We still don't understand magnetism

Overview

This episode dives into the fascinating history and implications of potentials in physics, exploring their evolution from mathematical tools to potentially fundamental aspects of reality. It covers the three-body problem, the development of potentials, the groundbreaking Aharonov-Bohm effect, and its implications for quantum mechanics and gravitational physics.

Notable Quotes

- The magnetic field could be just zero, and yet the presence of some vector potential could actually lead to observable effects. That wasn't supposed to happen, right? – On the surprising implications of the Aharonov-Bohm effect.

- Individual people can challenge entire paradigms. – Reflecting on how Aharonov and Bohm defied conventional physics.

- A is as real as B – realer, whatever that means. – Richard Feynman, on the physical significance of potentials.

🪐 The Three-Body Problem and Lagrange's Innovations

- The three-body problem, a centuries-old challenge, involves predicting the motion of three gravitationally interacting bodies. Unlike the solvable two-body problem, the three-body system is chaotic and unsolvable in general terms.

- Joseph Louis Lagrange introduced the concept of gravitational potential, simplifying calculations by converting vector-based problems into scalar-based ones. This led to the discovery of Lagrange points, regions of gravitational equilibrium.

- Lagrange's work laid the foundation for modern mechanics, including the Lagrangian approach, which simplifies complex systems like the double pendulum.

🌀 The Curl and Magnetic Potentials

- Magnetic fields differ fundamentally from gravitational and electric fields due to their looped nature, requiring a new mathematical approach.

- William Thompson (later Lord Kelvin) introduced the concept of curl to describe the relationship between magnetic fields and their potentials. This innovation revealed that magnetic vector potentials (A) could simplify calculations, much like gravitational and electric potentials.

⚛️ The Aharonov-Bohm Effect: A Quantum Revolution

- David Bohm and Yakir Aharonov proposed that potentials, not fields, directly influence quantum particles. Their theoretical experiment showed that even in regions with zero magnetic field, the vector potential could alter the phase of an electron's wave function.

- The Aharonov-Bohm effect was experimentally confirmed, most notably by Akira Tonomura in 1986, using a toroidal magnet to eliminate stray fields. This demonstrated that potentials could have physical effects, challenging long-held assumptions in physics.

🔍 Interpretations and Debates

- Physicists are divided into two camps:

- Camp 1: Potentials are physical and fundamental, possibly more so than fields.

- Camp 2: Fields remain primary, but they may act non-locally, influencing regions beyond their immediate presence.

- A third interpretation suggests that quantum particles explore all possible paths, interacting with fields in unexpected ways. This perspective aligns with quantum mechanical path integrals.

🌌 Gravitational Aharonov-Bohm Effect

- In 2022, researchers demonstrated a gravitational analog of the Aharonov-Bohm effect. Using ultra-cold rubidium atoms and a tungsten mass, they observed phase shifts in the atoms' wave functions caused by gravitational potentials, even in the absence of gravitational fields.

- This finding suggests that both electromagnetic and gravitational potentials can influence reality at the quantum level, challenging traditional physics paradigms.