Yukawa Mind

Hideki Yukawa and physics

Physics in the Yukawa era and the meson theory (5) Yukawa’s theory of mesons

Quantum mechanics and the theory of relativity

In the field of physics at the beginning of the 20th century, another breakthrough, Einstein’s theory of relativity, occurred just about when quantum mechanics was established. According to the special theory of relativity developed and proposed by Einstein in 1905, time and space is the same “spacetime” but viewed from different viewpoints. The advent of the special theory of relativity destroyed the concept of absolute time and absolute space that physicists believed in after Newton’s discovery.

However, an issue emerged soon after the establishment of quantum mechanics: Quantum mechanics was not consistent with the special theory of relativity. The quantum mechanics originally constructed by Heisenberg and Schrödinger did not take the consistency with the theory of relativity into consideration, so many physicists at that time strove to expand quantum mechanics and ensure its consistency with the theory of relativity but to no avail.

In 1928, Dirac announced the Dirac equation, which theoretically described the independently existing electrons and protons and satisfied both quantum mechanics and the special theory of relativity. As a result, the prospect of satisfying both the special theory of relativity and quantum mechanics in describing the motions of electrons and protons came into sight. According to that theory, the electron and proton, which behave according to the Dirac equation, toss a photon back and forth, and this results in an electromagnetic interaction. As mentioned earlier, the photon exchanged in the above process has zero mass. It is important to remember that photons are particles that have no mass.

This theory, however, had various issues and there was no guarantee in the 1930s that the theory was right. It was necessary to construct a new system of reasoning called the quantum field theory in order to formulate relativistic quantum mechanics. The quantum field theory was not completed until the middle of the 1940s. Incidentally, the quantum field theory was completed by a Japanese theoretical physicist, and Shin-ichiro Tomonaga, a high school and university classmate of Yukawa, contributed significantly to the construction of the theory. In recognition of that achievement, Tomonaga became the second Japanese to receive a Nobel Prize in Physics following Yukawa.

Yukawa’s theory of mesons

Now, we are ready to discuss Yukawa’s theory of mesons. Let’s start.

As stated before, Yukawa’s theory of mesons deals with the unknown interaction between protons and neutrons. If only the electromagnetic force and gravitational force acted between protons and neutrons, the protons and neutrons would repel from each other and separate in no time so the nuclei cannot exist stably. That tells us that there is an attractive interaction stronger than the electromagnetic force.

From the perspective of the quantum field theory, the electromagnetic force results from the tossing of a photon with no mass back and forth as I explained when I introduced Dirac’s theory previously. Likewise, the universal gravitation can be understood as a force resulting from the tossing of a particle called a graviton back and forth. The graviton is also a particle that has no mass.

The electromagnetic force and universal gravitation occur as a resulting of the exchange of a particle with zero mass. Why do the particles that mediate the interaction have no mass? Why don’t particles with masses mediate the interaction? Isn’t the force that acts between protons and neutrons mediated by such a particle? Those are the questions that inspired Yukawa to work on his theory.

The calculations of the interaction caused by the particle with a mass showed that the intensity of the interaction decreased sharply at a certain distance and the interaction practically had no effect when the distance became greater. When the distance at which the force got weaker was inversely proportional to the mass of the particle that was exchanged. The greater the mass was, the shorter the effective distance of the interaction. The interaction that has the abovementioned characteristic is presently called the Yukawa interaction.

The calculations showed that the characteristics of the Yukawa interaction were exactly the characteristics to be had by the force that acted between protons and neutrons. At a short distance, the interaction provided the strong force to overcome the electromagnetic force and keep the protons and neutrons in the nucleus, but the force decreased significantly as the distance increased. This explained why this new force could not be observed in the natural phenomena that occurred around us. In view of that, Yukawa theorized that the force resulting from the interaction caused by the exchange of the unknown particle was the force that acted between protons and neutrons. He posited that if that kind of force existed, particles having a mass should inevitably exist. He predicted the existence of such particles and named them mesons.

The explanation given so far may not accurately convey the impact that Yukawa’s theory had. The theoretical foundation was not solid in the 1930s when the theory postulating that the interaction was mediated by the exchange of a particle was just introduced. In those years, only the interactions caused by particles without a mass, namely the electromagnetic force and gravitational force, were known. Therefore, Yukawa’s theory was a very original, innovative and bold proposal.

Since the new interaction proposed by Yukawa can affect only a space as small as a nucleus, the mass of meson can be estimated. In nuclear physics, the unit of measurement, MeV (pronounced as “em ee vee”), is often used. Yukawa predicted the mass of meson to be approximately 100 MeV based on the characteristics of the nuclei known at that time. The mass of electron is approximately 0.5 MeV and the mass of proton is approximately 940 MeV. Since the mass of Yukawa’s particle was halfway between the mass of electron and that of proton, the particle was named the meson. The meson discovered in an experiment 12 years after the announcement of Yukawa’s theory had a mass of about 140 MeV, very close to the value predicted by Yukawa. Yukawa’s conjecture was supported by the experiment results.

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Physics in the Yukawa era and the meson theory (6) Yukawa’s theory and its future effect
Available on March 18 (Wednesday), 2020

(Written by Masakiyo Kitazawa)