This is an introduction to some of the people, and their ideas, that have contributed to our understanding of space and time...
Pythagoras of Samos lived around 500 bc, and was a mathematician, philosopher and religious teacher. He is best known for the mathematical theorem that bears his name. However, none of his writings survive, and it is apparent from megalithic carvings that the relationship between the sides of a right triange were known as early as 2,500 bc. So it seems that Pythagoras did not actually originated the theorem, but he may have provided the first rigorous proof.
The theorem is commonly summarised as "The square of the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides".
The theorem also applies to right triangles in three dimensional space. E.g. With a triangle opq with the upright oq lying along the z axis, and the base op lying between the x and y axes:
d2 = x2 + y2 + z2
where:
d is the hypotenuse (i.e. p to q).
x is distance along the x axis ( i.e. o to r).
y is the distance along the y axis (i.e. o to s).
z is the distance along the z axis (i.e. o to q).
Some time between 300 bc and 200 bc, Euclid of Alexandria collated and unified geometry. Many of Euclid's theorems were originated by earlier mathematicians, but Euclid showed how they formed a comprehensive and logical system.
His book "Elements" is one of the most influential texts in history, both for the method and the mathematics. It included both plane and solid geometry. From this the concept of Euclidean space is derived.
In 1632, Galileo Galilei described the concept of relativity in his "Dialogue Concerning the Two Chief World Systems". In it he used an example of a ship travelling at constant speed on a smooth sea. An observer doing experiments below the deck would not be able to tell whether the ship was moving or stationary.
Today one can make a similar observation while travelling in an aeroplane cruising at a set altitude. There is no discernable difference between being at rest and moving at a constant velocity. For example, we are oblivious to the fact that the Earth travels at approximately thirty kilometers per second in its orbit around the Sun. This effect is known as Galilean Invariance or Newtonian Relativity.
We may sumarise this concept as "all motion is relative". However, in addition to being relative, any effects of the motion are symmetrical in this version of relativity. We will discuss the relevance of that symmetry later.
Sir Isaac Newton's work on gravity and the laws of motion became the foundations of classical mechanics. His book Philosophić Naturalis Principia Mathematica, published in 1687, is considered to be one of the most influential book in the history of science.
Although Newton considered space and time to be absolute, the combination of Newton's mechanics and Galileo's concept of relativity "all motion is relative" led to what became known as Newtonian relativity.
Newtonian relativity differs from Einstein's relativity in that inertial frames are related by Galilean transformations, rather than Lorentz transformations. This means that all motion is symmetrical between frames of reference, and there is no contraction of physical distances, nor dilation of time.
Towards the end of the nineteenth century, Albert Michelson took part in one of the most momentous changes in modern physics. At the time, it was thought that light passed through a medium (called the aether) much like sound waves passing through air.
In 1887, Michelson, working with Morley, provided evidence that the aether did not exist. He did this by showing that measurements of the velocity of light remained constant, despite the speed of around 30 kilometers per second at which the Earth orbits the Sun.
Michelson used a device known as an interferometer. Coherent light enters the device, and is split into two beams by a half-silvered mirror. These beams of light are then reflected back by ordinary mirrors, and combined again by the half-silvered mirror. The resulting interference pattern is captured by a detector.
Allowing for experimental error, this showed that the velocity of light is constant.
Click here to run animation.
Hendrik Lorentz was a physicist who supported the then current belief that light required the existence of a medium, through which it travelled. This medium was called the luminiferous aether (or ether).
In 1892 he sought to explain the results of the Michelson-Morley experiment by suggesting that the apparatus was moving with respect to the aether, but the effect on the measurement of the velocity of light was being masked by another effect, which was known as the Lorentz contraction.
The Lorentz contraction was thought to affect the dimensions of the measuring equipment, due to its motion with respect to the aether. However, Einstein's Special Theory of Relativity made the idea of a light medium redundant. Instead, Einstein used the Lorentz contraction to describe the effect of relative velocities on the dimensions of spacetime itself. Hence it is now known as the Lorentz transformation.
The Lorentz transformation (for time) is:
In this equation:
t is the time elapsed in the rest frame of the observer.
T is the time elapsed in the rest frame of the object.
The only other variable is v (the velocity) and it is:
So the Lorentz transformation explains why the passage of time is dilated and distances contract at high velocities. However, these effects depend solely on the magnitude of the relative velocity. This constraint is important, and needs to borne in mind when we discuss some of the myths that have grown up around the theory.
Hermann Minkowski's place in the history of relativity is assured by the fact that, in 1908, he orignated the concept of spacetime, although the term "spacetime" was not coined until later.
Minkowski referred to it as the "postulate of the absolute world". Any point in space and time is a "world point" and the motion of any object could be described as a "world line" in four dimensional spacetime.
Minkowski showed that the Lorentz transformation, whereby physical distances are contracted as a result of relative motion, is a direct result of the geometry of spacetime.
Minkowski originated the terms "front cone" and "back cone" for the areas on a spacetime diagram.
For example, if we assume that A is an event in spacetime. Time is shown as the vertical (z) axis. space is represented by the horizontal (x and y) axes.
The front cone (on top) represents future events that can be causally related to event A. So event B, which is inside the front cone, could be caused by event A. Their relationship is said to be "timelike".
But event C, which is outside the front cone, could not be caused by event A. Neither could it have caused event A, as it is outside the back cone. This relationship is said to be "spacelike".
In 1905, Albert Einstein, aged 26, published his original theory of relativity, which is now known as the Special Theory of Relativity. Although it is indirectly based on the Galilean concept of relativity "all motion is relative", it was actually based on two postulates:
Einstein's Principle of Relativity:
"The same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good".
The Velocity of Light:
"Light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body".
This second postulate is not a simple as it may seem, and we discuss it further here.
In 1915 Einstein published his General Theory of Relativity. This drew on his earlier work, but also included the four dimensional spacetime continuum, tensor calculus, and his own work on gravity. This theory was therefore based on a different conceptual framework from the Special Theory. Nowadays, the term "special relativity" usually refers to the special case of the General Theory in which the gravitational field is uniform. Hence it is analogous to, but not the same as, Einstein's original theory.
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