Abstract
Foundational ideas such as 1+3-dimensional Minkowski space, world lines, proper time, causality, the process of measurement of space and time, and several centuries of effort to determine the speed of light form the core of this Chapter. Time is an additional coordinate needed to characterize an event, such as when we meet. Proper time is the time ticking in each body. Causality refers to irreversibility of sequence of events. Speed of light as measured on Earth and determined performing astronomical observations is the same as the speed of propagation of Electromagnetic (Maxwell) waves. Einstein’s elaborate views about the properties of non-material æther are presented: “Motion cannot be inherent to the æther.”
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Notes
- 1.
Hermann Minkowski (1864–1909), German mathematician who realized that time and space should be combined into a four dimensional space.
- 2.
H. Minkowski, address at the 80th Assembly of German Natural Scientists and Physicians (September 21, 1908); translated by the author; original text: “Die Anschauungen über Raum und Zeit, die ich Ihnen entwickeln möchte, sind auf experimentell-physikalischem Boden erwachsen. Darin liegt ihre Stärke. Ihre Tendenz ist eine radikale. Von Stund’ an sollen Raum für sich und Zeit für sich völlig zu Schatten herabsinken und nur noch eine Art Union der beiden soll Selbständigkeit bewahren.”
- 3.
H. Minkowski, Ref. 2 introduced the expression ‘proper time’, in his article: “Eigenzeit.”
- 4.
W. Rindler, “Einstein’s Priority in Recognizing Time Dilation Physically,” American Journal of Physics 38, 1111 (1970).
- 5.
The path to the letter \(c\) becoming the symbol for the speed of light is described by: K.S. Mendelson, “The story of \(c\),” Am. J. Phys. 74, 995 (2006). A few key points from this article: Einstein switches from \(V\) to \(c\) three years after inventing relativity. Why \(c\)? The latanized German writing “Constante” instead of ‘Konstante’ by W. Weber who interprets forces in pre-Maxwell world; and the Latin word for speed ‘celeritas’, though this interpretation appears explicitly first in 1959 work of I. Asimov “\(c\) for celeritas,” in The Magazine of Fantasy and Science Fiction. The general use of \(c\) follows M. Abraham 1903 work “Prinzipien der Dynamik des Electrons,” Ann. Phys. 10, 105 (1903) and his influential 1904 textbook on EM: M. Abraham, and A. Föppl Theorie der Elektrizität: Einführung in die Maxwellsche Theorie der Elektrizität (Leipzig, Teubner 1904). It is important to appreciate that Abraham according to the educational norms of his time could not avoid being fluent in Latin and thus certainly knew that speed=celeritas.
- 6.
With due deference to SI units, it is a mystery to this author why \(1\,c\,\mbox{ns}\simeq\, 0.984\,\mbox{ft}\equiv1\,\mbox{`lns'}\) (light nano second) by lucky chance a good scale both at the human and the fundamental length scale has not been adopted as the SI-unit of length. Several nuisance factors would disappear from the SI-unit tables: for example Eq. (1.2) simplifies since \(c=10^{9}\,\mbox{lns/s}\). Even today a unit of length based on lns could result in a more widely accepted unit system, perhaps uniting the US and European systems of measurement.
- 7.
James Bradley (1693–1762), English astronomer, Astronomer Royal from 1742. Appointed to the Savilian chair of astronomy at Oxford in 1721, Bradley’s work provided the first direct evidence for the movement of the Earth around the Sun as well as a precise measurement of the speed of light based on the newly discovered aberration effect.
- 8.
Samuel Molyneux (1689–1728), member of the British parliament and an amateur astronomer, Fellow of the Royal Society in 1712. Molyneux commissioned precise telescopes and engaged James Bradley.
- 9.
Robert Hooke (1635–1703), Oxford natural philosopher and polymath, opponent of Newton, Hooke’s law is named after him.
- 10.
Todd K. Timberlake, “Seeing Earth’s Orbit in the Stars: Parallax and Aberration” Phys. Teach. 51, 478 (2013).
- 11.
(Armand-Hippolyte-)Louis Fizeau (1819–1896), French physicist. In 1849 he published the first ‘terrestrial’ measurement of the speed of light, and in 1850 with Foucault, this measurement was considerably refined. In 1851 he demonstrated the Fresnel drag (see exercise III–10 on page 95).
- 12.
(Jean Bernard) Léon Foucault (1819–1868), French physicist, best known for the invention of the Foucault pendulum in 1851. In 1850, together with (Armand-Hippolyte-)Louis Fizeau, Foucault made a precise terrestrial measurement of the speed of light.
- 13.
An editorial review by Nature of May 13, 1886 entitled “The Velocity of Light,” pp. 29–32 presents in historical context a period-contemporary, æther embedded, review of the efforts to measure the speed of light.
- 14.
J. Clerk Maxwell, “A Dynamical Theory of the Electromagnetic Field,” Phil. Trans. R. Soc. Lond. 155, 459–512 (1 January 1865).
- 15.
Heinrich Rudolf Hertz, (1857–1894), German physicist, proved the existence and propagation in space of electromagnetic waves. The frequency unit ‘Hz’ is named after him. He has presented the Maxwell’s equations found in every book today. Thus in literature from before 1933 these equations are often called Maxwell-Hertz equations.
- 16.
E.B. Rosa, and N.E. Dorsey, “The Ratio of the Electromagnetic and Electrostatic Units”, Bulletin of the Bureau of Standards 3(6), 433 (1907) and Phys. Rev. (Series I) 22, 367 (1906).
- 17.
Letter to H.A. Lorentz of November 15, 1919, see page 2 in Einstein and the Æther, L. Kostro, Apeiron, Montreal (2000).
- 18.
Translated by the author from the original: “Allerdings erscheint die Ätherhypothese vom Standpunkte der speziellen Relativitätstheorie zunächst als eine leere Hypothese. In den elektromagnetischen Feldgleichungen treten außer den elektrischen Ladungsdichten nur die Feldstärken auf. Der Ablauf der elektromagnetischen Vorgänge im Vakuum scheint durch jenes innere Gesetz völlig bestimmt zu sein, unbeeinflußt durch andere physikalische Größen. Die elektromagnetischen Felder erscheinen als letzte, nicht weiter zurückführbare Realitäten, und es erscheint zunächst überflüssig, ein homogenes, intropes Äthermedium zu postulieren, als dessen Zustände jene Felder aufzufassen wären.”
- 19.
Translated by the author from the original, see Preamble, Ref. 10: “Das prinzipiell Neuartige des Äthers der allgemeinen Relativitätstheorie gegenüber dem Lorentzschen Äther besteht darin, daß der Zustand des ersteren an jeder Stelle bestimmt ist durch gesetzliche Zusammenhänge mit der Materie und mit den Ätherzuständen in benachbarten Stellen in Gestalt von Differentialgleichungen, während der Zustand des Lorentzschen Äthers bei Abwesenheit von elektromagnetischen Feldern durch nichts außer ihm bedingt und überall der gleiche ist.”
- 20.
See Preamble, Ref. 10: “Da nach unseren heutigen Auffassungen auch die Elementarteilchen der Materie ihrem Wesen nach nichts anderes sind als Verdichtungen des elektromagnetischen Feldes, …”
- 21.
Peter W. Higgs (1929–), British theoretical physicist who developed quantum vacuum structure ides leading to characterization of the mass of some elementary particles. Nobel Prize 2013.
- 22.
See for example J. Rafelski, “Melting hadrons, boiling quarks,” Eur. Phys. J. A 51, 114 (2015).
- 23.
This and many other conversations that follow actually took place, but we present generally an extended and/or dramatized versions. Here ‘student’ is a more seasoned helper to the Professor, and Simplicius is a novice.
- 24.
William of Ockham’s also written as ‘Occam’ (c. 1285–1349) razor is a principle urging, in the words of Ptolemy (c. AD 90–c. AD 168): “We consider it a good principle to explain the phenomena by the simplest hypothesis possible”.
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Rafelski, J. (2017). Space-Time. In: Relativity Matters. Springer, Cham. https://doi.org/10.1007/978-3-319-51231-0_1
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