Gravitation and Inertia by Ignazio Ciufolini (PDF)

Description

Einstein’s standard and battle-tested geometric theory of gravity–spacetime tells mass how to move and mass tells spacetime how to curve–is expounded in this book by Ignazio Ciufolini and John Wheeler. They give special attention to the theory’s observational checks and to two of its consequences: the predicted existence of gravitomagnetism and the origin of inertia (local inertial frames) in Einstein’s general relativity: inertia here arises from mass there. The authors explain the modern understanding of the link between gravitation and inertia in Einstein’s theory, from the origin of inertia in some cosmological models of the universe, to the interpretation of the initial value formulation of Einstein’s standard geometrodynamics; and from the devices and the methods used to determine the local inertial frames of reference, to the experiments used to detect and measure the “dragging of inertial frames of reference.” In this book, Ciufolini and Wheeler emphasize present, past, and proposed tests of gravitational interaction, metric theories, and general relativity. They describe the numerous confirmations of the foundations of geometrodynamics and some proposed experiments, including space missions, to test some of its fundamental predictions–in particular gravitomagnetic field or “dragging of inertial frames” and gravitational waves.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐6/10/2013 In light of quite constructive criticisms, I am elaborating on, and moderating, my original, quick review (archived below).Summary:Reading the Amazon preview of the cover flaps and Chapter One, one might expect the book to be a mathematically-approachable exploration of geometro-dynamics — the identity of space-time geometry, Gravity, and Inertia, as I did (much more on this later); reading the preview of the Mathematical Appendix, one might expect a hard-core mathematical exploration of the same. Neither would be correct, although the second chapter is a painfully concise mathematical summary of the theory. “‘This book is an ambitious walking tour through a host of topics in general relativity…’ — Robert Geroch, University of Chicago” And so it is. Presuming an understanding of the theory and its essential mathematics, it examines numerous familiar questions and unusual twists in various domains of General Relativity. Included are chapters on cosmology, the initial value problem, the gravimagnetic field, and tests of the theory. While quite varied and interesting, these do not add up to a book that should be titled “Gravitation and Inertia.” The inclusion of the aforementioned Chapter Two and Appendix is puzzling, as their largely coordinate-independent approach, while “elegant,” is not employed in the remainder, and their impenetrability renders them useless and off-putting to a reader who has not already mastered them; the only justification I can imagine for them is as a reference summary, rather than an exposition. Overall, the book is a grab-bag of diverse topics in gravitation, with a mix of intermediate and more advanced approaches, and while few will find every section to be of value to them (or worth the $80 list price!), there is something to interest every student and scholar of General Relativity, if you can get it at a price that suits you.Background:I came to buy this book as a reasonably prepared physics B.S., having already read and understood the “old-school,” coordinate-based approach (as well presented on many web sites and in Dirac’s excellent (albeit, illustration-free) booklet

⭐) and comfortable (if not confident!) with Tensor Calculus and the associated mathematics. I then broke down and purchased Wheeler, et al’s definitive and pricey tome,

⭐(the nerd’s “Godel, Escher, Bach,” i.e., something everyone has but no one gets far in!) and like so many others, found myself unable to penetrate the new-style math of coordinate-independent tensors, one-forms, fiber-bundles, the “star dual,” etc.. In this text, Cartan/Wheeler’s nifty insights about geometro-dynamics (the identity of Gravitation and Inertia, the Boundary-of-a-Boundary Principle, Sum of the bounding curvatures = 8 Pi x Momentum-energy enclosed) are explored at length, but the treatment has so far resisted my understanding.I then read Wheeler’s intriguing “coffee-table” book

⭐– (now available for a penny through Amazon marketplace!), where he attempts (and very nearly succeeds) to explain these concepts in terms of curvatures and geometry alone. The book is blessed with numerous helpful diagrams, a few more of which would have carried the ball over the finish line to allow almost anyone with a modest understanding of spatial relations to determine the qualitative structure of space-time in and around a mass. I found that some of the statements about curvature didn’t jibe with the calculations they inspired me to make (it seems that Wheeler is defining his curvatures from covariant vectors, which changes the sign of either the space-time or space-space planes, so his sum is my difference).Eager to resolve the discrepancy and get a more formal mathematical treatment, I searched here to see if Wheeler had written a book intermediate between “Journey…” and “Gravitation.” I was delighted when I read the listing for “Gravitation and Inertia,” which seemed to be that very book, an entire text fleshing out the identity of the two concepts. The cover flaps proclaim, “Einstein’s standard and battle-tested geometric theory of gravity–spacetime tells mass how to move and mass tells spacetime how to curve–is expounded in this book by Ignazio Ciufolini and John Wheeler.” The sample text consists of the brief first chapter and the Mathematical Appendix, and while the latter is quite advanced, the former is exactly what I was seeking, the continuation of the intuitive geometrodynamics of “Journey…” for physicists.Alas, when I received my purchase, I discovered that Chapter One belongs in a different book. So does Chapter Two, wherein geometrodynamics is presented as a concise mathematical summary of the treatment in “Gravitation,” with little attempt at teaching or approachability. I find it hard to believe that anyone who had not already been taught the very formal, abstract, mathematical approach of Chapter Two and the Mathematical Appendix could make much use of them, and they seem irrelevant to the later chapters, which employ the more-familiar coordinate-dependent notation. If their inclusion in the volume can be justified, it would be only as a summary review or a teaser for “Gravitation.” While Chapter Five takes another stab at *summarizing* geometrodynamics, it is only a summary.My personal interest in General Relativity at present lies in the realm of intuitive understanding between deep theory and experimental results, and while there is much to be learned from this book, it doesn’t grab my interest. Perhaps this is due to my limited grasp of the mathematics, perhaps I’m looking for an unreasonable level of approachability, “hand-holding” or intuitive/diagrammatic explanation that is possible, and hinted at in “Journey…,” but I cannot open this book without being deeply disappointed at what it is not.My original review:Don’t Waste Your Money, April 3, 2002I purchased my copy used (20$) and (after my initial delight at the bargain) was disappointed. I had hoped for a more technical intermediate-level expansion of Wheeler’s intriguing but vague “Journey into Gravity and Spacetime.” This book is instead largely a hodge-podge of specialty articles of interest only to advanced professionals in the field. Unless you have money to burn, invest it in another text, like “Gravitation,” by Thorne, Wheeler, etc., which isn’t great but is useful.

⭐John Archibald Wheeler does not need any introduction,neither by me, nor by anybody else:he is simply the greatest living authority on General Relativity!This book, written together with Ignazio Ciufolini,is as interesting as all his other books,and is well worth the price,despite what our friend Johngorno says!!However,Johngorno is right in one respect:when the authors say ,in the Preface(page ix),that the “book may be used as an introduction to general relativity…” ,they are misleading the prospective reader!As a matter of fact ,if you have not had at least an introductory course in GR ,such as “A first course in General Relativity” by B.F. Schutz,don’t even think about reading this book.Even the Mathematical Appendix at the end is not enough for someone not familiar with tensor calculus.The unaware reader who reaches page 21 ,for example,is hit on the head with the expression giving the Christoffel symbols as a function of the metric components: how is he or she supposed to guess that the comma represents a partial derivative,that sigma is a dummy index ,and therefore that there is a sum involved in this expression?He or she might turn to the mathematical index ,which will direct him or her to the Appendix,page 427,but this won’t help much:the summation convention is not explained there,but at page 425,and in a very inconspicuous fashion!So,albeit a great book on gravitation theory and experiment, this is definitely not an introduction to Einstein’s theory of gravitation.It is rather aimed at the real “cognoscenti” in the field.But if the book’s contents are outstanding, the same cannot be said with regards the form:the pictures are quite poor for a book priced at more than $90, and the paper is not that good either.Too bad!

⭐After revisiting Misner, Thorne and Wheeler’s Gravitation (1973, and re-printed 2017 Princeton University Press), I decided to have another look at this book, published 1995 with John Wheeler as a co-author and also published by Princeton University Press. If you have previously studied MTW’s Gravitation, then this 1995 book is useful as collateral reading to that 1973 text. Preface here reading: “…it may be used as an introduction to general relativity.” However, I would not recommend this book as an introduction. Keep this in mind: 20% of the material between these covers is comprised of an appendix (mathematics), notation (G=c=1, geometrized units) and references.(1) Preliminaries will occupy the first chapter. In particular, what does it mean when one says “mass ‘there’ determines ‘inertia’ here ? ” and “the boundary of a boundary principle.” (I do not believe chapter one is entirely successful).(2) Second chapter: “Einstein Geometrodynamics” You climb up a ladder of “equivalence principles” (that is: weak, medium, strong). The exposition is mathematically challenging. Glance at page 22, six theorems. Then, look ahead to the derivations of these formulas on page 26. The ‘alternative’ approach to Bianchi identities is nice (page 28). Black Holes touched upon: “…the black-hole is so immaterial, so purely geometrical, that no such direct evidence for its ‘spin’ is available. Evidence for the spin is obtainable by indirect means.” (page 65). I am dissatisfied with the description here of the Hawking process (page 68, read instead Hawking’s 1977 Scientific American article). Of dubious utility at this juncture is the Geon:”a collection of electromagnetic or gravitational energy–or, a mixture of the two–held together by its own gravitational attraction, that describes mass without mass.” (page 78).(3) Experiments, of eighty pages (ignoring references). Sagnac effect: “…examines propagation of light in rotating circuit” and “represents a gravitational analog of the Aharonov−Bohm effect in electrodynamics” (see Ashtekar, Journal of Mathematical Physics 16, 341,1975). Ciufolini and Wheeler: “we have assumed that, locally, in every freely falling frame, the laws of physics are independent of the spacetime location of an event. It is a consequence of this assumption that all the physical constants (e, h, c, m, G) must be time-independent.” (page 109). Is that really so ? Learn: “One of the important features of the general relativistic field equations is its nonlinearity, different from classical Poisson equation.”(4) Cosmology, next: Background Microwave Radiation introduced. Horizons and inflation theory touched upon (pages 214-220). A highlight is elaboration of this: “extrinsic curvature plus intrinsic curvature is proportional to energy-density” (page 226). A highlight: Raychaudhuri equation (also read: Baez, Meaning Of Einstein’s Equations, American Journal of Physics 73, 644, 2005).(5) Chapter five, Initial Value Problem. A discussion of thirty pages. Reading: “Space, in the large, must be compact.” (page 273). It’s that certain ? Now, read: “we shall demand that the spacetime manifold shall be spatially closed, that is spatially compact and spatially without boundary.” Also: “Time ? Three-geometry itself is carrier of information about time.” (pages 275-276). Feynman sum-over-histories (path integral) briefly described (page 279). Read more of geons and gravitons: “gravitational geon is a special example of gravitational wave” and “head-on encounter of two gravitons creates matter out of emptiness of space.” (page 295). Those statements will not make sense in a text intended as an introduction.(6) Chapter Six, Gravitomagnetism: “…may be thought of as a manifestation of the way inertia originates; mass-energy there rules inertia here” and “stressing that, despite the beautiful and illuminating analogies between classical electrodynamics and classical geometrodynamics, the two theories are fundamentally different.” (page 324). Final chapter, historical survey: Thomson’s depiction of “pulse of electromagnetic radiation generated by an accelerated charge” is modernized ( “analogies” highlighted). Yet, the diagram for accelerated charge (here, page 389) is located in Misner, Thorne, Wheeler (1973, page 111). Read: “the geometry of the spacetime, and therefore local inertia, in the sense of local inertial frames at each event along the worldline of every test particle, are determined by the distribution and flow of energy throughout all of space.” (page 395).(7) Concluding: What to make of this monograph ? It is a mixture of introductory and advanced material coupled with a mixture of theory and experiment. I choose to keep a copy of Clifford Will handy: Theory and Experiment in Gravitational Physics. I am rather dissatisfied with Ciufolini and Wheeler’s approach.A recent book that I recommend as collateral reading: Pfister and King’s “Inertia and Gravitation.” (2015).

⭐On retrouve la “patte” de John Archibald Wheeler, celui qui a sans doute le mieux compris la Relativité Générale, dans la génération juste après Einstein.

⭐

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