Quantum Quandary

Quantum field theories are buttressed by mathematics which provide only approximations – too coarse to inspire confidence. Positronium illustrates the dilemma.

Positronium is composed of an electron, with a negative charge, circling in orbit with a positron, with a positive charge: making what’s effectively an atom without a nucleus. With just 2 particles and free of the complexities of a nucleus, positronium is appealingly simple. Its simplicity means that positronium can be used to precisely test the theory of quantum electrodynamics, which explains how electrically charged particles interact.

In 1900 German physicist Max Planck theorized that energy radiation and absorption are discrete, not continuous. A quantum leaps or drops from one energy level to another, with a tiny gap between the 2 levels.

That separation is known as Planck’s constant or Planck’s action quantum. In atomic physics that gap gives insight into the fine structure of a particle.

An experiment to measure the fine structure of positronium found a gap of 18,501 megahertz. The predicted frequency had been 18,498 megahertz – a difference from actual results of ~0.02%. Given that the estimated experimental error was only about 0.003%, that’s a wide gap.

Physicists are puzzled. The experiment was well done. There is no unknown particle to account for the discrepancy. In quantum electrodynamics (QED), making predictions involves calculating to a certain level of precision, leaving out terms that are less significant and more difficult to calculate. Those additional terms are expected to be too small to account for the miscalculation, but “it’s conceivable that you could be surprised,” says American theoretical physicist Greg Adkins.

QED is not the only particle physics theory that isn’t up to snuff. Particle physics’ grand Standard Model (SM) is a patchwork of theories that doesn’t add up and leaves out much of what has been experimentally discovered. To say that SM is “incomplete” is a compliment to how deficient it is.

The crown jewel of SM – the Higgs boson – was experimentally discovered in 2012 at an energy level far from what SM predicted. Instead, a competing theory called supersymmetry had cranked out the winning lottery number. SM was subsequently tweaked once again to cover its mistake.

As a theoretical construct, supersymmetry (SUSY) has its own problems. For one, SUSY says electrons, which are perfectly round, should be oval. Of SUSY American mathematician Peter Woit said, “The whole setup is highly baroque and not very plausible.”

The mathematics behind Nature have proven elusive. But then, Nature itself is a ruse. That’s another story (which is explained in the works of Ishi Nobu).


L. Gurung et al, “Precision microwave spectroscopy of the positronium n = 2 fine structure,” Physical Review Letters (14 August 2020).

Emily Conover, “A measurement of positronium’s energy levels confounds scientists,” Science News (24 August 2020).

Ishi Nobu, “Quanta,” in Unraveling Reality (2019).

Ishi Nobu, “Higgs boson,” in The Science of Existence (2019).

Ishi Nobu, “Supersymmetry,” in The Science of Existence (2019).