There are three important characteristics that light possesses in virtue of which it is important for understanding space and time. The first is that the speed of light is finite. The second is that the speed of light is a "fastest signal," that is, no information can be transmitted from one part of the universe to another in a faster time than it takes a light signal to travel between those two points. Light thus acts as a limiting velocity, the significance of which turns out to be revolutionary for our understanding of space and time. The third is that, unlike any other stuff that travels with a finite speed, the speed of light is a constant for all observers. It should be immediately obvious that this fact alone presents a difficulty for Newtonian mechanics and the principle of Galilean invariance which is at the heart of that theory. For according to the principle of Galilean invariance, if two observers are moving with velocity V with respect to one another and the first sends a light signal (which he sees travelling at speed c) to the second, then the second ought to see the speed of that pulse of light as c+V or c-V depending on whether the two observers are moving towards or away from one another. See Figure 10-1
The resolution of this conflict led to the development of the Special Theory of Relativity.
In this chapter, we begin with a brief sketch of the discovery of the finite speed of light. Having established that light is something that travels with a finite speed, speculation focussed on what kind of stuff light was. A brief discussion of the classical alternatives, wave or particle, follows. The next section deals with the area of electromagnetic researches in the l9th century especially the experimental work and theoretical speculations of Michael Faraday and the development of a successful theory of electromagnetism by James Clark Maxwell in 1873. These results suggested that light is an electromagnetic phenomena, a wave disturbance being propagated in a luminiferous ether. Finally, this suggested to some that there might be a way to detect absolute motion (and, hence, verify the existence of absolute space) by using electromagnetic phenomena (subject to Maxwell's Theory) rather than mechanical phenomena (subject to Newton's Theory). The Michelson-Morley experiment was one such attempt. It is described and the null results discussed. Various attempts were made to explain away the null result, with the Special Theory of Relativity, based on Einstein's assumption that the speed of light is a universal constant for all observers, ultimately proving to be the most successful. The significance of the third characteristic, that the speed of light is a limiting velocity is explored in the following chapter. II. The Finite Speed of Light.
According to Aristotle, things are transparent in virtue of the fact that they contain within themselves a certain substance which is "also found in the eternal body which constitutes the uppermost shell of the physical Cosmos Li.e., the ether]" (De Anima, 418b8). Light is a property of this substance, an excited state, as it were, of the ether. Darkness is the opposite quality, or quiescent state of the same substance. As such, Aristotle denies that light is a thing at all. He also denies that it is proper to speak of light as "travelling." He says: Empedocles (and with him all others who used the same forms of expression) was wrong in speaking of light as 'travelling' or being at a given moment between the earth and its envelope, its movement being unobservable by us; that view is contrary both to the clear evidence of argument and to the observed facts; if the distance traversed were short, the movement might have been unobservable, but where the distance is from extreme East to extreme West, the drought upon our powers of belief is too great." (De Anima, 418b20ff). Aristotle's point seems to be that if light travelled from place to place at a finite speed then when the sun rose in the morning (in the extreme East) we should see first part of the sky light and the rest dark as the light travelled from the sun (in the East) to the West. We see no such thing. As soon as we can see that it is light in the East, if we turn immediately to the extreme West, it is light there as well. Aristotle's conclusion is that the substance which acquires the active property of light (and hence, appears transparent) does so all at once, that is, instantaneously, much as a container of water seems to turn instantaneously to ice when frozen. Aristotle's conclusion, needless to say, does not follow from his correct observation. It is compatible with the facts he cites that the speed of light should be finite although very, very fast. What prevents Aristotle from seriously entertaining this possibility is a certain lack of imagination since he thinks that something travelling at such a great speed as would be required by the facts is too great a strain upon our powers of belief.
Nevertheless, almost all writers on the subject up to the time of Descartes held to the view that light was instantaneously transmitted (which is to say, in effect, not transmitted at all since something can be properly said to be transmitted from A to B only if one can speak of its being at A or between A and B at some time before it is at B. Instantaneous transmission precludes this possibility). Before turning to Descartes and his view, we should say a word about Galileo and his attempt to put the question to experimental test. Galileo's discussion occurs in the First Day of the Dialogues Concerning Two New World Sciences which appeared in 1638. The basic idea was as follows. Two experimenters, each equipped with a lantern situate themselves some distance apart. Each lantern is equipped with a shutter that can be opened or closed. Initially, both stand with their lanterns shut. The first experimenter A then opens his lantern. Immediately upon seeing the light from A's lantern, the second experimenter B, opens his as well. A then notes when he sees the light from B's lantern. If the transmission of light is instantaneous, and if the experimenters are sufficiently skilled at opening and closing their lanterns, then, Galileo reasoned, there should be no sensible lapse between A's opening the shutter on his lantern and his seeing the light from B's lantern. We know from long experience that the speed of light, if finite, is extremely fast, hence, Galileo suggests that the experiment be performed at distances of 8 to 10 miles, where the observers would use telescopes to see each other's lanterns. As a matter of fact, in the Dialogues, one of the participants (Salvatio) reports that such an experiment was actually performed at a distance less than one mile. The result was that he was not able "to ascertain with certainty whether the appearance of the opposite light was instantaneous or not; but if [it is~ not instantaneous it is extremely rapid -- I should call it momentary;" (Galileo, Two New Sciences, 1914, 44). Salvatio goes on to suggest that he, at least, is of the opinion that the speed of light is finite, although very fast, on the grounds that when one observes lightning from a distance of 10 miles or so, one can see the lightning begin at a certain point in the clouds and then spread immediately to the surrounding clouds. With this remark, the discussion is brought to a close and the dialogue moves into other topics. Thus, Galileo might be inferred to accept the view that the speed of light is finite although extremely rapid. We now know, of course, that the evidence on which Galileo relied is misleading.
In the first place, although the speed of light is finite, it is so rapid that there is no hope of ever determining that fact using the experimental setup described by Galileo. Galileo, as his discussion shows, was sensitive to the fact that, unless practiced, the experimenters would not react swiftly enough to get a meaningful result. Modern psychological measurements of reaction times show that the time it would take for a human observer to carry out the sequence of operations that Galileo prescribes is much longer than the time of transmission of light from one observer to another even at a distance of 8 to 10 miles, let alone a distance of less than one mile. The human observer, for this purpose, is an inherently defective instrument. The tentativeness with which Galileo reports the result of the experiment actually tried, thus, does not reflect in any way the possible finite speed of light but, at best, is a measure of the reaction times of the observers in question. We should note that the experiment described by Galileo is not, in principle, impossible since the reaction time error can be made arbitrarily small by making the distance between A and B large enough. This can, in fact, be practically achieved by sending one observer off the earth in a rocket ship. Thus, the delays in transmission from Houston to the Apollo astronauts is modern evidence that the speed of light (in its guise as a radio signal) is finite. The further apart the observers are the more pronounced is the effect. The furthest objects that earth bound man has been in two way contact are the spaceships of the Voyager missions to Saturn and Jupiter. The signal delay from the orbit of Jupiter is about 42 minutes. Galileo's experiment can also be performed on the earth if it is suitably modified. One can achieve great distances by having the beam of light undergo multiple reflections using mirrors. If, in addition, better timing devices are used than were available to Galileo and his contemporaries, it is possible to perform a terrestrial determination of the speed of light. Such experiments were first performed in the 1800's by Fizeau (1849) and Fizeau and Foucault (1850).
The second misleading aspect of Galileo's discussion is his interpretation of the facts about distant lightning flashes. The problem is that the effect that Galileo (correctly) observed is not due to the finite speed of light but rather to the fact that lightning is an electrical disturbance which does not travel anywhere nearly so fast as does light. Nonetheless, with Galileo we see the modern emergence of the view that the speed of light is something which is open to experimental analysis and that there may be grounds for thinking that the speed of light although enormous is not infinite.
Descartes's published views on light first appeared in the Dioptric in 1637. Descartes was convinced that the speed of light was infinite, not only on experimental grounds, which were for him not so important, but on theoretical grounds since his whole conception of physics demanded that the speed of light should be infinite (Sabra, 1967, 49). Recall that, for Descartes, the Universe is a plenum. In his physical system, Descartes sought to explain the observable phenomena of this Universe by means of mathematical principles and certain physical postulates (much as Newton had done later with his three laws of motion and law of gravity). Sabra gives the following account of the structure of the Cartesian cosmos: "The formation of the stars and the planets, and the spatial distribution of the elements constituting, respectively, the planets, the heavens and the stars are described as follows. Having supposed that the original matter was actually divided into parts of various magnitudes which have been moved in various ways, and considering that rectilinear [straight line] movement is impossible in this solid plenum, the parts of the original matter assume a somewhat circular movement, around different centers. In the process of pushing one another some larger parts are separated so as to constitute the bodies of the planets. They are characterized by opacity and are known as the third element. Others are crushed and formed into small round particles which make up the second element, a fluid subtle matter which fills the heavens as well as the gaps between the parts of the grosser bodies. Fluidity of the subtle matter simply consists in the fact that its parts are moving in various ways among themselves with great speed. It is characterized by transparency or ability to transmit the action of light. Still smaller parts, forming the first element, are scraped off the subtle matter to fill the interstices between its little globules, and the surplus is pushed to the centers of motion thus forming there the bodies of the sun and the stars. Each of these has a rotational motion in the same direction as its proper heaven which forms a vortex carrying the planets around the centre (Sabra, 1967, 53)"
The speed of light is infinite in such a scheme because the bodies of the second element are so closely packed together that a disturbance is transmitted instantaneously, much as, so Descartes thought, an impulse imparted to one end of a stick is transmitted instantaneously to the other end (Sabra, 1967, 54). Because of Descartes's equation of matter with extension, it followed that seemingly empty spaces contain as much matter as these spaces which are occupied by more obviously solid bodies. The net result is that Descartes's plenum is an incompressible fluid, through which shocks travel instantaneously.
These theoretical considerations were based on the theoretical principles of Cartesian physics coupled with a mechanical analogy (a blind man with his stick). However, Descartes did cite experimental or rather observational evidence which he took to support his view. In response to an unknown correspondent in 1634, someone who believed in the finite speed of light and had suggested an experiment similar to the one discussed by Galileo in the Discourses, Descartes cited instead what he claimed was a better natural experiment the results of which had been observed thousands of times (Sabra, 1967, 57).
The experiment involves eclipses of the moon. The moon is eclipsed when the Earth gets in the path of the sun blocking its rays from being reflected from the moon. Consider the following typical lunar eclipse situation:
Suppose that when the earth is at B, the sun is perceived to be at A. Suppose in addition that the speed of light, although large, is still finite. If it takes half an hour for light to travel from B to C then, if the moon is to appear to be eclipsed at C, it must not be there yet. Suppose that the moon is seen just to enter the Earth's shadow at point C. That shadow was created by the Earth's blocking the sun's rays at B at To~ It then takes half an hour for this effect (the shadow) to reach the point C. At this time To + 1/2 hour the moon is just reaching C. Hence, at To the true situation looks like this.
At T + 1/2 hour, when the moon just enters the Earth's shadow at C the situation looks like this.
(The scale is somewhat exaggerated. The sun is presumed to be at rest.)
At T + 1/2 hour, the moon is still visible from the Earth and appears to be at C'. The effect of the eclipse will only be visible in a further 1/2 hour when the effect of the moon entering the Earth's shadow at C is reflected back to the earth, which by now has moved to B". This situation is illustrated in Figure 10-5
From the Earth at B", the moon is apparently being eclipsed at C (although its actual position is C") whereas the sun appears still to be at A. If one imagines that the Earth is at rest and the fixed stars rotate about it, then it is possible to fix the (apparent) motions of the sun and the moon with respect to the background of fixed stars. If the speed of light were such that it took an hour to complete the round trip distance from the Earth to the moon and back to the Earth again, then the calculated angle ~A'B"C is non-negligible. This reconstruction of Descartes's argument is based on the account of Huygens who takes the round trip time to be 2 hours rather than 1. Under that assumption ~A'B"C = 33deg.. But, the observation of thousands of eclipses indicates that when the moon is eclipsed, the sun and the moon are at opposite points in the ecliptic (i.e., the moon appears at A' rather than at C). Descartes concludes, therefore, that the speed of light is not finite. Again, his error was in not allowing his imagination free enough rein. The astronomical data does not rule out a finite speed for light, although it does rule out that it would take anything like an hour for the round trip time from the earth to the moon. Given that the distance from the earth to the moon is approximately 240,000 miles, the astronomical data entails that the speed of light must be much greater than 8,000 miles per minute. Perhaps, for Descartes in 1634, such a finite speed was inconceivable. Even so, Descartes was no doubt more persuaded by the theoretical demands of his system than by any such experimental constraints.
Nevertheless, in less than 50 years an astronomical observation had been made which gave the first solid evidence in favor of a finite speed for light.
In 1676, the Danish scientist, Ole Roemer, published an explanation of certain anomalies in the eclipses of Jupiter's moons by Jupiter which involved assuming that the speed of light was finite. Roemer's method resulted in precise determination of that velocity, calculated by Roemer to be 220,800 km/sec. which compares to the best modern determination of 299,792 km/sec. Roemer's method was based on anomalous eclipse behavior of Jupiter's innermost satellite. At the time, his conclusion was not universally accepted because his account implied that similar anomalies should be observed with respect to the other Jupiterian satellites, but were not (see Sabra, 1967, Chapter 8). The account given below is based on Huygens (Huygens, 1962, ).
The basic observations relate to the eclipses of the moons of Jupiter. The innermost moon rotates rapidly around Jupiter and is eclipsed roughly every 42 1/2 hours. As the earth travels in its orbit around the sun away from Jupiter, the observed occurrences of eclipses occur later than predicted. When the earth swings around the sun and starts travelling towards Jupiter, the observed eclipses occur earlier than predicted. Roemer showed that these results could be explained on the hypothesis that the speed of light is finite and that it takes light approximately 22 minutes to travel the distance of the diameter of the earth's orbit about the sun. The following diagram, adopted from Huygens, illustrates the point.
Suppose the Earth at El. If one imagines the Earth at rest, then the time between successive emergences of Jupiter's satellite (in orbit M) from the shadow Jupiter casts is 42 1/2 hours. Now assuming that this period is a constant, it ought to repeat itself regularly. A person fixed at El would then see the Jupiterian moon emerge from eclipse every 42 1/2 hours (ignoring for a moment the movement of Jupiter itself around the sun). However, of course, as Jupiter's moon is orbiting around Jupiter, the Earth is orbiting around the sun. Thus, if an observer on the Earth at El sees the moon emerge at 0, as it orbits around Jupiter and is eclipsed again, the earth has moved in its orbit towards E2. Let E2 represent the position of the earth in its orbit after 30 X 42 1/2 hours. If the speed of light were infinite, then an observer on the Earth at E2 would see Jupiter's moon emerge at O for the 30th time since the observed eclipse from El. As a matter of observational fact, however, Jupiter's satellite does not appear at O when the Earth is at E2, but only sometime later. A similar anomaly, in the opposite direction is observed as the earth moves from E3 to E4. Suppose that Jupiter's moon is observed at E3 just to enter Jupiter's shadow at I. Were the Earth at rest at E3, we would expect to see it at I 42 1/2 hours later. Actually, in that time the earth has moved somewhat towards E4. Let E4 be the position of the Earth 30 X 42 1/2 hours after E3. If the speed of light were infinite we should expect to observe Jupiter's moon at I just entering the shadow when the earth is at E4. As a matter of fact, however, the 30th eclipse of Jupiter's moon (after that observed at E3) has already started by the time the Earth gets to E4. Thus, on this leg of the Earth's orbit the eclipses are early, where on the other leg of the Earth's orbit the eclipses are late. Roemer hypothesized that the lateness was due to the fact that the light from O had to travel a distance PE2 further to get to E2 than it did to get to El. Likewise, the eclipse at E4 was earlier than expected because as the Earth moves from E3 to F.4 the light from I has less far to travel. From the discrepancies between the times of the predicted eclipses and the times of the observed eclipses, and taking into account the motion of Jupiter in its orbit around the sun, Roemer was able to estimate that the time for light to travel the distance dld2 was about 22 minutes.
It is clear from the above account that a similar effect should be observed with respect to the other Juperiterian moons. No such effect was observed. An alternative explanation argued that the observed effects were due to some irregularities in the orbit of Jupiter's innermost moon. Both Huygens and Newton, however, accepted Roemer's reasoning. Eventually, as other methods for measuring the speed of light were devised which gave results all congruent with one another, the finite speed of light was accepted as a hard fact.
Before turning to a consideration of the competing theories about the nature of light, we turn to a discussion of one other early determination of the finiteness of the speed of light: that of James Bradley in 1728. It was, in fact, Bradley's determination of a velocity for light which was in close agreement with that determined by Huygens which finally convinced everyone that the speed of light was, indeed, finite.
Bradley's method was based, as was Huygens's, on an astronomical anomaly. Bradley was not looking for a method for finding a velocity of light but was rather investigating the problem of parallax. Parallax is the apparent motion of certain stars in the heavens due to the rotation of the earth around the sun. It had originally been predicted by Copernicus, but the effect was so small that it was not experimentally detected until 1838. The effect is produced by the annual motion of the earth around the sun in the following way. Figure 10-7
The effect is produced for all stars but is greater for near stars and lesser for far stars. If the distance of a star A from the earth is sufficiently far, then the change in position of the earth as it orbits around the sun is miniscule in comparison and the net effect is that the star A (assumed at rest) always appears to be in the same place in the sky relative to the other stars. Now consider a closer star B. If we assume that A is fixed at some great distance, then it is clear from the diagram that, as the earth goes around the sun, the apparent position of B moves in an ellipse with respect to A. The size of this ellipse is a function of how far away from the Earth B is. The failure to find such an effect was prima facie evidence against the Copernican view. Copernicus and his defenders argued that the effect was not readily observable because the stars were so far away. They were right. Bradley was looking for this effect when he stumbled onto another effect which is called stellar aberration.
Bradley discovered all stars undergo an ellipsoidal displacement as the Earth orbits the sun. This effect is, unlike parallax, independent of the distance from the Earth to the star, but does depend on the position of the star with respect to the orbital plane of the Earth and the sun. The effect is a maximum for stars at right angles to the Earth's orbital plane and reduces to a straight line oscillation for stars in the Earth's orbital plane. The following diagram illustrates the effect.
Consider a star A, positioned at right angles to the Earth E. Imagine a telescope on the Earth at E pointed at A. The light from A enters the telescope
at T. If it takes light a finite time to travel then the light will reach the focus F at a time LC later, where C is the speed of light. In that time, the telescope will have moved a distance V(~), where V is the velocity of the Earth around the sun.
The image of the star will appear displaced from the center of the telescope by a like amount. If we now imagine the Earth and telescope to be at rest, the effect would be that the apparent position of the star has been displaced by the angle ~. Six months later the telescope has to be tilted by ~ in the other direction. That the apparent position is displaced is revealed by the fact that the velocity of the earth changes direction and magnitude. An analogous phenomenon has been known to plague motorcycle riders Suppose you are idling on your motorcycle at a stop sign when a rain shower begins. Assume that, as you sit there waiting for the light to change, the rain falls gently straight down on you. The light changes and you start off. All of a sudden, the direction (and intensity) of the rain changes. The rain now is falling at an angle into your face. As you slow down, the angle of fall apparently changes to the perpendicular again. To an observer at rest on the sidewalk waiting for a bus, the angle of fall has remained constant straight down. The shift in direction (and intensity) that you feel on the motorcycle is due to the fact that you are moving. If you decide to try to get the rain at your back by reversing your direction, you find it in your face again. Assuming that the real source of the rain has not changed and that the speed of the rain drops is finite, you conclude that the apparent source is an aberrational effect due to the combined motion of the rain and your motorcycle.
If the Earth were at rest, no adjustments would have to be made with respect to any star. Once located in the background of fixed stars the apparent position of a star would not change. Similarly, if the speed of light were infinite, then no such adjustment would have to be made either, for where the telescope points at A, the light from A entering the telescope at T falls on F at the very same instant. Thus, the telescope does not have time to move from its initial position and the image of A appears at F right in the center of the telescope just as we wanted.
For a star B, in the orbital plane of the Earth, a similar effect is found, except the apparent motion of B is an oscillation in a straight line. It should be clear that the required angle of displacement ~ will vary from O (for stars in the orbital plane of tile earth) to a maximum for stars at right angles to the orbital plane of the Earth. The angles are also dependent on V, the orbital velocity of the Earth which varies with the Earth's orbital position (Recall Kepler's Second Law). Knowing the maximum orbital velocity of the Earth, Bradley was able to estimate the value of C, the speed of light. His measurements were in close agreement to the value determined by Huygens and established once and for all that the speed of light was finite. III. Wave or Particle.
Having determined that the speed of light was definitely known to be finite by 1730, we turn to a consideration of the prevailing views as to the nature of light. We have already observed that, for Aristotle, light was not a thing at all but rather a property. Descartes's view was that light was a pressure, in effect, a shock wave transmitted through an incompressible fluid. The dominant view of the nature of light in the 1700's was that attributed to Newton, namely, that light was a particle. On this view, the light from a star, or any other source, was conceived to be a stream of small particles. A number of phenomena could be easily explained, at least, qualitatively, on this view. Light was observed to travel in straight lines and cast sharp shadows. Light as a hail of particles easily accounted for this behavior. The reflective properties of light could be easily understood on the analogy of bouncing a ball off a wall. When light passed from one transparent medium (e.g., air) to another (e.g., water), it was observed to bend toward the normal (perpendicular) to the surface of the denser medium. Newton adduced an ingenious explanation of this fact based on the assumption that light was a stream of particles, which in view of their attraction to the particles of the material medium travelled faster in denser media than in rarer ones.
The major rival view was put forth by a contemporary of Newton, Christiaan Huygens. The particle view was not capable of explaining all the facts about the behavior of light. One particular fact that the particle theory could not handle with ease is the ability of two beans of light to intersect and continue on their original course without any apparent disruption. If light were a stream of particles, one would expect that two such intersecting beams would scatter each other beyond repair. Another intriguing fact was the discovery that certain materials, in particular a crystal known as Iceland spar, were capable of producing multiple refracted beams when light was passed through them.
Huygens, a Cartesian of sorts, suggested that these phenomena could be explained by assuming that light was propagated as a wave through a medium he called the ether. Huygens showed how one could explain the rectilinear propagation of light, and also reflection and refraction, on the wave model. The wave theory of light, unlike Newton's particle theory, predicted that the velocity of light in denser media should be slower (not faster) than the velocity of light in less dense media. At the time, of course, there was no way to put the question to an experimental test because of the limitations of the existing technology. As they stood, neither view was completely successful, and the particle theory won the day more on Newton's prestige than on account of any intrinsic merits of its own. It was not until 1850 that the French physicist Leon Foucault performed an experiment that showed the speed of light in water was slower than the speed of light in air that the wave theory began to become the dominant view. Even so, both views turned out to be incorrect, although both turned out to be partly true. The wave theory of light, as the modern theory has it, is quite different from that proposed by Huygens. The crucial experiment of Foucault which supposedly disproved the particle theory turned out to be misleading. In the 20th century, further indications that light could, sometimes at least, act as if it were a particle, showed that the results of Foucault's experiment showed not so much that light was not a particle, but rather that it was not a Newtonian particle, that is, not a particle obeying the laws of Newtonian mechanics. In order to explain these newly discovered properties of light a new mechanics had to be invented --quantum mechanics.
But this is to get ahead of the story. The crucial development in the theory of light that led to its having a dramatic impact on our understanding of space and time was the realization, in the last half of the 18th century, that light was an electromagnetic phenomena. It is to these developments that we now turn. IV. Electromagnetism and the Concept of a Field.
In the beginning of the l9th century, experimental research suggested that electrical and magnetic phenomena were related. It was discovered that a moving wire which was conducting electricity generated a magnetic force and that moving magnets in the presence of an electrical conductor such as a wire could induce a current in the wire. That certain materials were magnetic had been known since ancient times. Many saw an analogy between gravitation and magnetism. Both seemed to be forces that acted at a distance, that is, that had effects over long distances without any contact between the source and the object affected. In the case of gravity, such action had seemed mysterious both to Newton and his critics. Leibniz had urged, against Newton's physical theory, that gravity, understood as a mysterious force that acted at a distance, involved the introduction of "occult qualities" back into physics from which they had been purged by Descartes and Bacon. Insofar as magnetism was a force that acted at a distance, it seemed mysterious as well. By the 1830's a number of empirical laws characterizing electromagnetic phenomena had been discovered, but as yet no coherent "Newtonian" system for electricity and magnetism had been produced.
Michael Faraday was one of the foremost of these experimental investi- gators and his own researches plus his reflections on the work of others convinced him that an action at a distance concept would not be adequate to explain electro-magnetic phenomena. Instead he proposed that electrical charges and magnets were the sources of "lines of force" which pervaded the space around them. The "lines of force" can be discerned by a simple experiment. Place a magnet under a sheet of paper and shake some iron filings on top of the paper over the magnet. The filings will then arrange themselves in a characteristic fashion thusly, in Figure 10-10 .
The filings provide a trace for the lines of force generated by the magnet. Faraday explained this result by postulating the existence of a real entity which was something which existed throughout space and which was modified by the presence of magnetic and electrical sources. Faraday thought these lines of force to be real physical forces (as opposed to merely mathematically convenient fictions) (Faraday, Experimental Researches, III 1855, 532). One of the factors he adduces in favor of the real existence of such an entity is "the strong conviction expressed by Sir Isaac Newton, that even gravity cannot be carried on to produce a distant effect except by some interposed agent fulfilling the conditions of a physical line of force..." (Faraday, 1855, 532).
This agent, which Faraday took to be a real physical agent, came to be known as a Field. In 1873, James Clerk Maxwell produced a unified theory of electromagnetic phenomena which turned out to be comparable to Newton's mechanics in its scope and explanatory power. Maxwell's conception relied heavily on the field idea as developed by Faraday, and Maxwell's equations are equations that describe the behavior of these electromagnetic fields.
One result of solving Maxwell's equations was that certain solutions entailed the existence of a wave disturbance propagated through the ether with a characteristic velocity with respect to the ether which was identical, within experimental error, to the experimentally determined speed of light. Maxwell proposed, therefore, that light was an electromagnetic wave phenomena.
In a short time, the success and power of Maxwell's theory led it to be considered a rival to Newton's mechanics. After the development of Newton's mechanics and its success, a program was developed for showing that all physical phenomena could be explained by Newtonian principles. Electrical and magnetic phenomena had resisted being so understood. Maxwell's theory, and its success, provided another model: perhaps all phenomena, including gravity and mechanical (matter in motion) phenomena was all, at base, electromagnetic. Attempts were made to either reduce one theory to the other or to find some unified theory which would accommodate them both. These attempts were thwarted by a fact that turned out to be of crucial importance for our understanding of space and time. Recall that in our discussion of Newton's theory we mentioned that certain frames of reference which are non-accelerating with respect to one another form privileged classes called inertial frames. The key point is that the (mechanical) physics of a given situation looks exactly the same to any two such inertial observers. It is this fact which prevents such observers from detecting absolute velocities by kinematical considerations alone. The experimental arguments which Newton put forward for the existence of Absolute Space and Absolute Time, remember, relied on dynamical features of certain rotating systems. The crucial fact which stands in the way of unifying classical Newtonian mechanics and Maxwell's theory of electromagnetism is that the observers who see the same 'mechanical' physics do not see the same electromagnetic phenomena. This is connected with the fact that moving magnetic fields produce electrical currents. Suppose A is an observer at rest on a magnet which is situated next to a copper wire. A observes and measures a magnetic field but detects no current. His friend B now comes along and moves past A at constant velocity V. A and B are, from Newton's point of view, a pair of inertial observers. They should see the same forces at work. But, B reports not only that there is a magnetic field at A's position but also that there is a current (a fluctuating electrical field) in the wire near A. From the electromagnetic point of view, the physics of the situation does not appear to be the same for both observers. B, in virtue of his moving at a constant velocity with respect to A seems some-thing that A does not detect.
At first this seemed to some to be a bonanza because it apparently opened up the possibility of detecting whether certain observers might be in absolute motion by means of electromagnetic phenomena. One could provide, once and for all, direct experimental evidence of absolute velocities and, hence, conclusive proof of the existence of Newton's Absolute Space. The asymmetry between the physical world as seen by A and the physical world as seen by B seemed to conclusively establish that B was really moving with respect to A and that A was only apparently moving with respect to B.
From Maxwell's equations, one could deduce that the speed of light with respect to the ether was C, the speed of light. The ether, it was assumed, was at rest with respect to Absolute Space. The Earth, on the other hand, as it revolves around the sun cannot always be at rest with respect to Absolute Space. By measuring the speed of light at different times in the Earth's orbit, one ought to be able, using the Galilean transformations of Newton's physics, to detect the velocity of the Earth with respect to the ether. On the assumption that the ether was at rest, one would have succeeded in measuring the velocity of the Earth with respect to Absolute Space. The direct measurement of such an Absolute motion would be a vindication of Newton's view of Absolute Space and, in the process, silence rumblings of the contemporary relationalist, Ernst Mach. The most famous such experiment was performed by Michelson and Morley in Cleveland in 1887. Using a sophisticated device called an interferometer, invented by Michelson, very precise measurements were possible. The results were very puzzling. No matter when in the Earth's orbit the measurements were made, the result was always the same --the velocity of the Earth through Absolute Space was effectively 0. Instead of vindicating Newton, it seemed as if Aristotle and Ptolemy had been vindicated: the Earth was at rest. Copernicus and all the moderns were wrong. Such a conclusion was, of course, completely unacceptable. But, then, what was wrong? When the explanation of the null-result of the Michelson-Morley experiment finally emerged it spelled the end of the Age of Newton. We turn now to a discussion of that experiment and its null result. The Michelson-Morley Experiment
In 1887 A. A. Michelson and E. W. Morley first performed an experiment that was designed to detect the motion of the earth with respect to the e+her. The basic idea of the experiment was to utilize ~he fact that, according to Newtonian physics, the velocity of light, equal to 3xlO meters per second with respect to the ether frame, should be a different value in a frame that is moving with respect to the ether. This is in accordance with the Galilean principle that velocities add according to the formula
Vc|a = Vc|b + Vb|a
where the ''I'' in the above relation is to be read "relative to". The earth, which orbits around the sun with an average speed of 30,000 meters per second, cannot be constantly at rest with respect to the ether. We show in Figure 10-11 the situation.
Thus a beam of light travelling parallel to he direction of motion of the earth should take a different time to travel a gi!en distance than would a similar beam which was directed perpendicularly ~o the direction of the earth's motion and travelling the Came distance. This follows from the fact that
time of travel = distance / effective velocity.
Since the velocities of light should be different in the two perpendicular directions it follows from the above relation that the times of travel should be different. Michelson and Morley designed and performed an experiment which WQS sensitive to this different time of travel. By measuring certain optical effects they fully expected to gain an indirect measurement of the ratio of the speed of the earth to the speed of light with respect to the ether.
In what follows we outline a schematic experimental arrangement of the famous Michelson-Morley experiment and take the reader through the argument. Refer to the diagram in Figure 10-12
Light from the source encounters a half-silvered mirror where it is split into two beams: one going along path O-M1-O and the other along path O-M2-O. The whole apparatus is rigidly attached to a table which is rigidly attached to the earth (somewhere in Cleveland 1887!). The earth is (at least!) moving around the sun with the orbital speed of 30,000 meters per second. Thus, if the ether exists, at some point in its yearly orbital trek around the sun the earth-bound apparatus should experience the ether "blowing" past it. This is the situation pictured in the diagram of the experimental set-up. The beam which travels along the path O-M1-O travels in a direction perpendicular to the "ether wind". The beam which travels along the path O-M2-O travels in a direction anti-parallel (from O to M2) and then paralleled (from M back to 0) to the "ether wind". The arrow in Fig.10-12 indicates the direction of the "ether wind", where v is the unknown "ether wind" speed. The Michelson-Morley experiment is designed to measure v. Notice that both beams are recombined at O and reflected into the telescope and observed. The basic idea is that the recombined beams will interfere with one another and produce fringes. When the apparatus is rotated through 90 Michelson and Morley expected the fringe pattern to shift. The degree of shift can be shown to be proportional to the ratio of v to the speed c of light with respect to the ether frame. The follow,ing simple calculation establishes this result. First we calculate the time required for the light to take the trip OMO. We indicate in Figure 10-13 sequence of events corresponding to the light leaving 0, arriving at M, and arriving back at 0. All of these events are indicated from the vantage point of an observer sitting at rest relative to the ether frame. Since the "ether wind" was blowing to the left, such an observer sees the apparatus moving to the right. Let L be the indicated hypotenuse, while vt is the distance the apparatus would move in the time t that it takes for the light to go from O to M, which is one half the time it takes light to travel the entire path OMO. According to Maxwell's theory of electromagnetism and optics, light travels at speed c relative to the ether frame. Thus, in time t the light travels a distance L = ct. Using the Pythagorean theorem
Solving for tM1-O we obtain:
The total time for the light to travel along the path O-M1-O is just twice this time, or
Next, we calculate the time required for the light to travel along the path OMO. The following diagram Figure 10-14 shows the situation for the two parts of this trip.
Again note that the calculation is done from the vantage point of an observer at rest with respect to the ether frame. In part (a), note that in the time to required for the light to traverse the distance 12 the mirror M2 has translated away by a distance v*t. Thus the distance that the light must travel is l2 plus this extra amount v*tOM2 . On the other hand. the speed of light is c with respect to the ether frame. If it takes the light a time tOM2 to travel the distance from O to M2 , then the actual distance travelled by the light beam is c*tOM2 . These two distances must be equal. Thus
Solving for ton , we obtain
Next, refer to part b of Fig.10.14. On the way back, the light travels a distance ctM2-O in the time tM2-O while the half-silvered mirror at O has moved a distance vtM2-O toward the on-coming beam of light. Consequently we have
Solving for tM2-O we obtain
The total time
The times toO-M1-O and tO-M2-O are clearly different. But how would this difference be manifested at the telescope? If we split up a beam of light of a given color (wavelength~ into two separate beams and let the two beams travel around two paths of different lengths and then recombine, the recombined beams will interfere with one another and produce what are called interference fringes. That is, alternating bright and dark "rings" or "lines" of light will be visible through the telescope which is placed in the path of the recombined light. This occurs because the two light waves are either "in phase" or "out of phase" with each other. When the waves are in phase, the light waves can combine to produce a beam of enhanced intensity. When the waves are out of phase, they cancel each other to produce a resultant beam of low intensity. The net effect is the production of alternating bands of bright (high intensity) and dark (low intensity) regions. In the Michelson-Morley experiment, the different times of travel around OMO and OMO results in there being an "optical path" length difference D which is just equal to the speed of light c with respect to the ether frame multiplied by the time difference tO-M1-O - tO-M2-O :
a depends on v, c, l1 , and l2. C, l1, and l2 are constants in a given experiment, so as as v stays the same D Will remain unchanged. Thus, if the apparatus were moving through the ether at an unchanging speed v , there would be a shift that would be unchanging. Thus)if one looks through the telescope of the Michelson-Morley experiment one could see a set of fringes but the number would not change unless v changed. Michelson and Morley were aware of this point. They cleverly arranged the apparatus so that it could be rotated through 90 . Consequently the direction of the two beams O-M1-O and O-M2-O would be changed so that the relative velocity of the beam and the "ether wind" would be altered. Thus they would perform the experiment at one setting and then rotate the apparatus by 90 and take the data again. Now in the rotated orientation the roles of l1 and l2 are interchanged. If we interchanged 11 and 12 in our formulas for tO-M1-O and tO-M2-O we find a new path difference D':
If we then compare the interference "fringes" for the two cases we would expect to find a shift of n wavelengths given by
where lambda is the wavelength of the light used in the experiment. Since v << c this is well approximated by
The distances l1 and l2 were meticulously fixed so that they were equal. Every precaution was taken to insure that each beam of light travelled through an equivalent amount of glass and air. Michelson was a master at these kinds of precision experimental arrangements. He fully expected to be able to record the presence of some kind of shift in the number of fringes. In fact the result of the experiment was that no fringe shift was observed' In all such experiments there has been a consistent, unchanging result: the speed of the earth through the ether is effectively zero. This result presents us with a dilemma. Either the very existence of the ether (and with it, absolute space~ is called into question or some alternative explanation consistent with Newtonian principles, must be generated to explain the null result.
Several attempts were made at the end of the nineteenth century to show that the results of the Michelson-Morley experiment were compatible with Newtonian principles and the existence of an ether frame at rest with respect to Absolute Space. Notable among them as the "contraction hypothesis" generated independently by the Dutch physicist H. A. Lorentz and the Irish physicist G. F. Fitzgerald. We mention it here in passing for completeness. These physicists made the assumption that the length of the arm of the apparatus parallel to the direction of motion is shortened relative to the length measured at rest with respect to the ether frame. In particular it was supposed that
It then follows that
Upon rotating the apparatus by 90 the roles of the two arms inter-change. An application of this "contraction hypothesis" then gives
That is we get the same result for D' as for D . Thus there would be no observed fringe shift since D' - D = O .
The Lorentz-Fitzgerald contraction hypothesis can be essentially ruled out by a slight modification of the original Michelson-Morley experiment. In 1932 one such experiment was reported. This is the Kennedy-Thorndike experiment wherein the arm lengths and l1 and l2 were purposely made different. In the original Michelson-Morley experiment they were carefully made equal, In the Kennedy- Thorndike variation l1 and l2 were made to differ by 16 centimeters, a value chosen so that good fringes still could be seen. Kennedy and Thorndike showed that with l1 is not equal to l2 , assuming the validity of the Lorentz-Fitzgerald contraction hypothesis, observations made when the velocity through the ether is changed should result in the presence of a fringe shift with the number of fringes approximately given by
here v and v are the velocities at which the two observations were made and c is the speed of light with respect to the ether frame. For example one might perform the experiment in January and then again in July. This is shown in Figure 10-15
The direction of the velocity of the earth around the sun would have reversed. Also every twelve hours the direction of the tangential velocity of Cleveland reverses. This is shown in the following Figure 10-16
No such shift in the fringes were observed either for the twelve-hour earth rotation cycle or for the six-month orbital velocity reversal.
Actually, long before 1932 most physicists had been convinced that attempts to save Newtonian mechanics were futile. Albert Einstein, in 1905, proposed the special theory of relativity which not only explained the null result of the Michelson-Morley experiment but also shattered the Absolute Structure of Newtonian space and time. The attempt to utilize light to establish the validity of the Newtonian world view had led, instead, to its downfall.
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