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0

See Greg Egan's applet. This will clear up all confusion, and ought to be viewed by any reporter who covers a "scientists break light speed" report. Subluminal shows how a wave composed of a multitude of frequencies moving at different velocities — all less than or equal to c, the speed of light in a vacuum — can appear to have features moving faster ...


7

Point a laser to the sky, track where it lands very far away from the Earth, and then move your arm. The point you are tracking in space is moving faster tha the speed of light, even though light itself isn't. This isn't the same as group velocity, but it is very similar. There is no problem in having arbitrary points you imagine going faster than light, ...


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If we take your case of amplitude modulating two frequencies with pulses which are a second wide - then these are not pure frequencies any more - they will have a bandwidth of approx 2Hz (depends on pulse shape) [because there will be two sidebands at +/- 1Hz from carrier]. These pulse therefore have a group velocity. Only if you emit a wave at a single ...


3

You have to be careful to interpret your statements 1 and 2 correctly. In statement 1 you are talking about an infinitely long wave train which is made up of only one single frequency. As soon as you have a wave train of finite length then the wave train is made up of the sum many frequencies. So in statement 2 what you think of as a pulse of a wave with a ...


10

The transitions between two frequencies will not move with the phase velocity! Nor will the beginning of transmission! Only in the steady plane wave parts in the middle, the wave crests will move faster than light. And that's just "appearance" in the sense that bewteen any two times, you can find a maximum of the electric field and pretend the wave moved ...


2

There is nothing in physics that describes the sort of folding shown in your picture. I'm afraid it is an invention of the Science-Fiction community. The best tool we currently have for describing spacetime is general relativity, but GR does not and cannot tell us anything about the global topological properties of spacetime. The sort of wormhole you show ...


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Actually, you can consider a transformation to a tachyonic frame where the relative velocity is greater than c. Then the solution becomes simple, and is no longer meaningless. In the Earth's frame, XYZ was launched before TY. In TY's frame, his spaceship was launched before XYZ. Hence, it is XYZ that needs to catch up to TY! Not the other way round. ...


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All theories are actually models we use trying to describe what we can see and measure. These models are not the Universe itself, we are just trying to find the model that fits best. As physics evolves, we create better models. These usually expand/modify the 'previous one'. In this meaning SR is the foundation of GR, but Newtonian physics is also foundation ...



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