Quantum mechanics is seen as challenging the idea that science provides objective descriptions of reality outside of our minds. The “measurement problem” seems to suggest that the act of observation creates the outcome that is observed. But physicist Antony Valentini argues that this picture rests on an enormous blunder by Erwin Schrödinger. After Louis de Broglie predicted the wave-like trajectories of particles, Schrödinger found the equation describing this. But whereas de Broglie envisaged particles riding on waves, Schrödinger kept the waves and threw away the particles. That single decision birthed the measurement problem—and it was completely unnecessary. Resurrect de Broglie’s original particle-based theory, Valentini argues, and we can dispel quantum mystery. Tap here for Valentini's full article.

In quantum mechanics, physical observables aren’t just numbers: they are mathematical operators acting on the wavefunction. As shown in this image, these operators transform classical variables into differential actions. For example, momentum pₓ becomes −iℏ ∂/∂x , while the Hamiltonian Ĥ (total energy E) defines the system’s energy and drives its time evolution.

The ABCs of Quantum Mechanics Here's a infographic that brings together core concepts and notation every student or enthusiast should know; from angular momentum, bound states, and Dirac notation |n⟩ to the Schrödinger equation, wavefunctions Ψ, uncertainty principle ΔxΔp, reduced mass, fine structure constant, and everything in between. A clean visual reference for the foundational language of quantum physics.

Whether imaginary numbers are indispensable features of quantum mechanics or mere mathematical conveniences affects our understanding of reality itself. “The mathematical formulation does guide what we infer about the nature of the physical world,” says philosopher of physics Jill North.

Dirac wrote it in 1928 so an electron could obey both quantum mechanics and special relativity; the γ matrices mix the components precisely as Lorentz transformations demand, while the mass term couples the two chiralities. A first-order equation for a four-component spinor that simultaneously carries energy, momentum, spin and the seed of antimatter. Gauged, the same compact line becomes the starting point of quantum electrodynamics and, with the appropriate internal symmetries, of the weak and strong interactions as well.

Penrose's claim that consciousness relies on non-computable quantum mechanics has been dismissed for decades: quantum states, critics say, collapse far too fast in a warm brain to matter. But neuroscientist Mike Wiest argues new evidence of stable quantum states at much higher temperatures means we must take the idea seriously again.