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The present hype about the speed of light that may (perhaps) 'exceed the speed of light' made me realize that one can actually show that the 'speed of darkness' may exceed the speed of light. Can you think of a thought-experiment to illustrate this?
At least one solution will be posted right here on Tuesday, September 4. There may be many…
Edit (September 1): With Spring in the air in the Southern hemisphere and this thread starting to 'fall apart' (just as I presume the Fall is starting in the North) I have decided to post the "At least one solution will be posted right here" right now.
The answer will obviously depend on how you define the 'speed of darkness'. I view it is like this: send a pulse of light out into dark, empty space. The speed of light is the speed of the wave front and the speed of darkness would then be the speed of the pulse trailing edge.
If the pulse length remains constant, then the speed of light and the speed of darkness are the same, but will this always be so? I have seen a helpful, down-to-earth analogy by Aephraim Steinberg, a quantum optics expert at the University of Toronto. He uses an analogy of a 'bullet train' to represent a 'wave train' of light. Here's a modified version of Steinberg's 'parable of the train'.
The bullet train runs at a constant speed, but at each station, the rearmost car is disconnected and stops there, while the rest of the train speeds past. So the front of the train will continue to run at a constant speed, but the rear of the (now shorter) train will appear to have experienced an instantaneous forward jump. The average speed of the rear end of the train is hence larger than the constant speed of the front of the train.
Light pulses can operate similarly under certain conditions, when photons are 'lost' along the way. The trailing edge of a light pulse that loses photons can exceed the speed of the wave front, which always travels at c in free space. Therefore, due to the way the speed of darkness has been defined above, the speed of darkness can exceed the speed of light.
I'm still working on how to use this speed of darkness to send information faster than the speed of light, but try as I might, I simply can't get the trailing edge of the 'wave train' to deliver any information. I suppose that's to be expected when the 'train' loses some 'rear-end-cars' along the way…
Jorrie
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