People are interested in superluminal, which generally refers to superluminal transmission of energy or information. According to the special theory of relativity, superluminal travel and superluminal communication in this sense are generally impossible. At present, most of the debates about superluminal are that some things can indeed travel faster than the speed of light, but they cannot be used to transmit energy or information. However, the existing theory does not completely rule out the possibility of superluminal in the true sense.
Let's discuss the first case first: it's not superluminal in the real sense.
1。 The speed of light in cherenkov effect medium is smaller than that in vacuum. The propagation speed of particles in the medium may exceed the speed of light. In this case, radiation will occur, and this is cherenkov effect. This is not superluminal in the true sense, but superluminal in the true sense refers to exceeding the speed of light in a vacuum.
2。 The third observer, if A moves eastward at a speed relative to C 0.6c and B moves westward at a speed relative to C0.6c. For C, the distance between A and B increases at a speed of 1.2c, and this "speed"-the speed of two moving objects relative to the third observer-can exceed the speed of light. But the relative motion speed of two objects will not exceed the speed of light. In this example, in the coordinate system of A, the speed of B is 0.88c. In the coordinate system of B, the speed of A is also 0.88c.
3。 Shadows and light spots shake your hand under the light, and you will find that shadows are faster than your hands. The ratio of the speed of shadow and hand shaking is equal to the ratio of their distance to the lamp. If you shake the flashlight at the moon, it is easy to make the light spot falling on the moon move faster than the speed of light. Unfortunately, information cannot travel faster than light in this way.
4。 When a rigid body touches one end of a stick, will the vibration immediately spread to the other end? Doesn't this provide a way of superluminal communication? Unfortunately, the ideal rigid body does not exist. Vibration propagates in a rod at the speed of sound, which is ultimately the result of electromagnetic action and cannot exceed the speed of light. An interesting question is, when you hold the upper end of a stick vertically and suddenly release it, does the upper end of the stick start falling first or the lower end of the stick start falling first? The answer is the upper end. )
5。 Phase Velocity The phase velocity of light in a medium can exceed the speed of light in a vacuum in some frequency bands. Phase velocity refers to the "propagation velocity" corresponding to the phase lag of a continuous sine wave propagating in a medium for a certain distance (assuming that the signal propagates for a long time and reaches a stable state). Obviously, a simple sine wave cannot convey information. In order to transmit information, it is necessary to modulate the slowly varying wave packet on the sine wave. The propagation speed of this wave packet is called group velocity, which is less than the speed of light. (Translator's Note: Sommerfeld and Brillouin's research on pulse propagation in the medium proves that the propagation speed of a signal with an initial time of [zero before a certain moment] in the medium cannot exceed the speed of light. )
6。 Superluminal galaxies The apparent speed of galaxies moving towards us may exceed the speed of light. This is an illusion, because the time reduction from the galaxy to us is not corrected (? )。
7。 Relativistic rocket man saw the rocket moving away at a speed of 0.8c on the earth, and the clock on the rocket was slower than that on the earth, which was 0.6 times that of the earth clock. If you divide the distance traveled by the rocket by the time spent on the rocket, you will get a "speed" of 4/3c. Therefore, the people on the rocket are moving at a speed "equivalent to" superluminal speed. For the people on the rocket, time has not slowed down, but the distance between galaxies has shrunk to 0.6 times, so they also feel that they are moving at the speed equivalent to 4/3c. The problem here is that the number obtained by dividing the distance in one coordinate system by the time in another coordinate system is not the real speed.
8。 The speed of gravity propagation Some people think that gravity travels faster than the speed of light. In fact, gravity travels at the speed of light.
9。 EPR Paradox 1935 Einstein, Podolski and Rosen published a thought experiment to show the incompleteness of quantum mechanics. They believe that there is an obvious distance effect when measuring two separated particles in an entangled state. Ebhard proved that it is impossible to use this effect to transmit any information, so superluminal communication does not exist. But the EPR paradox is still controversial.
10。 In quantum field theory, the force of virtual particles is transmitted through virtual particles. Because of Heisenberg's uncertainty, these virtual particles can travel at superluminal speed, but they are only mathematical symbols, and superluminal travel or communication still does not exist.
1 1。 Quantum tunneling Quantum tunneling is the effect of particles escaping from a barrier higher than their own energy, which is impossible in classical physics. Calculate the time for particles to pass through the tunnel, and you will find that the speed of particles exceeds the speed of light. (Reference: T.E. Hartman, J. APPL. PHYS.33,3427 (1962)) A group of physicists made an experiment of superluminal communication by using quantum tunneling effect: they claimed that Mozart's 40th symphony passed through a width of1/kloc-0 at a speed of 4.7c Most physicists believe that because of Heisenberg's uncertainty, it is impossible to use this quantum effect to transmit information faster than light. If this effect holds, it is possible to use similar devices to transmit information to the past in a high-speed moving coordinate system.
Ref:W. Heitmann and G. Nimtz, Phys A 196,154 (1994); A. Enders and G. Nimtz, phys Rev E48,632 (1993) Tao Zhexuan thinks that the above experiment is not convincing. It takes less than 0.4 nanosecond for the signal to travel through the distance of 1 1.4cm at the speed of light, but the acoustic signal of 1000 nanosecond can be predicted by simple extrapolation. Therefore, it is necessary to carry out experiments on superluminal communication or high-frequency random signals at a longer distance.
12。 Ghasemi effect When the distance between two uncharged conductor plates is very close, a very weak but still measurable force will be generated between them, which is the Casimir effect. Casimir effect is caused by vacuum energy. Scharnhorst's calculation shows that the speed of photon moving laterally between two metal plates must be slightly higher than the speed of light (for a gap of one nanometer, this speed is higher than the speed of light 10-24). Under some cosmic conditions (such as near [cosmic string] [if it exists]), this effect will be much more significant. However, further theoretical research shows that it is impossible to use this effect for superluminal communication.
Reference: K. scharnhorst, Physics Bulletin B236,354 (1990) S. Ben Menahem, Physics Bulletin B236, 133 (1990). Advanced learning). IAS SNS-AST-90-25 Barton & amp； Scharnhorst, Journal of Physics A26, 2037 (1993)
13。 Hubble's theory of cosmic expansion says that galaxies with a distance of d separate at HD speed. H is a constant independent of galaxies, called Hubble constant. Galaxies far enough away may separate from each other at a speed faster than the speed of light, but this is the separation speed relative to the third observer.
14。 The moon revolves around us at superluminal speed!
When the moon is on the horizon, let's say that we circle at the speed of half a cycle per second. Because the moon is 385,000 kilometers away from us, the rotation speed of the moon's appearance to us is 1, 2 1, 000 kilometers per second, which is about four times the speed of light! This sounds ridiculous, because we are actually spinning, but we say that the moon revolves around us. But according to general relativity, any coordinate system, including rotating coordinate system, can be used. Isn't this the moon moving at superluminal speed?
The problem is that in general relativity, the speeds in different places cannot be directly compared. The speed of the moon can only be compared with other objects in its local inertial system. In fact, the concept of speed is not very useful in general relativity, and it is difficult to define what is "superluminal" in general relativity. In general relativity, even "the speed of light, isn't it? Quot needs an explanation. Einstein himself said on page 76 of the Theory of Relativity that the narrow and broad theories of "constant speed of light" are not always correct. In the absence of absolute definitions of time and distance, how to determine the speed is not so clear.
Nevertheless, modern physics believes that the speed of light in general relativity is still constant. When distance and time units are linked by the speed of light, the speed of light is constant and is defined as a self-evident axiom. In the previous example, the speed of the moon is still less than the speed of light, because at any moment, it is in the future light cone of the current position.
15。 Make clear the definition of superluminal.
The specious examples of "superluminal" listed in the first part illustrate the difficulty of defining "superluminal". "Superlight" like shadows and spots? Quot is not superluminal, then what is superluminal? "World line" is an important concept in the theory of relativity, and we can give a clear definition of "superluminal" with the help of "World line".
What is the "world line"? We know that all objects are made of particles. If we can describe the position of particles at any moment, we describe the whole "history" of objects. Imagine a four-dimensional space composed of three-dimensional space and one-dimensional time. Because a particle can only be in a specific position at any time, its whole "history" is a continuous curve in this four-dimensional space, which is the "world line". The world line of an object is the set of the world lines of all the particles that make up it.
Not only the history of particles can form the world line, but also the history of some artificially defined "things", such as shadows and spots. Shadows can be defined by points on their boundaries. These points are not real particles, but their positions can be moved, so their "history" also constitutes the world line.
A point in four-dimensional space-time represents an "event", that is, three spatial coordinates plus one time coordinate. Any two "events" can define the space-time distance, which is the square of the space distance of two events MINUS the square of the product of their time interval and the speed of light, and then open the root sign. Special relativity proves that this space-time distance has nothing to do with the coordinate system, so it has physical significance.
Space-time distance can be divided into three categories: time-like distance: space interval is less than the product of time interval and light speed; Light-like distance: the space interval is equal to the product of time interval and light speed; Spacelike distance: the spatial interval is greater than the product of the time interval and the speed of light.
Next, we need to introduce the concept of "local". Smoothing curves "locally" is very similar to straight lines. Similarly, the four-dimensional space-time is flat locally, and the world line is similar to a straight line locally, which means that it can be described by uniform motion, which is the instantaneous velocity of particles. On the world line of photons, the distance between adjacent events is locally light-like. In this sense, we can say that the world line of photons is light-like.
The world line of any particle moving at a speed lower than the speed of light, locally, the distance between adjacent events is time-like. In this sense, we can say that this world line is synchronic. However, the world line of a "point" defined by particles or people moving faster than the speed of light is empty. When we say that the world line is space-like, we mean that the space-time distance between adjacent events is space-like locally.
Because there may be curved space-time, there may be such a world line: locally, the distance between adjacent events is time-like, and the particle's motion speed will not exceed the speed of light; But there are two events far apart, and their space-time distance is space-like. Is this a superluminal situation?
The significance of this problem is that we can define both local superluminal and global superluminal. Even if local superluminal is impossible, the possibility of global superluminal is not ruled out. Global superluminal speed is also worth discussing.
In a word, "superluminal" can be defined by space-like world line, which has the advantage of excluding the case that two objects move at superluminal speed relative to a third observer.