 Hi, I'm Zor. Welcome to a new Zor education. So we are starting a new course called theory of relativity or rather relativity for all. It will be about special theory of relativity and today will be the first lecture where I will talk about something which we call reference frame in physics. Okay, so reference frame. First of all, we are using numbers to characterize behavior of certain system of objects, right? Now, what are the numbers? Well, the time, the space position, speed, acceleration, some others, whatever. So where are these numbers are coming from? Well, obviously we need certain system where we can measure certain properties or movement or lengths or distance or time period, etc. So for this we need basically two things. Now, we have a space and we need some kind of system of coordinates in the space. Well, usually we are talking about three-dimensional Cartesian system of coordinates with perpendicular axes X, Y and Z and we use clock to measure the time. So basically the combination of time measurement device, the clock and space measuring system, which is system of Cartesian coordinates, with units of lengths on each axis. So this together is called a reference frame. Now, this is very important concept, the reference frame, because you can choose this reference frame differently. When I was back in school, we were talking about reference frame, which is kind of stable. It stays still and does not change with the time. How? Well, let's put the center, the origin of the space coordinates at, let's say, at the center of sun, of our sun and direct one of the axes, let's say X axis, towards some kind of a star, Sirius, for example, and to other perpendicular to this one, other axes. Well, we can consider this system as, well, relatively stable, because the position of stars on our sky relative to sun is relatively stable. I mean, it does change, but so slowly that we don't really notice it. And for that particular kind of approach, we are fine. And now, relative to this particular reference frame, we can say that something is standing still or moving. Now, if we approach it in a little bit more scientific way, first of all, we understand that there is no such system, which is absolutely at rest. And secondly, if you have one particular system, then there might be other systems, which are either moving or not moving relative to it. How should we consider these systems? Are they as well usable for the same purpose? And we will just have different numbers if we will measure the position and the speed. Can we do it, etc.? So one of the first concept, which was introduced into this particular theory, was a concept of inertial reference frame. Now, what is inertial reference frame? Well, imagine an object which is just going by inertia, which means either there are no forces at all or all the forces together nullify each other. So basically, it does not experience any influence from outside. Object just moves by itself. Okay, now, if we will choose certain system of coordinates, certain reference frame, certain clock, and we will measure how this particular object is moving, we can find out that there are certain, basically, like functions of time, x and y and z coordinates as functions of time, and we can have a trajectory of that particular movement in the reference frame, which we choose. And here is the very important thing. If this trajectory is a straight line in this system, in this reference frame, and the speed that moves along this straight line is uniform with a constant speed, then we can say that the system which we have chosen, the reference frame, which consists of systems of coordinates, Cartesian coordinates, and and the clock are inertial. So inertial system is a system where every object which moves by inertia, moves without any kind of outside forces, is moving along a straight line with a uniform speed. And it looks like it's a natural kind of definition. I personally don't see any problems with this. And if, for example, a spaceship which has its engines off just flies by itself in the space far from the gravitating bodies, far from stars. So, basically, all the gravity from all the outside is, well, basically nullifies each other. It goes along, well, we think it should go along a straight line, right? So the system of coordinates which we are using must be basically fitted in such a way that this looks like a straight line in this particular system. I mean, if we will take a look from the different system perspective, for example, if you have a spaceship which is flying somewhere far in stars, but we are on Earth and we are relating the frame of reference with our position on the Earth, which is basically rotating. We will definitely see the trajectory of this particular spaceship not as a straight line. I mean, it will do some kind of circling or arc or whatever. As the Earth is moving, obviously, from our perspective, if Earth is our system of reference, then it's a spaceship moving not exactly along the straight line. So it's very important this definition of the inertial system. I mean, in this case, we see that Earth considered as a system, as a reference frame, is not really an inertial one because it's rotating. Okay, but there are inertial frames. Not exactly, not absolutely inertial, but the one which I was talking about before centered at the Sun and directed to stars, which seems to be relative to a stable combination. It's almost inertial. Let's put it this way. Although, yes, all these galaxies are rotating around some center of galaxy, etc. So there is no absolutely inertial system. But there are systems which are relatively close to being inertial. And in physics, for our calculations, for our purposes, we can consider that there are inertial systems. And we can use this inertial system as probably the base to judge, to make certain judgment about movement of the objects. Okay, so that's basically about inertial system. Now let's talk about the time, to measure the time, to measure the clock. We need basically two things. Where is the time zero? And what's the unit of measurement? We did talk about units, by the way, before in the previous course, Physics 14s. Like second, for example, was established as a unit of measurement. But where is the point zero? I mean, is it like 1st of January of 1900? Like in many computer-related programs, it's basically used. Well, no, it's basically any kind of time, can be the beginning of time. And again, we are just assuming that we have chosen a certain moment of time, as the beginning of time, and call it time zero. It's our choice. In as much as the choice of inertial frame coordinate systems is our choice, the time zero and the unit of time is also our choice. And again, we assume that it's already kind of chosen by us. So we know our reference frame, we know our coordinate system. It's centered the direction of axes, the unit of measurement of the lengths, and we have chosen the beginning of time, the time equal to zero, and the unit of measurement of the time. When everything is chosen, and the system is inertial, according to the definition which I was talking about before, the object moving by inertia actually is moving along the straight line in the system with a constant speed. Then we are ready to start basically analyzing how the movement of certain object is expressed in one or another inertial system. Okay, now there is a very interesting concept. Consider you are in a rail car, and it's moving very, very smoothly along a straight line. It doesn't really vibrate, it goes with the same constant speed, and there are no windows. As you understand, it would be very difficult or basically impossible to determine whether you're moving or you're standing still on the same spot on the rails. Now this feeling actually, and understanding the difficulty or impossibility actually to detect your own movement, it grew into something which is called the relativity principle. The relativity principle is basically stating that if you are within inertial system, you cannot determine whether this is inertial system which is moving relative to another inertial system or not, because all the laws of physics expressed quantitatively in two different reference frames which are both inertial, which are both moving along a straight line from each other. So let's consider one inertial system moving with a constant speed, maintaining the parallelism between axes relative to another one. So if these two systems are moving relative to each other, all the laws of physics will be the same. So you cannot experimentally determine whether this is system A or system B. Maybe you can choose system A as basically standing still stationary, let's say, and then you're in the reference frame B in this railway car and you are basically your system is relative to the car, not relative to the earth. And there is no difference in the way how the laws of physics behave in these two systems. They are absolutely the same, so you cannot determine. This is called the relativity principle. Actually, it's related to Galileo actually who expressed the first ideas of this type. It's called Galilean invariance or Galilean principle or relativity principle. So basically all the inertial systems are the same in a way that all the physical laws are exactly the same and you cannot distinguish one system from another. From inside the system, you cannot say that this is not the same as, let's say, another system. So again, from the inside of the railway car, which is moving very slowly and smoothly along the straight line, you cannot determine whether it's moving relative to the earth's another inertial system as we have understood or it doesn't really move. So all the laws are exactly the same. And this is the principle of relativity which is very important in the theory which we are going to talk about in this course. So basically that's it for today. So my purpose was to introduce a concept of inertial reference frame, which basically is the frame where an object moving by inertia without any kind of external forces is moving along the straight line with a uniform speed. And the concept of Galilean invariance or Galilean principle or relativity principle of relativity, which basically states that all the laws of physics expressed quantitatively, let's say, like the second Newton's law, for example, where participating are speed and acceleration actually and force. So all these laws are exactly the same in all inertial systems moving relative to each other along the straight line with a constant speed. That's basically all I wanted to talk about today. And the next one will actually be dedicated in how we do measure certain things in these systems and how we are transforming time and coordinates from one system into another. That would be the next lecture. Okay, so thanks very much. I do suggest you to read the notes for this lecture. So you go to Unisor.com and choose relativity for all course. And that would be the first lecture about reference frames in this course. Thank you very much and good luck.