Space and time
Our current ideas about the motion of objects come from Galileo and Newton. Before them, people believed Aristotle, who said that the natural state of an object is static and only moves when it is subjected to force or impact. In this way, a heavy object falls faster than a light object, because it is pulled towards the earth with greater force.
Aristotle's traditional view also believes that people can find out the laws that restrict the universe with pure thinking: they don't need to be tested by observation. Therefore, Galileo was the first person who wanted to see if objects with different weights really fell at different speeds. It is said that Galileo dropped heavy objects from the leaning tower of Pisa, thus proving Aristotle's belief wrong. This story is almost impossible to be true, but Galileo did do something equivalent-let balls of different weights roll down a smooth slope. This situation is similar to that of a heavy object falling vertically, but it is easier to observe because of its lower speed. Galileo's measurement pointed out that no matter what the weight of an object is, its speed increases at the same speed. For example, if you release a ball on an inclined plane that descends every 10 m in the horizontal direction, the speed of the ball after 1 s is 1 m per second, and after 2 seconds, it is 2 m per second, no matter how heavy the ball is. Of course, the plumb falls faster than the feather, which is caused by the resistance of the air to the feather. If a person releases two objects free from any air resistance, such as two different plumbs, they will descend at the same speed.
Newton used Galileo's measurements as the basis of his laws of motion. In Galileo's experiment, when an object rolls down a slope, it is always subjected to a constant external force (its weight), and its function is to accelerate continuously. This shows that the real function of force always changes the speed of an object, not just making it move as originally imagined. At the same time, it also means that as long as an object is not subjected to external forces, it will keep moving in a straight line at a uniform speed. This idea was first clearly described by Newton in his book Principles of Mathematics published in 1996. It is called Newton's first law. The situation when an object is stressed is given by Newton's second law: when an object is accelerated or changes its speed, its change rate is proportional to the external force. (For example, if the force doubles, the acceleration doubles. The greater the mass of an object (or the amount of matter), the smaller the acceleration. The same force acting on an object with twice the mass will only produce half the acceleration. Cars can provide a well-known example. The greater the power of the engine, the greater the acceleration, but the heavier the car, the smaller the acceleration for the same engine.
In addition to his law of motion, Newton also discovered a law describing gravity: any two objects attract each other, and gravity is proportional to the mass of each object. In this way, if the mass of an object (for example, A) doubles, the attraction between two objects also doubles. This is what you can expect, because the new object A can be regarded as two objects with original mass, and each object attracts object B with the force, so the resultant force between A and B is doubled. If the mass of one object is twice that of the original and the mass of another object is three times that of the original, then the gravity will be six times that of the original. Now people can understand why falling objects always fall at the same speed: an object with twice the weight is pulled down by twice the gravity, but its mass is twice. According to Newton's second law, these two effects cancel each other out, so the acceleration is the same in all cases.
Newton's law of gravity also tells us that the farther the distance between objects is, the smaller the gravity is. According to Newton's law of gravity, the gravity of a star is only half the distance of 1. This law predicts the orbits of the earth, the moon and other planets very accurately. If this law becomes that the gravity of stars decreases faster with distance than this, then the orbits of planets are no longer elliptical, and they will spiral to the sun. If gravity falls more slowly, the gravity of distant stars will exceed that of the earth.
The great difference between Aristotle and Galileo-Newton is that Aristotle believes that there is a superior static state, which is adopted by any object that is not affected by external forces and shocks. In particular, he thinks that the earth is at rest. But according to Newton's law, there is no only static standard. People can say that object A is stationary and object B is moving at a constant speed relative to object A, or that object B is stationary and object A is moving, which are equivalent. For example, if we temporarily put aside the earth's rotation and revolution around the sun, we can say that the earth is stationary, a train is traveling north at 90 miles per hour, or the train is stationary, while the earth is traveling south at 90 miles per hour. If a person does experiments with moving objects on the train, all Newton's laws hold. For example, if you play table tennis on the train, you will find that table tennis obeys Newton's law, just like the table beside the railway track, so you can't know whether the train is moving or the earth is moving.
There is no absolute standard for stillness, which means that people can't decide whether two events that happened at different times happened in the same place in space. For example, suppose our table tennis jumps up and down on the train and hits the same place on the table twice a second. From the point of view of the people on the track, the two jumps took place at different positions about meters apart, because the train had already walked so far on the track during the interval between the two jumps. In this way, the absence of absolute stillness means that events cannot be given an absolute spatial position as Aristotle thought. The location of the incident and the distance between the incidents are different for people on trains and tracks, so there is no reason to think that one person's situation is superior to others.
Newton was very worried that there was no absolute position or absolute space, because it was inconsistent with the absolute God in his mind. In fact, he refused to accept the existence of absolute space, even though it was implicit in his laws. Because of this irrational belief, he was severely criticized by many people, the most famous of which was Bishop Becquerel, a philosopher who believed that all physical entities, space and time were illusory. When people told the famous Dr. Johnson about Becker's opinion, he kicked a big stone with his toe and said loudly, "I will refute it like this!" " "
Aristotle and Newton both believed in absolute time. In other words, they think that people can clearly measure the time interval between two events. As long as a good clock is used, the time is the same no matter who measures it. Time is completely separated and integrated with space. This is what most people regard as common sense. However, we must change this concept of time and space. Although this obvious common sense can deal with the slow movement of apples and planets, it is completely ineffective when dealing with objects moving at or near the speed of light.
The fact that light travels at a limited but very high speed was first discovered by Danish astronomer Orr christiansen Romer in 1920. He observed that Jupiter's satellites do not come out from behind Jupiter at equal intervals, unlike what people expected, if the satellites orbit Jupiter at a constant speed. 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. But his distance from Jupiter to the earth is not very accurate, so his speed of light is miles per second, and now it is miles per second. 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 1998 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 may be fluctuating disturbances 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 one tenth of a centimeter). The wavelength of visible light is between 40 parts per million and 80 parts per million centimeters. 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). In, albert michelson (who later became the first American Nobel Prize winner in physics) and Edward Morey conducted a very careful experiment at 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!
Between 1998 and 1998, there were several attempts to explain the Michelson-Morey experiment. 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 at that time, pointed out in a famous paper in 2006 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 the laws of science should be the same for observers regardless of their speed. 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 is the equivalence between mass and energy, which can be expressed by Einstein's famous equation E = MC 2 (where E is energy, M is mass and C is the speed of light) and 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.
Actually,
The meter is defined as the distance that light travels within 0. 5 meters. Seconds measured by platinum atomic clock (this special number is chosen because it corresponds to the historical definition of meter-according to the distance between two scales on a specific platinum pole 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 each observer can automatically measure the same speed of light (defined as 1 meter per 0. Second). 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 separated from space, but must be combined with space to form the so-called space-the object of time.
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 from one wall, 3 feet from another wall and 5 feet from the ground. People can also use a certain latitude, longitude and height to specify a point. People can easily choose any three suitable coordinates, although they are only effective in a limited range. People describe the position of the moon not by how many miles north and west of Piccadilly Circus in London and how many feet above sea level, but by the distance from the sun, the distance from the orbital plane of the planet, and the angle between the moon and the sun and nearby stars (such as α-Centauri). Even these coordinates are not very useful for describing the position of the sun in our galaxy or the position of our galaxy in a local galaxy. In fact, people can use a family of overlapping coordinate fragments to describe the whole universe. In each segment, people can use three different coordinates to represent the position of the point.
Figure 2.2
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 measure. 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. 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 four coordinates of an event as a means to specify its position in the so-called four-dimensional space of time and space. I think it's hard enough to 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. ) I usually 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 is along the diagonal, and it takes four years 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 a millionth of a second, the light scatters into a sphere with a radius of meters; After two millionths of a second, the radius becomes 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. Similarly, another cone called the past light cone can be drawn, which represents all events that can be propagated to events by light pulses (Figure 2.4).
Figure 2.4
The past and future light cone of an event P divides space-time into three areas (Figure 2.5): the absolute future of this event is the inner area of P's future light cone, which is all the events that may be affected by the events in P. Things starting from P cannot be transmitted to events outside P's light cone, because nothing travels faster than light, so they will not be affected by what happened in P. The points in the inner area of the past light cone are P's absolute past, which is all. So, this is all the events that may affect event P. If people know what happened in the past light cone of event P at a certain moment in the past, they can predict what will happen in space P-the remaining time is all events except the future and past light cone of event P.. This part of the event is neither influenced by P nor P. For example, if the sun stops emitting light at this moment, it will not affect the earth at this moment, because the moment of the earth is outside the light cone of the event (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 the moment: the light we see from distant galaxies was emitted millions of years ago, and as far as the farthest object we see is concerned, 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 1996, people will get a theory called special relativity. For every event in time and space, we can make a light cone (all possible trajectories of light emitted by the event). Because the speed of light in any direction is the same in any event, 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 have one 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 1998 to 1998, trying to find a theory of gravity that is compatible with special relativity. In, 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" because of 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 walk 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 several years ago and was taken as the first test 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 geodesic line 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. Because the First World War is going on, Einstein's prediction about light deflection can't be verified immediately in 2008. Until 1998, 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 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 2006 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 use satellites for very accurate navigation. If people don't know anything about the prediction of general relativity, the calculated position will be several miles away!
Newton's law of motion ended the concept of absolute position in space. On the other hand, relativity got 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.
Many years ago, 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; On the other hand, 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.