Abraham Pais

*'Subtle is the Lord:
The Science and the Life
of Albert Einstein*'

Limited Summary by Michael McGoodwin,

prepared 1988, revised 2008

Limited Summary by Michael McGoodwin,

prepared 1988, revised 2008

**
Acknowledgement**: This work has been only partially and sketchily summarized here, using the
1983 Oxford University Press paperback edition. Quotations are taken from that work, as
are paraphrases of its commentary.

**Overall impression**: A fine and erudite overview of the scientific
discoveries and intellectual development of Einstein (including some of the
arcane mathematics that is well beyond my abilities) by a physicist and contemporary who knew
Einstein well at Princeton during the last decade of Einstein's life. This is a difficult read. It is also not a tell all about his personal life. (The more recent 2007 detailed biography by Walter Isaacson is an excellent complement to this scientific history, as it is a more thorough review of the man's life in general, but is not as informative about the math and physics.) The men whose discoveries preceded Einstein's, along with his contemporaries and competitors are well laid out, including Isaac Newton, James Clerk Maxwell, Gustav Kirchoff, Ludwig Boltzmann, Ernst Mach, Hendrik Antoon Lorentz, Henri Poincaré, Max Planck, Marcel Grossman, David Hilbert, Niels Bohr, Werner Heisenberg, Erwin Schrödinger, Louis de Broglie, Paul Dirac, Max Born, Karl Schwarzschild, Satyendra Nath Bose, Arthur Compton, etc.

**Hyperlinks**: Links to selected webpages have been added that were current as of September 2008. Authoritativeness of these sources, many of which are from Wikipedia, is not assumed or implied.

Note: I have summarized some of the physical and mathematical principles of special and general relativity here.

Albert Einstein (AE) was born Aug. 8, 1876 in Ulm, Württemberg, Germany. His sister Maja (Maria) was born 1881—AE was always very close to her. It was a liberal household that did not observe Jewish rites. He took violin. He moves to Milan at 16. Attended college at ETH (Eidgenössische Technische Hochschule Zürich) in Zurich 1896-1900. Becomes Swiss citizen, renounces German citizenship. Difficulties getting job. Teacher. Becomes technical expert at Bern patent office 1902. His father Hermann Einstein dies 1902. He marries the Serbian Mileva Maric 1903. Son Hans Albert born 1904.

AE acknowledged as his principle scientific precursors these men: Newton (his classical mechanics based on 3 laws of motion and universal gravitation), Maxwell (electromagnetism), Mach (relativity and phenomenalism), Planck (formula for spectral radiance of a black body), and Lorentz (transformations). He was also influenced by Spinoza's view of a deterministic world in which an impersonal God prevails but does not directly intervene in human affairs. He hoped to retain Newton's causality (which was ultimately to die at the hands of quantum theory) but rejected Newton's empiricism. (Newton famously said "I frame no hypotheses"), but AE instead emphasized the value of free intellectual invention (thought experiments and formulation of postulates) that is only subsequently tested against experimental results.

1902-4: Early papers on thermodynamics. Derivation of energy fluctuation formula. Determination of Boltzmann's constant. Studies on entropy and probability. Foundations of statistical mechanics.

Lorentz's transformation. Fitzgerald suggests in 1889 that moving objects contract in length. PoincarĂ© (1898) questions the absoluteness of time and simultaneity.

1905 was Einstein's annus mirabilis, in which he wrote 6 major papers.

(1) The light quantum was first hypothesized and the photoelectric effect discussed in a paper completed March 1905 (*Annalen der Physik* 17:132 9 June 1905), "*On a Heuristic Viewpoint Concerning the Production and Transformation of Light"*, the stated basis for his 1921 Nobel prize.

(2) His doctoral thesis in April (*Annalen der Physik* 19:289 8 Feb. 1906) "*A New Determination of Molecular Dimensions*" dealt with determining molecular dimensions and the Avogadro number N from data for sugar dissolved in water (reinforcing the reality of atoms at a time when the existence of discrete atoms and molecules was still being debated).

(3) His May paper on Brownian motion *(Annalen der Physik* 17:549 18 July 1905), "*On the Motion Required by the Molecular Kinetic Theory of Heat of Small Particles Suspended in a Stationary Liquid*", developed a stochastic model explaining this phenomenon using a kinetic theory of liquids.

(4) His remarkable June 1905 paper (*Annalen der Physik*, 17:891, 26 September 1905), "*On the Electrodynamics of Moving Bodies*", laid out most of the principles of *Special Relativity*. Stellar aberration and Fizeau's measurement of c in moving water
helped to convince AE of the relativity of speed with respect to light. This paper postulates:

a. The Principle of Relativity: Physical laws
take the same form in all inertial frames, there is no absolute reference frame; and

b. The Principle of Invariant Light Speed: In any inertial frame, the speed of light c is the
same whether the light is emitted by a body at rest or moving.

From these simple postulates, he derives several important consequences:

He shows
that *absolute simultaneity* does not exist (has no universal invariant meaning) but instead that simultaneity is always "relative" to the inertial frames employed.
He derives the Lorentz transformations. He also derives the Lorentz/Fitzgerald
contraction of rods (length shortening), though the underlying mechanism is different from those postulated by Lorentz and Fitzgerald. He presents the formulas for the *relativistic addition of velocities*, the relativistic Doppler effect, and for *relativistic stellar aberration *(caused by relative motion of the observer on Earth with respect to a star). He describes how a moving (or
orbiting) clock positioned in frame S' will seem to run slower for an observer in a different inertial frame S (*dilation of time*)—this is a symmetric effect which would appear the same to S' if frame S had the clock. He proves the Lorentz covariance
of Maxwell-Lorentz equations and derives a "new manner of expression" for the Lorentz force (the force on a moving point charge due to electrical and magnetic fields). He derives the formula for relativistic kinetic energy, which approaches infinity as velocity approaches c, and concludes that velocities of matter exceeding c have no possibility of existence. He also derives the transformation law for the energy E of a light beam with respect to inertial frames. (He states the *total energy* formula, rest plus kinetic, in 1907.)

(5) The September 1905 paper (*Annalen der Physik*, 18:639, 21 November 1905), "*Does the Inertia of a Body Depend Upon Its Energy Content?*": Includes formula relating [rest] energy to [rest] mass, E = mc^{2} (implied by showing that when a
body gives off energy L in the form of radiation, its mass diminishes by L/c^{2}).
He wonders whether radium salts could be used to measure the mass defect (mass defecit).

(6) December 1906: a second paper on Brownian motion *(Annalen der Physik* 19:371 8 Feb. 1906).

Specific heat of solids 1906.

1910: Formula for scattering of light near the triple point of a gas
(*critical opalescence*). The many confirmations of Avogadro's number N confirm the existence of
molecules.

Einstein's excessive reliance on "mathematical construction". His self-assurance in avoiding careful literature search.

Becomes Privatdozent 1908 Bern, so can teach. Second son Edward born 1910. Becomes Associate Prof. in Zurich 1909. Full professor Prague 1911. Returns to Zurich 1912.

Moves to Berlin 1914. Separates from first wife Mileva. World War I begins in August. His radical pacifism arises.

Stomach ulcer. Marries his cousin Elsa. Bending of star light by the gravitational effect of the sun verified in eclipse May 29, 1919 (first predicted 1911). He becomes a world figure. Friendship with Helen Dukas. Increasing German anti-Semitism prompts move to Princeton 1933.

Planck derives the relativistic momentum-velocity relation, and the transformation laws for momentum. Minkowski (1908) describes
an inextricable union of space and time (space-time), puts Maxwell-Lorentz equations in modern *tensor* form, and introduces terms such as *light cone*, *world line*, etc.

AE realized in 1907 that a freely falling observer could
not sense gravitation and therefore that relativity should be extended from the
special case (applying to uniformly moving unaccelerated inertial frames, thus *special relativity*) to more generalized nonuniform accelerated motions (thus *general relativity*). He
suggests that acceleration of a reference frame and gravitation are equivalent
(*equivalence principle*). Concludes the need for *Riemannian geometry* for modeling gravitation Aug.
1912. He searches for transformations that leave ds^{2} invariant. Predicts gravitational red-shift of light (1907, the decrease in energy for photons climbing out of a gravity well) and gravitational bending of light (1907, remarkably demonstrated beginning in 1979 as gravitational lensing). He computes the correct value for the well-known *precession of the perihelion of Mercury* Nov. 18,
1915 (the modern value for the contribution attributable to general relativity is 42.98±0.04 arcsec/century). Predicts gravitational waves. Final equation for gravitation presented 25 Novermber 1915 at the Prussian Academy of Sciences.

"Subtle is the Lord, but malicious he is not." ("Raffiniert ist der Herr Gott, aber boshaft ist er nicht.", p. 113.) This is a 1921 statement of AE in reference to the short-lived possibility that the ether wind had been newly confirmed after all by Miller (a discovery which would presumably represent God playing a diabolical joke on AE, in contrast to the negative Michelson/Morley results of 1881 and 1887/1888).

Further developments post-1915 include the Schwarzschild's 1916 derivation of the Schwarzschild radius, and the prediction of event horizons and black holes. There are profound cosmological implications in the general theory of relativity. [Obviously, I need to do much more to summarize the vast sweep of general relativity presented in this book!]

In deriving Planck's formula for black body
radiation, Planck postulates that *discrete energy levels* differing by h*nu
exist. AE proposes light consists of *quanta *with energy E = h*nu (see 1905 paper above). He
explains the photoelectric effect with a postulated photoelectric equation.
In 1905 AE proposed the light-quantum hypothesis (monochromatic radiation at low
density behaves thermodynamically as if it consists of mutually independent
energy quanta of magnitude h*nu. He also proposed the *Heuristic principle *(that interactions of light and matter are constituted as if light consists of
energy quanta of h*nu, see above). AE describes quanta as point-like in 1909 and
predicted a "fusion of the wave and emission theory" (but could not
accept the fusion theory in 1925 when it arrives as quantum mechanics).
This fusion (the wave-particle duality) is called *complementarity*. Describes photon *momentum *1910 and derives formula for photon momentum = h*nu/c in 1916. (Compton scattering in 1922-3 confirmed photon momentum and affirmed particle aspect of the photon beyond reasonable doubt). Bohr's model of hydrogen atom 1913.
Bose's derivation of Planck's law proposes a new set of properties and
statistics 1924—i.e., that photons have 2 states of polarization and the number
of photons is not conserved. The 1st paper on quantum statistics. AE describes Bose-Einstein condensations. Louis de Broglie (1923) predicts wave properties such
as diffraction for matter particles (de Broglie hypothesis of wave-particle duality). Schrödinger's wave equation (*Psi-Funktion*) for hydrogen
atom 1926. AE's concern regarding underlying "objective reality" versus observed phenomena in face of quantum developments, and unhappiness with implications of quantum randomness. He states for instance in a 1926 letter to Born (quoted p. 443) "Quantum mechanics is very impressive. But an inner voice tells me that it is not yet the real thing. The theory produces a good deal but hardly brings us closer to the secret of the Old One. I am at all events convinced that *He* does not play dice..."

AE dies 1955 of ruptured aortic aneurysm after many frustrating and apparently fruitless years spent working to develop a Unified Field Theory which he hoped would unite electromagnetism with gravity (but which ignored newer forces and particles discovered in the 20th Century)..