Tuesday, November 29

# Eddington, Dirac and the possibility that fundamental constants are not really set in stone

“There are two types of constants: apparent and real. The apparent constants result simply from introducing arbitrary units, but they can be eliminated. Real constants are real numbers that God must have arbitrarily chosen when he deigned to create this world. This quote has been extracted from one of the letters that Albert Einstein sent to his former student and colleague Ilse Rosenthal-Schneider, and it reflects very well the role that universal constants have in current theories of physics.

In the domain of science, a physical constant is the value acquired by a certain magnitude involved in physical processes that has a fundamental characteristic: remains unchanged over time. That value is expressed in a specific unit prefixed in a system of units that can vary over time and with the development of science. We currently use the International System of Units created in 1960, but throughout history the same physical magnitude has not always been described using the same units.

The enigmatic nature of the fundamental constants stems from our inability to fully understand the physical processes in which they are involved.

The constants that we are going to talk about in this article, the fundamental ones, are closely linked to essential natural phenomena. Scientists have managed to measure them more precisely as science has developed, but, paradoxically, none of them have been able to explain where does the value come from of a single fundamental constant. These magnitudes cannot even be calculated from the value of other constants.

The enigmatic character of the fundamental constants has its origin in our inability to fully understand the physical processes in which they are involved. As I mentioned a few lines above, scientists have been able to measure them, and they are doing so more and more precisely, but nobody knows where they come from. Why do they have that value and not another?

Some fundamental constants The ones we are all somewhat familiar with are the speed of light in a vacuum, the elemental charge, and the gravitational and Planck constants, but there are others. Many others. In this table we collect only some of them:

Constant

symbol

worth

Unit

gravitation

G

6.67384 (80) 10⁻¹¹

m³kg⁻¹s⁻²

speed of light in a vacuum

c

299 792 458

ms⁻¹

Planck’s constant

h

6.62606957 (29) 10⁻³⁴

js

elemental charge

and

1.602176565 (35) 10⁻¹⁹

C

magnetic constant

µ₀

4π 10⁻⁷

NA⁻²

electrical constant

ε₀

1/µ₀c²

Fm⁻¹

electron mass

mₑ

9.10938291 (40) 10⁻³¹

kg

proton mass

mₚ

1.672621777 (74) 10⁻²⁷

kg

N(A)

6.02214129 (27) 10²³

mol⁻¹

boltzmann’s constant

k

1.3806488 (13) 10⁻²³

JK⁻¹

## Eddington, Dirac and the suspicion that hangs over universal constants

British astrophysicist Arthur Stanley Eddington made very important contributions to scientific development during the first half of the 20th century. One of them, and probably the one for which he is best known by the non-specialized public, was experimental verification of the General Theory of Relativity that Einstein had published four years earlier thanks to his observations of the solar eclipse of May 29, 1919.

During his professional career, Eddington played many styles, and one of them is deeply intertwined with the subject we are talking about. This scientist was convinced that a complete theory of physics should be able to explain the origin of the fundamental constants. He considered that measuring them, knowing their value, was not enough, and also that mathematics provided us with the tools we needed to understand their origin.

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Many other physicists of his time shared his dissatisfaction with regard to the curiosity to reveal the origin of the fundamental constants, but argued that in order to know it, it was necessary to better understand natural processes in which they are involved. However, Eddington decided to use mathematics to show why the constants had these values ​​and not others.

At first his colleagues, including Einstein himself, examined his proofs with curiosity and respect, but they soon realized that Eddington was resorting to far-fetched mathematical constructs and unclear reasoning. I was somehow playing with the numbers in an artificial way until he was able to conjecture what he wanted to prove. Little by little, the interest of the scientific community in this part of his work faded, but in a certain way it prompted other academics to wonder about the true nature of the fundamental constants.

In his 1937 article, Dirac pointed out the possibility that the universal gravitational constant had varied with the passage of time.

British mathematician and engineer Paul Dirac was one of them. He observed that many of the fundamental constants were described by very large numbers between which there was a certain relationship. There was some kind of coherence between them, which led him to conjecture that it must be some simple mathematical relationship to explain them. One of the many relationships he explored led him to compare the size of the visible universe, which is staggeringly large, and that of the electron, which is staggeringly small.

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But his most cathartic conclusion was not that. His analysis led him to publish in 1937 an article in the then prestigious scientific journal Nature in which he pointed out the possibility that the constant of universal gravitation would have changed over time. What Dirac was suggesting is that perhaps the universal constants have not been the same during the nearly 14 billion years of the universe.

His approach proposed looking at the laws of physics from a different, perhaps unifying, perspective. He even allowed us to glimpse that life was only possible in a universe in which the fundamental constants had acquired the value what do they have in ours. At first Dirac was not taken seriously, but little by little some of his colleagues realized that his explanation was so elegant that it should be considered. And more than eight decades later, his work in this area continues to serve as a source of inspiration for hundreds of scientists around the world.

Cover image: Arek Socha on Pixabay

Bibliography: ‘The Feynman Lectures on Physics’, Richard Feynman, Matthew Sands and Robert Leighton | ‘The universal constants’, Jesús Navarro | ‘Fundamental Constants in Mathematics & Physics: Are they universal codes?’, Shahin A. Shayan