Before and after the publication of Special Relativity, many experiments have demonstrated its correctness from different perspectives. Most of these experiments were based on actual measurements, but there also exist some “thought experiments”—experiments that only require logical reasoning and are practically impossible to perform. Below is a thought experiment I saw long ago in a certain book (apologies, I have truly forgotten the title) used to overturn the Galilean transformation of additive light speeds. With just a few sentences, it seemingly proves the fact that c+c=c (where c is the speed of light in a vacuum). However, c+c=c appears as a principle in Special Relativity and cannot be proven through logical reasoning. What is the actual truth? Let us first look at this experiment.
Select an arbitrary coordinate origin. Imagine there is a Plane 1 at a distance of c \cdot t_0 due North of the origin, flying South at the speed of light c; and a Plane 2 at a distance of c \cdot t_0 due West of the origin, flying East at the speed of light c. Assuming they continue in uniform motion, it is obvious that after time t_0, a tragedy will occur (the planes will collide).
Additionally, there is a stationary observer at a distance of c \cdot t_0 due South of the origin watching the scene.
Suppose that velocities can be directly added. Then the speed of the light emitted by Plane 1 toward the observer would be c+c=2c. That is to say, any information from Plane 1 is transmitted to the observer at a speed of 2c. Meanwhile, the speed of the light emitted by Plane 2 toward the South is just c, so it transmits information southward at speed c. After time t_0, the planes collide. What can the observer see?
Clearly, Plane 1 is destroyed. According to the previous argument, the observer sees Plane 1 destroyed after a time of \frac{c \cdot t_0}{2c} = \frac{t_0}{2}. Plane 2 is also destroyed, but the image of its destruction only reaches the observer’s eyes after a time of \frac{c \cdot t_0}{c} = t_0. In other words, in the observer’s view, the two events do not happen simultaneously. However, this tragedy clearly happened simultaneously; how could we first see Plane 1 break “for no reason” and then Plane 2 crash into it?
If we assume the speed of light for Plane 1 is c+c=c, then there is no contradiction. Thus, this quite perfectly demonstrates the principle of the constancy of the speed of light.
It indeed seems there is no problem, and when I first saw it, I also felt it was a good experiment for understanding the constancy of the speed of light. However, the more I thought about it later, the more I felt something was wrong. Imagine replacing the speed of light c with the speed of sound; the conclusion would be the same. Does that mean we should also derive a “principle of the constancy of the speed of sound”?? This is clearly untenable.
In fact, replacing “seeing” with “hearing” does not lead to any contradiction. The observer would hear the sound of the collision simultaneously because sound is a wave, and its speed relative to the medium is constant once emitted. If we insist that we must see the two collide simultaneously, then we are saying that light is actually similar to sound—a type of wave. This would explain it; roughly speaking, Maxwell’s electromagnetic equations simply replaced the sound wave propagation speed v with the speed of light c. However, the propagation of waves requires a medium, yet light can surprisingly propagate in a vacuum! This leaves only two possibilities: either light is not a wave, which contradicts the previous point; or there is an omnipresent medium in the vacuum. The latter assumption is the so-called “phantom”—the Ether.
Later, after numerous experiments denied the existence of the Ether, physics fell into great difficulty. We had to admit: light is something even more terrifying than a “phantom”; it is neither a wave nor a particle, yet it possesses both wave properties and particle properties—we call it a “wave-particle.”
Well, how did I end up drifting into quantum physics?? This experiment indeed gives us a strong intellectual shock. In my view, what it illustrates is not the principle of the constancy of the speed of light, but rather our understanding of “simultaneity.” If we follow the Galilean transformation, then this collision tragedy is not simultaneous in the observer’s view; if we want to say it is simultaneous, then we must abandon the Galilean transformation. In this thought experiment, “simultaneity” and “additivity of light speed” must be abandoned, or both.
Strictly speaking, this experiment describes the wave nature of light more than anything else.
However, there are still many points worth discussing in this thought experiment, or rather the arguments within it. Welcome everyone to discuss.
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