Editing Anthropic principle (section)

== Applications of the principle ==

=== The nucleosynthesis of carbon-12 ===
[[Fred Hoyle]] may have invoked anthropic reasoning to predict an astrophysical phenomenon. He is said to have reasoned, from the prevalence on Earth of life forms whose chemistry was based on [[carbon-12]] nuclei, that there must be an undiscovered [[resonance]] in the carbon-12 nucleus facilitating its synthesis in stellar interiors via the [[triple-alpha process]]. He then calculated the energy of this undiscovered resonance to be 7.6 million [[electronvolt]]s.<ref>University of Birmingham [http://www.np.ph.bham.ac.uk/research/anthropic.htm Life, Bent chains and the anthropic principle] {{Webarchive |url=https://web.archive.org/web/20090927094126/http://www.np.ph.bham.ac.uk/research/anthropic.htm |date=September 27, 2009 }}</ref><ref>{{Cite journal |doi=10.1103/RevModPhys.29.547 |volume=29 |title=Synthesis of the elements in stars |year=1957 |journal=Reviews of Modern Physics |pages=547–650  |last1=Burbidge |first1=E. Margaret |issue=4 |bibcode=1957RvMP...29..547B |doi-access=free }}</ref> [[William Alfred Fowler|Willie Fowler]]'s research group soon found this resonance, and its measured energy was close to Hoyle's prediction.

However, in 2010 [[Helge Kragh]] argued that Hoyle did not use anthropic reasoning in making his prediction, since he made his prediction in 1953 and anthropic reasoning did not come into prominence until 1980. He called this an "anthropic myth", saying that Hoyle and others made an after-the-fact connection between carbon and life decades after the discovery of the resonance.

{{Blockquote| An investigation of the historical circumstances of the prediction and its subsequent experimental confirmation shows that Hoyle and his contemporaries did not associate the level in the carbon nucleus with life at all.<ref>{{Cite web |last1=Kragh |first1=Helge |author-link=Helge Kragh |title=When is a prediction anthropic? Fred Hoyle and the 7.65&nbsp;MeV carbon resonance |url=http://philsci-archive.pitt.edu/5332/ |date=2010 |access-date=2 July 2019 }}</ref>}}

=== Cosmic inflation ===
{{Physical cosmology}}
{{Main|Cosmic inflation}}
[[Don Page (physicist)|Don Page]] criticized the entire theory of [[cosmic inflation]] as follows.<ref>{{Cite journal |first=D.N. |last=Page |year=1983 |title=Inflation does not explain time asymmetry |journal=Nature |volume=304 |page=39 |doi=10.1038/304039a0 |bibcode=1983Natur.304...39P |issue=5921 |s2cid=4315730 }}</ref> He emphasized that initial conditions that made possible a thermodynamic [[arrow of time]] in a universe with a [[Big Bang]] origin, must include the assumption that at the initial singularity, the [[entropy]] of the universe was low and therefore extremely improbable. [[Paul Davies]] rebutted this criticism by invoking an inflationary version of the anthropic principle.<ref>{{Cite journal |first=P.C.W. |last=Davies |author-link=Paul Davies |year=1984 |title=Inflation to the universe and time asymmetry |journal=Nature |volume=312 |page=524 |doi=10.1038/312524a0 |bibcode=1984Natur.312..524D |issue=5994| s2cid=4307546 }}</ref> While Davies accepted the premise that the initial state of the visible universe (which filled a microscopic amount of space before inflating) had to possess a very low entropy value—due to random quantum fluctuations—to account for the observed thermodynamic arrow of time, he deemed this fact an advantage for the theory. That the tiny patch of space from which our observable universe grew had to be extremely orderly, to allow the post-inflation universe to have an arrow of time, makes it unnecessary to adopt any "ad hoc" hypotheses about the initial entropy state, hypotheses other Big Bang theories require.

=== String theory ===
{{Main|String theory landscape}}

[[String theory]] predicts a large number of possible universes, called the "backgrounds" or "vacua". The set of these vacua is often called the "[[multiverse]]" or "[[String theory landscape|anthropic landscape]]" or "string landscape". [[Leonard Susskind]] has argued that the existence of a large number of vacua puts anthropic reasoning on firm ground: only universes whose properties are such as to allow observers to exist are observed, while a possibly much larger set of universes lacking such properties go unnoticed.<ref name="arXiv:hep-th/0302219"/>

[[Steven Weinberg]]<ref>{{Cite conference |author=Weinberg, S. |author-link=Steven Weinberg |year=2007 |title=Living in the multiverse |book-title=Universe or multiverse? |editor=B. Carr |publisher=Cambridge University Press |isbn=978-0-521-84841-1 |arxiv=hep-th/0511037 |bibcode=2005hep.th...11037W }}</ref> believes the anthropic principle may be appropriated by [[cosmologist]]s committed to [[nontheism]], and refers to that principle as a "turning point" in modern science because applying it to the string landscape "may explain how the constants of nature that we observe can take values suitable for life without being fine-tuned by a benevolent creator". Others—most notably [[David Gross]] but also [[Luboš Motl]], [[Peter Woit]], and [[Lee Smolin]]—argue that this is not predictive. [[Max Tegmark]],<ref>Tegmark (1998) op. cit.</ref> [[Mario Livio]], and [[Martin Rees]]<ref>{{Cite journal |author=Livio, M. |author2=Rees, M. J. |name-list-style=amp |title=Anthropic reasoning |journal=Science |volume=309 |pages=1022–1023 |year=2003 |doi=10.1126/science.1111446 |pmid=16099967 |issue=5737 |bibcode=2005Sci...309.1022L |s2cid=40089857 }}</ref> argue that only some aspects of a physical theory need be observable and/or testable for the theory to be accepted, and that many well-accepted theories are far from completely testable at present.

[[Jürgen Schmidhuber]] (2000–2002) points out that [[Ray Solomonoff]]'s [[Solomonoff's theory of inductive inference|theory of universal inductive inference]] and its extensions already provide a framework for maximizing our confidence in any theory, given a limited sequence of physical observations, and some [[prior distribution]] on the set of possible explanations of the universe.

[[Zhi-Wei Wang]] and [[Samuel L. Braunstein]] proved that life's existence in the universe depends on various fundamental constants. It suggests that without a complete understanding of these constants, one might incorrectly perceive the universe as being intelligently designed for life. This perspective challenges the view that our universe is unique in its ability to support life.<ref>{{cite journal |last1=Wang |first1=Zhi-Wei |last2=Braunstein |first2=Samuel L. |year=2023 |title=Sciama's argument on life in a random universe and distinguishing apples from oranges |journal=Nature Astronomy |volume=7 |issue=2023 |pages=755–756 |doi=10.1038/s41550-023-02014-9 |arxiv=2109.10241 |bibcode=2023NatAs...7..755W }}</ref>

{{Anchor|Spacetime}}

=== Dimensions of spacetime ===
[[File:Spacetime dimensionality.svg|thumb|300px|Properties of {{nowrap|(''n'' + ''m'')}}-dimensional spacetimes<ref>{{cite journal |last=Tegmark |first=Max |date=1997-04-01 |title=On the dimensionality of spacetime |journal=Classical and Quantum Gravity |volume=14 |issue=4 |pages=L69–L75 |doi=10.1088/0264-9381/14/4/002 |arxiv=gr-qc/9702052 |bibcode=1997CQGra..14L..69T |s2cid=250904081 |issn=0264-9381}}</ref>]]

There are two kinds of dimensions: [[spatial dimension|spatial]] (bidirectional) and [[temporal dimension|temporal]] (unidirectional).<ref name="Skow2007">{{Cite journal |author-link=Bradford Skow|last1=Skow |first1=Bradford |title=What makes time different from space? |journal=Noûs |year=2007 |volume=41 |issue=2 |pages=227–252 |url=http://web.mit.edu/bskow/www/research/temporality.pdf |access-date=13 April 2018 |doi=10.1111/j.1468-0068.2007.00645.x |citeseerx=10.1.1.404.7853 |archive-url=https://web.archive.org/web/20160824025031/http://web.mit.edu/bskow/www/research/temporality.pdf |archive-date=2016-08-24 }}</ref> Let the number of spatial dimensions be ''N'' and the number of temporal dimensions be ''T''. That {{nowrap|1=''N'' = 3}} and {{nowrap|1=''T'' = 1}}, setting aside the compactified dimensions invoked by [[string theory]] and undetectable to date, can be explained by appealing to the physical consequences of letting ''N'' differ from 3 and ''T'' differ from 1. The argument is often of an anthropic character and possibly the first of its kind, albeit before the complete concept came into vogue.

The implicit notion that the dimensionality of the universe is special is first attributed to [[Gottfried Wilhelm Leibniz]], who in the [[Discourse on Metaphysics]] suggested that the world is "[[wikiquote:Gottfried Leibniz|the one which is at the same time the simplest in hypothesis and the richest in phenomena]]".<ref name="Leibniz1686">{{Cite book |last1=Leibniz |first1=Gottfried |title=Die philosophischen schriften von Gottfried Wilhelm Leibniz |volume=4 |year=1880|publisher=Weidmann |pages=427–463 |chapter-url=https://en.wikisource.org/wiki/Discourse_on_Metaphysics |access-date=13 April 2018 |chapter=Discourse on metaphysics }}</ref> [[Immanuel Kant]] argued that 3-dimensional space was a consequence of the inverse square [[law of universal gravitation]]. While Kant's argument is historically important, [[John D. Barrow]] said that it "gets the punch-line back to front: it is the three-dimensionality of space that explains why we see inverse-square force laws in Nature, not vice-versa" (Barrow 2002:204).<ref group=note>This is because the law of gravitation (or any other [[inverse-square law]]) follows from the concept of [[flux]] and the proportional relationship of flux density and field strength. If {{nowrap|1=''N'' = 3}}, then 3-dimensional solid objects have surface areas proportional to the square of their size in any selected spatial dimension. In particular, a sphere of [[radius]] ''r'' has a surface area of 4''πr''{{sup|2}}. More generally, in a space of ''N'' dimensions, the strength of the gravitational attraction between two bodies separated by a distance of ''r'' would be inversely proportional to ''r''{{sup|''N''−1}}.</ref>

In 1920, [[Paul Ehrenfest]] showed that if there is only a single time dimension and more than three spatial dimensions, the [[orbit]] of a [[planet]] about its Sun cannot remain stable. The same is true of a star's orbit around the center of its [[galaxy]].<ref>{{Cite journal |last=Ehrenfest |first=Paul |author-link=Paul Ehrenfest |title=Welche Rolle spielt die Dreidimensionalität des Raumes in den Grundgesetzen der Physik? |trans-title=How do the fundamental laws of physics make manifest that space has 3 dimensions? |journal=Annalen der Physik |volume=61 |pages=440–446 |year=1920 |doi=10.1002/andp.19203660503 |issue=5 |bibcode=1920AnP...366..440E |url=https://zenodo.org/record/1424351 }}. Also see Ehrenfest, P. (1917) "In what way does it become manifest in the fundamental laws of physics that space has three dimensions?" ''Proceedings of the Amsterdam academy'' 20:200.</ref> Ehrenfest also showed that if there are an even number of spatial dimensions, then the different parts of a [[wave]] impulse will travel at different speeds. If there are <math>5 + 2k</math> spatial dimensions, where ''k'' is a positive whole number, then wave impulses become distorted. In 1922, [[Hermann Weyl]] claimed that [[James Clerk Maxwell|Maxwell]]'s theory of [[electromagnetism]] can be expressed in terms of an action only for a four-dimensional manifold.<ref>Weyl, H. (1922). ''Space, time, and matter''. Dover reprint: 284.</ref> Finally, Tangherlini showed in 1963 that when there are more than three spatial dimensions, electron [[atomic orbital|orbitals]] around nuclei cannot be stable; electrons would either fall into the [[atomic nucleus|nucleus]] or disperse.<ref>{{Cite journal |last=Tangherlini |first=F. R. |title=Schwarzschild field in ''n'' dimensions and the dimensionality of space problem|journal=Nuovo Cimento |volume= 27|issue= 3|pages= 636–651|year=1963 |doi=10.1007/BF02784569 |bibcode=1963NCim...27..636T |s2cid=119683293 }}</ref>

[[Max Tegmark]] expands on the preceding argument in the following anthropic manner.<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> If ''T'' differs from 1, the behavior of physical systems 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, if {{nowrap|''T'' > 1}}, Tegmark maintains that [[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" /> Lastly, if {{nowrap|''N'' < 3}}, gravitation of any kind becomes problematic, and the universe would probably be too simple to contain observers. For example, when {{nowrap|''N'' < 3}}, [[nerve]]s cannot cross without intersecting.<ref name="tegmark-dim" /> Hence anthropic and other arguments rule out all cases except {{nowrap|1=''N'' = 3}} and {{nowrap|1=''T'' = 1}}, which describes the world around us.

On the other hand, in view of creating [[black hole]]s from an ideal [[monatomic gas]] under its self-gravity, Wei-Xiang Feng showed that {{nowrap|(3 + 1)}}-dimensional spacetime is the marginal dimensionality. Moreover, it is the unique [[dimensionality]] that can afford a "stable" gas sphere with a "positive" [[cosmological constant]]. However, a self-gravitating gas cannot be stably bound if the mass sphere is larger than ~10<sup>21</sup> solar masses, due to the small positivity of the cosmological constant observed.<ref>{{cite journal |last=Feng |first=W.X. |date=2022-08-03 |title=Gravothermal phase transition, black holes and space dimensionality |url=https://journals.aps.org/prd/abstract/10.1103/PhysRevD.106.L041501 |journal=Physical Review D |volume=106 |issue=4 |pages=L041501 |arxiv=2207.14317 |doi=10.1103/PhysRevD.106.L041501 |bibcode=2022PhRvD.106d1501F |s2cid=251196731 }}</ref>

In 2019, James Scargill argued that complex life may be possible with two spatial dimensions. According to Scargill, a purely scalar theory of gravity may enable a local gravitational force, and 2D networks may be sufficient for complex neural networks.<ref>{{cite journal |last=Scargill |first=J. H. C. |date=2020-02-26 |title=Existence of life in 2 + 1 dimensions |url=https://link.aps.org/doi/10.1103/PhysRevResearch.2.013217 |journal=Physical Review Research |volume=2 |issue=1 |pages=013217 |arxiv=1906.05336 |doi=10.1103/PhysRevResearch.2.013217 |bibcode=2020PhRvR...2a3217S |s2cid=211734117 }}</ref><ref>{{Cite web |title=Life could exist in a 2D universe (according to physics, anyway) |url=https://www.technologyreview.com/2019/06/20/102942/life-could-exists-in-a-2d-universe-according-to-physics-anyway/ |access-date=2021-06-16 |website=technologyreview.com |language=en}}</ref>