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Chapter IV Superluminal and the Popularization of Relativity
In the study of physics, people put forward many paradoxes. The purpose of putting forward paradox is to sharpen the problem studied, so as to further clarify the basic concepts of the theory, or to find out what mistakes are made in logical argument, what assumptions are implied, or what other important factors are ignored, and so on. There have always been two paradoxes about the special theory of relativity, namely, the "twin paradox" and the "grandfather paradox" (that is, the causal inversion caused by time to go back or superluminal motion). The "twin paradox" was solved after the special relativity was extended to the general relativity, and the "grandfather paradox" will be solved in the further extension of the special relativity discussed in this paper.
First of all, the paradox of twins
Imagine two twin brothers, A and B. A travels in space by spaceship, and B stays on the ground and waits for A ... A's spaceship to accelerate to speed V in a very short time (speed V is close to the speed of light C). Then the spacecraft flew in a V-straight line at a constant speed. After flying for a period of time, the spacecraft quickly turned around and continued to fly in a V-straight line at a constant speed. When it returned to the ground, it slowed down crash landing and joined B already on the ground. A only has acceleration in three time periods: start-up, U-turn and slow landing, and the rest of the time is flying in a straight line at a constant speed, which is in the inertial system applicable to special relativity.
According to the relationship between the slowness of the moving clock derived from the Lorentz transformation in the first chapter.
Where △t is the elapsed time of the stationary clock in the inertial system S, and△ t/is the elapsed time of the stationary clock in the inertial system S/ moving at a speed v relative to S. ..
Because the time for A to start, turn around and slow down is very short, if these three periods are omitted, there are
τ is the time for A to fly in space, and T is the time for B to fly in earth space. It was A who made a high-speed space trip and found that B was older than A when he came back.
If the speed of the spacecraft is very close to the speed of light c, the relativistic effect will be very obvious. If v = 0.9999c, then T = 70.7438+0τ. That is, when the twin brothers were 20 years old, A flew by spaceship. A thought the flight time was only one year. When he returned to the ground, A was only 265,438+0 years old, but he found that B was an old man in his 90s, that is, B was much older than A..
However, we can look at the above situation from another angle. That is to say, for A who takes the spaceship, A is still on the spaceship. A saw B accelerate to speed V in the opposite direction in a very short time, and then B flew straight at speed V.. After flying for a period of time, B quickly turned around and continued to fly in a straight line at the speed V, and when it met A, it slowed down urgently ... In A's view, B only had acceleration during the three periods of starting, turning around and slowing down, and the rest of the time was flying in a straight line at a constant speed, which is also in the inertial system applicable to special relativity. Therefore, in A's view, if B's start-up, turn-around and deceleration are omitted (because these three periods are relatively short), the time spent by B/the time spent by A should also have the following relationship (special relativity generally records the time spent by a stationary clock in a system that makes a uniform linear motion relative to a stationary system as τ, which is called the original time of the system).
In this way, when Party A meets Party B, Party A becomes older than Party B. That is, if B flies in a straight line at a constant speed of v = 0.9999c, when B flies out of A and meets A one year later, B is only 2 1 year old, but he finds that A is an old man in his 90s, that is, A is much older than B. ..
It can be seen that from different angles, the conclusions are different and contradictory. Is B much bigger than A or A much bigger than B? Or are they all wrong? Should they all be the same young? This proposition is called "Twin Paradox".
The twin paradox has been debated for a long time. 19 18, Einstein wrote an article to explain the twin paradox by an interviewer and himself, and the twin paradox was solved.
When discussing the "twin paradox", people always think that the time of starting, turning around and slowing down is very short for the application of special relativity, so they ignore the time of starting, turning around and slowing down. However, the key to the "twin paradox" problem is precisely these neglected processes.
When considering the "twin paradox" from the first angle, B stays on the ground and waits for A and A to travel in space by spaceship. The acceleration and deceleration of A's spaceship are relative to B's inertial system, so these processes have no extra special effects, and the short time can be ignored. When we consider the "twin paradox" from the second angle, we not only consider that A and its spaceship are stationary, but also consider that when B flies away from A and its spaceship, the acceleration and deceleration of B in the process of starting, turning around and slowing down are all relative to the non-inertial system where A is located. According to the equivalence principle of general relativity, there is a gravitational field in the reference frame, which is equivalent to investigating the motion of B. Although both A and B are in this gravitational field, the gravitational field has different effects on them because of their different positions in the gravitational field. When B starts and slows down, the distance between A and B is close, and their gravitational field potentials are not much different, and the influence of gravitational field on their time passage is not much different, so this short period of time can still be ignored. When B turns around, because the distance between A and B is very far, B's gravitational field potential is much larger than A's, which makes B's time pass much faster than A's, or conversely, makes A's time pass much slower than B's. This influence exceeds the influence of velocity V on time when B moves at a uniform speed relative to A, so when B flies back and meets A, B is still bigger than A. Therefore, when considering the twin paradox, B's U-turn process cannot be ignored. The calculation results of general relativity show that there is also the following relationship between the time τ/of b and the time T/ of a.
or
That is, when B flew back to see A, A was still 2 1 year old, while B was over 90 years old.
1966 experiment shows that the average life of muons moving around a circle at high speed is longer than that of muons resting on the ground. 197 1 year, it is observed that the atomic clock placed on the satellite orbiting the earth is slower than the atomic clock on the ground. These experiments prove the correctness of general relativity and Einstein's argument about twin paradox.
Second, Sun Ye paradox.
People put forward the "Sun Ye Paradox" when studying the coordinate transformation of special relativity and considering the situation that the speed of motion V exceeds the speed of light C.
From the last section, we know that the time interval of two events is related to their spatial position and the motion state between the inertial systems of these two events. Even so, the sequence of the two events should still be absolute, and should not be changed because of their different spatial positions and the different motion states between the inertial systems of the two events, that is, the theory of relativity still follows the causal law of logical relations, that is, every cause has its consequences. For example, to travel in space, you must start first and then return; Agriculture needs to sow before harvest. People die after their husbands. Based on this consideration, people discussed the theory of relativity as follows.
Assuming that the inertial system s/ relative inertial system S moves in a straight line with a uniform speed V, there are two terms P 1(x 1, t 1) and P2(x2, t2) in the s/ system, and the coordinates of these two terms are (x 1/, t1.
According to the time transformation relation of Lorentz transformation
Considering that the causal relationship between these two events is unchanged in the two inertial systems, that is, their order is unchanged, there are
T2-t 1 & gt； 0 ; t2/-t 1/>0
So there is
Namely:
Because v
That is, the requirement of not destroying the law of causality is u≤c, that is, the propagation speed of all signals, including the propagation speed of interaction and the motion speed of objects, cannot exceed the speed of light c, otherwise, if u >；; C, there are always some inertial systems that make the signs of t2-t 1 and t2/-t 1/ opposite, which means that time to go back and causality will be reversed. Based on this, some people put forward the following proposition: If u>c, that is, there is superluminal time to go back, then imagine that someone has entered the superluminal world for a long time, and his time goes back not only to before his birth, but also to before his father's birth. At this time, he killed his grandfather and returned to our low-light-speed world. Do he and his father exist at this time? If so, how was his father born? People call this proposition "grandfather paradox" and "grandfather paradox".
Some people, regardless of the logical difficulties of "Grandfather Paradox" or "Grandfather Paradox", enjoy superluminal flight and go back in time in science fiction, science fiction movies and children's movies.
Third, the research status of superluminal motion (superluminal particles)
There are also people who have made various speculations about superluminal particles through intuition, conjecture or philosophical thinking. Especially now there is a UFO research craze. According to UFO sighting reports and other related reports, people conclude that there is superluminal flight, and also make various speculations about superluminal particles. These speculations lack theoretical basis and have not been strictly deduced. Therefore, the conclusions drawn from these speculations and conjectures are chaotic and cannot be generalized. Now only some of them are listed as follows. This article only attaches a comment after quoting the original text, which is a discussion with the original author and readers:
1, Asimov in "Do you know? -Title 5 1 written by One Hundred Questions of Modern Science (Popular Science Press 1984):
Since nothing can travel faster than the speed of light, what are superluminal particles that move faster than the speed of light?
Einstein's special theory of relativity requires that all objects in our universe cannot move at a relative speed that exceeds the speed of light in vacuum. It takes infinite energy just to force an object to reach the speed of light, and it takes more energy to push it beyond the speed of light, which is incredible.
However, let's assume that an object moves faster than the speed of light.
The speed of light is about 300,000 kilometers per second, so what happens if an object with a mass of 1kg and a length of 1cm moves at a speed of about 424,000 kilometers per second? If we apply Einstein's equation, it will tell us that the mass of an object will be equal to (negative square root of 1) kg, and its length will become (negative square root of 1) cm.
In other words, any object moving faster than the speed of light will have a mass and a length, which must be expressed by the so-called "imaginary number" in mathematics. We can't concretize the quality and length represented by imaginary numbers, so it's easy to think that since such things are unimaginable, they won't exist.
However, in 1967, Gerald feinberg of Columbia University thinks that it is very promising to concretize such mass and length (feinberg was not the first person to put forward superluminal particles, which were first assumed by Bilanuk and Su Dashan, but feinberg popularized this concept). Perhaps, the mass and length represented by "imaginary number" is just a way to describe that an object has, for example, bearing capacity-this object and the matter in our universe are not attracted by gravity, but repel each other.
Feinberg called the particles with virtual mass and virtual length "superluminal particles". If we assume that this superluminal particle can exist, can it follow Einstein's equation in another way?
Obviously, chopsticks will be like this. We can describe the whole universe composed of superluminal particles, which run faster than the speed of light, but follow the requirements of relativity. However, in order to enable fast players to do this, when it comes to energy and speed, the situation will be the opposite of what we are usually used to.
In our "slow universe", the energy of a stationary object is equal to zero, but when it gains energy, it moves faster and faster. If it gains infinite energy, it will be accelerated to the speed of light. In the "fast universe", superluminal particles with energy equal to zero move at infinite speed. The more energy it gets, the slower it moves. When the energy is infinite, its speed decreases to the speed of light.
In our slow universe, under no circumstances can an object be faster than the speed of light. In the fast universe, superluminal particles will not be slower than the speed of light under any circumstances. The speed of light is the boundary between the two universes and cannot be surpassed.
However, do superluminal particles really exist? We can assert that there may be a fast universe that does not violate Einstein's theory, but the possibility of existence does not necessarily mean existence.
One possible way to explore the fast universe is to consider that if the superluminal particle moves faster than the speed of light in a vacuum, it will leave a light trail that can be detected when it flies. Of course, most superluminal particles fly very fast-millions of times faster than the speed of light (just like most ordinary objects move very slowly, only one millionth of the speed of light).
General superluminal particles and their flashes have passed a long time before we found them. Only very rare high-energy superluminal particles will fly over our eyes at the speed of light. Even on this occasion, it only takes about a third of a second for them to fly over a kilometer, so it is a very nerve-racking thing to find them!
Comment: from the length and quality of imaginary number, realize the mutual exclusion of superluminal particles! But they think that when the tachyon flies by, it will leave a trace that may be detected, right? If so, wouldn't superluminal particles have been detected long ago? They also believe that when the speed of superluminal particles is infinite, its mass is zero?
2. Martin Harvitt of the United States wrote in the Concept of Astrophysics (Science Press/KOOC-0/98/KOOC-0/Edition/KOOC-0/Page 2/KOOC-0/3, 2/KOOC-0/4):
When Einstein first discovered the concept of special relativity, he clearly pointed out that the speed of motion of an object cannot be greater than the speed of light. He believes that the relationship between stationary mass and energy
It has been proved that in order to accelerate an object to the speed of light, infinite energy is needed. Therefore, if the rest mass of a particle is not zero, then it is impossible for the particle to reach the speed of light, let alone exceed the speed of light.
In recent years, many researchers have raised this question again. They think that continuous acceleration can't reach the speed of light, but this alone can't rule out the existence of superluminal matter, which is produced by other means. They call particles whose speed is faster than the speed of light superluminal particles, and study the possible properties of this entity.
The basic argument that we should study the possibility of superluminal particles is that Lorentz transformation is similar in form for both cases where the speed is greater than the speed of light and less than the speed of light, and the transformation itself does not rule out the possibility of superluminal particles.
Of course, the similarity of transformation does not mean that particles and superluminal particles have exactly the same performance properties. If we look at the relationship between stationary mass and energy, we find that when the particle velocity v >; The quantity in C is imaginary. Therefore, if the mass of superluminal particles (here, the rest mass m0) is a real number, then its energy should be an imaginary number. In fact, people regard the (stationary) mass of superluminal particles as an imaginary number, mainly because such a choice cannot be ruled out in observation. Maybe this is a negative way, but if we don't make this assumption, it will be more difficult for us to make progress, that is, there will be no way to make some predictions about the possible results of the experiment.
When the mass is an imaginary number, the energy e can become a real number, and at the same time, it is as follows
As shown in the figure, momentum is also a real number.
Now put the momentum-energy relationship
And the relationship between mass and energy, we get
When v becomes larger, it seems that e will become smaller, and the energy will become zero when the speed tends to infinity. But at this time, the momentum is still a finite value, and it keeps approaching the value of | m0c|.
At this point, we just broke away from the orthodoxy that quality is an imaginary number.
Preliminary experiments have been carried out to explore superluminal particles, but so far they have not been detected. However, they may be discovered one day.
It seems that superluminal particles are not easy to interact with ordinary matter, which is one of its shortcomings. If not, we may have found them by now.
Comment: The author of this paper thinks that it is negative for people to regard the rest mass m0 of the tachyon as an imaginary number, which seems to be out of helplessness! However, after taking the rest mass of superluminal particles as imaginary number, the moving mass m, energy and momentum of superluminal particles are real numbers, so superluminal particles have the same behavior as ordinary matter, so it can be concluded that superluminal particles can be detected. According to this theory, we can't understand why superluminal particles can't be detected, and we can only sigh that "superluminal particles can't easily interact with ordinary matter-this is one of its shortcomings." In fact, this is also one of the advantages of Kuaizi. When people really understand the tachyon, they will find that it provides us with a richer and more vivid world, enabling us to understand mysterious phenomena that we could not understand before, thus enabling people to better exert their potential.
3. Xu Keming really put forward in Yin Chang's "Ten Thousand Mysteries of the World Physics Volume" that "is the speed of light the limit of the speed of matter?" As a mystery:
Relativity clearly points out that the speed of any object (particle) is always less than C and at most equal to C. This theoretical result has been confirmed by a large number of experiments. But in some problems, there will also be superluminal situations. This seemingly contradictory situation can be unified as long as the concept of speed is further analyzed.
This is because the special theory of relativity only limits the speed of matter movement, or the speed of signal propagation and action transmission. It has no limit, and no speed can exceed the speed of light. Therefore, the possibility of superluminal particles in nature cannot be ruled out. We call particles less than the speed of light "slow" and particles greater than the speed of light "fast". Particles in nature can be divided into three categories: slow particles, photons and fast particles. In recent years, some people divide static mass into three categories according to its size: deceleration M02 >；; 0, photon m02 =0, superluminal particle m02
Comments: Similar to the above views, it is a representative view.
4. Tian Daojun of Nanjing University of Aeronautics and Astronautics listed the possible power principles of flying saucers in "Overview and Prospect of UFO Power System Research", one of which is:
Virtual mass principle According to Einstein's special theory of relativity, if the stationary mass of an object is m0, the relationship between its moving mass M and velocity V is
When the sub-light speed is 0 < V < C, there is m0m0. As V increases and approaches the speed of light C, the mass m will increase infinitely, which shows that it is impossible for any object with mass to reach the speed of light, let alone exceed it. Now, in order to realize interstellar flight, I want to ask: Is there any object in the universe that is faster than light? Secondly, how to make the flying saucer move faster than light? To this end, let's take a look first. In actual observation, in 1973, Australian scientists found that there were indeed particles moving faster than the speed of light, called "superluminal particles", and their speed was lower than the speed of light C (is this not contradictory to the above conclusion? Don't! Because the above conclusion refers to "objects with mass", there are indeed some objects without mass in the universe at rest, such as photons, the basic unit of all electromagnetic radiation, gravitons and so on. ), secondly, in theory, in order to extend the above formula to the range of superluminal v > C (but not with sublight v C, m is an imaginary number (that is, the mass of an object is correspondingly extended from the original real number range to the complex number range), which is called virtual mass, and this is the tachyon. The characteristic of superluminal particles is that the slower the speed, the greater the energy. If the superluminal particle is given a thrust to increase its energy, its speed will decrease. If the thrust is infinitely increased, its speed will be close to the speed of light, and the lower limit is the speed of light. On the contrary, when its energy is smaller, its speed will increase, that is to say, if a resistance is given in the direction of the movement of superluminal particles, such as blocking the medium to weaken its energy, its speed will increase until its energy disappears completely. Therefore, if a conversion device can be designed to convert every subatomic particle and its load into superluminal particles, it can fly out in an instant without any acceleration, and its speed is many times faster than the speed of light, and the speed can be controlled by adjusting the energy. After a few days, it can fly to another distant galaxy without any deceleration, and then the superluminal particles can be converted into subatomic particles through the conversion device, and finally it can be restored to the original UFO and its load. However, according to Xinmin Evening News1998 65438+1October 17, the scientific and technical personnel of the Institute of Experimental Physics in Innsbruck, Austria, initially completed the "long-distance transmission" (that is, a substance is converted into photons and quickly transmitted to a distant destination, and then converted into the original substance again) through an optical instrument control panel.
Comment: v> When C is directly applied to Einstein's mass-velocity relation, the quality obtained is not only imaginary, but also negative. Tian teacher didn't give any explanation, which is not desirable. As for 1973, through continuous observation and research, Australian scientists have found that there are indeed particles moving faster than the speed of light, which has not been recognized. Estimation is one of the pseudo-superluminal phenomena introduced below.
5. A more comprehensive introduction to the problem of superluminal:
Relativity and superluminal this article is compiled from (compiled by relativistic FAQ. Philip Gibsonho
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 less 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 of 0.6c relative to C, and B moves westward at a speed of 0.6c relative to C. 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 lamp, and you will find that the shadow is faster than your hand. 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 hits 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 (assuming that the signal propagates for a long time and reaches a stable state) after propagating in a medium for a certain distance. 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) The apparent speed of superluminal 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 When people on the earth see the rocket moving away at a speed of 0.8c, the clock on the rocket is slower than that on the earth, which is 0.6 times that of the earth. If you divide the distance traveled by the rocket by the time spent on the rocket, you will get the "speed" of 4/3 C. Therefore, the people on the rocket are moving at a speed "equivalent to" superluminal speed. For 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 a speed equivalent to 4/3 C. 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 the speed of gravity propagation exceeds the speed of light. In fact, gravity travels at the speed of light.
(9) EPR Paradox 1935 Einstein, Podolski and Rosen published an ideal experiment, which showed 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) Virtual particle In quantum field theory, force 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 is the effect that particles escape 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. A group of physicists made an experiment of superluminal communication by using quantum tunneling effect: they claimed that Mozart's 40th symphony was transmitted through a barrier with a width of 1 1.4 cm at a speed of 4.7c Of course, this has caused great controversy. 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.
Tao Zhexuan believes 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, there will be a weak but still measurable force between them, which is the Casimir effect. Casimir effect is caused by vacuum energy. Scharnhorst's calculation shows that the lateral movement speed of photons between two metal plates must be slightly higher than the speed of light. However, further theoretical research shows that it is impossible to use this effect for superluminal communication.
(13) Hubble's cosmological expansion theorem says that galaxies with a distance of d separate at the speed of HD. 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.
The moon revolves around me 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 ourselves, but we say that the moon revolves around us. But according to the general theory of 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 "constant speed of light" needs to be explained. 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) Clarify the definition of superluminal. A point in four-dimensional space-time represents an "event", that is, three empty spaces.