Reading Help Relativity: The Special and General Theory
Clickable text below...
Prev Next
Page #
spectrum was definitely established by Adams in 1924, by observations `
` on the dense companion of Sirius, for which the effect is about thirty `
` times greater than for the Sun. R.W.L. -- translator `
` `
` `
` `
` APPENDIX IV `
` `
` THE STRUCTURE OF SPACE ACCORDING TO THE GENERAL THEORY OF RELATIVITY `
` (SUPPLEMENTARY TO SECTION 32) `
` `
` `
` Since the publication of the first edition of this little book, our `
` knowledge about the structure of space in the large (" cosmological `
` problem ") has had an important development, which ought to be `
` mentioned even in a popular presentation of the subject. `
` `
` My original considerations on the subject were based on two `
` hypotheses: `
` `
` (1) There exists an average density of matter in the whole of space `
` which is everywhere the same and different from zero. `
` `
` (2) The magnitude (" radius ") of space is independent of time. `
` `
` Both these hypotheses proved to be consistent, according to the `
` general theory of relativity, but only after a hypothetical term was `
` added to the field equations, a term which was not required by the `
` theory as such nor did it seem natural from a theoretical point of `
` view (" cosmological term of the field equations "). `
` `
` Hypothesis (2) appeared unavoidable to me at the time, since I thought `
` that one would get into bottomless speculations if one departed from `
` it. `
` `
` However, already in the 'twenties, the Russian mathematician Friedman `
` showed that a different hypothesis was natural from a purely `
` theoretical point of view. He realized that it was possible to `
` preserve hypothesis (1) without introducing the less natural `
` cosmological term into the field equations of gravitation, if one was `
` ready to drop hypothesis (2). Namely, the original field equations `
` admit a solution in which the " world radius " depends on time `
` (expanding space). In that sense one can say, according to Friedman, `
` that the theory demands an expansion of space. `
` `
` A few years later Hubble showed, by a special investigation of the `
` extra-galactic nebulae (" milky ways "), that the spectral lines `
` emitted showed a red shift which increased regularly with the distance `
` of the nebulae. This can be interpreted in regard to our present `
` knowledge only in the sense of Doppler's principle, as an expansive `
` motion of the system of stars in the large -- as required, according `
` to Friedman, by the field equations of gravitation. Hubble's discovery `
` can, therefore, be considered to some extent as a confirmation of the `
` theory. `
` `
` There does arise, however, a strange difficulty. The interpretation of `
` the galactic line-shift discovered by Hubble as an expansion (which `
` can hardly be doubted from a theoretical point of view), leads to an `
` origin of this expansion which lies " only " about 10^9 years ago, `
` while physical astronomy makes it appear likely that the development `
` of individual stars and systems of stars takes considerably longer. It `
` is in no way known how this incongruity is to be overcome. `
` `
` I further want to rernark that the theory of expanding space, together `
` with the empirical data of astronomy, permit no decision to be reached `
` about the finite or infinite character of (three-dimensional) space, `
` while the original " static " hypothesis of space yielded the closure `
` (finiteness) of space. `
` `
` `
` K = co-ordinate system `
` x, y = two-dimensional co-ordinates `
` x, y, z = three-dimensional co-ordinates `
` x, y, z, t = four-dimensional co-ordinates `
` `
` t = time `
` I = distance `
` v = velocity `
` `
` F = force `
` G = gravitational field `
` `
` `
` `
` `
`
` on the dense companion of Sirius, for which the effect is about thirty `
` times greater than for the Sun. R.W.L. -- translator `
` `
` `
` `
` APPENDIX IV `
` `
` THE STRUCTURE OF SPACE ACCORDING TO THE GENERAL THEORY OF RELATIVITY `
` (SUPPLEMENTARY TO SECTION 32) `
` `
` `
` Since the publication of the first edition of this little book, our `
` knowledge about the structure of space in the large (" cosmological `
` problem ") has had an important development, which ought to be `
` mentioned even in a popular presentation of the subject. `
` `
` My original considerations on the subject were based on two `
` hypotheses: `
` `
` (1) There exists an average density of matter in the whole of space `
` which is everywhere the same and different from zero. `
` `
` (2) The magnitude (" radius ") of space is independent of time. `
` `
` Both these hypotheses proved to be consistent, according to the `
` general theory of relativity, but only after a hypothetical term was `
` added to the field equations, a term which was not required by the `
` theory as such nor did it seem natural from a theoretical point of `
` view (" cosmological term of the field equations "). `
` `
` Hypothesis (2) appeared unavoidable to me at the time, since I thought `
` that one would get into bottomless speculations if one departed from `
` it. `
` `
` However, already in the 'twenties, the Russian mathematician Friedman `
` showed that a different hypothesis was natural from a purely `
` theoretical point of view. He realized that it was possible to `
` preserve hypothesis (1) without introducing the less natural `
` cosmological term into the field equations of gravitation, if one was `
` ready to drop hypothesis (2). Namely, the original field equations `
` admit a solution in which the " world radius " depends on time `
` (expanding space). In that sense one can say, according to Friedman, `
` that the theory demands an expansion of space. `
` `
` A few years later Hubble showed, by a special investigation of the `
` extra-galactic nebulae (" milky ways "), that the spectral lines `
` emitted showed a red shift which increased regularly with the distance `
` of the nebulae. This can be interpreted in regard to our present `
` knowledge only in the sense of Doppler's principle, as an expansive `
` motion of the system of stars in the large -- as required, according `
` to Friedman, by the field equations of gravitation. Hubble's discovery `
` can, therefore, be considered to some extent as a confirmation of the `
` theory. `
` `
` There does arise, however, a strange difficulty. The interpretation of `
` the galactic line-shift discovered by Hubble as an expansion (which `
` can hardly be doubted from a theoretical point of view), leads to an `
` origin of this expansion which lies " only " about 10^9 years ago, `
` while physical astronomy makes it appear likely that the development `
` of individual stars and systems of stars takes considerably longer. It `
` is in no way known how this incongruity is to be overcome. `
` `
` I further want to rernark that the theory of expanding space, together `
` with the empirical data of astronomy, permit no decision to be reached `
` about the finite or infinite character of (three-dimensional) space, `
` while the original " static " hypothesis of space yielded the closure `
` (finiteness) of space. `
` `
` `
` K = co-ordinate system `
` x, y = two-dimensional co-ordinates `
` x, y, z = three-dimensional co-ordinates `
` x, y, z, t = four-dimensional co-ordinates `
` `
` t = time `
` I = distance `
` v = velocity `
` `
` F = force `
` G = gravitational field `
` `
` `
` `
` `
`