]

My silly picture? But Quarkhead, that isn't my picture. Have a look at page 7 of this paper.

It's Maxwell's picture.

Gotcha!

OK. Since I hold no cows to be sacred, let me rephrase my comment. "Leaving aside Maxwell's silly picture" please answer my substantive question.

PS Since I never open third party links when posted on a forum, I do not know what sort of argument Maxwell advanced for these pictures. Maybe you might like to explain - in your own words please i.e no quotations (after you have answered my question, of course)

 

[James R]

Farsight:

LOL! We know all that. It doesn't tell us anything. Quarkhead knows this, that's why he's done a runner again.

You're bluffing again. You didn't understand the maths. That's why you had to ask me. Then you didn't understand my explanation of the maths because you didn't understand some of the concepts I used in the explanation.

But why Daddy? Why?

.... I'm looking back pages, you haven't explained anything. $$\vec{F}=q\vec{E}$$ is just a restatement of your assertion that the direction of the force depends on whether the charge is negative or positive. You haven't explained why.

Actually, that equation is the explanation. Why? Because it defines what is meant by "electric field". The observable is the force. The field is a construct.

In other words, nature is such that like charges repel and unlike charges attract. That gives us $$F$$ and the above equation then defines $$E$$ for us. See?

I challenged Quarkhead to explain why he can't tell the electrons from the positrons.

You can't either. If you think you can, give me an experimental test using only the force observable that will tell the difference.

No, it has an electromagnetic field! This is basic stuff James.

I already agreed it has an electromagnetic field. That electromagnetic field is simply the electric field for a stationary charge.

No. Your motion alters the way you see it. It doesn't change just because you moved.

You keep repeating yourself. Assertion without proof meets assertion without proof. Stalemate. See how this works?

Aaaaagh! They don't create magnetic fields! The field is the electromagnetic field. read this.

You've linked to some guy who produced a theory of gravity (gravitomagnetism) that is demonstrably incorrect. And regarding his electromagnetic equations, perhaps you can explain why the potentials at time $$t$$ depend on an arbitrary past time $$t_r$$.

Maxwell's equations are consistent with electromagnetic waves. In fact, Maxwell himself discovered such waves as a result of formulating his equations.

An electron moves in a helical path in a magnetic field. A charged particle goes around the "magnetic field lines".

You really had no idea where to pitch your explanations when you talk to me, do you? You have no way of judging my level of knowledge. I throw mathematics at you, but since it's all a mystery to you, you think I'm lost in a world of mathematics and don't know the basic physics that precedes the mathematics. So one minute you try to bluff like you have a graduate-level understanding of things like relativity, and the next you think you need to explain school-level basics because I won't know them. The only explanation for such behaviour is that you're not sure what is school-level material and what is graduate level stuff. Because on wikipedia, your main source, it's all mixed in together. You can only cut and paste the pictures and some quotes. You have to skip over the maths because you don't understand it.

Anyway, back to the topic. When a charged particle goes around the magnetic field lines, the magnetic force on it at each point in its trajectory points radially inward. The force isn't a "twirly" force, or a "twisty" force or a "turn force" or a "screw force". It's just the usual kind of linear force. However, the force varies with position in such a way as to produce circular (or helical) motion.

No. Go and look it up.

I thought as much. In future , don't use terms you don't understand, Farsight. You'll get caught out again.

The electromagnetic field points this way:

Heh.

My question was a simple one: at a single point in space at which there is (part of) an electromagnetic wave, the electric field is at right-angles to the magnetic field. In such a case, which way does the "electromagnetic field" point?

And your answer is the mess above. Want to try again?

The maths is the maths you're used to, you just have to appreciate that E and B aren't fields, they're forces that result from the interaction of two electromagnetic fields.

You have no idea about the maths I'm used to, not being able to do maths yourself.

If you can't even get the dimensions of E and B correct, you're a lost cause I'm afraid, Farsight. I shouldn't have to explain such a basic thing to you twice.

 

[PhysBang]

"The maths is the maths you're used to" is Farsight trying to steal the mathematics from actual physics while sneaking in his own fantasy explanation. James R is correct that since he cannot do the mathematics, he cannot really understand what he is saying when it comes to the various mathematical terms.

 

[Farsight]

OK. Since I hold no cows to be sacred, let me rephrase my comment. "Leaving aside Maxwell's silly picture" please answer my substantive question.

What question? Looking at your previous post:

So suppose you are willing to drop your assertion that your diagrams refer to operator addition but rather to operator composition

Oh nitpick. So I used a + in my picture, the horror. You know full well that I said you combine the radial electric field lines and the concentric magnetic field lines to depict the electromagnetic field lines.

then what your words (but not your silly diagram) seem to say is curl(div). Noting that every student knows that div(curl) = 0, and using the above simple example, tell what is curl(div) for some field of your own choosing

Huh? You're talking about the divergence of the curl being zero. That's fine for a magnetic field because it's a "turn" field. Curl is also known as rot which is short for rotor. A "rotor" field is something like a turntable. The centre isn't rotating faster than the edge. But there are no pure magnetic fields because that would demand some region of space to be rotating like a roller-bearing, and space isn't like that. You get frame-dragging instead. You perceive a turn field because you are moving through a "twist" field and don't realise it. Or it's moving through you. What do you want me to tell you about the curl of the divergence? I've already said there are no sources and sinks here. The electron is not some bathtub vortex.

PS Since I never open third party links when posted on a forum, I do not know what sort of argument Maxwell advanced for these pictures. Maybe you might like to explain - in your own words please i.e no quotations (after you have answered my question, of course)

No. And you've just admitted you've never followed up on any of my references to Einstein or Minkowski or Maxwell or anybody or anything else. Ye Gods. No wonder it's so difficult to teach you anything. But I will give you a quote from beneath the picture:



"If we subtract from the general value of the vector function σ its value σ0 at the point P, then the remaining vector σ - σ0 will, when there is pure convergence, point towards P. When there is pure curl, it will point tangentially round P; and when there is both convergence and curl, it will point in a spiral manner."

Compare with my picture:

 

[krash661]

i also suggest farsight needs to learn and understand modes