| Light: Introductory Remarks.
Studying the Past.
In an earlier lecture, I described the
(collecting lunar rocks, studying neutrinos, and so forth), but pointed out that by far the most important way is that of looking out into space, using our unaided eyes or the world's great telescopes to collect the light which is flowing in our direction. It is important to realize that we are also looking into the past this way! If, for instance, we study a remote galaxy which is billions of light years away, we are seeing it as it was in the distant past.
This is true even on smaller scales, of course. We do not even know for certain that the sun is `really there' right now! If it were magically to vanish, this very instant, we would not discover that fact for eight more minutes. Likewise, when I look at you in the lecture hall, I am seeing each of you as you were some tiny fraction of a second ago. Since it takes the light only about a tenth of a microsecond to cross Theatre D, this is inconsequential in day-to-day life, but you can imagine the difficulty we would have if, say, it took a minute or two for light to cover a distance of ten metres. (How could you ever drive a car, or play sports, if everything you were seeing was a "picture from the past?")
This enforced delay perplexes many non-astronomers, who find it an awkward source of complexity and confusion, but in fact it is enormously helpful in many respects. For instance, by looking at remote galaxies we can study what the universe was like at a very much earlier time, shortly after the Big Bang (the moment the universe came into existence). Our telescopes are, in some senses, time machines!
Here's an analogy. Consider the case of an historian studying the life and times of Napoleon. In some senses, her work would be made more straightforward if mail and other messages from France took two hundred years to reach us across the Atlantic. Every shipment of mail would carry some interesting and immediately relevant bit of news -- the repercussions of the French revolution in 1793, for instance -- so there would be no need for her to 'filter out' other information of later provenance. But obviously our historian would have no idea at all of what modern-day France is like, or how things had evolved after Napoleon.
That's a rather contrived example, but it does point up one of the dangers of the enforced "looking back in time." Is it possible, even in principle, to say what the universe is like "right now" if everything we see is "as it once was"? Fortunately, things do not change very rapidly in astronomy, so if we want to study what galaxies are like in the present day, we can look at relatively nearby ones. Although they may be a couple of million light years away, so that we are seeing them as they were two million years ago, there will have been no significant changes in those galaxies over such times. (Similarly, if I see that you are wearing a blue shirt, I don't have to fear that I am mistaken, that you might have changed to a red shirt during the time that it took for the light to reach my eyes. No one can change shirts in a trillionth of a second!) If, on the other hand, we want to see what galaxies were like at the time of their birth, we can look at the very remote ones!
Obvious Questions and Historical Musings.There are two rather obvious questions you might ask about light: what is it?, and how fast does it travel? Through the centuries, many great thinkers have speculated about the nature of light. Some ancient scientists, for instance, imagined vision to be rather like touch. Just as we reach out our hands to feel a surface -- is it rough or smooth? wet or dry? -- they imagined the eyes sending out `feelers' of some intangible sort which would explore the nature of the world around us. On the other hand, we saw from the quotes I gave you earlier from that some ancients had broadly correct notions about the actual emission of light from luminous bodies like the sun, and its mere reflection from other objects, such as the moon. Newton speculated that light was `corpuscular' -- that is, he speculated that it was constituted of lumps of some sort, travelling like little bullets in straight lines. Other scientists, like Huygens and Young, proposed that light is more like a wave travelling through space, for reasons described in the next section. Your first reaction is probably to trust the idea put forward by Newton. After all, light seems to cast very sharp-edged shadows, which seems to imply that it travels in lines which are pretty nearly straight. As it happens, though, there is good evidence for the wave nature of light, and it is this interpretation which held sway for a couple of centuries. It was only in this century again that we realized that in some contexts it makes more sense, and indeed is essential, to think of light as a particle (which we now call a photon ). The paradoxical thing is that light behaves both as a wave, distributed over space, and as a particle, localized like a bullet! As counter-intuitive as that sounds, it is correct. Modern quantum physics (the physics of very small things) is like that. In the next section, we will consider the evidence for the wave nature of light, and return to the question of its particle-like nature later. But first let us consider the interesting question of its very great speed.
The Speed of Light - and That of Sound.How would you work out the speed of light? One interesting way to approach this question is to think of something analogous. To be specific, let us ask how we might work out the speed of sound. How is it determined? One simple way of measuring it takes advantage of the fact that light travels at an enormously greater speed, and works like this: Arrange for a friend to stand a kilometer away, looking at you with a small spyglass. Strike a huge bass drum as hard as you can. Your friend will see this happen effectively the moment it takes place (since light travels so very fast) and can start a stopwatch going. She stops the stopwatch when she hears the boom of the drum. From the measured delay, she can calculate the speed at which the sound covered the known distance between your locations. In this simple experiment, the light signal (your friend's observation of your action) tells her when the sound is produced; her own ears tells her when the sound arrives; and the measured delay is attributable to the modest pace at which sound travels. But is there a way we can measure the sound speed without involving a light signal at all? The answer is Yes; we can act both as the source and the recipient of a sound, as follows: Stand some distance from a tall vertical cliff, and pound on a big drum. Start a stopwatch as you do so. Listen attentively for the echo, and stop the timer as soon as you hear it. Measure the distance to the cliff, and determine the speed at which the sound must have travelled to cover twice that distance (to the cliff and back) in the elapsed time. As I have already noted, such measurements reveal that sound travels very much more slowly than light, a simple fact which we can use to advantage. For instance, it is the basis of the way in which every child is taught to work out the distance of a thunderstorm. When we see a flash of lightning, we start counting until we hear the boom of thunder. We see the flash at essentially the instant it actually happens in our vicinity (perhaps a few kilometers away). The sound, on the other hand, takes some time to reach us, since it travels at the measly pace of about 300 meters a second. Each three seconds of delay until we hear the thunder implies that the flash originated an additional kilometer from us. If, for instance, we hear the associated thunderclap six seconds after the flash of light, we can deduce that the lightning struck two kilometers from here. So much for sound. Now, how do we work out the speed of light? Can we try something analogous to one of the experiments we have just considered? Let us look at them in turn. In the first technique which we described, the precise moment of departure of the sound (the boom of the drum) was known to our distant friend because she could see us hit the drum at exactly that instant (or so soon thereafter that any tiny delay was utterly negligible). But if our friend is now supposed to determine the speed of light, she has to know, in some independent way, the very instant at which the light leaves our location on its way to her. How can this be accomplished? There is no faster signal which we can send to tell her ``The light is setting off now'' - nothing can outrace the light. (Don't make the mistake of assuming that we can be in telephone contact, with immediate messages sent from us to her. These messages themselves have to be sent electrically and cannot travel faster than light. They are not immediate at all!) Still, there is a way of carrying out this two-person experiment, or one very much like it. For instance, you could: Stand side by side with your colleague, and carefully synchronize your clocks so that they agree to the nearest millionth of a second (a precision which is easily accomplished with atomic clocks). Tell your colleague that you are going to send out a light signal precisely at noon tomorrow, say. [By the way, this light signal does not need to be a flash of visible light; it could instead be a signal emitted by a radio transmitter, since that is also light (electromagnetic radiation).] Now instruct your colleague to travel to some remote location -- say, one thousand kilometers away, in Western Ontario -- carrying her ultra-precise clock with her. Tell her to wait attentively and to expect to receive a light signal shortly after noon. When your own clock indicates precisely noon, send out the pre-arranged signal. She will discover that the signal reaches her when her clock reads one three-hundredth of a second past noon, so she will be able to calculate that light travels at a speed of three hundred thousand kilometers a second. By careful pre-arrangement, therefore, one can carry out the determination using two separate observers in two different locations. The only real problem is to guarantee that the clocks will remain precisely synchronized as they are moved around, which is not a trivial point. (In fact, one of the consequences of Einstein's relativity theory is that clocks which move with respect to one another do not run at the same rate! In principle, however, that complication can be dealt with.) Still, a second method is better - an `out-and-back' technique which is analogous to bouncing a loud sound from a nearby cliff. This approach has a long and noble history. For example, Galileo himself trained a couple of people to open the cover of a lantern as quickly as possible when they saw a flash of light. He then stationed these people at night some miles apart on two mountain tops, and had one of them open up a bright lantern. The other, on seeing the flash, opened his own lantern, and from the total time taken for the `return flash' of light to be seen by the first person, Galileo tried to calaculate the speed of light. His conclusion was that light travelled so very quickly that this experiment was essentially futile! He concluded, correctly, that the varied reaction times of the experimenters made the measurements too imprecise. This out-and-back approach is still the most practical method in modern times. We simply send out a beam of light and measure the time it takes to return to our location after it bounces off a distant reflecting surface. (It was for work of this sort in the late 1800's that the physicist Albert Michelson won the first Nobel Prize ever given to an American scientist.) Poor old Galileo had no way of generating a source of artificial light which could be turned on in an instant and yet which would be bright enough to make a detectable reflection from something like a shiny mirror on a distant mountaintop, so he had to resort to using people to simulate a `reflection.' Unfortunately, his imaginative efforts were frustrated by the uncertainties caused by the slow and variable reaction times of his observers. Modern technology, with electronic detectors and so forth, eliminates such complications. You may know that there are small reflectors on the moon, left there in well-mapped locations by the Apollo astronauts. From the MacDonald Observatory in Texas, astronomers send pulsed laser beams to these reflectors. The pulses of light return to us after a delay of about two-and-a-half seconds. What does this tell us? Well, if we knew the precise distance to the moon, we could once again work out the speed of light. (This is just a larger-scale example of the "echo" experiment.) The laser experiments, however, are more commonly used the other way around. That is, having already measured the speed of light very precisely here on Earth, we use the lunar laser-ranging experiments to monitor the moon's present distance, and in particular to see if that distance is changing (which it is! -- the moon is slowly drifting away from us. This is a consequence of the tides, as we will learn later).
Roemer's Studies of Jupiter, Timekeeping and Navigation.Before closing this topic, I'd like to point out that the first serious estimate of the speed of light was made in the study of an astronomical phenomenon, in the year 1675, by a Dane named Ole Roemer. By that time, scientists had known about the moons of Jupiter for over half a century, and had seen them go around and around Jupiter many times, with great regularity. Roemer realised that you could predict where the moons of Jupiter would be for many centuries to come. In short, Jupiter was a great example of a "cosmic clock" high in the sky, one which might be conveniently observed by people everywhere, just at the clock on 'Big Ben' can be seen by all the tourists in the central parts of downtown London. So Roemer drew up a complete tabulation of where you would expect to see the various moons on different dates and at different hours. (Tabulations of exactly that sort still appear every year in the "Observer's Handbook," a book published annually by the Royal Astronomical Society of Canada, for the benefit of keen amateur astronomers.) There was a very good practical reason for providing these tabulations, by the way. Roemer's intention was to provide a reliable aid to navigation, in a way which is best understood if you think about the following situation: Let us suppose you have an excellent clock on board a ship which is just about to sail away from London, England, in the year 1670 (say). You set it so that it is in perfect agreement with the clocks at the Admiralty Headquarters, and then set off on a long exploratory journey. A few weeks later, you notice that the clock tells you that it is exactly noon in London. But you notice that from your location the sun is only just beginning to rise. What does this tell you? Clearly, it means that you are now considerably west of London, and perhaps even getting dangerously close to the shores of Virginia or Florida. This kind of consideration can and must be made quite quantitative if it is to be of real use in navigation. If you know the exact time in London, but then see how advanced the day is in your location -- how high is the sun? -- you can figure out your longitude to a degree of precision which depends on the reliability of your clock. Roughly speaking, you need to know the time to a precision of better than a minute in order to determine your position to the nearest mile. If you think about it in this way, you will realise that good navigation requires you to carry along a very reliable clock -- or at least it used to! Nowadays, we have modern devices like Global Postioning Sensors which make this less necessary. (It's also worth noting that navigation at sea is the real problem. Once you are on land you can, in essence, 'pace out' the terrain you cover and make real measurements. At sea, contending with unpredictably variable currents and the lack of landmarks, it can be very hard to determine distances.) Conversely, if you have a clock which is less precise than that, you can't figure out your position very accurately -- unless, of course, you can see some well-known feature, like a previously-mapped point of land. At night, however, you may not be able to do that, and thus be unsure of your exact location. Knowing where you are to good precision can be a matter of life and death at sea! If you are five miles west of where you think you are, for instance, you might wind up wrecked on a reef or a sand bar. Indeed, a tragic example of this occurred in 1707, when four homeward-bound ships of the British fleet ran aground with the loss of almost two thousand men. The ships were considerably farther east than thought, and ran into the Scilly Islands. (On the day before the catastrophe, a brave sailor who challenged the positional determinations made by the navigators on board was hanged on the spot for mutiny.) As a consequence of this problem, the British Admiralty offered a reward which (in today's terms) was the equivalent of several million dollars to anyone who could design a truly reliable marine chronometer. (In those days, conventional clocks used pendulums, and were terribly unreliable on rough seas, as you can imagine. Spring-wound clocks had been invented but were far from perfected.) The problem was eventually solved by a man named Harrison, although the government battled long and hard to deny him the money he was owed. Before Harrison's success, however, came Roemer's proposal of the use of Jupiter as a reliable clock. As he pointed out, all you have to do is note the positions of Jupiter's moons, using a small telescope, to work out exactly what time it is. Problem solved! -- at least, in principle. In fact the method was never very practical, for a couple of reasons. The more serious of these is the fact that Jupiter is sometimes hidden for months at a time, when it and the Earth lie on opposite sides of the sun in their independent orbits. Even when it is in the night sky, however, it will not be observable on cloudy nights, which are not at all uncommon at sea. Moreover, making the required observations turned out to be trickier than expected. All in all, it would clearly be preferable to have a really good clock on shipboard. In Roemer's day, that technological breakthrough had not been made, so his idea seemed worth a serious trial. But something strange began to happen: The moons of Jupiter soon started to lag behind Roemer's predictions. His "cosmic clock" seemed to be slowing down. Why? The answer is best explained with reference to the attached pair of figures. In the first figure, we see the Sun, the Earth, Jupiter, and Io (one of the moons). Thanks to Roemer and others, we know that Io will take precisely 42 hours and 27 minutes to orbit Jupiter once. (For simplicity, let's call that precisely two days, or 48 hours. The actual number doesn't matter.) So if we notice that Io is just moving into Jupiter's shadow at a particular time, we can confidently say that it will do so again 48 hours later, and 96 hours later, and so on, for decades to come -- or indeed for centuries and millennia to come, regular as clockwork. Precisely one hundred and eighty days from now, for instance, we will expect to see Io just moving into Jupiter's shadow for the ninetieth time. There would be no problem, and we would see exactly that behaviour, if the situation were static. Unfortunately, the Earth and Jupiter are on the move. Since Jupiter moves relatively slowly, it is the Earth's motion that really matters, so look now at the second figure where I have shown how different things are 180 days -- nearly half a year -- after our first observation. The Earth is now on the far side of the sun, and much farther away from Jupiter. We expect to see Io move into Jupiter's shadow at the predicted moment, but to our surprise it seems to happen about a quarter of an hour too late! Why? The answer is that the phenomenon happened just as it was supposed to, but we did not learn about it until later than expected because the light from Jupiter had to travel an extra distance to reach us. The extra distance it travelled is approximately twice the distance of the Earth from the Sun, which is a total of about three hundred million kilometres, so the delay is about one thousand seconds -- a bit more than sixteen minutes. Roemer had the wit to realise what was going on, and used the then sketchy numbers for the distance to the sun to work out the speed of light. While his result was not precisely correct, it was important in one respect in particular: Roemer's observations demonstrated that the speed of light was finite, not infinite. This was a philosophically profound discovery. It means, for instance, that we cannot examine the present state of everything in the universe, even in principle. As noted earlier, the farther out we look, the farther back in time we are exploring. Roemer's suggested use of Jupiter as a clock could still have been practical, of course, because one could merely add a correction for the fact that we are sometimes closer to or farther away from Jupiter, but in fact this approach was never very successful because of the dubious prospect of always having clear skies and the more fundamental problem of being unable to see Jupiter all year round. Anyway, Harrison's very precise marine chronometer made such approaches of historical interest only. Previous chapter:Next chapter
0: Physics 015: The Course Notes, Fall 2004 1: Opening Remarks: Setting the Scene. 2: The Science of Astronomy: 3: The Importance of Scale: A First Conservation Law. 4: The Dominance of Gravity. 5: Looking Up: 6: The Seasons: 7: The Spin of the Earth: Another Conservation Law. 8: The Earth: Shape, Size, and State of Rotation. 9: The Moon: Shape, Size, Nature. 10: The Relative Distances and Sizes of the Sun and Moon: 11: Further Considerations: Planets and Stars. 12: The Moving Earth: 13: Stellar Parallax: The Astronomical Chicken 14: Greek Cosmology: 15: Stonehenge: 16: The Pyramids: 17: Copernicus Suggests a Heliocentric Cosmology: 18: Tycho Brahe, the Master Observer: 19: Kepler the Mystic. 20: Galileo Provides the Proof: 21: Light: Introductory Remarks. 22: Light as a Wave: 23: Light as Particles. 24: Full Spectrum of Light: 25: Interpreting the Emitted Light: 26: Kirchhoff's Laws and Stellar Spectra. 27: Understanding Kirchhoff's Laws. 28: The Doppler Effect: 29: Astronomical Telescopes: 30: The Great Observatories: 31: Making the Most of Optical Astronomy: 32: Adaptive Optics: Beating the Sky. 33: Radio Astronomy: 34: Observing at Other Wavelengths: 35: Isaac Newton's Physics: 36: Newtonian Gravity Explains It All: 37: Weight: 38: The Success of Newtonian Gravity: 39: The Ultimate Failure of Newtonian Gravity: 40: Tsunamis and Tides: 41: The Organization of the Solar System: 42: Solar System Formation: 43: The Age of the Solar System: 44: Planetary Structure: The Earth. 45: Solar System Leftovers: 46: The Vulnerability of the Earth: 47: Venus: 48: Mars: 49: The Search for Martian Life: 50: Physics 015 - Parallel Readings.
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(Sunday, 24 January, 2021.)