*16 May 2020*

# How constant are the constants of nature?

All of our mathematical and physical theories are built upon certain constants in nature, like the gravitational constant or the speed of light. But what makes the constants constant?

One important assumption underlying all of science is that the laws of physics are universal, being the same across the time and space of the cosmos. But what if this is not true, and the laws of physics were different in the past and will be different again tomorrow? Modern science would be rocked to its core.

The laws of physics are written in the language of mathematics, allowing us to calculate how things interact through the forces of the universe. Within this mathematics lie the “constants of nature”, numbers that determine the physics of the universe, dictating the relative strengths of forces, the action of quantum mechanics, or the masses of particles. Of these roughly twenty numbers, some, like the speed of light or Planck’s constant, are familiar. Others are more obscure, hidden deep in theories of quantum fields.

For scientists, the constants of nature have been surrounded by mystique. Without them, the laws of physics are sterile, but mathematics doesn’t predict their values. They can only be revealed through experimentation, and, despite their name, there is no particular reason why the constants are, well, constant.

## Science Check: What are the constants?

When scientists quantify their observations, the laws of nature seem to follow a certain set of numerical values that seem consistent across space and time. These values are known as physical constants and they appear to provide symmetry across the Universe - that is, a constant that can be measured on or near Earth will have the same quantity to the same constant measured off near the edge of the Galaxy in a distant cluster.

Two clear examples of this are the speed of light (c) and the gravitational constant (G). When we look out across the Universe, we can measure the speed of light to be the same everywhere, including when we are looking at the deep past. Light always travels at the same speed. Similarly, the value of gravity does not change when we observe it in far off places and previous times. These values are considered constant.

The importance of these constants cannot be understated - as theories of all observations are tested against them, and built upon them through experimentation, modeling, and simulation. These constants help define how scientists model the Universe around us.

## Physical Constants

The following table lists some (not all) of the physical constants. To see more, see this article.

Quantity | Value |
---|---|

Speed of light in a vacuum | 299 792 458 m/s |

Planck constant | 6.626 070 15 x 10^{-34} J s |

Newtonian gravitational constant | 6.674 30 x 10^{-11} m^{3} kg^{-1} s^{-2} |

Avogadro constant | 6.022 140 76 x 10^{23} mol^{-1} |

Fine structure constant | 7.297 352 5693 x 10^{-3} |

Stefan-Boltzman constant | 5.670 374 419 x 10^{-8} W m^{-2} K^{-4} |

Faraday constant | 96 485.332 12 C mol^{-1} |

Molar mass of Carbon-12 | 11.999 999 9958 x 10^{-3} mol^{-1} |

Vacuum electric permittivity | 8.854 187 8128 x 10^{-12} F m^{-1} |

Vacuum magnetic permittivity | 1.256 637 062 12 N A^{-2} |

Elementary charge | 1.602 176 634 x 10^{-19} C |

Boltzman constant | 1.380 649 x 10^{-23} J K^{-1} |

## The dimensionless number - fine-structure constant

In the 1930s, the great physicist, Paul Dirac, pondered this question as to why the constants are constant. Through an almost numerological argument, he argued that Newton’s gravitational constant, which calibrates the strength of gravity, could have changed over cosmic history, being stronger in the past, and weaker in the future. Searches for a changing gravitational constant have yielded null results.

The search continues, with Australian astronomers and collaborators peering deep into the universe to hunt down changes in the constants. Their target is the fine-structure constant, a dimensionless number, without units, which is related to the strengths of the electromagnetic force. Its value of almost exactly 1/137 has led many great minds, including Eddington, Pauli, Born, and Feynman, to wonder about its value, verging on numerology.

## Quasars step in

The astronomers realised that as light travels across the universe, its interaction with matter is determined by the fine-structure constant. Targeting quasars, hyper-luminous black holes that can be spied across the universe, they search for the tell-tale signature of absorption by intervening atoms, allowing them to measure the strength of the fine-structure constant billions of years in the past when the light and matter interacted.

The measurements are not easy, as the impact of a changing fine structure constant is subtle, with observations over several decades producing a confusing picture where no definitive measurement of change of the fine-structure constant over time. Their most recent observations focused upon quasar J1120+0641, whose light has travelled over 13 billion years to reach us. Again, they found that the observations don’t indicate a change in the fine-structure constant. Case closed?

Not quite. In 2010, the astronomers found that if they carved up their quasars into two samples, the fine-structure constant is systematically different on opposite sides of the sky. This “dipole” signal is completely unexpected, fitting nowhere in our scientific theories. This has led some to discount the idea of a spatially varying fine-structure constant, suggesting that the signal is too weak to be conclusive, but others wonder if this is revealing something new about the fundamental nature of the universe. Time, and more observations, will tell.

The paper appears on the Journal of Science Advances