Editing Special relativity (section)

==== Langevin's light-clock ====
{{anchor|Langevin's Light-Clock}}
[[File:Langevin Light Clock.gif|thumb|320px|Figure 4–3. Thought experiment using a light-clock to explain time dilation]]
[[Paul Langevin]], an early proponent of the theory of relativity, did much to popularize the theory in the face of resistance by many physicists to Einstein's revolutionary concepts. Among his numerous contributions to the foundations of special relativity were independent work on the mass–energy relationship, a thorough examination of the twin paradox, and investigations into rotating coordinate systems. His name is frequently attached to a hypothetical construct called a "light-clock" (originally developed by Lewis and Tolman in 1909<ref name="Lewis_Tolman_1909">{{cite journal |last1=Lewis |first1=Gilbert Newton |authorlink1=Gilbert N. Lewis|last2=Tolman |first2=Richard Chase| authorlink2=Richard Chase Tolman| title=The Principle of Relativity, and Non-Newtonian Mechanics |journal=Proceedings of the American Academy of Arts and Sciences |date=1909 |volume=44 |issue=25 |pages=709–726 |doi=10.2307/20022495 |jstor=20022495 |url=https://en.wikisource.org/wiki/The_Principle_of_Relativity,_and_Non-Newtonian_Mechanics |access-date=22 August 2023}}</ref>), which he used to perform a novel derivation of the Lorentz transformation.<ref name="Cuvaj_1971">{{cite journal |last1=Cuvaj |first1=Camillo |title=Paul Langeyin and the Theory of Relativity |journal=Japanese Studies in the History of Science |date=1971 |volume=10 |pages=113–142 |url=http://www.isc.meiji.ac.jp/~sano/hssj/pdf/Cuvaj_C-1972-Langevin_Relativity-JSHS-No_10-pp113-142.pdf |access-date=12 June 2023}}</ref>

A light-clock is imagined to be a box of perfectly reflecting walls wherein a light signal reflects back and forth from opposite faces. The concept of time dilation is frequently taught using a  light-clock that is traveling in uniform inertial motion perpendicular to a line connecting the two mirrors.<ref>{{Cite book |last1=Cassidy |first1=David C. |url=https://books.google.com/books?id=rpQo7f9F1xUC&pg=PA422 |title=Understanding Physics |last2=Holton |first2=Gerald James |last3=Rutherford |first3=Floyd James |publisher=[[Springer-Verlag]] |year=2002 |isbn=978-0-387-98756-9 |pages=422}}</ref><ref>{{Cite book |last=Cutner |first=Mark Leslie |url=https://books.google.com/books?id=2QVmiMW0O0MC&pg=PA128 |title=Astronomy, A Physical Perspective |publisher=[[Cambridge University Press]] |year=2003 |isbn=978-0-521-82196-4 |page=128}}</ref><ref>{{Cite book |last1=Ellis |first1=George F. R. |url=https://books.google.com/books?id=Hos31wty5WIC&pg=PA28 |title=Flat and Curved Space-times |last2=Williams |first2=Ruth M. |publisher=[[Oxford University Press]] |year=2000 |isbn=978-0-19-850657-7 |edition=2n |pages=28–29}}</ref><ref name="Feynman_Lectures_1">{{cite book |last1=Feynman |first1=Richard P. |last2=Leighton |first2=Robert B. |last3=Sands |first3=Matthew |title=The feynman lectures on physics; vol I: The new millennium edition |date=2011 |publisher=Basic Books |isbn=978-0-465-02414-8 |page=15-5 |url=https://www.feynmanlectures.caltech.edu/I_15.html |access-date=12 June 2023}}</ref> (Langevin himself made use of a light-clock oriented parallel to its line of motion.<ref name="Cuvaj_1971"/>)

Consider the scenario illustrated in {{nowrap|Fig. 4-3A.}} Observer A holds a light-clock of length <math>L</math> as well as an electronic timer with which she measures how long it takes a pulse to make a round trip up and down along the light-clock. Although observer A is traveling rapidly along a train, from her point of view the emission and receipt of the pulse occur at the same place, and she measures the interval using a single clock located at the precise position of these two events. For the interval between these two events, observer A finds {{tmath|1= t_\text{A} = 2 L/c }}. A time interval measured using a single clock that is motionless in a particular reference frame is called a ''[[proper time interval]]''.<ref name="Halliday_1988">{{cite book |last1=Halliday |first1=David |last2=Resnick |first2=Robert |title=Fundamental Physics: Extended Third Edition |date=1988 |publisher=John Wiley & sons |location=New York |isbn=0-471-81995-6 |pages=958–959}}</ref>

Fig. 4-3B illustrates these same two events from the standpoint of observer B, who is parked by the tracks as the train goes by at a speed of {{tmath|1= v }}. Instead of making straight up-and-down motions, observer B sees the pulses moving along a zig-zag line. However, because of the postulate of the constancy of the speed of light, the speed of the pulses along these diagonal lines is the same <math>c</math> that observer A saw for her up-and-down pulses. B measures the speed of the vertical component of these pulses as <math display=inline>\pm \sqrt{c^2 - v^2},</math> so that the total round-trip time of the pulses is <math display=inline>t_\text{B} = 2L \big/ \sqrt{ c^2 - v^2 } = {}</math>{{tmath|1= \textstyle t_\text{A} \big/ \sqrt {1 - v^2 / c^2} }}. Note that for observer B, the emission and receipt of the light pulse occurred at different places, and he measured the interval using two stationary and synchronized clocks located at two different positions in his reference frame. The interval that B measured was therefore ''not'' a proper time interval because he did not measure it with a single resting clock.<ref name="Halliday_1988"/>