The first principle of relativity

The principle of relativity constantly emerges in the context of space travel - for example, in the BBC article about the launch of the NASA Curiosity rover. The article was not bad, but, as is often the case in the media, there is one serious mistake in the text. Quote: "By the time the planet was launched toward the Red Planet, it was moving at a speed of 10 km / s."



Oh you my gods - 10 kilometers per second! It sounds very fast. On the highway, they usually allow a speed of 100-120 km / h.

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But this statement is completely meaningless.



In fact, right now you are sitting on your armchair, reading this cute little piece, moving at a speed of 30 km / s. In a sense. But no one will write you a penalty for exceeding or give a reward for the fact that you have overtaken the bullet (moving slower than a kilometer per second).



Did you know that Einstein did not invent the principle of relativity? The original principle of relativity — which includes claims that the laws of nature do not allow you to determine whether you are motionless, and therefore your speed must be determined relative to another object — goes back at least to Galileo, to which scientists attribute the wording of this principle. Einstein changed the details of the principle, in an unexpected and radical way, but without discarding Galileo’s basic idea that all speeds should be measured by comparing two objects relative to each other.



Galileo understood that if you are on a ship in calm waters, inside a cabin without windows, you will not be able to determine the speed of the ship. If you can throw a ball with a friend while on the beach, you can also throw a ball if the ship moves at a speed of five kilometers per hour, or fifteen, on the water - while it moves straight and is not thrown by the wind and waves. In the extreme version of the experience, you will be able to throw the ball in the same way, while aboard a jet airplane moving at speeds of hundreds of kilometers per hour, until there is turbulence. I'm not sure that this can be done on a passenger plane, but you can try to jump - like I did when I was nine years old, to see what would happen; you will find that all sensations will be exactly the same as from the jumps on the ground. And this is good. If Galileo’s principle of relativity did not work, it would be hard for us to eat, drink and walk on an airplane - the “fasten your seat belt” badge would burn for the entire flight.



What does a car speedometer actually measure? It measures the speed of the vehicle relative to the ground. Of course, when you travel behind the wheel, this is the speed you need - you need to know how long it will take you to move from the starting point to the goal of your journey, and since both these points do not move relative to the ground, the speed of your car tells you about how much time it takes you to travel between them.



But for the plane, two dimensions matter. One is speed relative to the ground, the other is speed relative to air. The ground speed indicates how quickly you cover the distance between the starting point and the end point. The speed relative to the air shows how fast the air flows around the wings of the aircraft. It is this speed determines whether the aircraft is flying, and how. Also, the maximum speed of flight will be speed relative to air, and not relative to the ground, since engines need to work against air resistance, which depends only on air speed.



If there was no wind, then the air and the earth would turn around the earth's axis exactly once a day, and the speeds of the earth and air would be the same. But there are strong winds in the atmosphere, so the speeds of air and land can vary greatly. At mid-latitudes, where people live from North America, Europe and most of Asia (as well as people from South America, South Africa and Australia), the winds at the heights, where jet planes fly, blow to the east. Most of the air movement takes place in the “jet streams” that reach the heights where the planes fly. This air "river" can move at a speed of from 100 to 250 km / h relative to the ground. This means that an airplane with a speed of 800 km / h relative to air will move relative to the earth at a speed of about 700 km / h if it flies to the west, and at a speed of about 900 km / h if it flies to the east. This roughly explains the fact why flights from Europe to the United States may take a couple of hours more than flights from the United States to Europe; the speed of the aircraft relative to the air is the same in both cases, and the speed relative to the ground is not. The same principle increases the duration of a boat trip if you go upstream, upstream, relative to a trip downstream. Boat engine allows the boat to move at a certain speed relative to the water, and this speed does not coincide with the speed relative to the coast, both for traveling upstream and downstream.



Of course, when you are on a plane (or in a boat), you do not feel the speed; you do not care if the speed relative to air is 800 km / h or 500 km / h, since in the plane you (and the air inside it) do not move relative to each other. In other words, you do not have any one speed. You have a lot of speeds relative to other things: speed relative to the aircraft (zero), relative to the air outside (800 km / h), relative to the ground (faster or slower than speed relative to the air, depending on where you are moving). Which one of your speeds is better? It depends on what you want to know; speed relative to the ground affects travel time, relative to air — important for the safety of the aircraft and its flight characteristics, and relative to the aircraft — affects how long it takes you to travel from your chair to the toilet.



What about a spaceship? The ship that carried the Curiosity planetary rover moved from Earth to Mars. He has speed relative to the earth. He has another speed, relative to Mars. And one more, excellent, relative to the Sun. Which one affects travel time? No! The starting and ending points of the flight of the aircraft are at a fixed distance from each other, and the spacecraft's task is more complicated, since Mars and Earth are moving relative to each other. And they move quite strongly during the journey of eighteen months! Speed ​​in space is not an easy thing, everything moves in relation to everything else. This is one of the reasons why the development of spacecraft requires very serious preparation!



In fact, due to the rotation and the rounded shape of the Earth, even the speed of an airplane relative to the ground and relative to air becomes a bit more complicated. In addition, airplanes do not always fly along the shortest route, they can use airflow and travel longer distances to reduce the flight time. The movements of the planets and the spacecraft flying in closed orbits around the sun are also complex. So if you really dive into this topic, then dive very deeply. But for the time being we can take advantage of the fact that in short time intervals all trajectories of movement are close to straight lines, and this allows us to refer to the Galilean principle of relativity.



Let us return to you, who is sitting on a chair. You may decide that you are still, but it is not. First, the Earth takes you with it, rotating around its axis at a speed of about 1000 km / h - depending on the latitude at which you are located. Even faster, the Earth moves around the Sun, and we all rush along with it at a speed of about 30 km / s relative to the Sun. You do not feel this for two reasons. First, you can feel what you touch, and you do not touch the sun. You touch the chair, the air in the room, and since you are still relative to them, you do not feel the movement. Secondly, your movement goes almost in a straight line (it is not straight, but bends very slowly), so the Galilean principle of relativity applies to you, to your chair and room.



And the Sun moves around the center of our Galaxy - the Milky Way, this giant megalopolis of stars, on the outskirts of which we live - at a speed of about 220 km / s. " Where you go, there I will go " - the Earth moves around the Sun, therefore our speed relative to the center of the Galaxy is about the same as that of the Sun. And the Galaxy is moving relative to other galaxies with speeds of even greater order - but we also do not feel them.



Let's return to the article with the BBC. The spacecraft moved, according to the newspaper, at a speed of 10 km / s. What about? I would think that this is speed relative to the earth. But in the article you need to write it right! Otherwise, the statement does not make sense. Since Mars is farther from the Sun and moving in its orbit more slowly than the Earth (about 24 km per second relative to the Sun), it is possible that the spacecraft, despite the use of rockets, actually slowed down relative to the Sun! That is, although it started, like the rest of the Earth, at a speed of 30 km / s relative to the Sun, then it could slow down (from the point of view of the Sun), so that it would be easier for it to then coincide with the movement of Mars in orbit. It would be quite interesting to know, but unfortunately, the Air Force did not report anything on this score.



And if you were on a spaceship? At the end of the work of the rockets, when the movement of the spacecraft is aligned, you will not sense any movement. According to Galileo’s principle of relativity, you will not know in which direction you are moving or how fast you are moving with respect to any planet or star, unless you carefully measure the changing location of the planets in the sky and observe how the sun decreases. And if it were not for your confidence in the engineers and scientists who convinced you that the rocket will send you at the required speed and in the right direction relative to Mars, the Earth and the Sun, you would not know whether you will ever come close to Mars, or simply to drift in space for a long time, like another micro-planet that carries numbers.