Space And Time

by Emile Borel

Overview

Borel was born the son of Honoré, a pastor, and Emilie Teissié-Solier Borel, in the French town of Saint-Affrique on January 7, 1871. His was a world heavily influenced by the recent humiliation of the Franco-Prussian War, and on a personal level, Borel, as the younger brother of two sisters, had to fight to distinguish himself. Distinction came early, however, with an invitation to study at several prestigious preparatory schools in Paris. Borel went on to the Ecole Normale Supériere, a preeminent school in science and mathematics with which he would remain connected for most of his life. After earning his doctorate in 1894, he returned to the Ecole Normale to teach. His work Space and Time helped make Albert Einstein's theory of relativity comprehensible to non-technically educated readers, and his work extended far beyond the world of mathematics. As an influential figure in French politics, he helped direct that country's policy toward scientific and mathematical research and education.

Product Details

ISBN-13:	9781406771046
Publisher:	Case Press
Publication date:	09/20/2007
Pages:	244
Product dimensions:	5.50(w) x 8.50(h) x 0.55(d)

Table of Contents

	Introduction: From Newton and Poincare to Einstein	1
	Curiosity about Einstein's Theories	1
	Geometry a Physical Science	4
	Invariable Bodies and Various Scales	6
	Geometry inseparable from Optics	10
	Difficulties due to Motion	11
	Scientific Importance of an Extra Decimal	14
	Time a Measurable Quantity	16
	Analogy between the Measurement of Time and the Measurement of Length	17
	Artificial Clocks and the Clocks of Astronomers	19
	The Influence of Gravitation upon Clocks	21
	The Slowing Down of Clocks in Accelerated Motion	25
	The Timing of Clocks	27
	The Necessity of Successive Approximations	27
	The Origin of Newton's Law	28
	The Experiments of Cavendish	31
	Gravitation an Isolated Phenomenon	32
	Centrifugal Force and Force of Inertia	34
	Gravitation a Force of Inertia	35
Chapter I	Geometry and the Shape of the Earth
1.	Origin of Geometry--Invariable Bodies	38
2.	Geometry of Position, and Metric Geometry	39
3.	Solid Bodies	40
4.	Cartesian Co-ordinates	41
5.	The Postulates of Euclid	42
6.	Analytical Geometry and M. Jourdain's Prose	44
7.	Analytical Geometry--Space on the Human Scale	45
8.	Number knows no Limitations	46
9.	Preservation of Landmarks	47
10.	Geographical Co-ordinates	47
11.	Geodetic Measurements	49
12.	The Unit of Length and Richer's Pendulum	51
13.	The Metric System and International Standards	54
14.	The Metre in Terms of Wave-lengths	55
15.	The Figure of the Earth	56
16.	The Earth regarded as a Level Surface	58
17.	Variation of the Poles--Tides in the Earth's Crust	60
18.	The Scientific Value of Exact Measurements	64
Chapter II	Space and Time in Astronomy
19.	Modern Astronomy is not Geocentric	66
20.	The Distances of the Planets are deduced from Newton's Laws	66
21.	The Absolute Value of the Dimensions of the Solar System	68
22.	Galilean Axes	70
23.	The Sidereal Day	71
24.	The Time of Astronomers	72
25.	Privileged Axes and Privileged Chronology	74
26.	Are the Privileged Axes and Chronology Independent of the Earth?	76
27.	Introduction of the Velocity of Light Necessary	77
28.	Approximate Results retain Scientific Value	78
29.	What do we know of Interstellar Space?	80
Chapter III	Abstract Geometry and Geographical Maps
30.	The Abstract Conception of Geometry	82
31.	A few Remarks on Mathematics	83
32.	Analytical Geometry a Means of Defining Geometrical Conceptions	84
33.	The Notion of Senes--It is incommunicable	85
34.	The Notion of Sense	87
35.	The Euclidean Schema	89
36.	Example of a Schema of Imaginary Geometrical Elements	90
37.	The Schema of Spherical Geometry--Riemann	92
38.	Plane Schema for Any Geometry	93
39.	Well-known Examples of a Schema	94
40.	Mercator's Projection	94
41.	Applicable Surfaces and Parallelism	96
42.	Geodesic Lines and the Invariance of Direction	99
43.	Utilization of the Linear Element	100
Chapter IV	Continuity and Topology
44.	The Very Small More Difficult to Reach than the Very Great	102
45.	Geometrical Intuition at Fault in the Infinitely Small	104
46.	The Sub-atomic Scale	106
47.	The Postulate of the Ellipsoid	107
48.	Geometry and the Quantum Theory	108
49.	Maps and the India-rubber Metre	109
50.	Discontinuity Inevitable in a Plane Map of a Sphere	110
51.	A Sphere has no Boundary	113
52.	Topology of the Anchor-ring	113
53.	Local Knowledge cannot give Knowledge of the Universe	114
54.	The Plane Topological Representation of a Sphere	116
55.	Topological Representation of a Hypersphere	118
56.	A Finite but Unbounded Universe	119
57.	The Ring and a Plane Network of Rectangles	120
58.	The Hypertore and a Periodic Image of the Universe	122
Chapter V	The Propagation of Light
59.	Fresnel's Theory and the Sinusoid	124
60.	Wave-length and Difference of Phase	126
61.	Measurement of Wave-lengths in Metric Units	127
62.	Measurement of the Velocity of Light	129
63.	Measurement of Very Short Intervals of Time	131
64.	X-rays and Crystal Structure	132
65.	Michelson and Morley's Experiment	133
66.	Michelson and Morley's Experiment	133
67.	Aberration of the Fixed Stars	136
68.	The Doppler-Fizeau Effect	137
69.	Fizeau's Experiment on Running Liquid	139
70.	Phenomena shown by Double Stars	140
Chapter VI	The Special Theory of Relativity
71.	What the Special or Restricted Theory of Relativity is	143
72.	Acoustic Signals and the Wind	144
73.	The Timing of Clocks by Means of Acoustic Signals	146
74.	The Specification of Motion by Means of Acoustic Signals	147
75.	Luminous Signals, and Intuitive Kinematics	151
76.	We must escape the Contradiction	154
77.	The Independence of Space and Time	154
78.	The Special Theory a Logical Consequence of the above Premises	155
79.	Examination of an Objection	156
80.	The Possibility of Continual Increase of a Velocity does not Involve the Conclusion that the Velocity may Increase Indefinitely	157
81.	Instantaneous Propagation has as Little Plausibility as a Velocity that cannot be Exceeded	158
82.	Spatial Measurement of Time: Einstein's Interval	161
83.	The Principle of Causality is not at Stake	163
84.	Restricted Relativity concerns only Translations	165
Chapter VII	The General Theory of Relativity
85.	The General Theory of Relativity is above all a Mathematical Theory	167
86.	Euclidean Geometry and Curvilinear Co-ordinates on Surfaces	167
87.	The Interval generalized by Means of the Quadratic Form in Four Variables	169
88.	Change of Variables in Mathematical Theories	172
89.	Can a Few Equations contain the Geometrical Universe?	173
90.	Is the World Simple?	175
91.	The Virtuoso and the Phonograph	176
92.	Mechanical Representations	178
93.	Einstein's Purely Geometrical Representation	180
94.	The Gaps: Statistical Theories and Discontinuities: the Theory of Quanta	182
Chapter VIII	Recent Theoretical and Experimental Researches
95.	The Equations of Electromagnetism	183
96.	The New Mathematical Theories	184
97.	Their Physical Significance still to be Found	185
98.	Miller's Experiments	185
99.	Miller's Experiments and other Phenomena	188
100.	Michelson and Gale's Experiment	190
101.	The Detractors of the Theory of Relativity	193
102.	The Misconceptions of the Philosophers	194
103.	It is now the Turn of Experiment	195
104.	Supplementary Note	196
Note I	The Kinematics of the Special Theory of Relativity	197
Note II	On the Fundamental Hypotheses of Physics and of Geometry	202
Note III	The Mathematical Continuum and the Physical Continuum
1.	The Scale of Rational Numbers	205
2.	The Measurement of Magnitudes	207
3.	Irrational Numbers	210
4.	The Mathematical Continuum	212
5.	The Practical Value of the Continuum	214
6.	Numerical Approximations	217
7.	The Physical Continuum	218
8.	The Relations between the Two Continua	220
Note IV	The Universe--Is It Infinite?
1.	A Finite Universe is Possible	222
2.	The Mean Density and the Curvature of the Universe	223
3.	The Hypothesis of an Infinitely Small Mean Density	225
4.	Of what Use are these Cosmological Speculations?	227
	Index of Names	229
	General Index	231