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Dimensionless physical constant
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=== Martin Rees's 'six numbers' === [[Martin Rees, Baron Rees of Ludlow|Martin Rees]], in his book ''Just Six Numbers'',<ref>Radford, T., [https://www.theguardian.com/science/2012/jun/08/just-six-numbers-martin-rees-review "''Just Six Numbers: The Deep Forces that Shape the Universe'' by Martin Rees—review"], ''[[The Guardian]]'', 8 June 2012.</ref> 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'' ≈ 10<sup>36</sup>: the ratio of the electrostatic and the gravitational forces between two [[proton]]s. This ratio is denoted ''α''/''α''<sub>G</sub> in Barrow and Tipler (1986). ''N'' governs the relative importance of gravity and electrostatic attraction/repulsion in explaining the properties of [[baryonic matter]];<ref name="Rees, M. 2000, p">Rees, M. (2000)</ref> * ''ε'' ≈ 0.007: The fraction of the mass of four [[proton]]s that is released as energy when [[nuclear fusion|fused]] into a [[helium]] nucleus. ''ε'' governs the [[Proton–proton chain reaction#Energy release|energy output of stars]], and is determined by the [[coupling constant]] for the [[strong force]];<ref>Rees, M. (2000), p. 53.</ref> * Ω ≈ 0.3: the [[Friedmann equations#Density parameter|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 {{nowrap|Ω ≥ 1}}, the universe may experience a [[Big Crunch]]. If {{nowrap|Ω < 1}}, the universe may expand forever;<ref name="Rees, M. 2000, p"/> * ''λ'' ≈ 0.7: The ratio of the energy density of the universe, due to the [[cosmological constant]], to the [[Critical density (cosmology)|critical density]] of the universe. Others denote this ratio by <math>\Omega_{\Lambda}</math>;<ref>Rees, M. (2000), p. 110.</ref> * ''Q'' ≈ 10<sup>−5</sup>: 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 ''mc''<sup>2</sup>;<ref>Rees, M. (2000), p. 118.</ref> * ''D'' = 3: the number of macroscopic spatial [[dimension]]s. ''N'' and ''ε'' govern the [[fundamental interaction]]s of physics. The other constants (''D'' excepted) govern the [[size of the universe|size]], [[age of the universe|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 does not have an uncertainty. 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.
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