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The challenge is how to explain the wonder of people ageing at different rates, with is not intuitive. And it is not intuitive because that kind of effect is completely negligible in the everyday life …

Let's examine a similar situation, where the test charge moves initially with the same velocity of the electrons. According to Lorentz force: $\vec F = q\vec v \times \vec B$ If the wire is in the $z$ …

The inertial frame here is the mass in a (hypothetical) free fall. From this frame of reference, there is an upward vertical acceleration due to gravity, and a centripetal acceleration due to the Eart …

For any two space-like non simultaneous events in a frame S, it is possible to find a frame S' such that they are simultaneous for S'. For example: now on Earth and 1 min from now on Mars. For a ship …

The situation becomes clear if we note how the clocks would be compared. One way is to have one clock per wagon in the train, all of them synchronized in the train's frame. The bystander would always …

What is the distance separating Alice and Bob at the U-turn? Instead of call Bob's frame as "immobile", it is more precise to take its frame as the reference for coordinate time. That means: there a …

The physical properties like frequencies of atoms are of course valid in the proper time of the object. One well known effect is the detection of muons. They are formed about twelve thousand meters in …

Before SR, I think that the word "dimension" was reserved for spatial dimensions. An event now in my place and another somewhere in Mars, $2$ minutes from now, has the same distance separation than if …

When using Lorenz transformations with $x\neq 0$ it is more difficult to interpret the results. It is true that $$t'=\gamma\left(t - \frac{vx}{c^2}\right) \implies \Delta t' = \frac{\gamma x}{c}$$ whe …

Yes. We can think for example that Alice and Bob are both in a airplane. In the moment that Bob jumps, Alice has a coordinate acceleration $g$ upward for him. Bob has a coordinate acceleration $g$ dow …

If so then the star should have moved close to me at faster than c. Note that if you invert the situation, and the star were accelerating to an inertial ship, it would not be coming faster than c. S …

Suppose that there are several synchronized clocks in the Earth's frame along the ship's path. Each time that the ship passes by one of that clocks, the difference with respect to the clock inside the …

We can think of 2 events in space-time. A pulse being emitted by the source and the spot receiving the pulse. Let's take the angle $\theta = 90^{\circ}$ to simplify the analysis, and the z axis being …

For a spacetime $1+1$: $$\frac{\partial g}{\partial x^{0}} = \frac{\partial g}{\partial y^0}\frac{\partial y^0}{\partial x^{0}} + \frac{\partial g}{\partial y^1}\frac{\partial y^1}{\partial x^{0}}$$ $ …

What happens is that the rules for finding relative velocities that we use are approximations. Very good approximations for ordinary speeds, that are much smaller than light speed. The formula is: $$\ …