Is the Electromagnetic Interaction Affected by Photon Position During Lifetime?

[Kruger]

The electromagnetic interaction can be described by the exchanche of virtual photons. These photons have a well defined momentum and can therefore be everywhere in space. So gets the em-interaction of two electrons smaller the more they are apart if these photons have no favourite position in space during there lifetime?

 

[ahrkron]

I'm not sure what you are asking...

Yes, the intensity of their interaction does decrease with distance.

 

[El Hombre Invisible]

He's asking why the EM interaction is distance-dependent when the mediators are equally likely to be found anywhere in space.

 

[selfAdjoint]

The electromagnetic interaction can be described by the exchanche of virtual photons. These photons have a well defined momentum and can therefore be everywhere in space. So gets the em-interaction of two electrons smaller the more they are apart if these photons have no favourite position in space during there lifetime?

Your problem is in your premise. Since virtual photons are unobservable, they have no well-defined momentum but remain in a general superposition of momentum states.

 

[hellfire]

He's asking why the EM interaction is distance-dependent when the mediators are equally likely to be found anywhere in space.

The uncertainty principle makes it possible for the virtual photons to have greater energies and momenta (greater than allowed by the mass-shell relation) when their lifetimes and their paths from their sources are shorter. For virtual photons traveling far away from its sources their lifetime is greater and their momenta is therefore smaller. Calculations show that the inverse square law can be derived from this (as done in Zee's QFT book, pp. 25-27).

 

[Kruger]

Ok, thanks, really good answers. Ahhh, this Zee's book. When I've time I must lend this one.

 

[marlon]

The uncertainty principle makes it possible for the virtual photons to have greater energies and momenta (greater than allowed by the mass-shell relation) when their lifetimes and their paths from their sources are shorter.

This is not entirely correct. Indeed energy becomes uncertain and the energy conservation law can be broken inbetween the vertex points of the interaction. But momentum is conserved at all times (in each vertex point). Just look at the Feynman diagram rules on page 53. Besides, i think you are mixing momentum with 4-momentum k here. Also, virtual particles have a DEFINITE momentum and an infinite spatial spread. You cannot localize them because of this infinite uncertainty. This clearly demonstrates that virtual particles need to be described in terms of "fluctuations of fields".

The momentum of virtual particles is definite because you can write the internal momenta in terms of the external (fixed) momenta thanks to momentum conservation. Look at the figure on page 56 of Zee's book. The only internal momentum k is summed over when calculating the amplitude. So each momentum value is fixed "when summing over the virtual transition states going from one vertex point to the next" and it is only the difference between k² and m that varies in this summation. This is the NON-conservation of energy.

Finally, if you look on page 55 equation 22, you will see the propagator associated with virtual particles. It's magnitude is determined by how big the difference between the four momenta and the mass is. in other words, the bigger this difference the smaller the amplitude of a virtual particle. Like Zee calls it : there is a cost of not being real.



marlon

 

[hellfire]

you are mixing momentum with 4-momentum k here

You are right, thank you for your clarification.

 

[Macro]

I say the EM inetecation of charged particles with light is what causes matter to slow light's speed.

Matter resists light by its EM field.

 

[marlon]

I say the EM inetecation of charged particles with light is what causes matter to slow light's speed.
Matter resists light by its EM field.

I would say this is a bad choice of words.

Light is NOT slowed down when it passes through a medium. The photon velocity is always c. The only thing that happens is when light passes through a medium, photons get absorbed by the medium's atoms. After emission, photons travel on with speed c until they get absorbed again. The net effect is that light takes more time to pass through a medium, thus it SEEMS to have slowed down.

The famous analogy in this case is the one of a car with constant velocity, traveling from A to B with 3 red lights in between, that has to stop three times because of red-lights. Though the velocity is constant, the car will take more time to travel from A to B.

marlon

 

[IndiAndy]

That Helps!

Awesome Marlon! That helps me understand the misunderstanding I used to have over the "slowing".
Appreciate it!

Andy

 

[marlon]

Awesome Marlon! That helps me understand the misunderstanding I used to have over the "slowing".
Appreciate it!
Andy

Ok, thank you very much

marlon

 

[Meir Achuz]

Since the wavelength of visible light is much longer than the distance between molecules, it does not get absorbed and reimitted by individual molecules.

 

[marlon]

Since the wavelength of visible light is much longer than the distance between molecules, it does not get absorbed and reimitted by individual molecules.

Yes,..., your point being ?

marlon

 

[Physics Monkey]

Since the wavelength of visible light is much longer than the distance between molecules, it does not get absorbed and reimitted by individual molecules.

There something I'm confused about here. Molecules emit and absorb infrared and microwave radiation all the time, and the wavelengths involved are much bigger than the size of the molecules. Atoms absorb and emit in the visible quite commonly and they are much smaller than the wavelengths of visible light.

I must have misunderstood your comment, so what have I missed?