do the particles ever collide in QED

[QuarkHead]

What's a field? I take note of Einstein saying it's a state of space, you've been taught it's some scalar/vector/etc value at every point in space.

Quite rightly too. Look....

The "space" outside my door contains many elements - grass, trees, dogs, kid's bikes etc. It also contains air, specifically air molecules. Each of these can be regarded a a subspace of the total space. So the vector field on the subspace "air" I call a "wind" in my own limited domain of observation.

Explain why this vector field is not a "state" of the the space of air molecules.

Incidentally, the E. quote that you are so fond of is specifically addressed to the point that, even in the absence of what he calls "ponderable matter", the spacetime metric tensor need not be zero, as is easily seen by inspection of the E. field equations, but is not really relevant to this thread

 

[Farsight]

The "space" outside my door contains many elements - grass, trees, dogs, kid's bikes etc. It also contains air, specifically air molecules. Each of these can be regarded a a subspace of the total space. So the vector field on the subspace "air" I call a "wind" in my own limited domain of observation. Explain why this vector field is not a "state" of the the space of air molecules.

It's describing the motion of air molecules through space, that's all. The "space of air molecules" isn't space. That's just a "mathematical space". It's an abstract thing rather than a real thing. A gravitational field isn't.

Incidentally, the E. quote that you are so fond of is specifically addressed to the point that, even in the absence of what he calls "ponderable matter", the spacetime metric tensor need not be zero, as is easily seen by inspection of the E. field equations, but is not really relevant to this thread

No problem. Einstein said the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy. You could say that this relates to what I've said elsewhere about inhomogeneous spatial energy. It has a mass equivalence and a gravitational effect. Space is dark, and there's a lot of it about.

 

[Arlich Vomalites]

How do you propose we measure or calculate the size of an electron?

I have read some papers describing models of a finite size electron, for example

http://arxiv.org/pdf/1206.0620v17.pdf

If the electron had a finite size, then calculating the energy needed for electrons to collide would be straightforward, wouldn't it?

I think so.

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?

I'm not entirely sure what you're asking. If you're asking what the force carrier is for the electric field, QED's answer is the photon.Now you have me confused. QED is a quantum field theory. Photons, electrons and so on are excitations of the field. A photon is nothing but a quantum of the electromagnetic field. Electric forces, in the QED picture, are transmitted by (virtual) photons from one charged particle to another.

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.

An electromagnetic field is just electric + magnetic fields. Thus, an electric field is just a special case of an electromagnetic field.

Yes. So why is the electric field not quantized, but EM-field is?

 

[Farsight]

I have read some papers describing models of a finite size electron, for example

http://arxiv.org/pdf/1206.0620v17.pdf

The size here is something like the size of the eye of a hurricane. Remember this: the electron's field is what it is.

 

[QuarkHead]

What's an electromagnetic field?

Then let's see if I can help

The E field and the B field are in fact vector fields, that is to say, at each point $$p$$ one has a vector which one may expand on an arbitrary basis as $$E(p)= \sum\nolimits_j E_j \epsilon^j$$ and likewise for each vector $$B(p)= \sum\nolimits_k B_k \epsilon^k$$.

Thus at each point $$p$$ I may define the tensor

$$F(p)=\sum\nolimits_j E_j \epsilon^j \otimes \sum\nolimits_k B_k \epsilon^k= \sum\nolimits_{jk}F_{jk}\epsilon^{jk}$$

This defines the field strength tensor at each point $$p$$. Then, ranging over our space I make $$\bigcup_p F(p)$$ for each point, which is a field F that completely defines the electromagnetic field.

It is customary to refer to tensors and tensor fields by their scalar components, so that our tensor field is $$F_{jk}$$ provided that the same tensorial basis $$e^{jk}$$ is valid at each point $$p$$.

So the electromagnetic field, or more precisely the Faraday field strength tensor field is $$F_{jk}$$

 

[Farsight]

Hmmmn. That doesn't help. Let's try to tease out the issue. Let's say we have one electron in front of us. It has an electromagnetic field, which is somehow in the space in front of us. But you've referred to the "electric field" and you've said it's a vector field. You might depict it like so:


Image credit Andrew Duffy, see http://physics.bu.edu/~duffy/PY106/Electricfield.html

Alternatively you'd might depict it like this:

Image credit mathematica, see http://mathematica.stackexchange.com/questions/37018/plotting-a-gravity-field

Your vectors point towards the middle. But what do they signify? A directional field of force? That's reasonable enough for the lower image, because it depicts a gravitational field. But it doesn't work for the electric field, because the force on another electron is away from the centre whilst the force on a positron is towards the centre. And if we were to swap the electrons and positrons around, you can't say which is which. Two electrons repel, two positrons repel, and your vectors do not allow you to distinguish them. As for taking it further, we then have a similar issue with a "magnetic field". Chuck an electron through a solenoid and the electron moves in a helical fashion. As does the positron. But the helicity is opposite. The vectors are opposite. How do you account for that via messenger photons or some magical mysterious action at a distance? How do account for it without accounting for it takes two to tango? You can't.

Exchemist, since you liked Quarkheads post, please can you explain the meaning of $$E(p)= \sum\nolimits_j E_j \epsilon^j$$. In your own words. Take your time. Only we wouldn't want to think there was any kind of Emperor's New Clothes going on here, now would we? You know, mathematical smoke-and-mirrors in lieu of a sensible sincere discussion. Perish the thought!

 

[krash661]

Exchemist, since you liked Quarkheads post, please can you explain the meaning of $$E(p)= \sum\nolimits_j E_j \epsilon^j$$. In your own words. Take your time. Only we wouldn't want to think there was any kind of Emperor's New Clothes going on here, now would we? You know, mathematical smoke-and-mirrors in lieu of a sensible sincere discussion. Perish the thought!

hilarious. you of all people asked this ?
how about you show and explain how to find the field lines for once, at least.

 

[Farsight]

Because they aren't field lines. Because the field is the electromagnetic field. Instead they're lines of force. Only the arrowheads do not denote the direction of the force.

 

[krash661]

Because they aren't field lines. Because the field is the electromagnetic field. Instead they're lines of force. Only the arrowheads do not denote the direction of the force.

do you ever listen to yourself ? ?
you should. and to be honest, if everyone would just ignore you, you will be forgotten, just like on anything you submit online, that's not an argumentative science site.

 

[OnlyMe]

Because they aren't field lines. Because the field is the electromagnetic field. Instead they're lines of force. Only the arrowheads do not denote the direction of the force.

The short and direct answer would have been, because you can't!

 

[OnlyMe]

do you ever listen to yourself ? ?

That is the only person he really listens to!

If you tell yourself the same thing long enough, you begin to believe it.., whether it is right or wrong or even real.

 

[Farsight]

Perhaps you'd like to explain $$B(p)= \sum\nolimits_k B_k \epsilon^k$$ and describe how a vector can point in two directions at once? Take your time.

 

[OnlyMe]

Perhaps you'd like to explain $$B(p)= \sum\nolimits_k B_k \epsilon^k$$ and describe how a vector can point in two directions at once? Take your time.

Farsight, you have proven that you can cut and paste math from someone else's post.

However, before the challenge in your above quoted post, can be considered valid.., you must demonstrate that the assertion (implied in your question), that a vector does point in two directions, is itself valid.

 

[QuarkHead]

And if you REALLY believe that $$B(p)= \sum\nolimits_k B_k \epsilon^k$$ describes a vector "pointing in 2 directions at the same time" then it is no small wonder that you regard ALL mathematics as "smoke and mirrors".

I believe you said you had a good knowledge of mathematics. Tell us why you think my equality above (which is day one linear algebra) implies "pointing" in any sense, and why you think it implies "pointing in 2 directions at once"

Take your time - in fact take eternity for all I care

Grrrrr

 

[krash661]

Perhaps you'd like to explain $$B(p)= \sum\nolimits_k B_k \epsilon^k$$ and describe how a vector can point in two directions at once? Take your time.

hilarious, you do not even know what you just posted, is.
are you just smashing symbols together in an attempt to show how knowledgeable you are ?
it's obvious to some of us that you are. seems like desperation for something.

 

[Farsight]

The clue is in the way you said it:

The E field and the B field are in fact vector fields, that is to say, at each point $$p$$ one has a vector which one may expand on an arbitrary basis as $$E(p)= \sum\nolimits_j E_j \epsilon^j$$ and likewise for each vector $$B(p)= \sum\nolimits_k B_k \epsilon^k$$.

A scalar is a quantity described by a magnitude. A vector is described by a magnitude and a direction. Note the singular. That's one direction, not two. As I explained in post #26 above, the E field has to point inwards and outwards. That's two directions at once. Similarly the B field has to point both this way C and that way Ɔ. So there's a problem. But don't worry, Exchemist and Krash661 and OnlyMe will pipe up, and all will be crystal clear. Any minute now.

 

[krash661]

The clue is in the way you said it:



A scalar is a quantity described by a magnitude. A vector is described by a magnitude and a direction. Note the singular. That's one direction, not two. As I explained in post #26 above, the E field has to point inwards and outwards. That's two directions at once. Similarly the B field has to point both this way C and that way Ɔ. So there's a problem. But don't worry, Exchemist and Krash661 and OnlyMe will pipe up, and all will be crystal clear. Any minute now.

pipe up about what ? you still do not understand.
i suggest listening to your self.
i also suggest showing me a 3d plot [that's not some fictitious image, which i'm sure is what is coming] of this nonsense.
now lets see who pipes up.

 

[OnlyMe]

The clue is in the way you said it:

A scalar is a quantity described by a magnitude. A vector is described by a magnitude and a direction. Note the singular. That's one direction, not two. As I explained in post #26 above, the E field has to point inwards and outwards. That's two directions at once. Similarly the B field has to point both this way C and that way Ɔ. So there's a problem. But don't worry, Exchemist and Krash661 and OnlyMe will pipe up, and all will be crystal clear. Any minute now.

Bingo! To most of us it has been crystal clear that you are crackers for quite some time now!

 

[Farsight]

Sigh. I know you'd side with maths you don't understand against explanations that you do. Such as: all this goes back to what Einstein said about fields and what Minkowski said in Space and Time:

Einstein: "the two types of field are causally linked in this theory, but still not fused to an identity. It can, however, scarcely be imagined that empty space has conditions or states of two essentially different kinds"

Minkowski: "in the description of the field caused by the electron itself, then it will appear that the division of the field into electric and magnetic forces is a relative one with respect to the time-axis assumed; the two forces considered together can most vividly be described by a certain analogy to the force-screw in mechanics; the analogy is, however, imperfect."

What Quarkhead thinks of as a field isn't a field. It isn't a state of space. The field of the electron is the electromagnetic field. That's a state of space, as is the gravitomagnetic field, where this NASA article says "space is twisted". E isn't a state of space. It just denotes the linear force we see when two or more electrons etc with no initial passing motion are near one another. B denotes the rotational force when they do have initial passing motion. Because of the "screw" nature of the field. All your currents-in-wires and balloons and magnets are contrivances featuring one or the other or both. And all you have to do to appreciate that I'm not talking out of my hat is to read what Einstein and Minkowski and Maxwell said, and then try to depict an electromagnetic field.

 

[krash661]

Sigh. I know you'd side with maths you don't understand against explanations that you do. Such as: all this goes back to what Einstein said about fields and what Minkowski said in Space and Time:

Einstein: "the two types of field are causally linked in this theory, but still not fused to an identity. It can, however, scarcely be imagined that empty space has conditions or states of two essentially different kinds"

Minkowski: "in the description of the field caused by the electron itself, then it will appear that the division of the field into electric and magnetic forces is a relative one with respect to the time-axis assumed; the two forces considered together can most vividly be described by a certain analogy to the force-screw in mechanics; the analogy is, however, imperfect."

What Quarkhead thinks of as a field isn't a field. It isn't a state of space. The field of the electron is the electromagnetic field. That's a state of space, as is the gravitomagnetic field, where this NASA article says "space is twisted". E isn't a state of space. It just denotes the linear force we see when two or more electrons etc with no initial passing motion are near one another. B denotes the rotational force when they do have initial passing motion. Because of the "screw" nature of the field. All your currents-in-wires and balloons and magnets are contrivances featuring one or the other or both. And all you have to do to appreciate that I'm not talking out of my hat is to read what Einstein and Minkowski and Maxwell said, and then try to depict an electromagnetic field.

i suggest listening to your self.
i also suggest showing me a 3d plot [that's not some fictitious image, which i'm sure is what is coming] of this nonsense.
now lets see who pipes up.