As I already wrote, the theory of relativity is ruled by mathematics. Many of the consequences of the theory of relativity contradict everyday experience and the «common sense» based on it.
Below I list the most interesting counter-intuitive implications of this theory. You have to understand that when I say that they contradict common sense, I do not mean at all that they are not true.
Our «common sense» does not work for the theory of relativity because it is based on our everyday experience. But in life we never encounter relativistic effects. Therefore, the conclusions that «common sense» suggests are usually erroneous.
Mathematics is the quintessence of logic. All consequences and conclusions from the theory of relativity are based on mathematics and are absolutely logical. Moreover, all these consequences have been confirmed experimentally. So let’s get down to the investigation.
This means that time depends on the frame of reference. Suppose we have a clock in a stationary frame of reference. And the second observer, moving at a speed close to the speed of light, has exactly the same clock. If after a while it turns out that less time has passed on the traveler’s clock.
Let’s say we have a stick 1 meter long in a fixed frame of reference. In the frame of reference of a spacecraft moving at a speed close to the speed of light, the length of the same stick will be shorter. And this is not an optical illusion, it is a physical effect.
Anyone familiar with classical mechanics will easily answer that in order to find out the relative speed of two, for example, trains moving towards each other, their speeds must be added. And this is true when it comes to pre-relativistic speeds. When speeds close to the speed of light come into play, simple speed addition stops working.
Instead, a special relativistic velocity addition formula is used. In fact, this formula is also valid for low speeds, just the difference in the results between the relativistic and classical formulas begins to become noticeable only with increasing speeds.
Regardless of whether we are approaching a light source or moving away from it, the speed of light will always be constant. Likewise, if a light source approaches us or moves away, this does not in any way affect the speed of the light emitted by it. The movement of the light source can be seen by the shift in the wavelength of the emitted light — if the object approaches us, then the light spectrum will be shifted towards the blue side and towards the red — otherwise.
The simultaneity and sequence of events can also be subject to different interpretations. For example, from our point of view, event A occurs before event B. There is always a moving frame of reference, for the observer in which the sequence of events will be different.
Summing up all of the above, I will note once again that the fact that the theory of relativity contradicts our everyday experience and common sense based on this experience in no way indicates that the theory of relativity is not true.
The theory of relativity has long been proven and verified experimentally to the extent that a theory can be proven and verified experimentally at all. All conclusions from the theory of relativity are confirmed by our observations.
An apparent contradiction arises because our common sense has been working with pre-relativistic effects all our lives. Those. we simply do not experience such speeds for the effects of the theory of relativity to have any effect. Therefore, our common sense gives incorrect predictions where relativistic effects come into force — it is not used to taking them into account and therefore is mistaken.
In other words, when the formulas of the theory of relativity predict one thing, and common sense predict another, you should believe the formulas.