For questions relating to Einsteins special relativity theory, the equivalence of physical laws in different inertial frames.
Questions tagged [special-relativity]
131 questions
4
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0 answers
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
- 41
1
vote
0 answers
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…
user273366
- 107
1
vote
1 answer
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…
1
vote
1 answer
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 $S$…
user572780
- 338
1
vote
1 answer
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
- 536
1
vote
1 answer
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:
$$
x \oplus_cy=\frac{\overbrace{(1+2c\langle x,y\rangle+c||y||_2^2)}^{A(c)}x +…
ndrizza
- 1,348
0
votes
1 answer
SRT - Distance to the moon for a rocket
I shall use units where time and distance are in seconds and speed is dimensionless between zero and one. Suppose a rocket $B$ passes by the earth $A$ on its way to the moon at speed $v$. At that event $(1)$ both clocks are synchronized to zero.…
alexanderyaacov
- 175
0
votes
1 answer
What is the hyperbolic angle as a function of $f(t)$ and, in general, two points?
What is the hyperbolic angle as a function of $f(t)$ and, in general, two points $(f(t),t)$ and $(f(t+a)$,$t+a)$?
Is the following a valid way to define hyperbolic angle using $f(t)$ and $t$?
Assumptions:
$t>f(t)$,
$\cosh \phi =…
ajay
- 1
0
votes
0 answers
Intuitive way of seeing velocities in Zero Momentum Frames
I have two particles, one of them is stationary, another one was speed $u$ in the lab's frame. I cna prove with Lorentz transformations that the speed of the zero momentum frame is
$$v=\frac{\gamma_u}{1+\gamma_u}u$$
I can also prove that if I have a…
zabop
- 1,011
0
votes
1 answer
Special relativity confusion
Alex is on Earth and the planet Flez is 5 light years away. Glen, is on a spaceship approaching Earth at $0.8$c along a direct path towards Flez. Unfortunately Flez explodes. According to Alex, this occurred two years after Glen passed Earth. Call…
Robben
- 223
0
votes
1 answer
Relativistic Limit
Excuse me.
I have a problem about double limit, namely, Relativistic Limit.
Let $c$ is positive real constant. Calculate
\begin{equation}
\lim_{v\to c}\lim_{V\to c}\frac{v - V}{1 - vV/c^2}.
\end{equation}
I have tried in many times, but I…
R. Tao R. H.
- 29
0
votes
0 answers
Valid Interpretation of Special Relativity in terms of Length Contraction of Relative Distances
Suppose I have three points $O_1, O_2, O_3$ floating in a universe that obeys galilean relativity
$O_2$ is located 10 metres east of $O_1$ (just pick a direction vector of your choice and call it east)
$O_3$ is located 20 metres east of $O_1$.
It…
Sidharth Ghoshal
- 16,771
0
votes
0 answers
Special Relativity: A showing question $c^2-v^2$ using Velocity transformations
I have been trying to do this question for ages now:
A particle has a velocity v ={$v_x,v_y,v_z$} in S and a velocity $\bf v'$={$ v'_x, v'_y,v'_z$} in S'. Prove from velocity transformations that
$c^2-v^2…
TICH
- 1
- 1
0
votes
0 answers
The reason of script expression of $\lambda^\mu_{\;\;\nu}$
I wonder why first making person who express
$$\lambda^\mu_{\;\; \nu}$$ made like that?
although $$\lambda^{\mu\nu},\lambda_{\mu\nu}, \lambda^{\;\;\mu}_\nu$$
are also possible!!
please teach me obvious reason!!
정재훈
- 27