Editing Fine-tuned universe (section)

== Examples ==
[[Martin Rees]] formulates the fine-tuning of the universe in terms of the following six [[dimensionless physical constant]]s.<ref name=":0" /><ref name="discover nov 2000 cover story">{{cite magazine|last1=Lemley|first1=Brad|title=Why is There Life?|date=1 November 2000|publisher=Kalmbach Publishing Co.|url=https://www.discovermagazine.com/the-sciences/why-is-there-life|access-date=25 April 2025|magazine=[[Discover magazine]]|archive-url=https://web.archive.org/web/20140722210250/http://discovermagazine.com/2000/nov/cover/|archive-date=2014-07-22}}</ref>
* ''N'', the ratio of the electromagnetic force to the gravitational force between a pair of protons, is approximately 10<sup>36</sup>. According to Rees, if it were significantly smaller, only a small and short-lived universe could exist.<ref name="discover nov 2000 cover story" /> If it were large enough<!--clarify by what extent -->, they would repel them so violently that larger atoms would never be generated.
* ''Epsilon'' (''ε''), a measure of the nuclear efficiency of [[Stellar nucleosynthesis#Hydrogen fusion|fusion from hydrogen to helium]], is 0.007: when four nucleons fuse into helium, 0.007 (0.7%) of their mass is converted to energy. The value of ''ε'' is in part determined by the strength of the [[strong nuclear force]].<ref>{{cite book|last1=Morison|first1=Ian|title=Introduction to astronomy and cosmology|date=2013|publisher=Wiley|location=Hoboken, NJ|isbn=978-1118681527|chapter=9.14: A universe fit for intelligent life}}<!--|access-date=13 May 2016--></ref> If ''ε'' were 0.006, a proton could not bond to a neutron, and only hydrogen could exist, and complex chemistry would be impossible. According to Rees, if it were above 0.008, no hydrogen would exist, as all the hydrogen would have been fused shortly after the [[Big Bang]]. Other physicists disagree, calculating that substantial hydrogen remains as long as the strong force coupling constant increases by less than about 50%.<ref name=macdonald /><ref name="discover nov 2000 cover story" />
* ''Omega'' (Ω), commonly known as the [[Density parameter#Density parameter|density parameter]], is the relative importance of gravity and expansion energy in the universe. It is the ratio of the mass density of the universe to the "critical density" and is approximately 1. If gravity were too strong compared with dark energy and the initial cosmic expansion rate, the universe would have collapsed before life could have evolved. If gravity were too weak, no stars would have formed.<ref name="discover nov 2000 cover story" /><ref>{{cite AV media | author=[[Sean Carroll (physicist)|Sean Carroll]] and [[Michio Kaku]] | title=How the Universe Works 3 | volume=End of the Universe | date=2014 | publisher=Discovery Channel}}</ref>
* ''Lambda'' (Λ), commonly known as the [[cosmological constant]], describes the ratio of the density of [[dark energy]] to the critical energy density of the universe, given certain reasonable assumptions such as that dark energy density is a constant. In terms of [[Planck units]], and as a natural dimensionless value, Λ is on the order of {{val|e=-122}}.<ref>{{cite journal|arxiv=1105.3105|doi=10.1007/s10714-011-1199-1|title=The value of the cosmological constant|journal=General Relativity and Gravitation|volume=43|issue=10|pages=2555–60|year=2011|last1=Barrow|first1=John D.|last2=Shaw|first2=Douglas J.|bibcode=2011GReGr..43.2555B|s2cid=55125081}}</ref> This is so small that it has no significant effect on cosmic structures that are smaller than a billion light-years across. A slightly larger value of the cosmological constant would have caused [[spacetime|space]] to expand rapidly enough that stars and other astronomical structures would not be able to form.<ref name="discover nov 2000 cover story" /><ref name=susskind>{{cite web|last=Ananthaswamy|first=Anil|author-link=Anil Ananthaswamy|title=Is the Universe Fine-Tuned for Life? |date=7 March 2012 |url=https://www.pbs.org/wgbh/nova/blogs/physics/2012/03/is-the-universe-fine-tuned-for-life/|publisher=Public Broadcasting Service (PBS)}}</ref>
* ''Q'', the ratio of the gravitational energy required to pull a large galaxy apart to the energy equivalent of its mass, is around 10<sup>−5</sup>. If it is too small, no stars can form. If it is too large, no stars can survive because the universe is too violent, according to Rees.<ref name="discover nov 2000 cover story" />
* ''D'', the number of spatial [[dimensionality|dimensions in spacetime]], is 3. Rees claims that life could not exist if there were 2 or 4 spatial dimensions.<ref name="discover nov 2000 cover story" /> Rees argues this does not preclude the existence of [[String theory#Number of dimensions|ten-dimensional strings]].<ref name=:0 />
[[Max Tegmark]] argued that if there is more than one time dimension, then physical systems' behavior could not be predicted reliably from knowledge of the relevant [[partial differential equation]]s. In such a universe, intelligent life capable of manipulating technology could not emerge. Moreover, [[proton]]s and [[electron]]s would be unstable and could decay into particles having greater mass than themselves. This is not a problem if the particles have a sufficiently low temperature.<ref name="tegmark-dim">{{cite journal| last = Tegmark| first = Max| author-link = Max Tegmark| title = On the dimensionality of spacetime| journal = Classical and Quantum Gravity| volume = 14 | issue = 4| pages = L69–L75| date= April 1997| url = https://space.mit.edu/home/tegmark/dimensions.pdf| doi = 10.1088/0264-9381/14/4/002| access-date = 2006-12-16 |arxiv = gr-qc/9702052 |bibcode = 1997CQGra..14L..69T| s2cid = 15694111}}</ref>

=== Carbon and oxygen ===
{{Further|Triple-alpha process#Improbability and fine-tuning}}
An older example is the [[Hoyle state]], the third-lowest energy state of the [[carbon-12]] nucleus, with an energy of 7.656&nbsp;MeV above the ground level.<ref>[[Evry Schatzman|Schatzman, E. L.]], & Praderie, F., ''The Stars'' ([[Berlin]]/[[Heidelberg]]: [[Springer Science+Business Media|Springer]], 1993), [https://books.google.com/books?id=FtZ_cNTPv8gC&pg=PA125&redir_esc=y#v=onepage&q&f=false pp. 125–27].</ref> According to one calculation, if the state's energy level were lower than 7.3 or greater than 7.9&nbsp;MeV, insufficient carbon would exist to support life. To explain the universe's abundance of carbon, the Hoyle state must be further tuned to a value between 7.596 and 7.716&nbsp;MeV. A similar calculation, focusing on the underlying fundamental constants that give rise to various energy levels, concludes that the [[strong force]] must be tuned to a precision of at least 0.5%, and the electromagnetic force to a precision of at least 4%, to prevent either carbon production or oxygen production from dropping significantly.<ref>{{cite journal|last1=Livio|first1=M.|authorlink1=Mario Livio|last2=Hollowell|first2=D.|last3=Weiss|first3=A.|last4=Truran|first4=J. W.|authorlink4=James W. Truran|s2cid=4273737|title=The anthropic significance of the existence of an excited state of 12C|journal=Nature|date=27 July 1989|volume=340|issue=6231|pages=281–84|doi=10.1038/340281a0|bibcode = 1989Natur.340..281L }}</ref>