Linked Questions
11 questions linked to/from Transformation of $4-$velocity
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How to prove a 4D vector is a 4-Vector?
This is a fairly open ended question.
Given a set of 4 Components, that is, a 4D Vector, what is the process for determining rather or not it is a "4-Vector" as defined in special relativity? I want ...
6
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3
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Why don't stationary charge feel force from a current carrying wire?
The current carrying wire doesn't apply any magnetic force on nearby charge $q$( positive stationary charge) because it has 0 velocity in lab frame. We found that there is no force on q by wire. But ...
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4
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Why is $dt/d\tau=\gamma$? What is $dt/d\tau$ supposed to mean exactly?
I'm a math student trying to learn some physics by reading Susskind's The Theoretical Minimum. In the volume on special relativity he derives that $\frac{dt}{d\tau}=\gamma=1/\sqrt{1-v^2}$ and uses it ...
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Why does the wave 4-vector of a photon satisfy the Lorentz transformation equations in Special Relativity?
Using robphy's answer to my initial question, I try to implement what I understand to be his suggested approach, and I get it to almost work, but I get a small error at the end that I hope someone can ...
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Two-Dimensional Lorentz Velocity Transformation Problem
Two spaceships A and B are approaching along perpendicular directions, as seen from earth.
If A is observed by a stationary Earth observer to have velocity $𝑢_𝑦$ = -0.90c and B to have
velocity ...
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4
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565
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Why does four-momentum have the same transformation matrix as spacetime coordinates?
I will outline my question in 1+1D for brevity. We can passively transform our coordinate system using a Lorentz boost; $\Lambda^{\bar{\nu}}_{\mu}x^{\mu}=x^{\bar{\nu}}$. I've seen that, by stipulating ...
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Which of these is the beta factor in special relativity? [closed]
Obviously, $\beta=v/c$. But in this case, I'm not too sure what $v$ represents. I've mostly done 1-D special relativity and therefore it is pretty clear in those cases. However say there are two ...
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Does Einstein velocity addition rule work only for speeds, or for velocity vectors as well?
Einstein's Velocity addition rule (https://en.wikipedia.org/wiki/Velocity-addition_formula#Special_relativity) was used to describe to replace galileo's in account for relativity.
However, in many ...
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1
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2
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On the proof that $4$-velocity transforms like vector
Let $U$ and $U'$ be the $4$-velocities associated to the coordinates $(t,x)$ and $(t',x')$ related through the Poincaré transformation $P:\mathbb R^4\to\mathbb R^4$, i.e. $(t',x')=P(t,x)$.$^1$
Of ...
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Transformation of derivatives of coordinates
I am quite new to this topic. Please bear with me.
Suppose we are given a transformation of both time and space coordinate's derivatives as
$$
\partial_t\to D_t=\partial_t-f(t,x)\partial_t\\
\nabla\to ...
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Transformation law for 3-velocity
I am kind of stuck with a problem mentioned in my current reading about special relativity. Given the Lorentz transformation
$$x^{\bar{i}} = L^i{}_k \, x^k \quad ,$$
one has to find the transformation ...
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