# Questions tagged [special-relativity]

The special theory of relativity describes the motion and dynamics of objects moving at significant fractions of the speed of light.

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### Is there a situation in which two photons/particles violate Lorentz transformation?

It does not necessarily have to be a pair production or anything with a name. Consider two photons moving away from or moving towards each other in the void. If imagining photons in relativity is ...
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### A puzzle about relativistic spin

I'm suffering from a confusion about relativistic spin. I don't believe my question has been asked before, and I'm sure I've made some silly mistake somewhere, but I can't spot it. So I'm appealing to ...
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### Time dilation in Einstein's train example (lightning strike)

In Einstein's famous thought example involving a fast-moving train (say with a velocity of $c/2$), we assume that lightning strikes occur simultaneously at the front and rear end of the train as ...
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### Apparent violation of Newton's Third Law in relativistic force transformation

In special relativity, we know that, relativistic force is defined as F = dp/dt, where p = γmv. For forces perpendicular to the direction of relative motion, force transforms as F' = γF. Consider two ...
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### Split Pauli Four-vector as quadratic terms of spinors

If I have the Pauli Four-vector $$x_{\mu}\sigma^{\mu} = \left(\begin{array}{cc} t+z & x-i y \\ x+i y & t-z \end{array}\right)$$ with $\sigma^0$ as Identity Matrix. Is there some way to write ...
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### Length Contraction: is $t'$ or $t = 0$?

To demonstrate my confusion - let's say there is a rod traveling with velocity +v relative to S, and in S, the length of the rod is measured to be $L$. If I want to go from S to S', the frame where a ...
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### Where does the angular momentum of relativistic objects go? [closed]

Suppose you are floating in outer space and there is a massive sphere of mass $1 \text{kg}$ next to you and radius $1$ meter and an angular velocity of $1$ revolutions a second. Using the formula for ...
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### Physical meaning of $vx/c^2$ in Lorentz transformation

In Lorentz transformation, this is the formula of time dilation $$t' = \gamma \left( t - \frac{vx}{c^2} \right)$$ It can be derivated from the formula of length contraction and be proved ...
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### Who will die first between two people on different spaceships, where both are in inertial frames? [duplicate]

Here's something that's really been confusing me. If two people on separate spaceships pass each other by, where both are in inertial frames, person A (on spaceship 1) could say that he is at rest and ...
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### Causality for gauge dependent operators in quantum field theories

Suppose that $\mathcal{A}_{ij...}(x)$ and $\mathcal{B}_{ij...}( x')$ are two gauge dependent (so non-observable) operator in some theory. If they are spacelike, should I impose the causality ...
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### What are the characteristics of a non-relativistic collision?

I have a physics test tomorrow on special relativity and one of the questions on the previous test was as follows: "A particle of mass m hits another particle of the same mass that was originally ...
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### Is the Dirac adjoint in the representation dual to Dirac spinor?

As seen in this Wikipedia page, the Lorentz group is not compact and the Dirac spinor (spin $\frac{1}{2}$) representation is NOT unitary. Therefore, the complex conjugate representation does NOT ...
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### Can you ever obtain a pure rotation from composing Lorentz transformations?

An exercise asks one to show that given $v, u$ speeds much smaller than $c$ and oriented orthagonally, the composition of the lorentz boosts $B(\mathbf{v})B(\mathbf{u})B(\mathbf{-v})B(\mathbf{-u})$ is ...
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### Black hole production via light speed [duplicate]

As a test particle with rest mass approaches $c$ relativistic mass increases to infinity, does this mean that the energy required to continue the acceleration will create a black hole (as time also ...
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### Relative speed in unpolarized cross-section

In section 5.1 of Peskin and Schroeder, we are presented the computation of the amplitude for the $e^+e^-\to \mu^+\mu^-$ reaction and then the computation of the unpolarized cross section. After ...
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### Kinematics of a two-body decay [closed]

I suspect a flaw in the reasoning below, but am unable to pinpoint it: Is there something inconsistent in terms of the application of conservation of momentum and energy? Thanks for any hints in ...
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### How does special relativity lead to anti-particles?

Anti-particles and spinors pop out of the Dirac equation very naturally, yet the Dirac equation is only a modified version of the Schrödinger equation which includes the relativistic energy-momentum ...
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### Why does the mass-energy equivalence apply to binding energy when it is derived purely through kinematic means?

I understand that by defining the four velocity, multiplying it by the rest mass and taking the entire thing's norm we get $E^2=m^2+p^2$, but how does this apply to binding energy, or in general ...
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### Magnetic field in different frames

If I move at the same velocity as that of a charge Q, I wouldn't be able to feel its magnetic field because it is stationary with respect to me. However, if I am to place a magnetic compass needle ...
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In Srednicki's book, we have \begin{align*} g_{\mu\nu}\Lambda^\mu{}_\rho\Lambda^\nu{}_\sigma=g_{\rho\sigma} \end{align*} and let $\Lambda \to \Lambda^{-1}$, use the relationship $(\Lambda^{-1})^\... • 37 0 votes 0 answers 30 views ### How is potential energy incorporated into mass in special relativity? [duplicate] I've seen it said before that we often ignore potential energy in relativity because it can be included in the mass term. It is commonly said that a hydrogen atom has less mass than the sum of its ... -4 votes 1 answer 99 views ### In SR, why do we claim length contraction rather than faster than$c\$ travel in the rocket frame? [closed]

In special relativity, a rocket traveling at .5c will take .86 years (in the astronauts frame) to travel 1 light year (in a stationary observer frame). There are two possible ways to look at this ...
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