# 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

paper abstract

# אלברט איינשטיין – דרכו ליחסות Albert Einstein – pathway to theory of relativity

My Einstein and Relativity Papers – Gali Weinstein

Einstein’s Pathway to the Special Theory of Relativity

Einstein’s Pathway to the General Theory of Relativity

The papers describe the genesis and history of special relativity and the discovery and history of general relativity – Einstein chases a light beam, the magnet and conductor thought experiment, Michelson-Morley experiment, emission theory, ether superfluous, Fizeau water-tube experiment, the principle of relativity and the principle of the constancy of the velocity of light (light postulate), The Step, Besso-Einstein meeting, Relativity 1905 paper. 1907 equivalence principle, lift experiments, Galileo principle, coordinate-dependant theory of relativity, Zurich Notebook, Einstein-Grossmann theory (Entwurf theory), deflection of light near the sun, Einstein’s struggles with Entwurf theory, hole argument, 1915 General Theory of Relativity: Hilbert – Einstein, precession or advance of Perihelion of Mercury, how Einstein found the generally covariant field equations, and Einstein’s 1916 general theory of relativity – Mach’s principle, rotating disk thought experiment, and point coincidence argument. These papers do not discuss the affine connection. For a discussion of the affine connection please consult Prof. John Stachel’s works

Philosophyof physics andof Special Relativity – papers discussing philosophical questions about space and time and interpretations of Special Relativity. A rigid body does not exist in the special theory of relativity, distant simultaneity defined with respect to a given frame of reference without reference to synchronized clocks, Einstein synchronization, challenges on Einstein’s connection of synchronization and Lorentz contraction, a theory of relativity without light – Ignatowski, Einstein’s composition of relative velocities – addition theorem for relative velocities, and space of relative velocities, Max Born and rigid body problem, Paul Ehrenfest’s paradox, relativity of simultaneity, Einstein’s clocks: Einstein’s 1905 Clock Paradox, Paul Langevin and the Twin Paradox

Poincaré and EinsteinThe inertial mass-energy equivalence, Lorentz’s theory of the electron violated the principle of action and reaction, Henri Poincaré trying to mend this violation, in 1905 Einstein showed that a change in energy is associated with a change in inertial mass equal to the change in energy divided by c2. Einstein and Poincaré– Method of clocks and their synchronization, Sur la dynamique de l’electron, Dynamics of the Electron, Einstein’s 1905 letter to Conrad Habicht, Poincaré’s 1905 letters to Lorentz, Poincaré’s spacetime mathematical theory of groups, As opposed to Einstein, before 1905 Poincaré stressed the importance of the method of clocks and their synchronization by light signals. Poincaré’s Lorentz group, Poincaré’s La Science et l’hypothèse  – Science and Hypothesis

Innovation never comes from the established institutions… – Eric Schmidt

מאמרי איינשטיין והיחסות שלי – גלי וינשטיין

דרכו של איינשטיין ליחסות הפרטית.

דרכו של איינשטיין ליחסות הכללית.

אני מתכננת לפרסם ספר ולכן המאמרים הם טיוטא ולא גרסא סופית.

“חידוש אף פעם לא מגיע ממוסדות מוכרים” – אריק שמידט.

Einstein Archives – Jerusalem and Einstein Papers Project – Caltech

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