Einstein's special relativity, introduced in 1905, completely revolutionized our understanding of space and time. It requires that the laws of physics are invariant under Lorentz transformations, and that time and space are relative and treated on equal footing. Einstein’s special theory of relativity has been confirmed in many experiments, including the observations of time dilation by different experimental groups. The Schrödinger's wave equation, formulated in 1926, on the other hand, is a fundamental equation describing the subatomic realm. It ushered in the era of quantum mechanics and successfully accounts for the diffraction of electrons, discrete spectra of atomic gases, particularly that of hydrogen, among many others. Two yeas later, Paul Dirac successfully obtained a relativistic wave equation, which fully accounts for special relativity in the context of quantum mechanics. In this video, we shall follow Dirac and understand his motivation and lines of reasoning that led him to his famous equation. We will derive the Dirac equation and understand why the bi-spinor or 4 components structure of the wavefunction is the minimal dimensionality to obtain a relativistic analog to the quantum wave equation. The Dirac equation also introduced conceptually difficult concepts such as negative energies solutions, the prediction of the positron, and the idea of the Dirac sea. In this video, we will use graphene to unravel some of these difficult concepts through tabletop experiments. You shall be amazed by how some of these esoteric ideas can be understood in very intuitive terms in simple experiments with graphene.
14 дек 2023
