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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Minkowski Metric Signature

When I learned about the Minkowski Space and it's coordinates, it was explained such that the metric turns out to be $$ ds^{2} = -(cdx^{0})^{2} +(dx^{1})^{2} + (dx^{2})^{2} + (dx^{3})^{2} $$ where $ ...
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Speed of light as a universal speed limit

It follows from special relativity that nothing can travel faster than light. Einstein believed this would have to hold so generally that he assumed the Einstein-Podolsky-Rosen paradox to indicate a ...
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What is the speed of light relative to?

Consider the scenario where you measure the time it takes for light to travel to the left 10 meters and to the right 10 meters. Both measurements will take the same time, even though we are moving ...
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How is time not a constant?

I am a visual person, so it's hard to imagine the information I keep getting, but shouldn't time be a constant? If you were traveling at the speed of light and your able to cover $299{,}792{,}458$ ...
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Tensor decomposition of $\partial_\mu A_\nu$

In the decomposition of a rank-2 Minkowski tensor into irreducible representations, I expect the 16 components of the tensor product $M_\mu N_\nu$ to reduce to the sum of a scalar (1), a rank-2 ...
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Is there always a frame in which spatially separated events are simultaneous?

In relativity, if two events are simultaneous in a specified frame, they cannot be simultaneous in any other frame. My question is this: given any two events, is there always a frame in which these ...
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Frequency of cosmic microwave background

Some people refer to cosmic microwave background's (CMB) frame of reference as an absolute one. If I understand correctly, we can measure 'absolute' velocity in this frame by using the Doppler effect. ...
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What does $\frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$ mean with respect to special relativity?

What does the following mean with respect to special relativity? $$\frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$$
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Time travel outside of light cone without causality violation

If one is able to travel into the past but at a spatial distance that puts him outside of his own past light cone would this be considered a causality violating trip? Looking at a Minkoski diagram, it ...
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Difference between “Lorentz transformation” and “proper orthochronous”

I'm doing an assignment and I've been given a list of $4 \times 4$ matrices and asked: Which of the following are Lorentz transformation matrices? Which are proper and orthochronous? But, as ...
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Why and how is the speed of light in vacuum constant, i.e., independent of reference frame?

I was told that the Galilean relative velocity rule does not apply to the speed of light. No matter how fast two objects are moving, the speed of light will remain same for both of them. How and why ...
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How does wind speed affect the velocity of light?

As you know, there is a maximum speed things can go called $c$, the "speed of light." Light in a vacuum goes $c$. Light in the atmosphere, however, goes a little less than $c$. My question is: what ...
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Does divergence of Taylor series for relativistic $E(p)$ for $p\ge m$ have any physical significance?

When one wants to include weak relativistic effects in classical equations, usually kinetic energy term is expanded into Taylor series about $p=0$. But the complete dispersion relation is ...
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How would one compute the angle of deflection, in a relativistic collision - underspecified system?

Consider the simplistic case of two identical mass particles colliding elastically with the second particle initially stationary and the first particle travelling with energy $E$. By conservation of ...
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Field interaction betweeen two point charges?

[SOLVED] Consider two particles A and B having equal charges and placed at some distance. The particle A is slightly displaced towards B.So, Does the EM force on B increase(+/-) as soon as the ...
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Construction of Observer Coordinates in General Relativity

In A First Course in General Relativity, Second Edition, by Bernard Schutz, on the bottom of Page 8, he is expanding on the spacetime diagrams in Figure 1.5. He states "[...] the four angles are ...
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Possible mechanics based on the known symmetries in the nature (investigating rumor)

Somewhere I've heard about a relative new mathematical result regarding mechanics. Specifically, there is a list of the known symmetries of mechanics (both Newtonian and relativistic), i.e. different ...
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Why does the (relativistic) mass of an object increase when its speed approaches that of light?

I'm reading Nano: The Essentials by T. Pradeep and I came upon this statement in the section explaining the basics of scanning electron microscopy. However, the equation breaks down when the ...
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How is the classical twin paradox resolved?

I read a lot about the classical twin paradox recently. What confuses me is that some authors claim that it can be resolved within SRT, others say that you need GRT. Now, what is true (and why)?
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Is there an upper limit on the radius of a rotating wheel?

Is there an upper limit on the radius of a real wheel which is rotating at an Angular frequency of $\,\omega \,$ along its axis, such that we just require a finite amount of energy to rotate it? ...
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Why does Minkowski space provide an accurate description of flat spacetime?

What is the chain of reasoning (beginning, of course, from observations about the universe) that leads one to predict that Minkowski space provides an accurate description of space-time in the ...
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37 views

How do you determine who is moving “faster” in relativity? [duplicate]

I suspect this question has a simple answer, but I can't get my head around it. The classic example of a person in orbit around the Earth at high speed experiencing a slower passage of time than the ...
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What is the relative speed of two near-light speed particles headed towards each other?

I understand that nothing can move faster than light due to time dilation. I want to build upon my understanding of Einstein's theory of Special Relativity, so I came up with this hypothetical problem ...
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Velocity in frame $S$ and $S'$

If I take the Lorentz position transforms between two inertial frames, $S$ and $S'$ moving with relative velocity $u$ along a common axis (say $x-x'$), then: $$x'=\gamma(x- ut)$$ $$y'=y$$ $$z'=z$$ ...
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Special Relativity Second Postulate

That the speed of light is constant for all inertial frames is the second postulate of special relativity but this does not means that nothing can travel faster than light. so is it possible the ...
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4-velocity and 4-acceleration in instantaneous rest frames

I am trying to solve this problem: Consider a rocket moving relative to an inertial frame $\mathcal{F}$ , such that its worldline is given by ...
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Confused about time dilation/length contraction [duplicate]

I have a following problem: A meson is generated $h$ meters above the earth's surface and begins to move towards the earth with velocity $v$. Its (proper) lifetime is $t_m$. What is $v$ if the meson ...
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Proof that 4-potential exists from Gauss-Faraday field equation

This is a problem concerning covariant formulation of electromagnetism. Given $$\partial^{[\alpha} F^{\beta\gamma]}= 0 $$ how does one prove that $F$ can be obtained from a 4-potential $A$ such ...
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Person in a special relativistic frame observes light refract on a passing ship

The speed of light is the same in all frames of reference. But imagine a scenario in which you passed by a ship which had (B=.78), while your ship had (B=.94). While somehow being able to look through ...
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Is special relativity axiomatic?

Can special relativity be somewhat described by the following statement? If the speed of light is a universal constant, and if light can be placed in separate frames of motion, then time must be ...
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What will I see in this scenario? Will this be faster than the speed of light?

Let say there's a particle that is travelling very near the speed of light. Lets say I have a camera capable of filming this high velocity particle and I film the particle on my camera then I fast ...
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Travelling faster than the speed of light

Let's say I fire a bus through space at (almost) the speed of light. If I'm inside the bus (sitting on the back seat) and I run up the aisle of the bus will I in fact be traveling faster than the ...
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Special Relativity Problem [closed]

I am having trouble with the following problem: Fry travels in a rocket ship towards Leela, at constant relative speed $v$: Fry is delivering a pizza, which in its rest frame stays hot for ...
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Derivation of proper acceleration in terms of rapidity

In the Wikipedia page for proper acceleration, an equation for proper acceleration in terms of rapidity is given as $\alpha = \frac{\Delta \eta}{\Delta \tau}$, where $\eta$ is the rapidity of the ...
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Everything is a Photon

If we accept $E=\hbar \omega$, $p=\hbar k$, and $E^2-(pc)^2=(m_0 c^2)^2$, then we find $$(m_0 c^2)^2 = (\hbar \omega)^2-(\hbar kc)^2 = \hbar (\omega^2 - (kc)^2)=0$$i.e. the rest mass of any particle ...
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I think only x and t need obey Lorentz transform rule, other 4 vectors not necessarily true

Lorentz transformation aims at an invariant speed of light for all reference frames. Speed only involves x and t. Therefore it's reasonable to understand the Lorentz transform can act on spacetime ...
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The wave equation in general relativity, special relativity, and Cartesian coordinates

The relativistic wave equation is $$\square\varphi=\rho$$ where $\varphi$ is the field, $\rho$ is the source, and $\square$ is the D'Alembert operator, defined by ...
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How to do calculation in relativity of simultaneity

I have great trouble in understanding simultaneity in special relativity. Let me illustrate it with a concrete example. Assuming there is a train, its two end points are $A$ and $B$, the length of ...
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Metric signature conventions: minus sign for $x^a$ or $x_a$?

Say I use the metric signature $(-+++)$. Then $\partial_a=(\partial_0,\partial_i)=(-\partial^0,\partial^i)$, but $\partial^a=(\partial^0,\partial^i)=(-\partial_0,\partial_i)$. The same goes for $p^a$ ...
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Question on energy mass conversion

I have a question regarding the energy-mass conversion. Well, when a particle starts moving with a speed comparable to that of light, its (relativistic) mass increases that means some matter is ...
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Relative Motion

I read the following: http://www.feynmanlectures.caltech.edu/I_15.html#Ch15-S4 "Now let us see what happens to the moving clock. Before the man took it aboard, he agreed that it was a nice, ...
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Dingle vs. Bondi: Twin Paradox Debate on BBC radio?

Herbert Dingle and H. Bondi debated the twin paradox on BBC radio before 1971. Does anyone have a link to the audio of this debate? thanks
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Does path integral and loop integral in a Feynman diagram violate special relativity?

Consider a correlation function between two points $A(x_1,t_1)$ and $B(x_2,t_2)$, we need to integrate over paths which could be infinite long. But the time length $(t_1-t_2)$ is finite, so if $A$ ...
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What does a sphere moving close to the speed of light look like?

What shape does the viewer in a reference frame with $v=0$ perceive? I suppose that since the sphere moves in one direction only (oX only, not oY) its section would change into an ellipse, where the ...
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Ion Drive Propulsion Top Speed

I would like to know if there is some formula / graph which would provide / show the efficiency of a certain type of propeller in space. Specifically, I'm interested in the acceleration attainable at ...
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Are length contraction and time dilation physical?

Are length contraction and time dilation real physical phenomena, or are they just a measurement issue?
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Twin Paradox: Still a Paradox?

Alright, so David Griffiths in his "Introduction to Electrodynamics" states that the Twin Paradox is not a paradox at all since the traveling twin returns to Earth. By returning to Earth, the twin had ...
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$E=mc^2$ resembles kinetic energy formula?

The simplest equation expressing mass–energy equivalence is the famous $E=mc^2$ where $c$ represents the speed of light. Compare this with $E_K = \frac{1}{2}mv^2$. Since $E=mc^2$ can be applied to ...
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How an accelerated object sees another accelerated body in special relativity?

Assume two objects are moving with a constant acceleration $a_1$ and $a_2$, which are the measured accelerations by respective object (or constant force being applied to each of the objects). My ...
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Why does GPS depend on relativity?

I am reading A Brief History of Time by Stephen Hawking, and in it he mentions that without compensating for relativity, GPS devices would be out by miles. Why is this? (I am not sure which relativity ...