‎Einstein‎

‎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. <p>First edition extremely rare offprints of Einstein & Straus's introduction of the 'Swiss-cheese' model of the universe. "By the spring of 1945 Einstein and Straus had found a new type of possible universe using Einstein's equations . 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 The Book of Universes pp. 106-107.</p>. 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 star". 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

Bookseller reference : 5054

‎Einstein, Lewis‎

‎The Italian Renaissance in England‎

‎paperback. Good. Access codes and supplements are not guaranteed with used items. May be an ex-library book. paperback‎

Bookseller reference : 1021658316.G ISBN : 1021658316 9781021658319

‎Einstein, Alfred‎

‎The Italian Madrigal – Volume II‎

‎Princeton Univ Pr 2019. Hardcover. New. 448 pages. 10.00x8.00x1.25 inches. Princeton Univ Pr hardcover‎

Bookseller reference : x-0691655936 ISBN : 0691655936 9780691655932

‎Einstein, Alfred,‎

‎The Italian Madrigal‎

‎new. unknown‎

Bookseller reference : 35857278-n ISBN : 0691200734 9780691200736

‎Einstein, Alfred,‎

‎The Italian Madrigal‎

‎new. unknown‎

Bookseller reference : 35857281-n ISBN : 0691655782 9780691655789

‎Einstein, Alfred,‎

‎The Italian Madrigal‎

‎like new. unknown‎

Bookseller reference : 35857277 ISBN : 0691627533 9780691627533

‎Einstein, Alfred,‎

‎The Italian Madrigal‎

‎like new. unknown‎

Bookseller reference : 35857278 ISBN : 0691200734 9780691200736

‎Einstein, Alfred‎

‎The Italian Madrigal: Volume I Princeton Legacy Library‎

‎Princeton University Press 2019-08-06. hardcover. New. 8.00x1.25x10.00. Buy with confidence. Excellent Customer Service & Return policy. Princeton University Press hardcover‎

Bookseller reference : DADAX0691655928 ISBN : 0691655928 9780691655925

‎Einstein, Alfred‎

‎The Italian Madrigal: Volume III Princeton Legacy Library‎

‎Princeton University Press 2019-08-06. hardcover. New. 8.00x0.81x10.00. Buy with confidence. Excellent Customer Service & Return policy. Princeton University Press hardcover‎

Bookseller reference : DADAX0691200734 ISBN : 0691200734 9780691200736

‎Einstein, Alfred‎

‎The Italian Madrigal: Volume III Princeton Legacy Library‎

‎Princeton University Press 2019-08-06. Reprint. paperback. New. 8.00x0.76x10.00. Buy with confidence. Excellent Customer Service & Return policy. Princeton University Press paperback‎

Bookseller reference : DADAX0691655847 ISBN : 0691655847 9780691655840

‎EINSTEIN, Alfred; Alexander H Krappe (et al, transl)‎

‎The Italian Madrigal 3 vols‎

‎Princeton: Princeton University Press 1949. First English Language Edition. Three quarto volumes. Burgundy cloth hardcovers in publisher's slipcase; xvi1-476; 477-8773; x333pp. A fine set in the original cloth bindings; slipcase is mildly rubbed and sunned with small paper loss to open edge still Very Good. <br /> <br /> Einstein's monumental study was the first scholarly treatise of its kind in any language and remains one of the essential works on early Italian secular music. Volumes I & II provide scholarly background on the history and evolution of madrigal form while the third volume compiles nearly 100 compositions produced between 1470 and 1650 including works by Tromboncino Verdalot De Rare Gabrielli and others. An uncommonly well-preserved set. Princeton University Press unknown‎

Bookseller reference : 88051

‎Einstein, Alfred; Sessions, Roger [Editor]; Strunk, Oliver [Editor]; Krappe, Alexander H [Editor];‎

‎The Italian Madrigal: Volume I Princeton Legacy Library‎

‎Princeton University Press 2019-08-06. Hardcover. Very Good. This is a new book that has some minor damage which is usually a tear a scratch dents or stain on the edge pages are clean no missing pages. Princeton University Press hardcover‎

Bookseller reference : B-gj24-23447 ISBN : 0691655928 9780691655925

‎Einstein, Alfred‎

‎The Italian Madrigal Volume 1-3‎

‎Princeton N.J.: Princeton University Press 1971. Hardcover. Good/Good Ex-library with stamps and labels on spine inside front and rear covers ffep and block. Overall light shelfwear to boards and block. Binding is tight and pages are otherwise clear. Three volumes bound in burgundy cloth with gilt spine lettering; tan dust jackets with mylar covers. Illustrated title pages bw illustrations throughout each volume. Text in English songs in Italian with English text translations. Vol. 3 contains "Texts of songs revised and translated by Antonio Illiano and Howard E. Smither" and scores of 97 madrigals. Princeton University Press hardcover‎

Bookseller reference : 186152 ISBN : 0691091129 9780691091129

‎Einstein, Alfred‎

‎The Italian Madrigal: Volume I Princeton Legacy Library‎

‎paperback. Good. Access codes and supplements are not guaranteed with used items. May be an ex-library book. paperback‎

Bookseller reference : 0691627533.G ISBN : 0691627533 9780691627533

‎Einstein, Alfred‎

‎The Italian Madrigal: Volume II Princeton Legacy Library‎

‎paperback. Good. Access codes and supplements are not guaranteed with used items. May be an ex-library book. paperback‎

Bookseller reference : 0691655782.G ISBN : 0691655782 9780691655789

‎Einstein, Alfred‎

‎The Italian Madrigal: Volume III Princeton Legacy Library‎

‎hardcover. Good. Access codes and supplements are not guaranteed with used items. May be an ex-library book. hardcover‎

Bookseller reference : 0691200734.G ISBN : 0691200734 9780691200736

‎Einstein, Alfred‎

‎The Italian Madrigal: Volume I Princeton Legacy Library‎

‎hardcover. Good. Access codes and supplements are not guaranteed with used items. May be an ex-library book. hardcover‎

Bookseller reference : 0691655928.G ISBN : 0691655928 9780691655925

‎Einstein, Lewis‎

‎The Italian Renaissance In England: Studies‎

‎paperback. Good. Access codes and supplements are not guaranteed with used items. May be an ex-library book. paperback‎

Bookseller reference : 1162963727.G ISBN : 1162963727 9781162963723

‎Einstein, Lewis 1877-1967‎

‎The Italian Renaissance in England; Studies‎

‎hardcover. Good. Access codes and supplements are not guaranteed with used items. May be an ex-library book. hardcover‎

Bookseller reference : 1018859489.G ISBN : 1018859489 9781018859484

‎Einstein, Alfred/ Sessions, Roger (Editor)/ Strunk, Oliver (Editor)/ Krappe, Alexander H (Editor)‎

‎The Italian Madrigal – Volume I‎

‎Princeton Univ Pr 2019. Paperback. New. reprint edition. 512 pages. 9.75x8.00x1.25 inches. Princeton Univ Pr paperback‎

Bookseller reference : x-0691627533 ISBN : 0691627533 9780691627533

‎Einstein, Alfred‎

‎The Italian Madrigal – Volume II‎

‎Princeton Univ Pr 2019. Paperback. New. reprint edition. 448 pages. 9.75x8.00x1.00 inches. Princeton Univ Pr paperback‎

Bookseller reference : x-0691655782 ISBN : 0691655782 9780691655789

‎Einstein, Lewis‎

‎The Italian Renaissance In England: Studies‎

‎Kessinger Publishing 2007-07-25. hardcover. New. 6.00x1.19x9.00. Buy with confidence. Excellent Customer Service & Return policy. Kessinger Publishing hardcover‎

Bookseller reference : DADAX0548121761 ISBN : 0548121761 9780548121764

‎Einstein, Albert‎

‎The Meaning of Relativity: Including the Relativistic Theory of the Non-Symmetric Field - Fifth Edition‎

‎Princeton University Press 1945. Hardcover. Acceptable. Former library book; Readable copy. Pages may have considerable notes/highlighting. ~ ThriftBooks: Read More Spend Less.Dust jacket quality is not guaranteed. Princeton University Press hardcover‎

Bookseller reference : G0691080070I5N10 ISBN : 0691080070 9780691080079

‎Einstein, Albert‎

‎THE MEANING OF RELATIVITY.‎

‎Methuen 1950-01-01. Hardcover. Good. 2.8179 in x 23.1724 in x 16.6773 in. Ex-library book usual marking. Clean copy in good condition. Without Dust Cover. Methuen hardcover‎

Bookseller reference : mon0000469800

‎Einstein, Albert ; introduction by Charles Sheffield‎

‎The Meaning of Relativity‎

‎Norwalk: Easton Press 1994. First Edition in this Format ; Collector's Edition. Hardcover. Book condition is Near Fine bound in full genuine leather with 22kt gold accents gilt page edges and a hubbed spine. Smyth sewn interior vaunts moire end papers acid-neutral paper won't yellow or become brittle over time and silk ribbon page marker. Very minimal rubbing and edge wear to exterior. Text is clean and unmarked. ; 8vo. 9"h x 6"w. Easton Press hardcover‎

Bookseller reference : 17293