Einstein-Infeld (an Einstein associate) trace the transition, forced by findings in the late 19th and early 20th century, between classical physics and modern physics that challenged the Newtonian explanation of the world. Newton, the authors state, was not so much replaced as he was incorporated into a higher-level, more encompassing paradigm.
In a way, the transition was fueled by Hegelian-like contradictions along several lines. The wave nature of particles (photons, electrons) was at odds with an atomic (hard, substantive, point-like particles) view of matter. Rather than seamless movement, energy was seen (with Planck, then Einstein) to come in discrete chunks of energy, energy packets (quanta), that moved in jump-like fashion from one level to another. Then, with Einstein (1905), matter and energy came to be seen as interconvertible entities. Matter contained energy and energy had a particle (quantum, albeit massless) nature. With the quantum world coming of age, Newton’s easy-to-grasp notions of causality (atoms in motion, hitting each other with straight-line effects) had to be replaced at the quantum level with probabilistic causality. Predictions no longer pertained to individual particles but only held true for some gross collection of particles.
From these emergent findings, Einstein and others concluded that the Newtonian model that separated matter and energy (1) had to be replaced with a quantum model that united them. Matter was concentrated energy; energy was extremely diluted matter (to the point of masslessness at the speed of light) per Einstein’s E=MC2 formulation that used the square of the speed of light (pure energy) as the conversion factor (equivalence for matter). (2) At the sub-atomic level, particles convert to energy and vice versa, which explains energy’s dual (particle-wave nature) via quantum jumps, and that all of this took place in a field (a cloud) of interactions rather than in a one-to-one cause-and-effect way. Quantum physics, the authors say, formulates laws of crowds, not individuals. Behavior is not that of bodies but rather it is something that exists between them - “the field.”
How this description - this addition to and incorporation of the Newtonian paradigm - relates to Einstein’s relativity theory is not clear to me. It has something to do with the nature (and speed) of light, which is energy void of mass and that lies on the non-mass pole of the energy continuum, and the deductions from this that lead Einstein to conclude that time as well as space cannot have an absolute, fixed standing. And it has something to do with the nature of gravitational mass that attracts lesser bodies. Such masses are also resisted by inertial mass, and the more massive a body is, the more resistance it provides. These countervailing forces are not just mass. That mass is really energy (“add more energy, more mass; more attraction, and more resistance”). It is as if the authors are saying that the relationship between two masses occurs, similar to what happens at the atomic and sub-atomic level, as a (gravitational) field. As at the microlevel where a field operates locally at the speed of light, the exchange between two mass bodies at the macrolevel is mediated by energy operating at the speed of light. (3) And, interestingly, the relative masses plus the square of the distance that affects attraction-resistance seems to almost operate by quantum jumps.
Einstein and Infeld’s attempt to unite relativity with the quantum world is focused on the field concept (matter operating as energy). Here, their central idea is rich:
“Can we think of matter and field as two distinct and different realities?...Before we learned about the relativity theory we could have tried to answer this question in the following way: matter has mass whereas field has not. Field represents energy, matter represents mass. But we already know that such an answer is insufficient in view of the further knowledge gained. From the relativity theory we know that matter represents vast stores of energy and that energy represents matter.”
“From the relativity theory we know that matter represents vast stores of energy and that energy represents matter. We cannot, in this way, distinguish qualitatively between matter and field, since the distinction between mass and energy is not a qualitative one. By far the greatest part of energy is concentrated in matter; but the field surrounding the particle also represents energy, though in an incomparably smaller quantity. We could therefore say: Matter is where the concentration of energy is great, field where the concentration of energy is small. But if this is the case, then the difference between matter and field is a quantitative rather than a qualitative one.”
“We cannot build physics on the basis of the matter-concept alone. But the division into matter and field is, after the recognition of the equivalence of mass and energy, something artificial and not clearly defined. Could we not reject the concept of matter and build a pure field physics? What impresses our senses as matter is really a great concentration of energy into a comparatively small space. We could regard matter as the regions in space where the field is extremely strong. In this way a new philosophical background could be created.”
If the authors are proposing a “pure field physics,” does their last quote suggest that in one fundamental sense Einstein’s famous energy-mass equivalence formulation is misleading: There are not two basic cosmic substances but one, energy, which comes in many different forms of matter that jump into and out of concentrated form.
There are a couple of other large questions that leap out of this book. First, Newton’s laws of motion state that a body moves in a straight line (or remains at rest) unless acted upon (accelerated) by an external force. At the macro level, Einstein has large cosmic masses depressing space-time. Though the discussion of Einstein’s theory often states that he didn’t see gravity as a force (4), this depression of space-time does create movement of matter and masses across the cosmos. Why does a body move in a straight line until it is acted upon, which always seems to be the case with gravitational effects? Answers to this question seem either non-existent or implied. At the subatomic and atomic level, energy radiates outward as light (electro-magentic spectrum). But what about large concentrations of energy, as mass-matter moving through space? Why do they, in theory and before gravitational effects, move in a straight (or, per Newton, “right”) line?
Second, Einstein-Leopold’s discussion of the equivalence between gravitational and inertial mass was particularly interesting. Gravity is one of the four forces, but it is touted as an attractive force only (two bodies attract each other) and it is distinctly not a repelling force as is with electro-magnetism. While gravity does not repel, it does via inertial mass, “resist” and, thereby, the notion that all energy-matter interactions involve some form of both attraction and resistance is retained. (5) This in turn leads to the balancing of energy differentials and equilibrium (until upset by external forces, whether self-propelled or other-directed), and equilibrium is, of sorts, “zero.” (6) Zero might be the basic cosmic concept - it is nothing yet it is everything. Or, it might be some sort of idle philosophical speculation: It may be something, or nothing. (7)
(1) “Classical physics introduced two substances: matter and energy. The first had weight, but the second was weightless. In classical physics we had two conservation laws: one for matter, the other for energy. We have already asked whether modern physics still holds this view of two substances and the two conservation laws. The answer is: ‘No.’ According to the theory of relativity, there is no essential distinction between mass and energy. Energy has mass and mass represents energy. Instead of two conservation laws we have only one, that of mass-energy.” Interestingly, the authors write, “In its own Newton’s time the concept of energy did not exist.” Newton thought of light as weightless corpuscles and each “color preserved its own substance character. Later, when the concept of energy was created and it was recognized that light carries energy, no one thought of applying these concepts to the corpuscular theory of light. Newton’s theory was dead and, until our own century, its revival was not taken seriously.”
(2) In discussing the problem in asserting that mass and energy were equivalent, Einstein and Infeld refer to “the very small rate of exchange between matter and energy. Compared to mass, energy is like a depreciated currency compared to one of high value….Energy was regarded as weightless for so long simply because the mass which it represents is so small.” This statement does, however, raise a question about the masslessness of energy - if energy has weight, however diluted, would it have mass, however diluted?
(3) “Maxwell’s equations” pertaining to the electro-magnetic field, Einstein and Infeld write, “connect events which happen here and now with events which will happen a little later in the immediate vicinity. They are the laws describing the changes of the electromagnetic field. Our new gravitational equations are also structure laws describing the changes of the gravitational field.” “The theoretical discovery of an electromagnetic wave spreading with the speed of light,” the authors add, “is one of the greatest achievements in the history of science.” Add the speed of light to field interactions, and the gravitational effects across vast spaces and time can be understood.
(4) Einstein-Infeld do say that large bodies show that a “force is directed toward the sun; this means the force is an attraction.”
(5) “Gravitational and inertial mass are equal,” the authors state (adding that “this identity of inertial and gravitational mass was fundamental for the formulation of the theory of relativity”). And, “all energy resists changes in motion.” Add more energy, and there is more resistance. But unlike classical physics that saw inertial resistance in terms of mass only, Einstein’s relativity theory has velocity adding to the resistance effect. Velocity adds (kinetic) energy so that a moving body has both mass and kinetic energy and it resists change of velocity more strongly than the resting body, and “the resistance becomes infinitely great as velocity approaches that of light.” The definitional difference between “repel” (drive away, almost like a counter-attack) and “resist” (withstand, or defend), is interesting. Regarding the equivalence between gravitational and accelerating effects, the authors seem to not only describe that there is space contraction and the slowing of time that happens as an object approaches the speed of light but also, unlike other writers, explain physically why this is so: The faster an object moves (accelerates), there is a compression-contraction of an object in the direction of the movement that shortens length and (the “rhythm of a clock keeping) time.
(6) Is “Zero” related to the law of conservation? “In a closed system, one isolated from external influences,” energy is conserved. And, “If we regard the whole universe as a closed system we can proudly announce with the physicists of the nineteenth century that the energy of the universe is invariant, that no part of it can ever be created or destroyed.” Cosmic rhythms move energy around (and manifested in different forms), but if the overall amount of energy is the same, there is neither more nor less, which is zero.
(7) My favorite quote from this book: “Philosophical generalizations,” the authors write, “must be founded on scientific results.”