 Hi, I'm Zor. Welcome to Unizor Education. We continue talking about basic concepts of physics, and today's basic concept is the time. Now, this course is presented on Unizor.com. It's called Physics for Teens. I do recommend you to watch it from this website rather than from any other source, because the website contains not only the link to this lecture, which is actually stored on YouTube, but also it contains notes and it contains exams. Also, there is a course of math for teens, rather complete, I would say, and above and beyond the site is completely free and doesn't have any advertisement. So, we are talking about time. Well, if you have started the Math 14 course on this website, you remember that there are certain concepts in mathematics which we just don't define. Basically, we are taking them as undefined. Well, if you have a theorem, you can prove it based on another theorem or that other theorem based on even earlier theorem, and then all the way to the axioms. In geometry, it's very obvious. For instance, in classical geometry, you have five postulates of Euclides and from there, we basically build the whole building of geometry. At axioms, we are just taking without any proof, not because we like it, just because there is no other choice. Now, same thing when we define certain objects. Again, back to geometry, we define a triangle, for instance, as a geometrical figure which basically contains three connected to each other segments. A segment is actually part of the line and what is line-line is undefined, as well as the point, as well as the plane, for instance. So there are certain undefined entities which are only used to build other more complicated entities. Now, how can we study these undefined entities by specifying their properties? So the point itself, for instance, in geometry, is not really defined. You cannot really say, okay, this is the point or explain, basically, what is the point. No, you cannot do this. However, the point has properties which we have kind of postulate, basically. We are axiomatized the properties and then we can learn everything about an object to be called the point by basically studying its properties. Same thing exactly with basic concepts of physics. Concepts like time, for instance, which we are going to discuss today, or the concept of a space, for instance. So time is an undefined entity in physics. However, as many other undefined entities, we are attributing certain properties and it's the properties which we are actually studying, calling this a studying of time, right? So we will concentrate on properties of the time. So I will try to explain how we measure time, how we count, et cetera, et cetera. But again, these are properties of the time. I don't know what the time is. Well, inasmuch as I don't know what the point actually is, but they do know the properties. And that's the properties which is important. So let's talk about time in the language of its properties. Well, first of all, as an explanatory statement, time is a form of existence of our world. I mean, it has many different forms, including spatial forms, for instance. And the time is also just one of the forms of existence. I understand it's not a definition of time. It's just certain descriptive language. Now, what is important is that everything in this world is basically changing. So we are observing certain processes which are happening in this world. And here is very, very important characteristic of time. Any change in the process, any process is related to change of time. And vice versa, if you have a change of time, then it necessitates certain change in the processes which are surrounding us. What it actually means is that we can identify the time or actually the process of time, the going of the time with certain process which we consider as a good measure as far as reliability, periodicity, stability, predictability and other nice features. So we can always say that whatever we can call this type of predictable, stable, repetitive, etc. process we call actually this process as a good equivalent of the time. So we don't know what the time is, but we can actually connect the going of the time with certain process which we all agree upon as being a representation of the time. So how can time be represented? I have already spoken about this in one of the previous lectures. That, for instance, the rotation of the Earth around its axis can be considered as a good representation of time. Why? Well, because it's relatively stable or at least we think it is stable. It's periodic, it's repetitive, it's predictable. So all these properties of the time which we would like it to have they can be represented by this rotation of the Earth. And that's exactly what people long, long time ago have decided to do. They say, okay, whatever the time is, we can measure it by comparing with rotation of the Earth because we have day and night, day and night, and we can always say that we have one rotation, they have divided into 24 hours, every hour into 60 minutes, every minute into 60 seconds, and they're saying, okay, now we can measure the time because we know what is one unit of time. All we have to do is to say, okay, this moment of time is the beginning of time and then measure every, let's say, second how much time has passed or we can go backwards with certain number of seconds which precede our conditional beginning of the time, it's not the beginning of the time, it's just some point which we have decided as the null point. And from that point we go forward or backward. Okay, that's fine. This is definitely a good measure of the time and the rotation of the Earth is a good representation of time. And then from there people have built certain other representations of the time which we usually call clocks or watches, whatever, and they all work fine, they can be synchronized if they're slightly off each other. And well, basically that's exactly the way how the concept of time was ingrained into our culture, into our science and in everything whatever we are doing basically. That's why it's so universal. Well, the only thing is the rotation of the Earth must be measured somehow, right? So how people did it? Well, they probably used a telescope which was fixed at certain position on the surface of the Earth, they pointed it to the sky, they saw some kind of a star and then as the Earth rotates this star obviously leaves this point of view of the telescope and then when it goes the full circle the star again is in the same place in the same telescope. Well, that's good enough. So this is the period which we have divided or they have divided into 24 hours and that was fine. Obviously for contemporary needs this precision is definitely not sufficient. First of all the stars are not really at the same place all the time they are moving, although very, very slowly. And the Earth is not exactly rotating at the same speed in certain very precise terms. So there are different variations within certain limits of course etc. But anyway for contemporary measures, for contemporary science we are using a different technology. Contemporary technology. Well, one of the most precise instruments which we are using right now is called atomic clock. Basically I'm not really sure how exactly it's working, but the idea is that certain atoms in this particular case they're using atoms of cesium, the research element, they have different states, energy states or something and they are oscillating between two different states very, very fast. And certain number of these oscillations occur in a second. Now they have decided to define an interval of time which is equal to one second to certain number of oscillations because it's considered that these oscillations are much more precise than anything else which we can deal with. So oscillations are really very fast, occurring very fast and somewhere I have a number. Yes, the number is 9,192,631,770 oscillations the period of time during which this number of oscillations within this atom are happening. This is called one second by definition. This is the definition of a second in a certain system of units. We have an international system of units, SI, System Internationale, I think it's French. So this international system of units basically declares that the period of one second is not really related to rotation of the earth, it's related to certain number of oscillations within the atoms of the cesium. Fine, whatever it is, it doesn't really matter. There is a definition of a second. We all understand that the second is actually a relatively short period of time and that's how we measure the time. Now we are talking about certain very important two axioms about the time. Now the first axiom is continuity of time. Well, we know that we have an interval of one second. How about half a second or one thousandth of a second or one millionth of a second? Do these intervals actually exist? Can I divide an interval of time into certain number subintervals and still get the certain valid time interval? Well, the answer is yes. So by definition, we just postulate basically that time is continuous, which means that any real number which represents, I mean any real number can represent certain number of seconds. For instance, like 3.5161, blah, blah, blah, blah, to whatever extent I want. Of seconds, we assume that this is a valid interval of time. So time changes in a continuous fashion. Now this is not exactly what contemporary quantum mechanics actually says, but we are not talking about contemporary quantum mechanics. We are talking about classical Newtonian mechanics, which was started in whatever, 17th century or whatever. And we assume as an axiom that the time is continuous. The continuity of time is very important. So that's very important first axiom, which means we can divide any interval of time into any number of subintervals. So that's how we have milliseconds, which are thousands of a second. We have microseconds, which is one millionths of a second. We have nanoseconds, picoseconds, et cetera, et cetera. So however small intervals we want, we consider that these are existing time intervals, however small, infinitesimally small, basically, because we're talking about continuous, which means all real numbers can represent certain amount, certain number of seconds in certain time interval. The second axiom. The second axiom is related to the following fact. For instance, you have conducted an experiment right now, today, and it has certain result. Now, what this axiom states that if you are able to duplicate completely conditions of your experiment tomorrow, it should produce exactly the same results. So the same experiment, identical experiment, at two different moments of time or two different intervals of time, should produce exactly the same results. It's called uniformity of time. Time changing does not really change the outcome of any experiment, of any physical process. So all modifications of physical process are related to some maybe modifications in the condition, in the environment of the experiment, but if the experiment is completely identical to another one performed at another moment in time, the results mustn't be the same. So that's uniformity. So we have continuity, continuity, and we have uniformity of time. These are two very, very important properties of time. I mean, I told you in the very beginning, we're talking about properties. So these are properties. And obviously we can measure the time using atomic clock with certain number of oscillations to be equal to one particular unit. And so we can actually do anything we want with the time. And in particular, we can use the time as an argument to three very important co-ordinate functions which we were discussing before. Now I can say that t is a real time. It's a real number which is a numerical characteristics of the interval passed from the beginning of time. So I have to have somewhere a moment of time when the time is equal to zero. And then I can say that after certain number of seconds measured by this parameter t, my physical object, which is actually a point, has these coordinates in the space. We are talking about Cartesian coordinates right now. So this way, the concept of time as a real number which represents certain number of seconds from certain conditional beginning of the time, that allows us to basically quantitatively address the position of our object at any moment in time. Now after this moment t is equal to zero or our time intervals are positive obviously, preceding this, they will be negative. So we can always say that for any moment of time before or after certain conditional beginning, we can define the position of our point or our object. It's basically like we have conditionally decided where is the year number zero. Now before this year, it was before our current era, and then whatever happened after this, that's after basically, which we kind of relate to birth of Christ in this particular case. Whatever the point zero is, we can always talk about time which follows and time which precedes positive and negative values of parameter t. And that's how our argument in these three coordinate functions actually constructed. Well, that's it for today. Thanks very much and good luck.