Proton-electron interactions interms of photons

[Unredeemed]

Try

http://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html.

I have actually looked at that before. But I didn't understand what he/she was trying to represent on the diagrams :s

Can anyone help?

 

[malawi_glenn]

The diagrams on the section "How can they be responsible for attractive forces?" are wavefunctions, i.e probability density plotted with respect to x (position) and probability density plotted with respect to p (momentum)

 

[Fredrik]

Or will I simply not be able to even sort of understand until I start a physics degree at university?

Most people don't understand it even when they have finished their degree.

I don't fully understand it myself. I don't remember seeing an explanation in Feynman's QED book (but it's still an awesome book).

 

[lightarrow]

[...]
You are right about the paths. We can't say which path the photon took.
[...]
The point is that I think we have forgotten something. When we find that an electron and a proton attract each other, there has to be a reason. You can give me the field concept of things, but a field is just another word for ether. What is this field made of. Photons.

You see, what you're throwing out of the door, comes back through the window: to explain why the photon has taken a certain path from A to B, you have to postulate the existence of some sort of field in between A and B...

 

[benk99nenm312]

Since when can we explain why a photon took a specific path? All we know is the probability. I thought this was the whole mystery of Quantum Mechanics.

If there's something I'm not thinking of, please tell me.

 

[lightarrow]

Since when can we explain why a photon took a specific path? All we know is the probability. I thought this was the whole mystery of Quantum Mechanics.

If there's something I'm not thinking of, please tell me.

How do you explain an interference pattern without using the concept of field?

 

[QuantumBend]

How do you explain an interference pattern without using the concept of field?

No, no electron want field not photon. You get wrong physics.

 

[Hans de Vries]

So then how does a proton attract an electron?

First you have to understand that the mathematical formalism is a plane wave
expansion and describes how waves interact with each other. A wave packet
of a free electron can easily get bigger as a micron in diameter.

If such a wave-function collides with the wave function of its positively charged
twin brother, the positron, spread in the same way, then they form a scattering
zone. Here is were the virtual photon exchange happens.

How does a virtual photon get exchanged between the two?

If the wave function of the electron changes speed from an initial momentum
to a final momentum then these two states will coexist for a little while.
The two wave function will form an interference pattern which is called the
transition current.

This is a sinusoidal varying charge/current density and spin density pattern.
If you take Maxwell's laws, (Yes the classical laws) then this sinusoidal pattern
will generate a sinusoidal electromagnetic pattern. This is the virtual photon.

The wave function of the positron can generate the exact opposite electro-
magnetic sinusoidal pattern by also changing from an initial to a final state.
The two patterns cancel each other and we say the photon is exchanged.

For this to happen we need the final states to show attraction compared to
the initial states, only in this case can the electromagnetic patterns cancel
each other out.

If the particles are more localized looking rather like the classical two points
on a distance then we can mathematically still do a Fourier transform which
describes them as a collection of plane waves which behave in the way
described above. This is already becoming more and more mathematical but
the calculations still give the correct answers.Regards, Hans

 

[QuantumBend]

First you have to understand that the mathematical formalism is a plane wave expansion and describes how waves interact with each other. A wave packet of a free electron can easily get bigger as a micron in diameter.

If such a wave-function collides with the wave function of its positively charged
twin brother, the positron, spread in the same way, then they form a scattering
zone. Here is were the virtual photon exchange happens.

Regards, Hans

OK what when electron more than micron and 10 centimeter from electron? Do wave packets go there - NO.

 

[Hans de Vries]

OK what when electron more than micron and 10 centimeter from electron? Do wave packets go there - NO.

It seems you haven't read my last paragraph. The Fourier decomposition
is a 100% mathematical equivalent alternative description. You need to
understand the Fourier transform.

Physicist typically think about scattering zones while novices struggle to
understand why this concept also works mathematically in a classical setup
where particles are separated by a large distance.

The quantum field concept is so useful because it offers a profound insight
in the decay, scattering, creation and annihilation of particles. It does much
more then just offering an alternative description of classical electrodynamics.Regards, Hans

 

[lightarrow]

If the wave function of the electron changes speed from an initial momentum to a final momentum then these two states will coexist for a little while.
The two wave function will form an interference pattern which is called the
transition current.
This is a sinusoidal varying charge/current density and spin density pattern.
If you take Maxwell's laws, (Yes the classical laws) then this sinusoidal pattern
will generate a sinusoidal electromagnetic pattern. This is the virtual photon.

So, reversing the concept, you could say how an EM wave creates a similar sinusoidal pattern interacting with a uniformly moving electron and so accelerating it?

 

[Hans de Vries]

So, reversing the concept, you could say how an EM wave creates a similar sinusoidal pattern interacting with a uniformly moving electron and so accelerating it?

Basically the new thing in QED is the interference pattern caused between the
initial state and the final state of the electron. This is for instance what causes
bremstralung. An electron which is suddenly stopped generates high frequency
x-ray radiation.

The EM radiation is high frequency sinusoidal because the interference pattern
between the initial and final state of the electron is a high frequency pattern.
Good old Maxwell's laws then describe how the EM radiation is caused by the
interference pattern.

The transverse EM components stem from the alternating spin density (magnetic
moment density) of the interference pattern. Spin plays an essential role in QED
processes.

This is another source of confusion in the attempt to describe the classical paths
of point like electrons in an electric by virtual photons. The electric force is
transmitted by longitudinal electromagnetic components components which only
virtual photons can posses. A "virtual photon" in this case is simply the classical
EM field belonging to a shifting sinusoidal charge density interference pattern. Regards, Hans

 

[lightarrow]

Basically the new thing in QED is the interference pattern caused between the
initial state and the final state of the electron. This is for instance what causes
bremstralung. An electron which is suddenly stopped generates high frequency
x-ray radiation.

The EM radiation is high frequency sinusoidal because the interference pattern
between the initial and final state of the electron is a high frequency pattern.
Good old Maxwell's laws then describe how the EM radiation is caused by the
interference pattern.

The transverse EM components stem from the alternating spin density (magnetic
moment density) of the interference pattern. Spin plays an essential role in QED
processes.

Very complicated.
Thank you Hans.

This is another source of confusion in the attempt to describe the classical paths
of point like electrons in an electric by virtual photons. The electric force is
transmitted by longitudinal electromagnetic components components which only
virtual photons can posses. A "virtual photon" in this case is simply the classical
EM field belonging to a shifting sinusoidal charge density interference pattern.
Regards, Hans

Then virtual photons have non zero mass?

 

[Hans de Vries]

Very complicated.
Thank you Hans.Then virtual photons have non zero mass?

As one says: They are not "on the mass shell".

Neither do virtual photons move at c. Yes the EM field propagates at c but
the sinusoidal EM pattern moves at just the same speed as its source, the
electron's interference pattern (The transition current)

This speed corresponds to the average rapidity of the initial and final
momentum state of the electron.

[tex]v ~~=~~ \tanh^{-1}\left(\,\frac{\theta_i+\theta_f}{2}\right)[/tex]

In the classical picture of an electron in an electrical field this speed is
comparable to the speed of the electron and its field itself. There are no
real photons going back and forward between electrons. Real photons are
sinusoidal EM fields which shift with the speed of light. Virtual photons are
distinctly different.Regards, Hans

 

[lightarrow]

As one says: They are not "on the mass shell".

Neither do virtual photons move at c. Yes the EM field propagates at c but
the sinusoidal EM pattern moves at just the same speed as its source, the
electron's interference pattern (The transition current)

This speed corresponds to the average rapidity of the initial and final
momentum state of the electron.

[tex]v ~~=~~ \tanh^{-1}\left(\,\frac{\theta_i+\theta_f}{2}\right)[/tex]

In the classical picture of an electron in an electrical field this speed is
comparable to the speed of the electron and its field itself. There are no
real photons going back and forward between electrons. Real photons are
sinusoidal EM fields which shift with the speed of light. Virtual photons are
distinctly different.
Regards, Hans

Interesting. This is another confirmation of my idea that, in relativity, rapidity is a more appropriate concept than velocity.