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 any level of physics that is "solved"? [closed]

At each level of physics, between rotating galaxies, orbiting planets, wind and motion of matter, to motion of molecules, atoms, particles, and maybe strings, there's always some degree of uncertainty ...
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(Lorentz-)Transform Length Between Reference Frames

I have two spaceships, $A$ and $B$, flying towards each other at a velocity $v$ (say: $\vec{v_a}=v\hat{x}$, $\vec{v_b}=-v\hat{x}$) with respect to the "lab" reference frame. Spaceship $A$ ...
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Question in prove infinitesimal Lorentz transformation is antisymmetric

I know we need prove this property by: \begin{align*}g_{\rho\sigma} = g_{\mu\nu}\Lambda^\mu_{\ \ \ \rho} \Lambda^\nu_{\ \ \ \sigma} \end{align*} and $$\Lambda^\mu_{\ \ \ \nu}=\delta^\mu_{\ \ \ \nu} + \...
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Speed of atoms being pushed away

It is said that it is impossible to calculate one-way speed of light. I have doubts in my small theory and I would like someone to correct me because I lack in knowledge in physics, and I'm surely ...
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Lorrentz Transformation in Rain Metric Derivation

In order to derive the rain coordinate system for a falling body in a black hole, we use Lorrentz Transformation of time instead of time dilation formula to go from shell time to rain time (Exploring ...
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Twin Paradox revisit

If we rephrase the twin paradox in such a way: George and Helen are twins. Helen is taking a rocket at a speed of 0.6c. When Helen flying passing the earth, they send each other a selfie, who are at ...
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Why isn't an observer on earth considered to be accelerating in the twin paradox?

This question has a duplicate, but answers to that question went miles above my head. Well, that was supposed to happen since I have just previewed special relativity that too on a high school level, ...
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Do these violate Relativity? [closed]

Two questions, classical answers to both defies the speed limit. [From Photoelectric Effect and Bohr's Atomic Model] : What will be the velocity of the electron which is ejected by a Hydrogen atom ...
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If traveling with relativistic speeds can observer find space denser than normal?

I know that outer space contains few particles per cubic meter, but I am curious if travelling that fast for our brave traveller all of these particles will look like a dense pool of molecules. And ...
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Nuclear reaction: loss of mass or conservation of mass?

Certain particles come together to form a nucleus, this causes a certain amount of energy to be released in the form of photons, the mass of the nucleus is less than the sum of the masses of its ...
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Conservation laws for Relativistic rocket [closed]

In my course i am given the following situation: A rocket is initially at rest (with respect to the inertial frame K). Then the engines are fired and the rocket starts moving. Assume that the exhaust ...
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Why can't unidirectional speed of light be measured using a clock external to both receiver and the emitter?

I know that this experiment to measure unidirectional speed of light will fail: attempting to measure it by first synchronizing the clocks of both the emitter of light and the receiver and then moving ...
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How to justify the time taken by a photon to travel from Sun to Earth? [duplicate]

The standard high school textbooks mention that light takes 499 seconds on an average to travel from the Sun to the Earth. Here, I have three questions: In which frame is this duration of 499 seconds ...
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$U(\Lambda)$ that implements Lorentz transformations on the states of Hilbert space is unitary

In Peskin & Schroeder QFT book p.59, they said: The operator $U(\Lambda)$ that implements Lorentz transformations on the states of Hilbert space is unitary, even thought for boosts $\Lambda_{1/2}$...
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What is light cone? Explain to mathematicians who understand the Lorentz group but not light cone

Mathematically the Lorentz group is precisely the $O(1,3)$ is the 4-vector rotation preserving the inner product of 4-vector under this metric $$ \eta_{\mu \nu}=(+1,-1,-1,-1). $$ There are four ...
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Proof that Kronecker's Delta is invariant under Lorentz transformation

There's an exercise in my book that says "Prove that the Kronecker $\delta$ is invariant under Lorentz transformations". The solution says that from the property $$\Lambda^Tg\Lambda=g$$ of ...
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Does this experiment demonstrated that light speed is actually instantaneous instead of moving at 300,000 km/s? [duplicate]

Hi I don't have clothesline in my home as I dried my clothes on steel clothes drying rack. So I wanna ask a question, some people visualized light speed with a taut clothesline with two clothespins on ...
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What is the quantum mechanical explanation of the Mass–energy equivalence?

What is the quantum or particle explanation of the equivalence between mass and energy described by Einstein? What mechanisms ensure this equivalence?
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How to calculate time dilation for particles inside an accretion disc which are superluminal only due to frame dragging?

How to calculate time dilation for particles inside an accretion disc which are superluminal only due to frame dragging? Is their mass also affected by the same effect?
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Question about how to get $V_{\rm min}$ [closed]

I was looking at this extra practice problem for a while now. It is not making sense to me. How lambda is related to $v$ is $$v= f\lambda$$ I got the mass of the hydrogen atom so I’m thinking I’m ...
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Laws of nature and relative motion [closed]

According to the principle of relativity, the laws of nature should be independent of the relative movement of different frames. My doubt is the meaning of "laws of nature". So, suppose a ...
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Basic special relativity question from old textbook [closed]

Can someone assist with the following problem from an old special relativity text that I'm baffled by? (no, this is not homework) It tells me: Two observers in the S frame, A and B are separated by ...
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Why do the cesium atoms in an atomic clock have to be tossed into the air like a fountain?

Even the NIST website for the standard F-1 clock and the new F-2 do not explain, exactly, why it helps (or is necessary) to make the cesium atoms appear, at least temporarily, weightless.... Wouldn't ...
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Measuring the speed of light in one direction? [closed]

I have this thought that probably is dumb. But regarding the problem to measure the speed of light in one direction, we know the refractive index is $c/v$. Now, by measuring the refraction we can ...
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System with $N$ atoms

Suppose a system (eg: rocket) consists of $N$ atoms. It starts moving away from the origin of an inertial frame at speed 0.9c. Will $N$ changes and if it changes where does this change come (if ...
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Welche physikalische Wechselwirkung hat die Zeit in der Natur? Bei Temperaturen unter 0 Grad Celsius wird Wasser zu Eis [closed]

Welche physikalische Wechselwirkung hat die Zeit in der Natur? Bei Temperaturen unter 0 Grad Celsius wird Wasser zu Eis. What physical interaction does time have in nature? At temperatures below 0 ...
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What is the meaning of complex distances in relativity?

In flat Minkowski space with the metric signature (-,+,+,+) the spacetime interval $ds^2$ is defined as $ds^2 = -c^2 dt^2 + x^2 + y^2 + z^2$ This interval (or better the square of the distance) can ...
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Can something be a black hole in one frame of reference but not in another? [duplicate]

So my understanding is because E=mc^2, and kinetic energy is included in E, something moving quickly relative to you gains mass in your reference frame, compared to that same object at rest. Black ...
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Is this the correct equation for the four force on a system in special relativity?

Four velocity is the derivative of spacetime coordinates with respect to proper time, and four acceleration is the derivative of four velocity with respect to proper time. Also the four force is the ...
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Does the 1/2 coefficient in kinetic energy stem from Newton, the De Broglie wavelength and length contraction? [closed]

This is my thinking. Everything has a De Broglie wavelength. From this the energy of an object can be calculated. Now due to Special Relativity anything with a velocity experiences length contraction. ...
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What can I assume about Mandelstam variables in four-photon scattering?

In the case of four-photon scattering, the Mandelstam variables must satisfy $s+t+u=0$ Where: $ s=-(p_1+p_2)^2, t=-(p_1+p_3)^2, u=-(p_1+p_4)^2 $ And we know that $s>0$ is true because it is the ...
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$k$-calculus in $3+1$ dimensions?

So I've recently been intrigued by $k$-calculus. Is there a formulation of $k$-calculus in $3+1$ dimensions? More specifically the relation between the $k$-factor and and a $4$-vector?
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Interaction of particles with a spectrum of waves, relativistic equation of motion

I have to work with a poorly documented code, that simulates the interaction of particles with a spectrum of waves. The previous author has made the equations of motion dimensionless by using the ...
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1answer
51 views

Acceleration and Reference Frames

If I'm in a car and hit the gas, an outside observer on the ground sees my car accelerate to some speed, and given the mass of my car and the horsepower of my engine, this obeys Newton's second law. ...
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Clarification of labeling of Lorentz transformation

I read a labeling of Lorentz matrix labeling $\Lambda^\mu_\nu$. To be more specific, it's used as $x^\mu\rightarrow \Lambda^\mu_\nu x^\nu$. I want to ask: What does the indices $\mu$, $\nu$ mean in $\...
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Covariant Maxwell equations

As we know, the covariant form of Maxwell's equations (there are 2 equations in this formulation) are covariant under Lorentz transformation. Are these equations covariant under general transformation,...
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Is mass relative? [duplicate]

Since time is relative to the observer's velocity, does that mean that velocities are also relative, since the same distance is covered in a different time, depending on your reference frame? If ...
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1answer
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Causality: Invariant Under Lorentz Transformation

I'll begin by stating that I have only studied a very small bit of special relativity: a couple of lectures or so around the end of the Physics course I took, intended just to "give us a taste&...
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Mechanism of Relativistic Momentum

The formula for relativistic momentum is $\vec{p}=\gamma m\vec{v}$. To derive this formula, one analyzes a collision while assuming the principle of relativity and the conservation of momentum ...
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Can I measure my velocity in a spaceship by measuring how much two static charges attract?

We know that parallel current in two parallel wires causes them to attract. The explanation is that moving charges generate attractive magnetic fields. https://youtube.com/watch?v=43AeuDvWc0k If I ...
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Confused about muon evidence of relativity

As I understand it: muons are created $20$km high in the troposphere and since they only have a half life of $\tau = 1.56 \mu s$, they should only be able to travel $660m$ before half are lost, so we ...
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How does the speed of light sameness in all 4 cordinal directions prove that the speed of light is constant?

From my reading of Einstein's experiments on the speed of light it is my understanding measured the speed of light in the 4 cardinal directions - North, East, South, and West - and found the speed the ...
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Apparent paradox in special relativity

I was recently set a simple homework problem. Bob sees Alice come past him in the positive $x$ direction. They have identical spaceships, each with three clocks spaced evenly along the ships. In the ...
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Speed of light in a rotating disc (tangential) [duplicate]

My son came with this "idea" to "exceed the speed of light" (he is still in school): Imagine a disc of radius $R$ that is rotating so fast [with angular speed $\omega$ so large] ...
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Relativistic many-particle dynamics as a field theory subsector

In more than 2 dimensions, the so-called "no-interaction theorem" of Leutwyler (see this article for a proof) states that naive attempts at constructing $n$-particle classical relativistic ...
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Derivation of time dilation formula [duplicate]

When we derive the formula of time dilation using light clocks, we always consider the projected light pulse in direction perpendicular to spaceship. What if we take the direction of light pulse in ...
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1answer
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Thought experiment and $E=mc^2$

Suppose we have an indestructible box that doesn't let through any matter or radiation or whatever. In the box, there is matter which is evenly distributed (state A). The energy content of the box ...
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How to yield the relativistic equations of motion for a particle in a plasma non-dimensionless

The relativistic equations equations of motion for the ions are: $$ \frac{d\vec{p}}{dt} \ = \ q (\vec{E}+ \vec{u} \times \vec{B}), \ \vec{p} \ = \ m \gamma\vec{v} $$ In many papers discussing test ...
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Emergence of spin from special relativity

I have pulled up and read as many answered questions as I can find here on why spin emerges as a consequence of making quantum mechanics compatible with special relativity- and still have problems ...
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Does the Unruh effect need the accelerating observer's Hilbert space to be smaller than the inertial one?

I've encounter two different approaches to the Unruh effect and I feel like they are not consistent with one another. Bogoliubov Transformation In this approach the basic statement is that the vacuum ...

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