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Hi! Thanks for answering my previous questions. Considering the fact that a particle moving at (.999)c could be seen as moving at a speed greater than c if observed on the hypotenuse (but contains no information), could not you create a situation where that particle does contain information? This is sort of based on the tachyon antitelephone example: Let's assume that you have one person at the ends of the hypotenuse, person one sends a signal at c (or vc along the hypotenuse, the reply could cover "more" distance in "less" time and appear to go against causality. Is this true? Would such a set-up go against causality (to one extent or the other)? Sorry for the long question, but thank you so much for your help!!
Answer 1:

There is no way to devise a situation where information travels faster than the speed of light. In your question, you describe a scenario where the reflection of a light pulse appears to exceed c due to constructing a hypotenuse with a longer path length. Thus, the paradox is that the light signal traveled a 'greater' distance over a 'shorter' time. However, the key point is that the distance you should use when calculating the speed of the signal is measured between the point where the signal originated and you or the sensor. There is no 'information' traveling along the hypotenuse, in the sense that if you changed the length of the hypotenuse, the signal would take the exact same amount of time to reach you or the sensor.


Answer 2:

I'm afraid I don't know what you mean by "moving on a hypotenuse". Your geometry confuses me. Do you mean that you are actually seeing the particle by observing its reflection off of something? If so, then yes, it can apparently move faster than c.

Have you heard of phenomena called "sprites" that occur above thunderstorms? Sprites are luminous excitations of the air in the stratosphere caused by some kind of charged particle emissions that move upward, out of the atmosphere, as a side-effect of lightning striking down below. So far as I understand, what causes the streams of charged particles that make sprites are not understood, but they are associated with what are called "elves" - expanding rings of light on the ionosphere that appear very briefly after the sprites. The elves expand across the ionosphere at superluminal speeds. What we think is actually happening is that the sprites emit an electromagnetic pulse, which expands at the speed of light and may or may not be spherical when emitted. Although the surface of the electromagnetic pulse shock is moving at c, the line where it and the ionosphere intersect may move more rapidly than c. In truth, no information is moving at superluminal speeds at any point: the elf is a response to the electromagnetic pulse from the sprite, which moves at c, and the light we see emitted from the elf also moves to us at c, as well as the light from the sprite itself that we see moves at c. Is this what you mean by us being "on a hypotenuse" from the point of origin (the sprite)?



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