- Reichenbach published his book "Philosophie der Raum-Zeit-Lehre" in 1927 which included an appendix discussing Weyl's unified field theory. Einstein reviewed the book positively, agreeing with Reichenbach's argument in the appendix that general relativity is not an attempt to reduce physics to geometry.
- Einstein also reviewed Meyerson's book "La déduction relativiste" positively, agreeing with its emphasis on the deductive-constructive nature of relativity theory and finding the term "geometrical" meaningless in the context of unified field theories. Both reviews supported Reichenbach's view that the goal of unified field theories was unification rather than geometrization.
'What is truth?' Einstein on Rods and Clocks in Relativity TheoryMarcoGiovanelli3
This paper offers a historical overview of Einstein's vacillating attitude towards 'phenomenological' and This 'dynamical' treatments of rods and clocks in relativity theory. In Einstein's view, a realistic microscopic model of rods and clocks was needed to account for the very existence of measuring devices of identical construction that always measure the same unit of time and the same unit of length. It will be shown that the empirical meaningfulness of both relativity theories depends on what, following Max Born, one might call the 'principle of the physical identity of the units of measure'. In an attempt to justify the validity of such a principle, Einstein was forced by different interlocutors, in particular Hermann Weyl and Wolfgang Pauli, to deal with the genuine epistemological, rather than the physical question of whether a theory should be required to describe the material devices needed for its own verification.
1. Albert Einstein developed the theories of special and general relativity and made many important contributions to the development of modern physics. He published groundbreaking papers on the photoelectric effect, Brownian motion, and the existence and behavior of atoms.
2. Einstein held academic positions in Switzerland and Germany. He was a director at the Kaiser Wilhelm Institute in Berlin and a professor at Princeton University. He received many honors for his revolutionary scientific work including the Nobel Prize in Physics in 1921.
3. Einstein is considered one of the most influential scientists of all time. He revolutionized our understanding of space, time, mass, and energy with his theories of relativity and he helped lay the foundation for modern physics with his work on quantum
Werner Heisenberg was a German physicist born in 1901 who made major contributions to the foundations of quantum mechanics. He studied mathematics and physics in university, developing an interest in theoretical physics. In 1925, he formulated the first complete quantum mechanics theory called matrix mechanics. This breakthrough established the new field and described the behavior of atoms and molecules. Although initially controversial due to its abstract nature, matrix mechanics was later shown to be equivalent to Erwin Schrodinger's wave mechanics formulation. Heisenberg also discovered the uncertainty principle in 1927, which states that the more precisely one property of a particle is known, the less precisely its complementary property can be known. Heisenberg's work was seminal in the development of modern physics.
The document summarizes biographies of three scientists:
1) Albert Einstein, a German physicist known for his theory of relativity and E=mc2 equation.
2) Isaac Newton, an English physicist and mathematician who formulated classical mechanics and laws of motion.
3) Stephen Hawking, an English cosmologist known for his work on black holes and predictions combining general relativity and quantum mechanics.
Werner Heisenberg was a German physicist who received the 1932 Nobel Prize in Physics for his work on quantum mechanics. He led Germany's atomic bomb program during WWII. Heisenberg was born in Germany in 1901 and studied physics, receiving his PhD from the University of Munich in 1923. He made seminal contributions to the development of quantum mechanics in 1925 and 1927. He held professorships in Germany and directed the Kaiser Wilhelm Institute for Physics in Berlin. Heisenberg received numerous honors for his scientific work and contributions.
The mystery person is Albert Einstein, a theoretical physicist born in Germany in 1879 who won the Nobel Prize in Physics in 1921 for his contributions to theoretical physics, including explaining the photoelectric effect and establishing the theory of relativity based on Riemannian geometry. He later declined an offer to be the president of Israel and died in 1955 in Princeton, New Jersey.
Advanced physics prize 2011 for finding the rate of expansion of Universe.VENKATESWARARAO ALAPATI
This document discusses the discovery of the accelerating expansion of the universe through observations of type 1a supernovae by independent research groups led by Saul Perlmutter and Brian Schmidt/Adam Riess in the late 1990s. It is believed this acceleration is caused by dark energy, which accounts for about 73% of the total energy density of the universe based on various cosmological observations. The document provides historical context on the development of theories of an expanding universe from Einstein's theory of general relativity in 1917 through the work of Friedmann, Lemaitre, Hubble and others in the 1920s and 1930s.
Albert Einstein (1879-1955) was a theoretical physicist known for developing the theory of relativity. He studied mathematics and physics at university and became a professor. Some of Einstein's major scientific works included his studies on the photoelectric effect, Brownian motion, special relativity, and mass-energy equivalence, which led to him receiving the 1921 Nobel Prize in Physics. He is quoted as saying "I want to go when I want, its of bad taste to prolong life artificially" shortly before his death in 1955 at the age of 76.
'What is truth?' Einstein on Rods and Clocks in Relativity TheoryMarcoGiovanelli3
This paper offers a historical overview of Einstein's vacillating attitude towards 'phenomenological' and This 'dynamical' treatments of rods and clocks in relativity theory. In Einstein's view, a realistic microscopic model of rods and clocks was needed to account for the very existence of measuring devices of identical construction that always measure the same unit of time and the same unit of length. It will be shown that the empirical meaningfulness of both relativity theories depends on what, following Max Born, one might call the 'principle of the physical identity of the units of measure'. In an attempt to justify the validity of such a principle, Einstein was forced by different interlocutors, in particular Hermann Weyl and Wolfgang Pauli, to deal with the genuine epistemological, rather than the physical question of whether a theory should be required to describe the material devices needed for its own verification.
1. Albert Einstein developed the theories of special and general relativity and made many important contributions to the development of modern physics. He published groundbreaking papers on the photoelectric effect, Brownian motion, and the existence and behavior of atoms.
2. Einstein held academic positions in Switzerland and Germany. He was a director at the Kaiser Wilhelm Institute in Berlin and a professor at Princeton University. He received many honors for his revolutionary scientific work including the Nobel Prize in Physics in 1921.
3. Einstein is considered one of the most influential scientists of all time. He revolutionized our understanding of space, time, mass, and energy with his theories of relativity and he helped lay the foundation for modern physics with his work on quantum
Werner Heisenberg was a German physicist born in 1901 who made major contributions to the foundations of quantum mechanics. He studied mathematics and physics in university, developing an interest in theoretical physics. In 1925, he formulated the first complete quantum mechanics theory called matrix mechanics. This breakthrough established the new field and described the behavior of atoms and molecules. Although initially controversial due to its abstract nature, matrix mechanics was later shown to be equivalent to Erwin Schrodinger's wave mechanics formulation. Heisenberg also discovered the uncertainty principle in 1927, which states that the more precisely one property of a particle is known, the less precisely its complementary property can be known. Heisenberg's work was seminal in the development of modern physics.
The document summarizes biographies of three scientists:
1) Albert Einstein, a German physicist known for his theory of relativity and E=mc2 equation.
2) Isaac Newton, an English physicist and mathematician who formulated classical mechanics and laws of motion.
3) Stephen Hawking, an English cosmologist known for his work on black holes and predictions combining general relativity and quantum mechanics.
Werner Heisenberg was a German physicist who received the 1932 Nobel Prize in Physics for his work on quantum mechanics. He led Germany's atomic bomb program during WWII. Heisenberg was born in Germany in 1901 and studied physics, receiving his PhD from the University of Munich in 1923. He made seminal contributions to the development of quantum mechanics in 1925 and 1927. He held professorships in Germany and directed the Kaiser Wilhelm Institute for Physics in Berlin. Heisenberg received numerous honors for his scientific work and contributions.
The mystery person is Albert Einstein, a theoretical physicist born in Germany in 1879 who won the Nobel Prize in Physics in 1921 for his contributions to theoretical physics, including explaining the photoelectric effect and establishing the theory of relativity based on Riemannian geometry. He later declined an offer to be the president of Israel and died in 1955 in Princeton, New Jersey.
Advanced physics prize 2011 for finding the rate of expansion of Universe.VENKATESWARARAO ALAPATI
This document discusses the discovery of the accelerating expansion of the universe through observations of type 1a supernovae by independent research groups led by Saul Perlmutter and Brian Schmidt/Adam Riess in the late 1990s. It is believed this acceleration is caused by dark energy, which accounts for about 73% of the total energy density of the universe based on various cosmological observations. The document provides historical context on the development of theories of an expanding universe from Einstein's theory of general relativity in 1917 through the work of Friedmann, Lemaitre, Hubble and others in the 1920s and 1930s.
Albert Einstein (1879-1955) was a theoretical physicist known for developing the theory of relativity. He studied mathematics and physics at university and became a professor. Some of Einstein's major scientific works included his studies on the photoelectric effect, Brownian motion, special relativity, and mass-energy equivalence, which led to him receiving the 1921 Nobel Prize in Physics. He is quoted as saying "I want to go when I want, its of bad taste to prolong life artificially" shortly before his death in 1955 at the age of 76.
Sir Isaac Newton was an influential English scientist in the late 1600s. He developed calculus and described universal gravitation and the three laws of motion. Newton invented the mathematical techniques of calculus, which helped unlock many scientific discoveries and advanced physics and engineering. He also made important contributions to optics and alchemy.
Isaac Newton was an influential English scientist who made seminal contributions to physics, mathematics, and optics in the 17th century. Some of his major accomplishments included formulating the laws of motion and universal gravitation, which helped usher in the Classical Mechanics era. He also developed calculus and made discoveries in optics such as color theory. Newton published his work Philosophiæ Naturalis Principia Mathematica in 1687, which synthesized previous scientific ideas and laid the foundations for mechanics. Overall, Newton is widely considered one of the most influential scientists in history.
1) Albert Einstein was born in Germany in 1879 and went on to revolutionize physics with his theories of special and general relativity and explanation of the photoelectric effect.
2) In 1905, known as his "miracle year", Einstein published four groundbreaking papers that challenged classical Newtonian concepts of space and time and established him as a leading scientist.
3) He later moved to America to escape the rise of the Nazis in Germany and spent the rest of his life at the Institute for Advanced Study in Princeton, New Jersey, continuing research but never completing his quest for a unified field theory.
Albert Einstein was born in Germany in 1879 and later became a Swiss citizen. He is considered one of the most influential physicists of the 20th century, making fundamental contributions to the special and general theories of relativity, quantum mechanics, and statistical mechanics. Some of his most important works included his 1905 paper on the special theory of relativity and his 1916 paper introducing the general theory of relativity. Einstein received numerous honors for his work, including honorary doctorates from many universities, and he held professorships in Europe and the United States. He died in 1955 in Princeton, New Jersey.
1) The document is a final creative project for an online course on Einstein's Special Theory of Relativity that visualizes key facts and concepts from Einstein's "miracle year" of 1905 through word clouds.
2) It presents word clouds created from terms related to Einstein and his work, including his name, birth year, theories, and achievements like e=mc^2.
3) The project aims to teach about Einstein's life and contributions in a novel visual way through freely available word cloud software tools.
Albert Einstein was a German-born physicist who developed the special and general theories of relativity. He was born in Ulm, Germany in 1879 and obtained his early education in Munich. He struggled in school initially but developed an interest in geometry at age 12. Einstein published over 300 scientific papers and 150 non-scientific works in his lifetime. He won the Nobel Prize in Physics in 1921 for his explanation of the photoelectric effect. Einstein is considered one of the most influential scientists of the 20th century.
Albert Einstein was a German-born physicist who developed the theory of relativity and helped lay the foundations for modern physics. In 1905, while working as a clerk in a patent office in Bern, Switzerland, he published his theory of special relativity and derived the mass-energy equivalence formula E=mc2. In 1915, he presented his theory of general relativity, which revolutionized concepts of gravity. His work helped establish cosmology as a field of physics and confirmed some of his predictions through observations of light bending during a solar eclipse in 1919. Einstein won the Nobel Prize in Physics in 1921 for his explanation of the photoelectric effect. He later immigrated to the United States in 1932 to escape the rise of Nazism in Germany and
Albert Einstein was born in 1879 in Germany to a middle-class Jewish family. As a child, he was fascinated by invisible forces after encountering a compass at age 5. He mastered higher mathematics by age 16. He studied at the Higher Technical School in Zurich, graduating in 1900. After graduation, Einstein worked in a patent office in Bern, Switzerland. In 1905, he published four groundbreaking papers, one establishing the photoelectric effect and the famous equation E=mc2. Einstein is renowned for his theories of special and general relativity. He won the Nobel Prize in Physics in 1921 for his services to theoretical physics and especially for his discovery of the law of the photoelectric effect.
Albert’s class was on the history teacher Mr. Braun asked Albert if the Prussians defeated the French to Waterloo. Albert told him that he didn’t know and he must have forgotten. This irritated the teacher. He asked Albert, why? Albert replied that he didn’t see a point in learning dates. One could learn about them from books. Ideas are more important than facts and figures. The teacher attributed to Albert that he didn’t believe in education. He talked in a sarcastic manner. Albert told him that education should be about ideas and not facts. The teacher said that Albert was a disgrace to be there Albert felt miserable when he left the school that afternoon.
He didn’t like this school. He would have to come to it again. He lived in a small room. It was one of the poorest quarters of Munich. The landlady beat her children regularly. Her husband came every Saturday and drank in the evening. He then beat her. He didn’t like the children’s crying every time. He told these things to Yuri. He hated the atmosphere of slum violence. Next time his cousin [elsa] came to Munich. She told Albert that if he tried he could pass the examination. There were more stupid boys than him. Moreover, passing the examination was not difficult. It was simply just to be able to repeat in the examination that Elsa that he was not good at learning things by heart. He liked music as it gave him comfort. Albert didn’t like to remain in school. He met Yuri after six months. He had an idea. He told Yuri that if he had a medical certificate that he suffered from a nervous breakdown, he could get rid of school. He asked Yuri if he had a doctor friend. Yuri told him that he had in Dr. Ernest Weil. However, Yuri told him not to deceive him. He must be frank with him. When Albert visited Dr. Ernest Weil he had really come near a nervous breakdown. Dr. Ernest issued him the certificate. His fees were that he should serve Yuri with a meal. Albert told Dr. Ernest about his future plans.
He would go to Milan. He hoped to get admission into an Italian college or institute. It was possible from the comments of the Mathematics teacher, Mr. Koch. Yuri told him to get a reference in writing from the Mathematics teacher before going to the head teacher. Mr. Koch, the mathematics teacher encouraged him.
Albert Einstein was born in Germany in 1879 and showed an early fascination with science through observing a compass. In 1905, while working as a patent clerk, he developed his Special Theory of Relativity which established that space and time are relative to the observer's frame of reference. This theory along with others he published that year, including his paper on the photoelectric effect, established him as a leading scientist. He went on to publish his General Theory of Relativity in 1915 which described gravity not as a force but as a curvature of spacetime. This became one of the most important scientific works of the 20th century and helped establish Einstein as a genius who revolutionized people's understanding of science and the universe.
The document discusses the contributions of several important physicists throughout history. It describes how Isaac Newton formulated the laws of motion and gravity. Benjamin Franklin is noted for his kite experiment which led to the invention of the lightning rod. Michael Faraday invented the generator, which uses magnets to produce electric current. Wilhelm Roentgen discovered X-rays in 1895, which advanced the field of nuclear physics. Albert Einstein formulated the theory of relativity and his famous equation relating energy and mass, E=mc2.
Reichenbach vs. the Unified Field Theory ProgramMarcoGiovanelli3
This paper analyzes correspondence between Reichenbach and Einstein from the spring of 1926, concerning what it means to 'geometrize' a physical field. The content of a typewritten note that Reichenbach sent to Einstein on that occasion is reconstructed, showing that it was an early version of Section 49 of the untranslated Appendix to his Philosophie der Raum-Zeit-Lehre, on which Reichenbach was working at the time. This paper claims that the toy-geometrization of the electromagnetic field that Reichenbach presented in his note should not be regarded as merely a virtuoso mathematical exercise, but as an additional argument supporting the core philosophical message of his 1928 monograph. This paper concludes by suggesting that Reichenbach's infamous 'relativization of geometry' was only a stepping stone on the way to his main concern-the question of the 'geometrization of gravitation'.
Meghnad Saha (1893-1955) set out his theory in a number of papers published in British journals during 1920-1921. The work was immediately recognized as laying the foundation of quantitative astrophysics.History chooses the hour; and the hour produces the hero. The only surprise was that the hour was seized not by any established research centre in the West but by a far-off Calcutta which was nowhere on the world research map.
Geometry is based on axioms and definitions rather than empirical observations. The propositions of geometry are considered "true" not because they correspond to objective reality, but because they are derived via logical deduction from axioms accepted as true by definition. However, the axioms themselves cannot be proven true - they are simply postulates that are assumed to be valid within the system of geometry. As such, the "truth" of individual geometrical propositions is reduced to the internal consistency of the axiomatic system, not its correspondence to empirical observations of space.
Albert Einstein was a renowned German-born theoretical physicist. Some of his most important contributions include his special theory of relativity, which reconciled mechanics and electromagnetism, and his general theory of relativity, which revolutionized concepts of space and time. He is best known for his mass-energy equivalence formula E=mc2. Throughout his career, Einstein published over 300 scientific works and more than 150 non-scientific works, received many honors including the Nobel Prize in Physics, and has become synonymous with genius.
The document provides biographical and scientific details about Albert Einstein. It discusses that he was born in Germany in 1879 and died in 1955, and that he made seminal contributions to 20th century physics through his theories of special and general relativity. It summarizes that the special theory of relativity abandoned the concept of the luminiferous ether and established that the speed of light is constant, and that the general theory of relativity described gravity as a consequence of the curvature of spacetime.
Famous Polish Mathematicians Kinga Sekuła 2dmagdajanusz
Karol Borsuk was a prominent Polish topologist who created the theories of retracts and shape. He was a professor at the University of Warsaw and helped reactivate the mathematical center there after World War II. Borsuk introduced important concepts in algebraic topology like cohomotopy groups. He authored around 200 scientific publications.
Stefan Banach was one of the most outstanding Polish mathematicians, known for his self-study and work establishing modern functional analysis. He made seminal contributions to the theories of topological vector spaces and real numbers. Banach's most important work was the Theory of Linear Operations.
Alfred Tarski was a Polish-American logician considered one of the greatest of all time.
Albert Einstein was a German-born theoretical physicist who developed the theory of relativity and made major contributions to the development of quantum mechanics. He is considered one of the greatest and most influential physicists of all time. In 1905, Einstein published four groundbreaking papers outlining the photoelectric effect, Brownian motion, special relativity, and mass-energy equivalence. He later developed general relativity and applied it to model the structure of the universe. Einstein received the 1921 Nobel Prize in Physics for his services to theoretical physics, especially his discovery of the photoelectric effect.
Werner Heisenberg was a German physicist born in 1901 who made major contributions to the foundations of quantum mechanics. He studied mathematics and physics in university, developing an interest in theoretical physics. In 1925, he formulated the first complete quantum mechanics theory called matrix mechanics. This breakthrough established the new field and described the behavior of atoms and molecules. Although initially controversial due to its abstract nature, matrix mechanics was later shown to be equivalent to Erwin Schrodinger's wave mechanics formulation. Heisenberg also discovered the uncertainty principle in 1927, which states that the more precisely one property of a particle is known, the less precisely its complementary property can be known. Heisenberg's work was seminal in the development of modern physics.
Werner Heisenberg was a German physicist born in 1901 who made major contributions to the foundations of quantum mechanics. He studied mathematics and physics in university, developing an interest in theoretical physics. In 1925, he formulated the first complete quantum mechanics theory called matrix mechanics. This breakthrough established the new field and described the behavior of atoms and molecules. Although initially controversial due to its abstract nature, matrix mechanics was later shown to be equivalent to Erwin Schrodinger's wave mechanics formulation. Heisenberg also discovered the uncertainty principle in 1927, which states that the more precisely one property of a particle is known, the less precisely its complementary property can be known. Heisenberg's work was seminal in the development of modern physics.
The document discusses Albert Einstein's theories of relativity and gravitation, including:
1) Einstein developed the general theory of relativity in 1915 to explain conflicts between relativity and gravity, proposing gravity as the curvature of space-time caused by objects with mass.
2) Einstein also concluded that light and matter follow the shape of space-time, and that gravity slows down time.
3) Einstein spent the last 30 years of his life unsuccessfully attempting to develop a unified field theory combining all fundamental forces.
Sir Isaac Newton was an influential English scientist in the late 1600s. He developed calculus and described universal gravitation and the three laws of motion. Newton invented the mathematical techniques of calculus, which helped unlock many scientific discoveries and advanced physics and engineering. He also made important contributions to optics and alchemy.
Isaac Newton was an influential English scientist who made seminal contributions to physics, mathematics, and optics in the 17th century. Some of his major accomplishments included formulating the laws of motion and universal gravitation, which helped usher in the Classical Mechanics era. He also developed calculus and made discoveries in optics such as color theory. Newton published his work Philosophiæ Naturalis Principia Mathematica in 1687, which synthesized previous scientific ideas and laid the foundations for mechanics. Overall, Newton is widely considered one of the most influential scientists in history.
1) Albert Einstein was born in Germany in 1879 and went on to revolutionize physics with his theories of special and general relativity and explanation of the photoelectric effect.
2) In 1905, known as his "miracle year", Einstein published four groundbreaking papers that challenged classical Newtonian concepts of space and time and established him as a leading scientist.
3) He later moved to America to escape the rise of the Nazis in Germany and spent the rest of his life at the Institute for Advanced Study in Princeton, New Jersey, continuing research but never completing his quest for a unified field theory.
Albert Einstein was born in Germany in 1879 and later became a Swiss citizen. He is considered one of the most influential physicists of the 20th century, making fundamental contributions to the special and general theories of relativity, quantum mechanics, and statistical mechanics. Some of his most important works included his 1905 paper on the special theory of relativity and his 1916 paper introducing the general theory of relativity. Einstein received numerous honors for his work, including honorary doctorates from many universities, and he held professorships in Europe and the United States. He died in 1955 in Princeton, New Jersey.
1) The document is a final creative project for an online course on Einstein's Special Theory of Relativity that visualizes key facts and concepts from Einstein's "miracle year" of 1905 through word clouds.
2) It presents word clouds created from terms related to Einstein and his work, including his name, birth year, theories, and achievements like e=mc^2.
3) The project aims to teach about Einstein's life and contributions in a novel visual way through freely available word cloud software tools.
Albert Einstein was a German-born physicist who developed the special and general theories of relativity. He was born in Ulm, Germany in 1879 and obtained his early education in Munich. He struggled in school initially but developed an interest in geometry at age 12. Einstein published over 300 scientific papers and 150 non-scientific works in his lifetime. He won the Nobel Prize in Physics in 1921 for his explanation of the photoelectric effect. Einstein is considered one of the most influential scientists of the 20th century.
Albert Einstein was a German-born physicist who developed the theory of relativity and helped lay the foundations for modern physics. In 1905, while working as a clerk in a patent office in Bern, Switzerland, he published his theory of special relativity and derived the mass-energy equivalence formula E=mc2. In 1915, he presented his theory of general relativity, which revolutionized concepts of gravity. His work helped establish cosmology as a field of physics and confirmed some of his predictions through observations of light bending during a solar eclipse in 1919. Einstein won the Nobel Prize in Physics in 1921 for his explanation of the photoelectric effect. He later immigrated to the United States in 1932 to escape the rise of Nazism in Germany and
Albert Einstein was born in 1879 in Germany to a middle-class Jewish family. As a child, he was fascinated by invisible forces after encountering a compass at age 5. He mastered higher mathematics by age 16. He studied at the Higher Technical School in Zurich, graduating in 1900. After graduation, Einstein worked in a patent office in Bern, Switzerland. In 1905, he published four groundbreaking papers, one establishing the photoelectric effect and the famous equation E=mc2. Einstein is renowned for his theories of special and general relativity. He won the Nobel Prize in Physics in 1921 for his services to theoretical physics and especially for his discovery of the law of the photoelectric effect.
Albert’s class was on the history teacher Mr. Braun asked Albert if the Prussians defeated the French to Waterloo. Albert told him that he didn’t know and he must have forgotten. This irritated the teacher. He asked Albert, why? Albert replied that he didn’t see a point in learning dates. One could learn about them from books. Ideas are more important than facts and figures. The teacher attributed to Albert that he didn’t believe in education. He talked in a sarcastic manner. Albert told him that education should be about ideas and not facts. The teacher said that Albert was a disgrace to be there Albert felt miserable when he left the school that afternoon.
He didn’t like this school. He would have to come to it again. He lived in a small room. It was one of the poorest quarters of Munich. The landlady beat her children regularly. Her husband came every Saturday and drank in the evening. He then beat her. He didn’t like the children’s crying every time. He told these things to Yuri. He hated the atmosphere of slum violence. Next time his cousin [elsa] came to Munich. She told Albert that if he tried he could pass the examination. There were more stupid boys than him. Moreover, passing the examination was not difficult. It was simply just to be able to repeat in the examination that Elsa that he was not good at learning things by heart. He liked music as it gave him comfort. Albert didn’t like to remain in school. He met Yuri after six months. He had an idea. He told Yuri that if he had a medical certificate that he suffered from a nervous breakdown, he could get rid of school. He asked Yuri if he had a doctor friend. Yuri told him that he had in Dr. Ernest Weil. However, Yuri told him not to deceive him. He must be frank with him. When Albert visited Dr. Ernest Weil he had really come near a nervous breakdown. Dr. Ernest issued him the certificate. His fees were that he should serve Yuri with a meal. Albert told Dr. Ernest about his future plans.
He would go to Milan. He hoped to get admission into an Italian college or institute. It was possible from the comments of the Mathematics teacher, Mr. Koch. Yuri told him to get a reference in writing from the Mathematics teacher before going to the head teacher. Mr. Koch, the mathematics teacher encouraged him.
Albert Einstein was born in Germany in 1879 and showed an early fascination with science through observing a compass. In 1905, while working as a patent clerk, he developed his Special Theory of Relativity which established that space and time are relative to the observer's frame of reference. This theory along with others he published that year, including his paper on the photoelectric effect, established him as a leading scientist. He went on to publish his General Theory of Relativity in 1915 which described gravity not as a force but as a curvature of spacetime. This became one of the most important scientific works of the 20th century and helped establish Einstein as a genius who revolutionized people's understanding of science and the universe.
The document discusses the contributions of several important physicists throughout history. It describes how Isaac Newton formulated the laws of motion and gravity. Benjamin Franklin is noted for his kite experiment which led to the invention of the lightning rod. Michael Faraday invented the generator, which uses magnets to produce electric current. Wilhelm Roentgen discovered X-rays in 1895, which advanced the field of nuclear physics. Albert Einstein formulated the theory of relativity and his famous equation relating energy and mass, E=mc2.
Reichenbach vs. the Unified Field Theory ProgramMarcoGiovanelli3
This paper analyzes correspondence between Reichenbach and Einstein from the spring of 1926, concerning what it means to 'geometrize' a physical field. The content of a typewritten note that Reichenbach sent to Einstein on that occasion is reconstructed, showing that it was an early version of Section 49 of the untranslated Appendix to his Philosophie der Raum-Zeit-Lehre, on which Reichenbach was working at the time. This paper claims that the toy-geometrization of the electromagnetic field that Reichenbach presented in his note should not be regarded as merely a virtuoso mathematical exercise, but as an additional argument supporting the core philosophical message of his 1928 monograph. This paper concludes by suggesting that Reichenbach's infamous 'relativization of geometry' was only a stepping stone on the way to his main concern-the question of the 'geometrization of gravitation'.
Meghnad Saha (1893-1955) set out his theory in a number of papers published in British journals during 1920-1921. The work was immediately recognized as laying the foundation of quantitative astrophysics.History chooses the hour; and the hour produces the hero. The only surprise was that the hour was seized not by any established research centre in the West but by a far-off Calcutta which was nowhere on the world research map.
Geometry is based on axioms and definitions rather than empirical observations. The propositions of geometry are considered "true" not because they correspond to objective reality, but because they are derived via logical deduction from axioms accepted as true by definition. However, the axioms themselves cannot be proven true - they are simply postulates that are assumed to be valid within the system of geometry. As such, the "truth" of individual geometrical propositions is reduced to the internal consistency of the axiomatic system, not its correspondence to empirical observations of space.
Albert Einstein was a renowned German-born theoretical physicist. Some of his most important contributions include his special theory of relativity, which reconciled mechanics and electromagnetism, and his general theory of relativity, which revolutionized concepts of space and time. He is best known for his mass-energy equivalence formula E=mc2. Throughout his career, Einstein published over 300 scientific works and more than 150 non-scientific works, received many honors including the Nobel Prize in Physics, and has become synonymous with genius.
The document provides biographical and scientific details about Albert Einstein. It discusses that he was born in Germany in 1879 and died in 1955, and that he made seminal contributions to 20th century physics through his theories of special and general relativity. It summarizes that the special theory of relativity abandoned the concept of the luminiferous ether and established that the speed of light is constant, and that the general theory of relativity described gravity as a consequence of the curvature of spacetime.
Famous Polish Mathematicians Kinga Sekuła 2dmagdajanusz
Karol Borsuk was a prominent Polish topologist who created the theories of retracts and shape. He was a professor at the University of Warsaw and helped reactivate the mathematical center there after World War II. Borsuk introduced important concepts in algebraic topology like cohomotopy groups. He authored around 200 scientific publications.
Stefan Banach was one of the most outstanding Polish mathematicians, known for his self-study and work establishing modern functional analysis. He made seminal contributions to the theories of topological vector spaces and real numbers. Banach's most important work was the Theory of Linear Operations.
Alfred Tarski was a Polish-American logician considered one of the greatest of all time.
Albert Einstein was a German-born theoretical physicist who developed the theory of relativity and made major contributions to the development of quantum mechanics. He is considered one of the greatest and most influential physicists of all time. In 1905, Einstein published four groundbreaking papers outlining the photoelectric effect, Brownian motion, special relativity, and mass-energy equivalence. He later developed general relativity and applied it to model the structure of the universe. Einstein received the 1921 Nobel Prize in Physics for his services to theoretical physics, especially his discovery of the photoelectric effect.
Werner Heisenberg was a German physicist born in 1901 who made major contributions to the foundations of quantum mechanics. He studied mathematics and physics in university, developing an interest in theoretical physics. In 1925, he formulated the first complete quantum mechanics theory called matrix mechanics. This breakthrough established the new field and described the behavior of atoms and molecules. Although initially controversial due to its abstract nature, matrix mechanics was later shown to be equivalent to Erwin Schrodinger's wave mechanics formulation. Heisenberg also discovered the uncertainty principle in 1927, which states that the more precisely one property of a particle is known, the less precisely its complementary property can be known. Heisenberg's work was seminal in the development of modern physics.
Werner Heisenberg was a German physicist born in 1901 who made major contributions to the foundations of quantum mechanics. He studied mathematics and physics in university, developing an interest in theoretical physics. In 1925, he formulated the first complete quantum mechanics theory called matrix mechanics. This breakthrough established the new field and described the behavior of atoms and molecules. Although initially controversial due to its abstract nature, matrix mechanics was later shown to be equivalent to Erwin Schrodinger's wave mechanics formulation. Heisenberg also discovered the uncertainty principle in 1927, which states that the more precisely one property of a particle is known, the less precisely its complementary property can be known. Heisenberg's work was seminal in the development of modern physics.
The document discusses Albert Einstein's theories of relativity and gravitation, including:
1) Einstein developed the general theory of relativity in 1915 to explain conflicts between relativity and gravity, proposing gravity as the curvature of space-time caused by objects with mass.
2) Einstein also concluded that light and matter follow the shape of space-time, and that gravity slows down time.
3) Einstein spent the last 30 years of his life unsuccessfully attempting to develop a unified field theory combining all fundamental forces.
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Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, revolutionizing physics in the early 20th century. Some of his most influential works included developing the photoelectric effect, mass-energy equivalence with E=mc2, and introducing the concept of photons that helped establish quantum theory. He received the 1921 Nobel Prize in Physics for his services to theoretical physics, particularly his discovery of the law of the photoelectric effect. Einstein is considered one of the most influential physicists of the 20th century and revolutionized how we understand space, time, gravity and the universe.
Albert Einstein was a German-born theoretical physicist who developed the general theory of relativity and the law of the photoelectric effect. He was born in Germany in 1879 and later became a Swiss citizen. Einstein received the 1921 Nobel Prize in Physics for his work on quantum theory. He later immigrated to the United States to escape the rise of the Nazis in Germany. Einstein published over 300 scientific papers and made major contributions to modern physics.
Erwin rudolf josef a]alexander schrödingerjaredshugart
Schrodinger was an Austrian physicist born in 1887 who made significant contributions to quantum mechanics. He discovered the Schrodinger wave equation in 1926 and received the Nobel Prize in Physics in 1933 along with Dirac. Schrodinger studied physics at the University of Vienna and later became the Director of the School for Theoretical Physics.
Erwin rudolf josef alexander schrödingerjaredshugart
Schrodinger was an Austrian physicist born in 1887 who made significant contributions to quantum mechanics. He discovered the Schrodinger wave equation in 1926 and received the Nobel Prize in Physics in 1933 along with Dirac. Schrodinger studied physics at the University of Vienna and later became the Director of the School for Theoretical Physics.
The document discusses Albert Einstein and his achievements for which he was awarded the Nobel Prize in Physics. Einstein was a German-born physicist and scientist who developed the theory of general relativity in 1915, which re-formulated the concept of gravity. In 1921, Einstein received the Nobel Prize in Physics for his work explaining the photoelectric effect and contributions to theoretical physics, not for his theory of relativity which was not fully understood at the time. Einstein is considered the most popular scientist of the 20th century.
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Albert Einstein was born in Ulm, Germany in 1879. As a child, he was fascinated by a compass and wanted to understand the invisible forces that guided it. In 1905, while working as a patent clerk in Germany, Einstein developed his Special Theory of Relativity and introduced the world to the idea that light exists as particles called photons. He went on to publish additional groundbreaking papers that year, including his famous equation E=mc2. Einstein later completed his General Theory of Relativity in 1915, which revolutionized the scientific understanding of gravity. He died in 1955 in Princeton, New Jersey at the age of 76, leaving behind a transformed scientific world.
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Unification vs. Geometrization Reichenbach and Einstein's Fernparallelismus-Field Theory
1. Unification vs. Geometrization
Reichenbach and Einstein’s Fernparallelismus-Field Theory
marco.giovanelli@unito.it
Philosophers and Einstein’s of Relativity
Napoli 26/11/2021
UNIVERSITÀ
DEGLI STUDI
DI TORINO
0 / 44
2. Introduction
Einstein (1949, 73-75) had always regarded his 1915 field theory of
gravitation, the general theory of relativity, as nothing but a stepping
stone toward a unified field theory which would overcome a double
dualism
• the dualism between gravitational and the electromagnetic field
• the dualism between matter and field
Einstein’s quest for the final field theory spans over most of Einstein’s
professional life from 1919 (Einstein, 1919) till his death in 1955
(Einstein and Kaufman, 1955)
in the 1920s Reichenbach was the only philosopher who possessed the
epistemological insight and mathematical savvy to find his bearings
among the intricacies of the various unification attempts.
1 / 44
3. Introduction
Einstein (1949, 73-75) had always regarded his 1915 field theory of
gravitation, the general theory of relativity, as nothing but a stepping
stone toward a unified field theory which would overcome a double
dualism
• the dualism between gravitational and the electromagnetic field
• the dualism between matter and field
Einstein’s quest for the final field theory spans over most of Einstein’s
professional life from 1919 (Einstein, 1919) till his death in 1955
(Einstein and Kaufman, 1955)
in the 1920s Reichenbach was the only philosopher who possessed the
epistemological insight and mathematical savvy to find his bearings
among the intricacies of the various unification attempts.
1 / 44
4. Introduction
Einstein (1949, 73-75) had always regarded his 1915 field theory of
gravitation, the general theory of relativity, as nothing but a stepping
stone toward a unified field theory which would overcome a double
dualism
• the dualism between gravitational and the electromagnetic field
• the dualism between matter and field
Einstein’s quest for the final field theory spans over most of Einstein’s
professional life from 1919 (Einstein, 1919) till his death in 1955
(Einstein and Kaufman, 1955)
in the 1920s Reichenbach was the only philosopher who possessed the
epistemological insight and mathematical savvy to find his bearings
among the intricacies of the various unification attempts.
1 / 44
5. Introduction
Einstein (1949, 73-75) had always regarded his 1915 field theory of
gravitation, the general theory of relativity, as nothing but a stepping
stone toward a unified field theory which would overcome a double
dualism
• the dualism between gravitational and the electromagnetic field
• the dualism between matter and field
Einstein’s quest for the final field theory spans over most of Einstein’s
professional life from 1919 (Einstein, 1919) till his death in 1955
(Einstein and Kaufman, 1955)
in the 1920s Reichenbach was the only philosopher who possessed the
epistemological insight and mathematical savvy to find his bearings
among the intricacies of the various unification attempts.
1 / 44
6. Introduction
Einstein (1949, 73-75) had always regarded his 1915 field theory of
gravitation, the general theory of relativity, as nothing but a stepping
stone toward a unified field theory which would overcome a double
dualism
• the dualism between gravitational and the electromagnetic field
• the dualism between matter and field
Einstein’s quest for the final field theory spans over most of Einstein’s
professional life from 1919 (Einstein, 1919) till his death in 1955
(Einstein and Kaufman, 1955)
in the 1920s Reichenbach was the only philosopher who possessed the
epistemological insight and mathematical savvy to find his bearings
among the intricacies of the various unification attempts.
1 / 44
7. Introduction
Reichenbach
provided the first, and possibly only, overall philosophical reflection on
the unified field theory program at that time of its peak
tried to unravel the key to Einstein’s success in formulating a field
theory of gravitation by uncovering the reasons for the failure of
subsequent attempts of a theory of the total field
theory of spacetime theories ante litteram*
*
Lehmkuhl, 2017.
2 / 44
8. Introduction
Reichenbach
provided the first, and possibly only, overall philosophical reflection on
the unified field theory program at that time of its peak
tried to unravel the key to Einstein’s success in formulating a field
theory of gravitation by uncovering the reasons for the failure of
subsequent attempts of a theory of the total field
theory of spacetime theories ante litteram*
*
Lehmkuhl, 2017.
2 / 44
9. Introduction
Reichenbach’s reflections on the unified field theory program can be
organized around three correspondences, which revolve around three
conceptual issues:
Reichenbach-Weyl correspondence*
(1920-1921)
• =⇒ coordination
Reichenbach-Einstein correspondence (1926-1927)
†
• =⇒ geometrization
Reichenbach-Einstein correspondence (1928-1929)
• =⇒ unification
*
Ryckman, 1996, Rynasiewicz, 2005.
†
Lehmkuhl, 2014, Giovanelli, 2016.
3 / 44
10. Introduction
Einstein-Reichenbach Debate on Fernparallelismus-field theory
(October 1928–January 1929)
Reichenbach’s correspondence with Einstein on Fernparallelismus
• =⇒ personal quarrel*
Reichenbach’s writings on Fernparallelismus
• =⇒ intellectual estrangement
*
Hentschel, 1990.
4 / 44
13. Setting the Stage
August of 1926: “unofficial associate professor” (nichtbeamteter
außerordentlicher Professor) at the University of Berlin
December of 1926: finished Philosophie der Raum-Zeit-Lehre
(Reichenbach to Schlick, 06-12-1926)
July of 1927: publication agreement with De Gruyter (Reichenbach to
Schlick, 02-07-1927)
October of 1927: Preface
October of 1927: Einstein read the galley proofs on his way to
Brussels (Solvay Conference)
“
I finished reading Reichenbach. To be so delighted with oneself
must be pleasing, but less so for other people
(Einstein to Elsa Einstein, 23-10-1927)
”
6 / 44
14. Setting the Stage
August of 1926: “unofficial associate professor” (nichtbeamteter
außerordentlicher Professor) at the University of Berlin
December of 1926: finished Philosophie der Raum-Zeit-Lehre
(Reichenbach to Schlick, 06-12-1926)
July of 1927: publication agreement with De Gruyter (Reichenbach to
Schlick, 02-07-1927)
October of 1927: Preface
October of 1927: Einstein read the galley proofs on his way to
Brussels (Solvay Conference)
“
I finished reading Reichenbach. To be so delighted with oneself
must be pleasing, but less so for other people
(Einstein to Elsa Einstein, 23-10-1927)
”
6 / 44
15. Setting the Stage
August of 1926: “unofficial associate professor” (nichtbeamteter
außerordentlicher Professor) at the University of Berlin
December of 1926: finished Philosophie der Raum-Zeit-Lehre
(Reichenbach to Schlick, 06-12-1926)
July of 1927: publication agreement with De Gruyter (Reichenbach to
Schlick, 02-07-1927)
October of 1927: Preface
October of 1927: Einstein read the galley proofs on his way to
Brussels (Solvay Conference)
“
I finished reading Reichenbach. To be so delighted with oneself
must be pleasing, but less so for other people
(Einstein to Elsa Einstein, 23-10-1927)
”
6 / 44
16. Setting the Stage
August of 1926: “unofficial associate professor” (nichtbeamteter
außerordentlicher Professor) at the University of Berlin
December of 1926: finished Philosophie der Raum-Zeit-Lehre
(Reichenbach to Schlick, 06-12-1926)
July of 1927: publication agreement with De Gruyter (Reichenbach to
Schlick, 02-07-1927)
October of 1927: Preface
October of 1927: Einstein read the galley proofs on his way to
Brussels (Solvay Conference)
“
I finished reading Reichenbach. To be so delighted with oneself
must be pleasing, but less so for other people
(Einstein to Elsa Einstein, 23-10-1927)
”
6 / 44
17. Setting the Stage
August of 1926: “unofficial associate professor” (nichtbeamteter
außerordentlicher Professor) at the University of Berlin
December of 1926: finished Philosophie der Raum-Zeit-Lehre
(Reichenbach to Schlick, 06-12-1926)
July of 1927: publication agreement with De Gruyter (Reichenbach to
Schlick, 02-07-1927)
October of 1927: Preface
October of 1927: Einstein read the galley proofs on his way to
Brussels (Solvay Conference)
“
I finished reading Reichenbach. To be so delighted with oneself
must be pleasing, but less so for other people
(Einstein to Elsa Einstein, 23-10-1927)
”
6 / 44
18. Setting the Stage
August of 1926: “unofficial associate professor” (nichtbeamteter
außerordentlicher Professor) at the University of Berlin
December of 1926: finished Philosophie der Raum-Zeit-Lehre
(Reichenbach to Schlick, 06-12-1926)
July of 1927: publication agreement with De Gruyter (Reichenbach to
Schlick, 02-07-1927)
October of 1927: Preface
October of 1927: Einstein read the galley proofs on his way to
Brussels (Solvay Conference)
“
I finished reading Reichenbach. To be so delighted with oneself
must be pleasing, but less so for other people
(Einstein to Elsa Einstein, 23-10-1927)
”
6 / 44
23. Einstein’s Reviews
Einstein’s Review of Reichenbach’s Philosophie der Raum-Zeit-Lehre
• “In the Appendix, the foundation of the Weyl-Eddington theory is treated in
a clear way and in particular the delicate question of the coordination of
these theories to reality” (Einstein, 1928c, 20).
• in the Appendix, “in my opinion quite rightly—it is argued that the claim
that general relativity is an attempt to reduce physics to geometry is
unfounded” (Einstein, 1928c, 20).
Einstein’s Review of Meyerson’s La déduction relativiste
• “the term ‘geometrical’ used in this context is entirely devoid of meaning”
(Einstein, 1928a, 165), the goal is unification*.
• Einstein very much appreciated Meyerson’s insistence on the
deductive-constructive character of relativity (Hegel) (Einstein, 1928a,
165).
*
Lehmkuhl, 2014.
9 / 44
24. Einstein’s Reviews
Einstein’s Review of Reichenbach’s Philosophie der Raum-Zeit-Lehre
• “In the Appendix, the foundation of the Weyl-Eddington theory is treated in
a clear way and in particular the delicate question of the coordination of
these theories to reality” (Einstein, 1928c, 20).
• in the Appendix, “in my opinion quite rightly—it is argued that the claim
that general relativity is an attempt to reduce physics to geometry is
unfounded” (Einstein, 1928c, 20).
Einstein’s Review of Meyerson’s La déduction relativiste
• “the term ‘geometrical’ used in this context is entirely devoid of meaning”
(Einstein, 1928a, 165), the goal is unification*.
• Einstein very much appreciated Meyerson’s insistence on the
deductive-constructive character of relativity (Hegel) (Einstein, 1928a,
165).
*
Lehmkuhl, 2014.
9 / 44
25. Einstein’s Reviews
Einstein’s Review of Reichenbach’s Philosophie der Raum-Zeit-Lehre
• “In the Appendix, the foundation of the Weyl-Eddington theory is treated in
a clear way and in particular the delicate question of the coordination of
these theories to reality” (Einstein, 1928c, 20).
• in the Appendix, “in my opinion quite rightly—it is argued that the claim
that general relativity is an attempt to reduce physics to geometry is
unfounded” (Einstein, 1928c, 20).
Einstein’s Review of Meyerson’s La déduction relativiste
• “the term ‘geometrical’ used in this context is entirely devoid of meaning”
(Einstein, 1928a, 165), the goal is unification*.
• Einstein very much appreciated Meyerson’s insistence on the
deductive-constructive character of relativity (Hegel) (Einstein, 1928a,
165).
*
Lehmkuhl, 2014.
9 / 44
26. Einstein’s Reviews
Einstein’s Review of Reichenbach’s Philosophie der Raum-Zeit-Lehre
• “In the Appendix, the foundation of the Weyl-Eddington theory is treated in
a clear way and in particular the delicate question of the coordination of
these theories to reality” (Einstein, 1928c, 20).
• in the Appendix, “in my opinion quite rightly—it is argued that the claim
that general relativity is an attempt to reduce physics to geometry is
unfounded” (Einstein, 1928c, 20).
Einstein’s Review of Meyerson’s La déduction relativiste
• “the term ‘geometrical’ used in this context is entirely devoid of meaning”
(Einstein, 1928a, 165), the goal is unification*.
• Einstein very much appreciated Meyerson’s insistence on the
deductive-constructive character of relativity (Hegel) (Einstein, 1928a,
165).
*
Lehmkuhl, 2014.
9 / 44
27. Einstein’s Reviews
Einstein’s Review of Reichenbach’s Philosophie der Raum-Zeit-Lehre
• “In the Appendix, the foundation of the Weyl-Eddington theory is treated in
a clear way and in particular the delicate question of the coordination of
these theories to reality” (Einstein, 1928c, 20).
• in the Appendix, “in my opinion quite rightly—it is argued that the claim
that general relativity is an attempt to reduce physics to geometry is
unfounded” (Einstein, 1928c, 20).
Einstein’s Review of Meyerson’s La déduction relativiste
• “the term ‘geometrical’ used in this context is entirely devoid of meaning”
(Einstein, 1928a, 165), the goal is unification*.
• Einstein very much appreciated Meyerson’s insistence on the
deductive-constructive character of relativity (Hegel) (Einstein, 1928a,
165).
*
Lehmkuhl, 2014.
9 / 44
28. Einstein’s Reviews
Einstein’s Review of Reichenbach’s Philosophie der Raum-Zeit-Lehre
• “In the Appendix, the foundation of the Weyl-Eddington theory is treated in
a clear way and in particular the delicate question of the coordination of
these theories to reality” (Einstein, 1928c, 20).
• in the Appendix, “in my opinion quite rightly—it is argued that the claim
that general relativity is an attempt to reduce physics to geometry is
unfounded” (Einstein, 1928c, 20).
Einstein’s Review of Meyerson’s La déduction relativiste
• “the term ‘geometrical’ used in this context is entirely devoid of meaning”
(Einstein, 1928a, 165), the goal is unification*.
• Einstein very much appreciated Meyerson’s insistence on the
deductive-constructive character of relativity (Hegel) (Einstein, 1928a,
165).
*
Lehmkuhl, 2014.
9 / 44
29. reconfiguration of Einstein’s
system of philosophical
alliances
Meyerson became Einstein’s
reference philosopher, a
position once proudly held by
Schlick and Reichenbach*
*
Giovanelli, 2018.
10 / 44
32. Einstein’s Fernparallelismus-Field theory
new geometry: Riemannian geometry with distant parallelism*
:
new formalism: set of mutually orthogonal, normal vectors (n-bein)
Aν
= hν
a
{
→ n-bein
Aa
*
Sauer2021.
11 / 44
33. Einstein’s Fernparallelismus-Field theory
new geometry: Riemannian geometry with distant parallelism*
:
new formalism: set of mutually orthogonal, normal vectors (n-bein)
Aν
= hν
aAa
gµν
{
→ metric
= hµahνa, ∆ν
µσ
{
→ affine conn. ∆
ν
µσ 6= ∆
ν
σµ
= hv
a
∂hµa
∂xσ
*
Sauer2021.
11 / 44
34. Einstein’s Fernparallelismus-Field theory
new geometry: Riemannian geometry with distant parallelism*
:
new formalism: set of mutually orthogonal, normal vectors (n-bein)
Aν
= hν
aAa
gµν = hµahνa, ∆ν
µσ = hv
a
∂hµa
∂xσ
Ri
k,lm
{
→ Riemann tensor
= −
∂∆i
kl
∂xm
+
∂∆i
km
∂xl
+ ∆i
αl∆α
km − ∆i
αm∆α
kl = 0
*
Sauer2021.
11 / 44
35. Einstein’s Fernparallelismus-Field theory
new geometry: Riemannian geometry with distant parallelism*
:
new formalism: set of mutually orthogonal, normal vectors (n-bein)
Aν
= hν
aAa
gµν = hµahνa, ∆ν
µσ = hv
a
∂hµa
∂xσ
Ri
k,lm = −
∂∆i
kl
∂xm
+
∂∆i
km
∂xl
+ ∆i
αl∆α
km − ∆i
αm∆α
kl = 0
“
The introduction of distant parallelism implies that, according to
this theory, there is something like a straight line; i.e., a line whose
elements are all parallel to each other; such a line is of course by
no means identical with a geodetic one.
(Einstein, 1928b)
”11 / 44
37. Einstein’s Fernparallelismus-Field theory
physical interpretation:
• hν
a 16 components whereas gµν 10 components
• the field equations from δ
Z
{Hdτ} = 0, where H depends on the hν
a field.
• variation of the action with respect to the variable hν
a, Einstein and
Maxwell field equations were recovered in first appr.
• search solutions describing elementary particles and their motion
12 / 44
38. Reichenbach’s Comments on Einstein’s theory
“
Dear Herr Einstein,
I did some serious thinking on your work on the field theory and I
found that the geometrical construction can be presented better in
a different form. I send you the ms. enclosed. Concerning the phys-
ical application of your work, frankly speaking, it did not convince
me much. If geometrical interpretation must be, then I found my
approach simply more beautiful, in which the straightest line at
least means something.
Reichenbach to Einstein, 17-10-1928
”
13 / 44
39. Reichenbach’s Comments on Einstein’s theory
“
Dear Herr Einstein,
I did some serious thinking on your work on the field theory and I
found that the geometrical construction can be presented better in
a different form. I send you the ms. enclosed. Concerning the phys-
ical application of your work, frankly speaking, it did not convince
me much. If geometrical interpretation must be, then I found my
approach simply more beautiful, in which the straightest line at
least means something.
Reichenbach to Einstein, 17-10-1928
”
13 / 44
40. Reichenbach’s Comments on Einstein’s theory
“
Dear Herr Einstein,
I did some serious thinking on your work on the field theory and I
found that the geometrical construction can be presented better in
a different form. I send you the ms. enclosed. Concerning the phys-
ical application of your work, frankly speaking, it did not convince
me much. If geometrical interpretation must be, then I found my
approach simply more beautiful, in which the straightest line at
least means something.
Reichenbach to Einstein, 17-10-1928
”
13 / 44
41. Reichenbach’s Comments on Einstein’s theory
“
Dear Herr Einstein,
I did some serious thinking on your work on the field theory and I
found that the geometrical construction can be presented better in
a different form. I send you the ms. enclosed. Concerning the phys-
ical application of your work, frankly speaking, it did not convince
me much. If geometrical interpretation must be, then I found my
approach simply more beautiful, in which the straightest line at
least means something.
Reichenbach to Einstein, 17-10-1928
”
13 / 44
42. Reichenbach’s Comments on Einstein’s theory
“
Dear Herr Einstein,
I did some serious thinking on your work on the field theory and I
found that the geometrical construction can be presented better in
a different form. I send you the ms. enclosed. Concerning the phys-
ical application of your work, frankly speaking, it did not convince
me much. If geometrical interpretation must be, then I found my
approach simply more beautiful, in which the straightest line at
least means something.
Reichenbach to Einstein, 17-10-1928
”
13 / 44
54. Reichenbach’s Manuscript
from a geometrical point of view Einstein’s Fernparallelismus not new:
• Einstein’s Fernparallelismus geometry was simply one of the possibilities
implicit in the Weyl-Eddington classification.
• Einstein uses a new formalism in which the Γτ
µν and the gµν are
considered as functions of a parameter hν
α
gµν = hµαhνα Γτ
µν = −hτ
α
∂hµα
∂xν
from a physical point of view Einstein’s Fernparallelismus not
convincing:
• “[t]he derivation of the Maxwellian and gravitational equation from a
variational principle was already achieved by other approaches”
(Reichenbach, 1928b, 6),
• a “real physical achievement is obtained only if, in addition, the operation
of displacement is filled with physical content” (Reichenbach, 1928b, 7).
18 / 44
55. Reichenbach’s Manuscript
from a geometrical point of view Einstein’s Fernparallelismus not new:
• Einstein’s Fernparallelismus geometry was simply one of the possibilities
implicit in the Weyl-Eddington classification.
• Einstein uses a new formalism in which the Γτ
µν and the gµν are
considered as functions of a parameter hν
α
gµν = hµαhνα Γτ
µν = −hτ
α
∂hµα
∂xν
from a physical point of view Einstein’s Fernparallelismus not
convincing:
• “[t]he derivation of the Maxwellian and gravitational equation from a
variational principle was already achieved by other approaches”
(Reichenbach, 1928b, 6),
• a “real physical achievement is obtained only if, in addition, the operation
of displacement is filled with physical content” (Reichenbach, 1928b, 7).
18 / 44
56. Reichenbach’s Manuscript
from a geometrical point of view Einstein’s Fernparallelismus not new:
• Einstein’s Fernparallelismus geometry was simply one of the possibilities
implicit in the Weyl-Eddington classification.
• Einstein uses a new formalism in which the Γτ
µν and the gµν are
considered as functions of a parameter hν
α
gµν = hµαhνα Γτ
µν = −hτ
α
∂hµα
∂xν
from a physical point of view Einstein’s Fernparallelismus not
convincing:
• “[t]he derivation of the Maxwellian and gravitational equation from a
variational principle was already achieved by other approaches”
(Reichenbach, 1928b, 6),
• a “real physical achievement is obtained only if, in addition, the operation
of displacement is filled with physical content” (Reichenbach, 1928b, 7).
18 / 44
57. Reichenbach’s Manuscript
from a geometrical point of view Einstein’s Fernparallelismus not new:
• Einstein’s Fernparallelismus geometry was simply one of the possibilities
implicit in the Weyl-Eddington classification.
• Einstein uses a new formalism in which the Γτ
µν and the gµν are
considered as functions of a parameter hν
α
gµν = hµαhνα Γτ
µν = −hτ
α
∂hµα
∂xν
from a physical point of view Einstein’s Fernparallelismus not
convincing:
• “[t]he derivation of the Maxwellian and gravitational equation from a
variational principle was already achieved by other approaches”
(Reichenbach, 1928b, 6),
• a “real physical achievement is obtained only if, in addition, the operation
of displacement is filled with physical content” (Reichenbach, 1928b, 7).
18 / 44
58. Reichenbach’s Manuscript
from a geometrical point of view Einstein’s Fernparallelismus not new:
• Einstein’s Fernparallelismus geometry was simply one of the possibilities
implicit in the Weyl-Eddington classification.
• Einstein uses a new formalism in which the Γτ
µν and the gµν are
considered as functions of a parameter hν
α
gµν = hµαhνα Γτ
µν = −hτ
α
∂hµα
∂xν
from a physical point of view Einstein’s Fernparallelismus not
convincing:
• “[t]he derivation of the Maxwellian and gravitational equation from a
variational principle was already achieved by other approaches”
(Reichenbach, 1928b, 6),
• a “real physical achievement is obtained only if, in addition, the operation
of displacement is filled with physical content” (Reichenbach, 1928b, 7).
18 / 44
59. Reichenbach’s Manuscript
from a geometrical point of view Einstein’s Fernparallelismus not new:
• Einstein’s Fernparallelismus geometry was simply one of the possibilities
implicit in the Weyl-Eddington classification.
• Einstein uses a new formalism in which the Γτ
µν and the gµν are
considered as functions of a parameter hν
α
gµν = hµαhνα Γτ
µν = −hτ
α
∂hµα
∂xν
from a physical point of view Einstein’s Fernparallelismus not
convincing:
• “[t]he derivation of the Maxwellian and gravitational equation from a
variational principle was already achieved by other approaches”
(Reichenbach, 1928b, 6),
• a “real physical achievement is obtained only if, in addition, the operation
of displacement is filled with physical content” (Reichenbach, 1928b, 7).
18 / 44
60. Reichenbach’s Manuscript
“
. . . that this is possible has been show previously by the author
(Reichenbach, 1928b, 8)
”
Reichenbach’s theory
d(l2
) = 0
Γτ
µν 6= Γτ
νµ
Rτ
µνσ(g) 6= 0
charged mass points move along
the straightest lines, uncharged
along the shortest line
Einstein’s theory
d(l2
) = 0
Rτ
µνσ(g) = 0
Γτ
µν 6= Γτ
νµ
straightest lines different from the
shortest line, but without physical
meaning
19 / 44
61. Einstein’s Comments on Reichenbach’s Manuscript
“
Dear Mr. Reichenbach,
[Your presentation] is possible, but is not the simplest [. . .]. The
best logical classification according to me seems to be the follow-
ing: One consider theories in which the local comparison of vector
length is given as meaningful [. . .]. For manifolds of this type, fur-
ther specializations are possible.
1. Neither the comparison of length at distance nor of direction
is meaningful (Weyl)
2. Comparison at distance of length but of direction is
meaningful (Riemann)
3. Comparison at distance of directions but of lengths (not
considered yet)
4. Comparison at distance of length and of direction is
meaningful (Einstein)
Of course one can also start with the displacement law, and spe-
cialize it [. . .] as you have done. But this is less simple and natural.
Einstein to Reichenbach, 19-10-1928
”20 / 44
62. Einstein’s Comments on Reichenbach’s Manuscript
“
Dear Mr. Reichenbach,
[Your presentation] is possible, but is not the simplest [. . .]. The
best logical classification according to me seems to be the follow-
ing: One consider theories in which the local comparison of vector
length is given as meaningful [. . .]. For manifolds of this type, fur-
ther specializations are possible.
1. Neither the comparison of length at distance nor of direction
is meaningful (Weyl)
2. Comparison at distance of length but of direction is
meaningful (Riemann)
3. Comparison at distance of directions but of lengths (not
considered yet)
4. Comparison at distance of length and of direction is
meaningful (Einstein)
Of course one can also start with the displacement law, and spe-
cialize it [. . .] as you have done. But this is less simple and natural.
Einstein to Reichenbach, 19-10-1928
”20 / 44
63. Einstein’s Comments on Reichenbach’s Manuscript
“
Dear Mr. Reichenbach,
[Your presentation] is possible, but is not the simplest [. . .]. The
best logical classification according to me seems to be the follow-
ing: One consider theories in which the local comparison of vector
length is given as meaningful [. . .]. For manifolds of this type, fur-
ther specializations are possible.
1. Neither the comparison of length at distance nor of direction
is meaningful (Weyl)
2. Comparison at distance of length but of direction is
meaningful (Riemann)
3. Comparison at distance of directions but of lengths (not
considered yet)
4. Comparison at distance of length and of direction is
meaningful (Einstein)
Of course one can also start with the displacement law, and spe-
cialize it [. . .] as you have done. But this is less simple and natural.
Einstein to Reichenbach, 19-10-1928
”20 / 44
64. Einstein’s Comments on Reichenbach’s Manuscript
“
Dear Mr. Reichenbach,
[Your presentation] is possible, but is not the simplest [. . .]. The
best logical classification according to me seems to be the follow-
ing: One consider theories in which the local comparison of vector
length is given as meaningful [. . .]. For manifolds of this type, fur-
ther specializations are possible.
1. Neither the comparison of length at distance nor of direction
is meaningful (Weyl)
2. Comparison at distance of length but of direction is
meaningful (Riemann)
3. Comparison at distance of directions but of lengths (not
considered yet)
4. Comparison at distance of length and of direction is
meaningful (Einstein)
Of course one can also start with the displacement law, and spe-
cialize it [. . .] as you have done. But this is less simple and natural.
Einstein to Reichenbach, 19-10-1928
”20 / 44
65. Einstein’s Comments on Reichenbach’s Manuscript
“
Dear Mr. Reichenbach,
[Your presentation] is possible, but is not the simplest [. . .]. The
best logical classification according to me seems to be the follow-
ing: One consider theories in which the local comparison of vector
length is given as meaningful [. . .]. For manifolds of this type, fur-
ther specializations are possible.
1. Neither the comparison of length at distance nor of direction
is meaningful (Weyl)
2. Comparison at distance of length but of direction is
meaningful (Riemann)
3. Comparison at distance of directions but of lengths (not
considered yet)
4. Comparison at distance of length and of direction is
meaningful (Einstein)
Of course one can also start with the displacement law, and spe-
cialize it [. . .] as you have done. But this is less simple and natural.
Einstein to Reichenbach, 19-10-1928
”20 / 44
66. Einstein’s Comments on Reichenbach’s Manuscript
Invitation for a tea with Schr̈odinger on December 5, 1928
Einstein and Reichenbach probably discussed:
further developments of Fernparallelismus-theory
not simply recovering Maxwell and Einstein equations, but new results
philosophical differences
21 / 44
67. Stodola-Festschrift
The only hope is to construct a theory “in a speculative way” (Einstein,
1929c, 128).
only motivation the deep conviction of the “formal simplicity of the
structure of reality” (Einstein, 1929c, 127).
the belief in the fundamental simplicity of the real is “so to speak, the
religious basis of the scientific endeavor” (Einstein, 1929c, 127).
“Meyerson’s comparison with Hegel’s program [Zielsetzung] lluminates
clearly the danger that one here has to fear” (Einstein, 1929c, 127)
search for the mathematical structure of the field (the gµν , Γτ
µν , hν
a, ,
etc..) =⇒ no physical interpretation needed
search for simplest generally covariant field equations which can be
obeyed by the field structure =⇒ variational or other approaches
22 / 44
68. Stodola-Festschrift
The only hope is to construct a theory “in a speculative way” (Einstein,
1929c, 128).
only motivation the deep conviction of the “formal simplicity of the
structure of reality” (Einstein, 1929c, 127).
the belief in the fundamental simplicity of the real is “so to speak, the
religious basis of the scientific endeavor” (Einstein, 1929c, 127).
“Meyerson’s comparison with Hegel’s program [Zielsetzung] lluminates
clearly the danger that one here has to fear” (Einstein, 1929c, 127)
search for the mathematical structure of the field (the gµν , Γτ
µν , hν
a, ,
etc..) =⇒ no physical interpretation needed
search for simplest generally covariant field equations which can be
obeyed by the field structure =⇒ variational or other approaches
22 / 44
69. Stodola-Festschrift
The only hope is to construct a theory “in a speculative way” (Einstein,
1929c, 128).
only motivation the deep conviction of the “formal simplicity of the
structure of reality” (Einstein, 1929c, 127).
the belief in the fundamental simplicity of the real is “so to speak, the
religious basis of the scientific endeavor” (Einstein, 1929c, 127).
“Meyerson’s comparison with Hegel’s program [Zielsetzung] lluminates
clearly the danger that one here has to fear” (Einstein, 1929c, 127)
search for the mathematical structure of the field (the gµν , Γτ
µν , hν
a, ,
etc..) =⇒ no physical interpretation needed
search for simplest generally covariant field equations which can be
obeyed by the field structure =⇒ variational or other approaches
22 / 44
70. Stodola-Festschrift
The only hope is to construct a theory “in a speculative way” (Einstein,
1929c, 128).
only motivation the deep conviction of the “formal simplicity of the
structure of reality” (Einstein, 1929c, 127).
the belief in the fundamental simplicity of the real is “so to speak, the
religious basis of the scientific endeavor” (Einstein, 1929c, 127).
“Meyerson’s comparison with Hegel’s program [Zielsetzung] lluminates
clearly the danger that one here has to fear” (Einstein, 1929c, 127)
search for the mathematical structure of the field (the gµν , Γτ
µν , hν
a, ,
etc..) =⇒ no physical interpretation needed
search for simplest generally covariant field equations which can be
obeyed by the field structure =⇒ variational or other approaches
22 / 44
71. Stodola-Festschrift
The only hope is to construct a theory “in a speculative way” (Einstein,
1929c, 128).
only motivation the deep conviction of the “formal simplicity of the
structure of reality” (Einstein, 1929c, 127).
the belief in the fundamental simplicity of the real is “so to speak, the
religious basis of the scientific endeavor” (Einstein, 1929c, 127).
“Meyerson’s comparison with Hegel’s program [Zielsetzung] lluminates
clearly the danger that one here has to fear” (Einstein, 1929c, 127)
search for the mathematical structure of the field (the gµν , Γτ
µν , hν
a, ,
etc..) =⇒ no physical interpretation needed
search for simplest generally covariant field equations which can be
obeyed by the field structure =⇒ variational or other approaches
22 / 44
72. Stodola-Festschrift
The only hope is to construct a theory “in a speculative way” (Einstein,
1929c, 128).
only motivation the deep conviction of the “formal simplicity of the
structure of reality” (Einstein, 1929c, 127).
the belief in the fundamental simplicity of the real is “so to speak, the
religious basis of the scientific endeavor” (Einstein, 1929c, 127).
“Meyerson’s comparison with Hegel’s program [Zielsetzung] lluminates
clearly the danger that one here has to fear” (Einstein, 1929c, 127)
search for the mathematical structure of the field (the gµν , Γτ
µν , hν
a, ,
etc..) =⇒ no physical interpretation needed
search for simplest generally covariant field equations which can be
obeyed by the field structure =⇒ variational or other approaches
22 / 44
73. Stodola-Festschrift
The only hope is to construct a theory “in a speculative way” (Einstein,
1929c, 128).
only motivation the deep conviction of the “formal simplicity of the
structure of reality” (Einstein, 1929c, 127).
the belief in the fundamental simplicity of the real is “so to speak, the
religious basis of the scientific endeavor” (Einstein, 1929c, 127).
“Meyerson’s comparison with Hegel’s program [Zielsetzung] lluminates
clearly the danger that one here has to fear” (Einstein, 1929c, 127)
search for the mathematical structure of the field (the gµν , Γτ
µν , hν
a, ,
etc..) =⇒ no physical interpretation needed
search for simplest generally covariant field equations which can be
obeyed by the field structure =⇒ variational or other approaches
22 / 44
75. Einstein in the Daily Press
November 4, 1928: the New York Times
announced the prospect of another epoch-making
breakthrough
December of 1928: difficulties with the theory
had started to become apparent by the end of
1928.
January 10, 1929: paper submitted for
publication in the Sitzungsberichte Prussian
Academy (Einstein, 1929d).
January 11, 1929: Einstein issued a brief
statement to the press
January 12, 1929: New York Times’s
sensationalistic article
January 16, 1929: leaks of some friends (Einstein
to Kerkhof, 16-01-1929)
23 / 44
76. Reichenbach’s Papers on Fernparallelismus
January 22, 1929: non-technical paper for the Zeitschrift für
Angewandte Chemie
January 22, 1929: technical paper for Zeitschrift für Physik
January 25, 1929: popular article for the Vossische Zeitung
(Reichenbach, 1929b).
24 / 44
77. Reichenbach’s Article for the Vossische Zeitung
“[T]wo vast bodies of laws stood at the pinnacle of physics,” Einstein’s
gravitational field equations and Maxwell’s electromagnetic field
equations (Reichenbach, 1929b; tr. 1978, 1:261).
These two sets of equations had “nothing to do with each other; the
world of physics was divided into two kingdoms, one ruled by Einstein,
and the other by Maxwell” (Reichenbach, 1929b; tr. 1978, 1:261).
“The temptation to attempt a supreme union was irresistible: however,
nature proved to be more stubborn than had been anticipated”
(Reichenbach, 1929b; tr. 1978, 1:261)
25 / 44
78. Reichenbach’s Article for the Vossische Zeitung
“
But today Einstein has taken a new step [. . .] And indeed, the new
theory succeeds in uniting the fundamental laws of relativity me-
chanics and the fundamental laws of electricity into a single for-
mula. [. . .] Einstein is able to show that the previously known
laws can be derived from this formula [. . .] Yet the new formula
achieves still more; it represents the older theory of two systems
as a special case and makes new assertions concerning the relation
between gravitation and electricity in relatively complicated fields.
Thus, the new theory is of more than merely formal significance,
for it asserts the existence of an effect of gravitation upon electri-
cal events and vice versa
(Reichenbach, 1929b; tr. 1978, 1:262)
”
26 / 44
79. Reichenbach’s Article for the Vossische Zeitung
“
But today Einstein has taken a new step [. . .] And indeed, the new
theory succeeds in uniting the fundamental laws of relativity me-
chanics and the fundamental laws of electricity into a single for-
mula. [. . .] Einstein is able to show that the previously known
laws can be derived from this formula [. . .] Yet the new formula
achieves still more; it represents the older theory of two systems
as a special case and makes new assertions concerning the relation
between gravitation and electricity in relatively complicated fields.
Thus, the new theory is of more than merely formal significance,
for it asserts the existence of an effect of gravitation upon electri-
cal events and vice versa
(Reichenbach, 1929b; tr. 1978, 1:262)
”
26 / 44
80. Reichenbach’s Article for the Vossische Zeitung
“
But today Einstein has taken a new step [. . .] And indeed, the new
theory succeeds in uniting the fundamental laws of relativity me-
chanics and the fundamental laws of electricity into a single for-
mula. [. . .] Einstein is able to show that the previously known
laws can be derived from this formula [. . .] Yet the new formula
achieves still more; it represents the older theory of two systems
as a special case and makes new assertions concerning the relation
between gravitation and electricity in relatively complicated fields.
Thus, the new theory is of more than merely formal significance,
for it asserts the existence of an effect of gravitation upon electri-
cal events and vice versa
(Reichenbach, 1929b; tr. 1978, 1:262)
”
26 / 44
81. Reichenbach’s Article for the Vossische Zeitung
“
But today Einstein has taken a new step [. . .] And indeed, the new
theory succeeds in uniting the fundamental laws of relativity me-
chanics and the fundamental laws of electricity into a single for-
mula. [. . .] Einstein is able to show that the previously known
laws can be derived from this formula [. . .] Yet the new formula
achieves still more; it represents the older theory of two systems
as a special case and makes new assertions concerning the relation
between gravitation and electricity in relatively complicated fields.
Thus, the new theory is of more than merely formal significance,
for it asserts the existence of an effect of gravitation upon electri-
cal events and vice versa
(Reichenbach, 1929b; tr. 1978, 1:262)
”
26 / 44
82. Reichenbach’s Article for the Vossische Zeitung
“
But today Einstein has taken a new step [. . .] And indeed, the new
theory succeeds in uniting the fundamental laws of relativity me-
chanics and the fundamental laws of electricity into a single for-
mula. [. . .] Einstein is able to show that the previously known
laws can be derived from this formula [. . .] Yet the new formula
achieves still more; it represents the older theory of two systems
as a special case and makes new assertions concerning the relation
between gravitation and electricity in relatively complicated fields.
Thus, the new theory is of more than merely formal significance,
for it asserts the existence of an effect of gravitation upon electri-
cal events and vice versa
(Reichenbach, 1929b; tr. 1978, 1:262)
”
26 / 44
83. Einstein’s Reaction
January 25, 1929: Einstein complained to the Vossische Zeitung
(Einstein to Vossische Zeitung, 25-01-1929).
January 26, 1929: Jacobs apologizes but defended the newspaper
(Jacobs to Einstein, 26-01-1929)
January 21, 1929: Reichenbach complained behavior (Reichenbach
to Jacobs, 21-01-1929)
January 27, 1929 Reichenbach felt betrayed by Einstein’s behavior
(Reichenbach to Einstein, 27-01-1929)
January 30, 1929: Einstein was somewhat pleased by Reichenbach’s
reaction (Einstein to Reichenbach, 30-01-1929)
January 31, 1929: Reichenbach closed the incident (Reichenbach to
Einstein, 31-01-1929)
Hentschel, 1990.
27 / 44
85. Geometrization vs. Unification
history of the unified field theory program
progressive downfall of the geometrization program
and the concurrent rise of the unification program
28 / 44
86. Geometrization vs. Unification
Einstein: geometrical interpretation of the gravitational field via the
gµν
Weyl: geometrical interpretation of the electromagnetic field via the κσ
d(l2
) = l2
κσ
{
change of length←
dxσ Kµν,σ = gµν κσ
{
→ electromagnetic four-potential
Weyl1: coordinative definition of displacement: “an influence of the
electric field on transported rods and clocks” (Reichenbach, 1929a,
122).
• measuring rod objection (no second clock effect)
Weyl2: no coordinative definition of the process of displacement in
terms of rods-and-clocks readings
• purely formal theory
29 / 44
87. Geometrization vs. Unification
“
However, mathematicians did not give up on the new idea. If a
direct physical interpretation of Weylean space was not possible,
they tried an indirect approach. They regarded Weyl’s space as a
type a mathematical apparatus [. . .] [that] opened the possibility
for a unification of the electrical and gravitational equations. The
actual geometrical sense of Weyl’s approach was therefore com-
pletely abandoned, and the extended type of space was only used,
so to speak, in the sense of a calculating machine, [to find the field
equations]. [. . .] In this sense, several influential researchers have
tried to develop Weyl mathematics into a physical theory, in ad-
dition to Weyl, above all [. . .] Eddington [. . .] and also Einstein
himself.
(Reichenbach, 1929a, 122)
”
30 / 44
88. Geometrization vs. Unification
“
However, mathematicians did not give up on the new idea. If a
direct physical interpretation of Weylean space was not possible,
they tried an indirect approach. They regarded Weyl’s space as a
type a mathematical apparatus [. . .] [that] opened the possibility
for a unification of the electrical and gravitational equations. The
actual geometrical sense of Weyl’s approach was therefore com-
pletely abandoned, and the extended type of space was only used,
so to speak, in the sense of a calculating machine, [to find the field
equations]. [. . .] In this sense, several influential researchers have
tried to develop Weyl mathematics into a physical theory, in ad-
dition to Weyl, above all [. . .] Eddington [. . .] and also Einstein
himself.
(Reichenbach, 1929a, 122)
”
30 / 44
89. Geometrization vs. Unification
“
However, mathematicians did not give up on the new idea. If a
direct physical interpretation of Weylean space was not possible,
they tried an indirect approach. They regarded Weyl’s space as a
type a mathematical apparatus [. . .] [that] opened the possibility
for a unification of the electrical and gravitational equations. The
actual geometrical sense of Weyl’s approach was therefore com-
pletely abandoned, and the extended type of space was only used,
so to speak, in the sense of a calculating machine, [to find the field
equations]. [. . .] In this sense, several influential researchers have
tried to develop Weyl mathematics into a physical theory, in ad-
dition to Weyl, above all [. . .] Eddington [. . .] and also Einstein
himself.
(Reichenbach, 1929a, 122)
”
30 / 44
90. Geometrization vs. Unification
“
However, mathematicians did not give up on the new idea. If a
direct physical interpretation of Weylean space was not possible,
they tried an indirect approach. They regarded Weyl’s space as a
type a mathematical apparatus [. . .] [that] opened the possibility
for a unification of the electrical and gravitational equations. The
actual geometrical sense of Weyl’s approach was therefore com-
pletely abandoned, and the extended type of space was only used,
so to speak, in the sense of a calculating machine, [to find the field
equations]. [. . .] In this sense, several influential researchers have
tried to develop Weyl mathematics into a physical theory, in ad-
dition to Weyl, above all [. . .] Eddington [. . .] and also Einstein
himself.
(Reichenbach, 1929a, 122)
”
30 / 44
91. Geometrization vs. Unification
“
However, mathematicians did not give up on the new idea. If a
direct physical interpretation of Weylean space was not possible,
they tried an indirect approach. They regarded Weyl’s space as a
type a mathematical apparatus [. . .] [that] opened the possibility
for a unification of the electrical and gravitational equations. The
actual geometrical sense of Weyl’s approach was therefore com-
pletely abandoned, and the extended type of space was only used,
so to speak, in the sense of a calculating machine, [to find the field
equations]. [. . .] In this sense, several influential researchers have
tried to develop Weyl mathematics into a physical theory, in ad-
dition to Weyl, above all [. . .] Eddington [. . .] and also Einstein
himself.
(Reichenbach, 1929a, 122)
”
30 / 44
92. Geometrization vs. Unification
“
However, mathematicians did not give up on the new idea. If a
direct physical interpretation of Weylean space was not possible,
they tried an indirect approach. They regarded Weyl’s space as a
type a mathematical apparatus [. . .] [that] opened the possibility
for a unification of the electrical and gravitational equations. The
actual geometrical sense of Weyl’s approach was therefore com-
pletely abandoned, and the extended type of space was only used,
so to speak, in the sense of a calculating machine, [to find the field
equations]. [. . .] In this sense, several influential researchers have
tried to develop Weyl mathematics into a physical theory, in ad-
dition to Weyl, above all [. . .] Eddington [. . .] and also Einstein
himself.
(Reichenbach, 1929a, 122)
”
30 / 44
93. Geometrization vs. Unification
sacrifice the geometrical interpretation (no coordinative definition of
Γτ
µν , κσ and so on)
use the field structures (Γτ
µν , κσ and so on) as calculation device for
finding the field equations
“
The last stage on this path is the new work that [Einstein] recently
presented to the Academy
(Reichenbach, 1929a, 123)
”
31 / 44
94. Geometrization vs. Unification
The field variables hν
a do not receive a geometrical interpretation.
• “Einstein was guided” by abstract mathematical considerations “about
invariants in Weylean space and the possibilities of deriving equations
from them” (Reichenbach, 1929a, 123).
Electromagnetic field and gravitational field are unified.
• “a certain concatenation of both systems of equations occurs in such a
way that a physical dependence between electricity and gravity is
asserted” (Reichenbach, 1929a)
32 / 44
95. Geometrization vs. Unification
The field variables hν
a do not receive a geometrical interpretation.
• “Einstein was guided” by abstract mathematical considerations “about
invariants in Weylean space and the possibilities of deriving equations
from them” (Reichenbach, 1929a, 123).
Electromagnetic field and gravitational field are unified.
• “a certain concatenation of both systems of equations occurs in such a
way that a physical dependence between electricity and gravity is
asserted” (Reichenbach, 1929a)
32 / 44
96. Geometrization vs. Unification
The field variables hν
a do not receive a geometrical interpretation.
• “Einstein was guided” by abstract mathematical considerations “about
invariants in Weylean space and the possibilities of deriving equations
from them” (Reichenbach, 1929a, 123).
Electromagnetic field and gravitational field are unified.
• “a certain concatenation of both systems of equations occurs in such a
way that a physical dependence between electricity and gravity is
asserted” (Reichenbach, 1929a)
32 / 44
97. Geometrization vs. Unification
The field variables hν
a do not receive a geometrical interpretation.
• “Einstein was guided” by abstract mathematical considerations “about
invariants in Weylean space and the possibilities of deriving equations
from them” (Reichenbach, 1929a, 123).
Electromagnetic field and gravitational field are unified.
• “a certain concatenation of both systems of equations occurs in such a
way that a physical dependence between electricity and gravity is
asserted” (Reichenbach, 1929a)
32 / 44
99. The Duality of Unifications
unification?
formal unification: the new system does not claim more than the other
two combined;
• empirically equivalent theories (Einstein vs. Minkowski)
inductive unification: the new theories claim more than the other two
combined;
• empirically nonequivalent theories (Newton vs. Einstein)
34 / 44
100. The Duality of Unifications
Reichenbach: proper geometrical interpretation without proper
unification
“
The author [Reichenbach] has shown that the first way can be re-
alized in the sense of a combination of gravitation and electricity
to one field, which determines the geometry of an extended Rie-
mannian space; it is remarkable that thereby the operation of dis-
placement receives an immediate geometrical interpretation, via
the law of motion of electrically charged mass points. The straight-
est line is identified with the path of electrically charged mass
points, whereas the shortest line remains that of uncharged mass
points. [. . .] By the way [the theory introduces] a space which
is cognate to the one used by Einstein, i.e., a metrical space with
non-symmetrical Γτ
µν . The aim was to show that the geometrical in-
terpretation of electricity does not mean a physical value of knowl-
edge per se
(Reichenbach, 1929c, 688)
”35 / 44
101. The Duality of Unifications
Reichenbach: proper geometrical interpretation without proper
unification
“
The author [Reichenbach] has shown that the first way can be re-
alized in the sense of a combination of gravitation and electricity
to one field, which determines the geometry of an extended Rie-
mannian space; it is remarkable that thereby the operation of dis-
placement receives an immediate geometrical interpretation, via
the law of motion of electrically charged mass points. The straight-
est line is identified with the path of electrically charged mass
points, whereas the shortest line remains that of uncharged mass
points. [. . .] By the way [the theory introduces] a space which
is cognate to the one used by Einstein, i.e., a metrical space with
non-symmetrical Γτ
µν . The aim was to show that the geometrical in-
terpretation of electricity does not mean a physical value of knowl-
edge per se
(Reichenbach, 1929c, 688)
”35 / 44
102. The Duality of Unifications
Reichenbach: proper geometrical interpretation without proper
unification
“
The author [Reichenbach] has shown that the first way can be re-
alized in the sense of a combination of gravitation and electricity
to one field, which determines the geometry of an extended Rie-
mannian space; it is remarkable that thereby the operation of dis-
placement receives an immediate geometrical interpretation, via
the law of motion of electrically charged mass points. The straight-
est line is identified with the path of electrically charged mass
points, whereas the shortest line remains that of uncharged mass
points. [. . .] By the way [the theory introduces] a space which
is cognate to the one used by Einstein, i.e., a metrical space with
non-symmetrical Γτ
µν . The aim was to show that the geometrical in-
terpretation of electricity does not mean a physical value of knowl-
edge per se
(Reichenbach, 1929c, 688)
”35 / 44
103. The Duality of Unifications
Reichenbach: proper geometrical interpretation without proper
unification
“
The author [Reichenbach] has shown that the first way can be re-
alized in the sense of a combination of gravitation and electricity
to one field, which determines the geometry of an extended Rie-
mannian space; it is remarkable that thereby the operation of dis-
placement receives an immediate geometrical interpretation, via
the law of motion of electrically charged mass points. The straight-
est line is identified with the path of electrically charged mass
points, whereas the shortest line remains that of uncharged mass
points. [. . .] By the way [the theory introduces] a space which
is cognate to the one used by Einstein, i.e., a metrical space with
non-symmetrical Γτ
µν . The aim was to show that the geometrical in-
terpretation of electricity does not mean a physical value of knowl-
edge per se
(Reichenbach, 1929c, 688)
”35 / 44
104. The Duality of Unifications
Reichenbach: proper geometrical interpretation without proper
unification
“
The author [Reichenbach] has shown that the first way can be re-
alized in the sense of a combination of gravitation and electricity
to one field, which determines the geometry of an extended Rie-
mannian space; it is remarkable that thereby the operation of dis-
placement receives an immediate geometrical interpretation, via
the law of motion of electrically charged mass points. The straight-
est line is identified with the path of electrically charged mass
points, whereas the shortest line remains that of uncharged mass
points. [. . .] By the way [the theory introduces] a space which
is cognate to the one used by Einstein, i.e., a metrical space with
non-symmetrical Γτ
µν . The aim was to show that the geometrical in-
terpretation of electricity does not mean a physical value of knowl-
edge per se
(Reichenbach, 1929c, 688)
”35 / 44
105. The Duality of Unifications
Einstein: proper unification without proper geometrical interpretation
“
On the contrary, Einstein’s approach, of course, uses the second
way since it is a matter of increasing physical knowledge; it is the
goal of Einstein’s new theory to find such a concatenation of gravi-
tation and electricity, that only in first approximation it is split in the
different equations of the present theory, while is in higher approx-
imation reveals a reciprocal influence of both fields, which could
possibly lead to the understanding of unsolved questions, like the
quantum puzzle. However, it seems that this goal can be achieved
only if one dispenses with an immediate interpretation of the dis-
placement, and even of the field quantities themselves. From a
geometrical point of view, this approach looks very unsatisfying.
Its justification lies only on the fact that the above-mentioned con-
catenation implies more physical facts that those that were needed
to establish it
(Reichenbach, 1929c, 688)
”36 / 44
106. The Duality of Unifications
Einstein: proper unification without proper geometrical interpretation
“
On the contrary, Einstein’s approach, of course, uses the second
way since it is a matter of increasing physical knowledge; it is the
goal of Einstein’s new theory to find such a concatenation of gravi-
tation and electricity, that only in first approximation it is split in the
different equations of the present theory, while is in higher approx-
imation reveals a reciprocal influence of both fields, which could
possibly lead to the understanding of unsolved questions, like the
quantum puzzle. However, it seems that this goal can be achieved
only if one dispenses with an immediate interpretation of the dis-
placement, and even of the field quantities themselves. From a
geometrical point of view, this approach looks very unsatisfying.
Its justification lies only on the fact that the above-mentioned con-
catenation implies more physical facts that those that were needed
to establish it
(Reichenbach, 1929c, 688)
”36 / 44
107. The Duality of Unifications
Einstein: proper unification without proper geometrical interpretation
“
On the contrary, Einstein’s approach, of course, uses the second
way since it is a matter of increasing physical knowledge; it is the
goal of Einstein’s new theory to find such a concatenation of gravi-
tation and electricity, that only in first approximation it is split in the
different equations of the present theory, while is in higher approx-
imation reveals a reciprocal influence of both fields, which could
possibly lead to the understanding of unsolved questions, like the
quantum puzzle. However, it seems that this goal can be achieved
only if one dispenses with an immediate interpretation of the dis-
placement, and even of the field quantities themselves. From a
geometrical point of view, this approach looks very unsatisfying.
Its justification lies only on the fact that the above-mentioned con-
catenation implies more physical facts that those that were needed
to establish it
(Reichenbach, 1929c, 688)
”36 / 44
108. The Duality of Unifications
Einstein: proper unification without proper geometrical interpretation
“
On the contrary, Einstein’s approach, of course, uses the second
way since it is a matter of increasing physical knowledge; it is the
goal of Einstein’s new theory to find such a concatenation of gravi-
tation and electricity, that only in first approximation it is split in the
different equations of the present theory, while is in higher approx-
imation reveals a reciprocal influence of both fields, which could
possibly lead to the understanding of unsolved questions, like the
quantum puzzle. However, it seems that this goal can be achieved
only if one dispenses with an immediate interpretation of the dis-
placement, and even of the field quantities themselves. From a
geometrical point of view, this approach looks very unsatisfying.
Its justification lies only on the fact that the above-mentioned con-
catenation implies more physical facts that those that were needed
to establish it
(Reichenbach, 1929c, 688)
”36 / 44
109. Success of General Relativity
general relativity
the theory provided a proper geometrical interpretation of the
gravitational field, since it introduced a coordinative definition of the
field variables gµν , in terms of the behavior of those that were
traditionally considered geometrical measuring instruments, like rods
and clocks
the theory provided a proper unification by predicting that the
gravitational field had certain effects on such measuring instruments
that were not implied by previous theories of gravitation—like
gravitational time dilation
physical hypothesis =⇒ equivalence principle
37 / 44
110. Two strategies
after general relativity
geometrization strategy: general relativity was a successful theory
because it had provided a geometrical interpretation of the
gravitational field
• Weyl
unification strategy: general relativity was a successful theory because
it had achieved the unification of two different fields, gravitational and
inertial field
• Einstein
physical hypothesis =⇒ mathematical simplicity of nature
38 / 44
111. Two strategies
after general relativity
geometrization strategy: general relativity was a successful theory
because it had provided a geometrical interpretation of the
gravitational field
• Weyl
unification strategy: general relativity was a successful theory because
it had achieved the unification of two different fields, gravitational and
inertial field
• Einstein
physical hypothesis =⇒ mathematical simplicity of nature
38 / 44
112. Two strategies
after general relativity
geometrization strategy: general relativity was a successful theory
because it had provided a geometrical interpretation of the
gravitational field
• Weyl
unification strategy: general relativity was a successful theory because
it had achieved the unification of two different fields, gravitational and
inertial field
• Einstein
physical hypothesis =⇒ mathematical simplicity of nature
38 / 44
113. Two strategies
the core of Reichenbach’s philosophy was the separation of
mathematical necessity and physical reality.
in the search of a unified field theory, Einstein had come implicitly to
question this very distinction, ultimately pleading for a reduction of
physical reality to mathematical necessity
“
. . . even God could not have established these connections other-
wise than they actually are, just as little as it would have been in
his power to make the number 4 a prime number
Einstein, 1929c
”
39 / 44
115. Conclusion
January 30, 1929: Einstein’s new derivation of the
Fernparallelismus-field equations was published (Einstein, 1929d).
February 3, 1929: popular writing in the The Times of London
February 4 and February 5, 1929: popular writing in the New York
Times (Einstein, 1929a,b)
40 / 44
117. Conclusion
Einstein insisted on “the degree of formal speculation, the slender
empirical basis, [. . .] [t]he fundamental reliance on the unity and
comprehensibility of the secrets of [nature]” (Einstein, 1930, 114).
Einstein was not afraid to side with “Meyerson in his brilliant studies on
the theory of knowledge” who had emphasized the ‘Hegelian’ nature of
physics’ enterprise, “without thereby implying the censure which a
physicist would read into this” (Einstein, 1930, 115).
Reichenbach (or Schlick) =⇒ Meyerson
41 / 44
121. Conclusion
“The problem of gravitation made me to a believing rationalist [zu
einem gläubigen Rationalisten], that is, one who seeks the only
trustworthy source of truth in mathematical simplicity” (Lanczos to
Einstein, 01-03-1938)
“However, I think that there was no point in asking that [the
mathematical structure] should be of a geometrical nature; we all
agree that this is just a way of speaking, without a clear meaning”
(Lanczos to Einstein, 01-03-1938)
44 / 44