Introducing Volume 15 of The Collected Papers of Albert Einstein

From fraudulent science to hope for European reunification, the newest volume of The Collected Papers of Albert Einstein conveys the breakneck speed of Einstein’s personal and professional life. Volume 15, covering June 1925 to May 1927, is out now!

THE COLLECTED PAPERS OF ALBERT EINSTEIN
Volume 15: The Berlin Years
Writings & Correspondence, June 1925-May 1927, Documentary Edition

Edited by Diana Kormos Buchwald, József Illy, A. J. Kox, Dennis Lehmkuhl, Ze’ev Rosenkranz & Jennifer Nollar James

Princeton University Press, the Einstein Papers Project at the California Institute of Technology, and the Albert Einstein Archives at the Hebrew University of Jerusalem, are pleased to announce the latest volume in the authoritative COLLECTED PAPERS OF ALBERT EINSTEIN. This volume covers one of the most thrilling two-year periods in twentieth-century physics, as matrix mechanics—developed chiefly by W. Heisenberg, M. Born, and P. Jordan—and wave mechanics—developed by E. Schrödinger—supplanted earlier quantum theory. The almost one hundred writings, a third of which have never before been published, and the more than thirteen hundred letters demonstrate Einstein’s immense productivity at a tumultuous time.

Within this volume, Einstein grasps the conceptual peculiarities involved in the new quantum mechanics; falls victim to scientific fraud while in collaboration with E. Rupp; and continues his participation in the League of Nations’ International Committee on Intellectual Cooperation.

ENGLISH TRANSLATION SUPPLEMENT

Every document in The Collected Papers of Albert Einstein appears in the language in which it was written, and this supplementary paperback volume presents the English translations of select portions of non-English materials in Volume 15. This translation does not include notes or annotation of the documentary volume and is not intended for use without the original language documentary edition which provides the extensive editorial commentary necessary for a full historical and scientific understanding of the documents.

Translated by Jennifer Nollar James, Ann M. Hentschel, and Mary Jane Teague, Andreas Aebi and Klaus Hentschel, consultants

THE COLLECTED PAPERS OF ALBERT EINSTEIN

Diana Kormos Buchwald, General Editor

THE COLLECTED PAPERS OF ALBERT EINSTEIN is one of the most ambitious publishing ventures ever undertaken in the documentation of the history of science.  Selected from among more than 40,000 documents contained in the personal collection of Albert Einstein (1879-1955), and 20,000 Einstein and Einstein-related documents discovered by the editors since the beginning of the Einstein Papers Project, The Collected Papers provides the first complete picture of a massive written legacy that ranges from Einstein’s first work on the special and general theories of relativity and the origins of quantum theory, to expressions of his profound concern with international cooperation and reconciliation, civil liberties, education, Zionism, pacifism, and disarmament.  The series will contain over 14,000 documents as full text and will fill close to thirty volumes.  Sponsored by the Hebrew University of Jerusalem and Princeton University Press, the project is located at and supported by the California Institute of Technology and has made available a monumental collection of primary material. It will continue to do so over the life of the project. The Albert Einstein Archives is located at the Hebrew University of Jerusalem. The open access digital edition of the first 14 volumes of the Collected Papers is available online at einsteinpapers.press.princeton.edu.

ABOUT THE SERIES: Fifteen volumes covering Einstein’s life and work up to his forty-eighth birthday have so far been published. They present more than 500 writings and 7,000 letters written by and to Einstein. Every document in The Collected Papers appears in the language in which it was written, while the introduction, headnotes, footnotes, and other scholarly apparatus are in English.  Upon release of each volume, Princeton University Press also publishes an English translation of previously untranslated non-English documents.

ABOUT THE EDITORS: At the California Institute of Technology, Diana Kormos Buchwald is professor of history; A. J. Kox is senior editor and visiting associate in history; József Illy and Ze’ev Rosenkranz are editors and senior researchers in history; Dennis Lehmkuhl is research assistant professor and scientific editor; and Jennifer Nollar James is assistant editor.

Celebrate Pi Day with Books about Einstein

Pi Day is coming up! Mathematicians around the world celebrate on March 14th because the date represents the first three digits of π: 3.14.

In Princeton, Pi Day is a huge event even for the non-mathematicians among us, given that March 14 is also Albert Einstein’s birthday. Einstein was born on March 14, 1879, in Ulm, in the German Empire. He turns 139 this year! If you’re in the Princeton area and want to celebrate, check out some of the festivities happening around town:

Saturday, 3/10/18

  • Apple Pie Eating Contest, 9:00 a.m., McCaffrey’s (301 North Harrison Street). Arrive by 8:45 a.m. to participate.
  • Einstein in Princeton Guided Walking Tour, 10:00 a.m. Call Princeton Tour Company at (855) 743-1415 for details.
  • Einstein Look-A-Like Contest, 12:00 p.m., Nassau Inn. Arrive early to get a spot to watch this standing-room-only event!
  • Pi Recitation Contest, 1:30 p.m., Prince William Ballroom, Nassau Inn. Children ages 12 and younger may compete. Register by 1:15 p.m.
  • Pie Throwing Event, 3:14 p.m., Palmer Square. Proceeds to benefit the Princeton Educational Fund Teacher Mini-Grant Program.
  • Cupcake Decorating Competition, 4:00 p.m., House of Cupcakes (34 Witherspoon Street). The winner receives one free cupcake each month for the rest of the year.

Wednesday, 3/14/18

  • Princeton School Gardens Cooperative Fundraiser, 12:00 p.m. to 6:00 p.m., The Bent Spoon (35 Palmer Square West) and Lillipies (301 North Harrison Street). All proceeds from your afternoon treat will be donated to the Princeton School Gardens Cooperative.
  • Pi Day Pop Up Wedding/Vow Renewal Ceremonies, 3:14 p.m. to 6:00 p.m., Princeton Pi (84 Nassau Street). You must pre-register by contacting the Princeton Tour Company.

Not into crowds, or pie? You can also celebrate this multifaceted holiday by picking up one of PUP’s many books about Albert Einstein! In 1922, Princeton University Press published Einstein’s The Meaning of Relativity, his first book produced by an American publisher. Since then, we’ve published numerous works by and about Einstein.

The books and collections highlighted here celebrate not only his scientific accomplishments but also his personal reflections and his impact on present-day scholarship and technology. Check them out and learn about Einstein’s interpersonal relationships, his musings on travel, his theories of time, and his legacy for the 21st century.

Volume 15 of the Collected Papers of Albert Einstein, forthcoming in April 2018, covers one of the most thrilling two-year periods in twentieth-century physics, as matrix mechanics—developed chiefly by W. Heisenberg, M. Born, and P. Jordan—and wave mechanics—developed by E. Schrödinger—supplanted the earlier quantum theory. The almost one hundred writings by Einstein, of which a third have never been published, and the more than thirteen hundred letters show Einstein’s immense productivity and hectic pace of life.

Einstein quickly grasps the conceptual peculiarities involved in the new quantum mechanics, such as the difference between Schrödinger’s wave function and a field defined in spacetime, or the emerging statistical interpretation of both matrix and wave mechanics. Inspired by correspondence with G. Y. Rainich, he investigates with Jakob Grommer the problem of motion in general relativity, hoping for a hint at a new avenue to unified field theory.

Readers can access Volumes 1-14 of the Collected Papers of Albert Einstein online at The Digital Einstein Papers, an exciting new free, open-access website that brings the writings of the twentieth century’s most influential scientist to a wider audience than ever before. This unique, authoritative resource provides full public access to the complete transcribed, annotated, and translated contents of each print volume of the Collected Papers. The volumes are published by Princeton University Press, sponsored by the Hebrew University of Jerusalem, and supported by the California Institute of Technology. Volumes 1-14 of The Collected Papers cover the first forty-six years of Einstein’s life, up to and including the years immediately before the final formulation of new quantum mechanics. The contents of each new volume will be added to the website approximately eighteen months after print publication. Eventually, the website will provide access to all of Einstein’s writings and correspondence accompanied by scholarly annotation and apparatus, which are expected to fill thirty volumes.

The Travel Diaries of Albert Einstein is the first publication of Albert Einstein’s 1922 travel diary to the Far East and Middle East, regions that the renowned physicist had never visited before. Einstein’s lengthy itinerary consisted of stops in Hong Kong and Singapore, two brief stays in China, a six-week whirlwind lecture tour of Japan, a twelve-day tour of Palestine, and a three-week visit to Spain. This handsome edition makes available, for the first time, the complete journal that Einstein kept on this momentous journey.

The telegraphic-style diary entries—quirky, succinct, and at times irreverent—record Einstein’s musings on science, philosophy, art, and politics, as well as his immediate impressions and broader thoughts on such events as his inaugural lecture at the future site of the Hebrew University in Jerusalem, a garden party hosted by the Japanese Empress, an audience with the King of Spain, and meetings with other prominent colleagues and statesmen. Entries also contain passages that reveal Einstein’s stereotyping of members of various nations and raise questions about his attitudes on race. This beautiful edition features stunning facsimiles of the diary’s pages, accompanied by an English translation, an extensive historical introduction, numerous illustrations, and annotations. Supplementary materials include letters, postcards, speeches, and articles, a map of the voyage, a chronology, a bibliography, and an index.

Einstein would go on to keep a journal for all succeeding trips abroad, and this first volume of his travel diaries offers an initial, intimate glimpse into a brilliant mind encountering the great, wide world. 

More than fifty years after his death, Albert Einstein’s vital engagement with the world continues to inspire others, spurring conversations, projects, and research, in the sciences as well as the humanities. Einstein for the 21st Century shows us why he remains a figure of fascination.

In this wide-ranging collection, eminent artists, historians, scientists, and social scientists describe Einstein’s influence on their work, and consider his relevance for the future. Scientists discuss how Einstein’s vision continues to motivate them, whether in their quest for a fundamental description of nature or in their investigations in chaos theory; art scholars and artists explore his ties to modern aesthetics; a music historian probes Einstein’s musical tastes and relates them to his outlook in science; historians explore the interconnections between Einstein’s politics, physics, and philosophy; and other contributors examine his impact on the innovations of our time. Uniquely cross-disciplinary, Einstein for the 21st Century serves as a testament to his legacy and speaks to everyone with an interest in his work. 

The contributors are Leon Botstein, Lorraine Daston, E. L. Doctorow, Yehuda Elkana, Yaron Ezrahi, Michael L. Friedman, Jürg Fröhlich, Peter L. Galison, David Gross, Hanoch Gutfreund, Linda D. Henderson, Dudley Herschbach, Gerald Holton, Caroline Jones, Susan Neiman, Lisa Randall, Jürgen Renn, Matthew Ritchie, Silvan S. Schweber, and A. Douglas Stone.

On April 6, 1922, in Paris, Albert Einstein and Henri Bergson publicly debated the nature of time. Einstein considered Bergson’s theory of time to be a soft, psychological notion, irreconcilable with the quantitative realities of physics. Bergson, who gained fame as a philosopher by arguing that time should not be understood exclusively through the lens of science, criticized Einstein’s theory of time for being a metaphysics grafted on to science, one that ignored the intuitive aspects of time. Jimena Canales tells the remarkable story of how this explosive debate transformed our understanding of time and drove a rift between science and the humanities that persists today.

The Physicist and the Philosopher is a magisterial and revealing account that shows how scientific truth was placed on trial in a divided century marked by a new sense of time.

 

After completing the final version of his general theory of relativity in November 1915, Albert Einstein wrote a book about relativity for a popular audience. His intention was “to give an exact insight into the theory of relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus of theoretical physics.” The book remains one of the most lucid explanations of the special and general theories ever written.

This new edition features an authoritative English translation of the text along with an introduction and a reading companion by Hanoch Gutfreund and Jürgen Renn that examines the evolution of Einstein’s thinking and casts his ideas in a broader present-day context.

Published on the hundredth anniversary of general relativity, this handsome edition of Einstein’s famous book places the work in historical and intellectual context while providing invaluable insight into one of the greatest scientific minds of all time.

 

Steven S. Gubser: Thunder and Lightning from Neutron Star mergers

As of late 2015, we have a new way of probing the cosmos: gravitational radiation. Thanks to LIGO (the Laser Interferometer Gravitational-wave Observatory) and its new sibling Virgo (a similar interferometer in Italy), we can now “hear” the thumps and chirps of colliding massive objects in the universe. Not for nothing has this soundtrack been described by LIGO scientists as “the music of the cosmos.” This music is at a frequency easily discerned by human hearing, from somewhat under a hundred hertz to several hundred hertz. Moreover, gravitational radiation, like sound, is wholly different from light. It is possible for heavy dark objects like black holes to produce mighty gravitational thumps without at the same time emitting any significant amount of light. Indeed, the first observations of gravitational waves came from black hole merger events whose total power briefly exceeded the light from all stars in the known universe. But we didn’t observe any light from these events at all, because almost all their power went into gravitational radiation.

In August 2017, LIGO and Virgo observed a collision of neutron stars which did produce observable light, notably in the form of gamma rays. Think of it as cosmic thunder and lightning, where the thunder is the gravitational waves and the lightning is the gamma rays. When we see a flash of ordinary lightning, we can count a few seconds until we hear the thunder. Knowing that sound travels one mile in about five seconds, we can reckon how distant the event is. The reason this method works is that light travels much faster than sound, so we can think of the transmission of light as instantaneous for purposes of our estimate.

Things are very different for the neutron star collision, in that the event took place about 130 million light years away, but the thunder and lightning arrived on earth pretty much simultaneously. To be precise, the thunder was first: LIGO and Virgo heard a basso rumble rising to a characteristic “whoop,” and just 1.7 seconds later, the Fermi and INTEGRAL experiments observed gamma ray bursts from a source whose location was consistent with the LIGO and Virgo observations. The production of gamma rays from merging neutron stars is not a simple process, so it’s not clear to me whether we can pin that 1.7 seconds down as a delay precisely due to the astrophysical production mechanisms; but at least we can say with some confidence that the propagation time of light and gravity waves are the same to within a few seconds over 130 million light years. From a certain point of view, that amounts to one of the most precise measurements in physics: the ratio of the speed of light to the speed of gravity equals 1, correct to about 14 decimal places or better.

The whole story adds up much more easily when we remember that gravitational waves are not sound at all. In fact, they’re nothing like ordinary sound, which is a longitudinal wave in air, where individual air molecules are swept forward and backward just a little as the sound waves pass them by. Gravitational waves instead involve transverse disturbances of spacetime, where space is stretched in one direction and squeezed in another—but both of those stretch-squeeze directions are at right angles to the direction of the wave. Light has a similar transverse quality: It is made up of electric and magnetic fields, again in directions that are at right angles to the direction in which the light travels. It turns out that a deep principle underlying both Maxwell’s electromagnetism and Einstein’s general relativity forces light and gravitational waves to be transverse. This principle is called gauge symmetry, and it also guarantees that photons and gravitons are massless, which implies in turn that they travel at the same speed regardless of wavelength.

It’s possible to have transverse sound waves: For instance, shearing waves in crystals are a form of sound. They typically travel at a different speed from longitudinal sound waves. No principle of gauge symmetry forbids longitudinal sound waves, and indeed they can be directly observed, along with their transverse cousins, in ordinary materials like metals. The gauge symmetries that forbid longitudinal light waves and longitudinal gravity waves are abstract, but a useful first cut at the idea is that there is extra information in electromagnetism and in gravity, kind of like an error-correcting code. A much more modest form of symmetry is enough to characterize the behavior of ordinary sound waves: It suffices to note that air (at macroscopic scales) is a uniform medium, so that nothing changes in a volume of air if we displace all of it by a constant distance.

In short, Maxwell’s and Einstein’s theories have a feeling of being overbuilt to guarantee a constant speed of propagation. And they cannot coexist peacefully as theories unless these speeds are identical. As we continue Einstein’s hunt for a unified theory combining electromagnetism and gravity, this highly symmetrical, overbuilt quality is one of our biggest clues.

The transverse nature of gravitational waves is immediately relevant to the latest LIGO / Virgo detection. It is responsible for the existence of blind spots in each of the three detectors (LIGO Hanford, LIGO Livingston, and Virgo). It seems like blind spots would be bad, but they actually turned out to be pretty convenient: The signal at Virgo was relatively weak, indicating that the direction of the source was close to one of its blind spots. This helped localize the event, and localizing the event helped astronomers home in on it with telescopes. Gamma rays were just the first non-gravitational signal observed: the subsequent light-show from the death throes of the merging neutron stars promises to challenge and improve our understanding of the complex astrophysical processes involved. And the combination of gravitational and electromagnetic observations will surely be a driver of new discoveries in years and decades to come.

 

BlackSteven S. Gubser is professor of physics at Princeton University and the author of The Little Book of String TheoryFrans Pretorius is professor of physics at Princeton. They both live in Princeton, New Jersey. They are the authors of The Little Book of Black Holes.

Everyone’s favorite genius takes the spotlight

Along with Einstein fans everywhere, we’re fairly excited to binge-watch National Geographic’s upcoming series, “Genius”, premiering Tuesday, April 25. The first episode shows a young Einstein (Johnny Flynn), poring over the nature of time, a concept well covered in our An Einstein Encyclopedia along with most any other topic that could interest an Einstein devotee, from fame, to family, to politics, to myths and misconceptions. In Genius, prepare to see a show-down between a feisty young Einstein and a particularly rigid teacher. Engrossing to watch—and bound to leave viewers wanting more. Not to worry: “Teachers, education and schools attended” are covered in depth in the Encyclopedia, as are “Rivals”.

Episode 2 of Genius promises to show Einstein embarking, after much head-butting, on a love affair with the determined Mileva Maric. Often remembered as the lone, eccentric, Princeton-based thinker, Einstein’s youthful relationship with Maric sometimes comes as a surprise even to Einstein fans. And yet in 1903, a young Albert Einstein married his confidante despite the objections of his parents. Her influence on his most creative years has given rise to much discussion—but theirs was only one of several romantic interests over the course of Einstein’s life that competed with his passion for physics. Einstein’s love life has been the subject of intense speculation over the years, but don’t believe everything you hear: “Romantic Interests: Actual, Probable, and Possible”, all included in the Encyclopedia, won’t leave you guessing.

Mileva Maric, first wife of Albert Einstein

 An Einstein Encyclopedia is the single most complete guide to Einstein’s life, perfect for browsing and research alike. Written by three leading Einstein scholars who draw on their combined wealth of expertise gained during their work on the Collected Papers of Albert Einstein, this accessible reference features more than one hundred entries and is divided into three parts covering the personal, scientific, and public spheres of Einstein’s life.

With science celebrated far and wide along with Earth Day this past weekend, what better time to get your dose of genius and #ReadUp.

 

 

PUP math editor Vickie Kearn: How real mathematicians celebrate Pi Day

Who doesn’t love Pi (aka Pie) Day? Residents here in Princeton, NJ love it so much that we spend four days celebrating. Now, to be honest, we’re also celebrating Einstein’s birthday, so we do need the full four days. I know what I will be doing on 3.14159265 but I wondered what some of my friends will be doing. Not surprisingly, a lot will either be making or eating pie. These include Oscar Fernandez (Wellesley), Ron Graham (UCSD), and Art Benjamin (who will be performing his mathemagics show later in the week). Anna Pierrehumbert (who teaches in NYC) will be working with upper school students on a pi recitation and middle school students on making pi-day buttons. Brent Ferguson (The Lawrenceville School) has celebrated at The National Museum of Mathematics in NYC, Ireland, Greece, and this year Princeton. Here he is celebrating in Alaska:

Pi

The Princeton University Math Club will be celebrating with a party in Fine Hall. In addition to eating pie and playing games, they will have a digit reciting contest. Tim Chartier (Davidson College) will be spending his time demonstrating how to estimate pi with chocolate chips while also fielding interview requests for his expert opinion on March Madness (a lot going on this month for mathematicians). Dave Richeson (Dickinson College) goes to the local elementary school each year and talks with the fifth graders about pi and its history and then eats creatively rendered pi themed pie provided by the parents.

You might be wondering why we celebrate a mathematical constant every year. How did it get to be so important? Again I went back to my pi experts and asked them to tell me the most important uses of pi. This question is open to debate by mathematicians but many think that the most important is Euler’s Identity, e(i*pi) + 1 = 0. As Jenny Kaufmann (President of the Princeton University Math Club) puts it, “Besides elegantly encoding the way that multiplication by i results in a rotation in the complex plane, this identity unites what one might consider the five most important numbers in a single equation. That’s pretty impressive!” My most practical friend is Oscar and here is what he told me: “There are so many uses for pi, but given my interest in everyday explanations of math, here’s one I like: If you drive to work every day, you take many, many pi’s with you. That’s because the circumference of your car’s tires is pi multiplied by the tires’ diameter. The most common car tire has a diameter of about 29 inches, so one full revolution covers a distance of about 29 times pi (about 7.5 feet). Many, many revolutions of your tires later you arrive at work, with lots and lots of pi’s!” Anna is also practical in that she will be using pi to calculate the area of the circular pastry she will be eating, but she also likes the infinite series for pi (pi/4 = 1 – 1/3 + 1/5 – 1/7 etc.). Avner Ash (Boston College) sums it up nicely, “ We can’t live without pi—how would we have circles, normal distributions, etc.?”

One of the most important questions one asks on Pi Day is how many digits can you recite? The largest number I got was 300 from the Princeton Math Club. However, there are quite a few impressive numbers from others, as well as some creative answers and ways to remember the digits. For example, Oscar can remember 3/14/15 at 9:26:53 because it was an epic Day and Pi Time for him. Art Benjamin can recite 100 digits from a phonetic code and 5 silly sentences. Ron Graham can recite all of the digits of pi, even thousands, as long as they don’t have to be in order. Dave Richeson also knows all of the digits of pi which are 0,1,2,3,4,5,6,7,8,and 9.

No matter how you celebrate, remember math, especially pi(e) is useful, fun, and delicious.

Vickie Kearn is Executive Editor of Mathematics at Princeton University Press.

J. Richard Gott: What’s the Value of Pi in Your Universe?

Carl Sagan’s sci-fi novel Contact famously introduced wormholes for rapid transit between the stars. Carl had asked his friend Kip Thorne to tell him if the physics of wormholes was tenable and this led Thorne and his colleagues to investigate their properties. They found that traversable wormholes required exotic matter to prop them open and that, by moving the wormhole mouths one could find general relativity solutions allowing time travel to the past. A quantum state called the Casimir vacuum whose effects have been observed experimentally, could provide the exotic matter. To learn whether such time machines could be constructible in principle, we may have to master the laws of quantum gravity, which govern how gravity behaves on microscopic scales. It’s one of the reasons physicists find these solutions so interesting.

But in Contact there is lurking yet another fantastic sci-fi idea, which gets less publicity because it was not included in the movie version. In the book, the protagonist finds out from the extraterrestrials that the system of wormholes throughout the galaxy was not built by them, but by the long gone “old ones” who could manipulate not only the laws of physics but also the laws of mathematics! And they left a secret message in the digits of pi. In his movie Pi, Darren Aronofsky showed a man driven crazy by his search for hidden meanings in the digits of pi.

This opens the question: could pi have been something else? And if so, does pi depend on the laws of physics? Galileo said: “Philosophy is written in this grand book…. I mean the universe … which stands continually open to our gaze…. It is written in the language of mathematics.” The universe is written in the language of mathematics. Nobel laureate Eugene Wigner famously spoke of the “unreasonable effectiveness of mathematics” in explaining physics. Many philosophers take the Platonic view that mathematics would exist even the universe did not. And cosmologist Max Tegmark goes so far as to say that the universe actually is mathematics.

Yet maybe it is the other way around. The laws of physics are just the laws by which matter behaves. They determine the nature of our universe. Maybe humans have simply developed the mathematics appropriate for describing our universe, and so of course it fits with what we see. The mathematician Leopold Kronecker said, “God created the integers, all the rest is the work of man.” Are the laws of mathematics discovered by us in the same way as we discover the laws of physics? And are the laws of mathematics we discover just those which would have occurred to creatures living in a universe with physics like ours? In our universe, physics produces individual identical particles: all electrons are the same for example. We know about integers because there are things that look the same (like apples) for us to count. If you were some strange creature in a fractal universe containing only one object—yourself—and you thought only recursively, you might not ever think of counting anything and would never discover integers.

What about π = 3.14159265.…? Might it have a different value in a different universe? In our universe we have a fundamental physical dimensionless constant, the fine structure constant α which is related to the square of the value of the electric charge of the proton in natural geometrical Planck units (where the speed of light is 1 and the reduced Planck constant is 1 and Newton’s gravitational constant is 1). Now 1/α = 137.035999… Some physicists hope that one day we may have a mathematical formula for 1/α using mathematical constants such as π and e. If a theory for the fine structure constant could be developed giving a value in agreement with observations but allowing it to be calculated uniquely from pure mathematics, and if more and more digits of the constant were discovered experimentally fulfilling its prediction, it would certainly merit a Nobel Prize. But many physicists feel that no such magic formula will ever be discovered. Inflation may produce an infinite number of bubble universes, each with different laws of physics. Different universes bubbling out of an original inflating sea could have different values of 1/α. As Martin Rees has said, the laws of physics we know may be just local bylaws in an infinite multiverse of universes. String theory, if correct, may eventually give us a probability distribution for 1/α and we may find that our universe is just somewhere in the predicted middle 95% of the distribution, for example. Maybe there could be different universes with different values of π.

Let’s consider one possible example: taxicab geometry. This was invented by Hermann Minkowski. Now this brilliant mathematician also invented the geometrical interpretation of time as a fourth dimension based on Einstein’s theory of special relativity, so his taxicab geometry merits a serious look. Imagine a city with a checkerboard pattern of equal-sized square blocks. Suppose you wanted to take a taxicab to a location 3 blocks east, and 1 block north of your location, the shortest total distance you would have to travel to get there is 4 blocks. Your taxi has to travel along the streets, it does not get to travel as the crow flies. You could go 1 block east, then 1 block north then 2 blocks east, and still get to your destination, but the total distance you traveled would also be 4 blocks. The distance to your destination would be ds = |dx| + |dy|, where |dx| is the absolute value of the difference in x coordinates and |dy| is the absolute value of the difference in y coordinates. This is not the Euclidean formula. We are not in Kansas anymore! The set of points equidistant from the origin is a set of dots in a diamond shape. See diagram.

Gott

Image showing an intuitive explanation of why circles in taxicab geometry look like diamonds. Wikipedia.

Now if the blocks were smaller, there would be more dots, still in a diamond shape. In the limit where the size of the blocks had shrunk to zero, one would have a smooth diamond shape as shown in the bottom section of the diagram. The set of points equidistant from the origin has a name—a “circle!” If the circle has a radius of 1 unit, the distance along one side of its diamond shape is 2 units: going from the East vertex of the diamond to the North vertex of the diamond along the diagonal requires you to change the x coordinate by 1 unit and the y coordinate by 1 unit, making the distance along one side of the diagonal equal to 2 units (ds = |dx| + |dy| = 1 + 1 units = 2 units). The diamond shape has 4 sides so the circumference of the diamond is 8 units. The diameter of the circle is twice the radius, and therefore 2 units. In the taxicab universe π = C/d = C/2r = 8/2 = 4. If different laws of physics dictate different laws of geometry, you can change the value of π.

This taxicab geometry applies in the classic etch-a-sketch toy (Look it up on google, if you have never seen one). It has a white screen, and an internal stylus that draws a black line, directed by horizontal and vertical control knobs. If you want to draw a vertical line, you turn the vertical knob. If you want to draw a horizontal line you turn the horizontal knob. If you want to draw a diagonal line, you must simultaneously turn both knobs smoothly. If the distance between two points is defined by the minimal amount of total turning of the two knobs required to get from one point to the other, then that is the “taxicab” distance between the two points. In Euclidean geometry there is one shortest line between two points: a straight line between them. In taxicab geometry there can be many different, equally short, broken lines (taxicab routes) connecting two points. Taxicab geometry does not obey the axioms of Euclidean geometry and therefore does not have the same theorems as Euclidean geometry. And π is 4.

Mathematician and computer scientist John von Neumann invented a cellular automaton universe that obeys taxicab geometry. It starts with an infinite checkerboard of pixels. Pixels can be either black or white. The state of a pixel at time step t = n + 1 depends only on the state of its 4 neighbors (with which it shares a side: north, south, east, west of it) on the previous time step t = n. Causal, physical effects move like a taxicab. If the pixels are microscopic, we get a taxicab geometry. Here is a simple law of physics for this universe: a pixel stays in the same state, unless it is surrounded by an odd number of black pixels, in which case it switches to the opposite state on the next time step. Start with a white universe with only 1 black pixel at the origin. In the next time step it remains black while its 4 neighbors also become black. There is now a black cross of 5 pixels at the center. It has given birth to 4 black pixels like itself. Come back later and there will be 25 black pixels in a cross-shaped pattern of 5 cross-shaped patterns.

Come back still later and you can find 125 black pixels in 5 cross-shaped patterns (of 5 cross-shaped patterns). All these new black pixels lie inside a diamond-shaped region whose radius grows larger by one pixel per time step. In our universe, drop a rock in a pond, and a circular ripple spreads out. In the von Neumann universe, causal effects spread out in a diamond-shaped pattern.

If by “life” you mean a pattern able to reproduce itself, then this universe is luxuriant with life. Draw any pattern (say a drawing of a bicycle) in black pixels and at a later time you will find 5 bicycles, and then 25 bicycles, and 125 bicycles, etc. The laws of physics in this universe cause any object to copy itself. If you object that this is just a video game, I must tell you that some physicists seriously entertain the idea that we are living in an elaborate video game right now with quantum fuzziness at small scales providing the proof of microscopic “pixelization” at small scales.

Mathematicians in the von Neumann universe would know π = 4 (Or, if we had a taxicab universe with triangular pixels filling the plane, causal effects could spread out along three axes instead of two and a circle would look like a hexagon, giving π = 3.). In 1932, Stanislaw Golab showed that if we were clever enough in the way distances were measured in different directions, we could design laws of physics so that π might be anything we wanted from a low of 3 to a high of 4.

Back to the inhabitants of the von Neumann universe who think π = 4. Might they be familiar with number we know and love, 3.14159265…? They might:

3.14159265… = 4 {(1/1) – (1/3) + (1/5) – (1/7) + (1/9) + …} (Leibnitz)

If they were familiar with integers, they might be able to discover 3.14159265… But maybe the only integers they know are 1, 5, 25, 125, … and 4 of course. They would know that 5 = SQRT(25), so they would know what a square root was. In this case they could still find a formula for

3.14159265. . . =
SQRT(4) {SQRT(4)/SQRT(SQRT(4))}{SQRT(4)/SQRT(SQRT(4) + SQRT(SQRT(4)))}{SQRT(4)/ SQRT(SQRT(4) + SQRT(SQRT(4) + SQRT(SQRT(4))))} …

This infinite product involving only the integer 4 derives from one found by Vieta in 1594.

There are indeed many formulas equal to our old friend 3.14159265… including a spectacular one found by the renowned mathematician Ramanujan. Though every real number can be represented by such infinite series, products and continued fractions, these are particularly simple. So 3.14159265… does seem to have a special intimate relationship with integers, independent of geometry. If physics creates individual objects that can be counted, it seems difficult to avoid learning about 3.14159265… eventually—“If God made the integers,” as Kronecker suggested. So 3.14159265… appears not to be a random real number and we are still left with the mystery of the unreasonable effectiveness of mathematics in explaining the physics we see in our universe. We are also left with the mystery of why the universe is as comprehensible as it is. Why should we lowly carbon life forms be capable of finding out as much about how the universe works as we have done? Having the ability as intelligent observers to ask questions about the universe seems to come with the ability to actually answer some of them. That’s remarkable.

UniverseGottJ. Richard Gott is professor of astrophysics at Princeton University. His books include The Cosmic Web: Mysterious Architecture of the Universe. He is the coauthor of Welcome to the Universe: An Astrophysical Tour with Neil DeGrasse Tyson and Michael A. Strauss.

Neil DeGrasse Tyson & Stephen Colbert: Make America Smart Again

On November 9, Neil DeGrasse Tyson joined Stephen Colbert on The Late Show to talk about Welcome to the Universe and to blow his own mind. Watch the clip here:

 

Even celebrities misquote Albert Einstein

Calaprice_QuotableEinstein_pb_cvrAlice Calaprice is the editor of The Ultimate Quotable Einstein, a tome mentioned time and again in the media because famous folks continue to attribute words to Einstein that, realistically, he never actually said. Presidential candidates, reality stars, and more have used social media make erroneous references to Einstein’s words, perhaps hoping to give their own a bit more credibility. From the Grapevine recently compiled the most recent misquotes of Albert Einstein by public figures and demonstrated how easy it is to use The Ultimate Quotable Einstein to refute those citations:

Albert Einstein was a wise man, even outside the science laboratory. He has inspired painters, young students and comic book creators. Even budding romantics take advice from him.

So it should come as no surprise, then, that so many people today quote Einstein. Or, to be more precise, misquote Einstein.

“I believe they quote Einstein because of his iconic image as a genius,” Alice Calaprice, an Einstein expert, tells From The Grapevine. “Who would know better and be a better authority than the alleged smartest person in the world?”

Read more here.

 

A Mere Philosopher?

The Physicist and the Philosopher by Jimena CanalesOn the 6th of April, 1922, two men met at the Société française de philosophie to discuss relativity and the nature of time. One was the winner of the previous year’s Nobel Prize in Physics, Albert Einstein, renowned for a series of extraordinary innovations in scientific theory. The other was the French philosopher, Henri Bergson. In The Physicist and the Philosopher, Jimena Canales recounts the events of that meeting, and traces the public controversy that unfolded over the years that followed. Bergson was perceived to have lost the debate and, more generally, philosophy to have lost the authority to speak on matters of science.

Perhaps the greatest evidence of that loss is that it is hard to imagine an equivalent meeting today, the great physicist and the great philosopher debating as equals. While the physical sciences enjoy unprecedented prestige and funding on university campuses, many philosophy departments face cutbacks. Yet less than a century ago, Henri Bergson enjoyed enormous celebrity. His lecture at Columbia University in 1913 resulted in the first traffic jam ever seen on Broadway. His work was translated into multiple languages, influencing not only his fellow philosophers but also artists and writers (Willa Cather named one of her characters after Bergson). His writings on evolutionary theory earned him the condemnation of the Catholic Church. Students were crowded out of his classes at the Collège de France by the curious public.

The young Bergson showed promise in mathematics, but chose instead to study humanities at the École Normale. His disappointed math teacher commented “you could have been a mathematician; you will be a mere philosopher” — a harbinger of later developments? Einstein and his supporters attacked Bergson’s understanding of relativity and asserted that philosophy had no part to play in grasping the nature of time. Bergson countered that, on the contrary, it was he who had been misunderstood, but to no avail: the Einstein/Bergson debate set the tone for a debate on the relationship between philosophy and the sciences that continues to this day. At a recent roundtable discussion hosted by Philosophy Now, biologist Lewis Wolpert dismissed philosophy as “irrelevant” to science. In this, do we hear an echo of Einstein’s claim that time can be understood either psychologically or physically, but not philosophically?

Spotlight on…Scientists

Nikola Tesla, by W. Bernard Carlson

Nikola Tesla
by W. Bernard Carlson

Genius is no guarantee of public recognition. In this post we look at the changing fortunes and reputations of three very different scientists: Alan Turing, Nikola Tesla, and Albert Einstein.

With the success of the recent movie, the Imitation Game (based on Andrew Hodges’ acclaimed biography Alan Turing: The Enigma), it’s easy to forget that for decades after his death, Turing’s name was known only to computer scientists. His conviction for homosexual activity in 1950s Britain, his presumed suicide in 1954, and the veil of secrecy drawn over his code-breaking work at Bletchley Park during the Second World War combined to obscure his importance as one of the founders of computer science and artificial intelligence. The gradual change in public attitudes towards homosexuality and the increasing centrality of computers to our daily lives have done much to restore his reputation posthumously. Turing received an official apology in 2009, followed by a royal pardon in 2013.

Despite enjoying celebrity in his own lifetime, Nikola Tesla’s reputation declined rapidly after his death, until he became regarded as an eccentric figure on the fringes of science. His legendary showmanship and the outlandish claims he made late in life of inventing high-tech weaponry have made it easy for critics to dismiss him as little more than a charlatan. Yet he was one of the pioneers of electricity, working first with Edison, then Westinghouse to develop the technology that established electrification in America. W. Bernard Carlson’s Nikola Tesla tells the story of a life that seems drawn from the pages of a novel by Jules Verne or H. G. Wells, of legal battles with Marconi over the development of radio, of fortunes sunk into the construction of grandiose laboratories for high voltage experiments.

By contrast, the reputation of Albert Einstein seems only to have grown in the century since the publication of his General Theory of Relativity. He is perhaps the only scientist to have achieved iconic status in the public mind, his face recognized as the face of genius. Children know the equation e=mc2 even though most adults would struggle to explain its implications. From the publication of the four 1905 papers onwards, Einstein’s place in scientific history has been secure, and his work remains the cornerstone of modern understanding of the nature of the universe. We are proud to announce the publication of a special 100th anniversary edition of Relativity: The Special and the General Theory, and the recent global launch of our open access online archive from the Collected Papers of Albert Einstein, the Digital Einstein Papers.

Happy Birthday Albert Einstein

“Learn from yesterday, live for today, hope for tomorrow. The important thing is to not stop questioning.” – Albert Einstein

This is a huge year for Einstein at Princeton University Press. December marked the celebrated launch of The Digital Einstein Papers, a free open-access website that puts The Collected Papers of Albert Einstein online for the very first time. Today is Albert Einstein’s 136th birthday, as well as Pi Day, which, as Steven Strogatz writes in The New Yorker, is far “more than just some circle fixation.” So once you’ve rung it in with this Pi Day recipe, you might like to check out this book list in honor of the influential scientist and writer, who fittingly enough, shares his birthday with the popular mathematical holiday. Sample chapters for several Einstein related books are linked below.

 

bookjacket

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

Fifth edition
Albert Einstein
With a new introduction by Brian Greene
Chapter 1

The Collected Papers of Albert Einstein, Volume 14:
The Berlin Years: Writings & Correspondence, April 1923–May 1925

Documentary edition
Albert Einstein
Edited by Diana Kormos Buchwald, József Illy, Ze’ev Rosenkranz, Tilman Sauer & Osik Moses

Chapter 1

 

bookjacket  The Road to Relativity:
The History and Meaning of Einstein’s “The Foundation of General Relativity” Featuring the Original Manuscript of Einstein’s Masterpiece

Hanoch Gutfreund & Jürgen Renn
With a foreword by John Stachel
Released April 2015

 

bookjacket The Physicist and the Philosopher:
Einstein, Bergson, and the Debate That Changed Our Understanding of Time

Jimena Canales
Released May 2015

 

bookjacket

Philosophy of Physics:
Space and Time

Tim Maudlin
Released May 2015Introduction

 

 

Two new exhibits about Albert Einstein on Google Cultural Institute

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Two new, expertly written and illustrated exhibits about Albert Einstein are now available for free on Google Cultural Institute. These archives feature information from the Einstein Papers Project and the Hebrew University archives.

Einstein’s Trip to the Far East and Palestine

In late 1922 and early 1923, Albert Einstein embarked on a five-and-a-half-month trip to the Far East, Palestine, and Spain. In September 1921, Einstein had been invited by the progressive Japanese journal Kaizo to embark on a lecture tour of Japan.   The tour would include a scientific lecture series to be delivered in Tokyo, and six popular lectures to be delivered in several other Japanese cities. An honorarium of 2,000 pounds sterling was offered and accepted.

Einstein’s motivation for accepting the invitation to Japan was threefold: to fulfil his long-term desire to visit the Far East, to enjoy two long sea voyages “far from the madding crowds” and to escape from Berlin for several months in the wake of the recent assassination of Germany’s Foreign Minister Walther Rathenau, who had belonged to Einstein’s circle of friends. Rathenau had been gunned down by anti-Semitic right-wing extremists in June 1922 and there was reason to believe that Einstein’s life was also at risk.

Credit: Einstein’s Trip to the Far East and Palestine

Albert Einstein German, Swiss and American?

In a letter to his superiors, the German ambassador, Constantin von Neurath, quotes from a Copenhagen newspaper: „Although a Swiss subject by birth and supposedly of Jewish origin, Einstein’s work is nevertheless an integral part of German research“.

Von Neurath uses this flawed statement with good reason: The  Swiss Jew whom he would rather disregard, unfortunately proves to be one of the few “Germans” welcome abroad.

On April 26, 1920, for example, Albert Einstein was nominated member of the  Royal Danish Academy of Sciences and Letters.

The more appreciated Einstein becomes abroad, the greater Germany’s desire to claim him as one of their own.

Credit: Albert Einstein German, Swiss and American?

On the occasion of these exhibits, Diana K. Buchwald of the Einstein Papers Project at California Institute of Technology said, “The Einstein cultural exhibit gives us a splendid glimpse into rare documents and images that tell not only the story of Einstein’s extraordinary voyage to publicize relativity in Japan in 1922, and to lay the cornerstone of the Hebrew University in Palestine in 1923, but also the dramatic trajectory of his entire life, illustrated by his colorful passports that bear testimony to the vagaries of his personal life.”

Prof. Hanoch Gutfreund, Former President, The Hebrew University of Jerusalem, Chair of the Albert Einstein Archives echoed her Buchwald’s enthusiasm noting, “The cooperation between the Google Cultural Institute, the Hebrew University of Jerusalem and the Einstein Papers Project in Caltech has produced two exhibitions exploring two specific topics on Einstein’s life and personality. Thus, Google has provided an arena, accessible to all mankind, which allows the Hebrew University to share with the general public the highlights of one of its most important cultural assets–the Albert Einstein Archives, which shed light on Einstein’s scientific work, public activities and personal life.

Learn more about Princeton University Press’s Einstein-related books, including the print editions of the Einstein Papers Project, here.