This is knowing the universe, the history, and philosophy of astronomy. I'm Chris Impey, distinguished professor of astronomy at the University of Arizona. In this module, we're going to look at the quantum theory. We'll start with the history of the quantum theory. This photograph, the Solvay Conference in 1927 gathers together all the founding fathers, and you'll see one mother in there, Madam Curie of the quantum theory, the time early in the last century when our knowledge of the fundamental nature of matter and radiation and how the physical world works was transformed. It's an amazing period of time. The atomic theory, of course, starts with the ideas of Democritus, a long time ago, that material is composed of individual atoms. It continues with the work of Isaac Newton who gave us the aggregate properties of matter in terms of its gravitational force. Then it progresses through pivotal thinkers of the 19th century. But the real revolution happens with Max Planck early in the 20th century, and then Albert Einstein, who decide that matter and radiation are equivalent and that radiation has to be considered in small quantized discreet packets called quanta, and hence we have the quantum theory, also, that atoms interact with the world in discrete amounts of energy, and these are quanta as well. The world is fundamentally grainy at the level of quanta. These are invisibly small and operate on energy scales far below our normal everyday life. That's why it took a lot of experimentation in the field of physics to understand the atomic theory. Classical mechanics is the mechanics of everyday objects like tables and chairs, and they were, and still are governed perfectly well by the laws of Isaac Newton. His three laws of motion which you see here, they still work completely well for everyday life. Classical mechanics was the dominant theory of moving objects for centuries from the time of Newton's Principia, his gravity theory through Lagrange's books on mechanics, Hamilton's book on mechanics, and Maxwell's equations of electromagnetic theory in the mid-19th century. This is how physics work for hundreds of years with essentially no fly in the ointment or no sense of a problem. But actually, by the beginning of the 20th century and late in the 19th century there were experiments being carried out that defied explanation according to Newtonian physics and Newtonian mechanics. They were, for example, the ultraviolet catastrophe, the Stern-Gerlach experiment, the nature of the hydrogen spectrum or spectrum of any element, and the photoelectric effect. We can see here why something had to change. The ultraviolet catastrophe starts with a very simple question, why don't atoms just disintegrate in nanoseconds? Why is matter stable at all? Because if an electron is orbiting, then according to classical physics, it's accelerating, and accelerating charges emit electromagnetic radiation. That's how we get light. That's how we make radiation. Therefore, electrons orbiting atoms should lose energy. If you work out the time it would take them to decay into the nucleus, it's a nanosecond, and yet normal matter is clearly stable, not just for seconds but for billions of years. This is a profound mystery. It was connected to a calculation about why objects that are hot don't emit more ultraviolet light because classical electromagnetic theory again, suggested that they would have most of their modes of emission at short wavelengths. The calculation suggested an infinite amount of energy coming at short wavelengths in the ultraviolet. This was the ultraviolet catastrophe. Max Planck had to solve this problem by making a radical supposition that light could not have any energy, but could only have quantized values of energy. That's why he's called the father of quantum mechanics or quantum physics. The Stern-Gerlach experiment was a little more subtle but also had a dramatic outcome. The question was, why do atoms have discrete values of angular momentum? If you send silver atoms through a magnetic field they are deflected. If their spin orientations would be random their deflection angles will be smoothly distributed, like the blue line on the right side of this diagram. But in fact, what you see are two pileups at either end of the apparatus. The spin apparently is discrete and quantized. These two pileups correspond to the spin-up of the particle or spin-down with nothing in between. The photoelectric effect, we've already talked about, the question is, why is red light incapable of knocking electrons out of materials like a metal, no matter how bright the intensity or how much light you shine on it, and yet blue light or green light could do so easily even at modest intensities? This was the photoelectric effect, and Einstein could only explain it in terms of photons. This is how he won the Nobel Prize. Then the spectrum of hydrogen or other metals. It had been known since early in the 19th century from Wollaston, smearing the sun's light out with a prism and seeing that there were sharp lines superimposed on the spectrum. Fraunhofer also did this in 1911, even better. It turns out that if you have a hot gas in the lab and use a spectrograph or prism to spread out the light, you see sharp lines. The sharp lines are distinctive of each element. Each atom has a different fingerprint, if you like, in spectral form. This light is coming off from excited atoms that only very specific wavelengths or frequencies, not smoothly across all wavelengths and frequencies. Heavier elements in these spectra have more complex spectra with more lines. But the nature of the lines was not understood and it cannot be explained with classical physics. Quantum mechanics was a theory developed to explain these results and it has become most successful physical theory in history. It starts with Max Planck and his definition of the scale of quanta, which is defined by his constant. It's an incredibly small number in the metric system, 10 to the minus 37 and that's what means that Planck's constant and quantum effect only appear on microscopic and tiny energy scales. It then goes through Bohr's model of the atom and then other innovations like the Schrodinger equation that describes particles and waves and how they interact and behave over time. There were further innovations in the theory through the 40s and 50s and now it has become a mature field of physics with explanatory power into many fields. Let's see how Planck came up with the quantum theory originally and why. Where did quantum theory come from? It started not as a crazy idea, but with a light bulb. In the early 1880s, the German Bureau of Standards asked Max Planck how to make light bulbs more efficient so that they would give out the maximum light for the least electrical power. The first task Planck faced was to predict how much light a hot filament gives off. He knew that light consists of electromagnetic waves with different colors of light carried by different frequency waves. The problem was to ensure that as much light as possible was given off by visible waves rather than ultraviolet or infrared. He tried to work out how much light of each color a hot object emits. But his predictions based on electromagnetic theory kept disagreeing with experiments. Instead, in what he later called an act of despair, he threw the existing theory out the window and worked backwards from experimental measurements. The data pointed him to a new rule of physics. Light waves carry energy only in packets with high-frequency light consisting of large packets of energy, and low-frequency light consisting of small packets of energy. The idea that light comes in packets or quanta may sound crazy, and it was at the time. But Einstein soon related it to a much more familiar problem, sharing. If you want to make a kid happy, give them a cookie. But if there are two kids and you only have one cookie, you'll only be able to cheer them up half as much and if there are four or eight, 1600,000 you're not going to make them very happy at all if they have to share one cookie between them. In fact, if you have a room with infinitely many kids, but not infinitely many cookies, if you share the cookies evenly, each kid will only get an infinitesimally small crumb, and none of them will be cheered up, and they'll still eat all your cookies. The difference between light waves and kids is that you can't actually have infinitely many kids in a room. But because light waves come in all sizes, you can have arbitrarily small light waves, so you can fit infinitely many into a room and then the light waves would consume all your cookies, I mean energy. In fact, all these infinitesimal waves together would have an infinite capacity to absorb energy and they'd suck all the heat out of anything you put in the room, instantly freezing the tea in your cup, or the sun, or even a supernova. Luckily, the universe doesn't work that way because as Planck guessed, the tiny high-frequency waves can only carry away energy in huge packets. They're like fussy kids who only accept exactly 37 cookies or a 162,000 cookies. No more and no less, because they're so picky, the high-frequency waves lose out and most of the energy is carried away in lower frequency packets that are willing to take an equal share. This common average energy that the packets carry is in fact what we mean by temperature so a higher temperature just means higher average energy, and thus by Planck's rule, a higher frequency of light emitted. That's why as an object gets hotter, it glows first infrared than red, yellow, white, hotter and hotter towards blue, violet, ultraviolet, and so on. Specifically, Planck's quantum theory of fussy light tells us that light bulb filaments should be heated to a temperature of about 3,200 Kelvin to ensure that most of the energy is emitted as visible waves. Much hotter and we'd start tanning from the ultraviolet light. Actually, quantum physics has been staring us in the face since long before light bulbs and tanning beds. Human beings have been gazing into fires for millennia with the color of the flames spelling out quantum all along. There were other innovations around this time and discoveries that surprised the world, not just physicists. X-rays for example were discovered by Wilhelm Conrad Rontgen. The discovery is linked with his name of all time although he himself called them X-rays. He received the very first Nobel Prize in Stockholm in 1901. These are as now we know, a new form of energy called rays on the account of their propagating themselves in straight lines as light does. At the time, the actual constitution of this radiation energy was unknown. Radioactivity was found around the same time, Henri Becquerel found salts whose energy emitted and it showed light. Was there a relation between his vacuum tube induced phosphorescence and this natural form of phosphorescence from material you could dig from the ground? Marie and Pierre Curie found that it was and they called it radioactivity. There were two hypotheses that an unknown radiation fills all of space and the radioactive elements are the ones that are able to transform this radiation to observable forms. Or the supposition that the transformation is far-reaching than any ordinary chemical transformation and that the existence of the atom is at stake. That one is in the presence of a transformation of the elements. That's indeed what they had seen. Elements could transmute the alchemists speculation was correct. Heavy elements decayed radioactively with the emission of energy to become different elements. Radium become a highly sought after item in the field of science, more expensive than gold or diamonds. Moving it into the world of the popular culture, it was valuable and used in a variety of applications in the early 20th century. Luminous paint for military watches and instruments. Factory girls were encouraged to point the brushes with their lips when they were using it to apply to tools and other items. For fun, they even painted their nails, teeth, and their faces. Unfortunately, the body treats radium just like it does calcium, it's stored in the bones. Because of this sad time, the radium girls as they were called, many died years later from cancers as a result of the radioactivity. The right of any individual worker to sue for damages from corporations due to labor abuse was established as a result of the radium girls case. We see Pierre Curie in 1905 saying and speculating about both the good and the evil that could come from these forms of radioactive material. It can even be thought that radium could become very dangerous in criminal hands. Here the question can be raised whether mankind benefits from knowing the secrets of nature, whether it is ready to profit from it, or whether this knowledge will not be harmful for it and again, he said, the discoveries of Nobel is characteristic as powerful explosives have enabled man to do wonderful work. There are also a terrible means of destruction in the hands of great criminals who are leading the peoples towards war. We see in this example how the power of physics, the power of the atom could be used for good or for ill. Also around this time the electron is discovered by JJ Thomson in 1905. We have the role of experiment in beavering down into the atom and finding out its fundamental constituents. This is the first fundamental or elementary particle to be found in a century. He said, thus the atom is not the ultimate limit to the fourth subdivision of matter. We may go further. The core puzzles appear to be a form of all kinds of matter. It seems natural therefore to regard it as one of the bricks of which atoms are built and indeed there are as many electrons in the universe as there are atoms. Another remarkable discovery in the same period of time was that of anti-matter. Anti-matter was predicted by solving the relativistic wave equation, an early piece of mathematical apparatus for quantum theory for describing how atoms work. A symmetric solution in the theory and the equation involve taking the square root of either positive or negative numbers. They're equally valid in the mathematics of the theory. The positive case is real and was applied to explain how matter behaves. Dirac wondered, what was the point of the square root of the imaginary number, the negative number. What does that correspond to? He believed we should trust the mathematics. Then his equation was suggesting a mirror form of matter that had opposite properties in the quantum sense and that will be anti-matter. Anti-matter, anti-protons, and anti-electrons or positrons were discovered decades later by Carl Anderson. This was a remarkable example of the fact that the pure mathematics at the heart of the quantum theory was leading us to imagine new types of situations in the real physical world if we would trust the results of the mathematics. Atomic theory has several principles at its foundation and these come particularly from the work of Niels Bohr. From quantum mechanics, we must somehow retrieve the normal classical laws that work so well for large objects and so it was the case that the people working on the theory had to show that it tended towards the classical mechanics result in the limit of large numbers of atoms. Quantum behavior is not apparent in the macroscopic world and we have to have a theory that says why it's not. Another idea was complementarity. The fact that mutually exclusive descriptions must be accepted. This is a more uncomfortable implication of quantum theory. An experiment might show a quantum had particle-like properties or wave-like properties, but not both at the same time. They are equally valid. Niels Bohr said, "The present state of atomic theory is characterized by the fact that we not only believe the existence of atoms to be proved beyond a doubt, but also we believe that we have an intimate knowledge of the constituents of the individual atoms." Short telling a story about Niels Bohr. He won the Nobel Prize and a New York Times journalist ventured to his lab in Copenhagen to interview him. As they were about to enter the lab, the journalist noticed that above the door of the lab was an inverted horseshoe and he stopped Bohr and said, "Professor Bohr, you're a physicist, a rationalist, scientist, just won the Nobel Prize in physics. Surely you of all people are not superstitious?" Bohr just looked at him, matter of fact, and said, "I've heard that it works whether you believe in it or not." Another key part of quantum theory is the uncertainty principle. It's based on an obvious premise, which is that when you measure something, you interact with the thing you're measuring, this interaction necessarily touches the object. By touch, we might just mean a photon of light, not an actual instrument or a probe. The more precisely we want to know where something is, the harder we have to measure it. Logically, when we look at something and measure its position, we interact with it and may give it a kick. To see this, imagine a thought experiment of being in a closed room with a flashlight to find an object in the room. If the object is just a ball or a table or a chair, shining the light will show you where it is. But now imagine the object gets smaller and smaller and your flashlight can get smaller and smaller too and emit less light. As the object becomes smaller, like a grain of sand, the flashlight will still work to find the grain of sand because it shines light to it, some fraction of those photons or light waves come back to your eye and you see where the sand grain is. But the uncertainty principle comes in when the object we're trying to find is at the level of an atom, then the photon we send to measure its position interacts with it and kicks it or moves it because the thing is so small. Even if the light comes back to you, at that point, the object has moved and so you don't know where it is, you've changed its motion, you've given it momentum. Unavoidably, we alter the velocity of the particle under study. The uncertainty principle in physics says that the product of the position uncertainty and the momentum uncertainty, which involves the motion, is a very small number. In other words, this uncertainty doesn't appear in the everyday world, but it's dominant at microscopic scales of atoms. There's a second equivalent form of the equation involving the uncertainty in the energy we might measure for something and the time at which we measurement. In other words, we cannot know both position and momentum or speed with infinite precision nor can we know energy and the time of measurement with infinite precision. There's a floor on our ability to understand nature. It's important to realize that the uncertainty principle has got nothing to do with bad equipment or apparatus, or sloppy experimenters, or scientists, it's more about imprecision than uncertainty; it is a truly fundamental limit on our knowledge of the physical world. Here we see the physicists all gathered in 1927 and remarkably 17 of the 29 participants at this conference, you can see Einstein centrally in the front row, won Nobel Prizes either before or after this photo was taken. You'll also notice the heavy maleness of the physics profession, the only woman in the picture is Madam Curie, also in the front row. Quantum mechanics is universally applicable, it applies to all objects no matter how big or small. But for large object, its effects are really not very obvious. Quantum mechanics, at the base of these chains, applies to atoms or molecules. It also applies to large molecules and collections of molecules and big objects, but just at such a level that we'll never notice it. Small objects, how small are we talking? How small is very small? We have one-meter objects like a book or a chair or a person, they are classical. Even one-millimeter objects say like a grain of sand are classical. Even down to the level of a micron, smaller than the width of a human hair, the world is classical. The boundary where things start to display quantum effects it's about a nanometer or a billionth of a meter, and at that level, we are in the world of quanta. That might make it sound like quantum mechanics is not very important, but it very much is. How important? Well, without quantum mechanics, biological reactions would not occur and so life would not exist, chemical bonding would be impossible and so all molecules would disintegrate, also, all atoms would be unstable and essentially the universe would quickly explode. That's the end of this topic.
