The first principle of relativity

Original author: Matt Strassler
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The principle of relativity constantly pops up in the context of space travel - for example, in a BBC article on the launch of NASA's Curiosity planet 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 rover was launched towards the Red Planet, it was moving at a speed of 10 km / s.”

Oh my gods - 10 kilometers per second! It sounds very fast. After all, a speed of 100-120 km / h is usually allowed on the highway.

But this statement is completely meaningless.

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

Do you know that Einstein did not invent the principle of relativity? The initial principle of relativity - which includes statements 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 - dates back to the least Galileo, to which scientists refer 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 must 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, then you will not be able to determine the speed of the ship. If you can throw a ball with a friend while on the shore, 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 it is not thrown by the wind and waves. In the extreme version of the experiment, you can also throw the ball while aboard a jet plane moving at speeds of hundreds of kilometers per hour until there is turbulence. I'm not sure that you can do this on a passenger plane, but you can try to jump - as I did when I was nine years old to find out what would happen; you will find that all the sensations will be exactly the same as from jumping on the ground. And this is good.

What does a car’s speedometer actually measure? It measures the speed of a car relative to the ground. Of course, when you are driving, 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 trip, and since both of these points do not move relative to the ground, the speed of your car tells you how much time it takes you to travel between them.

But for an airplane, two dimensions matter. One is speed relative to the ground, the other is speed relative to air. Ground speed indicates how quickly you cover the distance between the starting and ending points. Speed ​​relative to air shows how quickly air flows around the wings of an airplane. It is this speed that determines whether the plane is flying, and how. Also, the maximum flight speed 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 were no wind, then the air and the earth would rotate 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 speed of air and earth can vary greatly. At mid-latitudes, where people from North America, Europe and most of Asia (as well as people from South America, South Africa and Australia) live, winds at heights where jet planes fly fly east. Most of the air movement occurs in "jet currents" reaching the heights where airplanes fly. This air "river" can move at a speed of 100 to 250 km / h relative to the ground. This means that an aircraft with a speed relative to air of 800 km / h will move relative to the ground at a speed of about 700 km / h if it flies to the west, and at a speed of about 900 km / h, if he is flying east. This roughly explains the fact why flights from Europe to the USA can take a couple of hours longer than flights from the USA to Europe; the speed of the aircraft relative to air is the same in both cases, but the speed relative to the ground is not. The same principle increases the duration of the boat trip if you go upstream, against the stream, relative to the trip downstream. The outboard motor 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. The same principle increases the duration of the boat trip if you go upstream, against the stream, relative to the trip downstream. The outboard motor 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. The same principle increases the duration of the boat trip if you go upstream, against the stream, relative to the trip downstream. The outboard motor 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 in an airplane (or in a boat), you do not feel the speed; you don’t care whether the speed relative to air is 800 km / h or 500 km / h, because in an airplane 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 many speeds relative to other things: speed relative to the plane (zero), relative to air outside (800 km / h), relative to the ground (faster or slower than speed relative to air, depending on where you are moving). Which of your speeds is better? It depends on what you want to know; speed relative to the ground affects the travel time, relative to air - it is important for the safety of the aircraft and its flight characteristics, and relative to the plane - affects

What about a spaceship? The ship carrying the Curiosity planet rover moved from Earth to Mars. He has speed relative to the Earth. He has a different speed relative to Mars. And another, excellent, relative to the Sun. Which one affects travel time? No! The starting and ending points of the plane’s flight are at a fixed distance from each other, and the task of the spacecraft is more complicated, since Mars and Earth move relative to each other. And they move quite strongly during a journey of eighteen months! Speed ​​in space is not an easy thing, everything moves relative 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 round shape of the Earth, even the speed of an airplane relative to the earth and relative to the air becomes a little more complicated. In addition, airplanes do not always fly the shortest route, they can use the air flow and travel a greater distance 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 plunge into this topic, then plunge very deeply. But so far we can take advantage of the fact that at small time intervals all the trajectories are close to straight lines, and this allows us to turn to the principle of Galileo's relativity.

Back to you sitting in a chair. You may decide that you are motionless, but it is not. First, the Earth takes you away with it, rotating around its axis at a speed of the order of 1000 km / h - depending on the latitude at which you are. Even faster, the Earth moves around the Sun, and we all rush with it at a speed of about 30 km / s relative to the Sun. You do not feel this for two reasons. Firstly, you can feel what you touch, but you do not touch the sun. You touch the chair, the air in the room, and since you are motionless relative to them, you do not feel movement. Secondly, your movement is almost in a straight line (it is not a straight line, but it bends very slowly), so the principle of Galileo's 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 margins 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, so 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 an even higher order - but we also do not feel them.

Back to the article with the BBC. According to the newspaper, the spacecraft was moving at a speed of 10 km / s. Regarding what? I would think that this is speed relative to the Earth. But in the article you need to write it directly! Otherwise, the statement makes no sense. Since Mars is farther from the Sun and moves in its orbit slower 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 he started, like the rest of the Earth, at a speed of 30 km / s relative to the Sun, then he could slow down (from the point of view of the Sun), so that it would be easier for him then to coincide with the motion of Mars in orbit. It would be quite interesting to know, but unfortunately, the Air Force did not report anything on this subject.

And if you were on a spaceship? At the end of the rocket’s work, when the spacecraft’s motion is aligned, you will not feel 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 in relation to any planet or star, unless you carefully measure the changing position of the planets in the sky and observe how the Sun decreases. And if it weren’t for your confidence in the engineers and scientists who convinced you that the rocket will send you at the right speed and in the right direction relative to Mars, Earth and the Sun, you would not know whether you would ever come close to Mars, or just be very to drift for a long time in space, as another microplanet, of which there are no numbers.

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