In 1905, Swiss government worker Albert Einstein published his paper on special relativity, building on the work of the physicist Hendrik Lorentz and the mathematician Henri Poincare. It was called “special” because for simplicity it avoided dealing with the effects of gravity or acceleration. The principle of relativity, which was known prior to Einstein’s paper, stated that all physical laws behave the same whether the entire system is at rest or moving in a straight line at fixed speed.
For Maxwell’s equations to conform to the principle of relativity, they had to be altered with a mathematical transformation discovered by Lorentz. Under Newton’s equations, if you were travelling with a given speed v towards a light source, you would expect the closing speed between you and the emitted light to be c + v because of your motion relative to the light. But Einstein proposed that the speed of light in a vacuum was the same for all observers. Therefore, under this scheme, the closing speed remained c, the speed of light.
When Einstein applied Lorentz’s transformation to Newton’s equations, he found that Newton’s signature formula, F = ma, was not correct. Einstein had to replace with a variable expression which accounts for changes in “rest mass” depending on the velocity of the object. At rest or at the kinds of speeds we typically encounter on earth, the new mass term hardly changes. But as speeds approach that of light, the mass term increases enormously. In other words, at low speeds, Newton’s equations were very accurate. At very high speeds, they weren’t. The growing realization that Newton’s laws of motion did not hold under all circumstances was staggering.
There were several implications from Einstein’s formulation. Suppose you were looking through the window of a rapidly moving spaceship as an external observer at rest. Several non-intuitive effects would become apparent. First, time on the spaceship, as shown by the clock visible within the spaceship, passes more slowly than for you, the stationary observer. Second, the spaceship shrinks in the direction of travel from your perspective. Third, if there are flashes of light emitted from each end of the ship such that a passenger aboard would observe these simultaneously, they will not appear simultaneous to you. If the spaceship is travelling at half the speed of light, and a bullet is fired within the spaceship in the direction of travel, also at half the speed of light, you would expect to see the true speed of the bullet as the speed of light (half the speed of light plus half the speed of light). However, this will not be so. Instead, you will observe the bullet moving at about four fifths of the speed of light. All these effects are predicted by Einstein’s theory of special relativity.
Einstein’s system differs from the three-dimensional Euclidean coordinate system we saw earlier, because it uses a four-coordinate system where time is the fourth quantity. The four-coordinate system is called “space-time”. The four coordinates are taken to be nearly equivalent in nature, except that the time axis is different in two ways from the other axes. Firstly, movement on the time axis can only be in one direction; time never moves “backwards”. Einstein also effectively proposed that any movement in any of the dimension axes must always be accompanied by movement in the time axis.
An important result from Einstein’s special relativity was the famous equation, E = mc2 (where E represents energy, m represents mass, and c is a constant term equal to the speed of light in a vacuum). This united the law of the conservation of mass and the law of the conservation of energy into a single relationship.[1]
Einstein published his theory of general relativity in 1915. This took acceleration and gravity into account, unlike his earlier special relativity. It has often been said that general relativity is effectively a theory of gravitation.
In general relativity, anything with energy responds to gravity. Therefore light, which has energy, but no mass in the conventional sense, can be deflected weakly by gravity.[2]
Another aspect of general relativity is that in a gravitational field, a clock at greater height, or gravitational potential, will run very slightly faster than one at a lesser height, or a position of lower gravitational potential.
But what is gravity? Did Einstein have more to say than Newton?
He did, and again this is related to the geometry he used—a non-Euclidean geometry. As we saw above, Euclidean geometry is characterized by triangles whose angles sum to 180 degrees and circles whose ratio of circumference to diameter is approximately 3.14. Under non-Euclidean geometries neither of these relationships holds. In particular, non-Euclidean circles feature a positive or negative amount of “excess radius”, depending on the geometry being considered. Einstein stated that the amount of excess radius in space-time is proportional to the mass of the object. Effectively, space-time is curved by the effect of mass, which we interpret as a gravitational field.
Einstein’s general relativity ended Newton’s occult “action at a distance” idea of gravity and replaced it with the concept of the gravitational field. Einstein had found a higher and more accurate generalization which encompassed Newton’s mechanics (or laws of motion). He had essentially demoted Newton’s empirical causal model science to useful empirical descriptive-model science.
At a presuppositional level, Euclidean geometry, which had underpinned the study of astronomy for around 2000 years—from the ancient Greeks through to Newton in the eighteenth century—was finally superseded. The ether, too, was out. This marked a major point in science in that not only had the Ptolemaic system been replaced during the Copernican revolution, but the Greek mathematical foundations had also been superseded.
[1] Carmeli, 2002, p. 87.
[2] Feynman, Leighton, & Sands, 2010, p. 7~11 (Vol 1).