The fact that light travels at a limited but very high speed was first discovered by Danish astronomer Orr christiansen Romer in 1676. He observed that Jupiter's moons did not come out from behind Jupiter at equal intervals. If the moon orbits Jupiter at a constant speed, it will not be as expected. When the earth and Jupiter both revolve around the sun, the distance between them is changing. Romai noticed that the farther away we are from Jupiter, the later the eclipse of Jupiter will appear. His argument is that it takes longer for light from Jupiter and the moon to reach us when we are farther away. However, the change of the distance between Jupiter and the Earth he measured is not very accurate, so the value of the speed of light is 1 40,000 miles per second (1 mile = 1.609 kilometers), and the current value is186,000 miles per second (1mile =/kl). Nevertheless, Luo Mai not only proved that light moves at a limited speed, but also measured the speed of light, and his achievement is outstanding-you know, all this was done 1 1 year before Newton published Principles of Mathematics.
It was not until 1865 that james maxwell, a British physicist, successfully unified some theories used to describe electricity and magnetism at that time, and the real theory of light propagation came into being. Maxwell's equation predicts that there can be fluctuations in the combined electromagnetic field, which move at a fixed speed, just like ripples on the surface of a pond. If the wavelength of these waves (the distance between two peaks) is 1 meter or longer, this is what we call radio waves. Waves with shorter wavelengths are called microwaves (several centimeters) or infrared rays (longer than 1 cm). The wavelength of visible light is between 65438+40 ppm and 65438+80 ppm. Shorter wavelengths are called ultraviolet rays, x-rays and gamma rays.
Maxwell's theory predicts that radio waves or light waves should move at a fixed speed. But Newton's theory has got rid of the concept of absolute rest, so if we assume that light travels at a fixed speed, people must find out what this fixed speed is measured relative to. Thus, it is proposed that even in a "vacuum", there is an ubiquitous object called "ether". Just like sound waves in the air, light waves should pass through the ether, so the speed of light should be relative to the ether. Compared with different observers of the movement of the ether, we should see that the light is directed at them at different speeds, but the speed at which the light is directed at the ether is constant. Especially when the earth revolves around the sun and passes through the ether, the speed of light measured in the direction where the earth moves through the ether (when we move towards the light source) should be greater than that measured perpendicular to the direction of movement (when we don't move towards the light source). During the period of 1887, albert michelson (who later became the first American Nobel Prize winner in physics) and Edward Morey conducted a very careful experiment at the Cass Institute of Applied Science in Cleveland. They will compare the direction of the earth's movement with the speed of light perpendicular to this direction. To their surprise, they found that the two speeds of light were exactly the same!
From 1887 to 1905, people tried to explain Michelson-Morey experiment several times. The most famous is the Dutch physicist Hendrick Rolloz, who is based on the mechanism that objects moving relative to the ether contract and the clock slows down. However, Albert Einstein, an unknown employee of Swiss Patent Office, pointed out in a famous paper 1905 that as long as people are willing to abandon the concept of absolute time, the whole concept of ether is redundant. A few weeks later, Henri Poincare, one of the most important mathematicians in France, put forward a similar view. Einstein's argument is closer to physics than Poincare's argument, because the latter thinks it is a mathematical problem. Usually this new theory is attributed to Einstein, but Poincare's name plays an important role in it.
The basic assumption of this theory of relativity is that no matter what speed observers move freely, the laws of science should be the same for them. This is certainly true for Newton's laws of motion, but now this concept has been extended to include Maxwell's theory and the speed of light: no matter how fast the observer moves, he should measure the same speed of light. This simple concept has some extraordinary conclusions. Perhaps the most famous person is the equivalence of mass and energy, which can be expressed by Einstein's famous equation E = mc2 (where e is energy, m is mass and c is the speed of light) and the law that nothing can be faster than the speed of light. Since energy and mass are equal, the energy generated by the motion of an object should be added to its mass. In other words, accelerating it will become more difficult. This effect has practical significance only when the object moves at a speed close to the speed of light. For example, when an object moves at a speed of 10%, its mass only increases by 0.5% compared with the original one, while the mass of an object moving at a speed of 90% becomes more than twice the normal mass. When an object approaches the speed of light, its mass rises faster and faster, and it needs more and more energy to accelerate further. In fact, it will never reach the speed of light, because at that time, the mass will become infinite, and according to the principle of mass-energy equivalence, it needs infinite energy to do it. For this reason, the theory of relativity restricts any normal object from moving at a speed lower than the speed of light forever. Only light or other waves without intrinsic mass can move at the speed of light.
An equally remarkable achievement of relativity is that it has changed our concepts of space and time. In Newton's theory, if a light pulse is sent from one place to another, different observers will have no objection to the time spent in this process (because time is absolute), but they will not agree on the distance of light propagation (because space is not absolute). Since the speed of light is equal to the distance divided by the time it takes, different observers measure different speeds of light. On the other hand, in the theory of relativity, all observers must agree on the speed of light. However, they can't agree on the propagation distance of light. So now they won't agree how long it will take. In any case, the time spent by light is the speed of light, which is consistent for all observers, and the distance traveled by removing light is inconsistent for them. ) In short, the theory of relativity ends the concept of absolute time! In this way, each observer has the time measured by his own clock, and the readings of the same clock carried by different observers may not be consistent.
Figure 2. 1 Time is measured on the ordinate, and the distance from the observer is measured on the abscissa. The observer's path in space and time is represented by the vertical line on the left. The path of light in and out of the event is shown diagonally.
Every observer can use the light pulse or radio wave emitted by radar to determine the time and place of the event. After part of the pulse is reflected by the event, the observer can measure the time when he receives the echo. The time of the event can be considered as the midpoint between the time when the pulse is sent out and the time when the pulse is reflected back and received. The distance of an event can be multiplied by the speed of light by half the round trip time. In this sense, an event is something that happens at a certain point in a specific space and at a certain point in a specific time. This meaning has been shown in Figure 2. 1. This is an example of Shi Kongtu. With this step, mutually moving observers can be given different times and locations for the same event. No particular observer's measurements are more accurate than others', but all these measurements are related. As long as the observer knows the relative speed of others, he can accurately calculate the time and position that others should give for the same event.
Now we use this method to measure distance accurately, because we can measure time more accurately than length. In fact, the definition of meter is the distance traveled by light measured by platinum atomic clock in 0.0000000335640952 seconds (this special number is chosen because it corresponds to the definition of meter in history-according to the distance between two scales on a specific platinum rod preserved in Paris). Similarly, we can use a more convenient unit of length called light seconds, which is simply defined as the distance that light travels in one second. Now in the theory of relativity, we define the distance according to time and the speed of light, so that every observer can automatically measure the same speed of light (defined as every 0.0000003540952 seconds 1 meter). There is no need to introduce the concept of ether, because Michelson-Morey experiment shows that the existence of ether can't be detected anyway. However, the theory of relativity forces us to fundamentally change our concept of time and space. We must accept the view that time cannot be completely divorced from and independent of space, but must be combined with space to form the so-called space-time object.
Our usual experience is that three numbers or coordinates can be used to describe the position of a point in space. For example, people can say that a point in a room is 7 feet away from one wall (1 ft =0.3048 m), 3 feet away from the other wall (1 ft =0.3048 m) and 5 feet higher than the ground (1 ft =0.3048 m). People can also use a certain latitude, longitude and height to specify a point. People can freely choose any three suitable coordinates, although they are only effective in a limited range. People don't express the position of the moon according to how many miles north and west of Piccadilly Circus in London (1 mile = 1.609 km) and how many feet above sea level (1 foot =0.3048 m), but according to the distance from the sun, the orbital plane of the planet, the connection between the moon and the sun, and the sun and a nearby star, such as α. Even these coordinates are not very useful to describe the position of the sun in our galaxy, or the position of our galaxy in our local galaxy group. In fact, people can use a family of overlapping coordinate fragments to describe the whole universe. In each segment, people can use three different sets of coordinates to represent the position of the point.
Figure 2.2 Distance to the Sun (unit: 10 12 miles, 1 mile = 1.609 kilometers)
An event is something that happens in a specific time and space. In this way, people can use four numbers or coordinates to determine it, and the choice of coordinate system is arbitrary; People can use any defined spatial coordinates and any time measurement. In relativity, there is no real difference between time and space coordinates, just as there is no real difference between any two space coordinates. For example, a new set of coordinates can be selected so that the first spatial coordinate is a combination of the old first and second spatial coordinates. For example, the mileage of a point on the earth is not measured in the north and west of Piccadilly Circus in London, but in its northeast and northwest (1 mile = 1.609 km). Similarly, people can use a new time coordinate in the theory of relativity, which is the old time (in seconds) plus the distance from Piccadilly Street to the north (in seconds).
Figure 2.3
It is often helpful to use the four coordinates of an event as a means to specify its position in the so-called four-dimensional space-time I can hardly imagine three-dimensional space! However, it is easy to draw a two-dimensional space map, such as the earth's surface. The surface of the earth is two-dimensional, because the position of points on it can be determined by two coordinates, such as latitude and longitude. ) Usually I will use a two-dimensional graph, with the upward direction being time and the horizontal direction being one of the spatial coordinates. The other two spatial coordinates are not considered, or sometimes one of them is represented by perspective. (These are called Shi Kongtu, as shown in Figure 2. 1. For example, in Figure 2.2, time is upward, measured in years, while the straight-line distance from the sun to α-Centauri is measured in miles in the horizontal direction. The paths of the sun and α-Centauri in time and space are represented by vertical lines on the left and right sides of the figure. The light from the sun goes along the diagonal, and it takes four years to walk from the sun to α-Centauri.
We have seen that Maxwell's equation predicts that the speed of light should be the same regardless of the speed of the light source, which has been confirmed by accurate measurement. In this way, if a light pulse is emitted from a point in a specific space at a specific moment, it will spread out in the form of a light ball over time, and the shape and size of the light ball have nothing to do with the speed of the source. After 1 10,000 years 1 s, the light scatters into a sphere with a radius of 300 meters; 1 million seconds later, the radius becomes 600 meters; Wait a minute. Just like throwing a stone into a pond, the ripples on the water surface spread around, and the ripples spread in a round form, getting bigger and bigger. If it is assumed that the three-dimensional model includes two-dimensional pond water surface and one-dimensional time, the circle of these magnified water waves will draw a cone, and its vertex is the place and time when the stone hits the water surface (Figure 2.3). Similarly, the light scattered by the event forms a three-dimensional light cone in four-dimensional space-time, which is called the future light cone of the event. In the same way, another cone called the past light cone can be drawn, which represents the set of all events that can be propagated to events by light pulses (Figure 2.4).
Figure 2.4
For a given event p, people can divide other events in the universe into three categories. Those events that can be reached by particles or waves moving at a speed equal to or less than the speed of light of event P are called the future of P. They are in or on the expanding photosphere emitted by event p. In this way, in Shi Kongtu, they are in or on P's future light cone ... Because nothing travels faster than light, what happens in P can only affect P's future events.
Similarly, the past of P can also be defined as the set of all the following events, from which it can be concluded that the speed of event P is equal to or less than the speed of light. In this way, it is a collection of all events that can affect P, and events that are not in P's future or past are said to be elsewhere in P (Figure 2.5). What happened in this event can neither affect what happened in P nor be affected by what happened in P. For example, the sun stops emitting light at this moment, and this moment will not affect the earth, because the moment of the earth is outside the light cone of the event when the sun goes out (Figure 2.6). We can only know this event after 8 minutes, which is the time it takes for light from the sun to reach us. Only then will the events on earth be in the future light cone of the sun extinction event. Similarly, we don't know what is happening farther away in the universe at this moment: the light we see from distant galaxies was emitted millions of years ago, and for the farthest objects, it was emitted 8 billion years ago. So when we observe the universe, we are observing its past.
Figure 2.5
Figure 2.6
If people ignore the gravitational effect, as Einstein and Poincare did in 1905, people get a theory called special relativity. For each event in time and space, we can make a light cone (the collection of all possible trajectories of light emitted by the event). Because in every event, the speed of light in any direction is the same, all light cones are congruent and face the same direction. This theory tells us that nothing travels faster than light. This means that the trajectory of any object through time and space must be represented by a line that falls within the light cone of each event on it (Figure 2.7).
Figure 2.7
Special relativity has successfully explained the fact that the speed of light is the same for all observers (as proved by Michelson-Morey experiment) and successfully described the behavior of an object when it approaches the speed of light. However, it is incompatible with Newton's theory of gravity. Newton's theory says that the attraction between objects depends on the distance between them. This means that if we move an object, the force on another object will change immediately. Or in other words, the gravitational effect must be transmitted at infinite speed, not at or below the speed of light as required by special relativity. Einstein made many unsuccessful attempts from 1908 to 19 14, trying to find a theory of gravity that is compatible with special relativity. 19 15 years, he finally put forward what we call general relativity today.
Einstein put forward a revolutionary view that gravity is not like other kinds of forces, but only the result of uneven time and space. As he assumed earlier, space-time is bent or "distorted" by the distribution of mass and energy in it. An object like the earth does not move along a curved orbit because of a force called gravity, but along a trajectory called geodesic, which is closest to a straight line in a curved space. Geodesic is the shortest (or longest) path between two adjacent points. For example, the surface of the earth is a curved two-dimensional space. The geodesic line on the earth is called the Great Circle, which is the shortest path between two points (Figure 2.8). Because geodesic is the shortest distance between two airports, this is the route that the pilot tells the pilot to fly. In general relativity, objects always move along a straight line in four-dimensional space-time. Nevertheless, in our three-dimensional space, it seems to follow a curved path (it's like watching an airplane fly over a very mountainous ground. Although it flies in a straight line in three-dimensional space, its shadow follows a curved path on the two-dimensional ground.
Figure 2.8
The mass of the sun causes the curvature of space-time, which makes the earth follow a straight trajectory in four-dimensional space-time, but in three-dimensional space, it makes us look like we are moving along a circle. In fact, the orbits of planets predicted by general relativity are almost the same as those predicted by Newton's gravity theory. However, for the planet Mercury, which is closest to the sun, has the strongest gravitational effect and has a fairly long orbit, general relativity predicts that the long axis of its orbital ellipse revolves around the sun at a speed of about 1 degree every ten thousand years. Although this effect is very small, it was noticed before 19 15 years ago and was regarded as the first verification of Einstein's theory. In recent years, even smaller orbital deviations of other planets and those predicted by Newton's theory have been measured by radar and found to be consistent with the prediction of general relativity.
Light must also follow the geodesics of time and space. The fact that space bends again means that light doesn't seem to follow a straight line in space. In this way, general relativity predicts that light must be bent by gravitational field. For example, the theory predicts that due to the mass of the sun, the cone of light at a point near the sun will deflect slightly inward. This shows that the light from a distant star will bend at a small angle when it passes near the sun, and the star seems to be in a different position to the observer on the earth (Figure 2.9). Of course, if the light emitted by a star always passes very close to the sun, we can't know whether the light is deflected or whether the star is actually where we see it. However, when the earth revolves around the sun, different stars pass behind the sun and their light will be deflected. Therefore, relative to other stars, they changed their apparent positions.
Figure 2.9
In general, it is difficult to observe this effect, because the light of the sun makes it impossible for people to observe the stars in the sky that appear near the sun. However, it may be observed during a solar eclipse, when the sun's rays are blocked by the moon. As the First World War is going on, Einstein's prediction about light deflection cannot be verified immediately in 19 15. Until 19 19, a British expedition observed the solar eclipse from West Africa and pointed out that the light was indeed deflected by the sun as predicted by the theory. This time, Germany's theory was proved by the British and was hailed as a great act of reconciliation between the two countries after the war. Ironically, people later checked the photos taken on this expedition and found that the error was as big as the effect they tried to measure. The scientific community generally believes that their measurements are purely luck, or that the results they want are known. However, the deflection of light was accurately confirmed by many subsequent observations.
Another prediction of general relativity is that time seems to pass more slowly near a massive object like the earth. This is because light energy is related to its frequency (the number of light vibrations per second): the greater the energy, the higher the frequency. When light goes up from the earth's gravitational field, it loses energy, so its frequency drops (which indicates that the time interval between two peaks becomes larger). From the people above, it seems that what happens below will take longer. This prediction was verified in 1962 by using a pair of very accurate clocks installed at the top and bottom of the water tower. It is found that the clock whose bottom is closer to the earth moves slower, which is completely consistent with general relativity. The speed of clocks at different heights on the earth is different, which is of great practical significance at present, because people have to use the signals sent by satellites for very accurate navigation. If people don't know anything about the prediction of general relativity, the calculated position will have an error of several miles (1 mile = 1.609 km)!
Newton's law of motion ended the concept of absolute position in space. Opposites get rid of absolute time. Consider a pair of twins. Suppose one of them goes to the top of the mountain to live and the other stays at sea level. The first one will get older than the second one. So, if they meet again, one will be older than the other. In this case, the age gap is very small. However, if a child travels a long distance in a spaceship near the speed of light, the difference will be much greater. When he comes back, he will be much younger than the other person left on earth. This is the so-called twin paradox. However, this is only a paradox for people who still have the concept of absolute time in their minds. There is no unique absolute time in relativity. On the contrary, everyone has his own time scale, which depends on where he is and how he moves.
Before 19 15, space and time were regarded as fixed stages of events, and they were not affected by the events that occurred in them. Even in the special theory of relativity. When objects move, forces will attract and repel each other, but time and space will extend completely unaffected. Space and time are naturally considered to extend forward indefinitely.
However, in general relativity, the situation is quite different. At this time, space and time become the driving force: when the object moves or acts forcefully, it affects the curvature of space and time; Conversely, the structure of space-time affects the way in which objects move and forces act. Space and time are not only affected, but also affected by everything that happens in the universe. Just as it is impossible to talk about events in the universe without the concepts of space and time, it is meaningless to talk about space and time outside the boundaries of the universe in general relativity.
In the next few decades, a new understanding of space and time will change our world view. The old idea of a basically unchanging universe that has existed and will continue to exist indefinitely has been replaced by the idea that the universe is moving, expanding and seems to start from a finite past and will end in a finite future. This change is the content of the next chapter. A few years later, it was the starting point for me to study theoretical physics. Roger penrose and I pointed out that it can be inferred from Einstein's general theory of relativity that the universe must have a beginning or an end.