Editing Scientific method (section)

==== Invariance ====

Principles of invariance have been a theme in scientific writing, and especially physics, since at least the early 20th century.{{efn-lg|name=invariantTheme}} The basic idea here is that good structures to look for are those independent of perspective, an idea that has featured earlier of course for example in [[Mill's Methods]] of difference and agreement—methods that would be referred back to in the context of contrast and invariance.<ref name="O&H 1995">{{cite journal | last1=van Overwalle | first1=Frank J. | last2=Heylighen | first2=Francis P. | title=Relating covariation information to causal dimensions through principles of contrast and invariance | journal=European Journal of Social Psychology | volume=25 | issue=4 | date=1995 | issn=0046-2772 | doi=10.1002/ejsp.2420250407 | pages=435–455 | url=http://pcp.vub.ac.be/Papers/Contrast&Invariance.html| url-access=subscription }}</ref> But as tends to be the case, there is a difference between something being a basic consideration and something being given weight. Principles of invariance have only been given weight in the wake of Einstein's theories of relativity, which reduced everything to relations and were thereby fundamentally unchangeable, unable to be varied.<ref name="Wigner1967"/>{{efn |name=WeinertEddingtonEinstein}} As [[David Deutsch]] put it in 2009: "the search for hard-to-vary explanations is the origin of all progress".<ref name="DD_TED">{{Cite AV media | time=15:05min | url=https://www.ted.com/talks/david_deutsch_a_new_way_to_explain_explanation | title=A new way to explain explanation |date=October 2009 | last=Deutsch | first=David | publisher=TED talk | access-date=16 September 2018 | archive-date=4 November 2018 | archive-url=https://web.archive.org/web/20181104012430/https://www.ted.com/talks/david_deutsch_a_new_way_to_explain_explanation |url-status=live }} Also available from [https://www.youtube.com/watch?v=folTvNDL08A YouTube] {{Webarchive|url=https://web.archive.org/web/20221108112725/https://www.youtube.com/watch?v=folTvNDL08A |date=8 November 2022 }}.</ref>

An example here can be found in one of [[Einstein's thought experiments#Falling painters and accelerating elevators|Einstein's thought experiments]]. The one of a lab suspended in empty space is an example of a useful invariant observation. He imagined the absence of gravity and an experimenter free floating in the lab. — If now an entity pulls the lab upwards, accelerating uniformly, the experimenter would perceive the resulting force as gravity. The entity however would feel the work needed to accelerate the lab continuously.{{efn| name=WeinertEddingtonEinstein |[[Arthur Eddington]], 1920: "The relativity theory of physics reduces everything to relations; that is to say, it is structure, not material, which counts." — Weinert, giving the Einstein example and quoting: "Eddington, Space, Time and Gravitation (1920), 197"<ref name="Weinert 2004"/>}} Through this experiment Einstein was able to equate gravitational and inertial mass; something unexplained by Newton's laws, and an early but "powerful argument for a generalised postulate of relativity".<ref name="Einstein1916">{{cite book|last1=Einstein|first1=Albert|title=Relativity: The Special and the General Theory|date=1961|publisher=Crown Publishers, Inc.|location=New York|isbn=978-0-517-88441-6|edition=15th|pages=75–79}}</ref>

{{Blockquote|quote=The feature, which suggests reality, is always some kind of invariance of a structure independent of the aspect, the projection.|source=[[Max Born]], 'Physical Reality' (1953), 149 — as quoted by Weinert (2004)<ref name="Weinert 2004"/>}}

The discussion on [[invariance (physics)|invariance]] in physics is often had in the more specific context of [[symmetry (physics)|symmetry]].<ref name="Wigner1967">{{cite book | last=Wigner | first=Eugene Paul | date=1967 | title=Symmetries and reflections | publisher=Indiana University Press | page=15}} : Wigner also differentiates between geometrical invariance principles, and the "new" ones that arose in the wake of Einstein's theories of relativity that he calls dynamic invariance principles.</ref> The Einstein example above, in the parlance of Mill would be an agreement between two values. In the context of invariance, it is a variable that remains unchanged through some kind of transformation or change in perspective. And discussion focused on symmetry would view the two perspectives as systems that share a relevant aspect and are therefore symmetrical.

Related principles here are [[falsifiability]] and [[testability]]. The opposite of something being ''hard-to-vary'' are theories that resist falsification—a frustration that was expressed colourfully by [[Wolfgang Pauli]] as them being "[[not even wrong]]". The importance of scientific theories to be falsifiable finds especial emphasis in the philosophy of Karl Popper. The broader view here is testability, since it includes the former and allows for additional practical considerations.<ref>{{cite book |last=Keuth |first=Herbert |author-link=:de:Herbert Keuth |chapter=From falsifiability to testability |title=The philosophy of Karl Popper |date=2004 |orig-year=Published in German 2000 |edition=1st English |location=Cambridge, UK; New York |publisher=[[Cambridge University Press]] |pages=[https://books.google.com/books?id=wxzoBfQYhYAC&pg=PA48 48–49] |chapter-url=https://books.google.com/books?id=wxzoBfQYhYAC&pg=PA48 |isbn=9780521548304 |oclc=54503549 |quote=Consequently, the ''universal statements'', which are contradicted by the basic statements, ''are not strictly refutable''. Like singular statements and probability statements, they are empirically testable, but their tests do not have certain, definite results, do not result in strict verification or falsification but only in temporary acceptance or rejection.}}</ref><ref name="l921">{{cite book | last=Krantz | first=S.G. | title=Mathematical Apocrypha Redux: More Stories and Anecdotes of Mathematicians and the Mathematical | publisher=Mathematical Association of America | series=MAA spectrum | year=2005 | isbn=978-0-88385-554-6 | url=https://books.google.com/books?id=8mBdvAjk_gQC | access-date=29 August 2024 | page=194}}</ref>