How Long Does an Electromagnetic Field Oscillation Last in Ground State?

[Kruger]

Where does a photon in vacuum come from if it creates a pair? In QFT there shoudn't be a photon available in vacuum because the number operator is zero.

 

[dextercioby]

For the quantum theory of the em field,the vacuum state has 0 particles...

But QED means INTERACTING quantum fields:Dirac & Maxwell.

Daniel.

 

[Kruger]

Which Dirac theory? I know the Hole theory. But this theory does only describe the positron and electron, not the virtual photon. Can you tell me?

thanks dextercioby

 

[dextercioby]

Dirac field.The vacuum for a free field has 0 energy,0 momentum,0 electric charge & 0 particles (remember the necessity of defining the normal product of creation & annihilation operators).But the vacuum for an interacting field theory is different.Remember that the quantum corrections to the Green functions are nonzero.

Daniel.

 

[Kruger]

Can you please explain me, why the quantum corrections for this aren't as normal. Normal we have E=hw/4pi.

 

[dextercioby]

Nope.The normal product deals with "residual" energy.The vacuum of a free theory has 0 energy.

Daniel.

 

[marlon]

Where does a photon in vacuum come from if it creates a pair? In QFT there shoudn't be a photon available in vacuum because the number operator is zero.

Here we go again. I urge you to read the 'on virtual particles' entry of my journal. Vaccuum fluctuations only arise in NON-free field theories. In these theories the number operator is NOT conserved because it does not commute with the Hamiltonian. The actual fluctuations arise because of the HUP and this non-conservation of the number operator. Energy can become uncertain for a very short time. During this time, energy conservation is violated and the number operator will change...

marlon

https://www.physicsforums.com/journal.php?s=&action=view&journalid=13790&perpage=10&page=2

you will need to scroll a bit

 

[Kruger]

But if I derive the ground state of the electromagnetic field I would get the zero point energy of this quantum field. And there aren't photons in there. And that's why I think there aren't photons in the vacuum (not real photons and not virtual photons <--- in an empty space where only ground state oscillations can exist). If we put in a strong electric field Dirac's hole theory predicts virtual pair creation. But for this it is a virtual photon needed with many energy and ground state oscillation hasn't this energy.
I know that Heisenberg's uncertainty principle play a role in this but we used it in deriving the ground state of the em field. And that's actionally the point where I get problem.

OR DO WE CALL THIS GROUND STATE OSCILLATION "VIRTUAL PHOTONS"?

 

[marlon]

If we put in a strong electric field Dirac's hole theory predicts virtual pair creation. But for this it is a virtual photon needed with many energy and ground state oscillation hasn't this energy.

You need to distinguish between two things here. Virtual particles either arise because of vacuum fluctuations, but they also originate as the force mediating particles between matter particles. In your example, the energy for the virtual particles does NOT come from the vacuum but comes from the actual interaction between two matter particles. If you have two electrons that interact via the exchange of a virtual photons, then this photon arises as the fluctuation of a spin 1 field (this is a tricky issue however because of the zero photon mass). These fluctuations are caused by the two electrons. Think of the two electrons as if they were sitting on a mattress that will start to vibrate. These vibrations correspond to the virtual particle that goes from one electron to another. Both repulsive and attractive forces are treated this way in QFT. A force is represented by the exchange of this virtual particle that transports a definite momentum and therefore (because of HUP) the field corresponding to this virtual particle is everywhere in space...This really needs to be the case because when working with Feynman diagrams and when calculating the photon propagator, we integrate over all spatial coordinates.

Now, the vacuum can have an influence on this. If the vacuum is filled with virtual particle anti-particle pairs, each with opposite charge, these pairs will act as good old dipoles and they will try to align with the electric field of the two electrons. Basically what happens is that the vacuum plays the role of a dielectric that screens (ie : make more interactions more difficult) the electron's charges. That is why we have the concept of bare and dressed charge in field theory. This vaccuum-influence is expressed by the polarization insertion in QFT and this is nothing else then the self energy of the photon propagator

marlon

 

[Kruger]

thanks dextercioby and marlon

In all books I read about the vacuum there is written something like this:

///In vacuum there are all electrons on their lowest state. There are also negative energy states which are occupied. If a virtual photon collide with such a negative energy particle then this negative particle gets positive energy and it leaves a hole back (negativ states) that behaves like a positron. After time d(t) (Uncertainty) the electron will go back in the negativ energy state.
///

the energy for the virtual particles does NOT come from the vacuum but comes from the actual interaction between two matter particles.

How do they interact or better which particle interacts with whicht? I mean in Dirac's theory there isn't an electron that interacts. The negativ energy particle just raise into a positive energy state.

 

[Kruger]

All the oscillators in the mattress are in their SAME lowest energy-state but each oscillator has virtual vibrations. So you have one particle with energy given by hbar*omega/2 but surrounded with many other virtual particles.

And another question about what you have written (journal).
If I look on quantum field theory then this mattresses don't contain particles. ?

 

[marlon]

And another question about what you have written (journal).
If I look on quantum field theory then this mattresses don't contain particles. ?

No, they do not.

It's the vibrations that correspond to what we call particles

regards
marlon

 

[Kruger]

But you wrote ""So you have one particle with energy given by ...""

 

[marlon]

But you wrote ""So you have one particle with energy given by ...""

I don't know what you are talking about. Please be more specific so that i can understand

regards
marlon

 

[Kruger]

Sorry marlon.

All the oscillators in the mattress are in their SAME lowest energy-state but each oscillator has virtual vibrations. So you have one particle with energy given by hbar*omega/2 but surrounded with many other virtual particles.

I mean the last sentence you wrote. And I think that there aren't particles in the vacuum with this energy. (you wrote this in you journal (virtual particles)).

Virtual particles either arise because of vacuum fluctuations, but they also originate as the force mediating particles between matter particles. In your example, the energy for the virtual particles does NOT come from the vacuum but comes from the actual interaction between two matter particles.

If we work with Diracs hole theory how can this be understood with your explanation? There aren't really two particles (only one) and that's the "electron" in the negative energy state that raise on a positive state (for short time d(t)) if a virtual photon interacts with it. But from where exactly does the virtual photon come from? <--- Please, can you explain me that in easy language (I only startet with QM and QFT, I'm not an expert like you, marlon and dexter)

Thanks

 

[marlon]

Sorry marlon.



I mean the last sentence you wrote. And I think that there aren't particles in the vacuum with this energy. (you wrote this in you journal (virtual particles)).

OK i get your point. Well, if the mattress vibrates, there are several energies possible. One energy will be 'on mass shell' meaning it respects the Einstein energy relation. But apart from this energy, there are many other energies that do not respect the Einstein energy relation. These corrspond to the virtual particles. So indeed, there are no virtual particles that have the groundstate energy of the EM-field because it respects the Einstein energy relation. However, other energies are possible during a time delta t...Those are the virtual particles that arise and vanish shortly after.

regards
marlon

 

[Kruger]

Ok, I think I got the case of my problem now. Thanks marlon you're very helpful.

 

[Kruger]

other energies are possible during a time delta t...Those are the virtual particles that arise and vanish shortly after.

So If there is created a virtual particle then the state of the mattress will raise. And after its annihilation the state will lower and go back to ground state.

These virtual particles (photons) are they a "product (intermediate state)" of an interaction or can they arise from vacuum (in case of virtual pair creation)? In the case of pair creation the e+e- pair isn't there at the beginning and the virtual photon must be an off mass shell interacting particle, so fom where does this photon come from (which particle send it)?

 

[marlon]

So If there is created a virtual particle then the state of the mattress will raise. And after its annihilation the state will lower and go back to ground state.

yes, besides, go check my latest entry in my journal and see how NASA explains these zero point fluctuations

These virtual particles (photons) are they a "product (intermediate state)" of

They are the actual intermediate stage in some interaction between matter particles : ie the internal lines in Feynman diagrams

or can they arise from vacuum (in case of virtual pair creation)?

yes, that is the second possibility : ie the vacuum fluctuations or zero point energy fluctuations.

In the case of pair creation the e+e- pair isn't there at the beginning and the virtual photon must be an off mass shell interacting particle, so fom where does this photon come from (which particle send it)?

Well pair creation can indeed be the end result of some interaction that was mediated by virtual particles. However, there had to be some kind of energy available (exactly equal to the total energy of the created e-e+ pair) that ignites or triggers this interaction: i mean that the virtual photon arises as the vibration of a quantumfield, but indeed there had to be some energy that makes the actual field vibrate. Even, virtual particles can become real if enough energy is available to given them a legitimate reason to exist, you see ?


regards
marlon

 

[Kruger]

@marlon: Yes I can see. Thanks.

Question:
What's the lifetime of an electromagnetic field in ground state? I mean the liftime of one such oscillation (infiniti or dt from HUP)?