Topic 9

 

Prelude

Copernicus and Galileo both knew about relativity for 'space'. Galileo formalized the ideas in terms of 'frames of reference'. If one is on a ship and sees another ship pass by, it is not possible to tell which ship is moving without some other independent frame of reference such a coastline or island. They both knew that an object dropped from a ship at rest fell to the deck directly below. If the ship was moving with uniform linear motion (defined by Galileo), the object also fell to the deck directly below. Galileo used this argument to show that one cannot prove which ship is moving on the basis of dropping a ball (or any other test). Thus all motion had to be relative to something else.

That worldview was put into mathematical terms by Newton. As a simple example, consider a person on the shore watching a ship sail by with velocity v. To a person on the ship, they are not moving at all relative to the ship. But to each other, the people are moving at a speed v with respect to each other. If the person on ship walks toward the bow with speed w, his speed as seen by the person on shore will be v+w but his speed relative to the ship will just be w. Such physics can account for almost everything we see today including the motion of anything on the planet Earth as well as the motions within the Solar System. It was not until about 100 years ago that those ideas were found to be in error under certain circumstances (velocities approaching the speed of light).

 

The Nature of Light

Roemer (1676, before Newton's Principia Mathematica was published) observed that the time taken for Jupiter's moons to be eclipsed by Jupiter changed depending on how far away an Earth-based observer was from Jupiter. His correct conclusion was that the difference was due to the amount of time it took (reflected) light from the moons to reach Earth. He estimated light speed to be 140,000 miles/second! We now know that speed to be more like 186,284 miles/sec (in a vacuum), but he was amazingly close given the technology 300 years ago.

Newton was the first person to try and explain the physics of light in a systematic scientific manner. His theory attempted to explain the following known (~1680 AD) features of light:

- light travels through a vacuum (empty glass vessel)

- light travels in straight lines called rays (sharp shadows can be seen)

- light rays are reflected on hard surfaces (normal light of Moon)

- light rays are refracted when passing from one translucent medium to another

- light can have different colors

- speed of light depends on medium in which it travels (fastest in vacuum)

Newton thought there were particles of light which he called 'corpuscles'. They are emitted by lighted bodies, can travel through translucent materials, and be reflected off non-translucent surfaces. Refraction must be due to short-range acting on light corpuscles depending on density of material. Colors are due to different kinds of corpuscles, each a particular color. Colored corpuscles are normally mixed and appear white. On refraction (like a rainbow), different colors appear due to the short-range forces.

As Newton was developing a 'particle' theory for light, a Dutch physicist named Huygens developed a 'wave' theory of light. It was obvious from general observation that certain physical processes could be explained by the action of waves. For example, the propagation of waves (ripples) on the surface of a pond is due propagation of momentum from one water particle to another (remember what happens to objects floating in water when a wave passes). The individual water particles don't move far, they are just displaced locally by another particle hitting them and they soon come back to some equilibrium position. Many of the properties of light noted above can be explained by light behaving in a 'wave-like' manner. In fact, one could explain refraction without need of a special short-range force as proposed by Newton. The problem for Huygens was what moved to propagate the light 'waves'? He proposed a 'luminiferus ether', which is weightless and transparent, which permeates the entire universe.

Due to Newton's prestige, the particle (corpuscular) nature of light was believed for almost a 120 years until early 19th Century experiments clearly showed that light can diffract (be bent around a sharp corner). This is one reason for why shadow boundaries are more commonly diffuse. Only wave-like disturbances can behave like that; true particles will always be stopped at a sharp boundary.

James Clerk Maxwell unified the scientific studies of electricity and magnetism in 1865 and showed that they were just two sides of a single force called electromagnetism. He proposed that electromagnetism is propagated by waves of varying frequency. Light is simply electromagnetic waves of a certain range of frequencies. Other forms of electromagnetic radiation include radio waves, x-rays, gamma-rays, FM-TV waves, infrared radiation, and ultraviolet radiation.

Electromagnetic waves can be thought of like water waves in that they can be defined by a wavelength (L) that is the distance from one wave peak (or trough) to the next peak (or trough). The period (P) of the wave is then the time required for one wavelength to pass an observer (P=time/L). Frequency (F) is the number of periods (cycles) to occur per unit of time. If electromagnetic waves travel at some velocity (V), then V=LF.

(For sound waves, we have all experienced an effect called the Doppler Shift. If you are in a car moving toward some sound with a velocity Vc, the sound (which is moving toward you at some velocity Vs) seems to increase its frequency because F=Vs/L becomes F'=(Vs+Vc)/L. Once your car passes the sound, the frequency gets lower because F"=(Vs-Vc)/L. we will consider an analogous condition for light in a later lecture.)

An additional problem which Maxwell created in his equations to explain electromagnetism (Maxwell's equations) was that the speed of light should be a constant (in vacuum). How can one do that if spatial relativity denies any absolute reference frame for measuring the speed of light? Maxwell argued that the ether within the universe provides such an absolute framework. Speed of light is constant in that framework, but can vary in others which are moving at arbitrary constant velocities.

The last problem which faced 19th Century science was then the nature of the 'luminiferous ether' needed to propagate electromagnetic waves and provide an 'absolute' reference frame. Lots of experiments were carried out, but no consensus was formed.

Then around 1900 a famous set of experiments were carried out by Michelson and Morley which provided the last straw (so to speak) for ether. They found that the speed of light (in a vacuum) is exactly the same for light traveling in the direction of the Earth's revolution around the Sun and perpendicular to it! Newtonian physics could not explain that. Newtonian physics predicted speed of light in direction of revolution should be 186,284 miles/sec plus speed of Earth relative to Sun (~20 miles/sec), while light speed at right angles should be just 186,284 miles/sec. Careful experiments repeatedly said, not so!

 

Einstein's Special Theory of Relativity

In 1905, Einstein argued that one could explain the properties of light and its speed by taking a somewhat different view of the universe. He said, let us assume (postulates) that the laws of science hold no matter what inertial reference frame (one moving at some arbitrary constant velocity) one is in, and that the speed of light is a constant. Then the following set of equations will let one relate actions in one reference frame (primed) moving at velocity v relative to any other reference frame (unprimed):

 

In Newtonian physics, these equations would be t'=t, L'=L, c'=c, m'=m, and F'=F. These equations work well enough when v<<C and we can view Newtonian physics as relativity under conditions of low speeds in inertial reference frames.

There are a number of consequences of the Special Theory of Relativity. First comes the correspondence between energy and matter:

For example, a mass of 1 gram at rest, has a mass of 1.005 grams when moving at 0.1c and a mass of 2 grams when moving at 0.9c. As its speed increases, mass approaches infinity. Can't happen.

Next comes a lack of simultaneity. No two observers in different reference frames will agree of distance between two objects of time needed to move at some velocity between them.

Mr. Thompkin's first visit to the Land of Relativity is a good example of Special Theory.

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