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!

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Review: The Cambridge Companion to Einstein

I recommend this recent publication, The Cambridge Companion to Einstein, edited by Michel Janssen and Christoph Lehner.
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It is a real good book: The scholarly and academic papers contained in this volume are authored by eminent scholars within the field of Einstein studies.

The first paper introduces the term “Copernican process”, a term invented by scholars to study scientists’ and Einstein’s achievements. The Copernican process describes a complex revolutionary narrative and the book’s side of the divide.

First, Einstein did not consider the relativity paper a revolutionary paper, but rather a natural development of classical electrodynamics and optics; he did regard the light quantum paper a revolutionary paper.

Carl Seelig wrote, “As opposed to several interpreters, Einstein would not agree that the relativity theory was a revolutionary event. He used to say: ‘In the [special] relativity theory it is no question of a revolutionary act but of a natural development of lines which have been followed for centuries'”.

Why did Einstein not consider special relativity a revolutionary event? The answer was related to Euclidean geometry and to measuring rods and clocks. In his special theory of relativity Einstein gave a definition of a physical frame of reference. He defined it in terms of a network of measuring rods and a set of suitable-synchronized clocks, all at rest in an inertial system.

The light quantum paper was the only one of his 1905 papers Einstein considered truly revolutionary. Indeed Einstein wrote Conrad Habicht in May 1905 about this paper, “It deals with the radiation and energy characteristics of light and is very revolutionary”.

A few years ago Jürgen Renn introduced a new term “Copernicus process”: […] “reorganization of a system of knowledge in which previously marginal elements take on a key role and serve as a starting point for a reinterpretation of the body of knowledge; typically much of the technical apparatus is kept, inference structures are reversed, and the previous conceptual foundation is discarded. Einstein’s achievements during his miracle year of 1905 can be described in terms of such Copernican process” (p. 38).

For instance, the transformation of the preclassical mechanics of Galileo and contemporaries (still based on Aristotelian foundations) to the classical mechanics of the Newtonian era can be understood in terms of a Copernican process. Like Moses, Galileo did not reach the promised land, or better perhaps, like Columbus, did not recognize it as such. Galileo arrived at the derivation of results such as the law of free fall and projectile motion by exploring the limits of the systems of knowledge of preclassical mechanics (p. 41).

Einstein preserved the technical framework of the results in the works of Lorentz and Planck, but profoundly changed their conceptual meaning, thus creating the new kinematics of the theory of special relativity and introducing the revolutionary idea of light quanta. Copernicus as well had largely kept the Ptolemaic machinery of traditional astronomy when changing its basic conceptual structure.

Although Einstein did not consider his relativity paper a revolutionary paper, he explained the new feature of his theory just before his death: “the realization of the fact that the bearing of the Lorentz transformation transcended its connection with Maxwell‘s equations and was concerned with the nature of space and time in general. A further new result was that the ‘Lorentz invariance’ is a general condition for any theory. This was for me of particular importance because I had already previously recognized that Maxwell‘s theory did not represent the microstructure of radiation and could therefore have no general validity”.

Planck assumed 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.

Planck believed, in accord with Maxwell’s theory that, the energy of the electromagnetic field itself could change continuously. Einstein first recognized that Maxwell’s theory did not represent the microstructure of radiation and could have no general validity. He realized that a number of phenomena involving interactions between matter and radiation could be simply explained with the help of light quanta.

Using Renn and Rynasiewicz phraseology, Planck “did not reach the promised land”, the light quanta. Moreover, he even disliked this idea. Einstein later wrote about Planck, “He has, however, one fault: that he is clumsy in finding his way about in foreign trains of thought. It is therefore understandable when he makes quite faulty objections to my latest work on radiation”.

In an essay on Johannes Kepler Einstein explained Copernicus’ discovery (revolutionary process): Copernicus understood that if the planets moved uniformly in a circle round the stationary sun (one frame of reference), then the planets would also move round all other frames of reference (the earth and all other planets): “Copernicus had opened the eyes of the most intelligent to the fact that the best way to get a clear group of the apparent movements of the planets in the heavens was to regard them as movements round the sun conceived as stationary. If the planets moved uniformly in a circle round the sun, it would have been comparatively easy to discover how these movements must look from the earth”.

Therefore Einstein’s revolutionary process was the following: Einstein was at work on his light quanta paper, but he was busily working on the electrodynamics of moving bodies too. Einstein understood that if the equation E = hf holds in one inertial frame of reference, it would hold in all others. Einstein realized that the ‘Lorentz invariance’ is a general condition for any theory, and then he understood that the Lorentz transformation transcended its connection with Maxwell’s equations and was concerned with the nature of space and time in general.

 

 

 

 

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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