Some of the topics discussed in my first book, Einstein’s Pathway to the Special Theory of Relativity

People ask questions about Einstein’s special theory of relativity: How did Einstein come up with the theory of special relativity? What did he invent? What is the theory of special relativity? How did Einstein discover special relativity? Was Einstein the first to arrive at special relativity? Was Einstein the first to invent E = mc2?

Did Poincaré publish special relativity before Einstein? Was Einstein’s special theory of relativity revolutionary for scientists of his day? How did the scientific community receive Einstein’s theory of special relativity when he published it? What were the initial reaction in the scientific community after Einstein had published his paper on special relativity?

In my book, Einstein’s Pathway to the Special Theory of Relativity, I try to answer these and many other questions.The topics discussed in my book are the following:

I start with Einstein’s childhood and school days.

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I then discuss Einstein’s student days at the Zurich Polytechnic. Einstein the rebellious cannot take authority, the patent office, Annus Mirabilis, University of Bern and University of Zurich, Minkowski’s space-time formalism of special relativity.

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Young Einstein, Aarau Class 1896

Additional topics treeated in my book are the following: Fizeau’s water tube experiment, Fresnel’s formula (Fresnel’s dragging coefficient), stellar aberration, and the Michelson and Michelson-Morley Experiments.

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Albert Einstein at the Patent office

Mileva Marić and Einstein

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Eduard Tete, Mileva Marić and Hans Albert

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Einstein’s road to the special theory of relativity: Einstein first believes in the ether, he imagines the chasing a light beam thought experiment and the magnet and conductor thought experiment. Did Einstein respond to the Michelson and Morley experiment? Emission theory, Fizeau’s water tube experiment and ether drift experiments and Einstein’s path to special relativity; “The Step”.

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Henri Poincaré’s possible influence on Einstein’s road to the special theory of relativity.

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Einstein’s methodology and creativity, special principle of relativity and principle of constancy of the velocity of light, no signal moves beyond the speed of light, rigid body and special relativity, the meaning of distant simultaneity, clock synchronization, Lorentz contraction, challenges to Einstein’s connection of synchronisation and Lorentz contraction, Lorentz transformation with no light postulate, superluminal velocities, Laue’s derivation of Fresnel’s formula, the clock paradox and twin paradox, light quanta, mass-energy equivalence, variation of mass with velocity, Kaufmann’s experiments, the principles of relativity as heuristic principles, and Miller ether drift experiments.

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The book also briefly discusses general relativity: Einstein’s 1920 “Geometry and Experience” talk (Einstein’s notion of practical geometry), equivalence principle, equivalence of gravitational and inertial mass, Galileo’s free fall, generalized principle of relativity, gravitational time dilation, the Zurich Notebook, theory of static gravitational fields, the metric tensor, the Einstein-Besso manuscript, Einstein-Grossmann Entwurf theory and Entwurf field equations, the hole argument, the inertio-gravitational field, Einstein’s general relativity: November 1915 field equations, general covariance and generally covariant field equations, the advance of Mercury’s perihelion, Schwarzschild’s solution and singularity, Mach’s principle, Einstein’s 1920 suggestion: Mach’s ether, Einstein’s static universe, the cosmological constant, de Sitter’s universe, and other topics in general relativity and cosmology which lead directly to my second book, General Relativity Conflict and Rivalries.

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My books

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My book: Einstein’s Pathway to the Special Theory of Relativity

2015 marks several Albert Einstein anniversaries: 100 years since the publication of Einstein’s General Theory of Relativity, 110 years since the publication of the Special Theory of Relativity and 60 years since his passing.

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What is so special about this year that deserves celebrations? My new book on Einstein: Einstein’s Pathway to the Special Theory of Relativity has just been returned from the printers and I expect Amazon to have copies very shortly.

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The Publisher uploaded the contents and intro.

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I hope you like my drawing on the cover:

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Einstein, 1923: “Ohmmm, well… yes, I guess!”

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The book is dedicated to the late Prof. Mara Beller, my PhD supervisor from the Hebrew University of Jerusalem who passed away ten years ago and wrote the book: Quantum Dialogue (Chicago University Press, 1999):

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Have a very happy Einstein year!

June 30. Ether is superfluous: Faraday and Einstein

On this day in 1905 Albert Einstein’s paper, “On the Electrodynamics of Moving Bodies,” arrived at the editorial offices of the journal Annalen der Physik. The paper was published three months later, and the theory later became known as special relativity. Physics Today.

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On April 15, 1846 Faraday gave a lecture at the Royal Institution. The talk was delivered under the title “Thoughts of Ray Vibrations”.  

Faraday began saying: “I incline to believe that when there are intervening particles of matter (being themselves only centers of force), they take part in carrying on the force through the line, but when there are none, the line proceeds through space… we can at all events affect these lines of force in a manner which may be conceived as partaking of the nature of a shake or lateral vibration…
It may be asked, what lines of force are there in nature which are fitted to convey such an action and supply for the vibrating theory the place of the aether?” The lines of force could be electrical, magnetic or gravitational. “…all I can say is, that I do not perceive in any part of space, whether (to use the common phrase) vacant of filled with matter, anything but forces and the lines in which they are exerted…
The view which I am so bold to put forth considers, therefore, radiation as a high species of vibration in the lines of force which are known to connect particles and also masses of matter together. It endeavours to dismiss the aether, but not the vibrations”.
In addition, Faraday explains that the vibrations that occur on the surface of disturbed water, or the waves of sound in gases or liquids, are “direct or to and fro from the centre of action”, whereas the (radiant) vibrations are “lateral”.
Faraday then explains the problem that is inherent in an ether model. He writes that it seems to him, “that the resultant of two or more lines of force is an apt condition for that action which may be considered as equivalent to a lateral vibration; whereas a uniform medium, like the ether does not appear apt, or more apt than air or water”.

Faraday’s lines of force inspired Maxwell in developing electric and magnetic field theory, but Maxwell did not follow Faraday in rejecting the ether. Maxwell developed mechanical models for the ether.

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Michael Faraday

Einstein, apparently not knowing about Faraday’s 1846 rejection of the ether, started his 1905 relativity paper with the problematic asymmetries that were inherent in the electrodynamical explanation of the phenomenon of induction by Faraday. Hence, Einstein started with Faraday.

According to Faraday, when a magnet and a closed electric circuit are in relative motion, an electric current is induced in the electric circuit. This current is actually a result of the relative motion between the magnet and the conductor.
If the conductor is at rest in the ether and the magnet is moved with a given velocity, a certain electric current is induced in the conductor. If the magnet is at rest, and the conductor moves with the same relative velocity, a current of the same magnitude and direction is in the conductor. The ether theory gives a different explanation for the origin of this current in the two cases. In the first case an electric field is supposed to be created in the ether by the motion of the magnet relative to it (Faraday’s induction law). In the second case, no such electric field is supposed to be present since the magnet is at rest in the ether, but the current results from the motion of the conductor through the static magnetic field.

This asymmetry of the explanation is foreign to the phenomenon, because the observable phenomena (the current in the conductor) depend only on the relative motion of the conductor and the magnet.

Parts of Faraday’s talk are also quoted in “Fields of Force: The Development of a World View from Faraday to Einstein”,  By William Berkson, pp. 97-99.

איינשטיין ותורת הקוונטים Einstein and the Light Quantum

In 1905 Planck, a coeditor of the Annalen der Physik, accepted Einstein’s paper on light quanta for publication, even though he disliked the idea of “light quanta”. Einstein’s relativity paper was received by the Annalen der Physik at the end of June 1905 and Planck was the first scientist to notice Einstein’s relativity theory and to report favorably on it. In the 1905 relativity paper Einstein used the notion, “light complex”, and he did not invoke his novel quanta of light heuristic with respect to the principle of relativity. He chose the language “light complex” for which no clear definition could be given. But with hindsight, in 1905 Einstein made exactly the right choice not to mix concepts from his quantum paper with those from his relativity paper. He focused on the solution of his relativity problem, whose far-reaching perspectives Planck already sensed. x

In the Electrodynamical part of the Relativity paper Einstein considers the system K. Very far from the origin of K, there is a source of electromagnetic waves. Let part of space containing the origin of coordinates 0 be represented to a sufficient degree of approximation by plane waves. Einstein asks: What characterizes the waves when they are examined by an observer at the same point 0, but at rest in the system k, moving relatively to K with constant speed v? x

Einstein applies the Lorentz transformation and transformation equations for electric and magnetic fields to the equations of the plane electromagnetic wave with respect to K. He obtains the Doppler principle, i.e., the frequency of electromagnetic waves as it appears in the system k and K: f’/f.   x

Einstein then finds the amplitude of the waves as it appears in the system k; the amplitude of the electric or magnetic waves A or A’, respectively, as it is measured in the system K or in the system k. Einstein gives the equation for the square of amplitude, Pointing vector. x

We expect that the ratio of the square of the amplitude of a given light complex “measured in motion” and “measured at rest” would be the energy if the volume of a light complex were the same measured in K and k. However, says Einstein, this is not the case.  x

Einstein thus instead considers a spherical surface of radius R moving with the velocity of light. He is interested in the light energy enclosed by the light surface. No energy passes outside through the surface of the spherical light surface, because the surface and the light wave both travel with the velocity of light. He calculates the amount of energy enclosed by this surface as viewed from the system k, which will be the energy of the light complex relative to the system k. The spherical surface – viewed in the system k – is an ellipsoidal surface. If we call the energy of the light enclosed by this surface E when it is measured in system K, and E’ when measured in system k, we obtain the equation that relates between E and E’.  x

Einstein realizes that, “It is noteworthy that the energy and the frequency of a light complex vary with the observer’s state of motion according to the same law”. x

Namely, E’/E = f’/f.     x

John Stachel read my manuscript and said that this formula corresponds to that of the light quantum hypothesis, and in hindsight this supplies extra evidence for the later hypothesis. Einstein’s aim is to show that the equation E = hv that he uses in the quantum paper takes the same form in any inertial frame. That is, E = hv is transformed to E’ = hv’ and thus the relativity postulate is not violated.  x

I wrote in my manuscript that Rynasiewicz wrote in 2005 (and even before that) that, “Einstein wraps up his derivation with what is clearly an allusion to the light quantum hypothesis”. Rynasiewicz adds that “What he does not draw attention to there is the intimate relation of this result to the relative character of simultaneity”.  x

However, Stachel told me that he was the first to notice that in his relativity paper Einstein implicitly referred to the light quantum hypothesis and he told me to delete Rynasiewicz’s comment. x

Then in light of my manuscript Stachel wrote the following paragraph, which reflects my manuscript, and also the collected papers of Einstein, which he edited

Before submitting his 1905 special relativity paper, Einstein had submitted the light quantum paper – the only one of his 1905 papers he considered truly revolutionary. “On a Heuristic Viewpoint Concerning the Generation and Transformation of Light”, sent to the Annalen on March 17th, 1905, and received by the Annalen a day afterwards. Indeed Einstein wrote Habicht in May 1905 about this paper, “It deals with the radiation and energy characteristics of light and is very revolutionary”.  x

This paper extended the range of application of Planck’s 1900 quantum hypothesis. In order to explain his law of black body radiation, which had been well-verified empirically, Planck was forced to assume that oscillators interacting with the electromagnetic field could only emit and/or absorb energy in discrete units, which he called quanta of energy. The energy of these quanta was proportional to the frequency of the oscillator: E = hv. But Planck believed, in accord with Maxwell’s theory, that the energy of the electromagnetic field itself could change continuously. x

Einstein now showed that, if this formula were extended to the electromagnetic field energy itself, a number of phenomena involving interactions between matter and radiation, otherwise inexplicable classically, could now be simply explained with the help of these light quanta. x

But, he was at work on his relativity paper too; so the question naturally arose, if the equation E = hv holds in one inertial frame of reference, will it hold in all others. If not, then Einstein’s relativity principle would be violated. Since h, the so-called quantum of action, is a universal constant, the question reduces to: Do the energy and frequency of a light quantum transform in the same way in passing from one inertial frame to another. And this is just what he demonstrates in his paper. x

Hence, not wanting to introduce a discussion of his still-quite-speculative light quantum hypothesis into a paper which he regarded as simply an extension of well accepted classical ideas from mechanics to electromagnetism and optics, he confined his proof to the classical level. x

Instead of “light quanta”, in his proof he introduced the rather awkward term “light complex”, a term that he soon dropped. x

In my paper discussing relativity and light quanta I bring both opinions and I also refer to Einstein’s Collected Papers. x

HUJI, Lucien Chavan

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איינשטיין ותורת היחסות הפרטית: איינשטיין במשרד הפטנטים Einstein and Relativity: Patent Office

Einstein’s business card, Princeton  כרטיס ביקור

In the Patent Office Einstein hatched his most beautiful ideas, and there he spent his “Happy Bern Years”. These wonderful ideas led to his miraculous year works of 1905. Einstein was not an expert in academic matters, and he was out of academic world. Neither did he meet influential professors, or attend academic meetings. He discussed his ideas with his close friends and colleagues from the Patent Office. In 1907 he finally got his foot into the academic doorway; Einstein became a privatdozent and gave lectures at the University of Bern. However, his first students consisted again of his two close friends and another colleague from the Patent Office. Read my papers in the link below

Einstein and the Theory of Relativity

Helge Kragh Writes in his paper “A Sense of Crisis: Physics in the fin-de-siecle Era”:

If mass is of electromagnetic origin it will increase with the speed or kinetic energy of the body in question, such as shown by Abraham, Lorentz and other electron theorists in the early twentieth century. It followed that the concepts of mass and energy could not be strictly separate, but that they must be connected by an equivalence relation of the same kind that Einstein famously proposed in 1905 (namely, E = mc2). According to this point of view, matter was not really dead, it had merely metamorphosed into energy. Proposals of a mass-energy relationship predated Einstein’s theory of relativity, and they added to the feeling that the entire foundation of physics had to be reconsidered. Young Einstein agreed, but for very different reasons. He saw no merit in the fashionable electromagnetic research program”. x

I don’t agree with Kragh. Einstein was the first to propose the inertial mass-energy equivalence (namely, E0 = m0c2). Abraham, Lorentz, and Poincaré (fin-de-siecle scientists) did not explore the inertial mass-energy equivalence, “an equivalence relation of the same kind that Einstein famously proposed in 1905”. In 1908 Einstein wrote the German physicist Johannes Stark: “I was a little surprised to see that you did not acknowledge my priority regarding the relationship between inertial mass and energy”. See my paper. x

איינשטיין פקיד במשרד פטנטים.

נתחיל בשתי תובנות קלאסיות של חבריו של איינשטיין, שהן אופייניות מאוד לעולם האינטיליגנציה:

מקס תלמוד כתב ב-1932: “מצאתי את חברי [איינשטיין בברן]. סביבתו העידה על מידה רבה של עוני. הוא גר בחדר קטן ומרוהט בעוני. למדתי שהיה לו מאבק חיים קשה עם משכורת דחוקה של פקיד במשרד הפטנטים. קשייו הועצמו בגלל אנשים שקינאו בו והניחו בדרכו מכשולים. כבונוס חברי נתן לי עותק של פרסומו הראשון [על קפילאריות]”.

פרידריך אדלר [חברו של איינשטיין לספסל הלימודים בפוליטכניון] כתב לאביו ב-19 ליוני 1908 לאחר שזכה בתחרות מול איינשטיין על משרת פרופסורה באוניברסיטת ציריך ובסוף ויתר לאיינשטיין על המשרה: “איש בשם איינשטיין, שלמד באותו הזמן בו אני למדתי. אפילו שמענו כמה הרצאות יחד. התפתחותנו נראתה מקבילה: הוא התחתן עם סטודנטית בערך באותו הזמן כמוני ויש לו ילדים. אבל אף אחד לא תמך בו ולמשך זמן הוא כמעט גווע ברעב. כסטודנט הפרופסורים התייחסו אליו בבוז, הספרייה פעמים רבות הייתה סגורה בפניו, ועוד. לא הייתה לו כל הבנה כיצד להסתדר עם האנשים החשובים… לבסוף, הוא מצא משרה במשרד הפטנטים בברן, ובמהלך כל התקופה הוא המשיך בעבודתו התיאורטית למרות כל ההפרעות”.

איינשטיין במשרד הפטנטים

ב-23 ליוני 1902, בשמונה בבוקר בדיוק איינשטיין התייצב לעבודה במשרד הפטנטים הפדראלי השווצרי. הוא עלה למשרדו בבנין הדואר והטלגרף שליד מגדל השעון המפורסם מעל שער העיר ברן. תפקידו היה עורך פטנטים; מומחה טכני זמני בדרגה 3 והוא הרוויח משכורת של 3500 פרנקים לשנה. הוא העריך פניות פטנטים, כתב שוב את הפניות שהתקבלו במשרד, כדי להגן על הממציא כנגד השגות גבול אפשריות. הוא בדק המצאות מקוריות והשלמות להמצאות שהוגשו למשרד; ניסח בבהירות את מהותן והיה צריך לבדוק בזהירות רבה האם הן מקוריות או לא. העבודה דרשה ידיעה של חוק הפטנטים ויכולת לקרוא ספציפיקציות טכניות, וידע בהנדסה ובפיזיקה, למעשה פיזיקה מאוד מעשית. בסירובו לפניות פטנטים מסוימות לא פעם הוא כתב: “פניית פטנט זו היא בלתי נכונה, בלתי מדויקת וכתובה לא ברור”. כאשר שאלו את איינשטיין כיצד פועל משרד הפטנטים? הוא הסביר, שיותר מכל, צריך להיות מסוגל לבטא בבהירות ונכון את הפטנט המקורי מתוך התיאור של התגלית והטיעונים של מגיש הפטנט.

אינשטיין הרגיש בבית במשרד הפטנטים ובין ערימות הפטנטים. כילד הוא הביט בדודו יעקב המהנדס והממציא במפעל המשפחתי, שהגיש ששה פטנטים על המצאותיו. במעבדה של פרופסור הינריך פרידריך וובר הוא לבטח גם כן בא במגע עם המצאות חדשות עליהן הוגשו פטנטים. חרף ניסיונות אלה, נדרשה מאיינשטיין רמת דיוק ואובייקטיביות, שהרי הקריטריונים לפיהם נבדקו הפטנטים לא פעם יכלו להיות נדונים בבית המשפט. איינשטיין היה פיסיקאי והיה לו מעט ניסיון בקריאה ובפירוש של איורים טכניים ובטח היה חסר ניסיון הנדסי, ולכן מנהל משרד הפטנטים פרידריך האלר הדריכו בקפדנות.

באקדמיה לעומת זאת, המקוריות והיצירתיות לא היו הקריטריון הראשי לטיפוס בסולם האקדמי, בייחוד בעולם דובר הגרמנית. לו איינשטיין היה מתקבל לאקדמיה הוא היה חש לחץ להתאים עצמו לדעות הקדומות או לממסד ולדעה המקובלת של פטרוניו, להתקבל כאסיסטנט לפרופסור, “קריירה אקדמית שבה אדם מאולץ ליצור כתבים מדעיים בכמויות עצומות יוצרת סכנה של שטחיות אינטלקטואלית”, אינשטיין אמר פעם מאחור יותר. כתוצאה יד המקרה שהביאה לו את משרד הפטנטים בברן, במקום משרה באקדמיה היוקרתית, כנראה שעודדה כמה מהתכונות שנועדו לגרום לו להיות מוצלח: עצמאות חשיבה יצירתית ושיפוט שאפשרו לו לערער על הנחות היסוד הבסיסיות. לא היה לחץ ודחיפה מצד בוחני הפטנטים להתנהג אחרת.

העבודה במשרד הפטנטים הייתה יצירתית למדי וכנראה שסיפקה לאיינשטיין חומר למחשבה בכיוונים חדשים בפיסיקה. הוא קיבל שכר קבוע ולכן הוא היה פטור מהדאגות החומריות. כעבור שלוש שנים במשרד הפטנטים, האלר הודיע לאיינשטיין בסוף שנת 1905 על העלאתו בדרגה. ומה הייתה תגובתו של אינשטיין? “אבל מה אני אעשה עם כל הכסף הזה?”

בזאת הצליח אינשטיין להתפנות לעבודה האמיתית – העבודה היצירתית המדעית הפיסיקאלית. כך החלה תקופת ברן במשרד הפטנטים של אינשטיין מ-1902 ועד 1909, שבמהלכה אינשטיין השתחרר מדאגות היומיום כדי להפיק את עבודתו היוצרת הטובה ביותר שלו. אינשטיין אהב לתאר את משרד הפטנטים לחבריו כ”מנזר החילוני” שלו.

ניתן ללמוד על תקופת שהותו של אינשטיין במשרד הפטנטים ממכתבו לחברו הטוב קונרד הביכט מספטמבר 1905. אינשטיין כותב להביכט, “אם תצוץ הזדמנות אתן לך דחיפה אצל האלר. אולי נצליח להבריח אותך בין נערי הפטנט. תגלה עדיין שזה נעים למדי. האם למעשה תהיה מוכן לבוא? תחשוב שמלבד שמונה שעות עבודה כל יום, בכל יום ישנן שמונה שעות של שעשועים, ואחר כך ישנו גם יום ראשון. אני מאוד אשמח אם תהיה כאן […] אינך צריך להיות מוטרד מזמני היקר, לא תמיד ישנו נושא רגיש להרהר עליו. לפחות לא כזה מרגש”.

במשרד פטנטים זה איינשטיין בילה את שבע השנים היצירתיות ביותר של חייו – אפילו אחרי שכתב את המאמרים ששינו את פני הפיזיקה. הוא היה מגיע כל יום בשמונה בבוקר, ששה ימים בשבוע ובודק בקשות לפטנטים. הוא בילה שמונה שעות במשרד ולפחות שעה אחת בשעורים פרטיים. אחר כך, בנוסף, הוא עשה עבודה מדעית כלשהי. אבל בדיקת בקשות לפטנטים לא הייתה עבודת פרך. איינשטיין עד מהרה למד שהוא יכול לעבוד על בקשות פטנטים כה מהר שזה הותיר לו זמן לחשוב על המדע במהלך היום.

אנטון רייזר, חתנו של אינשטיין מספר בביוגרפיה שלו, “הוא מהר מאוד גילה שהוא יכל למצוא זמן כדי להקדיש למחקריו המדעיים של עצמו במידה ועשה את עבודתו בפחות זמן. אבל שיקול דעת היה נחוץ, כי למרות שהממונים יכלו להיות מרוצים מהעבודה האיטית, החיסכון בזמן לעיסוקים אישיים היה אסור רשמית. אינשטיין המודאג הקפיד, שגיליונות הנייר הקטנים עליהם כתב ושרטט, ייעלמו לתוך מגירת שולחנו מיד כאשר הוא שמע צעדים מתקרבים מאחורי הדלת. אילו היו מגלים אותו, היו לועגים לו וגם פוגעים בו; המנהל היה צוחק בנוסף לכך שהיה כועס. הוא היה יותר מידי פוזיטיביסט מכדי שיחשוב על מדע ספקולטיבי”.

חמישים שנה אחרי משרד הפטנטים – פרינסטון תמונות של LIFE Ralph Morse

 fifty years after the patent Office – Einstein’s desk

בזמן שגיליונות ניירות מחקריו הזעירים היו נעלמים לתוך מגירת שולחן עבודתו במשרד הפטנטים בעת שהאלר היה מסתובב ושומר, איינשטיין כתב את מאמריו הגדולים ביותר של שנת 1905 ואלה גרמו בסוף למהפכה במאה ה-20.

האם יש לחוש צער על זה שאיינשטיין עבד בהתגנבות, בעודו מנודה מהאכסדרות של האקדמיה? אינשטיין עצמו האמין להפך, שמצב זה היה דווקא יתרון למדע שלו. שם במשרד הפטנטים הרעיונות הטובים ביותר שלו נבטו, כפי שהעיד בפני חברו מיקל’ה בסו מאוחר יותר.

How many scientists did it take to make the discovery of Relativity – Special and General Theories? x

 Albert Einstein? or Albert Einstein, Michele Besso, Marcel Grossmann?… Read my latest paper

Besso, Special Relativity: Einstein ends his 1905 relativity paper by saying that he is indebted to Besso for several valuable suggestions. What could Besso’s valuable suggestions have been? Einstein’s biographer, Carl Seelig, wrote: “Later Besso […] used the following analogy: Einstein the eagle has taken Besso the sparrow under his wing. Then the sparrow fluttered a little higher: ‘I could not have found a better sounding-board in the whole of Europe’, Einstein remarked when the conversation turned one day to Besso. This way Einstein and Besso became inseparable”. x

In 1952 Besso recounted, “Another little fairy tale of mine concerning my view that I had participated in [the formulation of] the special theory of relativity. It seemed to me, as an electrical engineer, I must have brought up, in conversations with you, the question, within the context of Maxwell’s theory, of what is induced in the inductor of an alternator […]”: the Magnet and Conductor thought experiment that opens Einstein’s 1905 Relativity Paper. Maxwell’s theory was not yet on the official program of the Polytechnic School ETH (Einstein’s and Besso’s collage). It was probably Einstein’s self-reading about Maxwell’s theory, who explained to Besso about this theory. Only after such explanation could Besso within the context of Maxwell’s theory refer to his technical work and speak with Einstein or remind him about induction of which Einstein had already read about in books

Einstein and his closest friend, Michele Besso

Grossmann, General Relativity: When Einstein came back to Zurich in 1912 Marcel Grossmann looked through the literature, and discovered that the mathematical problem was already solved by Riemann, Ricci and Levi-Civita. Einstein collaborated with Grossmann and this led to the Einstein-Grossmann theory published in two joint papers. Just before writing the first paper with Grossmann, Einstein had struggled with these new tools in the Zurich Notebook. Einstein wrote Grossmann’s name and considered candidate field equations he would come back to in the first 1915 paper on General Relativity

In this paper Einstein wrote in the introduction, “I completely lost trust in my established field equations [of the Einstein-Grossmann theory], […]. Thus I arrived back at the demand of a broader general covariance for the field equations, from which I parted, though with a heavy heart, three years ago when I worked together with my friend Grossmann. As a matter of fact, we then have already come quite close to the solution of the problem given in the following”. x

Marcel Grossmann, Albert Einstein, Gustav Geissler and Marcel’s brother Eugen
during their time as students at the ETH- here

Besso, General Relativity: During a visit by Besso to Einstein in Zurich in June 1913 they both tried to solve the Einstein-Grossmann theory field equations to find the perihelion advance of Mercury in the “Einstein-Besso manuscript”. Besso was inducted by Einstein into the necessary calculations. Besso collaborated with Einstein on the wrong gravitational Einstein-Grossmann theory, and their calculation based on this theory gave a wrong result. In October 1915 Einstein abandoned the Einstein-Grossmann theory; he transferred the basic framework of the calculation from the Einstein-Besso manuscript, and corrected it according to his new 1915 General Relativity Theory with which he got the correct precession so quickly, because he was able to apply the methods he had already worked out two years earlier with Besso. Einstein though did not acknowledge his earlier work with Besso, and did not mention his name in his 1915 paper that explains the anomalous precession of Mercury

Einstein considered his best friend Michele Besso as a sounding board and his class-mate from the Polytechnic Marcel Grossman – as his active partner. Yet, Einstein wrote that Grossman will never claim to be considered a co-discoverer of the Einstein-Grossmann theory – a theory very close to Einstein’s general theory of relativity that he published in November 1915. He only helped in guiding Einstein through the mathematical literature, but contributed nothing of substance to the results of the theory. Hence, Einstein neither considered Besso or Grossmann as co-discoverers or co-inventors of the relativity theory which he himself invented

Read also this paper, “How many scientists does it take to make a discovery? The era of the lone genius , as epitomised by Albert Einstein, has long gone”. Prof. Athene Donald, the author of the paper writes, “Ask people to conjure up an image of a scientist and Albert Einstein is most likely to pop into their head. The iconic image is of a lone genius beavering away in some secluded room until that familiar equation – E=mc2 – crystallised in his brain sufficiently to be written down. I very much doubt doing science was ever quite like that, but it is even more unlikely to apply now”. What do you think? x