Quantum and relativity are not completely dissimilar

Difficulty level:   ★ ★ ★

The historical connections between relativity and quantum mechanics are stronger than I had realised.

Most physicists have heard of Louis de Broglie, the Nobel Prize winner who was an inspiration for the celebrated Schrödinger equation, the basic equation in quantum mechanics. However he achieved more than just the de Broglie wavelength (which one lecturer described as “the distance at which the wavelike nature of particles becomes apparent”). By requiring consistency with relativity (in technical terms, Lorentz covariance), de Broglie waves with a group velocity v must have a phase velocity c^2/v, where c is the speed of light. Hence de Broglie waves, which are a precursor of Schrödinger’s wavefunction, are solidly grounded in relativity. Tsamparlis 2019  §18.11.2 motivates them clearly.

Another point, which is well known, is that Schrödinger first tried a relativistic wave equation: the Klein-Gordon equation. Not having success, he settled for the Schrödinger equation, which is a non-relativistic limit (slow speeds). Today, the Klein-Gordon equation is viewed as an accurate description of some particles, but subject to strong limitations. Greiner 1990  §1 is an oft-cited textbook here. [Edit: I am referring to the single-particle interpretation.] (Personally, I wonder if some of those limitations can be pushed back…)

Another connection is that Einstein made greater contributions to quantum mechanics than most people had realised. It is relativity that Einstein is justly famous for, however he should also be credited as being one of the founders of quantum physics, apparently. (I must read the popular history book Einstein and the quantum .) OK, so his Nobel prize was actually for a quantum effect. But the typical view has been that Einstein didn’t really understand quantum physics, and that he was out of touch: clinging to an obsolete view of reality. But now some are revising this view, claiming Einstein’s concerns about non-locality, determinism, and whether quantum mechanics is complete or needs additions, are respectable intellectual positions. Irrespective of whether one agrees with him, Einstein had a unique and insightful perspective.

Historically, special relativity was published in 1905, whereas quantum mechanics was developed in the 1920s, so it is not unexpected the former influenced the latter. (Today, the influence should be a two-way street, of course.) The historical connections mentioned above suggest the two theories are more similar than I had realised, or at least, less dissimilar. This gives me increased hope that quantum physics and general relativity can be more fully reconciled, which has been the physics dream for a century now.

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