As part of our effort to discern the top numbers of key importance within our little universe for the Big Board-little universe Project, we have begun to study the work of Lord Sir Martin Rees of Cambridge, particularly his book of the title, Just Six Numbers: The Deep Forces That Shape the Universe, 1999, Weidenfeld & Nicolson, London (173 pages)
His six numbers are:
- N, the ratio of the strength of the electrical force to the gravitational force (reviewer, Peter Roberts, Visions.
- ε (epsilon)( definition of limits?)
- Ω (omega), measures the amount of material in the universe
- λ (lambda) (?)
- Q, the degree of structure in the universe
- D, the number of spatial dimensions, 3
Here is what Wikipedia says:
“Martin Rees, in his book Just Six Numbers, mulls over the following six dimensionless constants, whose values he deems fundamental to present-day physical theory and the known structure of the universe:
- N ≈ 1036: the ratio of the fine structure constant (the dimensionless coupling constant for electromagnetism) to the gravitational coupling constant, the latter defined using two protons. In Barrow and Tipler (1986) and elsewhere in Wikipedia, this ratio is denoted α/αG. N governs the relative importance of gravity and electrostatic attraction/repulsion in explaining the properties of baryonic matter;
- ε ≈ 0.007: The fraction of the mass of four protons that is released as energy when fused into a helium nucleus. ε governs the energy output of stars, and is determined by the coupling constant for the strong force;
- Ω ≈ 0.3: the ratio of the actual density of the universe to the critical (minimum) density required for the universe to eventually collapse under its gravity. Ω determines the ultimate fate of the universe. If Ω>1, the universe will experience a Big Crunch. If Ω < 1, the universe will expand forever;
- λ ≈ 0.7: The ratio of the energy density of the universe, due to the cosmological constant, to the critical density of the universe. Others denote this ratio by ;
- Q ≈ 10−5: The energy required to break up and disperse an instance of the largest known structures in the universe, namely a galactic cluster or supercluster, expressed as a fraction of the energy equivalent to the rest mass m of that structure, namely mc2;
- D = 3: the number of macroscopic spatial dimensions.
“N and ε govern the fundamental interactions of physics. The other constants (D excepted) govern the size, age, and expansion of the universe. These five constants must be estimated empirically. D, on the other hand, is necessarily a nonzero natural number and cannot be measured. Hence most physicists would not deem it a dimensionless physical constant of the sort discussed in this entry.
“Any plausible fundamental physical theory must be consistent with these six constants, and must either derive their values from the mathematics of the theory, or accept their values as empirical.”
“A long-sought goal of theoretical physics is to find first principles from which all of the fundamental dimensionless constants can be calculated and compared to the measured values.”