Violating unitarity in physics—allowing probabilities to diverge from a sum of one—is the most fundamental violation possible in theoretical physics, causing a physicist who violates unitarity to be 'in big big trouble'.

Maxwell's equations of electricity and magnetism predict that light exists and travels at a specific speed determined by the electromagnetic constants, and this prediction was validated experimentally to within a few percent, making it the greatest discovery in physics because it shows how to predict entirely new phenomena from first principles.

The universe is defined by two extreme scales: the largest scale is approximately 10^25 meters, defined by dark energy and the cosmic horizon beyond which we can never see due to accelerating expansion, and the smallest scale is the Planck length of approximately 10^-35 meters, the scale at which quantum gravity effects become dominant and space-time breaks down.

The universe to describe its large-scale structure requires only one number—the variation in density across space is one part in 100,000—which is fewer parameters than needed to describe a single hydrogen atom, making the universe the simplest object we know of.

A theoretical physicist is 'an imaginary person' while an experimental physicist like Art McDonald who 'builds things' is a 'real person,' reflecting the distinction that theoretical physicists work with abstract mathematical structures while experimentalists construct material apparatus to test reality.

The fundamental equation of physics (the Lagrangian of the standard model) summarizes nearly all known physical phenomena in a single mathematical expression containing Einstein's theory of gravity (spacetime curvature), Maxwell's electromagnetic theory, the weak and strong nuclear forces, and Dirac's equation for electrons, making it the most compact summary of known physics.

Paul Dirac developed an equation describing the electron as a relativistic quantum entity, leading to the prediction of antimatter and the discovery that all particles have corresponding antiparticles—one of the deepest insights in physics emerging from demanding consistency between relativity and quantum mechanics.

The ishango bone, carved 22,000 years ago in the Congo with 60 notches on each side in particular arithmetical patterns, represents the earliest evidence of mathematical thinking and the study of number patterns by humans.

The variations in temperature and density measured across the cosmic microwave background sky exhibit 'synchronicity'—all oscillations were excited simultaneously at the Big Bang and have oscillated in phase ever since, analogous to a bell struck once whose vibrations remain synchronized, which we observe through Fourier analysis of the CMB power spectrum.

If light were purely a wave as Maxwell's theory suggests, the sun and all hot objects would radiate all their energy into infinitely short wavelengths (a problem called the ultraviolet catastrophe) because there are infinitely many possible short wavelengths and thermal equilibrium would distribute energy equally among all modes, causing the sun to cool instantly—but the sun exists stably because light carries energy only in discrete packets (quanta).

The vacuum of quantum chromodynamics contains gluon fields everywhere, and these gluons are responsible for holding together atomic nuclei; without this vacuum structure, nuclei would fall apart—demonstrating that 'empty' vacuum has real physical energy.

The vacuum energy density calculated from quantum field theory (energy contributions from electron fields, electromagnetic fields, Higgs field, and gluon fields in quantum chromodynamics) sums to an incredibly tiny number—0.0000...0001 with 120 zeros—yet because vacuum permeates all space, this tiny density dominates the universe's energy budget.

Black holes form when matter collapses under gravity to create a singularity, and it is possible that singularities within black holes represent the birthplace of new universes—a speculative but mathematically permissible possibility.

In an expanding universe where space itself stretches, light waves emitted in the early universe have their wavelengths stretched along with spacetime, causing them to become increasingly redshifted as space expands, which is how we observe the light from the Big Bang today as the cosmic microwave background.

Time dilation—the slowing of time for objects moving at high velocities—is a direct consequence of relativity: observers watching a fast-moving object will measure its internal time as passing more slowly than their own, a counterintuitive but empirically confirmed effect.

In the first billionth of a second after the Big Bang, smooth acoustic waves filling space evolved into sharp shocks through nonlinear dynamics, and these shocks then collided to generate interesting physical effects including vortices and potentially gravitational waves.

Most theoretical physicists are dismayed by recent discoveries showing the universe is simpler than predicted models, because the models were predicting specific features that didn't materialize—for example, the Higgs boson was found to be 'lonely' without the many companion particles most theorists predicted would accompany it.

As a theorist, one should be happy when proven wrong because it means the idea was testable and worth discussing; if an idea cannot be proven wrong, it is not worth talking about, which makes supersymmetry predictions at the LHC valuable even if they are not detected.

Mathematics is logic crystallized, and the most proven ideas in mathematics are those derived through rigorous proof, whereas physics applies logic to the real world by discovering which mathematical rules nature actually obeys.

The Pythagorean theorem applies not only in two dimensions to triangles but also in any number of dimensions, such that for a three-dimensional box the sum of the squares of the three edge lengths equals the square of the long diagonal, and this multi-dimensional generalization becomes crucial for quantum mechanics.