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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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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Would the universe shrink to a point in light's frame? [closed]

Hypothetical: If "light-based life" somehow existed and the universe was in fact finite (choose your topology), would the universe appear 2-dimensional? Would length contract to a point in ...
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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?

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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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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Are brains quantum or relativistic? [closed]

Are brains quantum or relativistic? They involve high speeds for the electricity.
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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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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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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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This is a doubt regarding special theory of relativity [closed]

If a beam of light is seen from a moving spaceship in same direction as spaceship, we will observe that speed of light hasnt changed as our time has slowed down but what would happen if we see a light ...
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How much time passes for a pilot traveling at the speed of light? [closed]

PS.: I guess I have to mention that this is an entirely theoretical question, otherwise it may get downvoted, with (This is not possible, hahaha) Let's say we have a ship capable of light speed, and ...
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What is the relationship between the Galilean group and the Poincaré group?

What is the relationship between the Galilean group and the Poincaré group? Are they siblings within the Lie group? Or does the Poincaré group contain the Galilean group as a subgroup? I'm not so much ...
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Hypersurface vs Hyperplane

What is the difference between a hypersurface and a hyperplane (in the context of special relativity)? Is it right to think that a hyperplane is also a hypersurface but not vice versa?
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Hypothesis in particle-dimension sub-spaces [closed]

9-9-2021 Am puzzling over this hypothesis. Please comment. We hypothesize a particle in multiple dimensional space-time in which multiple vierbein Minkowski sub-spaces exist. Thus, if, for example, ...
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Why do electrons in a current spread apart, from their point of view?

There are many videos explaining how special relativity causes magnetism, with the most relevant part being that from the reference frame of the electrons, the positively charged ions in the wire have ...
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Here we have 3 events and 3 inertial frame moving with different velocities. I have to prove some time based inequalities [closed]

This is my homework question for relativity. I am not sure where to start. I mean we dont know what are the velocities of R, S, and Q or the difference between their velocities (stating which is more ...
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Macroscopic particle thought experiment

I have been daydreaming about the following question and would enjoy any knowledgeable comments. A sphere consisting of 1 µg of iron slams into a concrete wall 10 meters from me traveling at c/2. ...
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Question about superluminal group velocity from Schrödinger equation

According to the Schrödinger equation (SE) for a free particle, we have solutions of the form $Ae^{ikx} + Be^{-ikx}$. The wavenumber $k \in (-\infty, \infty)$. It is standard to point out that these ...
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Why is there a loss of energy when charge is redistributed among two objects?

I am a high schooler so forgive me if I got anything wrong. I had a question today stating that when charges are re-distributed among any two objects, there would be some loss of energy. The question ...
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What does this spacetime diagram mean?

I'm reading a book called "Reality is not what it seems: the journey to quantum gravity" by Carlo Rovelli and I'm struggling to understand this diagram that is part of the chapter about ...
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Covariant form of the electric field

I'm a bit confused about some expressions about the relativity of the electric field. The usual treatment ($c=1$) defines the four potential $A_\mu$ and $F = dA$ is the anti-symmetric 2-tensor. Then $...
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If length in a frame moving with respect to a stationary frame contracts, how do we define the speed of the moving frame?

Under Galilean transformations, the speed of a moving system $k$ with respect to a stationary system $K$ is straightforward. Assuming the origins of $k$ and $K$ coincide at t=0, the spatial ...
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Spinning a rod in relativistic speed

This is a random question that just comes into my mind. Say you have a rod with a length of 6 x $10^8$ m and I spin it at its mid point at 1 rad/s. By classical mechanics the end of the rod would have ...
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Whats happening with the timelike component in non-relativistic approx.?

If we look at the non-relativistic approximation of an equation in Minkowski space, what happens to the timelike component in general? Like, my question is not the call for a specific Problem, but ...
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What does the $O$ mean in "$O(v^4)$"?

I am currently studying General Relativity and I am using the book by Schutz. I encountered a problem when I was reading about the gravitational redshift experiment. Here is the website (it is not the ...
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Some help in understanding energy conservation relating to special relativity

Consider the decay of particle $A$ into particles $B$ and $T$ where $T$ is the tachyon particle. The conservation of energy equation can thus be expressed as $$m_A=\sqrt{p^2+m^2_B}-\sqrt{p^2-m^2_T}\,.$...
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Confusion about twin paradox

Suppose that a man departs from Earth to reach a planet that is ninety-nine light-years away with 0.9802 light speed, c. According to special relativity, it takes him 40 years (measured by his own ...
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Why does the derivation for the Michelson & Morley time difference assume Earth moves in only one direction relative to the Aether?

In the Michelson and Morley experiment, we predict with Galilean relativity and the assumption of the existence of a luminiferous aether that there should be a time difference between the two beams of ...
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Does a relativistic rocket's combustion slow with time dilation?

If a relativistic rocket travels slower in time, does that mean the actual combustion in the thrusters happens slower and slower from an outside frame of reference? Is this part of what causes a ...
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Would this equation for electromagnetic four force be valid when the energy of electromagnetic radiation is negligible?

The first piece of information I used in my derivation is that, with respect to electric charge, anti-matter is mathematically equivalent to ordinary matter traveling backwards in time, which means ...
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Speed of photons in Cosmic Microwave Background Radiation relative to the earth (or solar system)

At https://living-universe.com/questions-and-answers/absolute-motion-of-photons-in-the-2-7cbr/, we are told that the Cosmic Microwave Background Radiation (CMBR) is propagating relative to the earth (...
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Special relativity - Center of mass frames vs Laboratory frames

In the reaction where particle A hits particle B, which is at rest. This produces particles C and D. For the minimum energy of particle A for the reaction to take place I have two calculations. I don'...
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Need serious help with deriving the Lorentz Transformation from Time Dilation and Length Contraction

Seriously struggling right now, and I could really use some help. I am trying to follow this derivation of Lorentz Transformations from time dilation and length contraction below: Time dilation and ...

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