## really a virtual particle sea?

I've often heard the argument that vacuum is full of virtual particle pairs that get created and annihilated, but in fact the ground state of the harmonic oscillator is orthogonal to all excitation states, so shouldn't the vacuum, when in ground state, actually be empty of all particles? What is this virtual particle sea stuff really?

 Quote by jostpuur I've often heard the argument that vacuum is full of virtual particle pairs that get created and annihilated, but in fact the ground state of the harmonic oscillator is orthogonal to all excitation states, so shouldn't the vacuum, when in ground state, actually be empty of all particles? What is this virtual particle sea stuff really?
The point is that the virtual particles do not exist long enough to be classified as "excitation states" ! They are a bit special in the sense that their lifetime is very limited (determined by the Heisenberg uncertainty principle).

It was Dirac who came up with the idea that the vacuum was filled with virtual positron and electron pairs (the reason that they were pairs has to do with conservation laws like that of electrical charge). You can break up such a pair and make the particles real when you have enough energy coming from some interaction between two charged particles that were placed inside the vaccuum.
 I understand that when an oscillator is in ground state, there is a nonzero probability to observe it arbitrarily far from the origo. For example, in vacuum there is a nonzero probability for fields to have arbitrarily large values. I've thought that this is quantum fluctuation. However, I don't understand how an oscillator, when in ground state, could have a nonzero probability to be on an excitation state! Orthogonal is orthogonal: Zero overlapping.

## really a virtual particle sea?

 Quote by marlon The point is that the virtual particles do not exist long enough to be classified as "excitation states" ! They are a bit special in the sense that their lifetime is very limited (determined by the Heisenberg uncertainty principle).
I just remembered that the time energy uncertainty principle was the particularly mysterious one. What ever it means, I would prefer sticking with the Schrödinger's equation, which at least is not wrong. According to SE, an energy eigenstate remains as an eigenstate.
 look up 'dielectric'.

 Quote by jostpuur However, I don't understand how an oscillator, when in ground state, could have a nonzero probability to be on an excitation state! Orthogonal is orthogonal: Zero overlapping.
Again, the virtual particles popping up cannot be compared to the excitation states you are referring to. The vacuum fluctuations only exist for a short amount of time and their energy is uncertain. While they become real for this short period, total energy conservation is not respected ! This is allowed because of the Heisenberg uncertainty principle. In between final and initial states of a process, energy is uncertain during a certain amount of time, so...

 Quote by jostpuur I just remembered that the time energy uncertainty principle was the particularly mysterious one. What ever it means, I would prefer sticking with the Schrödinger's equation, which at least is not wrong.
What do you mean ? That it is incorrect ?

marlon

 Quote by marlon Again, the virtual particles popping up cannot be compared to the excitation states you are referring to.
All particles are excitation states of fields.

 The vacuum fluctuations only exist for a short amount of time and their energy is uncertain.
So excitation states exist only for short amount of time?

 What do you mean ? That it is incorrect ?
Not really. Statement, whose meaning is not clear, cannot be incorrect yet.
 When a system is on an energy eigenstate $|\psi_n\rangle$ corresponding to an energy $E_n$, then according to the SE the time evolution is trivial phase rotation $$|\psi(t)\rangle = e^{-i(t-t_0)E_n/\hbar}|\psi_n\rangle.$$ I have never seen Heisenberg uncertainty principle $$\Delta E\;\Delta t \geq \hbar$$ used in arguing that there would be some fluctuation in the time evolution of a system. It is always the phase rotation only.

Recognitions:
 Quote by jostpuur When a system is on an energy eigenstate $|\psi_n\rangle$ corresponding to an energy $E_n$, then according to the SE the time evolution is trivial phase rotation $$|\psi(t)\rangle = e^{-i(t-t_0)E_n/\hbar}|\psi_n\rangle.$$ I have never seen Heisenberg uncertainty principle $$\Delta E\;\Delta t \geq \hbar$$ used in arguing that there would be some fluctuation in the time evolution of a system. It is always the phase rotation only.
Try a Google on Leon Van Hove and correlation, or "resonance". It will help you get to the next level.

Regards,
Reilly Atkinson
'

 Quote by jostpuur All particles are excitation states of fields.
You did not get the point. I meant to say that virtual particles do not follow the rules of total energy conservation. Your excitation states DO !

 So excitation states exist only for short amount of time?
Vacuum fluctuations do YES

 Not really. Statement, whose meaning is not clear, cannot be incorrect yet.
What is not clear about it ?

marlon

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Recognitions:
 Quote by jostpuur I've often heard the argument that vacuum is full of virtual particle pairs that get created and annihilated, but in fact the ground state of the harmonic oscillator is orthogonal to all excitation states, so shouldn't the vacuum, when in ground state, actually be empty of all particles? What is this virtual particle sea stuff really?
You are right. The vacuum does not contain any particles. The concept of a "virtual particle" or a "virtual state" is not even defined by general principles of quantum theory. Thus, it is misleading to think in terms of "virtual" anything.

Nevertheless, in the vacuum the value of the field, and consequently the value of energy, is uncertain. Consequently, the average energy is larger than zero.

http://xxx.lanl.gov/abs/quant-ph/0609163 [Found. Phys. 37 (2007) 1563]
especially Sec. 9.3.

 Quote by Demystifier You are right. The vacuum does not contain any particles. The concept of a "virtual particle" or a "virtual state" is not even defined by general principles of quantum theory. Thus, it is misleading to think in terms of "virtual" anything.
In QFT virtual particles do "exist" in the sense that they arise due to vibrations of quantum fields. To such field one can assign particle like concepts such as momentum ! That how basic QFT works : assign particle like concepts to field vibrations

marlon

 Quote by marlon In QFT virtual particles do "exist" in the sense that they arise due to vibrations of quantum fields. To such field one can assign particle like concepts such as momentum ! That how basic QFT works : assign particle like concepts to field vibrations
Hello,

is what you wrote true in QFT in general or only in pertubative QFT ?
I have some idea of what is a "virtual" particle in QFT. But, when it is no more pertubative, I do not understand.

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Recognitions:
 Quote by Barmecides Hello, is what you wrote true in QFT in general or only in pertubative QFT ? I have some idea of what is a "virtual" particle in QFT. But, when it is no more pertubative, I do not understand.
You are right, a notion of a "virtual particle" makes sense only as an "interpretation" of some mathematical terms in the perturbative method of calculation.

 Quote by Barmecides Hello, is what you wrote true in QFT in general or only in pertubative QFT ? I have some idea of what is a "virtual" particle in QFT. But, when it is no more pertubative, I do not understand.
If you take into account how the notion of particle arises in QFT, i don't quite get your point here. Could you elaborate ?

marlon

marlon, do you agree that particles are excitations, corresponding to some Fourier modes, of fields?

Here you explain so
 Quote by marlon In QFT virtual particles do "exist" in the sense that they arise due to vibrations of quantum fields. To such field one can assign particle like concepts such as momentum ! That how basic QFT works : assign particle like concepts to field vibrations
but here you explain the opposite
 Quote by marlon The point is that the virtual particles do not exist long enough to be classified as "excitation states" ! They are a bit special in the sense that their lifetime is very limited (determined by the Heisenberg uncertainty principle).
This gets complicated.
Quote by marlon
 Quote by jostpuur So excitation states exist only for short amount of time?
Vacuum fluctuations do YES
So when virtual particles exist for short time, then the excitation states exist only for a short time? So the virtual particles are excitation states, after all?

Are all particles excitation states, or are they not?

 Quote by marlon If you take into account how the notion of particle arises in QFT, i don't quite get your point here. Could you elaborate ? marlon
Sorry marlon,

this was a mistake in writing. I was only meaning that "I have some idea of what is a "virtual" particle in perturbative QFT" and only in perturbative QFT because I think this is an artefact of perturbative approximation of quantum mecanics.

But, if you can proove the contrary, I will be eager for an explanation as my current understanding might be wrong.