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Einstein, Albert
The Evolution of Physics
paperback. Good. Access codes and supplements are not guaranteed with used items. May be an ex-library book. paperback
Référence libraire : 0671201565.G ISBN : 0671201565 9780671201562
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Einstein, Albert, Infeld, Leopold
The Evolution of Physics
Touchstone. Used - Acceptable. Acceptable condition. With remainder mark. A readable intact copy that may have noticeable tears and wear to the spine. All pages of text are present but they may include extensive notes and highlighting or be heavily stained. Includes reading copy only books. Touchstone unknown
Référence libraire : K09C-02169 ISBN : 0671201565 9780671201562
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Einstein, Alfred and Leopold Infeld
The Evolution of Physics
Cambridge University Press. Collectible - Good. Great Britain: Cambridge at the Univ Press 1938. 1st UK 1st issue with gold lettering on spine and both endpapers present. Hardcover 12mo 319 pgs. Medium blue cloth gold gilt on spine. B/w plates and illustrations. Near very good book in a fair dust jacket. Corners and spine ends lightly bumped and worn. Contents clean and binding sound. Bookplate to front endpaper with writing in Latin name of Andrzei Falkiewicz written in and Alberto H R Ball Rectore at bottom edge. Jacket is edgeworn chipped and torn. Rear panel and spine are toned. Orig price 8s 6d on front flap. stem science physics Inquire if you need further information. Cambridge University Press hardcover
Référence libraire : B34915-SC
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EINSTEIN, Albert and INFELD, Leopold
The evolution of physics
New York: Simon and Schuster 1938. FIRST EDITION THIRD PRINTING. Original cloth; interior clean. A newspaper article pasted onto the paste-down plus the flaps from the dust jacket pasted in. Ownership signature of Charles Schuchert 1858-1942 American paleontologist that was the leader in the development of paleogeography on the fly-leaf. First edition third printing. Intended as an explanation of the totality of Einstein’s accomplishments for the layperson the publication of this extraordinarily successful work was also used in an attempt to find Infeld a university position he eventually ended up in Canada. According to the preface “the book is a simple chat between you and us. You may find it boring or interesting dull or exciting but our aim will be accomplished if these pages give you some idea of the eternal struggle of the inventive human mind for a fuller understanding of the laws governing physical phenomena.â€<br /> <br /> Weil 201. Simon and Schuster unknown
Référence libraire : 15852
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Einstein, Albert, and Leopold Infeld
The Evolution of Physics: The Growth of Ideas from Early Concepts to Relati vity and Quanta
Simon and Schuster. 1961. Paperback. UsedGood. Paperback; 9th printing; scuffing light soiling and shelf wear to exterio r; former owner's name written on front endpaper; fade spots to page edges; small amount of underlining and a few margin marks; in good condition with firm binding. . Simon and Schuster paperback
Référence libraire : 90079
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Einstein, Albert
The Evolution of Physics
Touchstone. Very Good. 1966. Soft Cover. 0671201565 W134 . Touchstone paperback
Référence libraire : 602880 ISBN : 0671201565 9780671201562
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Einstein, Albert; Infeld, Leopold
The Evolution of Physics
Touchstone 1967-10-30. 18th Printing. Paperback. Good. Book has slight shelf wear from storage and use; otherwise the book is in good condition. Touchstone paperback
Référence libraire : S32F191101009 ISBN : 0671201565 9780671201562
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Einstein, Albert; Infeld, Leopold
The Evolution of Physics
Touchstone 1967. Paperback. Good. Pages can have notes/highlighting. Spine may show signs of wear. ~ ThriftBooks: Read More Spend Less.Dust jacket quality is not guaranteed. Touchstone paperback
Référence libraire : G0671201565I3N00 ISBN : 0671201565 9780671201562
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Einstein, Albert; Infeld, Leopold
The Evolution of Physics
New York: Simon and Schuster 1938. First Edition. Hardcover. Very Good. First edition first printing. Previous owner signature of Albert K. Chapman to front free end paper. Chapman served as the president of the Eastman Kodak Company from 1952-1960 then as chairman until he retired in 1967.Publisher's navy blue cloth binding stamped in gilt. Near Fine with a small scuff to front cover. In a Very Good dust jacket with price intact moderate rubbing and edge wear and a slightly toned spine panel. Simon and Schuster hardcover
Référence libraire : 180902007
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Einstein, Albert And Leopold Infeld
The Evolution Of Physics The Growth Of Ideas From Early Concepts To Relativity And Quanta
New York: Simon & Schuster 1938. First American Edition 1st Printing. Blue Cloth. Very Good/Very Good. Illustrated with Black and White Photographs Charts and Diagrams. X 319 Pp 1 Pp Ads At Rear. Blue Cloth Gilt Yellow Endpapers. One Of 6000 Copies Of The American First Printing; Publisher's Note On Dj States That The Uk Dutch And American Editions Were Being Issued Simultaneously. Book Is Very Good Gilt Very Bright Cloth Clean Rear Hinge Cracked In Upper 2 3/4" Clean Unmarked Pages; One Quarter Inch Square Area Of Fading At Upper Left Of Spine Panel. With Heraldic Bookplate On Front Pastedown Mostly Under Flap Of Dj. First Issue Dj Priced $2.50 At Bottom Of Rear Flap With Price Much Nearer The Gold Border Than The Bottom Edge; On Later Printings The Price Is Aligned Midway. Dj Clean Spine Lettering Somewhat Browned Light Wear 1/2" Triangular Chip At Top Of Rear Panel Still Present But Loose; Minute Losses At Corners; Browning To Edges Of White Rear Panel But No Browning At All To Front Panel. <br/> <br/> Simon & Schuster hardcover
Référence libraire : 035775
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Einstein, Albert; Infeld, Leopold
The Evolution of Physics
Touchstone. New. BRAND NEW GIFT QUALITY! NOT OVERSTOCKS OR MARKED UP REMAINDERS! DIRECT FROM THE PUBLISHER! Touchstone unknown
Référence libraire : OTF-S-9780671201562 ISBN : 0671201565 9780671201562
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Einstein, Albert
The evolution of physics: The growth of ideas from early concepts to relativity and quanta
Simon and Schuster 1/1/1938. Hardcover. Very Good. 17th Printing. Hardcover. No dust jacket. Good binding and cover. Top page end blue dull from dust. Minimal shelfwear. Scattered pencil markings. Ships daily. Simon and Schuster hardcover
Référence libraire : 1412310090
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Einstein, Albert
The Evolution of Physics
Touchstone. New. Special order direct from the distributor Touchstone unknown
Référence libraire : ING9780671201562 ISBN : 0671201565 9780671201562
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Einstein, Albert
The Evolution of Physics
Touchstone 1967-10-30. Illustrated. paperback. New. 5.31x1.10x8.25. Buy with confidence. Excellent Customer Service & Return policy. Touchstone paperback
Référence libraire : DADAX0671201565 ISBN : 0671201565 9780671201562
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Einstein, Albert
The Evolution of Physics
Touchstone 1967-10-30. Illustrated. paperback. Used: Good. 5.31x1.10x8.25. Buy with confidence. Excellent Customer Service & Return policy. Touchstone paperback
Référence libraire : SONG0671201565 ISBN : 0671201565 9780671201562
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Einstein, Albert & Leopold Infeld
THE EVOLUTION OF PHYSICS: From Early Concepts to Relativity and Quanta
New York: Simon & Schuster 1967 302pp illus. slight soiling & shelfwear to cover. Trade Paperback. Very Good -/No Jacket. Simon & Schuster Paperback
Référence libraire : 10-1380
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Einstein, Albert
THE EVOLUTION OF PHYSICS: FROM EARLY CONCEPTS TO RELATIVITY AND QUANTA
1966. 1966 Einstein Albert and Leopold Infeld THE EVOLUTION OF PHYSICS: FROM EARLY CONCEPTS TO RELATIVITY AND QUANTA NY: Clarion Books/Simon and Schuster c1966 much later printing 302pp 8vo As new trade paperback. unknown
Référence libraire : 52808 ISBN : 0671201565 9780671201562
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Einstein, Albert, and Infeld, Leopold
The evolution of physics; the growth of ideas from early concepts to relativity and quanta
New York: Simon and Schuster 1961. Trade paperback. Good. No dust jacket. Signed by previous owner. first 3 pages at bottom have puch hole in. xvi 302 p. illus. 21 cm. An Essandess paperback. Includes Illustrations. Simon and Schuster paperback
Référence libraire : Alibris.0005067
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Einstein, Albert
The Evolution of Physics: From Early Concepts to Relativity and Quanta
Old Tappan New Jersey U.S.A.: Touchstone. Soft cover. Very Good. 16th Large sturdy softcover glossy black with design of small white ovals on front wrapper on white back lightly browned praise from Waldemar Kaempffert in New York Times Prof. E.T. Bill in Saturday Review and others 301 lightly browned pages. Very slight wear at top front tip slight wear at spine top and bottom edges. Very Good. <br/> <br/> Touchstone paperback
Référence libraire : 37902 ISBN : 0671201565 9780671201562
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Einstein, Albert; Leopold Infeld
The Evolution of Physics: From Early Concepts to Relativity and Quanta
Touchstone Books 1967. Wraps have light wear. Pages are clean text has small amount of pencil markings. Soft Cover. Good. 8vo - over 7¾" - 9¾" tall. Touchstone Books Paperback
Référence libraire : 242555 ISBN : 0671201565 9780671201562
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Einstein, Albert
The Expanded Quotable Einstein
Princeton University Press 5/30/2000 12:00:01 A. hardcover. Very Good. 1.1102 in x 9.1299 in x 6.5709 in. Princeton University Press hardcover
Référence libraire : 5FSZKJ0008PA ISBN : 0691070210 9780691070216
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Einstein, Albert
The Expanded Quotable Einstein
Princeton University Press. Used - Good. Former library book; may include library markings. Used book that is in clean average condition without any missing pages. Princeton University Press unknown
Référence libraire : GRP21203430 ISBN : 0691070210 9780691070216
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Einstein, Albert; Calaprice, Alice
The Expanded Quotable Einstein
Princeton University Press. 2nd. Good. It's a preowned item in good condition and includes all the pages. It may have some general signs of wear and tear such as markings highlighting slight damage to the cover minimal wear to the binding etc. but they will not affect the overall reading experience. Princeton University Press unknown
Référence libraire : 0691070210-11-1 ISBN : 0691070210 9780691070216
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Einstein, Albert; Alice Calaprice (editor)
The Expanded Quotable Einstein
Princeton NJ: Princeton University Press. Fine copy in fine dust jacket. 2000. 1st. hardcover. 8vo 407 pages With a foreword by Freeman Dyson. . Princeton University Press hardcover
Référence libraire : BOOKS107057I ISBN : 0691070210 9780691070216
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Einstein, Albert
The Expanded Quotable Einstein
hardcover. Good. Access codes and supplements are not guaranteed with used items. May be an ex-library book. hardcover
Référence libraire : 0691070210.G ISBN : 0691070210 9780691070216
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Einstein, Albert
The Expanded Quotable Einstein
Princeton University Press. Used - Very Good. Used book that is in excellent condition. May show signs of wear or have minor defects. Princeton University Press unknown
Référence libraire : 753672-6 ISBN : 0691070210 9780691070216
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Einstein, Albert; Alice Calaprice (editor)
The Expanded Quotable Einstein
Princeton NJ: Princeton University Press. Fine copy in fine dust jacket. 2000. 2nd prt. hardcover. 8vo 407 pages With a foreword by Freeman Dyson. . Princeton University Press hardcover
Référence libraire : BOOKS071800I ISBN : 0691070210 9780691070216
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Einstein, Albert
The Expanded Quotable Einstein
Princeton University Press 2000-05-30. 2nd. hardcover. Used: Good. 4.72x1.18x7.48. Buy with confidence. Excellent Customer Service & Return policy. Princeton University Press hardcover
Référence libraire : SONG0691070210 ISBN : 0691070210 9780691070216
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Einstein, Albert
The Fight Against War
hardcover. Good. Access codes and supplements are not guaranteed with used items. May be an ex-library book. hardcover
Référence libraire : 1258099454.G ISBN : 1258099454 9781258099459
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Einstein, Albert
The Fight Against War
paperback. Good. Access codes and supplements are not guaranteed with used items. May be an ex-library book. paperback
Référence libraire : 1258203766.G ISBN : 1258203766 9781258203764
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EINSTEIN, ALBERT
The Fight Against War
<p>Original wrappers. Price neatly blacked out at lower corner. Tiny chip from back wrapper. Very good.</p><p>FIRST EDITION.</p><p>This scarce collection of Einstein's writings on war and peace was published in 1933 the year the Nazis took power in Germany and the year Einstein left Germany for the United States. In his prefatory note Einstein writes "Mr. Lief the editor Alfred Lief has taken great trouble in collecting utterances of mine having pacifistic content and he presents them with my authorization. … I consider it my duty to confess my pacific conviction publicly. May the seriousness of my purpose be transferred to you my readers! A. Einstein."</p> John Day paperback
Référence libraire : 32820627
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Einstein, Sergei M.
The Film Sense
Faber & Faber 1948. This is an ex-library book and may have the usual library/used-book markings inside.This book has hardback covers. In fair condition suitable as a study copy. No dust jacket. Please note the Image in this listing is a stock photo and may not match the covers of the actual item350grams ISBN: Faber & Faber hardcover
Référence libraire : 2922795
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Einstein, Charles, ed. Intro. Ford Frick
The Fireside Book of Baseball
Simon & Schuster 1956. Hardcover. Acceptable. Missing dust jacket; Readable copy. Pages may have considerable notes/highlighting. ~ ThriftBooks: Read More Spend Less.Dust jacket quality is not guaranteed. Simon & Schuster hardcover
Référence libraire : GB00SXERCDSI5N01
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Einstein, Charles
The Fireside Book of Baseball
Touchstone 1987. Paperback. Very Good. May have limited writing in cover pages. Pages are unmarked. ~ ThriftBooks: Read More Spend Less.Dust jacket quality is not guaranteed. Touchstone paperback
Référence libraire : G0671638122I4N00 ISBN : 0671638122 9780671638122
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Einstein, Charles, editor
The Fireside Book of Baseball
New York: Simon and Schuster c1987. Fourth Edition. Paperback. Very good condition. 444p. <br/><br/> Simon and Schuster paperback
Référence libraire : 31773 ISBN : 0671638122 9780671638122
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Einstein, Albert
The Foundation of the Generalized Theory of Relativity Find Yo Genius Edition By ALBERT EINSTEIN
Blurb 2025-07-23. paperback. New. Blurb paperback
Référence libraire : 9798331203092
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Einstein, Albert
The Foundation of the Generalized Theory of Relativity
hardcover. Good. Access codes and supplements are not guaranteed with used items. May be an ex-library book. hardcover
Référence libraire : 1715276949.G ISBN : 1715276949 9781715276942
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Einstein, Albert
The Foundation of the Generalized Theory of Relativity
Blurb 2024-08-23. hardcover. New. 6.00x0.38x9.00. Buy with confidence. Excellent Customer Service & Return policy. Blurb hardcover
Référence libraire : DADAX1715276949 ISBN : 1715276949 9781715276942
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Einstein, Alfred (editor)
The Golden Age of the Madrigal. Twelve Italian Madrigals for Five-Part Chorus of Mixed Voices Never before Published in a Modern Edition. Selected Edited and Annotated by Alfred Einstein with English Versions by Gustave Reese
New York: G. Schirmer. Good. First Edition Thus. Library Buckram. 95 pages. With library stamps & labels. New endpapers. Slight wear to spine covers & corners. ; Ex-Library; Quarto . G. Schirmer hardcover
Référence libraire : 18714
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Einstein, Alfred
The Golden Age of the Madrigal : Twelve Five-part Mixed Choruses
USA: G Schirmer 1942. Words and Music. ENGLISH AND ITALIAN. Copywright date of 1942 printed on the bottom page margins at intervals. Book is in very good condition with minor signs of wear and/or age BUT top RH corner of front cover turned up. New Revised Edition. Paperback. VG. G Schirmer Paperback
Référence libraire : L023.241
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Einstein, Alfred
The golden age of the madrigal; twelve Italian madrigals for five-part chorus of mixed voices never before published in a modern edition
New York: G. Schirmer inc. c1942. Paperback. Very good condition. 95 p. 26 cm. <br/><br/> G. Schirmer, inc. paperback
Référence libraire : 44499
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EINSTEIN, Albert, & Leopold Infeld.
The Gravitational Equations and the Problem of Motion. II.
Princeton: Princeton University Press 1940. Elucidating the Einstein-Infeld-Hoffman equations First edition offprint issue of Einstein's last major contribution to the general theory of relativity. It formed part of his mathematical investigations into the structure of the theory which he spent the latter part of his life refining. "During the development of the general theory Einstein had intended to hold fast to the conservation of energy and momentum in the usual special relativistic sense as far as possible. At the same time he was driven by other considerations toward the idea that the laws should be generally covariant. These two desires proved mutually incompatible. The problem of the equation of motion of bodies is the following. The 1916 theory had a classical structure in the sense that there were both field equations the curvature of space-time is determined by the mass and motion of bodies in space-time and equation of motion of bodies the world line of small mass is a geodesic. Einstein showed that if matter is represented by a point singularity of the metric field these singularities are located on world lines that are geodesics of space time provided its metric satisfies the equation of general relativity" DSB IV p. 329. The first part of the paper was published in 1938. Large octavo pp. 10. Original wrappers wire-stitched as issued front cover printed in black. Wrappers gently toned: a near-fine copy. Boni 236.1; Weil 205. unknown
Référence libraire : 180281
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EINSTEIN, A., L. INFELD & B. HOFFMANN. - EINSTEIN'S LAST CONTRIBUTION TO GENERAL RELATIVITY - THE ROUND OFF OF GENERAL RELATIVIT
The gravitational Equations and the problem of Motion. I- II. Part II only with Infeld.
Baltimore Princeton University Press 1938 a.1940. Royal8vo. Bound in 2 full cloth gilt lettering to spines. In: Annals of Mathematics" Series 2 Vol. 39 and vol. 40. Entire volumes offered. The papers: pp. 65-100 a. pp. 455-464. Clean and fine.også on a generalization. pais p. 496 <br/><br/><em>First appearance of these two importent papers on the General theory of Relativity in which is shown that the equation of motion follows directly from the field equation that defined the geometry."Einstein's last importent contribution to general relativity deals again with the problem of motion. It is the work done with Leopold Indfeld and Banesh Hoffmann on the N-body problem of motion. In these papers the gravitational field is no longer treated as external. Instead it and the motion of its singular sources are treated simultaneously. A new approximation scheme is introduced in which the fields are no longer necessarily weak but in which the source velocities are small compared with the light velocity. These equations are widely used in analyses of planetary orbits in the solar system."Pais "Subtle is the Lord" pp. 290-91.Weil: 202 a. 205 both with an asterix denoting a major paper. - Boni: 236 a. 236.1. </em> hardcover
Référence libraire : 46954
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EINSTEIN, A., L. INFELD, and B. HOFFMANN. - THE ROUND OFF OF GENERAL RELATIVITY - ASSOCIATION COPY.
The gravitational Equations and the Problem of Motion. Part I. Received June 16 1937. II. Received May 29 1939. 2 Papers Paper II only Einstein and Infeld.
Princeton NJ. Annals of Mathematics 1938 a. 1940. Both papers in orig. printed wrappers. Offprints from "Annals of Mathematics" Vol. 39 No. 1 january 1938 and Vol. 41 No. 2 April 1940. Pp. 65-100 and pp. 455-464. Both clean and fine. This copy has belonged to Abraham Pais 1918-2000 - the famous Einstein scholar theoretical physicist and Einsteins collegue at Princeton - and having his name on top of both frontwrappers "A Pais". <br/><br/><em>First editions in the scarce offprint versions of Einstein's last and highly important contributions to General relativity and in which is shown that the equation of motion follows directly from the field equation that defined the geometry."Einstein's last importent contribution to general relativity deals again with the problem of motion. It is the work done with Leopold Infeld and Banash Hoffmann on the N-body problem of motion. In these papers the gravitational field is no longer treated as external. Instead it and the motion of its singular sources are treated simultaneously. Anew approximationscheme is introduced in which the fields are no longer necessarily weak but in which the source velocities are small compared with the light velocity . The equations obtained have found use in situations where Newtonian interaction must be included. 'These equations are widely used in analyses of planetary orbits in the solarsystem. For example the Cal Tech Jet Propulsion Laboratory uses them in modified form to calculate ephmerides for high-precision tracking of planets and spacecraft."Pais "Subtle is the Lord" p. 290-91."The problem of the equation of motion of bodies is the following. The 1916 theory had a classical structure in the sense that there were both field equations the curvature of space-time is determined by the mass and motion of bodies in space-time and equations of motion of bodies the world line of small mass is a geodesic. Are these two statements really separate If the field equations were linear they indeed would be. They are not linear however and Einstein showed in the papers offered that if matter is represented by a point singularity of the metric field these singularities are located on world lines that are geodesics of space-time provided its metric satisfies the equation of general relativity."DSB.Weil: 202 a. 295 both with an asterix denoting a major paper. - Boni: 236 a. 236.1. </em> unknown
Référence libraire : 46475
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Einstein, Albert [introduction]; Eliot, George Fielding [commentary]
The H Bomb
New York: Didier 1950. good fair to good. 175 DJ somewhat worn and soiled: edge tears creases and small pieces missing DJ in plastic sleeve. Contributors include Stewart Alsop Robert Bacher Hanson W. Baldwin Hans Bethe David E. Lilienthal Walter Lippman Brien McMahon Hans Morgenthau Leo Szilard Harold Urey and Richard K. Winslow. Topics covered include the political significance of the Hydrogen Bomb the military value of the Hydrogen Bomb the scientific problems of building a Hydrogen Bomb and how those problems may be solved and a bold plan for world atomic peace. Didier unknown
Référence libraire : 56788
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Einstein, Xavier
The Honeymooners Trivia Mania : TV Greats
paperback. Good. Access codes and supplements are not guaranteed with used items. May be an ex-library book. paperback
Référence libraire : 0821717316.G ISBN : 0821717316 9780821717318
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Einstein, Lewis
The Humanists' Library: The Defence of Poesie &C Classic Reprint
hardcover. Good. Access codes and supplements are not guaranteed with used items. May be an ex-library book. hardcover
Référence libraire : 0332493121.G ISBN : 0332493121 9780332493121
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Einstein, David G.
The Indestructible Faith
New York: Bloch Publishing Company 1927. First Edition. Cloth. Very Good/No Jacket. 8vo. vii 207 pp. Owner's signature on ffep. Bloch Publishing Company unknown
Référence libraire : 7550
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EINSTEIN, Albert, & Ernst G. Straus.
The Influence of the Expansion of Space on the Gravitation Fields Surrounding the Individual Stars;
Lancaster Pennsylvania: American Physical Society 1945 & 1946. His most significant later contribution to cosmology First editions offprint issues of the papers that introduced the Swiss-cheese model of the universe. Einstein and Straus revised the FLRW metric by suggesting that the universe is in fact inhomogeneous. "In two ground-breaking papers Einstein and Straus showed how galaxies fit into a Universe with zero pressure. This model helps to describe the universe observed today" Harwit p. 573. Quarto pp. 5. Disbound wire-stitched as issued. Nicks and creasing to extremities short closed tears to outer margins pp. 120-1 of Influence detached rear blank almost detached: in very good condition. Boni 252 & 252.1; Weil 216. Martin Harwit Astrophysical Concepts 2010. unknown
Référence libraire : 180350
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EINSTEIN, Albert & STRAUS, Ernst Gabor
The Influence of the Expansion of Space on the Gravitation Fields Surrounding the Individual Stars. WITH: Corrections and Additional Remarks to Our Paper … Offprints from: Reviews of Modern Physics vols. 17 no. 2/3 April-June 1945 & vol. 18 no. 1 January-March 1946
Lancaster PA: American Physical Society 1945. First edition. EINSTEIN’S ‘SWISS-CHEESE’ MODEL OF THE UNIVERSE - OFFPRINT ISSUE. <p>First edition extremely rare offprints of Einstein & Straus’s introduction of the ‘Swiss-cheese’ model of the universe. “After a decade and a half of sometimes intense work on cosmology Einstein returned to the subject only occasionally in his later years. His most significant later contribution was a discussion of the impact of cosmological expansion on the gravitational field surrounding a star i.e. the offered papers … This was an important first step in understanding the impact of global cosmological expansion on local physics†Janssen & Lehner pp. 257-8. In the 1920s and 1930s a general relativistic model of the universe was developed called the Friedmann-Lemaître-Robertson-Walker FLRW model which correctly described the expansion of the universe discovered by Edwin Hubble. But the FLRW model was ‘homogeneous’ – it described a universe which looks the same wherever the observer is located. The actual universe however is manifestly inhomogeneous – it contains stars galaxies and clusters of galaxies. Einstein and Straus’s papers represent the first serious attempt to model an inhomogeneous universe. “By the spring of 1945 Einstein and Straus had found a new type of possible universe using Einstein’s equations. It described a universe which looked largely like one of the simple expanding universes of Friedmann and Lemaître containing material like galaxies which exerted no pressure. But it had spherical regions removed from it like bubbles in a Swiss cheese. Each empty hole then had a mass placed at its centre. The mass was equal in magnitude to what had been excavated to create the hole. This was a step towards a more realistic universe in which the matter was not smoothly spread with the same density everywhere but gathered up into lumps like galaxies which were spread about in empty space†Barrow pp. 106-107. Not on OCLC; no copies in auction records.</p> <br /> <p>In 1916 just a few months after Einstein had formulated his general theory of relativity Karl Schwarzschild had found a solution of Einstein’s equations which described the gravitational field in the vicinity of a spherical distribution of mass such as a star or to anticipate later developments a black hole. This was in fact the first exact solution of Einstein’s equations to be found – Einstein had earlier calculated an approximate solution which was enough to show that his theory correctly accounted for the advance of Mercury’s perihelion. However at great distances from the star Schwarzschild’s solution approaches the flat Minkowski spacetime with zero curvature and not the FLRW solution that represented an expanding universe. It seemed therefore that Schwarzschild’s solution could not correctly describe the gravitational field of a star in an expanding FLRW universe. If the expansion of the universe meant that Schwarzschild’s solution had to be modified this could make it possible to detect and measure the expansion of the universe by making local observations rather than by observing the motion of distant galaxies as Hubble had done. The problem of describing the gravitational field of a star in an expanding FLRW universe was addressed by Einstein and Straus in the offered papers.</p> <br /> <p>“In the early 1930s theorists began to develop a richer account of the evolution of the universe based on expanding models. Hubble’s results qualitatively agreed with the redshift effect calculated in these models but the utility of the simple dynamical models depends on whether the universe is approximately uniform. The status of this assumption was the focus of lively debate … Relativistic cosmologists regarded the idealized uniformity of the FLRW models as a simplifying assumption … The unrelenting uniformity built into the FLRW models conflicts with the clear non-uniformity of the stars star clusters and galaxies of the local universe but the models might still serve as a useful approximation if the non-uniformities are negligible at larger scales†Janssen & Lehner p. 256.</p> <br /> <p>“By 1944 Einstein had recruited a new assistant at Princeton. His assistants were always talented young mathematicians who could make up for Einstein’s self-confessed weakness in this area. Ernst Straus 1922-1983 was something of a mathematical prodigy … He was born in Munich but after the Nazis came to power in 1933 his family fled to Palestine where he was educated at high school and at the Hebrew University in Jerusalem. Straus didn’t stay to take an undergraduate degree and instead while still a teenager moved to New York’s Columbia University in 1941 to begin graduate research. In 1944 he found himself recruited as Einstein’s new research assistant at the Institute for Advanced Study in Princeton. The young Straus had no background in physics and his mathematical inclinations were towards number theory and ‘pure’ mathematical topics but he lost no time in filling the gap left by the departures of Nathan Rosen 1935-45 and Leopold Infeld 1936-38†Barrow pp. 105-6.</p> <br /> <p>Einstein and Straus found an exact solution of the equations of general relativity in which a spherical ‘hole’ is cut out of an FLRW universe and the hole is replaced by a single mass point e.g. a star surrounded by a spherical cavity. The initially homogeneous matter within the cavity can be thought of as having been “condensed into the starâ€. Einstein and Straus found that the interior of the cavity is described by the standard Schwarzschild solution. The radius of the hole is such that at its spherical boundary the outward pull from the cosmological masses is just balanced by the inward pull from the star. The cavity boundary expands according to the Hubble expansion of the whole universe. The universe outside the cavity is described by the standard expanding homogeneous FLRW solution. The possibility of exactly matching the Schwarzschild solution near the star to the FLRW solution outside it showed that it was not in fact possible to detect the expansion of the universe by making observations close to the star. There were similar solutions with more than one hole – Einstein said that this reminded him of the holes in Swiss cheese. The static vacuum region inside the cavity is now called an ‘Einstein-Straus vacuole’.</p> <br /> <p>The methods introduced by Einstein and Straus in these papers have been used extensively to model inhomogeneities in the universe. For example in 1968 Martin Rees and Dennis Sciama investigated the effects of large-scale inhomogeneities such as superclusters of galaxies on the cosmic microwave background the so-called ‘Rees-Sciama effect’. The Swiss-cheese model has also been used in the study of inflationary models of the early universe. According to this theory the universe expanded exponentially in the first tiny fraction of a second after the big bang with some parts of space-time expanding more quickly than others. This created ‘bubbles’ in space-time. The Swiss-cheese “embodies a natural way to model physical problems such as describing the boundary between a galaxy and intergalactic space or the relation between bubbles at the end of an inflationary era by taking two different regions where the behaviour is smooth and joining them at a surface of discontinuity†Ellis et al. p. 426.</p> <br /> <p>In the last decade several authors have suggested that Swiss-cheese models might solve a long-standing problem on the rate of expansion of the universe. Distant supernovas have been observed to be dimmer than expected on the basis of standard cosmological theories indicating that the universe is expanding faster than these theories predict. This has been explained by hypothesizing the existence of ‘dark energy’ although exactly what dark energy might be is a mystery. But if the light from distant supernovas had to cross large vacuoles in reaching an observer on the earth these would act like concave lenses making the supernovas appear dimmer and further away than they really are. Other authors have noted that the Milky Way is near the centre of a region that has fewer galaxies than other parts of the universe and that we might be living near the centre of a particularly large vacuole perhaps more than a billion light years in diameter see for example Bonnor.</p> <br /> <p>Weil 216. Barrow The Book of Universes 2011. Bonnor ‘A generalisation of the Einstein-Straus vacuole’ Classical and Quantum Gravity 17 2000 pp. 2739-2748. Ellis Maartens & MacCallum Relativistic Cosmology 2012. Janssen & Lehner eds. The Cambridge Companion to Einstein 2014.</p> <br/> <br/> Together two offprints 4to 267 x 200 mm pp. 120-124 & 148-149. Stapled as issued in original self-wrappers. American Physical Society unknown
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