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the last equation implies that the magnetic field in question is the one generated by the moving charge That is incorrect. The charge is at rest for $O'$ and it doesn't generate any magnetic field. …

Note in the last equation, first line, the first and second terms: $$ e^{-ik(c\Delta t - \Delta x)} $$ and $$ e^{ik(c\Delta t - \Delta x)} $$ Are very similar, you obtain the first one by doing the su …

We are not applying it twice, what happens is that this is how rank 2 tensors transform. A rank n tensor will transform like $$ F^{'}_{a_1,a_2,\dots,a_n} = \Lambda_{a_1}^{b_1} \Lambda_{a_2}^{b_2} \dot …

I think the problem is in the sentence "The same applied force". In your expressions, you have $$ \left |{dp^\mu\over d\tau}\right|^2_{Lin} = \gamma^6 a^2_{lin} $$ For linear case and $$ \left |{dp^\ …

Let's try to calculate it. I'll consider a double slit experiment where the slits are a distance $d$ apart from each other in the $y$ axis, the wave moves in the $x$ direction with frequency $f$ and t …

Your question might be connected with the Wheeler Delayed choice Experiment, where the possible paths seems to change during the photon's flight. Please also check the Elitzur-Vaidman-bomb tester, whe …

The phenomenon of reflection is closely related to the phenomenon of absorption, since the reflected intensity depends on the imaginary part of the complex index of refraction, as Feynman explains in …

If I got it, the difference is only in the element $(3,3)$ of the product matrix. By the expressions that you provided $$ (\mathbf L'\mathbf L)_{3,3} = \mathbf L'_{3,3}\mathbf L_{3,3} = 1+(\gamma'-1){ …

The return trip does not cancels any effect of the trip. Even if it could be arguable for light traveling a path exactly parallel to the aether wind, it is not true for the arm perpendicular to the wi …

I would answer that there is no such a thing as "general definition". The problem is that symmetries in quantum mechanics have more than one inspiration and more than one purpose. For example, rotatio …

For simplicity, let's consider a plane monochromatic wave propagating in $\hat z$ direction. If we parametrize the Stokes parameters in terms of the propagating electric field (see Born and Wolf, Prin …

When I was studying special relativity, I've learned that the relativistic action for a free particle is defined as $$ S = \lambda \int_{\tau_0}^{\tau_1} d\tau $$ Where $\lambda$ is a constant that is …