Why can’t the speed of light be exceeded?

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People who are accustomed to think in terms of three-dimensional Euclidean space and build on it an understanding of physical reality, as a rule, do not fully understand the expression «nothing can move faster than light».

Often they understand this as if people simply have not yet found a way to accelerate something to a speed exceeding the speed of light. I am often asked questions, the implication of which boils down to the fact that the advancement of technology will sooner or later make travel faster than the speed of light possible.

And we are not talking about some kind of wormholes or space distortions like the Alcubierre bubble, when the ship moves at subluminal speed in curved space, which does not contradict physics, although we do not know how to do this yet. Speech in questions of this kind is about precisely superluminal motion in space-time with zero or close to that curvature.

So, when a physicist says that the speed of light is a limit, he is not talking about the technical limit of humanity, but about the fundamental speed limit that exists in nature. There is no speed greater than the speed of light, which could be determined within the framework of physics. The possibility of moving faster than the speed of light simply disappears when the object reaches the speed of light, since the very concept of speed at this moment loses its meaning. This is because space-time, in general, is not geometrically Euclidean.

If we learn to understand the Universe through its true geometry, then this fact will seem no more fantastic than, for example, the fact that one cannot go anywhere north of the North Pole, or that, for example, one cannot invent a color darker than black. These statements are true by definition. For similar reasons, the geometry of spacetime imposes speed limits. Let’s take a closer look at this.

The speed of an object in space is equal to the distance that the object travels (from the point of view of the observer) divided by the amount of time that passes for that observer.

Let’s imagine we launch a very powerful rocket capable of accelerating at 1 g for 10,000 years. Throughout the voyage, the rocket crew will experience an increase in speed of 9.8 meters per second every second. As the speed of the rocket changes, so does how time passes for the rocket crew. In the rocket reporting system, time will begin to slow down relative to the time in the observer’s frame of reference remaining on Earth.

The meaning of this is that although each person on board the rocket will experience an acceleration equal to 9.8 m / s², from the point of view of an observer on Earth, the acceleration of the rocket will constantly decrease and asymptomatically approach zero as the rocket speed asymptomatically approaches the speed Sveta.

Thus, the natural limitation on maximum speed is related to how interconnected and how space and time interchange as the speed increases. In fact, the speed of light is the speed at which time in the rocket’s frame of reference will stop. If the ship reached the speed of light, it would move through the universe without experiencing a change in time.

As we remember, the speed is equal to the distance divided by the time for which this distance is covered. But if time has stopped in the rocket’s frame of reference, then the time in this formula is equal to zero, which leads us to a contradiction: in the denominator we have zero, the result tends to infinity.

This emerging infinite value is one of the reasons why the speed of light is constant for any frame of reference: infinity is equidistant from all points of the universe. By changing the frame of reference, we can change the value in the numerator of the fraction, but since zero still remains in the denominator, the result will still be the same!