# 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

# Albert Einstein and Hermann Minkowski’s Space-time Formalism

Vesselin Petkov writes: “Minkowski’s contributions to modern physics have not been fully and appropriately appreciated. […] Einstein called Minkowski’s approach ‘superfluous learnedness’. Also, Sommerfeld’s recollection of what Einstein said on one occasion can provide further indication of his initial attitude towards Minkowski’s development of the implications of the equivalence of the times of observers in relative motion: ‘Since the mathematicians have invaded the relativity theory, I do not understand it myself any more’. […] Despite his initial negative reaction towards Minkowski’s four-dimensional physics Einstein relatively quickly realized that his revolutionary theory of gravity would be impossible without the revolutionary contributions of Minkowski”. x

First let us correct a myth here: it is not quit true that Minkowski’s contributions have not been appreciated. Hermann Minkowski was Einstein’s former mathematics professor at the Zürich Polytechnic. During his studies at the Polytechnic Einstein skipped Minkowski’s classes; but Einstein also skipped Prof. Carl Friedrich Geiser’s lectures as much as he skipped Prof. Adolf Hurwitz’s classes… They were all mathematicians. Einstein never showed up the classes of mathematicians. At that time Einstein was less interested in mathematics than in the visible process of physics. He found it difficult to accept for a long time the importance of abstract mathematics, and found high mathematics necessary only when developing his gravitation theory – he discovered the qualities of high mathematics around 1912 Einstein and his wife around 1905

Second, On September 21, 1908, in the 80th annual general meeting of the German Society of Scientists and Physicians at Cologne, Minkowski presented his famous talk, “Space and Time”. x Minkowski

May years later his assistant, the physicist Max Born wrote: “I went to Cologne, met Minkowski and heard his celebrated lecture ‘Space and Time’, delivered on 21 September 1908. […] He told me later that it came to him as a great shock when Einstein published his paper in which the equivalence of the different local times of observers moving relative to each other was pronounced; for he had reached the same conclusions independently but did not publish them because he wished first to work out the mathematical structure in all its splendor. He never made a priority claim and always gave Einstein his full share in the great discovery”. x

Scott Walter writes, “This story of Minkowski’s recollection of his encounter with Einstein’s paper on relativity is curious, in that the idea of the observable equivalence of clocks in uniform motion had been broached by Poincaré in one of the papers studied during the first session of the electron-theory seminar. It is possible, of course, that Poincaré’s operational definition of local time escaped Minkowski’s attention, or that Minkowski was thinking of an exact equivalence of timekeepers”. [In the
summer of 1905, Minkowski and David Hilbert led an advanced seminar on electrodynamical theory]. x

Before 1905 Poincaré stressed the importance of the method of clocks and their synchronization by light signals. He gave a physical interpretation of Lorentz’s local time in terms of clock synchronization by light signals, and formulated a principle of relativity. However, Poincaré did not pronounce “the equivalence of the different local times of observers moving relative to each other”. Einstein was the first to do so Poincaré

John Stachel explains Poincaré’s clock synchronization: “Poincaré had interpreted the local time as that given by clocks at rest in a frame moving through the ether when synchronized as if – contrary to the basic assumptions of Newtonian kinematics – the speed of light were the same in all inertial frames. Einstein dropped the ether and the ‘as if’: one simply synchronized clocks by the Poincaré convention in each inertial frame and accepted that the speed of light really is the same in all inertial frames when measured with clocks so synchronized”. x Einstein in the Patent Office

In the text of the lecture of the Cologne talk immediately after presenting Lorentz’s local time it is written: “However, the credit of first recognizing sharply that the time of the one electron is just as good as that of the other, i.e., that t and t’ are to be treated the same, is of A. Einstein”. And Minkowski referred to Einstein’s 1905 relativity paper and to his 1907 review article

Read my short paper (a note) on Einstein, Minkowski and Max Born’s recollections of Minkowski’s work

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# Albert Einstein and the Theory of Relativity איינשטיין ותורת היחסות

Age 16. Between 1894 and 1895 Einstein writes an essay and sends it to his uncle Caesar Koch. He believes in the ether. Einstein is also familiar with the principle of relativity in mechanics

A year later, in 1895-1896, while in Aarau, Einstein conceives of a thought experiment: Einstein chases a light beam

In 1899 Einstein studies Maxwell’s electromagnetic theory

Around 1898-1900Einstein invents the magnet and conductor thought experiment

Between 1899 and 1900 Einstein is occupied with the contradiction between the Galilean principle of relativity and the constancy of the velocity of light in Maxwell’s theory

Between 1899 and 1901 Einstein is interested in ether drift experiments, and appears to have designed at least two experiments, the first in 1899

In 1901 Einstein still accepts the Galilean kinematics of space and time, in which the Galileian principle of relativity holds good

In 1902 Einstein reads Hendryk Antoon Lorentz’s 1895 seminal work on electron theory Between 1901 and 1903 Einstein is working with the Maxwell-Hertz equations for empty space. He tries to find solutions to two problems

Magnet and conductor experiment and Faraday’s induction law lead to a conclusion that there is an asymmetry in the explanation depending on whether the magnet moves or the conductor moves. Einstein analyzed the magnet and conductor thought experiment according to Maxwell’s theory and the Galilean transformations. But covariance of Maxwell equations failed

Einstein confronts a conflict between the principle of Galilean relativity and the constancy of the velocity of light

Between 1901 and 1903 Einstein drops the ether hypothesis and chooses the principle of relativity instead of the postulate of the constancy of the velocity of light, and finds a (temporary) solution for his conflict in the form of an emission theory

Einstein seems to have pondered with this problem for an extra year, from 1903-1904 until almost spring-summer 1904. Einstein discusses Fizeau’s experiment using emission theory. He demonstrates, by using Fizeau’s celebrated experimental result, why this standpoint of emission theories cannot hold true

Towards spring-summer 1904 Einstein dropps emission theory and returns to Lorentz’s theory. He spends almost a year in vain trying to modify the idea of Lorentz in the hope of resolving the above problem. Einstein tries to discuss Fizeau’s experiment in Lorentz’s theory [In 1895 Lorentz managed to derive the Fresnel Formula from the first principles of his theory (stationary ether and moving electrons) without the need of any partial ether drag. Lorentz thus adhered to Fizeau’s original 1851 experimental result, but not to Fresnel’s theoretical interpretation of partial ether drag hypothesis, used to derive his dragging coefficient]. Finally

Age 26. In spring 1905, Einstein found the final solution, the “step”, which solved his dilemma

For footnotes, references, and further details please consult my papers 