“According to the Special Theory of Relativity, the velocity of a moving body is always less than the velocity of light. Since the energy of motion of a body depends on its inertial mass and its velocity, it follows that if the energy of a body is increased indefinitely by the continual application of a force, the inertial mass of the body must be increased too; for, if not, the velocity would ultimately increase indefinitely and exceed the velocity of light. Einstein found that, corresponding to any increase in the energy content of a body, there is an equivalent increase in its inertial mass. Mass and energy thus appeared to be different names for the same thing, the energy associated with a mass M being Mc2, where c is the velocity of light; and the mass M of a body moving with velocity v he found to be given by the following formulaM = \frac {m}{\sqrt{(1 - \frac {v^2}{c^2}}}</center”

— Gerald James Whitrow

The Structure of the Universe: An Introduction to Cosmology (1949)

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Gerald James Whitrow 39

British mathematician 1912–2000

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“… the principle of the limiting character of the velocity of light. This statement… is not an arbitrary assumption but a physical law based on experience. In making this statement, physics does not commit the fallacy of regarding absence of knowledge as evidence for knowledge to the contrary. It is not absence of knowledge of faster signals, but positive experience which has taught us that the velocity of light cannot be exceeded. For all physical processes the velocity of light has the property of an infinite velocity. In order to accelerate a body to the velocity of light, an infinite amount of energy would be required, and it is therefore physically impossible for any object to obtain this speed. This result was confirmed by measurements performed on electrons. The kinetic energy of a mass point grows more rapidly than the square of its velocity, and would become infinite for the speed of light.”

Hans Reichenbach (1891–1953) American philosopher

The Philosophy of Space and Time (1928, tr. 1957)

“I must now explain what I mean by the quantity of action. A certain action is necessary for the carrying of a body from one point to another: this action depends on the velocity which the body has and the space which it describes; but it is neither the velocity nor the space taken separately. The quantity of action varies directly as the velocity and the length of path described; it is proportional to the sum of the spaces, each being multiplied by the velocity with which the body describes it. It is this quantity of action which is here the true expense (dépense) of nature, and which she economizes as much as possible in the motion of light.”

Pierre Louis Maupertuis (1698–1759) French mathematician, philosopher and man of letters

Histoire de l'Academie (1744) p. 423; Les Oeuvres De Mr. De Maupertuis (1752) vol. iv p. 17; as quoted by Philip Edward Bertrand Jourdain, The Principle of Least Action https://books.google.com/books?id=y3UVAQAAIAAJ (1913) p. 5.

“The discovery that mass changes with velocity, a discovery made when minute bodies came under consideration, finally forced surrender of the notion that mass is a fixed and inalienable possession of ultimate elements or individuals, so that time is now considered to be their fourth dimension.”

John Dewey (1859–1952) American philosopher, psychologist, and educational reformer

Time and Individuality (1940)

“Momentum may be roughly described as quantity motion. A body moving at a speed of say twenty an hour, has a certain quantity of motion. If the body goes forty miles an hour there is twice as motion; or if twice as much matter goes twenty miles hour, there is also twice as much motion. Momentum is measured by the quantity of matter moving at a rate mass \times velocity.”

William Kingdon Clifford (1845–1879) English mathematician and philosopher

"Energy and Force" (Mar 28, 1873)

“E = mc2 really applies only to isolated bodies at rest. In general, when you have moving bodies, or interacting bodies, energy and mass aren't proportional. E = mc2 simply doesn't apply. …For moving bodies, the correct mass-energy equation is
E=\frac {mc^2} {\sqrt{1-\frac{v^2} {c^2}}}
where v is the velocity. For a body at rest (v=0), this becomes E = mc2. …we must consider the special case of particles with zero mass… examples include photons, color gluons, and gravitons. If we attempt to put m = 0 and v = c in our general mass-energy equation, both the numerator and denominator on the right-hand-side vanish, and we get the nonsensical relation E = 0/0. The correct result is that the energy of a photon can take any value. …The energy E of a photon is proportional to the frequency f of the light it represents. …they are related by the Planck-Einstein-Schrödinger equation E = hf, where h is Plank's constant.”

Frank Wilczek (1951) physicist

when the velocity <math>v</math> approaches the speed of light c, the denominator approaches 0 thus E approaches infinity, unless m = 0.
Source: The Lightness of Being – Mass, Ether and the Unification of Forces (2008), Ch. 3, p. 19 & Appendix A

“Gravitation is not only similar to inertia in its generality, it is also measured by the same number… the mass. The inertial mass is what Newton calls the "quantity of matter": it is a measure for the resistance offered by a body to a force trying to alter its state of motion. It might be called the "passive mass." The gravitational mass, on the other hand, is a measure of the force exerted by the body in attracting other bodies. We might call it the "active" mass. The equality of active and passive, or gravitational and inertial, mass was in Newton's system a most remarkable accidental co-incidence, something like a miracle. Newton himself decidedly felt it as such, and made experiments to verify it, by swinging a pendulum with a hollow bob which could be filled with different materials. The force acting on the pendulum is proportional to its gravitational mass, the inertia to its inertial mass: the period of its swing thus depends on the ratio between these two masses. The fact that the period is always the same therefore proves that the gravitational and inertial masses are equal.”

Willem de Sitter (1872–1934) Dutch cosmologist

Kosmos (1932), Above is Beginning Quote of the Last Chapter: Relativity and Modern Theories of the Universe -->

“In developing his theory of gravitation, Newton assigned to every material body another property which is called its gravitational mass. Gravitational mass determines the force exerted by the body on other bodies, and so its function appears to be quite distinct from that of inertial mass. Nevertheless, the two are found to be identical in magnitude. Newton made experiments to verify this remarkable equality by swinging a pendulum with a bob which could be made with different materials. The period of the swing depended on the ratio of the inertial and gravitational masses of the pendulum, but in all cases it was found to be the same… In 1890 Eötvös made a much more refined test with the aid of a… torsion balance. Repeated experiments showed that inertial mass and gravitational mass were equal to within one part in 100 million. Einstein suggested that this was because inertia and gravitation are identical.”

Gerald James Whitrow (1912–2000) British mathematician

p, 125
The Structure of the Universe: An Introduction to Cosmology (1949)

“A question which has long troubled astronomers and physicists is what becomes of the energy that is continually being poured out into space by the sun and the stars. To this question a complete answer is given by the new theory. It is used up, diluted, or degraded, by the expansion of the universe. …the light travelling through the expanding universe and, so to say, trying to reach a particular star, or stellar system, which is continually receding with great velocity, is losing energy in trying to catch up with it. It is this degradation of the light, technically known as the redshift of the spectral lines, by which we become aware of the receding velocities of the extra-galactic nebulae. It can be shown that the decrease of the total amount of radiant energy in the universe by this degradation exceeds the increase by the radiation of the stars. It would not be correct, however, to conclude that the expansion is caused by the energy thus lost by the radiation…”

Willem de Sitter (1872–1934) Dutch cosmologist

Kosmos (1932)

“[ Futurism's].. superficial expression of velocity, the aeroplane, the racing-car and so on, is but a weak expression of the inner velocity of thought compared to which the velocity of radium represents nothing but inertia... The mimetic expression of velocity (whatever its form may be: the aeroplane, the automobile, and so on) is diametrically opposed to the character of painting, the supreme origin of which is to be found in inner life.”

Theo van Doesburg (1883–1931) Dutch architect, painter, draughtsman and writer

Quote from Dutch art-magazine: 'Eenheid' (Dutch, for Unity) no. 127, 9 November 1912; as cited in Theo van Doesburg, Joost Baljeu, Studio Vista, London 1974, p. 16
1912 – 1919

“Arc, amplitude, and curvature sustain a similar relation to each other as time, motion, and velocity, or as volume, mass, and density.”

Carl Friedrich Gauss (1777–1855) German mathematician and physical scientist

"Gauss's Abstract of the Disquisitiones Generales circa Superficies Curvas presented to the Royal Society of Gottingen" (1827) Tr. James Caddall Morehead & Adam Miller Hiltebeitel in General Investigations of Curved Surfaces of 1827 and 1825 http://books.google.com/books?id=SYJsAAAAMAAJ& (1902)

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