Questions tagged [special-relativity]

For questions relating to Einsteins special relativity theory, the equivalence of physical laws in different inertial frames.

131 questions
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Rocket to a ray of light

$A$ and $B$ are two stationary points on a line $30,000,000$ km apart. A light flashes at $B$, and at that precise moment a rocket takes off at $A$ at $180,000$ km/second. The rocket is considered stationary relative to itself, and thus Point $B$ is…
Leibel
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an apparent "inconsistency" in lorentz transformations?

why the Lorentz transformations forbid passing to a reference system with the speed equal to that of light despite there are particles (photons) traveling at this speed? in other words I see the fact that the Lorentz transformations forbid placing…
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Einstein says that this equation is true, but WolframAlpha says it's not always true. Who is right?

Einstein says $$\cos\mathrm{i}x=\frac1{\sqrt{1-\left(\mathrm{i}\tan\mathrm{i}x\right)^2}},$$ but WolframAlpha says that this isn't true for $x=\pm2$ and $x=\pm9/5$. What's happening? From page 34 of The Meaning of…
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Deriving the relativistic rocket equations.

I am trying to derive the relativistic rocket equations found here [(4),(5),(6),(7),(8)] but I do not understand proper time, proper velocity and proper acceleration. Define a point $P$ with spacetime coordinates $(t,x,y,z)$ in reference frame $S$…
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Show that a reference frame exists where the spatial separation is zero.

question I am trying to show that if the Lorentz Invariant Interval is positive $$c^2 \Delta t^2 - \Delta x^2>0$$ then there exists a reference frame $S^{'}$ where $\Delta x^{'}=0$. context consider a pair of reference frames $S$ and…
Conor
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Derivative of (Norm of) Möbius Addition w.r.t. Curvature

Does anyone know a resource showing the formula for the derivative of the (norm) of the Möbius addition? This is the Möbius addition: $$ x \oplus_cy=\frac{\overbrace{(1+2c\langle x,y\rangle+c||y||_2^2)}^{A(c)}x +…
ndrizza
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SRT - Distance to the moon for a rocket

I shall use units where time and distance are in seconds and speed is dimensionless between zero and one. Suppose a rocket $B$ passes by the earth $A$ on its way to the moon at speed $v$. At that event $(1)$ both clocks are synchronized to zero.…
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What is the hyperbolic angle as a function of $f(t)$ and, in general, two points?

What is the hyperbolic angle as a function of $f(t)$ and, in general, two points $(f(t),t)$ and $(f(t+a)$,$t+a)$? Is the following a valid way to define hyperbolic angle using $f(t)$ and $t$? Assumptions: $t>f(t)$, $\cosh \phi =…
ajay
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Intuitive way of seeing velocities in Zero Momentum Frames

I have two particles, one of them is stationary, another one was speed $u$ in the lab's frame. I cna prove with Lorentz transformations that the speed of the zero momentum frame is $$v=\frac{\gamma_u}{1+\gamma_u}u$$ I can also prove that if I have a…
zabop
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Special relativity confusion

Alex is on Earth and the planet Flez is 5 light years away. Glen, is on a spaceship approaching Earth at $0.8$c along a direct path towards Flez. Unfortunately Flez explodes. According to Alex, this occurred two years after Glen passed Earth. Call…
Robben
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Relativistic Limit

Excuse me. I have a problem about double limit, namely, Relativistic Limit. Let $c$ is positive real constant. Calculate \begin{equation} \lim_{v\to c}\lim_{V\to c}\frac{v - V}{1 - vV/c^2}. \end{equation} I have tried in many times, but I…
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Valid Interpretation of Special Relativity in terms of Length Contraction of Relative Distances

Suppose I have three points $O_1, O_2, O_3$ floating in a universe that obeys galilean relativity $O_2$ is located 10 metres east of $O_1$ (just pick a direction vector of your choice and call it east) $O_3$ is located 20 metres east of $O_1$. It…
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Special Relativity: A showing question $c^2-v^2$ using Velocity transformations

I have been trying to do this question for ages now: A particle has a velocity v ={$v_x,v_y,v_z$} in S and a velocity $\bf v'$={$ v'_x, v'_y,v'_z$} in S'. Prove from velocity transformations that $c^2-v^2…
TICH
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The reason of script expression of $\lambda^\mu_{\;\;\nu}$

I wonder why first making person who express $$\lambda^\mu_{\;\; \nu}$$ made like that? although $$\lambda^{\mu\nu},\lambda_{\mu\nu}, \lambda^{\;\;\mu}_\nu$$ are also possible!! please teach me obvious reason!!