In Einstein's "Theory of Relativity", there is a core idea called "the speed of light cannot be surpassed", which can be simply described as: it is impossible for any object with static mass to reach or exceed the speed of light, and in addition, no information can be transmitted faster than the speed of light (note: the speed of light in this article refers to the speed of light in a vacuum, for the sake of description, we will simply refer to it as the speed of light, please pay attention to the distinction).
Although this theory has long been accepted by the scientific community, many people still find it difficult to accept, and have put forward various thought experiments to try to show that at least in terms of "the speed of information transmission", the speed of light should be achievable, for example, someone has proposed such a thought experiment: can a 300,000-kilometer-long rope achieve faster than the speed of light?
The idea of this thought experiment is roughly like this: in daily life, if A and B are each pulling on the two ends of the rope, then A pulls the rope, and B can feel it instantly, so if A and B discuss in advance what the various details of the rope (such as frequency, strength, etc.) represent, then they can transmit information through the rope.
Now the length of the rope pulled by A and B is set to 30 kilometers, and the speed of light is about 300,000 kilometers per second, that is, it takes 1 second to run 30 kilometers at the speed of light, and since A pulls the rope, B can feel it instantly, so in this case, it is possible to transmit information faster than the speed of light.
It can be seen that in this thought experiment, the key point to achieve the speed of light is that the force generated by A pulling the rope will be instantly transmitted to the other end of the rope, and then B will feel it. Is that really the case? Unfortunately, the answer is no.
The rope can be thought of as a solid, but at the microscopic level, it is actually composed of a large number of atoms, that is, inside the rope, the atoms and atoms are arranged and tightly bound together in a specific way through their interaction with each other. In this case, the force generated by pulling the rope does not act instantaneously on all the atoms that make up the rope, but rather on a transmission process.
We can simply understand this process as follows: after A pulls the rope, the force generated by it will first act on the nearest "first-layer" atoms from his end, and these atoms will be displaced after the force, which will then drive the farther "second-layer" atoms, and the "second-layer" atoms will move the farther "third-layer" atoms after the displacement...... And so on "layer by layer" until the force is transferred to the end of B.
(↑ Simplified model of mechanical wave propagation in a medium)
Theoretically, the propagation velocity (v) of the mechanical wave in the medium is closely related to the elastic modulus of the medium (K) and the density of the medium (ρ), which can be calculated by a simple formula "v = √(K/ρ)".
Here we might as well assume that the rope in this thought experiment is a wire rope, the density of steel is known to be about 7.85 x 10^3 kg per cubic meter, and the elastic modulus of the wire rope can be taken as 200 GPa, which can be substituted into the formula, and the propagation speed of mechanical waves in the wire rope is about 5 kilometers per second.
In daily life, the rope we use is generally not more than 50 meters, that is, if there is a 50-meter wire rope, A pulls the rope, then B will feel it after about 0.01 seconds, because of such a short delay time, it is difficult for us humans to perceive, so we usually think that it is instantaneous.
But for a 300,000 km long rope, the situation is completely different, a simple calculation can be seen, if this rope is a wire rope, then after A pulls the rope, B will need about 1,000 minutes to feel, obviously, such a long delay time, not at all "instant feeling".
Even carbon nanotubes, which are currently considered to be the best materials for ropes, have an elastic modulus and density of 1TPa and 2.1 x 10^3 kilograms per cubic meter, and the propagation speed of mechanical waves in them is only about 690 kilometers per second, which is still far below the speed of light, let alone to achieve faster than the speed of light.
(Carbon nanotubes)
Seeing this, some people may ask, if a material with an infinite elastic modulus is used to make a rope, is it possible to transmit information at the speed of light? Theoretically speaking, this is true, but in fact, the material with an infinite elastic modulus is actually an "absolute rigid body", and we all know that at least in the universe as we know it, "absolute rigid body" cannot exist.