### The Casimir effect: a force out of nowhere?

The Casimir effect is an excellent example of the sad state of postmodern theoretical physics. I will show in this post why this effect cannot be used to prove the existence of the speculative quantum vacuum.

The Casimir effect is the phenomenon of attraction between two nearby uncharged parallel conducting plates. The corresponding force is called the Casimir force.

According to folklore, this force is "caused by quantum vacuum fluctuations of the electromagnetic field" and is often invoked as proof of the existence of the quantum vacuum [1,2]. This is wrong for at least three reasons. First, the term "quantum vacuum" is a misnomer because it is anything but empty. Second, the claim that the "arrival of quantum mechanics" completely changed our notion of the concept of vacuum is physically and historically incorrect, because there is no vacuum in quantum mechanics and the concept of quantum vacuum was introduced with quantum field theory [3]. Third, and perhaps most relevant to this post, Casimir forces are not caused by fluctuations in any quantum vacuum.

Recent research [4] shows that the vacuum evaluation of the Hamiltonian term commonly associated to the electromagnetic field cannot produce the needed force unless tricks are applied to change some functional dependencies of the quantities involved in the calculation. Alternative calculations of the Casimir force without reference to zero-point energies are not new [5]. The Casimir effect can be explained using relativistic van der Waals forces. Using a generic particle-particle potential of the type

$V = -\frac{B}{r^\gamma} ,$

where $$B$$ and $$\gamma$$ are parameters, and $$r$$ is the distance between particles, we can derive the force $$F$$ between two parallel dielectric plates with $$N$$ particles, area $$A$$, and separated by a distance $$d$$.

$F = \frac{2\pi BN^2}{(\gamma - 2) (\gamma - 3)} \frac{A}{d^{\gamma - 3}}$

For the relativistic van der Waals potential, $$\gamma = 7$$, and we obtain the characteristic $$d^4$$ dependence of the Casimir force. The parameter $$B$$ depends on the fine structure constant, but the commonly cited expression [1,2] for the Casimir force does not. The reason for this omission is that the derivation of the expression from field theory is based on idealizing the metallic plates as perfect conductors before imposing boundary conditions on the electromagnetic field. The expression we obtained, however, includes "finite conductivity corrections" [5] to the ordinary Casimir effect.

It is really interesting that Astrid Lambrecht mentions [1] how Lifshitz and Schwinger studied the temperature dependence of the Casimir force, but does not mention that both authors concluded that this force is not a consequence of any vacuum. The last part of [1], where Astrid Lambrecht claims that high-precision measurement of the Casimir effect could be used to prove the existence of the extra dimensions associated with string theory, is the typical postmodern nonsense published by Physics World. Similar nonsense can also be found in Michio Kaku’s latest popular book, but that book has a proper answer in my detailed Review of the God equation.

## REFERENCES AND NOTES

1. https://physicsworld.com/a/the-casimir-effect-a-force-from-nothing/
2. https://math.ucr.edu/home/baez/physics/Quantum/casimir.html
3. Despite a common misconception, quantum field theory and quantum mechanics are incompatible theories. Most physicists omit that quantum mechanics is not the nonrelativistic limit of quantum field theory; notable exceptions were Dirac and Landau. Some quantum field theory textbooks mention some of the differences from quantum mechanics.
4. Proof that Casimir force does not originate from vacuum energy.
5. Casimir effect and the quantum vacuum.