Classical/QFT Vacuum Fluctuations

[HeavyWater]

I want to ask a question about the Quantum Vacuum, but I want to make a few statements about my understanding of the Classical concept of a vacuum to act as a background.

1.)As I understand it, the classical vacuum is a place where there is nothing.
2.)Two attributes of the classical vacuum are the constants: epsilon-zero and mu-zero.
3.)We know that (c^2)(epsilon-zero)(mu-zero)=1, where "c" is the speed of light.
4.)A charged capacitor in this vacuum has an Electric Field E.
5.)Though there is an E field, the values of epsilon and mu between the plates of this capacitor are epsilon-zero and mu-zero.

I will ask the QFT question over the weekend if all of this sounds consistent in the context of classical physics. Any comments are welcome. Thanks,

 

[Orodruin]

As I understand it, the classical vacuum is a place where there is nothing.

What do you mean by "nothing"? There classical fields are still around, although they (except the Higgs field) have a value of zero.

2.)Two attributes of the classical vacuum are the constants: epsilon-zero and mu-zero.
3.)We know that (c^2)(epsilon-zero)(mu-zero)=1, where "c" is the speed of light.

do not confuse the classical vacuum around which we expand our quantum fields with the classical electromagnetic vacuum where the permeability and permittivity take their vacuum values.

4.)A charged capacitor in this vacuum has an Electric Field E.

If there is an electric field and a capacitor, this is not vacuum in the sense of the state around which you will expand your qft. The electric field is essentially a coherent quantum state and the capacitor is a complex mixture of excitations of several fermion and gauge fields.

 

[HeavyWater]

What do you mean by "nothing"? There classical fields are still around, although they (except the Higgs field) have a value of zero.

do not confuse the classical vacuum around which we expand our quantum fields with the classical electromagnetic vacuum where the permeability and permittivity take their vacuum values.

If there is an electric field and a capacitor, this is not vacuum in the sense of the state around which you will expand your qft. The electric field is essentially a coherent quantum state and the capacitor is a complex mixture of excitations of several fermion and gauge fields.

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Wow. Your response is beyond all I expected. Thank you. I will think about your comments and clarify. Thanks for the quick and overwhelming response.

 

[HeavyWater]

Thank you. Your response is much more than I expected. I will clarify and get back to you and the rest of the community.

 

[stedwards]

A classical vacuum could have "stuff" in it such as electric, magnetic and gravitational fields. Ponderable matter would be absent.

 

[HeavyWater]

Thank you stewards.

 

[HeavyWater]

Thank you to all that have commented to me online and in person.

By the classical vacuum, I was thinking of the type of vacuum your science teacher made in seventh grade. A bell jar with a vacuum pump. Yes, I do agree that a classical vacuum may still be associated with fields.

Let me continue and end the classical part of my question, before I move into QFT. Let's assume that there is a charged capacitor with an E-field in this classical vacuum. If we shine a light beam into the vacuum and through the space between the parallel plates, do we find that the speed of light between the parallel plates is the same as the speed of light before the light beam enters the parallel plates? Remember, I'm not yet talking about QFT, Higgs bosons, condensates, and whatever. I'm just talking about classical physics.

Thanks,

 

[Jano L.]

Thank you to all that have commented to me online and in person.

By the classical vacuum, I was thinking of the type of vacuum your science teacher made in seventh grade. A bell jar with a vacuum pump. Yes, I do agree that a classical vacuum may still be associated with fields.

Let me continue and end the classical part of my question, before I move into QFT. Let's assume that there is a charged capacitor with an E-field in this classical vacuum. If we shine a light beam into the vacuum and through the space between the parallel plates, do we find that the speed of light between the parallel plates is the same as the speed of light before the light beam enters the parallel plates? Remember, I'm not yet talking about QFT, Higgs bosons, condensates, and whatever. I'm just talking about classical physics.

Thanks,

Yes, EM theory implies the speed of EM waves in vacuum does not depend on the presence of other fields or their field strength.

 

[morrobay]

Yes, EM theory implies the speed of EM waves in vacuum does not depend on the presence of other fields or their field strength.

So because the vacuum permittivity equals one and c = √1/ε₀μ₀
then the EM field in vacuum does not effect c ? http://maxwells-equations.com/materials/permittivity.php
What is the a reason the EM field in light is not affected by the EM field in the vacuum ?

 

[Orodruin]

What is the a reason the EM field in light is not affected by the EM field in the vacuum ?

There is only one electromagnetic field, not one field per source. The field in which light are waves is the same field to which a point charge gives a static radially directed contribution.

The reason you can treat sources independently is that Maxwell's equations are linear.

 

[morrobay]

So because the vacuum permittivity equals one and c = √1/ε₀μ₀
then the EM field in vacuum does not effect c ? http://maxwells-equations.com/materials/permittivity.php
What is the a reason the EM field in light is not affected by the EM field in the vacuum ?

Correction : Vacuum permittivity , ε₀ = 8.85 ⋅10^-12 F/m
Permeability μ₀ = 4π ⋅10^-7 H/m
It is relative static permittivity . ε_s/ε₀ = 1 .
Also that should just be the electric field in the vacuum