einstein - the meaning of relativity 6th ed (routledge, 1956) ww

[...]... test for co-variance the equations which express the dependence of the stress components upon the properties of the matter, and set up these equations for the case of a compressible viscous fluid with the aid of the conditions of co-variance If we neglect the viscosity, the pressure, p, will be a scalar, and will depend only upon the density and the temperature of the fluid The contribution to the stress... co-ordinates of our space of reference, then the spherical surface will be expressed in our two systems of co-ordinates by the equations 5 6 the meaning of relativity ∑∆xν2 = const (2) ∑∆x′ν2 = const (2a) How must the x′ν be expressed in terms of the xν in order that equations (2) and (2a) may be equivalent to each other? Regarding the x′ν expressed as functions of the xν, we can write, by Taylor’s theorem,... co-ordinates, xν, and a time t, as soon as we have speci ed the time of the clock at the origin which is simultaneous with the event We therefore give 15 16 the meaning of relativity (hypothetically) an objective significance to the statement of the simultaneity of distant events, while previously we have been concerned only with the simultaneity of two experiences of an individual The time so speci ed. .. independent of the position of the system of co-ordinates in our space of reference, and is therefore an invariant with respect to the transformation (3) It is postulated that the system of equations expressing the laws of pre -relativity physics is co-variant with respect to the transformation (3), as are the relations of Euclidean geometry The isotropy and homogeneity of space is expressed in this... tensor space and time in pre -relativity physics We consider next the equations of motion of a continuous medium Let ρ be the density, uν the velocity components considered as functions of the co-ordinates and the time, Xν the volume forces per unit of mass, and pνσ the stresses upon a surface perpendicular to the σ-axis in the direction of increasing xν Then the equations of motion are, by Newton’s... oriented at rest, relatively to our space of reference, in a multiplicity of ways If, now, the points of this space can be referred to co-ordinates x1, x2, x3, in such a way that the differences of the co-ordinates, ∆x1, ∆x2, ∆x3, of the two ends of the interval furnish the same sum of squares, s2 = ∆x12 + ∆x22 + ∆x32 (1) for every orientation of the interval, then the space of reference is called Euclidean,... velocity of the earth The most important of these experiments are those of Michelson and Morley, which I shall assume are known The validity of the principle of special relativity with respect to electromagnetic phenomena also can therefore hardly be doubted On the other hand, the Maxwell-Lorentz equations have proved their validity in the treatment of optical problems in moving bodies No other theory... the aid of the calculus of tensors We now inquire whether there is a relativity with respect to the state of motion of the space of reference; in other words, whether there are spaces of reference in motion relatively to each other which are physically equivalent From the standpoint of mechanics it appears that equivalent spaces of reference do exist For experiments upon the earth tell us nothing of. .. considered in writing down the equations of motion relatively to the earth It appears, therefore, as if there were Cartesian systems of co-ordinates, the so-called inertial systems, with reference to which the laws of mechanics (more generally the laws of physics) are expressed in the simplest form We may surmise the validity of the following proposition: if K is an inertial system, then every other system... that the state of motion of a clock had no influence on its rate, then this assumption would be physically validated For then clocks, similar to one another, and regulated alike, could be distributed over the systems K and K′, at rest relatively to them, and their indications would be independent of the state of motion of the systems; the time of an event would then be given by the clock in its immediate . blank CONTENTS Space and Time in Pre -Relativity Physics 1 The Theory of Special Relativity 24 The General Theory of Relativity 57 The General Theory of Relativity (continued)81 Appendix I On the ‘Cosmologic Problem’. & Francis e-Library, 2004. ISBN 0-2 0 3-4 495 3-3 Master e-book ISBN ISBN 0-2 0 3-4 577 0-6 (Adobe eReader Format) This book, originally published in 1922, consisted of the text of Dr. Einstein s Stafford. Relativistic Theory of the Non-symmetric Field 136 index 171 A NOTE ON THE SIXTH EDITION For the present edition I have completely revised the ‘Generaliza- tion of Gravitation Theory’ under the title