131 The Yukawa Particle and the Heisenberg Uncertainty Principle Revisited

Yukawa's Revolutionary Idea

By the early 1930s, physicists understood that protons and neutrons were held together inside atomic nuclei by the strong nuclear force. Although this force is much stronger than the electrical repulsion between positively charged protons, it acts only over extremely short distances—approximately the diameter of an atomic nucleus. Explaining why the force was both so strong and so short-ranged became one of the central problems of nuclear physics.

In 1935, Japanese physicist Hideki Yukawa proposed an elegant solution. He suggested that forces are transmitted through the exchange of particles, now called carrier particles. Rather than acting instantaneously across empty space, particles continuously exchange these carriers, producing the attractive or repulsive forces observed in nature. This idea became one of the foundations of modern particle physics and, in more sophisticated forms, is now used to describe all of the fundamental interactions.

Virtual Particles and the Heisenberg Uncertainty Principle

Yukawa predicted that the carrier of the nuclear force would be a previously unknown particle, now called the pion. Because the pion has mass, creating one requires energy. Under ordinary circumstances, the law of conservation of energy prevents particles from appearing spontaneously. However, quantum mechanics allows very small, temporary violations of energy conservation, provided they occur over extremely short time intervals.

This behavior is described by the Heisenberg uncertainty principle, which relates the uncertainties in energy and time:

Here, h is Planck's constant. A larger uncertainty in energy may exist only for a correspondingly shorter time. If a particle of mass m is created temporarily, the required energy is approximately

As a result, heavier particles can exist only for very short times before disappearing. During this brief interval, the particle can travel only a limited distance—approximately

where c is the speed of light. These short-lived particles are called virtual particles. They cannot be detected directly because they exist only temporarily, but their effects can be measured through the forces they produce. Yukawa realized that the short range of the strong nuclear force could therefore be used to estimate the mass of the particle responsible for transmitting it.

Discovery of the Pion

When Yukawa proposed his theory in 1935, no particle matching his prediction had been observed. If his model was correct, however, sufficiently energetic collisions should be capable of producing real pions that could be detected experimentally.

In 1947, pions were discovered in cosmic-ray experiments, and only a few years later they were routinely produced in particle accelerators. Three varieties of pions were identified: the positively charged [latex]\pi^+[/latex], the negatively charged [latex]\pi^-[/latex], and the neutral [latex]\pi^0[/latex]. Their measured masses—approximately 140 MeV/[latex]c^2[/latex] for the charged pions and 135 MeV/[latex]c^2[/latex] for the neutral pion—were remarkably close to Yukawa's original prediction.

Because their masses lie between those of electrons and nucleons, pions belong to a family of particles called mesons. Today the term meson refers to an entire class of particles composed of one quark and one antiquark.

Around the same time, physicists also discovered another particle with a mass of about 106 MeV/[latex]c^2[/latex]: the muon. Initially, researchers thought the muon might be Yukawa's predicted particle because its mass was similar. However, experiments soon showed that muons do not participate in the strong nuclear force, ruling them out as the force carrier. This surprising discovery prompted physicist Isidor I. Rabi to famously ask, "Who ordered that?" The quote has become one of the best-known remarks in particle physics and reflects how unexpected new particles often challenge our understanding of nature.

Section Summary

• Hideki Yukawa proposed that forces can be transmitted through the exchange of particles, introducing the concept of carrier particles.
• To explain the short range of the strong nuclear force, Yukawa predicted the existence of a particle called the pion, which is exchanged between neighboring protons and neutrons.
• The Heisenberg uncertainty principle allows temporary fluctuations in energy over very short time intervals, making the brief existence of virtual particles possible.
• Virtual particles cannot be observed directly, but their effects can be measured through the forces they produce.
• Using the measured range of the strong nuclear force and the uncertainty principle, Yukawa estimated the pion's mass to be approximately 100 MeV/[latex]c^2[/latex], remarkably close to the experimentally measured value.
• Pions were discovered in 1947, providing strong experimental support for Yukawa's theory and helping establish the modern field of particle physics.
• Today, the interaction between nucleons is understood as a residual strong force that can be modeled by meson exchange, while the fundamental strong interaction between quarks is mediated by gluons.