- How did Einstein apply Planck's quantum hypothesis to explain the heat capacity of solids?
- Why was this the first successful application of quantum ideas to matter rather than light?
Quantum Mechanics
The foundational theory of matter and energy at small scales.
- How did the two clouds Kelvin described end up resolving into quantum mechanics and relativity?
- How did Niels Bohr's 1913 atomic model later explain the regular pattern Lyman had observed in 1908?
- Why did the Geiger counter make it possible to observe radioactive decay as discrete quantum events rather than bulk averages?
- What pattern in the measured charges told Millikan that electric charge came in discrete units?
- How did the gap in Wien's formula give Planck the opening to introduce the quantum hypothesis in 1900?
- What rule did Bohr impose on electron orbits to keep atoms from collapsing?
- In what sense was the Bohr model later shown to be wrong even though it worked so well?
- Which of Sommerfeld's quantum numbers survived the transition to full quantum mechanics?
- What are the three ways Einstein described an atom interacting with light in his 1917 paper?
- What was the ultraviolet catastrophe that Planck was trying to fix?
- Why did Planck call his own quantum assumption a 'formal trick' and an 'act of desperation'?
- How does the idea that energy comes in discrete quanta connect to modern technologies like lasers and transistors?
- Why did Planck's Nobel Prize arrive eighteen years after his original 1900 insight?
- What is the Stark effect, and how does a strong electric field split an atom's spectral lines?
- Why did light below a certain threshold frequency fail to eject electrons no matter how bright the lamp?
- How did the discovery that light arrives in discrete packets make quantum mechanics unavoidable?
- How did Bohr's model restrict electron orbits compared to what classical physics would allow?
- Why did Bohr encourage younger physicists like Heisenberg and Pauli to replace his own model?
- Why did precise X-ray wavelength measurements matter for testing quantum theories of atomic structure?
- What is a Bose-Einstein condensate, and how does it behave differently from ordinary matter?
- How long did it take physicists and the Nobel committee to recognize what the 1914 experiment had shown?
- What exactly does the Pauli exclusion principle forbid two electrons in an atom from doing?
- How does the exclusion principle explain the structure of the periodic table, like why noble gases are inert?
- Why does the exclusion principle explain why solid matter resists being compressed?
- How did Pauli arrive at the exclusion principle if not through a theoretical derivation?
- Why did Heisenberg travel to Heligoland in June 1925, and how did that trip lead to matrix mechanics?
- What was wrong with the existing quantum theory that Heisenberg was trying to fix?
- What kind of quantities did Heisenberg insist his new theory be built only from?
- Who helped Heisenberg turn his ideas into the complete formal framework of matrix mechanics?
- How did Schrödinger's equation describe electrons differently from the classical picture of particles orbiting a nucleus?
- What did it mean for physics that wave mechanics and Heisenberg's matrix mechanics turned out to be mathematically equivalent?
- Why did physicists find the wave picture of quantum mechanics more intuitive to work with than the alternatives?
- How did Schrödinger's 1925 Christmas holiday in Arosa lead to the most productive stretch of his career?
- What does squaring the amplitude of a wave function actually tell you about where a particle will be found?
- Why did Born's interpretation of the wave function overturn the idea that the universe is fully deterministic?
- Why did Einstein object to Born's probabilistic reading of quantum mechanics for the rest of his life?
- Why did Born wait until 1954 to receive a Nobel Prize for an idea proposed in 1926?
- What discredited the classical, continuous-wave picture of radiation?
- What exactly does the uncertainty principle say about position and momentum?
- Why isn't quantum uncertainty just a limitation of measuring instruments?
- What role did Niels Bohr play in refining Heisenberg's 1927 paper?
- How old was Heisenberg when he formulated the uncertainty principle?
- What did de Broglie's formula λ = h/p claim about particles like electrons?
- Why can't position and momentum both be precisely known for a particle, according to the uncertainty principle?
- How did Heisenberg's matrix framework replace the classical picture of electron orbits?
- Why was Heisenberg's 1932 Nobel Prize awarded for work he had done seven years earlier, in 1925?
- What modern technologies trace their existence back to the development of quantum mechanics?
- What does the Schrödinger equation actually describe if not the exact location of a particle?
- Why is the Schrödinger equation considered foundational to modern chemistry and semiconductor physics?
- Why did Rabi's precise measurements of nuclear spin matter for testing quantum theory in the 1930s?
- What does the Pauli exclusion principle actually state about electrons in an atom?
- Why would matter lose its rigidity and become compressible without the exclusion principle?
- Why did the Nobel Committee wait twenty years after Pauli's 1925 proposal to award the prize?
- What was the 'Pauli effect' that colleagues joked about?
- What problem with the radiation spectrum of a heated black body led Planck to propose that energy comes in discrete packets?
- Why did Planck initially regard his own quantum hypothesis as a mathematical trick rather than a physical truth?
- How did Einstein, Bohr, Heisenberg, and Schrödinger each build on Planck's original idea of quantized energy?
- What did Max Born's interpretation of the squared amplitude of Schrödinger's wavefunction actually claim about where a particle is?
- Why did Einstein resist Born's probabilistic interpretation of quantum mechanics, and how did that argument get resolved?
- Why did Born receive his Nobel Prize nearly three decades after the papers it was awarded for?
- Why did Pauli himself doubt the neutrino could ever be detected?
- How did Erwin Schrödinger's 1926 wave equation reframe quantum particles as probability distributions rather than points on trajectories?
- What point was Schrödinger's cat thought experiment originally meant to illustrate about the Copenhagen interpretation?
- In what practical fields, such as chemistry and semiconductor design, is the Schrödinger equation still used today?
- How did Bohr's 1913 atomic model explain electrons jumping between discrete energy levels?
- What is the principle of complementarity, and why did it matter for interpreting quantum mechanics?
- What did Einstein, Podolsky, and Rosen argue in 1935 about hidden variables and quantum mechanics?
- What did John Stewart Bell's 1964 proof show about any local hidden-variable theory?
- How did later experiments by Clauser, Freedman, and Aspect test and violate Bell's inequalities?
- What does it mean to say Bell's theorem turned a philosophical argument into an experimentally testable one?
- How does shining polarised light on a group of atoms let physicists sort them by quantum spin state?
- What did the Stern-Gerlach experiment demonstrate about the angular momentum of silver atoms?
- What is Samuelson's correspondence principle, and how does it link stable equilibria to testable predictions?
- How did Van Vleck's earlier work explain how magnetic moments arise and interact within matter?
- Why did the pairing mechanism in helium-3 require theorists to extend existing frameworks of quantum order?
- Why does cooling atoms to near absolute zero make quantum effects easier to observe?
- Why did solving Schrödinger's equation directly for a many-electron molecule become computationally hopeless as atoms were added?
- What claims did Deepak Chopra make about quantum mechanics underpinning consciousness and healing?
- Why did the Ig Nobel committee single out Chopra's use of quantum terminology specifically for its tenuous relationship to actual physics?
- Why did Abrikosov and Ginzburg's theory of quantised magnetic filaments make high-field superconducting magnets possible?
- What makes superfluid helium-3 behave so differently from an ordinary liquid?
- Why does observing a quantum system normally destroy the superposition being studied?
- What did John Bell's 1964 theorem propose as a way to test whether hidden variables underlie quantum mechanics?
- How did Alain Aspect's experiments close the loopholes left open by Clauser's original 1972 test?