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Cosmological Special Relativity: The Large-Scale Structure of Space, Time and Velocity
This book presents Einstein's theory of space and time in detail, and describes the large-scale structure of space, time and velocity as a new cosmological special relativity. A cosmological Lorentz-like transformation, which relates events at different cosmic times, is derived and applied. A new law of addition of cosmic times is obtained, and the inflation of the space at the early universe is derived, both from the cosmological transformation. The relationship between cosmic velocity, acceleration and distances is given. In the appendices gravitation is added in the form of a cosmological general relativity theory and a five-dimensional unified theory of space, time and velocity. This book is of interest to cosmologists, astrophysicists, theoretical physicists, mathematical physicists and mathematicians.
224 pages, Hardcover
First published January 1, 1997
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October 22, 2024
AN ISRAELI THEORETICAL PHYSICIST OUTLINES HIS THEORIES
Moshe Carmeli (1933–2007) was the Albert Einstein Professor of Theoretical Physics at Ben Gurion University and President of the Israel Physical Society. He is most noted for his work on gauge theory and his development of the theory of cosmological general relativity, which extends Einstein's theory of general relativity from a four-dimensional spacetime to a five-dimensional space-velocity framework. He has written other books such as 'Relativity: Modern Large-scale Spacetime Structure of the Cosmos,' 'Gauge Fields: Classification and Equations of Motion,' 'Cosmological Relativity: The Special And General Theories For The Structure Of The Universe,' 'Group Theory and General Relativity,' 'Classical Fields: General Relativity and Gauge Theory,' etc.
He wrote in the Preface of this 1997 book, “The study of cosmology in recent years has become one of the most important and popular subjects. Cosmological theory connects different fields of research in physics, from elementary particles to the large-scale structure of the Universe… In this monograph we formulate cosmology, in the limit of NEGLIGIBLE gravitational field, as a new special relativity describing the large-scale structure of space, time and velocity in the Universe. The theory unites space and velocity just as Einstein’s special relativity theory does with space and time. Observers at different placed in the Universe are subsequently related to each other by RELATIVE cosmic times just as those at different inertial systems are related by relative velocities in special relativity.
“Subsequently, the group of cosmological transformations which relate distances and velocities at different cosmic times is derived, and the transformation is written down explicitly… A substantial portion of the book is devoted to special relativity theory, which is presented along the lines of Einstein’s original version. The stress is on the deep meaning of the theory rather than on technicalities, in order to emphasize the analogy to the cosmological special relativity… The whole book is written … so as to enable the nonexpert as well as expert readers to easily understand its content. The book is intended for physicists, astrophysicists, cosmologists, mathematicians, and astronomers.” (Pg. vii-viii)
He summarizes, “The large-scale structure of the cosmos is analysed in detail in this monograph under the assumption that gravitation is NEGLIGIBLE and thus space is flat. A comparison is made between the present-day cosmology and the prerelativistic physics; it is shown that there is an analogy between the structure of space and time as it is understood these days, and the structure of space and velocity in cosmology. The cosmic time takes the role of velocity; observers at different locations in the Universe are related to each other by RELATIVE (rather than absolute) cosmic times, just as observers in different inertial systems are related to each other by relative velocities. As a result, we are able to develop a special relativity theory of cosmology which unites space and velocity, in complete analogy to Einstein’s special relativity theory that unites space and time.” (Pg. 3)
He argues, “As is well known much of the support for the existence of dark matter is due to the observed very high velocities of gas molecules or galaxies. For example galaxies in the far-off Coma cluster are observed whirling around one another faster than the laws of physics would allow. So is the mysteriously rapid rotation of spiral galaxies… the observed velocity by us is not the velocity measured by a local observer at a relative time ‘t’ with respect to us. He measures a smaller velocity, and the more back in time the more the velocity decreases. Does this mean that the hypothetical dark matter can be abolished just as the ‘luminiferous ether’ was proved to be superfluous by special relativity?” (Pg. 23)
He explains, “As observed from the coordinate system K, the clock is moving with the velocity v, and the time which elapses between two of its successive strokes is not one second but … a longer time. Thus the clock goes MORE SLOWLY when it is in motion than when it is at rest. Such a phenomenon is called the ‘dilation of time.’ The same conclusion would have been reached, of course, if the clock was placed in the system K and its time was judged from K’. Again the clock will be seen to run slower. The analogous to this phenomenon in cosmological relativity is, of course, the velocity contraction…” (Pg. 62)
This book is heavily mathematical and somewhat technical, but it may be an easier “introduction” to Carmeli than some of this other books.
Moshe Carmeli (1933–2007) was the Albert Einstein Professor of Theoretical Physics at Ben Gurion University and President of the Israel Physical Society. He is most noted for his work on gauge theory and his development of the theory of cosmological general relativity, which extends Einstein's theory of general relativity from a four-dimensional spacetime to a five-dimensional space-velocity framework. He has written other books such as 'Relativity: Modern Large-scale Spacetime Structure of the Cosmos,' 'Gauge Fields: Classification and Equations of Motion,' 'Cosmological Relativity: The Special And General Theories For The Structure Of The Universe,' 'Group Theory and General Relativity,' 'Classical Fields: General Relativity and Gauge Theory,' etc.
He wrote in the Preface of this 1997 book, “The study of cosmology in recent years has become one of the most important and popular subjects. Cosmological theory connects different fields of research in physics, from elementary particles to the large-scale structure of the Universe… In this monograph we formulate cosmology, in the limit of NEGLIGIBLE gravitational field, as a new special relativity describing the large-scale structure of space, time and velocity in the Universe. The theory unites space and velocity just as Einstein’s special relativity theory does with space and time. Observers at different placed in the Universe are subsequently related to each other by RELATIVE cosmic times just as those at different inertial systems are related by relative velocities in special relativity.
“Subsequently, the group of cosmological transformations which relate distances and velocities at different cosmic times is derived, and the transformation is written down explicitly… A substantial portion of the book is devoted to special relativity theory, which is presented along the lines of Einstein’s original version. The stress is on the deep meaning of the theory rather than on technicalities, in order to emphasize the analogy to the cosmological special relativity… The whole book is written … so as to enable the nonexpert as well as expert readers to easily understand its content. The book is intended for physicists, astrophysicists, cosmologists, mathematicians, and astronomers.” (Pg. vii-viii)
He summarizes, “The large-scale structure of the cosmos is analysed in detail in this monograph under the assumption that gravitation is NEGLIGIBLE and thus space is flat. A comparison is made between the present-day cosmology and the prerelativistic physics; it is shown that there is an analogy between the structure of space and time as it is understood these days, and the structure of space and velocity in cosmology. The cosmic time takes the role of velocity; observers at different locations in the Universe are related to each other by RELATIVE (rather than absolute) cosmic times, just as observers in different inertial systems are related to each other by relative velocities. As a result, we are able to develop a special relativity theory of cosmology which unites space and velocity, in complete analogy to Einstein’s special relativity theory that unites space and time.” (Pg. 3)
He argues, “As is well known much of the support for the existence of dark matter is due to the observed very high velocities of gas molecules or galaxies. For example galaxies in the far-off Coma cluster are observed whirling around one another faster than the laws of physics would allow. So is the mysteriously rapid rotation of spiral galaxies… the observed velocity by us is not the velocity measured by a local observer at a relative time ‘t’ with respect to us. He measures a smaller velocity, and the more back in time the more the velocity decreases. Does this mean that the hypothetical dark matter can be abolished just as the ‘luminiferous ether’ was proved to be superfluous by special relativity?” (Pg. 23)
He explains, “As observed from the coordinate system K, the clock is moving with the velocity v, and the time which elapses between two of its successive strokes is not one second but … a longer time. Thus the clock goes MORE SLOWLY when it is in motion than when it is at rest. Such a phenomenon is called the ‘dilation of time.’ The same conclusion would have been reached, of course, if the clock was placed in the system K and its time was judged from K’. Again the clock will be seen to run slower. The analogous to this phenomenon in cosmological relativity is, of course, the velocity contraction…” (Pg. 62)
This book is heavily mathematical and somewhat technical, but it may be an easier “introduction” to Carmeli than some of this other books.
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