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The Proton-Neutron Mass Difference Illustrates Fine-Tuning

Our daily lives depend on neutrons, protons, and electrons. These building blocks of atoms determine how those atoms behave, how long they last, and so many other things. Although protons and neutrons both exceed the mass of electrons by almost a factor of 2,000, the relatively tiny difference in mass between protons and neutrons plays a critical role in our existence. Here’s how.

In units that physicists prefer to use (MeV), neutrons, protons, and electrons have masses of 939.566, 938.27, and 0.511, respectively. This gives a mass difference (Δm) between protons and neutrons of 1.293 MeV, or 2.53 times the mass of an electron. Assuming Δm could change, any changes would radically alter the structure of the universe.1

Δm smaller than the electron mass (around a third of the actual value of Δm) means a neutron is a lower-energy configuration than a proton plus an electron. Thus, protons and electrons would combine to produce neutrons and neutrinos until there were no protons left in the universe! (Keep in mind that the number of particles with a positive charge—mostly protons—and those with a negative charge—mostly electrons—in the universe today match to better than one part in 1037 and likely are exactly the same). Without protons, no atoms could exist—that condition is obviously bad for life.

Even a hypothetical Δm greater than the electron mass, but smaller than its own actual value, diminishes the conditions necessary for life. In this scenario, processes in the early universe (when temperatures were much higher) will convert protons into neutrons more efficiently. For Δm, the neutron-to-proton ratio just before the epoch of big bang nucleosynthesis (BBNS) was 1:7. This ratio resulted in a universe with 75 percent hydrogen and 25 percent helium after BBNS. A Δm between 0.5 and 1.0 MeV results in a larger neutron-to-proton ratio before BBNS and, consequently, a greater fraction of the hydrogen converts into helium. For a neutron-to-proton ratio between 1:1 and 2:1, virtually no hydrogen remains. Again, such a scenario is obviously bad for life.

Similarly, a Δm larger than its actual value also affects the universe’s capacity to support life. Virtually all elements heavier than helium formed in the hearts of stars. However, because neutrons outside of a nucleus decay in a few minutes, the formation process requires two hydrogen combining to create a deuterium nucleus. Given the temperatures inside stars, this reaction typically takes a billion years to happen for any two hydrogen nuclei and is the reaction that limits how quickly stars fuse hydrogen into helium. A larger value for Δm would slow this reaction even further, causing negligible amounts of elements heavier than helium (like carbon and oxygen) to exist in the universe. No oxygen means no water, and without water or carbon, life cannot exist.

While this fine-tuning of the proton-neutron mass difference has been known for a while, recent research shows how to calculate this quantity directly from the underlying theories, which is a remarkably difficult technical achievement. A simplistic model indicates that the proton should be more massive than the neutron (another detrimental scenario because protons would decay into neutrons). Neutrons and protons have components of similar mass. However, the electric charge on a proton should add an additional mass component not relevant to the neutron. Yet detailed calculations performed utilizing quantum chromodynamics (the theory describing quarks) and quantum electrodynamics (the theory describing charged particles) accurately reproduce the mass of protons, neutrons, and many other subatomic particles.2

These calculations reaffirm the fine-tuning described above. More importantly, they provide a tool to improve our understanding of many other important situations such as neutron stars and supernovae. I expect to see more evidence verifying the fine-tuning of our universe for life as scientists apply these new calculation tools in the future.

  1. Frank Wilczek, “Particle Physics: A Weighty Mass Difference,” Nature 520 (April 2015): 303–4.
  2. Sz. Borsanyi et al., “Ab Initio Calculation of the Neutron-Proton Mass Difference,” Science 347 (March 2015): 1452–55.