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The electron doesn't absorb the photons, it scatters them. The energy absorbed by an interaction depends on the scattering angle - this can be determined using the Compton formula for the wavelength of the scattered photon. And the electron tends to scatter more at different angles (proportional to the Thomson differential cross section). From this I found ...

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You can obtain the trajectory starting from the conserved quantities, which are the total energy and the angular momentum. By parametrizing the motion using polar coordinates in the plane of the orbit (the orbit is in a plane owing to conservation of angular momentum) you get E=\frac{1}{2} m \dot{r}^2 + \frac{1}{2} m r^2 \dot{\theta}^2 ...

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It's the same question but now we've specialized on length contraction. Right on. Why we can say what we're saying You can work this out from Lorentz transforms if you want, but Lorentz invariants let you simply write it down: a particle has an invariant 4-velocity $\gamma~[c, \vec v]$ and we can form the inner product of this with the local 4-positions ...

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Let object A move at relativistic velocity relative to a frame O. Any effect exists even at smaller nonzero velocities, it's just that the effects are smaller. People have even measured relativistic effects at everyday velocities by using very precise measurements. In 4D space-time (Minkowski diagram) the space view of O at any given moment of its ...

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Your interpretation is formally correct. At least in the special relativity realm. You can prove this by noting that transformations between systems in relative speed to each other are actual rotations in a space with an extra dimension. Think like this: if the world is bidimensional, and you have a circle, and let's assume that it lasts for certain time ...

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The "different hypersurfaces" effect should be enough to describe the relativity of simultaneity; you will probably not have completely described length contraction or time dilation with your explanation. As long as you're not trying to completely describe everything but just to describe part of them, then no, there are no formal objections to the ...

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You have surely seen slit experiments, where waves which pass through the slit and scatter to produce a pattern on a screen placed behind the slits. In the far-field approximation (also known as Fraunhofer diffraction) this pattern is precisely the Fourier transform of the slits. Perhaps you even remember that waves passing by lines produce the same pattern ...

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Once one specifies a quantum field theory, typically in the form of a Lagrangian density, one can calculate the probabilities of various outcomes in collisions. A quantum field theory is a theory based on fields that obeys quantum mechanics and special relativity. The so-called Standard Model is perhaps the most famous quantum field theory, and certainly ...

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This is actually an open question. So far what we are able to state from theoretical considerations are restrictions in terms of the conservation laws that we have observed. These tells you for example that the whole momentum in a reaction is conserved, an the mass-energy, or some quantum numbers. And this already constraints much of what can come out from ...

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