Classical/QFT Vacuum Fluctuations

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Discussion Overview

The discussion revolves around the concept of the classical vacuum in the context of physics, particularly as a precursor to questions about quantum field theory (QFT). Participants explore the nature of the classical vacuum, its properties, and its implications for electromagnetic fields and light propagation.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that the classical vacuum is a space devoid of matter, while others clarify that classical fields still exist in this vacuum, albeit with zero values (except for the Higgs field).
  • There is a discussion about the constants epsilon-zero and mu-zero, with some cautioning against conflating the classical vacuum with the electromagnetic vacuum where these constants take their vacuum values.
  • Participants debate whether the presence of an electric field and a capacitor constitutes a true vacuum state for QFT expansion, with some arguing that the electric field represents a coherent quantum state.
  • One participant describes a classical vacuum as akin to a bell jar vacuum created in a classroom, acknowledging that fields may still be present.
  • A question is raised regarding whether the speed of light remains constant when passing through the space between capacitor plates in a classical vacuum, with some asserting that electromagnetic theory implies it does not depend on other fields.
  • There is a discussion about the independence of the electromagnetic field in light from the vacuum's electromagnetic field, with references to the linearity of Maxwell's equations.
  • Participants provide corrections regarding the values of vacuum permittivity and permeability, emphasizing their significance in the context of electromagnetic fields.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the classical vacuum and its implications for QFT. While some agree on certain properties of the vacuum, there is no consensus on the implications of electric fields and the behavior of light within this context.

Contextual Notes

Limitations include varying interpretations of what constitutes a vacuum, the dependence on definitions of classical versus quantum fields, and unresolved questions about the behavior of light in the presence of electric fields.

HeavyWater
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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,
 
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HeavyWater said:
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.
HeavyWater said:
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.
HeavyWater said:
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.
 
Orodruin said:
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.
@@@@@@
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.
 
Thank you. Your response is much more than I expected. I will clarify and get back to you and the rest of the community.
 
A classical vacuum could have "stuff" in it such as electric, magnetic and gravitational fields. Ponderable matter would be absent.
 
Thank you stewards.
 
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,
 
HeavyWater said:
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.
 
Jano L. said:
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 ?
 
  • #10
morrobay said:
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.
 
  • #11
morrobay said:
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 . εs/ε0 = 1 .
Also that should just be the electric field in the vacuum
 

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