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In relativity there is no standard-clock that tells you which time is "right". That's the point about relativity. There is no need for a absolute reference to compare with. Everything is just the way you observe it (that is, relative to you). Things may slightly differ from observer to observer but the qualitative behaviour stays the same just as classical ...


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You evidently understand that any constant can be added to a potential without affecting the physics -- or equivalently, any place can be taken to have zero potential. You also suggest, rightly, that there are really only two "natural" places to define the zero of the potential: either $r=\infty$ or $r=0$. For example, there's no particular reason to ...


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Yes, there's a very famous example: muons produced in the upper atmosphere can be detected on the surface of the Earth. Moving at nearly the speed of light, it takes them over 300 microseconds to get down to the Earth's surface, but the average muon decays after 2.2 microseconds. If it were not for time dilation, only a few in every $10^{60}$ muons (so, ...


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What you're missing is that the speed of light is not constant. There's this modern-day myth that says "Einstein told us that the speed of light is constant". But search the Einstein digital papers on "speed of light" or "velocity of light" for examples like this: The speed of light is spatially variable. And that isn't some discarded idea from 1911, see ...


3

In a rotating reference frame, the coordinate velocity of an object can exceed $c$. However, this doesn't mean that they're moving "faster than light". If we were to look at the light-cones at these distant locations, we would see that the four-velocities of these objects are still confined within the light-cones at those locations. To put this another ...


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How does the kinetic energy of a ballerina increase? Conservation of angular momentum: $$L_1=L_2 \implies I_1\omega_1=I_2\omega_2\quad\quad (1)$$ Pulling in your arms reduces moment of inertia $I$, since the same mass is now distributed over a volume closer to the spin centre, $I=\sum mr^2$. As you say, reducing $I$, so $I_2<I_1$, implies ...


3

From a Newtonian perspective, the difference between being accelerated by gravity in freefall (which includes orbits) and being accelerated in a car has to do with the fact that you only "feel" accelerations when the external force is only being applied to one part of your body, rather than accelerating every particle equally as with gravity. For example, if ...


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First off, traveling at constant velocity in flat spacetime is not the same as traveling g in a uniform circular motion. Quite the contrary, free falling towards the gravitational source is actually equivalent to moving with constant velocity in flat spacetime. This is so because the objects are following a geodesic path defined by the geodesic equation. I ...


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This shows the situation as viewed by the Schwarzschild observer i.e. an observer far from the black hole: (Note that the angle $\theta$ is not connected to the Schwarzschild $\theta$ coordinate.) The angle $\theta$ is (obviously) given by: $$ \tan\theta = \frac{b}{a} = \frac{b}{r_2 - r_1} $$ But we've calculated the angle using the Schwarzschild $r$ ...


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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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For a classical point charge, the field is divergent at $r=0$, and if you were to take the potential to be zero there, it would be infinite everywhere else. Meanwhile, you can approximate $r=\infty$ as the region with no interaction, so it's reasonably naturally to treat it in the way you would treat ground.


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Just to complement John Rennie's answer, one can always perform a Lorentz transformation to a coordinate system such as the particle is at rest for a given time. It's called instantaneous rest frame (IRF). This frame changes point to point, unless the particle's velocity is constant. In such a frame, we have $ ds^2 = -c^2d\tau^2, $ where $\tau$ is the ...


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This is accurate, and it ultimately comes down to the fact that we can get arbitrarily close to an electric point charge in classical E&M. That means that the field right up next to the point charge could be arbitrarily large. So you get these huge, singular potentials close to point charges, which is really more-or-less fine. For instance, that huge ...


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There is no reference object that transcends all inertial frames of reference. Everything in this universe has an inertial frame of reference, and none of them are privileged. If there were any object that existed independently of the relativistic effects of acceleration/gravity or of observer movement, then theoretically it could provide a reference to ...


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reading special relativity [...] I pictured a frame of reference being grid Of course there is no definitive requirement for the grid constituents to be rigid with respect to each other, or being in any particular way "regularly spaced" or "regularly moving". Required is (only) for the grid constituents to be distinctive, for any two grid ...


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There are different kinds of frames. A common frame to use is a coordinate frame. For that all you need to imagine is each region of spacetime has a coordinate system that you can use in that region to find and label all the events in that region. An advantage to this is that you can practice using arbitrary coordinate systems even while still doing ...



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