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.


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.


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.


Albert Einstein at the Patent office

Mileva Marić and Einstein




Eduard Tete, Mileva Marić and Hans Albert


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”.


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


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.


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.


My books



Review: The Cambridge Companion to Einstein

I recommend this recent publication, The Cambridge Companion to Einstein, edited by Michel Janssen and Christoph Lehner.

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.





End of complementarity? Was Einstein right after all?…

Whereas the wavefunction is usually interpreted statistically, and it reflects our inability to know the quantum particle’s state prior to the act of measurement, a quite new paper interprets it, instead, without any respect to observation or measurement. This is the popular account and now to the more serious one…


In philosophy we usually make a distinction between two views: the view that something corresponds directly to reality, observation-independent: refers to what is there, what is “physically real”, and independent of anything we say, believe, or know about the system.

In this case, quantum states represent knowledge about an underlying reality, real objects, real properties of quantum systems.

If we consider Schrodinger’s cat gedankenexperiment, then from the above point of view, Schrödinger’s cat in superposition of two states is a monster inside a box: both alive and dead cat at the same time. How come then when we open the box and observe (and measure) the both alive and dead cat at same time, we only see alive cat or dead cat? The orthodox interpretation of quantum mechanics invokes the collapse of the wave function whereby the act of observing the cat causes it to turn into alive-cat or dead-cat state. If the quantum state is a real physical state, then collapse is a mysterious physical process, whose precise time of occurrence is not well-defined. Accordingly, people who hold this view are generally led to alternative interpretations that eliminate the collapse, such as Everett’s relative state formulation of quantum mechanics, many-worlds theory.

The “state of knowledge” view, observation-dependent: refers to experimenter’s knowledge or information about some aspect of reality; what we think, know, or believe what is reality. We presuppose tools of observation and measurement.

In this case, the quantum state does not represent knowledge about some underlying reality, but rather it only represents knowledge about the consequences of measurements that we might make on the system; states that undergo a discontinuous change in the light of measurement results; it does not imply the existence of any real physical process.

From this point of view (anti-realist or neo-Copenhagen point of view), collapse of the wavefunction need be no more mysterious than the instantaneous Bayesian updating of a probability distribution upon obtaining new information: Hence Schrodinger’s cat is also not at all mysterious. When we consider superposition of states, both alive and dead cat at the same time, we mean that it has a fifty percent probability of being alive and a fifty percent probability of being dead (what is the likelihood of the cat being dead or alive). The process depends for its action on observations, measurements, and the knowledge of the observer. The collapse of the wave function corresponds to us observing and finding out whether the cat is dead or alive.

Erhard Scheibe introduced the notions of epistemic and ontic states of a system. The Ontic state of the system is the system just the way it is, it is empirically inaccessible. It refers to individual systems without any respect to their observation or measurement. On the other hand, the epistemic state of the system depends on observation and measurement; it refers to the knowledge that can be obtained about an ontic state.

As commonly understood, Bohr was advocating epistemic physics while Einstein was considering ontic physics. And indeed Jaynes wrote that the two physicists were not discussing the same physics: “needless to say, we consider all of Einstein’s reasoning and conclusions correct on his level; but on the other hand we think that Bohr was equally correct on his level, in saying that the act of measurement might perturb the system being measured, placing a limitation on the information we can acquire and therefore on the predictions we are able to make. There is nothing that one could object to in this conjecture, although the burden of proof is on the person who makes it”. Hence, the famous Bohr-Einstein debate was never actually resolved in favor of Bohr – although common thinking even among physicists and philosophers of science is that it was.


The million-dollar question is: What does a quantum state represent? What is the quantum state? Is the quantum wavefunction an ontic state or an epistemic state? Using the terminology of Harrigan and Spekkens, let us ask: is it possible to construct a ψ-ontic model? A ψ-ontic hidden variable model is a quantum state which is ontic, but we construct some underlying ontic hidden variable states theory. Hidden variable theories are always ontic states theories.

Or else, is it possible to construct a ψ-epistemic model? A ψ-epistemic hidden variable model is a quantum state which is epistemic, but there is some underlying ontic hidden state, so that quantum mechanics is the statistical theory of this ontic state.

In a paper entitled, “The Quantum State Cannot be Interpreted Statistically” by Matt Pusey, Jon Barrett and Terry Rudolph (henceforth known as PBR), PBR answer the above question in the negative, ruling out ψ-epistemic theories, and attempting to provide a ψ-ontic view of the quantum state.

PBR present a no-go theorem which is formulated for an ontic hidden variable theory: any model in which a quantum state represents mere information about an underlying physical state of the system must make predictions which contradict those of quantum theory.

In the terminology of Harrigan and Spekkens, the PBR theorem says that ψ-epistemic models cannot reproduce the predictions of quantum theory.

The PBR theorem holds only for Systems that are prepared independently, have independent physical states (independent preparations). A system has an ontic hidden state λ. A quantum state ψ describes an experimenter’s information which corresponds to a distribution of ontic hidden states λ. PBR show that when distinct quantum states ψ correspond to disjoint probability distributions of ontic hidden variables (i.e., what PBR call independent preparations, they do not have values of ontic hidden variables in common), these quantum states ψ are ontic and they are not mere information. And if the states of a quantum system do not correspond to ontic disjoint probability distributions (the distributions of the values of ontic hidden values overlap), the quantum wavefunctions are said to be epistemic.

The PBR theorem is in the same spirit as Bell’s no-go theorem, which states that no local theory can reproduce the predictions of quantum theory. Bell’s theorem was formulated for ontic hidden variable theory as well. Bell’s theorem shows that a ψ-epistemic hidden variable theory which is local is forbidden in quantum mechanics, i.e, any ψ-epistemic hidden variable theory must be non-local in order to reproduce the quantum statistics of entanglement (EPR).

PBR ended their paper by saying: “For these reasons and others, many will continue to view the quantum state as representing information [epistemic]. One approach is to take this to be information about possible measurement outcomes [epistemic], and not about the objective state of a system [ontic]”; i.e., one approach is not to take this as a ψ-epistemic model. Hence, why not follow a ψ-ontic model?

Einstein would finally not emerge victorious. Although the PBR theorem favors “Einstein” who believes that quantum physics is not ontic complete, it does not rule “Bohr” who believes in quantum physics that is epistemic complete (Wavefunctions are epistemic, but there is no underlying ontic hidden variable states theory). Indeed PBR are aware of this possibility.


It seems that the PBR theorem does not end the century-old debate about the ontology of quantum states. It does not prove, with mathematical certitude, that the ontic interpretation is right and the epistemic one is wrong.

Read my paper on the PBR theorem and Einstein.


Another no-go theorem, Kochen–Specker (KS) theorem: non-contextual (does not depend on the context of the measurement) deterministic hidden variable theories are incompatible with quantum mechanics.

Kochen, Simon B., and Ernst .P. Specker, “On the problem of hidden variables in quantum mechanics”, Journal of Mathematics and Mechanics 17, 1967, pp. 59–87.

Centenary of the Death of Poincaré – Einstein and Poincaré 2012 פואנקרה ואיינשטיין

לרגל מאה שנה למותו של פואנקרה, פרסמתי בשלושה חלקים מחקר על הנרי פואנקרה, תרומתו בתחום של תורת האלקטרון והאלקטרודינמיקה של הגופים בתנועה והשאלה האם פואנקרה הגיע לתורת יחסות ולגילויים שאותם אנו מוצאים בתורת היחסות הפרטית לפני או במקביל לאיינשטיין. כמובן שהשאלה היא מעט יותר מורכבת ולא פשטנית כפי שהצגתי אותה כאן. בנושא זה כתבתי את עבודת הדוקטורט שלי והמאמרים הם סיכום ועדכון של הדוקטורט שלי שנכתב לפני 14 שנה.

A Biography of Poincaré  – Researcher in dynamics of the electron and electrodynamics –  2012 Centenary of the Death of Poincaré. Here

On January 4, 2012 (the centenary of Henri Poincaré’s death) a colloquium was held in Nancy, France the subject of which was “Vers une biographie d’Henri Poincaré”. Scholars discussed several approaches for writing a biography of Poincaré


I present a personal and scientific biographical sketch of Poincaré and his contributions to electrodynamics of moving bodies, which does not in any way reflect Poincaré’s rich personality and immense activity in science. When Poincaré traveled to parts of Europe, Africa and America, his companions noticed that he knew well everything from statistics to history and curious customs and habits of peoples. He was almost teaching everything in science. He was so encyclopedic that he dealt with the outstanding questions in the different branches of physics and mathematics; he had altered whole fields of science such as non-Euclidean geometry, Arithmetic, celestial mechanics, thermodynamics and kinetic theory, optics, electrodynamics, Maxwell’s theory, and other topics from the forefront of Fin de Siècle physical science

As opposed to the prosperity of biographies and secondary papers studying the life and scientific contributions of Albert Einstein, one finds much less biographies and secondary sources discussing Poincaré’s life and work. Unlike Einstein, Poincaré was not a cultural icon. Beginning in 1920 Einstein became a myth and a world famous figure. Although Poincaré was so brilliant in mathematics, he mainly remained a famous mathematician within the professional circle of scientists. He published more papers than Einstein, performed research in many more branches of physics and mathematics, received more prizes on his studies, and was a member of more academies in the whole world. Despite this tremendous yield, Poincaré did not win the Nobel Prize

Most famous is Poincaré’s philosophy of conventionalism, which sprang out of his research into geometry during a period (the end of the 1880’s) when non-Euclidean geometries were a matter of a consistent possibility. Poincaré developed two kinds of conventionalism, conventionalism applicable to geometry and conventionalism for the principles of physics. Both sprang from Poincaré’s mathematical group theory

In addition to the geometries of Euclid, Lobachewski, and Riemann, Poincaré proposed another geometry, the truth of which was not incompatible with the other geometries; he called it the “fourth geometry”. The first time that Poincaré’s fourth geometry appeared in print was in 1891

Einstein did not feel at ease with Poincaré’s standpoint. In 1992 Michel Paty commented on Einstein’s presentation of Poincaré’s conventionalism in 1921, “Actually this is not exactly Poincaré’s point of view, but a translation of it made by Einstein in his own perspective, that is according to his conception of physical Geometry”. See

Scott Walter’s papers here

And Peter Galison’s book Einstein’s Clocks, Poincare’s Maps here

Review by John Stachel: here and by Alberto Martínez here

Scientific contributions in electrodynamics: Before 1905, Poincaré stressed the importance of the method of clocks and their synchronization, but unlike Einstein, magnet and conductor (asymmetries in Lorentz’s theory regarding the explanation of Faraday’s induction) or chasing a light beam and overtaking it, were not a matter of great concern for him

In 1905 Poincaré elaborated Lorentz’s electron theory from 1904 in two papers entitled “On the Dynamics of the Electron”. Poincaré’s theory was a space-time mathematical theory of groups at the basis of which stood the postulate of relativity; Einstein’s 1905 theory was a kinematical theory of relativity

Poincaré did not renounce the ether. He wrote a new law of addition of velocities, but he did not abandon the tacit assumptions made about the nature of time, simultaneity, and space measurements implicit in Newtonian kinematics

Although he questioned absolute time and absolute simultaneity, he did not make new kinematical tacit assumptions about space and time. He also did not require reciprocity of the appearances, and therefore did not discover relativity of simultaneity

These are the main hallmarks of Einstein’s special theory of relativity. Nevertheless, Poincaré had arrived at many novel findings that went way beyond Fin de Siècle physics. here


Read other point of views: Olivier Darrigol’s papers here and here

Darrigol, Olivier, “Henri Poincaré’s criticism of fin de siècle electrodynamics”, Studies in History and Philosophy of Modern Physics 26, 1995, pp. 1-44. here

Darrigol, Olivier, Electrodynamics from Ampère to Einstein, 2000, Oxford: Oxford University Press. Here

Mass-energy equivalence: In 1900 Poincaré considered a device creating and emitting electromagnetic waves. The device emits energy in all directions. As a result of the energy being emitted, it recoils. No motion of any other material body compensates for the recoil at that moment. Poincaré found that as a result of the recoil of the oscillator, in the moving system, the oscillator generating the electromagnetic energy suffers an “apparent complementary force”. In addition, in order to demonstrate the non-violation of the theorem of the motion of the centre of gravity, Poincaré needed an arbitrary convention, the “fictitious fluid”

Einstein demonstrated that if the inertial mass E/c2 is associated with the energy E, and on assuming the inseparability of the theorem of the conservation of mass and that of energy, then – at least as a first approximation – the theorem of the conservation of the motion of the centre of gravity is also valid for all systems in which electromagnetic processes take place

Before 1905 (and also afterwards) Poincaré did not explore the inertial mass-energy equivalence

Einstein was the first to explore the inertial mass-energy equivalence. 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


For a different point of view: Darrigol, Olivier, “Poincaré, Einstein, et l’inertie de l’énergie”, Comptes rendus de l’Académie des sciences IV 1, 2000, pp. 143-153. Here

See also this paper by Stephen Boughn and  Tony Rothman. A report of the paper here


Did Poincaré influence Einstein on his way to the Special theory of relativity? One differentiates two kinds of questions here

  1What was the effect of Poincaré’s studies on the development of the Special Theory of relativity? and

 2What was the effect Poincaré’s research may have had on the development of Einstein’s own pathway towards the Special Theory of Relativity? hence

Poincaré did contribute to the theory of relativity a great deal. His 1905 space-time theory of groups greatly influenced Minkowski on his way to reformulate and recast mathematically the special theory of relativity. In addition, he arrived at many interesting ideas. However, it appears from examining the primary sources that Poincaré did not influence Einstein on his route to the special theory of relativity. See my papers here