Classical mechanics, the laws of which were formulated by Newtons at the end of the 17th century, was considered all explanatory and infallible for about two hundred years. Until the 19th century, its principles seemed omnipotent and constituted the basis of physics. However, by the indicated period new facts began to appear that could not be squeezed into the usual framework of known laws. Over time, they received a different explanation. This happened with the advent of the theory of relativity and mysterious science - quantum mechanics. In these disciplines, all previously accepted ideas about the properties of time and space underwent a radical revision. In particular, the relativistic law of velocity additions eloquently proved the limitations of classical dogmas.
Simple addition of speeds: when is this possible?
Newton’s classic in physics is still considered true, and its laws are used to solve many problems. It should only be borne in mind that they operate in a world familiar to us, where the speeds of various objects, as a rule, are not significant.
Imagine a train traveling from Moscow. Its speed is 70 km / h. And at this time, in the direction of travel from one car to another, a passenger travels, running 2 meters in one second. To find out the speed of its movement relative to houses and trees flickering outside the train window, these speeds should simply be added. Since 2 m / s corresponds to 7.2 km / h, the desired speed will be 77.2 km / h.
World of high speeds
Photons and neutrinos are another matter; they obey completely different rules. For them, the relativistic law of addition of velocities applies, and the principle shown above is considered completely inapplicable to them. Why?
According to the special theory of relativity (SRT), any object cannot move faster than light. In extreme cases, it is only capable of being approximately comparable with this parameter. But if we imagine for a second (although in practice this is impossible) that in the previous example the train and passenger move in approximately this way, then their speed relative to the objects resting on the ground, past which the train passes, would be almost two light. But this should not be. How are the calculations made in this case?
The relativistic law of addition of velocities, known from the class of 11th grade physics, is represented by the formula given below.
What does it mean?
If there are two reference systems, the speed of a certain object relative to which is V 1 and V 2 , then for calculations you can use the specified ratio, regardless of the value of certain values. In the case when both of them are much less than the speed of light, the denominator on the right side of the equality is practically 1. This means that the formula of the relativistic law of addition of speeds turns into the most usual one, that is, V 2 = V 1 + V.
It should also be noted that when V 1 = C (that is, the speed of light), for any value of V, V 2 will not exceed this value, that is, it will also be equal to C.
From the realm of fiction
C is a fundamental constant, its value is 299 792 458 m / s. Since the time of Einstein, it is believed that not a single object in the Universe can surpass the movement of light in a vacuum. This is how one can define briefly the relativistic law of velocity addition.
However, science fiction writers did not want to come to terms with this. They invented and continue to compose many amazing stories whose heroes refute such a restriction. In the blink of an eye, their spaceships move to distant galaxies located many thousands of light years from the old woman of the Earth, nullifying all established laws of the universe.
But why is Einstein and his followers sure that this cannot happen in practice? We should talk about why the light limit is so unshakable and the relativistic law of velocity addition is inviolable.
The relationship of cause and effect
Light is the medium of information. It is a reflection of the reality of the universe. And the light signals reaching the observer recreate pictures of reality in his mind. This happens in the world familiar to us, where everything goes on and obeys the usual rules. And from birth we are accustomed to the fact that it cannot be otherwise. But if you imagine that everything around has changed, and someone went into space, traveling at super speed? Since he is ahead of the photons of light, the world begins to appear to him as in a film rolled back. Instead, tomorrow comes yesterday for him, then the day before yesterday, and so on. And tomorrow he will never see until he stops, of course.
By the way, science fiction writers also actively adopted a similar idea, creating an analogue of a time machine based on these principles. Their heroes fell into the past and traveled there. However, causal relationships were collapsing. And it turned out that in practice this is hardly possible.
Other paradoxes
The reason cannot be ahead of the investigation. This is contrary to normal human logic, because in the universe there must be order. However, SRT suggests other paradoxes. She broadcasts that even if the behavior of objects obeys the strict definition of the relativistic law of addition of velocities, it is also impossible for him to exactly match the speed of movement with photons of light. Why? Yes, because magical transformations begin to take place in the full sense. The mass is infinitely increasing. The dimensions of a material object in the direction of motion unlimitedly approach zero. And again, over time, perturbations cannot be completely avoided. Although it does not move backward, but when it reaches the speed of light it completely stops.
Eclipse of Io
STO claims that photons of light are the fastest objects in the universe. In this case, how did you manage to measure their speed? Just human thought was quicker. She was able to solve a similar dilemma, and its consequence was the relativistic law of velocity addition.
Similar issues were resolved during the time of Newton, in particular, in 1676 by the Danish astronomer O. Roemer. He realized that the speed of ultrafast light can only be determined if it travels enormous distances. Such, he thought, was possible only in heaven. And the chance to bring this idea to life soon presented itself when Roemer observed through the telescope an eclipse of one of the moons of Jupiter called Io. The time interval between the entrance to the blackout and the appearance in the field of view of this planet for the first time was about 42.5 hours. And this time, everything corresponded approximately to the preliminary calculations carried out according to the well-known period of the conversion of Io.
A few months later, Roemer again made his experiment. During this period, the Earth was significantly removed from Jupiter. And it turned out that Io was late to show his face for 22 minutes in comparison with earlier assumptions. What did it mean? The explanation was that the satellite did not stop at all, but the light signals from it took some time to overcome a significant distance to the Earth. Having made calculations based on these data, the astronomer calculated that the speed of light is very significant and amounts to about 300,000 km / s.
Fizeau Experience
The forerunner of the relativistic law of velocity addition, the Fizeau experiment, made almost two centuries later, correctly confirmed Roemer's guesses. Only the famous French physicist in 1849 conducted laboratory experiments. And to implement them, a whole optical mechanism was invented and designed, an analog of which can be seen in the figure below.
The light emanated from the source (it was stage 1). Then it was reflected from the plate (stage 2), passed between the teeth of the rotating wheel (stage 3). Then the rays hit a mirror located at a considerable distance, measured in the value of 8.6 kilometers (step 4). In conclusion, the light was reflected back and passed through the teeth of the wheel (step 5), fell into the eyes of the observer and was fixed by him (step 6).
The rotation of the wheel was carried out at different speeds. When moving slowly, light was visible. With increasing speed, the rays began to disappear, not reaching the viewer. The reason is that the rays needed some time to move, and during this period, the teeth of the wheel shifted slightly. When the rotation speed increased again, the light again reached the observer's eyes, because now the teeth, moving faster, again allowed the rays to penetrate through the gaps.
SRT principles
Relativistic theory was first introduced to the world by Einstein in 1905. This work is devoted to the description of events occurring in a variety of reference systems, the behavior of magnetic and electromagnetic fields, particles and objects when they move, as comparable as possible to the speeds of light. The great physicist described the properties of time and space, and also examined the behavior of other parameters, the sizes of physical bodies and their masses under the indicated conditions. Among the basic principles, Einstein called the equality of any inertial reference systems, that is, he had in mind the similarity of the processes taking place in them. Another postulate of relativistic mechanics is the law of velocity addition in a new, non-classical version.
Space, according to this theory, appears as a void where everything else functions. Time is defined as a kind of chronology of ongoing processes and events. It is for the first time called as the fourth dimension of space itself, now receiving the name "space-time".
Lorentz Transforms
Confirm the relativistic law of addition of the rates of the Lorentz transformation. So it is customary to call mathematical formulas, which in their final form are presented below.
These mathematical relationships are central to the theory of relativity and serve to transform coordinates and time, being written for four-seater space-time. The presented formulas received the indicated name at the suggestion of Henri Poincaré, who, developing a mathematical apparatus for the theory of relativity, borrowed some ideas from Lorentz.
Such formulas prove not only the impossibility of overcoming the supersonic barrier, but also the inviolability of the causality principle. According to them, it became possible to mathematically substantiate time dilation, shortening of object lengths and other miracles occurring in the world of superhigh speeds.