What are the six numbers that allow life to exist?

A Goldilocks universe

The values of many fundamental constants appear to lie within narrow boundaries that allow life to exist. In 2000, the UK's Astronomer Royal Martin Rees boiled them down to six in his book Just Six Numbers

 

First number

N, the ratio of the strengths of two fundamental forces, electromagnetism and gravity
Value
about 10³⁶
In what way is it fine-tuned?
N determines the minimum size of sun-like stars. It tells us how big an object must be before its gravity can overcome the repulsive electromagnetic forces that keep atomic nuclei apart, igniting nuclear fusion. A larger value would not matter very much, but if N were lower, stars would be smaller and burn through their fuel more quickly, making the evolution of life unlikely.

 

Second number

ε, the proportion of the mass of a hydrogen atom that is released as energy when it is fused into helium inside a star
Value
0.007         
In what way is it fine-tuned?
The fusion of hydrogen into helium is the first step in forming heavier elements and thus makes complex chemistry, and life, possible. If ε were slightly smaller, nuclear fusion would be impossible and the universe would consist only of hydrogen. If it were slightly larger, all the universe's hydrogen would have been consumed during the big bang and stars would not exist.

 

Third number

Ω, the ratio of the actual density of matter in the universe to the theoretical "critical density" which would cause the universe to collapse eventually under its own gravity
Value
about 0.3         
In what way is it fine-tuned?
Ω is one of the factors that determines how fast the universe expands. If it were higher, the universe would have collapsed long ago; if it were lower, expansion would have been too rapid to allow stars and galaxies to form.

 

Fourth number

λ, the cosmological constant, or the energy that arises from quantum fluctuations of the vacuum
Value
about 0.7         
In what way is it fine-tuned?
λ is the leading contender for the mysterious force that is accelerating the expansion of the universe. A smaller value would not be a problem, but if it were much larger the universe would have expanded so rapidly that stars or galaxies would not have had time to form.

 

Fifth number

Q, the amount of energy it would take to break up a galactic supercluster as a proportion of the total energy stored in all of its matter
Value
about 10^-5
In what way is it fine-tuned?
Q is a proxy measure of the size of the tiny fluctuations in the early universe that were eventually amplified into stars and galaxies. If it were smaller the universe would be inert and structureless; larger and the universe would be dominated by black holes by now. Neither case would support life.

 

Sixth number

D, the number of spatial dimensions
Value
3             
In what way is it fine-tuned?
With four spatial dimensions the orbits of planets would be unstable, while life would be impossible with just two.

• From issue 2822 of New Scientist magazine, page 34-35.