Discussion Notes for Einstein.1
Einstein, Essays in Science.2
1. The Mechanics of Newton and their Influence on the Development of Theoretical Physics.3
Newton—inventor of key methods; also unique command of empirical materials and inventive of mathematical and physical proofs.
Before Newton no self-contained system of physical causality which was capable of representing any of the deeper features of the empirical world.
Great materials of Ancient Greece—series of atomic movements, independent of any creature’s will
Descartes—same quest.
Objective self-contained causal system, regular and independent of external influence. (Description of a comprehensive principle—in methodic4 not ontic interpretation)
Newton’s question: Is there such a thing as a simple rule by which one can calculate the movements of the heavenly bodies in their planetary system completely, when the state of motion of all these bodies at one time is known?
(N.B. logistic method dealing with data referred to comprehensive principle—simple rule bringing them all together.)
Kepler’s empirical laws, Tycho Brahe’s observations. Kepler gave complete answer to question how the planets move; but his laws do not satisfy the demand for causal explanations.
Three logically independent rules revealing no connection with each other. Integral not differential laws. Concern the movement as a whole, not the question how the state of motion of a system gives rise to that which immediately follows it in time.
Differential law satisfies the modern physicists’ demand for causality. Newton—clear conception of the differential law; need also for mathematical formalism—found in differential and integral calculus.
Galileo—progress toward knowledge of the law of motion. Law of inertia and law of bodies falling freely in gravitational field of earth
(N.B. mass has become mass-point).
Newton law of motion.
Both refer in their form to the motion as a whole.
Newton—how does the state of motion of a mass-point behave in an infinitely short time under the influence of an external force. Formula which applies to all motions. Concept of force, from the science of statics, which had reached a high state of development. New concept of mass—supported by an illustory [illusory?] definition.
Double c[r]ossing of frontiers. (2)
Causal conception of motion not achieved,—force given in equation. Newton—idea of force operating on the masses situated at sufficiently small distance from the mass in question. The completely causal conception of motion achieved.
Kinetic forces acting on stars and gravity. Combination of law of motion with law of attraction. The only things which figure as causes of the masses of a system are these masses themselves.
Explanation of motions of the planets, moons and comets; tides and processional movement of the earth
Discovery that the cause of motions of heavenly bodies identical with gravity.
Not only satisfactory basis for mechanics. Program of work in theoretical physics. Law of force widened and adapted. Newton—optics, assuming light corpuscular. Even wave theory of light.
Kinetic theory of heat. Law of the conservation of energy; theory of gases; second law of thermodynamics.
Electricity and magnetism. Clerk Maxwell, Boltzman, Kelvin.
Newton’s fundamental principle satisfactory from logical point of view; demands of empirical fact.
Weaknesses in intellectual structure.
1. Absolute space and time—experiment with rotating vessel of water. Space not only variable distance—also physical reality.
Wisdom and also weak side of theory. This shadowy concept—only mass points and distances enter into laws.
2. Forces acting directly and instantaneously at distance. Gravity. Newton—law of reciprocal gravitation not supposed to be final explanation but rule derived from induction from experience.
3. No explanation of fact that weight and inertia both determined by mass.
None of these points logical objection to theory—unsatisfied desire for a complete and unitary penetration of natural events by thought.
Newton’s doctrine of motion—first shock from Clerk Maxwell’s theory of electricity. Not forces propagated instantaneously but processes propagated through space at finite speed.
Faraday—“field”—in addition to point-mass and its motion. First hypothetical medium—then electro-dynamic field as the final irreducible constituent of physical reality.
Hertz—separation from mechanics; Lorentz from material substratum. Substratum physical, empty space (with physical functions). No more action at a distance, even in gravitation—though no field theory
Led to attempt (once Newton’s hypothesis of forces acting at a distance abandoned) to explain the Newtonian law of motion on electro-magnetic lines—or field theory.
Clerk Maxwell and Lorentz—led to special theory of relativity. No forces at a distance—or absolute simultaneity. Mass not a constant quantity, depends on amount of energy content.
Newton’s law of motion—limiting law valid for small velocities. New law in which speed of light in vacuo critical velocity.
(N.B. Special theory—frames of reference relative to observer—all concepts except speed of light relative to frame. Typical operational method substituted for Newtonian logistic method—remnant of comprehensive principle in velocity of light—a constant).
N.B. sequence of theories—
Galileo—law of motion—in terms of time a distance—three motion.
v = dt; a = vt or dt2.
Operational method, comprehensive principle.
Descartes—introduction of concept of mass, and force—concept of momentum—
m = mv or mdt.
Logistic method; comprehensive [principle]
Leibniz and Newton—differentiation of momentum and force. f = ma or mdt2
Logistic method, comprehensive principle. Logistic element but reversible time.
Einstein—introduction and development [of] concept of energy.
K.E. = 1/2 mv2 or 1/2 m d2t2, both distance and time reversible—field theory possible.
General theory of relativity—slight quantitative change; profound qualitative change.
Inertia, gravitation, and all metrical behavior of bodies and clocks reduced to single field quality; this field placed in dependence on bodies. (Poisson)
Space and time not divested of reality but of causal absoluteness (affecting but not affected).
Generalized theory of inertia takes over the function of Newton’s law of motion.
Looks as if law of motion could be deduced from field (p. 5).
In more formal sense also Newton’s mechanics prepared for field theory—discovery and application of partial differential equations.
Limit of serviceableness of whole intellectual structure today. Arguments that not only the differential law but the law of causation has collapsed.
Possibility of a spatio-temporal construction, which can be unambiguously coordinated with physical events, is denied.
de Broglie-Schrödinger method—localization of mass particles without strictly causal laws.
Who decides whether the law of causation and the differential law must be given up?
Einstein, What is the theory of relativity?5
Distinction of various kinds of theories in physics. (p. 6)
(a) Most of them constructive—kinetic theory of gases. Built out of hypothesis of molecular motion.
(b) “principle theories”—analytics not synthetic method
Elements which form their basis and starting point not hypothetically constructed but empirically discovered—general characteristics of the natural processes, principles that give rise to mathematically formulated criteria which the separate processes or the theoretical representations of them have to satisfy.
Science of thermodynamics seeks by analytical means to deduce necessary connect[ion] s from the universally experienced fact that perpetual motion is possible
Advantages of the constructive theory are completeness, adaptability and clearness. Principle theories are logical perfection and security of the foundations.
(N.B. these distinctions of theories are distinctions of principles—“principle theories” are those based on universal principles (without distinction of comprehensive—which Einstein has in mind—and reflexive); constructive theories are those based on particular principles. [)]
Theory of relativity—“principle-theory.” Two stages[:] special—all phenomena except gravitation; general—law of gravitation and its relation to other forces of nature.
Since Greeks to describe movement of a body—second body needed. The co-ordinate system. Laws of mechanics of Galileo and Newton.
State of motion of co-ordinate system may not be arbitrarily chosen (must be free from rotation and acceleration).
Co-ordinate system admitted in mechanics called an “inertial system.”
Not uniquely determined by nature: co-ordinate system moved uniformly in a straight line relatively to an inertial system is also an inertial system.
Special theory of relativity—generalization of this definition to include any natural event whatever.
Second principle of special theory—constant velocity of light in vacuo (independent of observer or source). (N.B. effect to exclude simple and actional principles) Based on electrodynamics of Clerk Maxwell and Lorentz.
Both principles based on experience but seem to be logically irreconcilable. Reconciled by special theory by modification of kinematics—doctrine of laws relating to space and time.
Simultaneity meaning only in a given co-ordinate system. Measuring devices and clocks depend on it.
Laws of motion of Galileo and Newton did not fit this theory.
Relativistic kinematics determined mathematical conditions to which natural laws had to conform; physics had to be adapted to these two principles:
Laws of rapidly moving mass-points, like electrically charged particles.
Results affected the inert mass of corporeal systems—the inertia of system depends on it[s] energy content: inert mass simply latent energy.
Special theory development of electrodynamics of Clerk Maxwell and Lorentz.
Should independence of physical laws be restricted to uniform translatory motion of co-ordinate systems in respect to each other? What is the nature of our coordinate systems and their state of motion?
Co-ordinate systems arbitrarily introduced (N.B. this would have been actional principle)—laws ought to be independent of this choice—general principle of relativity.