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Ivan Seeking

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- Thread starter Ivan Seeking
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Ivan Seeking

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drag

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Greetings !

First of of all, it's not just the electric field if you're

talking about photons, it's the electromagnetic field.

As for the frequency of the photons, I believe it can

be calculated from and described as a quality of the

energy density of the electromagnetic field. (I'm afraid

I can't help you with Maxwell's equations that describe this,

my knowledge of this is strictly theoretical, for now.)

Live long and prosper.

- #3

Ivan Seeking

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Originally posted by drag

Greetings !

First of of all, it's not just the electric field if you're

talking about photons, it's the electromagnetic field.

I may, but I'm very thin on this idea. I mean for a static electric field. For example, for a charged sphere. The electric field measured about the sphere can be described by a photon exchange. I understand to some extent how we get attraction and repulsion by this. Beyond these two points I get in trouble really fast.

- #4

HallsofIvy

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Photons are the quantization of the electromagnetic field.

- #5

drag

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Greetings !

I believe you are referring to virtual particles ?Originally posted by Ivan Seeking

I may, but I'm very thin on this idea. I mean for a static electric field. For example, for a charged sphere. The electric field measured about the sphere can be described by a photon exchange. I understand to some extent how we get attraction and repulsion by this. Beyond these two points I get in trouble really fast.

Well, look at it this way. The enitial mathematical discriptions

of forces used geometrical discriptions - continous dimensions

that deform by the effect of the source of the force and

thus effect other bodies with a certain "charge" relevant to

this force. This is the way GR works - a space-time geometry

deformed by the gravitational charge - mass.

QM deals with things in a different manner - everything is

quantified - cut into individual packets. This is where

virtual particles appear - instead of discribing a geometry

we discribe (according to QM's interpretation) individual

packets that "transport" the electric and other forces.

You should make a search for Feynman Diagrams that explain

this theorized virtual particles' interaction. They're

easy to find online and provide a nice graphic discription

and explanation of this process.

Live long and prosper.

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Ivan Seeking

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Originally posted by drag

Greetings !

I believe you are referring to virtual particles ?

Well, look at it this way. The enitial mathematical discriptions

of forces used geometrical discriptions - continous dimensions

that deform by the effect of the source of the force and

thus effect other bodies with a certain "charge" relevant to

this force. This is the way GR works - a space-time geometry

deformed by the gravitational charge - mass.

QM deals with things in a different manner - everything is

quantified - cut into individual packets. This is where

virtual particles appear - instead of discribing a geometry

we discribe (according to QM's interpretation) individual

packets that "transport" the electric and other forces.

You should make a search for Feynman Diagrams that explain

this theorized virtual particles' interaction. They're

easy to find online and provide a nice graphic discription

and explanation of this process.

Live long and prosper.

I read QED years ago but I don't remember this issue [virtual photon frequency] being addressed. I will take a look. Also, I didn't remember them as being virtual; so long as the charged body interacts with another.

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- #7

drag

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Greetings !

I never read it so far so I can't adress it I'm afraid.Originally posted by Ivan Seeking

I read QED years ago but I don't remember this issue [virtual

photon frequency] being addressed.

I believe that it still relates to energy density of the

field, but I do not know if there are precise frequencies

for 3 of the forces or like in the case of the gravitational

force - there is a problem of plotting (I believe it's called

"normalising" ?) the interaction since you get any number of

1 to infinity of virtual particles' interaction loops.

Or something like that... On to the experts with this.

Live long and prosper.

- #8

jeff

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Originally posted by Ivan Seeking

...When we talk about photon exchange as the electric field, what determines the frequency of the photons? I would tend to assume that the electric field strength goes as photon frequency, but since classically the field strength can depend entirely on the quantity of charge [assuming no magnetic field] present, which seems to mean that a stronger electric field has more photon exchanges but not stronger ones, I don't see what would detemine frequency of the photons. Is this a function of distance that manifest generally as the inverse square law?

Why does electromagnetic field strength grow as it's sources are approached, or in quantum theoretic terms, why are high energy photons encountered only near their sources? The answer is that the time-energy uncertainty principle allows photons to have greater energies (or equivalently, frequencies) than allowed by the relation p

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Ivan Seeking

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Originally posted by jeff

Why does electromagnetic field strength grow as it's sources are approached, or in quantum theoretic terms, why are high energy photons encountered only near their sources? The answer is that the time-energy uncertainty principle allows photons to have greater energies (or equivalently, frequencies) than allowed by the relation p^{μ}p_{μ}= -m^{2}= 0 satisfied classically by their 4-momenta as long as their lifetimes and hence the distances they travel are sufficiently short. Such photons are called "virtual" and their 4-momenta are said to be "off the mass shell", i.e. p^{μ}p_{μ}≠ 0.

Are you saying that the inverse square law is a special case of the time-energy uncertainty relationship?

- #10

jeff

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Originally posted by Ivan Seeking

Are you saying that the inverse square law is a special case of the time-energy uncertainty relationship?

No. Inverse square laws are a consequence of the structure of tree amplitudes for the exchange of bosons that result from the fact that the lagrangian densities involve two powers of the spacetime derivative. In momentum space, the relevant part of the energy E of interaction between electrically charged particles at

E = - (1/2π)

where r ≡ |

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Ivan Seeking

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Originally posted by jeff

No. Inverse square laws are a consequence of the structure of tree amplitudes for the exchange of bosons that result from the fact that the lagrangian densities involve two powers of the spacetime derivative. In momentum space, the relevant part of the energy E of interaction between electrically charged particles atx_{1}andx_{2}following from these amplitudes is

E = - (1/2π)^{3}∫d^{3}k exp[ik⋅(x_{1}-x_{2})](ik^{2}+m^{2})^{-1}= - (1/4πr)e^{-mr}

where r ≡ |x_{1}-x_{2}|. Setting the mass m equal to zero for the photon in the case of the electromagnetic interaction and computing ∂E/∂r yields the familiar inverse square law of coulomb for the electromagnetic force.

Then for a large charged surface we must write an equation for every combination of charged interacting pairs? Say for example if we have two large charged spheres. How does one calculate the energy for a particular photon exchange between these two spheres; thus the related frequency?

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jeff

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Originally posted by Ivan Seeking

How does one calculate the energy for a particular photon exchange...?

The expression E = - (1/2π)

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Ivan Seeking

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Originally posted by jeff

The expression E = - (1/2π)^{3}∫d^{3}k exp[ik⋅(x_{1}-x_{2})](ik^{2}+m^{2})^{-1}says that of the particles exchanged between sources a distance r apart, only those with momentum of magnitude k roughly of order 1/r or less contribute nonnegligibly to the energy. We can regard this heuristically as resulting from the cancellation of the contributions with k large compared to 1/r due to the oscillations of the phase factors exp[ik⋅(x_{1}-x_{2})]. This is consistent with the uncertainty principle since it says that higher energy particles are encountered as sources are approached. This expression also tells us that the characteristic distance of interactions mediated by field particles of mass m is just 1/m since the phase factor shows that k takes it's characteristic value m when k ≈ 1/r. Thus very light or massless particles like the photon mediate long-range interactions.

Jeff, thanks for all of your great answers!

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yogi

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jeff

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Originally posted by yogi

...QED does not lead to a derivation of Coulombs inverse squared law...

As I've shown, QED does produce coulomb's law. If you're remark was true, QED wouldn't produce correct predictions. In fact any theory that makes correct predictions must produce the corresponding classical expressions at low energies.

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yogi

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jeff

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Originally posted by yogi

Jeff - where have you shown QED derives the inverse squared law

Inverse square laws are a consequence of the structure of tree amplitudes for the exchange of bosons that result from the fact that the lagrangian densities involve two powers of the spacetime derivative. In momentum space, the relevant part of the energy E of interaction between electrically charged particles at

E = - (1/2π)

where r ≡ |

- #18

yogi

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I know the argument that the photon must be massless for the force to extend to infinity - and the notion that uncertainty allows borrowing from the medium temporarily ... but these are all hypothetical rationales ... you cannot get a qualitative value for "e" from this, or if you can - show me. As Lord Kelvin once said - "When you can talk about something with numbers, you know something about it - when you cannot, your knowledge is of a meager and unsatisfactory nature."

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jeff

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Originally posted by yogi

...the physics are introduced by hand...

As always.

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yogi

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jeff

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Originally posted by yogi

if we had a complete (correct) theory we would not have to put in the electron charge by hand - the theory would predict what the charge should be...

Such a theory would be expected to explain the success of QED, the subject of this thread. In the absence of such a theory, the best I can do is show how QED produces the inverse square law, which is what Ivanseeking wanted to know. Do you understand QFT?

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yogi

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jeff

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Originally posted by yogi

I take it then that you don't understand QFT.

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yogi

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take it as you will

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