The Theory of Relativity and other essays by Albert Einstein

The Theory of Relativity and other essays by Albert Einstein is a compilation of 7 of his essays spanning the years from 1936-1950 and covering his largest contributions to both the practical science and its philosophical interpretation. I will attempt to give a survey of his essays glossing over the more philosophical points and focusing on the physical theories.

1. The Theory of Relativity (1949)

The Theory of Relativity is the “consistent physical interpretation” of motion, space and time. The term relativity derives from its idea that all motion is relative motion, and motion is never in regards to an absolute space like the ether. Though Newtonian mechanics assumes an absolute space, Einstein argues that this is natural, since the earth provides a reference point and that relativistic effects aren’t observed easily at speeds that we normally deal with.

In classical geometry and physics, there is the notion that everything can be measured or located on a 3 or 4 dimensional graph of x,y,z or x,y,z,t. And that such a graph with an origin 0,0,0,0 accurately describes reality. Thus things that occurs with the same time coordinate are simultaneous. But special relativity removes this idea of simultaneity in favor of a measurable definition. For special relativity, the time of an event x relative to me is the time it takes for light to reach me from the event minus the travel time of the light. From this “coincidence” of the light reaching me I can describe which events are simultaneous, through a physical measure. But since the speed of light is always constant (L-Principle) events simultaneous to me, will not be simultaneous to another observer unless they are equidistant between the events as well.

Distance between four dimensional events are described by the Lorentz transform: ds²=dx²+dy²+dz²-cdt² The General Theory of Relativity uses this equation to help describe the “field” which warps time and space about masses. The General theory also describes any inertial frame as equivalent to an accelerated frame. According to Einstein the General Theory is incomplete, as it does not yet describe the “total field”, though he expected the General Theory to be the stepping stone for the final theory.

2. E = MC² (1946)

In this essay, Einstein simply describes the historical development of E=mc². Using a pendulum as the basis for the equivalence of Potential and Kinetic Energy, he attains the equation: mgh=.5mv². But experience shows that the pendulum will stop, due to friction. So what happens? Heat is given off, which was discovered as proportional to the energy radiated. So energy is always conserved, which lead to other areas adopting conservation laws (Einstein cites chemical, electromagnetic, and “all fields”.)

He then continues to explain how mass conservation gets tied into the conservation of energy. He explains that previously this conservation was unnoticed due to the fact that adding an amount of energy that we normally experience to any object would not be able to over come the denominator c² in the equation m=E/c². The amount of energy would have to be enormous or the original mass would have to be comparable to its increase… thus very small. This is why only with atomic physics we begin to see the equivalence.

3. Physics and Reality (1936)

General Consideration Concerning the Method of Science

Einstein argues that due to the radical upheavals in physics today, physicists have to be philosophers, since they alone know the problems intimately. He then does some basic philosophy in the nature of sense experience and his belief that the world is intelligible (he supports this claim with the fact that our theories do actually predict outcomes) amongst other philosophical excursions.

Mechanics and the Attempt to Base all Physics Upon It

Einstein next delves into understanding the concepts of space, body and time. Two properties that we assign to “body” are an existence independent of time and observation. From the concept of body, space arises as a body of a special type. This special type of body is formed from notions of position. Which is best described as a type of contact with space. Time appeared objective, from everyday experience, as things that were seen as occurring simultaneously were assumed to have occurred simultaneously, despite their distance from the observer and the time required for the travel of light.

Einstein considers these understandings (or misunderstandings) of nature to have been fortunate for the development of mechanics. This lead to the concepts of material points, law of inertia, law of motion, and laws of force.

The Field Concept

Einstein traces the development from Newton’s particle view of E&M to Maxwell’s field view. Which is incomplete due to singularities reached from the total differential equations used to solve the field. From this Einstein argues that “the whole theory must be based solely on partial differential equations and their singularity-free solutions.”

The Theory of Relativity

Maxwell’s theory with Lorentz transforms were so successful that the question of an absolute space came back into question. The question was: is speed of light constant in all frames? If it wasn’t constant, then there is a preferred frame of reference, which would be absolute space (possibly in the form of an ether). If it was constant, then there wouldn’t be an absolute space. From this and experimental knowledge, the invariance of the speed of light was raised to the level of a principle (the “Light Principle” or “Light Postulate”, LP for short). This principle led to the Lorentz transforms being applied to a metric in 4-d space in the form of: ds²=dx₁²+dx₂²+dx₃²-dx₄². Where x_1-3 are spatial coordinates and x₄ is time. This application of the LP led to the denial of an absolute time. Also, another postulate had to be declared to account for the equivalency of different inertial and accelerated frames (Principle of Relativity, or PR).

These two together the LP and PR are compatible with Maxwell’s equations, but not with classical mechanics. This is due to the action at a distance and “absolute instantaneousness” of classical concepts and with the contradictory field idea of Relativity. General relativity takes the 4-d metric and moves it to a “general (Reimannian) metric of Bane ds²=g_uvdx_udx_v (summed over u and v)” This results from an incorporation of gravitation into the theory.

Quantum Theory and the Fundamentals of Physics

Classical physics failed as the speed of light failed to be infinite, and instead finite, it also failed as the size of particles failed to be zero, and instead finite (values determined by Plank’s constant). He again states the Probability interpretation of Quantum Mechanics(QM), and then states EPR’s argument for the incompleteness of QM.

Relative Theory and Corpuscles

Einstein tries to show that using partial differential equations, one can come to a complete field for bodies (especially corpuscles) without singularities.

Summary

Einstein makes the claim that the truth of a theory should be judged on criteria of usefulness of the theory’s theorems via observed sense data. He also argues for intuition and a priori theories that can then correlate to sense experience to create more a priori theories. A chain that gets “harder and longer”. He also briefly summarizes the whole paper.

4. The Fundamentals of Theoretical Physics (1940)

Einstein defines physics as “that group of natural sciences which base their concepts on measurements. And whose concepts and propositions lend themselves to mathematical formulation.” Part of physics is the search for the foundations of all physics; the unified theory of those natural sciences. Unlike the foundations of buildings, these foundations are the ones most weathered by new insights.

Newton was the first to strive for a unified theory (according to Einstein). Though E&M, and light were not very well accounted for in his theory. The wave nature of light and E&M are what slowly eroded Newtonian physics, by leading to field theories that challenged action at a distance theories as ad hoc. Theories that eventually equated light and E&M thanks to Maxwell, et al. From this came Special Relativity and Quantum Mechanics; two theories that seemed to have widened the gap in the search for unity of theories.

Using Lorentz transforms and shifts in frames of reference, Special Relativity unified Maxwell’s equations and unified mass, energy and E&M. General Relativity applied field theory to gravitation. But its greatest weaknesses are that gravity and electromagnetic theories are separated, and that it fails to describe quantum phenomena.

Quantum physics begins with the discovery of quanta by Max Plank as he was trying to solve the UV catastrophe. This idea of quanta was quickly applied to atomic phenomena especially absorption and emission spectra. From this derived Schrodinger’s wave mechanics and Born’s probabilistic interpretation which showed Schrodinger’s waves were probability waves that described the likelihood of finding a system in a particular location or state. This and other aspects of Quantum Mechanics leads to the denial of any “rigorously deterministic structure of nature”. Though Einstein still holds hope for the ability to represent reality without probability.

5. The Common Language of Science (1941)

Is a foray into the understanding of language, and the dominance of Science. Science is understood as striving for simplicity, “clarity and acuteness” of meaning that permits symbols and meanings to be manipulated transnationally. This leads to a superiority that given a goal can show itself, without a goal it is solely a useless tool.

6. The Laws of Science and the Laws of Ethics (1950)

Is a brief paper that discusses his thoughts on the laws of ethics. Stating ethics’ premises are ultimately based on logical arbitrariness, but also psychological and genetic reality. He then comments on their worthiness as a field of endeavor and their truth for humanity.

7. An Elementary Derivation of the Equivalence of Mass and Energy (1946)

Is exactly that. It utilizes the law of conservation of momentum, a radiation expression, and a “well known expression of for the aberration of light”.

These essays together show the broad genius of Einstein and together show his understanding of science and its impact upon life.