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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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How to Construct Proper Spherical Coordinates in Minkowski Spacetime?

In $n$ dimensional Euclidean space, we only need one radial coordinate, and $n-1$ angular coordinates, where one ranges from $[0, 2π)$ and the rest range from $[0, π]$ Spherical Minkowski coordinates ...
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Length Contraction of a rotating object

When observing an object, such as a spinning ring, what velocity is used to calculate its length contraction? I know it depends on the observer, but let's say theoretically an observer is just ...
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What happens to the energy of an absorbed photon?

Photons are electromagnetic wave fields that travel at the speed of light. When they are absorbed by an object, their momentum and energy is transferred to the absorbing object. What is that ...
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How does the momentum conservation law hold for gravitational interactions in special relativity with Newton's third law being invalid?

Griffiths' argument that Newton's third law is invalid in special relativity The selected answer to the post above talked about momentum conservation in electrodynamics – Newton's third law ...
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3 variations of the Twin Paradox [duplicate]

Here I state and try to answer three variations of the twin paradox 1) "Classical" problem, no acceleration, no turn around Consider the case where there's a stationary planet, and a moving ...
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Is the Lorentz transform of a bound current - a bound current?

The bound (magnetization) current is $\mathbf{J}_\mathrm{M} = \nabla \times \mathbf{M}$. The charge density of a moving magnet that is electrically neutral in its own rest frame satisfies the ...
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Have there been any papers on a relativistic relative state (“MWI”) interpretation of QM with continuous spectra?

I've read the original papers on the relative state interpretation ("MWI") of Quantum Mechanics. They seem compelling, but they only addressed a nonrelativistic system and operators with discrete ...
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Query about using lorentz transforms to describe muon decay

Image from https://brilliant.org/practice/cosmic-ray-muons/?p=5. On the above diagram, $T$ and $X$ correspond to the axis of an observer on Earth and $T'$ and $X'$ correspond to the axis of the ...
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Length contraction and electromagnetism [duplicate]

No physics guy so forgive any stupid questions or incorrect wording. I think I get the length contraction, looking at a moving train, the light coming to my eyes are really emitted at different points ...
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Why do we need time dillation? [duplicate]

I was wondering why we need time dillation . I close my eyes , I take the assumption that the speed of a light beam is constant for every rest frame.The lifht beam is travelling inside a box . I am ...
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Confusion regarding conservation of momentum and conservation of energy [closed]

When solving the problem under in the two different ways listed, i end up getting different answers. An electron is moving with $v_1=0.87c$ perpendicular to a positron moving with $v_2=0.98c$ in an ...
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What is the relationship between relativity and the Doppler effect?

My sister just watched this video about space contraction (Spanish), and asked me if this is related to doppler effect. In the clip they also introduce the idea that a bat would be affected by ...
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It is said that an object cannot exceed the speed of light, because high speed makes the object closer to infinite mass, but speed relative to what?

That is, the speed of an object, when getting closer to speed of light, makes the mass of the object closer to infinite, but isn’t speed relative? So a man on earth feels a metal ball on the table has ...
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Query about the Michelson interferometer

Say I am cycling past a Michelson interferometer set up. Someone at rest with the experiment will see both beams travelling a distance $L_0$ and hence conclude that $T_{AB}=T_{AC}=\frac{2L_0}{c}$. ...
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2answers
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Trouble deriving the Lorentz transforms

After separately arriving at the two equations $x'=\gamma(v^2)(x-vt)$ and $t'=\phi(v^2)(t-\frac{vx}{c^2}$). Where $x'$ and $t'$ are the coordinates a moving observer ascribes to events. I had to show ...
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Invariant mass in special relativity [closed]

I'm following a special relativity course and I'm trying to understand how the invariant mass works. In particular I don't get how the following passages work. We have a collision between two ...
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Will the log of wood sink in the water?

Imagine the water in a river is flowing with speed very close to the speed of light. There is a log of wood tied to any object outside the river so that it doesn't go ahead with water and is at rest ...
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Question (mostly) About Relativity

Before I get into the actual question, I'd like to say that my only knowledge on Einstein's Theory of Relativity (both Special and General) have been obtained through about an hours worth of videos ...
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The path of minimum time difference in special relativity

Suppose there are two points A and B in the inertial reference frame S. Suppose traveler x started from point A and travelled to point B. In reference frame S, it took traveler x an amount of time, T, ...
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Subtle problem in length contraction

Suppose a particle moves with respect to objects. Does length contraction refer to the contraction of the particle, or to the separation between objects? It seems to me it can't be both. The former ...
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How is time “homogeneous”?

My book$^1$ states: Let's consider a clock moving freely over a curve such as: \begin{equation} \frac{dx^i}{dt}=\text{const} \tag{1.20} \end{equation} We define the proper time $\tau$ as the ...
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1answer
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Signs in relative vector addition

So I know the formula for relative vector addition is $$w = \frac{v-u}{1-\frac{uv}{c^2}}.$$ How do I chose when to use this formula or its inverse transformation for solving vector addition problems ...
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Question regarding Lorentz Transformation formula

So the Lorentz Transformation formation equation are $$x′=\gamma(x−vt),$$ Does $x′$ and t represent time and position at one event(one instance) or do they represent two events- meaning is $x'$ ...
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Why is the idea that two points on a rigid body always correspond to the same distance so important in special relativity?

In Einstein's chapter on physical meaning of geometrical propositions (The special and general theory of relativity) he wrote about supplementing Euclidean geometry with the idea that two points on a ...
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1answer
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Charged particle and magnet, can this event vary relatively?

suppose we take a charged particle and a magnet and place them at some particular distance apart .Now let's take 2 frame of reference. [the charged particle and the magnet are in rest with respect ...
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Invariance of $ds^2$ from invariance of all null intervals

Is this linear algebra statement true? Let $\eta= \begin{pmatrix}1&0&0&0\\0&-1&0&0\\0&0&-1&0\\0&0&0&-1\end{pmatrix}$. If $x^T (\Lambda^T\eta\Lambda) x$...
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Thomson Exercise 2.12: Why is $p_i^2 = m_i^2$?

I'm just working on some problems from Thomsons Modern Particle Physics. I' having a hard time understanding the last step in this calculation: The relativistic energy-momentum relation is $E^2 = m^2 ...
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6answers
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Conservation of Mass and Energy [duplicate]

I was thinking about some physics (relativity in particular), when it suddenly occurred to me that all my life I had been balancing chemical equations assuming conservation of mass, but I was ...
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1answer
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Length and velocity of a pulse of particles

We are given a pulse of protons of duration $10^{-7}s$ and energy $2KeV$. I know I am supposed to use the uncertainty principle to solve this. I need to get the length and the indetermination of the ...
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1answer
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Recordings of journey traveling near speed of light

If you had two identical video cameras and started recording synchronized atomic clocks recording at the same speed and you put one on the spaceship and sent it out traveling at 99% of the speed of ...
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3answers
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Understanding Einstein notation in special relativity

I'm entering the realm of special relativity and amazingly the hardest part about it is the notation! I'm confused on exactly how to intuitively build an understanding, and this may be hindering the ...
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The hypotenuse of the triangle in the Michelson and Morley experiment

In Michelson and Morley experiment, light is travelling from light source to partially silvered glass plate. The plate splits an incoming beam of light, and the two resulting beams continue in ...
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Prove invariance for a particular transformation

Consider inertial frames $\Sigma$ and $\Sigma'$ that are coincident at time $t\boldsymbol{=}t'\boldsymbol{=}0$. The relative velocity of $\Sigma'$ with respect to $\Sigma$ is $\vec \upsilon$, not ...
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Relativistic collisions (elastic) - stationary target, equal mass [closed]

A moving electron with energy $E$ hits a stationary electron. Question is to find the scattering angle (the angle between the paths of the two electrons after collision) in terms of the energy $E$ and ...
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2answers
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Do photons have any relativistic mass?

In some books I found they are writing photon momentum $mc$ rather than $E/c $. Which one is right? But if I put $v=c$ in relativistic mass equation, $$m=\frac{m_0}{\sqrt{1-v^2/c^2}},$$ it becomes ...
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2answers
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How is mass defined by special relativity?

I am eagerly interested in all kinds of areas of physics. As the question of mass has been around for a pretty long time, I am interested about what modern physics namely special relativity says about ...
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MTW Exercise 4.4: Rotation free 1-forms [closed]

MTW in Exercise 4.4 calls a 1-form $A_\alpha$ a rotation free 1-form if $$\textbf{A}\wedge\textbf{dA}=0.$$ And claims that all such 1-forms may be written as $$\textbf{A}=\phi\,\textbf{d}\psi$$ for ...
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2answers
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Special relativity - mass energy and momentum [closed]

I've just started studying relativity and I think I have just about gotten my head around time dilation and length contraction and I have now been able to derive the two equations $$t=\frac{t_0}{\...
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Question about position dependence of time dilation?

I found this picture from a physics stack exchange question on time dilation: Time dilation all messed up! I am now returning to it a few weeks later and was wondering if I am correctly interpreting ...
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Hafele–Keating experiment

So what times would be shown on the various clocks if the Hafele–Keating experiment was done North-South rather than West-East? Which clock(s) would be slower and why? There will be the same ...
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1answer
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Tensor Derivatives in Index Notation in Special Relativity

The energy-momentum tensor $T^{\mu\nu}$ is not uniquely defined because we can add a term $\partial_{\lambda}X^{\lambda\mu\nu}$ to it, where $X^{\lambda\mu\nu} = - X^{\mu\lambda\nu}$, and show that it ...
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1answer
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Train and lightning bolts: why the time difference does not depend on the position of the moving person?

So imagine two lightning bolts hit the ground, simultaneously to a stationary observer. There is also a person on a train traveling to the right at a constant velocity. I know that if he started in ...
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2answers
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Relativistic mass

I've always seen older books talking about relativistic mass all over their special relativity introduction $m=\gamma m_0$. But I can't stand it. It makes no sense to define this quantity at all. To ...
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4answers
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Is there a frame of reference in which I was born before I was conceived?

I'm struggling to understand the relativity of simultaneity and position. If my conception and birth are separated by time but not space, a frame of reference in which my birth and conception are ...
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1answer
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Four momentum squared and collisions

So, I am not asking is the square of four-momentum of a particle an invariant to Lorentz trasnformations, but rather,is it invariant in dynamic situations? It seems to me that this also has to hold. ...
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The Special Relativity springs from the space-time nature? [duplicate]

Suppose we have 2 clocks in the same reference system which are synchronized. These two clocks exchange signals every second. Now suppose that one of the two starts to move away (instantly with $||v||=...
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Is Levi cita tensor an invariant in curved space?

The Minkowski metric and Levi cita tensor is an invariant quantity in Euclidean flat space. But in curved space metric tensor varies. Analogous to it, is the Levi cita tensor varies in any Non-...
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2answers
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Conserved and invariant quantities in a nuclear reaction

For a reaction $$a+X\rightarrow Y+b$$ in the book, Introductory Nuclear Physics by Krane, he has written that the total energy and the total momentum both in RHS and LHS remains conserved in Lab frame,...
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Would a human age faster if these certain conditions are met?

So, a human would travel in a rocket in outer space. There is little to no gravity, and the pressure may or may not have an affect (?) on what i'm about to ask. It has been proven that when a human ...
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0answers
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Covariance of applying a four-force to a stress-energy tensor with forward Euler

I've run into a great deal of confusion on what I expected to be a very simple issue of covariance. I have an equation $$T^{\mu\nu}_{~~~~;\mu} = -G^{\nu}.$$ This is manifestly covariant; so far so ...