Light

Newton

One of Newton's other fascinations with physics was optics and light. In his younger years he would insert thin utensils between his eyeball and skull to see what the effect of distorting the eyeball's shape would have on his vision. He also carried out experiments with prisms in which he showed that sunlight was broken up into colours by the prism, but if one inserted a lens to send the light back to another complementary prism, those multiple colours would recombine into white light. Colours were not just the property of objects, but were also the property of light itself.

He though of what light was, and came up with the idea that light was particles, just like other small bodies. These particles would travel with various velocities, and could be affected by gravity (although he did not make that connection explicit).

Galileo had discovered the moons of Jupiter, and it was rapidly realised that this gave a way of determining Longitude on the surface of the earth. The satellites were eclipsed regularly by Jupiter, and the times could be calculated into the future using Kepler's laws. Observing an eclipse of one of Jupiter's moons by Jupiter in two places on the earth you could know that those observations were taken at the same time. With tables of Jupiter's orbit or of the moon you could determine where in the sky (with respect to the stars) Jupiter or the moon should be at the various longitudes on the earth (The further west you were, the further toward the east any particular star should be as the stars travelled around the earth from your point of view.)

In 1666 G. Cassini took the job of compiling the tables of the eclipses of moons of Jupiter, and in 1672 hired O Roemer as his assistant. By carefully measuring the times of the eclipses they discovered that the times between eclipses got shorter when the earth was approaching Jupiter, and longer as it receded, such that the eclipses occurred about 17 min later when the Jupiter was on the far side of the sun from the earth than when it was on the near side. (Due to the difficulty in determining exactly when the eclipse occurred due to both the finite size of the moons, and problems with the telescopes and with their clocks-- it had only been about 20 years since Huygens had used Galileo's discovery of the independence of the time of oscillation with amplitude to make accurate clocks-- they got a somewhat smaller value for this variation, and Roemer ascribed this to the finite velocity of light-- it would take time for the light to travel an additional distance equal to the diameter of the earth's orbit. Ie, he got a speed of light of about one earth's orbit diameter in 17 min. Of course one problem was that the diameter of the earth's orbit was still very badly known.

Bradley

In 1720's Bradley, wanted to see if he could observe the parallax of the stars due to the earth's orbit around the sun. The lack of any parallax had been what had led T Brahe to reject Copernicus's model for a model in which all the planets orbited the sun, except the sun orbited the earth. He could see no parallax for any of the stars, and thought it highly unlikely that they could so far away that he could see no parallax. They would have to be about 3500 times the earth's orbit away for him not to see parallax. With the telescopes, especially at the observatory that had been set up an Greenwich in London to determine time (by seeing when various stars were directly overhead at Greenwich), he felt that he could get down to an accuracy approaching 1 second of arc (1/200000 of a radian) in seeing whether the relatively bright star Beta Draconis went overhead in London. (In the east west direction, since clocks were nowhere near sufficiently accurate, you could not tell if the star came a bit early or late, but north south you could use the telescope to determine if it came a bit north or a bit south of where it should). Since London is north (at about 50 degrees north of the equator), the earth has a component of its velocity toward or away from Gamma Draconis , and thus had motion perpendicular to the direction to the star which would create parallax. The parallax should be maximum when one had moved a maximum amount toward or away from the star. This should have occurred in winter and in summer.

He found that the direction to Gamma Draconis did change over the year, but at the wrong times. The maximum deflections occurred in spring and fall, when there should be little aberration. However, at these times the velocity of the earth perpendicular to the direction to the star was a maximum. The maximum displacement was 20.2 seconds of arc.

It took him a long time to figure out what was going on. He finally realised that if light has a finite speed, then when the earth was travelling at its maximum velocity north-south, you would be running into the light and its angle would tilt toward the direction you were travelling (Like rain when riding a bicycle always seems to come from in front of you, no matter which way you ride). This tilt is caused by the velocity of the earth, and the angle implies that the light must be travelling at a speed of about 10,000 times as fast as the earth does.

This was the first demonstration that the earth must have a velocity-- the earth goes around the sun-- and required that light have a finite velocity.

Wave

Both Huygens and Hooke thought that light was not a particle but a wave. Huygens may have done so because of his influence by Descartes that all of space was full a "plenum" or "Aether" in which you might expect waves to travel, like sound waves in air. He used this to explain a number of features of optical phenomena (like refraction-- the change in direction of light as it enters a medium like glass or water, anomalous diffraction-- some light bends differently depending on its "polarization" etc. But Newton was the grand Pooh Bah of Physics so what he said must be true:-). Almost everyone believed for over a century that light was particles.

There were some problems with the particle picture. Newton has showed that colour was a property of light, not of our eyes or of objects. But what particle property could it correspond to? If the speed of the particles, then in looking say at Jupiter, you would see, say, the blue coloured Jupiter in front of the red coloured one, because the blue light would get here faster than the red. No such effect had ever been seen. For waves however, they have the property of the frequency of their undulation which could care the colour information. And for many waves, the speed of the wave is independent of the frequency.

But around 1800 a number of people began to prove that it must be a wave. This was via interference. If light is a wave, then it oscillates, like the surface of sea. If one wave meets another wave, then the up oscillation of one wave meeting the down of another would cancel, and one would have no light there. If the up oscillation ( down) oscillation of one would meet the up (down) of the other, they would add and the intensity of light would be higher.

Thomas Young (also famous as one of the people who figured out how to translate hieroglyphics on the Rosetta Stone, and the developer of a temperament for tuning pianos, harpsichords, organs,...) developed an experiment in which he scratched to parallel and very close transparent slits into a glass slide covered with smoke and shone light on it. Looking at the light transmitted, he found that there was not simply a blob of light on the other side, but a bunch of parallel lines of brightness. parallel to the slits. If he put in just one slit, he would see what looked like a blob of light. He ascribed this to the difference in travel time from each of the slits to the point of observation. In some place that difference was such that wave crests from one of the slits met wave crests from the other, and troughs met troughs, and in others, crests met troughs and the light was cancelled. There was no way that a particle picture of light could produce this effect. Particle would just add. A particle from one slit would meet a particle from the other and they would just make twice as many particles.


A photograph of the shadow of ball bearing
in the light from a point source.
Note the tiny point of light in the middle of the shadow.
Note also the rings at the edges of the shadow
which also due to interference.

A number of others also came up with demonstrations of the wave nature. Poisson in France showed that if you look at the shadow of a sphere cast by a small light source, that shadow had a bright spot right in the middle. This could only come from the interference of light which was bent around the edges of the sphere (again because of the wave nature) and all constructively (crest meet crest) interfered right in the middle where the distance from the edges of the sphere were all the same. Again, there is simply no way that a particle picture of the nature of light would work.

But this wave nature of light raised the problem as to what the light travelled in. Waves are disturbances of a medium, and what was the medium? They gave it a name --the Aether, or the Luminiferous Aether-- but had not other reason to believe it exists. It must be really really strange as a medium. Light travels incredibly quickly-- about 300000 km/sec. That it travels quickly makes sense from the very small aberration angle Bradley found. But for waves in a medium, and especially for waves which vibrate in a direction perpendicular to the direction of travel, which light seemed to do, the material would have to be incredibly stiff. It is the stiffness that causes the next bit of material to start moving when one piece starts moving. the less stiff the material (think of jello) the slower the waves. The stiffest material, say steel, has a sound speed of about 5km/sec. This is about 100000 times as fast, and sthe stiffness has to be the square so either the aether would have to be 10billion times as stiff, or 10billion times less dense than steel (but maintaining steel's stiffness) or...

How could the earth travel through such an incredibly stiff material and now be slowed down.

Experiment were carried out to try to see if the earth did travel through this material. If the earth were moving through the aether, the velocity of light in the same direction as the earth moves would appear to be slower, while in the opposite direction it would be faster, and in the transverse direction it would be intermediate. But this would mean that if light travelled up stream to a mirror travelling with you (and the earth) and then back down, it would take slightly longer than if it were travelling in a direction across the the direction of travel. Michelson and Morley in Cincinnati tried to do this experiment, using the fact that the earth travels in different directions at various times of the year. They found no effect. Light travels at the same speed no matter which direction it went. The option that the earth is at rest simply was not viable anymore.

Maybe when the earth went through the aether, it dragged along the aether with it, so that there is a bubble of aether around the earth with was dragged with the earth. But why would that not lead to friction and eventually stop the earth? And people (Fizeau) did experiment to see if light travelling in flowing water ( which should drag the aether) was different than say in air. No effect.

Faraday and Maxwell

In the meantime there was a whole bunch of work on electricity and magnetism. Both has been discovered thousands of years ago. The static electricity when say one uses fur to rub a piece of glass was well known, and it had been discovered that two things which one had "charged up" would attract or repel each other, with a one of distance squared force just as with gravity. Volta had developed the first batteries, and could make current flow.

Magnetism, in the form of Lodestones (naturally occurring pieces of iron), had been known for thousands of years, with a mysterious attraction as well for certain materials of for other lodestones. Ampere had shown that there was some sort of mysterious relation between these flowing charges and magnetism. A flowing current would deflect a magnet.

Micheal Faraday, his father was a blacksmith in London, received virtually no formal education, and taught himself to read and read voraciously, helped by his being apprentice to a bookbinder. He brought himself to the attention of H Davy, one of the top chemists in London, who hired him as a research assistant.

He became interested in especially magnetism, and its interaction with electrical currents. He invented the first motor, a wire hung above a magnet and the bottom immersed in a bath of mercury. The wire rotated abound the magnet. He showed that if you move a wire past a magnet, or a magnet past a wire, an electric current would be induced in the wire, the basis of all electromagnetic generators (eg that power your home).

One of his biggest contributions to theory was the idea of the "field". While Newton had thought of the gravitational force as just reaching out from say the sun to the planet and accelerating the planet, with nothing in between, Faraday began to think of both magnetism and electricity as existing in the vacuum outside the magnet. He thought of the wire in a motor as "cutting the lines of magnetism" with existed for him outside the magnet, and this resulted in a voltage in the wire which created the current. He thought of a charge as having lines of electricity around it, and this thing is what would interact with other charges and cause that other charge to feel a force.

For a magnet you could "see" those lines of force by sprinkling iron powder over a magnet. The little pieces of iron would arrange themselves into strings which pointed in certain directions. For him these were the iron filings rearranging themselves along the magnetic lines, making them visible. They were not particles, they were some kind of stuff which penetrated almost every where, and had values everywhere as if they were a king of fluid, which has a temperature say everywhere. In the case of the fluid, the temperature is a property of the fluid itself, it is not something extra. For him, the magnetic field was a separate property only of itself, caused by the magnet, but separate from the magnet. One could regard the magnetic field, as Newton would have, as just the force from one object (one magnet say) to another. But Faraday gave a different picture that physicists could use to imagine the world around them. They are things that exist not because of the existence of other things made up of particles, but in their own right, and everywhere. The compass needle points to the north (magnetic) pole not because of some mysterious force between the top of the earth and the little magnet, but because the earth creates (because of convection currents in the hot liquid interior which is largely iron which make the interior act like a generator which creates electrical currents which have magnetic fields around them) magnetic fields outside the earth, and the compass magnet interacts with the magnetic fields outside the earth. It was this concept of fields, in addition to his incredible ability to make use of electric currents and magnetism, which was one of his chief legacies for physics in the future. Because of relativity, it turned out in the 20th century that all physics had to be described, not as particles, which were in a fundamental way incompatible with special relativity, but as fields.

Maxwell

It was the Scotsman with well-to-do parents, James Clerk Maxwell(1831-1879), U Edinburgh Undergraduate and Cambridge Graduate student, and one of the most brilliant Mathematics students. After becoming a Fellow at Trinity in Cambr. he applied for a job at Aberdeen U, and got it, where he would lecture for 15hrs a week in addition to his research. Like Newton he was fascinated with optics and especially colours, and developed the colour chart still used, and postulate that the eye makes up the colours it sees from three separate colour receptors. He wrote an essay for the Adam's prize given by St John's college, Cambr. and won it with an essay arguing that Saturn's rings must be made up of particles and dust, and could not be solid or fluid, as both would be unstable. (This theoretical argument was only confirmed when the Voyager satellites flew by Saturn). But none of the above is why he is of interest here. That was done by his work on Electricity and Magnetism. Through Coulomb, Ampere, Faraday and others, one had a fairly decent set of equations which related the Electric and magnetic fields. Electrical currents could create magnetism. Magnetism could affect electric currents. But there was a gap in the equations. If one placed a capacitor-- two large plates with a tiny gap between them, one could have a current which caused charges to accumulate on the metal plates, with an electric field produced between the plates. The circuit was not quite a closed one, because of the gap between the plates. But the equations for current producing magnetic fields had a certain mathematical structure, that suggested that in addition to the current producing magnetism, that changing electric field between the plates should also produce magnetism. Not just currents but also changing electric fields should, if the suggestive equations were right, produce magnetism as well. Faraday had already shown that changing magnetism produced electric fields. Maxwell added a term to the known sets of equations, an suddenly "upset" everything. The changes in the electric fields produced magnetic fields. The changing magnetic fields produced electric fields. The two could support each other. One of the first things he noticed about these equations was this support produced waves of changing electricity and magnetism. But more radically, when he calculated the speed of such waves, what came out was the speed of light.

Noone had suspected that there was any link between electricity, magnetism and light. They were simply two entirely different things. How could they be related? And here were electromagnetic waves, which travelled at the same speed as light. These waves were furthermore of a peculiar structure. The changing electric field would produce a magnetic field perpendicular to itself. The changing magnetic field would produce and electric field perpendicular to the electric field. And both would be perpendicular to the direction in which the wave travelled.

Faraday's concept of fields, of electricity and magnetism being independent of the what ever formed them, was completely crucial to this enterprise. Without that notion of independence Maxwell would have got nowhere. While the equations he worked with would have been completely consistent when written as various kinds of forces of one set of charges on another, waves were something different. They were something which was independent of the sources. They existed and travelled on their own.

When he started, Maxwell, primarily in order to keep straight and have an intuition for the kinds of mathematics he was doing, saw both electricity and magnetism in terms of a mechanistic result of a space filled with a sea of little wheels and gears. Just as two gears both rotating in the same direction, need a little "idler gear" between them, so he visualized the magnetic field as if it were those big gears, and the idler gears were similar to his electric fields. If the two big gears rotated at slightly different rates, the idler gear would more. Or if the idler gears moved, the big Greer would be caused to rotate at different rates.

But it became clear to him very quickly that the equations he found could stand on their own. The gears were superfluous. One could postulate the existence of the electromagnetic fields on their own, affecting each other but cause by nothing else, including a sea of gears. However he still believed that there was a Luminiferous aether despite his rejection of his model of it. But, while one could dispense with the gears ( and he did, after the first edition of the book in which he presented his results, those gears never again reared their heads), one could not so easily get rid of the problems. The electromagnetic waves had one speed only. They could not be slowed down in the vacuum (because of interactions with matter they could have their speeds altered, but that was only with other matter). That would seem to imply that there was a rest frame for the universe, something Newton had firmly believed existed, but Galileo and Huygens rejected. Only in that frame would the speed of light be the same in all directions. If one were moving, then one could catch up to the waves, and the waves travelling with you would be travelling more slowly (according to you) than the was travelling opposite to your motion. Only if you were at rest would the velocity be the same in all direction.

As mentioned, the Michelson-Morley experiment was precisely designed to see this effect because of the earths velocity. So, while Maxwell's electromagnetic waves did not need a medium to travel in, they still had the same problems as waves in a medium did. The aether need not be there with all of problems of stiffness and of friction, but the analysis of the behaviour of the waves in the aether did not really depend on the aether. Getting rid of the aether did not solve many of the problems that had been identified.

How to get around this, especially when the experiments indicated that effects of motion, which were there in Maxwell's theory, simply did not exist?

Lorentz and Poincare

The primary attack on this problem ( by a couple of the people worried about it) was to say, well maybe there is something strange about matter. For example, in the Michelson Morley experiment, the problem was that the change in the speed of the waves upstream and downstream caused the trip up/downstream to take slightly longer than the equal length trip across the stream. Matter might well be made up of matter, and that matter had charges of various types in it. Maybe the problem is in the way that matter behaves. What is because of its motion, through the aether, or through the electromagnetic field, the matter changes and compresses very very slightly all you would need as a fractional compression equal to $\sqrt{1-velocity^2\over speed~of~light)^2}$. Even for the earth this is tiny. The velocity of the earth is about 15Km/s, while the speed of light is 300000km/sec. The ration is 5/100000 and the square of that is 25 in 10 billion. This is tiny. It is only surprizing that Michelson and Morley could do an experiment so accurately.

Maybe the length of the apparatus got slightly squished by the motion through the aether.

Of course the question would be why it would get squished only by just enough to give a zero result to M-M. After all most matter has very different properties. Take Jello and compare it with high strength steel. They react totally differently to stresses. Why would the stuff that their experiment was made from react is just just the right way? i

They also looked at Maxwell's equations. They could ask-- how would things have to transform so that Maxwell's equations would not change? Especially Henrick Lorentz spent time on this. He discovered that if he changed the Electric and Magnetic fields it was not sufficient. He also had to change the structure of space and time. For example the above length contraction was seemingly necessary, but not sufficient. A similar transformation was needed on time, but this for him was an artificial, not real time. How could one make matter behave so as to make the EM radiation at least look like it was not picking out some special inertial frame?

copyright W Unruh (2018)