 Hi, I'm Zor. Welcome to UNISOR education. Today we will talk about Galileo's Relativity Principle. Now this lecture is part of the course called Physics for Teens presented on UNISOR.com and I do suggest you to go to this website UNISOR.com to watch this and any other lecture, because every lecture is also has notes, very detailed notes, where basically I'm explaining, well, the same thing, but it's like in a textbook, so you can always refer to a specific topic and read about it, not necessarily to listen to me. Plus the website has many problems and exams for all those who are ready to be challenged. All right, so back to Galileo's Relativity Principle. Now it's called Relativity Principle, but it should not be mistaken for Einstein's theory of relativity. Einstein developed his theory in the beginning of the 20th century and this principle is about 300 years earlier than that. Now although very important developments of contemporary physics like atomic bomb was related to Einstein's Relativity Principle, this Galileo's Relativity Principle is very, very important because the entire history, like 300 years of development in physics, well basically are in some way related to this particular principle. It's the foundation of the physics. Now in the previous lecture we're talking about inertial frame references. Well, this principle is about inertial frame references. Now let me just get into details one after another. First of all the most important formulation of this particular principle is that an experiment which is actually conducted under exactly the same conditions and it's kind of difficult to specify what kind of conditions, but if everything is the same basically. One experiment is conducted in one inertial system and another in another inertial system. There should be no difference in the results. So whatever mechanical experiment you are conducting like throwing a stone or rolling a ball or do whatever else. If you are doing exactly the same thing in two different inertial systems, results must be the same. This is the principle which in more mathematical language means it's an axial. So all these inertial systems are equivalent in the respect that all the experiments conducted in different inertial systems are actually having exactly the same results. Now this principle is very very important from two different standpoints. One standpoint is what's not said in this axiom, what's emitted in this axiom. This is very important and here is why. We do not have any reference to the time. So we are saying that in any two inertial systems results will be the same and we are not mentioning that one should be conducted at exactly the same time as another. One can be in the future or in the past relative to another, which means that the time is actually not a particular argument into this function, the function being the result of the experiment. It does not depend on time. Today the experiment will do exactly the same as tomorrow. What it actually means in more scientific terms that the time is invariant relative to the well particular moment in time or there is another word isomorphic. Isomorphic, which means basically isomorphic, which in plain language means the same. The time is the same. Today, tomorrow, whatever. So the time is isomorphic or uniform or whatever other term you can or invariant, whatever term you can use, that's okay. The only difference is there is no peculiarities in one moment of time relative to another. Now that is a consequence of emitting the time parameter in this particular axiom, in this Galileo's relativity principle. Now another thing which is emitted is location. It doesn't say that these two experiments must be conducted at the same location in different inertial frames of reference, which means location is also irrelevant in this particular case. This location is exactly the same as that location or that location. The entire space is basically uniform as far as the results of the experiment. If the experiment is exactly the same conducted in this particular location, we'll give exactly the same results as in that particular location. So now we have exactly the same isomorphism. The space is isomorphic. It's uniform in every particular location. And the third thing, which is also emitted, that is related to direction. So we can arrange our apparatus, which we are using to make our experiment in one particular direction, or we can turn it in another direction. Or if we are throwing the ball, for instance, as an experiment, we can throw it in this direction or in that direction. Again, direction is emitted from the formulation of the principle, which means our space is, well, unidirectional. I know how to characterize it. Isomorphic is in relation to a direction or there is another scientific term, isotropic. So our space is isotropic, which means it's invariant relative to a direction. So it's isotropic and it's isomorphic, and the time is isomorphic. So these are very important characteristics of space and time where all these experiments are conducted. Now, obviously, this is an approximation and they're not talking about this. It's an ideal kind of a thing. It's like mathematics is not exactly what we have the real world around us. Mathematics is some kind of an abstraction. Now, this particular concept of inertial system and the time isomorphic and the space isomorphic, etc., these are all abstractions, which we believe are relatively close to a reality. And that's why we can live in this much simpler abstract world where our laws are very nicely formulated and receive reasonable results, which are applicable to our real concrete world. So, we were talking about something which was omitting, omitted from the relativity principle. Now, let's talk about what is explicitly specified. Now, what's explicitly specified is that two inertial systems, the same experiment, the same results. What it means is that being in one inertial system, you cannot actually distinguish what is this inertial system is. Maybe it's moving relative to something else to, let's say, stars. Maybe it's not moving. Maybe it's just changing still. Now, you can imagine, for instance, two people, one standing still on the ground and another in the train, which is moving along a very, very straight line with a very, very constant speed. Which we can approximately consider to be an inertial system, as well as the person who is standing on the ground can also be considered as being in the inertial system related to our planet. And we disregard the curvature of the Earth because Earth is very big. We also disregard gravitational force because it's balanced by the force of reaction of the ground. So our gravitation goes down, reaction from the ground goes up, and that's why we're standing still. We're not going down to the center of the Earth, right? Same thing, the person on the train, it does not fall down through the floor because the floor resists. So the gravity goes down, the floor reaction of the floor goes up, and the person can actually sit still in the train. So these two people, they can conduct exactly the same experiment, and one person who is in the train, if the windows are closed, if he doesn't really know whether the train is moving or not moving, he will not be able to differentiate standing still or moving with a constant speed along a straight line. That's what basically this principle is all about. Okay. Now, what kind of experiments actually can be conducted in this case to exemplify this situation? Well, first of all, both people, the one who is in the train and the one who is standing on the ground, can roll the ball. So if the balls are of the same mass, the same size, the same material, etc., they will roll relative to their system of reference in case of the person standing on the ground. So the ball will roll relative to the ground. And for the person who is on the train, the ball will roll relative to the floor of the train. And we can measure the relative speed for one relative to the ground for another relative to the floor. And the speed will be exactly the same. Speed, acceleration, whatever else you can measure. Now, what else, what kind of experiments? Okay, part of water. If you take the part of water and just put it on the train, which moves with a constant speed, it will be no ripples, no waves. It will be a horizontal level of the water. Exactly the same as the level of the pot standing on the ground when there is nothing touching it, right? So that's another experiment. So we can also weight certain things. For instance, you have some kind of a weight and you are weighing one particular object. In one case, on the train, the same kind of object on the ground, they will weigh exactly the same weight. Okay, I think that's enough of different examples. Now, what is very important, what I was just talking about, I was saying that you can measure the speed, the acceleration, the location, the whatever relative to corresponding system of coordinate corresponding frame of reference. For the person who is standing on the ground, this frame of reference is connected to the ground. And for the person who is in the train, it's connected to the train. And these two systems, these two frame references are both inertial. So this relative to individual inertial system is a very, very key word in this particular case. And that's why actually the principle is called the principle of relativity. Because everything is somehow related to the frame of reference. Any movement related to some frame of reference. Because if I am standing still and somebody else is walking past me, now he is actually moving relative to the frame which is connected to me. And I'm considering myself in this frame as standing still and he is moving. But at the same time, there is nothing wrong for him to connect the reference frame to himself. And if he is moving along a straight line with a constant speed, that frame will be inertial. In which case, he will consider himself as standing still and me moving past him. That's what relativity means. Excuse me. Everything is moving somewhere relative to something else. And maybe it's standing still relative to something else. So it's very important whenever we are solving any kind of a problem, we really have to realize what kind of a frame reference we are talking about. What is the frame reference relative to which we are calculating certain things. Okay. Now, another thing is very important. All these relative things. What are these relative things? Location is relative to the frame of reference. Speed, acceleration. Now, all these motion related things are related to some frame of reference, which means they are relative. I'm moving relative to something else. Well, however, the time is not relative. The time is considered to be absolute in the classical physics. By the way, it's not the case with theory of relativity with contemporary physics, but we will talk about this separately. In the classical physics, which was accepted as the reality, which, well, basically, it's an abstraction which corresponds to reality. Let's put it this way. We are assuming that the time is absolute. Now, what it means that the time is absolute? It means that if I have an ideal clock and the person on the train moving with a constant speed on a straight line has a clock, and we have synced that particular, these two clocks at some moment in time. Then the guy is moving somewhere, wherever he is moving. Whatever time passes, our clocks will still show exactly the same time. So, the time is considered to be absolute. Location, speed, acceleration, they are all relative to one or another inertial, usually inertial frame of reference. But the time is considered to be an absolute, the same for everybody. We are considering that everybody's time is moving with exactly the same speed, whatever the speed of time is. If one passenger on the train, then exactly the same second has passed for the person who is extending still on the ground. One second here is equal to one second there. So, there is no frame of reference, so to speak, for the time. I mean, we can always find the time, whatever the time we are accepting as a zero point, and starting from this, we can count an absolute time. But usually the time is measured not from some abstract point, but we are measuring the time interval. So, the time interval will be the same in one case or another, moving or stanging or moving with another speed or a different direction, whatever else. Time is absolute in the classical physics. Yes, Einstein has corrected this slightly. But that's another topic and we will address it in some other time in the future. In the absolute future. All right, so basically that's it for today. Thank you very much. I would suggest you to read the notes for this lecture. It's on unison.com. Go to this course. And that's it. Thanks and good luck.