 I'm Professor Stephen Sakura and welcome to Physics 1303. In this course, which is known as Introduction to Mechanics, we'll begin to take a look at force and energy and its effect on material objects. This is what is meant by mechanics. Now this course will provide a foundation in the ideas of physics that are needed to understand the universe around us in whole and in part, but let's begin by asking a simple question, what is physics? Well, physics is the study of energy, matter, space and time. And since everything we can see in the universe around us possesses energy, matter, or moves in space and time, really physics is the science of the foundations of everything, the whole universe. It's a past, it's present, and possibly even understanding its fate. Physics is a science with twin foundations, mathematics and observation and experiment. That makes physics a practical science. So what do I mean by its mathematical foundations? Well, mathematics is the symbolic language that humans have developed to describe the features of the natural world, but mathematics itself is not limited to the natural world. In fact, you can write down completely self-consistent, absolutely correct mathematical statements, but they don't necessarily tell you anything about a manifestation in the physical world of some behavior. Physics comes in and filters the mathematical statements that you can write down based on observations of the natural world to tell you which of those statements are correct and which of those statements are incorrect. And so that's where experiment, observation and measurement comes in. It is observation of the natural world, does the prediction of a mathematical framework that you have developed manifest in the natural world. That is the final arbiter of the kind of truth that physics as a science is invested in trying to understand. And so it is these twin tools, mathematics and the ability to describe and predict, but also experiment, observation and measurement as the arbiter of accurate ideas and inaccurate ideas that you can call from the mathematics. It's these twin tools that are the arsenal at the heart of physics, and that's what makes physics such an effective way of understanding the natural world. Now these self-consistent mathematical statements that you can write down based on observation and experiment and previous experience with the natural world, if they survive long enough, if they hold up, if they make predictions and those predictions hold up in laboratory tests or observations of the universe writ large, then they eventually become accepted as laws of physics. These are self-consistent mathematical statements that reliably predict and describe features of the natural world. Now the laws of physics are really a small set of equations. There's only a few of them, and they seem to describe extremely well nearly everything that in our everyday experience we have access to, and even to many things that as humans we don't notice going on in the universe, but are there anyway. They are by no means a complete and exhaustive list of laws. We don't know everything about the universe, and that's a good thing. That puts physics as a science at a frontier of human knowledge, where the frontier continues to be pushed out by men and women every year working to understand the natural world. Now in order to make progress as a science, we have to have a framework in which we can do things like make measurements and observations, and the framework that we will eventually utilize for this is space and time. Now observation is fairly straightforward, so for instance if I look at the flag pole down the quad, a little bit behind me here, I will observe that the flag is flapping to the left of the pole, that the flag pole has a certain height, and that it's located some distance behind me. Observation is fairly straightforward, with the right tools, a good set of eyes, a good set of ears, good data taking skills, writing with a computer, whatever you like, you can make observations. But observations themselves don't tell you anything about the why of the natural world. In order to get to the why of things, you have to be able to actually make measurements, and then understand patterns that may or may not be present in those measurements. Now to make measurements, for instance what if I wanted to know my distance from my current location to the base of the flag pole, that's much trickier. In order to get an answer to that question, what's my distance from where I am to the base of the flag pole, I'm going to have to define some kind of framework in which I can make numerical statements about things like distance, and then I'm going to have to take that framework and divide it up into little equal sized units, and then share that with other people, so that across cultural boundaries, across national boundaries, across continental boundaries, we can all make the same measurements and see whether or not they agree on the details of the observations themselves. The framework as I said that we're going to use for this are space and time. Let's take a look at space and time separately, and come to a slightly better understanding of these things. As a material object, I know that I can move myself forward, and I can move myself backward from where I was originally standing. I can move myself to the left of where I was standing, and I can move myself to the right of where I was standing. And if I'm careful, I can jump up and come back down. So already as a thinking object, I'm aware of the fact that I can move in three independent directions. I can move forward, backward, left, right, and I can move up, down. Moving forward and backward doesn't mean I have to go left or right or up and down. And so we already have some sense that forward, backward is independent of left, right is independent of up, down. And so what we say is that we live in a three dimensional world where the space has three independent dimensions along which I can move. We'll give them more formal mathematical definitions later, but for now it's sufficient to note that it's forward, backward, left, right, and up, down. Space is great for marking off where a physical object like myself or that camera or that flagpole is located. But space itself would be extremely boring without its companion time. Why? Well, we have to think about what time is. Time is another measure of something, but it's not a measure of spatial location. You can think of time, for instance, as a measure of change in spatial location, going from point one to point two in a three dimensional universe. Time, without a difference between where you were and where you are now, without some measure of that displacement between two events, being in place one and being in place two. The universe would be static and unchanging and extremely boring, and we wouldn't be here to have this conversation in the first place. Change is extremely important. And because the locations of material objects can change in both space and time, we need the ideas at the heart of physics and mechanics in particular, not only to describe that motion, but to make predictions about that motion in the future. It's possible because there are laws of nature to do that. So again, time you can think of as a displacement between two events. So for instance, the flag flapping to the left of the flagpole, and then whipping back and forth. Each ripple in the flag's fabric surface is an event, and we can think of one ripple and then another ripple as two events displaced from each other in time. Now, because of this framework of space and time, we can start to ask questions about the natural world. For instance, we can ask things like are two events in the universe related to one another. Does the first event cause the second event? This is the notion of cause and effect or causality. And physics, because it describes a universe that appears to have regular laws with lots of interesting features about how information travels in this universe, can actually make predictions about whether or not two events could be causally connected to one another. And that's sort of an interesting thing we can get to later in the course. It's also important to note that you might think of space and time as a game board on which the pieces of matter in the universe move. But you would then be sort of missing something very crucially important about space and time. A game board is not per se a player in the activities of the game. It sets out the rules. It sets out the places where matter can be and where it can't be and where it is and where it isn't and so forth. And that would make you think that matter and energy are somehow disconnected from space and time. Matter and energy can move through space and time, but they don't really have anything to do with each other. And that's just not the case. And as we'll glimpse later in the course, space and time are as much active players in the life of the cosmos as our matter and energy. And we'll see that they're all intertwined with one another at one point or another in this course. Now I mentioned units. We have to be able to subdivide the universe into regular pieces like pieces of space or pieces of time and agree on how we define those pieces in order to make measurements reliable and reproducible measurements of the universe and its properties. The standard unit of space that we will use in this course and which is really the globally accepted standard as you'll see in a moment is the meter. And the standard unit of time is the second. And the standard unit of substance of material properties, mass as we call it, is the kilogram. So let's take a slightly deeper dive into the systems of units and what their exact meanings are. To make measurements, humans have agreed on an international standard of a system of units of measurement, centered around the meter for distance, the kilogram for mass, and the second for time. This is known as the System Internationale or SI. And in English we would simply refer to this as the International System of Units. Now let's consider the standard definition for the unit of length, which is the meter. This is probably an instrument that's familiar to most of you, in one form or another. It's a stick that has been graded in various ways in order to mark off units of distance. And the full length of this stick from end to end is supposed to be one meter. Now the definition of the meter is something which has evolved over time. In fact, at one point in the history of this particular unit of measurement, there were competing definitions of the meter. But it was eventually agreed upon that the meter would be considered one 10 millionth of the distance from the north pole of the earth to the south pole of the earth along a line on the surface of the earth that ran through Paris, France. Nowadays, we have a much more reliable way of defining the meter. And for a long time, that had been something which was another object. It was a platinum iridium rod. And it was robust against temperature and pressure. And it was considered the standard unit representing the meter against which all other things that claimed to be a meter had to be set. But that rod did, in fact, have problems. It was only accurate to about 0.0001 meter, or about one 10,000th of a meter. And today, we have a much better way of defining the meter, and that is to use the fastest thing we know of in the universe. That is light. Light, regardless of the motion of its source of emission, or the motion of the detector that you use to find it, moves at a fixed speed in empty space. This is known as the speed of light. And that speed is, in fact, constant no matter what state of motion the emitter or the observer are in. It's an interesting fact that we will eventually get to in physics. The meter today is defined as the distance that light will travel in 1, 299,792,458th of one second. Now, of course, that definition depends on the definition of time. And I mentioned that that in the international system of units is the second. We're used to measuring time very easily. We all have devices like this in our pockets, or most of us do at least. We have some way of keeping record of the passage of time, the moment between one event and the next. But you have to have events in order to keep time. And so what sequence of events are you going to use to define the second? Well, originally, the second was defined as 1,86,400th of a solar day. But the problem with that particular definition is that you all have to agree upon what it means to have one solar day. This is an astronomical definition. And in fact, that definition of the solar day evolved as our knowledge of planetary motion evolved. It's better, of course, to find something that all observers can not only get access to, but then measure the same property of and get the same answer. And so these days, in fact, as of 1997, the standard of time was altered to use the behavior of an atom of cesium 133, one of the atomic elements. And in fact, the second is defined as the duration required for a cesium 133 atom to execute 9,192,631,770 transitions between two well-defined energy levels in the cesium atom. That cycling between those energy levels is something that is insensitive to temperature and pressure. And your changing definition of a solar day as planetary motion evolves over the history of the planet in the solar system. This is much more reliable. Now, I mentioned earlier that space and time are the game board upon which the chess pieces or the go pieces of matter are arranged and through which they move. Matter, as we study it on Earth, thinking about material objects like this little chunk of metal here, we study this in laboratories. We can observe matter beyond the Earth, the Moon, our Sun, other planets in our solar system, other stars in the universe, other galaxies containing stars just like our own. And everywhere we look, we see the thumbprint of atoms in the light that we can study from those objects. So it seems that the whole universe of visible information that we have accessible to us is composed of atoms. And we learn about atoms, really, for the first time in a course like chemistry. In chemistry, it seems often a very rote exercise in memorizing the properties of atoms, their masses or atomic weights, the number of electrons a specific atom has, the number of neutrons, a specific isotope of an atom has, the exact energies available to the electrons in a specific atom. These all seem like features of the universe we have to commit to memory. But in fact, physics gives us the toolkit to understand where all of those facts are set. Physics explains those energy levels. It explains the numbers of electrons and why and how they're arranged in different atoms the way they are. It is the laws of physics that help us to understand those tiniest bits of matter we call atoms. Now mass, which is the final unit of the international system of units that I will discuss today, is standard measure is a kilogram. So what is a kilogram? Well, originally a kilogram was defined as a volume of water and the mass associated with that volume of water. And what was the volume of water? Well, you could imagine a cube 10 centimeters by 10 centimeters by 10 centimeters in dimension. Make that entirely out of water, and that would represent the kilogram. Now water is a fickle thing. It expands and contracts as temperature and pressure changes. A little bit of it splashes out. You've just changed your definition of the kilogram, and you may not even notice that those water molecules have left. They can evaporate. Water is a difficult thing to work with, albeit fundamental to life as we know it. So instead, similar to the definition of the meter, in the 1800s it was decided to use a platinum iridium block. And that block was very carefully isolated and protected to keep material from flaking off, at least as much as possible. And to this day, that platinum iridium block is considered the standard definition of the kilogram. All kilograms that you have available to you, and so for instance, this block of metal that I hold here in my hand, which is supposed to represent one kilogram, will have to be ideally calibrated against that single block of platinum iridium at the International Standards Bureau. Now of course, that's perhaps not the most stable definition of mass. In fact, it's entirely possible that atoms of platinum and iridium are lost from that block over time, and its mass can change. After all, mass really is a measure of the sum total of the masses of the atoms that make up the material. Every block of material is the sum of its parts, and those parts are atoms. And they can flake off this little block of metal without me even noticing. And that makes atoms a very difficult thing to work with. Now this lets me lead finally into the last subject in this introductory lecture, and that is measurement. For me as an experimental scientist, measurement is my bread and butter. It's the foundation of everything that I do. And I have to not only be good at doing it, but also understand that nobody is perfect at measurement. And in fact, some measurements have a limit to how perfect they can ever be. These are features given to us by nature. You will learn more about that in physics later. We can consider a measurement and begin to understand the challenges involved in making reproducible observations of the natural world. As I said, this is supposed to be a kilogram. And in fact, if I take away these smaller weights, this single block of metal here is supposed to be 500 grams or 1 half of a kilogram, a kilogram being 1,000 grams. That's what's stamped on this block. I have here a holder, a little metal hanger, and I can slide the metal block onto it. Very convenient. And I have here a scale, which is supposed to tell me the mass that is placed on this tray on your left. Now, the way that this works is a balancing act. There are weights associated with this arm of the balance. They can slide around. When I place a new weight over here on the tray, the balance will go out of equilibrium. It will start to move. It will experience a force. That force will cause a motion, and eventually that motion should settle down to an equilibrium point. If I've done a good job of making the claim that this is, in fact, half a kilogram of mass, when I place it on this little tray here, the whole device will begin to move. And over here, on your right, there's a little arrow. When the arrow points to zero, it means that the weight in the rest of the scale balances the weight here. And it can, in practice, tell us the mass of this block, which is supposed to be 500 grams. So let's take a close look at some of these numbers. This mass is supposed to be 500 grams. Here, however, I have reached equilibrium, where the arrow on the balance is pointing just about at zero. And you'll notice that I have a 500 gram mass over here. But in order to balance out the mass I put on the tray, I had to add a little extra mass over toward the right of this scale. I had to add a little bit more than 500 grams to get this system to balance. So who is correct? Is it the manufacturer of this mass who stamped 500 grams on it, or is it the manufacturer of this balance who claimed that this should be able to somehow accurately measure the mass that's placed on the tray? Now, I should say that I went through a little bit of an exercise before this. You might say, well, you put some extra mass on here. This is 500 grams, but this hanger adds mass. In fact, it's 50 grams according to the manufacturer. When I place this on the tray and I let this balance out, when the motion settles down, I will see that I do not have 550 grams measured on the balance. I have 500 and a tiny bit. We're far from 550 grams. I already factored in the mass of this when I set up the scale. So again, who's right? The manufacturer who stamped the mass or the manufacturer who made the balance? This is the challenge to the experimental scientist. If we are to understand nature, we must not only agree on a system of measurement, distance and time and mass, the number of atoms and a material, but we must also understand that our methods for assessing the natural world have limitations. They have uncertainties. We must understand where they come from. We must assess them as best we can. We must report them faithfully. And that is measurement. It is not just a number, 500 grams. It is 500 grams plus the limits of my knowledge of that statement. And that is what differentiates science from all other ways of knowing. It's not just about learning something. It's about learning the limitations of learning and quantifying them, and doing better and better as you make more measurements and mature your methods. So welcome to Physics 1303. I'm looking forward to a very exciting semester with you as we explore the cosmos from these most basic foundations of observation, measurement and units.