How is it not possible to transfer information faster than the speed of light by use of shadows?

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Questa volta abbiamo cercato una curiosità scientifica:

Let's say we point a very powerful flashlight at the moon, and at both sides of the moon is an observer, and both observers see the light from earth. If we then shut off the flashlight from earth, both observers should see the light turn off at the same time (not factoring the curvature of the moon). This way, both observers know that the light must be off for the other observer as well – faster than light could travel between the observers. How does this not break the law?

Ed ecco le risposte degli esperti:

This is close to the light-house paradox – another of the classic apparent paradoxes in special relativity. There’s even a version with the Moon!

The resolution is that predicting an event is not the same as communication. There is no actual signal between the two sites on the Moon. Instead, based on the assumption that everything is working as you might expect, you can reasonably predict that the other site sees the light switch off at the same time as you. But it doesn’t violate special relativity for something odd to happen at the other site to prevent them from seeing the light turn off. Maybe the other moon-person has a spaceship floating just above them, set up to perfectly replicate the appearance of the light from Earth. That may be unlikely, but you can’t confirm that directly without a direct speed-of-light communication from the other site. Otherwise, you’re just making a guess or prediction. And a prediction is not faster-than-light communication, no matter how accurate the prediction might be.

In your scenario, the only transfer of information happening is from earth to the moon. If the two observers on either side the moon wanted to use the earth light/shadows to communicate with the other observer, theyd be limited by the speed of light in sending their message to earth and the same for the message from earth to the other observer.

if you and your neighbor are both tuning in to the same radio channel you would both know what the other was listening to by listening to your own radios. at no point does information have to flow between the two of you in order for that statement to be true. all that matters is the information flow between each listener and the radio tower.

No information travels from one side of the moon to the other when the flashlight is switched. There fact that you know that the person on the other side sees the they light go off is because information traveled from earth to you at light speed, and this information, coupled with your prior information (e.g. coordinating with the other person using radio waves) resulted in your knowledge.

Shadows are the absence of light, appearing the moment photons are not present, which coincides with the distance from the light source divided by the speed of light to get the time it takes for the shadow to appear from the light switch being turned off.

Turning off the light/laser does not stop the beam of photons at the terminal end of the wave.

This is where the idea that the sun disappearing miraculously would take 8 minutes for the world to even register it by light or gravitationally.

Edit^1 :

It has been pointed out that the system may have been intended to be a trigonometry problem similar to einstein’s lightning thought experiment instead of just being curious about how shadows work and why they can’t be used to convey FTL data.

If one does not fully understand the implications of wave/particle duality and what causes shadows to update, discerning the implications of multiple observers in a dynamic system is going to end in to much information to comprehend.