Gravitational Coupling Constant

Much like there is a coupling constant for the electromagnetic force (also called the fine structure constant), there is one for the gravitational force, called, believe it or not, the gravitational coupling constant. It is used to define the gravitational attraction between two elementary particles having some mass.


The way it is defined is as the gravity between two electrons and is a unitless quantity.

Where:

• G is the gravitation constant  (6.67x10^-11 m³/s²kg)
• m_e is the mass of an electron (9.109x10^-31 kg)
• ℏ is the Planck constant over 2π (called the reduce Planck constant, 1.05457x10^-34 J*s)
• c is the speed of light (3x108 m/s)

Compare this to the fine coupling constant which is approximately 1/137 and we can see that the electromagnetic force is 10⁴³ times stronger than the gravitational force for electrons. Depending on what elementary particles are used (proton-electron or proton-proton), the ratio between them can vary, but in all cases, the electromagnetic coupling constant is magnitudes greater than that for gravity. In Martin Rees' case, he compares the fine structure constant to the gravitational coupling constant for two protons, and the ratio is 10³⁶. Any variance of this ratio can lead to the universe not being the way we see it.


To calculate the gravitational coupling constant for two protons, replace m_e with m_p in the top equation. To calculate it for the attraction between a proton and an electron, replace one m_e with m_p.    

The Anthropic Principle

There has always been a question about why our universe is the way it is. Physics tells us that the laws of physics and the constants we measure are perfect for life to exist. If any laws were slightly different or any constants were a little smaller or larger than what they are, we would not be here to question any of this. This idea is called the Anthropic Principle and in a way, it's a circular argument. The universe is the way it is because we are here and we are here because the universe is the way it is.


Because we are here, we are able to question what makes the universe unique to allow stars, galaxies, planets, and life itself to form. Martin Rees surmised that there are six fundamental numbers that dominate the cosmos to allow the universe we see to exist. We will go over these six numbers in the following posts, but the numbers can be broken down into a variety of the four fundamental forces: the strong nuclear force, the weak nuclear force, the electromagnetic force, and the gravitational force.

1. The strong nuclear force is the force that hold the nucleus of an atom together. Without it, nuclei would not be stable because nuclei are made up of protons, which are all positively charged. This is the strongest of the four forces, but acts on the smallest scale.
2. The weak nuclear force is the force responsible for nuclear decay, the decay of subatomic particles (like the proton and neutron) and fission of atoms.
3. The electromagnetic force is the force responsible for the electron orbiting the nucleus of an atom, the existence of electromagnetic radiation, even the force between magnets.
4. The gravitational force is the force that interacts between masses. It is what keeps our feet on the surface of the Earth and what allows bodies to orbit one another. In terms of size, it is actually the weakest of the four forces, but acts on the highest scales. Because it is weaker than the electromagnetic force, it is the reason why electrons orbit the nucleus, rather than falling into the nucleus.

The six numbers that Martin Rees surmised control the cosmos are:

1. The ratio between the fine structure constant (electromagnetism) and gravitational coupling constant
2. The fraction of the mass of four protons to one helium nucleus
3. The mass density ratio
4. The energy density ratio
5. The energy required to break up the largest structures in the universe
6. The number of spatial dimensions

We will talk more about these as we continue.