# Chapter 12: Special Relativity

The speed of light wasn’t always constant, or so most thought.

In the late nineteenth century, the good physicists were all busy studying the wave like nature of light, and our dear Dr. Einstein was busy working at the Swiss patent office, probably verifying the uniqueness of the latest automated apple peeler.

There is a mountain of data that shows, empirically, that light travels in waves. Wave motion is something that is readily studied and familiar to the human experience. All you need is a few pebbles and a pond and you are ready to conduct your own wave experiments. When you throw a pebble in, the impact of the falling stone on the surface of the water creates a disturbance of the surface which sets up a harmonic oscillation between the surface tension of the water and gravity.

You see ripples. And these ripples travel outward from the source of the disturbance in a radial fashion creating ever enlarging circles of higher and lower water levels that are best interpreted as waves. As it turns out, there are many phenomena that exhibit wave-like behavior, especially, and most notably, sound.

Waves have their own special characteristics. They can amplify each other when they are in phase and have matching peaks (constructive interference); and they can cancel each other out when they are out of phase, and give the appearance that that region is in the ground state (destructive interference). And it was by studying these interference patterns that scientists came to better understand the motion and the rules that govern it.

A typical pattern of wave interference is shown below. This is an example of a two point source interference pattern, where the constructive interference points show up as light spots, and the destructive interference points are dark.

Linearized waves from distant sources like the sun (rather than the highly circular wave shown above) can also be transformed from their linear state into an interference pattern of mild curves by forcing them through a slit, as shown in the photo and drawing below. We call this phenomenon diffraction

This was discovered in a famous set of slit based experiments performed by Thomas Young in 1801. Light, when forced to go only through slits in a masking surface, displays the characteristics of diffraction and interference, very much as do the ripples on the surface of a liquid, as does sound in air; so the logical conclusion was that light too, must be propagated through waves in a medium.

From the diagram above, it is easy to see why the results of the experiment performed by Young eliminated Newton’s corpuscular light theory from serious consideration. If light were a particle moving in a relatively straight line, it would never be able to traverse the ‘maze’ of the slits, much less create an interference pattern on the screen.

This is important to the discussion about Special Relativity for two reasons. First, as alluded to in the beginning of this book, it was believed that light energy, in the form of massless waves, must be transported through a medium. For the ripples on a pond, the surface of the pond serves as the transmittance medium. The wave energy is transmitted radially without creating a similar linear movement in the medium (pond). The same is true of sound. Sound is transmitted as pressure waves that race through the medium (air) at speeds far in excess of those that would be possible if the lateral movement of the air molecules was required. Clearly and by definition, a wave, having no physical substance, must have a medium to excite in order to exist and be propagated.

This was all well and good, but for light as a wave to be transmitted across the dark regions of space, it must be resident in some sort of structure or medium. And it must be an invisible medium or you couldn’t see the stars. That medium must be massless as well, for otherwise the light would constantly lose energy while it traveled to the observer and could never propagate long distances, such as the vastness of space.

The wave scientists dubbed this medium the ‘the Luminiferous Aether’, surmised that the Aether permeated all space, and gave it the qualities required to agree with the calculations (sort of like we do with regard to Dark Matter and Dark Energy today). And therein lies the problem. This Aether must have a homogeneous velocity (either non-moving or moving with a constant velocity, called the ‘Aether Wind’), otherwise the stars would appear to move. Most thought that the Aether was unmoving, static, and almost rigid. But there were others, most notably Hendrik Lorentz who surmised that the Aether itself could have a velocity, and through the transformation equations that he developed, showed how the moving Aether could be interpreted by Earthlings as a non-moving field.

Furthermore, which ever position one took with regard to the motion of the Aether, it was clear that the Earth must be moving relative to it. (Only a myopic geocentrist would consider otherwise). So if the Aether was static, or moving homogeneously, what was the relative velocity of the Earth with respect to it and how could one demonstrate and measure that?

This led to great discussion and controversy. So to settle this question and provide that measurement, Dr.’s Michelson and Morley devised an experiment to determine what, and which direction that relative velocity must be, which we’ll discuss in a few paragraphs.

The other important thing about waves and their interaction is the fact that they interfere with each other. This fact actually allows for the possibility of making highly accurate measurements. Think about this: If you take a beam of coherent light, and split it into two smaller beams, make each them travel some distance independently, and then reunite them, you can determine whether the distances traveled by each were the same length, due to the fact that if they did, the split off light beams would still be in phase when reunited. If they weren’t, you would get interference when you brought them back together. This means that you can measure relative distances to the accuracy of a fraction of a wavelength of the light used, which is a very small number; rendering your relative measurement extremely sensitive and accurate. We call the device that does this an Interferometer.

Dr. Albert Michelson was a professor of Physics and became the first American to win a Nobel prize in a scientific category. He was appointed to the Naval academy in 1869, and went on to study the subject matter that was his passion; sciences, especially optics. In 1883, he became a professor at the school then called the Case School of Applied Science, that eventually became Case Western Reserve University or as it is commonly called, just ‘Case’. He spent his entire life in a quest for measurements relating to the speed of light, some of that time at the Mt. Wilson Observatory in California, but he became most famous for the ‘failed’ experiment that he performed with Edward Morley in 1887.

In order to determine the relative velocity of the Earth with respect to the Aether Wind and settle these discussions, Michelson and Morley built a light Interferometer. A really big interferometer that was floated on a very large stone in a pool of Mercury (where was the EPA?) so that they could rotate the entire assembly with respect to the Earth. And they put it in the basement of a building at Case in Cleveland, Ohio, and operated it only at night, when the trolleys weren’t running and the horse traffic was low to minimize the vibration of the device. They reasoned that if they turned it in one orientation, tuned it in to be in phase and then turned it 90 degrees, the velocity of the Earth with respect to the Aether would cause the beams to be out of phase, due to the change in the relative motion of the device with respect to the medium (the Aether).

And lo and behold, they found nothing. No change. No relative motion. This was seen by the scientific community as astounding. A complete conundrum. All the great theoretical development that had preceded this experiment, the edifice of a larger more comprehensive construction of a unified theory of matter and energy and the relationship between them; and when it came down to a high precision experiment that was predicted to show the motion that must be there, it wasn’t.

Scientists were baffled. This experiment was designed to show what the relative velocity was, not if there was one. Lorentz modified his equations to show that they could predict this result, but the scientific community was unimpressed.

And then along came this funny looking little guy with frizzy hair who was working in a patent office in Switzerland with a radical suggestion:

“The speed of light in a vacuum is constant.”

What an unimposing little statement. But clearly, if one assumed that this was true, then it was perfectly obvious that the results observed by Michelson and Morley were correct, because, if the speed of light was a constant, it must have the same speed for any orientation of the interferometer regardless of the velocity of the Aether. However, the reason that no one had made that assumption before was because it means that, if the speed of light is constant, then other measurements, such as time, mass and distance were not.

You see, Dr. Einstein utilized the Lorentz transformations to explain how light must interact with the universe as a whole, and to explain how the speed of light could appear to be the same for all observers. As a result of that and the need to incorporate the perspective of observers traveling at velocities that were a meaningful percentage of the speed of light, and utilizing them, it became clear that those other quantities that used to be considered invariant (distance, mass and time), must in fact be subject to and altered by the velocity of the observed with respect to the observer.

The other assumption of Special Relativity is that for every observer, the space surrounding them obeys the same laws of physics. This is a little more intuitive, but it creates many perceived paradoxes, some of which we’ll talk about in later chapters.

And it was from these assumptions that Dr. Einstein developed the most famous equation ever:

E = mc2

which we’ll also discuss at greater length later on. But there are a few conclusions that need to be delineated here.

First, this equation, subtle though it may be, points out the fact that matter and energy are, under certain conditions, equal. Let’s let that sink in.

Matter and Energy. Equal. The same thing. Interchangeable.

Furthermore, by doing just a little mathematical reorganizing we find that:

E/m = c2

Now c, that represents speed of light, is, as pointed out above, a constant. Which in turn means that the ratio between energy and mass E/m, as shown in the above equation must also be a constant, since it is equal to the constant, c, squared. Therefore, the more energy that something has, the more mass it must have also, since we have shown that the ratio between them two must remain constant.

But the real point of this chapter is this: Dr. Einstein changed all of physics, half of a millennium of accumulated thought, literature and calculations (more or less depending on how you count it) with the assumption that a velocity (in this case, the speed of light) is the measurement constant. Not length. Not time. Not even mass, the most fundamental of all physical aspects of matter, could be constant to all observers. Only the speed of light, which is a velocity.

But because he didn’t take this observation and his logical conclusions quite far enough, we are still stuck in the physics quagmire that we are today; but I digress……

And there is one other lesson here, and that is: sometimes, the best answer to a seeming contradiction (listen up, Dr. Heisenberg!) comes from an observation that is fully outside of the common and accepted train of thought. For, at its most fundamental level, that is what the Special Theory of Relativity is all about. Dr. Einstein realized that since there was no possible agreement between classical theory and the observations, then, there must be something wrong with the classical theory. And classical theory at that time assumed that space, mass and time are always the same for all observers. So much for the old way of thinking! Heave-ho!

There is so much more that could be said about this subject, but there are also many more and important concepts that must be put into place before providing an alternate description, which is, after all, the purpose of this book. So with that in mind, we’ll move on to:

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