What sense does it make to "weigh" a Casimir cavity?

[timmdeeg]

TL;DR Summary

It seems it isn't proofed that the Casimir effect originates from quantum fluctuations. If so, does it still make sense to weigh a Casimir cavity?

This Paper takes reference to quantum fluctuations within a Casimir cavity:

Towards weighing the condensation energy to ascertain the Archimedes force of vacuum
I. INTRODUCTION
... About a decade ago, it was pointed out that a possible way to verify the interaction of vacuum fluctuations with gravity was to weigh a (suitably realized, layered) rigid Casimir cavity [7]. ...

These two Papers show, that the Casimir effect does not or not necessarily originate from quantum fluctuations:

R.L.Jaffe The Casimir Effect and the Quantum Vacuum
Abstract.
In discussions of the cosmological constant, the Casimir effect is often invoked as decisive evidence that the zero point energies of quantum fields are “real”. On the contrary, Casimir effects can be formulated and Casimir forces can be computed without reference to zero point energies.

Hrvoje Nikolic: Proof that Casimir force does not originate from vacuum energy
https://www.sciencedirect.com/science/article/pii/S0370269316304567#:~:text=Therefore%2C%20at%20the%20fundamental%20level,forces%20between%20the%20material%20plates.

ABSTRACT
We present a simple general proof that Casimir force cannot originate from the vacuum energy of
electromagnetic (EM) field

I seem to overlook something, but what?

The experiment is on the way: High-bandwidth beam balance for vacuum-weight experiment and Newtonian noise subtraction

​

 

[Demystifier]

These two Papers show, that the Casimir effect does not or not necessarily originate from quantum fluctuations

No, they show that Casimir effect does not originate from vacuum energy, i.e. vacuum fluctuations. Quantum fluctuations exist in all quantum states, not only in quantum vacuum. Quantum fluctuations are essential for Casimir effect, but those quantum fluctuations do not need to be vacuum fluctuations.

However, it does not mean that that papers which describe Casimir effect in terms of vacuum energy are wrong. It can be described that way too, but in this case one has to be very careful about what one means by the word "vacuum". That word has several different meanings in physics and part of the confusion arises from not distinguishing different notions of "vacuum". For more details see also
https://arxiv.org/abs/1702.03291
and
http://thphys.irb.hr/wiki/main/images/2/2c/Casimir.pdf (especially last page)

 

[timmdeeg]

(especially last page)

Thanks for your helpful answer! Especially for clarifying the different "types" of vacuum.

I wonder if there is any physical relation between the Casimir effect and the cosmological constant, in which case there could be a hint to the vacuum energy supposedly due to this constant if one successful weighs a Casimir Cavity.

According to Sean Caroll The cosmological constant turns out to be a measure of the energy density of the vacuum - the state of lowest energy - and although we cannot calculate the vacuum energy with any confidence, this identification allows us to consider the scales of various contributions to the cosmological constant

In your "last page" you say: Casimir vacuum is not 5 [(5) - state with lowest possible energy (ground state)].
So it seems the Casimir effect has nothing to do with the cosmological constant. Would agree to that?

Further, could you kindly elaborate a bit point 3) which refers to the Casimir vacuum - state annihilated by some lowering operators in a less technical sense if possible? In other words what would one eventually learn by weighing said Casimir Cavity and thus the Casimir vacuum?

 

[Demystifier]

In your "last page" you say: Casimir vacuum is not 5 [(5) - state with lowest possible energy (ground state)].
So it seems the Casimir effect has nothing to do with the cosmological constant. Would agree to that?

I would agree.

 

[Demystifier]

In other words what would one eventually learn by weighing said Casimir Cavity and thus the Casimir vacuum?

One would "learn" what we already know, that potential energy contributes to mass.

 

[vanhees71]

As we already know since Einstein 1915 it's not mass that is the source of the electromagnetic field but the energy-momentum-stress tensor of all the other fields except the gravitational field (in short usually called the "matter fields", but clearly also including the em. field), represented by the energy-momentum tensor of these fields, and correspondingly it's the energy-momentum tensor that is defined by the variation of $g_{\mu \nu}$ in the "matter-field action".

As one should avoid "relativistic mass" already in special relativity one should avoid "gravitational mass" in general relativity. In accordance with Einstein's equivalence principle in relativistic physics the measure of inertia is energy and not mass as in Newtonian physics.

 

[Demystifier]

As we already know since Einstein 1915 it's not mass that is the source of the electromagnetic field but the energy-momentum-stress tensor

Sure, but when we weigh things, we don't measure the source of gravity. We measure the force needed to keep the test body static in the gravitational field, which is proportional to the body's mass. In particular you cannot weigh photon (it cannot be static and has a zero mass), even though it is a source of gravity.

 

[timmdeeg]

One would "learn" what we already know, that potential energy contributes to mass.

Hm, if I remember correctly the energy density between the Casimir plates is less relativ to the energy density outside. If so, would weighing the Casimir vacuum (relativ to outside the plates) confirm this and would it yield the difference of the energy density?

 

[Demystifier]

Hm, if I remember correctly the energy density between the Casimir plates is less relativ to the energy density outside. If so, would weighing the Casimir vacuum (relativ to outside the plates) confirm this and would it yield the difference of the energy density?

I expect so, yes.

 

[timmdeeg]

I appreciate your helpful answers, thanks.