# Exchange of photons/virtual photons and electrostatic or EM force

1. Nov 21, 2007

### Labyrinth

How does the exchange of photons/virtual photons give rise to the electrostatic or electromagnetic force?

Why do like charges repel and opposite charges attract?

2. Nov 22, 2007

### Hans de Vries

You see this question often here.... Key is to understand the role
of the wave behavior of the electron.

According to the Pauli-Weisskopf interpretation, the wavefunction
should be regarded as a distributed charge/spin density. Now imagine
an electron wave-packet moving in an initial direction, with an initial
momentum and energy. At the end of an interaction it will move in
a final direction with a final momentum/energy.

Between the two states it can be viewed as being in a superposition
of these two states. The two states will interfere with each other
giving rise to an interference component (technically: $\bar{\psi}_f \gamma_\mu \psi_i$ )

The interference component is a sinusoidal charge/spin distribution.
Such a distribution will radiate electromagnetically, basically just
like it would do classically. This radiation can be associated with
the (virtual) photon.

A photon can be emitted or absorbed. In the latter case external
radiation comes in and the reaction of the charge/spin density to
the external excitation causes opposite radiation which cancels the
incoming electromagnetic fields: The photon is absorbed.

The magnetic spin/distribution of the wave function plays an very
important role since it determines the polarization of the photon.

Feynman diagrams typically describe a scattering zone. They use,
for simplicity, a plane wave representation. The Fourier domain of
plane waves with, in principle, infinite size and duration. Nevertheless,
this can be an extremely good representation, giving results which
are accurate in 12 or more digits compared with experiments.

When is this representation accurate and when not? Lets look at
some cases.

1) A free electron's wave function may easily expand to a size of
1 micrometer. It collides with an X-ray photon with a one nano
meter wavelength. The ratio scattering zone versus wavelength
is ~1000:1. The plane wave representation is a good representation.

2) A bound electron has a much smaller size, less than one nanometer.
It interacts with an incoming photon with a wavelength of one micro-
meter. This situation is typically not described by Feynman diagrams
since the bound electron isn't a plane wave.

Now, even though there is a 1:1000 ratio now spatially, temporally, there
is a long overlapping time since the wave function of the electron is
"infinite" in time and the photon oscillates many times. The ratio interaction
time versus oscillation time is >> 1 so the picture of photon absorption
and emission, caused by the interference between the initial and final
state of the electron's wave function is very accurate.

3) The bound electron now interacts with a strong single cycle laser
pulse. The interaction thus has a very short duration. The electric field of
the single pulse is transversal to the direction motion and can be controlled
to be either to the left or to the right. What happens in the experiment?

Well. the atom becomes ionized and the electron flies off either to the
left or the right depending on the direction of the electric field.

So, the geometry plays a very important role, nevertheless, all inter-
actions are the result of the same physics, and the various pictures
may be used universally.

Now, take the picture of a "classical" electron in an electron field.
We can use here the picture of the electron's wave function in
a initial state interfering with the final state of the wave function.
The interference pattern can be seen as a very small fraction of
the gradient of the potential field.

Very important however is the concept of quantization, photons
come in single units and have unitary propagation. There are various
formal methods to incorporate this behavior in our mathematical
description of quantum physics: canonical quantization, path
integral quantization.

Even so, the unitary behavior of photons, proved in many experiments
remains quite a mystery. Its total range of validity, especially at the
very low frequencies, is still a research topic.

Regards, Hans.

Last edited: Nov 22, 2007
3. Nov 22, 2007

### wawens

Electrosatic Forces

The 'story' is that virtual particles supply the force to attract or repel the charges as in Feynman Diagrams. Or maybe, is there a sort of curved 'electrostaic space' that compels the electron to move along its contours.
Are the virtual photons of fixed momentum and is there some uncertainty about there position? Don't ask, you'll only get b******t, I don't think anyone really knows. Unless....

4. Nov 23, 2007

### Labyrinth

Thank you for the responses. Upon much deeper study I think I understand at least to some degree how the exchange of photons causes repulsion and even attraction.

My next question is, what is charge then? What makes for example, the electron a "negatively" charged particle?

5. Nov 24, 2007

### Phred101.2

Charge is something that is fundamentally conserved. It has something to do with the way a neutron can 'become' two charged particles, or "matter-waves", a proton and an electron (and some other book-keeping 'bits'). This is also fundamental to the exchange (photons) between these bits of matter that have 'charge'.
It's a word otherwise, that we use to explain certain behaviour that we can observe.

6. Nov 24, 2007

### blechman

There is also a slightly more "formal" way to define charge: it is a topological quantity that defines the global nature of the electromagnetic field. Putting it a slightly different way: all bodies in nature have the (potential) ability to "kink" the electromagnetic field, and charge is a quantity that measures by exactly how much a body can do this (where I'm implicitly allowing for the possibility of zero charge, meaning that it cannot kink the field). Of course, you can still ask why anything should have that ability, but physics cannot answer that question. As Phred101.2 says: it's an observed phenomenon.

7. Nov 24, 2007

### Labyrinth

Say for example I press my hand against a wall. It does not go through the wall. The electron clouds in the atoms of my hand repel the electron clouds in the atoms of the wall.

This can be said to be because the electron clouds are both negatively "charged", and like charges repel.

I was under the impression that this was caused by photon exchanges, which become much more likely to occur the closer the two atoms become.

What is it about the electron that makes it inherently negative? The positron inherently positive? When two "particles" attract this is also caused by an exchange of photons only an opposite type of emitting/absorbing is happening right? Why do positively "charged" particles behave a certain way towards negatively "charged" particles and vice versa?

Is the "negativity" or "positivity" simply an amplitude for certain types of couplings or is there a greater understanding of the cause known?

8. Nov 24, 2007

### blechman

That is correct.

That is correct as well. I don't think there's any "deep" understanding of what makes an electron and a proton have different charges (of course, whether I call them "negative" or "positive" is purely a convention!). Rather, the fact that the electron has a charge of $-1.6\times 10^{-19}$ Coulombs is purely a phenomenological fact (including the sign) - there is no "reason" why it had to be this way that I know of. But it is.

Again, as has been said many times on this forum: physics cannot really answer that kind of question, since we cannot construct a new universe where the electron had a different charge and see whether such a universe could exist! These kinds of questions must be given over to the religious experts.

We do understand why like charges repel and opposite charges attract - that's just a consequence of the the value of the scattering amplitude. Nothing more, nothing less.

9. Nov 25, 2007

### Phred101.2

And again about charge being negative: this doesn't mean that it's something that gets subtracted, because of its sign, or anything. Like bits on a magnetic tape, it has to be something: you can't store a message using non-existent bits, or non-photons, you have to decide what feature to use --which is always a real physical variable like polarisation say), the key is to use the different states. Negative and positive charge are different versions of the same thing. but they're opposite in direction, is all. You can bring opposite charges together, and they cancel each other (at least at the classical level), but they don't disappear, or annihilate each other. If they get separated, charge becomes apparent (to us) again.

Last edited: Nov 25, 2007
10. Nov 25, 2007

### Phred101.2

One of the things a lecturer in CS should tell you is that 1s and 0s aren't (and can't be) actually something and nothing (how would you send a message of all '0's?). What bits (in a computer) are, are representations. The representation uses a language that has only 2 characters in its alphabet, but these are used to create longer strings, using either of these two states (this is the representation).

A single photon is the minimum 'communication' possible, so the photon itself can't be the information, you have to use some aspect, or physical trait, that photons have, to do it (say polarisation angle, or frequency). Otherwise the only possibility is what's called a "Schrodinger's cat" -an indeterminate state- is the message going to come or not?: there's only the expectation of receiving some message (and this is related to the concept of entropy, btw)...

Last edited: Nov 25, 2007
11. Nov 25, 2007

### wawens

What is a positive charge

The question was 'what are negative and positive charges' and we have got back obfuscationary answers that 'sound' cool but avoid the question much like a politician
would. Or shall we leave it to the 'religeous experts' as 'physics cannot answer
that'?
Can someone have a go at getting to the root of positive and negative charges
in one sentence (we all know they are electrostatic thjings that cause attraction and/or repulsion)?

12. Nov 25, 2007

### Phred101.2

Someone? How about you, maybe you could tell everyone your opinion of where the politics of the current model of charge should lie (since we're discussing politics, that is). Negative and positive viewpoints please, in no more than a sentence or two.

13. Nov 25, 2007

### Staff: Mentor

Electric charge is the conserved quantity associated (via Noether's Theorem) with the local U(1) gauge symmetry that the universe apparently has.

14. Nov 25, 2007

### blechman

This post is a little misleading, Phred101.2. The charges do get subtracted when you compute the corresponding fields they generate. It is very natural to represent charges as "positive" or "negative", rather than as "apple" and "orange", since they appear the same way in Maxwell's Equations with the correct signs.

So the choice of charge representation as "positive" and "negative" is not as arbitrary as it might first sound.

15. Nov 25, 2007

### Labyrinth

Thanks blechman! I have one more question about how the mysterious number 1/137 is found.

Which was saying that 1/137 was found by q^2/(h)(c). I'm wondering if this is correct though, because it seems like no matter what I put in there I cannot get 1/137. Can someone show me how this is properly calculated?

This number is the amplitude for an electron to emit or absorb a photon correct?

16. Nov 25, 2007

### blechman

$$\alpha=\frac{e^2}{4\pi\epsilon_0\hbar c}$$

where e is the electron charge and $\epsilon_0$ is the permittivity of vacuum. Choose your units consistently, and you should get the famous 1/137 (.something).

not exactly. It is related to that. It is (in certain units) the magnitude of the electrostatic potential between two electrons a unit distance apart. The amplitude you mentioned is a little more complicated than that. Check out (for example) Griffith's Intro to Particle Physics (or anything more advanced than that).

17. Nov 26, 2007

### Phred101.2

No, my intention was to say that negatively charged electrons don't lose their charge when they encounter a proton.

18. Nov 28, 2007

### wawens

'Electric charge is the conserved quantity associated (via Noether's Theorem) with the local U(1) gauge symmetry that the universe apparently has'
Thanks PF Mentor, this answer is the best I have ever seen.

19. Nov 29, 2007

### reilly

Virtual particles are a metaphorical idea -- words to make easier the explanation of, say, the quantum origins of the Coulomb force. In the particle physics trade, we talk of "one-photon exchange" and not "one-virtual- photon exchange" Anyway..

Electromagnetic forces, like many others, come from the interaction of charged particles with the electromagnetic field, which in turn interacts with the charged particles, which in turn.......In QED it's the same thing. In fact, Maxwell's Eq. hold classically and in QED(in operator form).

Let's talk Coulomb Gauge, in which case the potential obeys Poisson's eq.The charge density, in non-relativistic cases, is just the absolute square of the charged particle wave function. But, the solution is the standard 1/r point particle potential, suitably weighted by the charge density. True in QM, true in classical physics. So, here's a derivation, loosely speaking, of the Coulomb interaction in QED that does not talk about photons at all. So, where are they?

They live in momentum space. The Fourier transform of the Coulomb potential goes as (1/p)^^2, more-or-less the photon propagator, K. If you work it out, the matrix element, to lowest order in charge, for particle-particle interaction is
Q1 K Q2. This, of course, can be represented by a Feynman diagram of the form

>-----<.

There are circumstances, in tunneling and resonant scattering for example, in which virtual particles are given a more direct physical interpretation -- radioactive decay of nuclei is an example.

Regards,
Reilly Atkinson
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20. Nov 30, 2007

### Marco_84

I think jtbell is right, we know about charges (electric,strong,weak "gravity") via gauge simmetries using Noether theorem and others algebraic tools.
I mean that this is the mathematical sense we give to what we see in our experiment.
It is not so difficult to figure that out. see any book on QFT.