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Just Six Numbers

September 7, 2013

Just Six Numbers by Martin Rees

“Just Six Numbers” is a very accessible book about how some universal constant values were exactly required for the development of complex life.

Ν ≈ 10^36 is the ratio of the strength of the electromagnetic and gravity forces. This number is why in chemistry gravitational attraction between atoms and particles are ignored. If N was smaller like 10^30, there would be no stable planetary systems because of more frequent stellar interactions, and the increased power of gravity would cause more massive objects to collide forming more black holes and neutron stars. On a smaller scale, as an example even insects would require larger legs because the ability of legs to resist gravity is based on the chemistry (electromagnetic force).

ε ≈ 0.007 is the fraction of the mass of 4 protons released as energy when fused into helium. If this value was 0.006 then deuterium would be an unstable isotope of hydrogen, which would make fusing hydrogen into helium very difficult. Deuterium being critical for the proton-proton chain fusion in most stars. If the value was larger 0.008 then hydrogen would readily bind into heavier elements leaving virtually no hydrogen remaining. Noteworthy, is that the exactly value 0.007 is required for the formation of carbon as explained by Fred Hoyle in the Triple-alpha process.

Ω ≈ 0.3 is the ratio of the actual matter density to the critical matter density in the universe. If this value was smaller, then there would be no chance for any structure to form because the expansion of the universe would overpower gravity’s ability to create structures. If this value was bigger, then the big crunch would happen.

λ ≈ 0.7 is the ratio of the energy density due to the cosmological constant (“vacuum energy”) to the critical density of the universe. Notice that the matter+energy densities sum to approximately 1. Ω + λ ≈ 1.0

Q ≈ 10^-5 is the fraction of rest energy (mc^2) of a large structure (star, galaxy, cluster of galaxies) required to disperse the structure. If Q was smaller it would be to easy to destroy aggregate structures and galaxies would be anemic. If Q was larger, extremely large structures and collections of matter would exist and grow ultimately ending in black holes.

D = 3 is the number of observable spatial dimensions. If D = 4, then the inverse square law would become the inverse cubed law and would be far less forgiving in slight variations in orbital speed and it’s impact on a stable orbit. If D = 2, then things like a nervous system would be impossible without each pathway intersecting.

In addition to a great explanation of these six numbers and their significance, the book is filled with lots of interesting information and references.Planck length is the smallest length that has meaning because the wavelengths of photons required to probe that scale would require so much energy it would create a black hole effectively destroying it. Also, Planck time is defined in terms of Planck length: the time it takes for light traveling at c to traverse 1 planck length.

Cosmic Background Radiation keeps the void of space above absolute zero at 2.7 Kelvin.

Powers of Ten video (Youtube)

10^24 meters = 100 million lightyears

10^78 atoms in the observable universe.

10^28 atoms in the human body.

Ratio of proton to electron is approximately 1836. Ratios like this are useful scientific communication without an agreed system of measure since they use elementary particles and are dimensionless.

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