On January 4, 2025, seven of us started exploring Sean M. Carroll’s Something Deeply Hidden with a question: What does it mean to understand? Is understanding the ability to make predictions? Newton reduced motion to an object’s position and momentum, allowing classical mechanics to predict where a rock lands when someone throws it. What about air resistance or the gravitational pull of Alpha Centauri? The calculation can account for air resistance, and the gravitational pull of another star is negligible allowing the laws of motion still to make precise predictions.
Toward the end of the 19th century, physicists thought that their science solved the problems of motion and energy, and even combined electric and magnetic fields to make electromagnetic (EM) radiation. However, some phenomena could not be explained by classical mechanics. When a black body, an idealized physical object, is heated and left to cool, it radiates but never above a certain frequency. The Black Body Ultraviolet Catastrophe asks: What prevents black bodies from emitting light at higher frequencies? Planck found a constant that limits the size of a quanta packet, setting a limit to the frequency of light emitted from a black body. Furthermore, Einstein explained the photoelectric effect by theorizing that light is made of photons, quanta of discrete packets of energy. Only high-frequency EM radiation, UV, has enough energy to dislodge electrons from a metallic surface.
After Rutherford probed the structure of the atom, he proposed that electrons orbit a nucleus made of protons, as pictured on the United States Atomic Energy Commission emblem. However, according to Maxwell’s equations, electrons orbiting the nucleus in a circular path would continuously radiate energy, causing them to lose energy and eventually spiral into the nucleus. Niels Bohr used the hydrogen atom as a model and proposed electrons reside in concentric shells surrounding the nucleus. Bohr’s model predicted the wavelengths of light absorbed when an electron moves from a lower shell to a higher one, and the wavelengths of light emitted when the electrons move from a higher orbit to a lower one, matching the wavelengths found in the absorption and emission spectra of hydrogen.
Classical mechanics can determine the position and speed of satellites orbiting Earth but the same cannot be done for electrons moving within its shells around the nucleus. Heisenberg concluded no one can know both an electron’s position and speed at any particular time, forming the Copenhagen Interpretation of quantum mechanics. Schrödinger’s equation describes matter as a wave function and was a more elegant way to show Heisenberg’s Uncertainty Principle.
At the Solvay Conference on Physics in 1927, notable physicists met to debate how to interpret quantum mechanics. Bohr and Heisenberg defended the Copenhagen Interpretation as a true depiction of reality and not a mathematical contrivance. In contrast, Einstein and Schrödinger held that it was an incomplete explanation that needed another constant or a calculation, yet to be defined, to determine the position and speed of an electron at the same time.
According to Carroll, the Copenhagen Interpretation of Quantum Mechanics is taught to students and can be described in five rules: 1. Set up a wave function, psi; 2. Evolve a system using Schrödinger's equation; 3. There are certain observable quantities we can choose to measure such as position or speed; 4. The probability of getting a result can be calculated from the wave function; and 5. Upon measurement, the wave function collapses. According to Carroll, the Copenhagen Interpretation evolves smoothly and deterministically according to Schrödinger's equation as long as we are not looking and dramatically collapses when we do look. The rest of the book answers how this happens and why it matters.
We invite you to join our shared inquiry to find out how Sean M. Carroll found a meaningful point of view that will help us understand Something Deeply Hidden: Quantum Worlds and the Emergence of Space-time, QC173.96.S66 2019, on January 18, 2025, from 2 PM to 4 PM using Google Meet.
