Is AdS Space Present Between Casimir Plates?

  • Context: Graduate 
  • Thread starter Thread starter robousy
  • Start date Start date
  • Tags Tags
    Energy Space
Click For Summary

Discussion Overview

The discussion centers around the nature of the space between Casimir plates and whether it can be characterized as Anti-de Sitter (AdS) space due to the negative energy density associated with the Casimir effect. Participants explore the implications of the cosmological constant and the definitions of AdS space in relation to the Casimir energy calculations.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant calculates the Casimir energy for plates and compares it to the cosmological constant, suggesting the space between the plates might be AdS due to negative energy density.
  • Another participant argues that it would be incorrect to classify the space as AdS because AdS solutions require a global negative cosmological constant.
  • Concerns are raised about the definition of AdS, particularly regarding negative curvature and the presence of a warp factor, which some participants argue does not apply in this context.
  • A participant reflects on their understanding of AdS and its relation to negative curvature, questioning whether the local conditions between the plates could be described as having a negative cosmological constant.
  • Another participant references the Friedmann equations to explore the implications of negative energy density on cosmic expansion dynamics, suggesting a transition from inflation to deflation could be analogous to conditions between the plates.

Areas of Agreement / Disagreement

Participants express differing views on whether the space between the Casimir plates can be considered AdS space. There is no consensus on this matter, with multiple competing interpretations of the definitions and implications of negative energy density and cosmological constants.

Contextual Notes

Participants note that the definitions of AdS space involve specific geometric properties, such as negative curvature and warp factors, which may not be applicable in the case of Casimir plates. The discussion also highlights the complexity of relating local energy conditions to broader cosmological models.

robousy
Messages
332
Reaction score
1
Hey Folks,

Had a thought - if you work out the Cosmological constant in SI units it works out to be around [tex]10^{-10} J/m^3[/tex]. I performed a quick calculation for the Casimir energy (EM modes) for a plate measuring [tex]1 m^2[/tex] for a plate separation of [tex]1 \mu m[/tex] and found it to be on the order of [tex]- 10^{-9} J[/tex] which works out to be around [tex]- 10^{-3} J/m^3[/tex].

Note this is NEGATIVE energy, and significantly more negative then the comsological constant is positive.

Would it be wrong (and if so why) to say that the space between the plates is AdS space, eg a space with a negative cosmological const?
 
Physics news on Phys.org
robousy said:
Would it be wrong (and if so why) to say that the space between the plates is AdS space, eg a space with a negative cosmological const?

It would be wrong because AdS solutions have a global negative cosmological constant.
 
Also AdS is defined by negative curvature, and a warp factor, neither of which exist in your case. The space between the plates is still flat.
 
BenTheMan said:
Also AdS is defined by...a warp factor

Maybe I'm misunderstanding you. I know that warp factors appear in flux compactifications and that these solutions are AdS before lifting to De Sitter, but I've never seen the idea of warp factors presented as part of the definition of AdS.
 
josh1 said:
Maybe I'm misunderstanding you. I know that warp factors appear in flux compactifications and that these solutions are AdS before lifting to De Sitter, but I've never seen the idea of warp factors presented as part of the definition of AdS.

Josh---

You are most likely correct. My experiences with AdS have al been from Randall-Sundrum. It was my impression that AdS was negatively curved, and the negative curvature in the radial direction was called the ``warp factor''.

Perhaps I missed the point---the cosmological constant IS negative curvature.
 
Last edited:
Aaah, ok, so would it be correct to say that there was a local NEGATIVE comsological constant between the plates?

Or how about the following: the Freidmann equations tell us:

[tex]\ddot{a}=-\frac{4}{3}G(\rho+3p)a[/tex]

Let p go to zero, if you flip the sign of [tex]\rho[/tex] you would flip from inflation to deflation, which is what is happening between the plates. Comments??
 

Similar threads

Graduate "Monstrous Higgs and Leech Spacetime"
  • · Replies 0 ·
Replies
0
Views
4K
Calculating Magnetic Energy Between Plates
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Casimir effect and vacuum energy and a bit of relativity....
  • · Replies 46 ·
2
Replies
46
Views
7K
Undergrad Is capacitor energy the electrostatic energy of the whole system?
  • · Replies 9 ·
Replies
9
Views
2K
Graduate Derivation of the Casimir energy in flat space
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Atoms Of Space, Gravity and the Cosmological Constant
  • · Replies 1 ·
Replies
1
Views
2K
Graduate "The 7 Strangest Coincidences in the Laws of Nature" (S. Hossenfelder)
  • · Replies 62 ·
3
Replies
62
Views
12K
Undergrad Trying To Conceptualize Two Dimensions Of Time
  • · Replies 2 ·
Replies
2
Views
5K
Undergrad What Are the Empirical Challenges Facing Quantum Gravity Theories?
  • · Replies 105 ·
4
Replies
105
Views
16K
Undergrad Deur Gravitational self-interaction Doesn't Explain Galaxy Rotation Curves
  • · Replies 72 ·
3
Replies
72
Views
11K