### The quantum vacuum

We saw in a previous post that the Casimir effect cannot be used to prove the existence of the quantum vacuum. In this post, I will explain why the quantum vacuum is not a true state of emptiness and why it is an artifact of quantum field theory.

Reference [1] states:

"In the old days of classical mechanics the idea of a vacuum was simple. The vacuum was what remained if you emptied a container of all its particles and lowered the temperature down to absolute zero. The arrival of quantum mechanics, however, completely changed our notion of a vacuum. All fields – in particular electromagnetic fields – have fluctuations."

A similar misunderstanding is found in [2] and many other places. Quantum mechanics did not change our notion of a vacuum. The concept of emptyness in quantum mechanics is the same concept that is used in classical mechanics.

The modern concept of quantum vacuum was introduced by quantum field theory, but quantum field theory is not the application of quantum mechanics to fields. As Paul Dirac once wrotes, quantum mechanics and quantum field theory are two "disjoint theories". Evgeny Lifshitz, Lev Landau, and Lev Pitaevskii dedicate part of their famous Course of Theoretical Physics to explaining the differences between quantum mechanics and quantum field theory (concretely quantum electrodynamics).

Modern textbooks on quantum field theory often ignore this distinction (Franz Mandl and Graham Shaw [3] are a notable exception as they mention a fundamental difference between the two theories). One of the worst offenders is Michio Kaku's textbook because he claims that quantum field theory is the quantum mechanics of systems with an infinite number of degrees of freedom, and that "quantum field theory describes multiparticle states, while ordinary quantum mechanics is based on a single-particle interpretation." This makes no sense. An analysis of his words and the equations in his book requires another issue of this newsletter, but let us get back on topic.

## WHY IS IT NOT EMPTY?

The 'vacuum' of quantum field theory is not empty because it is not a true vacuum. Quantum field theory is based in some mistaken symmetries, including what Julian Schwinger called the "principle of space-time uniformity". This principle introduces nonphysical degrees of freedom in the description of matter and its interactions and, as a consequence, the excitations of quantum fields do not represent real particles.

Contrary to what is stated in [2], the energy levels of the quantized electromagnetic field are not "what we usually identify as different numbers of photons". The quantum of a field is only a part of the particle associated with that field. The excitation of an electromagnetic field is not a photon, the excitation of a Dirac field is not an electron, and so on. To make a real particle, the bare quantum from the excitation of a free field has to be surrounded by a 'cloud' of virtual particles from the 'vacuum' [4].

In quantum mechanics we have a correct description of the particles and when there is zero particles we recover a true vacuum. Quantum field theory lacks this correct description and needs to attribute energy, momentum, and other properties to its 'vacuum' in order to describe what we see in experiments. In short, the description of particles in quantum field theory is based in the next mathematical decomposition

And this is why the 'vacuum' of quantum field theory cannot be a true vacuum. If it was a true state of emptyness, then they theory could describe the particles that we observe in experiments. Quantum field theory and its invalid symmetries would be abandoned and replaced by a proper quantum theory of particles.

## NOTES

- https://physicsworld.com/a/the-casimir-effect-a-force-from-nothing/
- https://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html
- Quantum field theory; 2nd edition 2010: John Wiley & Sons, Ltd, Chippenham. Mandl, Franz; Shaw, Graham.
- Often the excitations of free fields are called "bare particles" (bare electron, bare photon...), but those are not the particles (electron, photon...) that we detect in experiments.