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It is an artificial distinction to say one is more fundamental than the other. The geometry of flat spacetime is given by the Minkowski metric: $$ ds^2 = -c^2dt^2 + dx^2 + dy^2 + dz^2 $$ and this is fundamental in the sense that all of special relativity is described by this equation. But it is also fundamental that the parameter $c$ in the equation (which ...


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Which is more fundamental is probably a meaningless question, but you can think of the geometric notion of a manifold (the mathematical abstraction of spacetime) as being more general than Lorentzian manifolds, i.e. ones whose metric is locally like that given in John Rennie's Answer. So one could in principle conceive of universes that were described by ...


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The basic point is that you can't shine light away from the centre of a black hole once you are inside the event horizon. Far away from the black hole, light cones are oriented so that propogating light from an event can travel anywhere inside a cone bounded by two lines at 45 degrees in a standard (Schwarzschild coordinates) space-time diagram. Nearing ...


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Light moves at about a foot per nanosecond, or a meter every three nanoseconds. In order to capture it propagating across a room over a few frames, you would need to gather something like a billion frames per second. No consumer camera -- indeed no camera on Earth -- is capable of this. Now there have been people playing with "fempto-photography," but they ...


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You are basically correct. In the presence of any charged particles a light wave interacts with the particles to form an entangled system. Once this has happened we no longer have a photon and (for example) an electron, but instead we have a single system described by a single wavefunction that includes both particles. For weak interaction the system is ...


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The cameras are at the same place, because we ignore the small distance between the cameras, right? When the cameras are at the same place, then the same information arrives at the same time at both cameras. The person in the train picture will look the same age as the person in the ground picture.


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This question is a little naive but interesting. A common mistake is to confound speed of information and effective bandwidth. ie : my network documentation tells me that a flow of ( unzipped ) information travels at "speed of light" * k , with k between 0.3 and 0.6. After a new software release, using high compression , I see that I can send my ...


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The Lorentz transformations are used to transform between different inertial frames. For example if you and I are in relative motion then the Lorentz transformations convert the positions of spacetime points in my rest frame to the positions of spacetime points in your rest frame. However anything travelling at the speed of light has no rest frame, so the ...


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The observer sees you travel from A to B - a distance that, in his frame of reference, is greater than one light year. He sees that you take more than a year. He concludes you are traveling at less than the speed of light. You, traveling so fast, "see" a much shorter distance (this is the concept of length contraction) $L' = L_0/\gamma$ where $\gamma = ...


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Your "live stream" would be affected by the Doppler effect. Since the speed you mentioned is far from relativistic you don't have to consider the relativistic Doppler effect. If $t_0$ is the time when the camera was launched, $t$ is the time at which you watch a certain frame, $t_f$ is the time the events on that frame took place, $v$ is the speed of the ...


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You're right that there would be a disagreement over who signed the treaty first, but it would not be between the diplomats on the train; it would be between the people on the train and the people not on the train. The setup initially is that the two diplomats are sitting in the dining car with the curtains drawn, for security. Let's say the light that the ...


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The speed of light in a vacuum, or c, is 299,792,458 meters per second. Any other medium will slow light down. For example light takes about 40% more time to go through glass than vacuum. But media that would increase the velocity of light would violate fundamental laws of physics and can therefore not exist.


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First, we will look at the energy of a free relativistic particle of (rest) mass $m$ moving with velocity $v$: $$E = \frac{mc^2}{\sqrt{1-\frac{v^2}{c^2}}}$$ where $E=mc^2$ when $v=0$. We now consider a few cases: $m\ne0$: In this case, $E\rightarrow\infty$ as $v\rightarrow c$. Therefore, a massive particle that at any point of time is moving at less than ...


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Every particle needs to have energy to be a particle (if it had none it wouldn't even exist). Since energy is equivalent to mass and therefore gravitates I would say YES, all particles that have a speed less than the speed of light must also have mass. Because the speed of the particle is less than the speed of light an observer could travel with the same ...



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