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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Book recommendation for relativistic classical mechanics

I need some good resource recommendations for the relativistic hamiltonian mechanics under special theory of relativity, with a good discussion on relativistic Hamilton-Jacobi formulation.
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Interstellar medium shock heating

How fast would a hypothetical spacecraft need to get to experience significant heating from interaction with the interstellar medium (ISM)? Significant, in this context, means a steady-state ...
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Relativistic Aberration Formula Derivation: looking for a hint

The literature on relativistic beaming / doppler beaming is scarce, so I hope the community can shed some "light" on this topic. I want to derive a formula for the phenomenon known as relativistic ...
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Explanation of desynchronization of clocks in Special Theory of Relativity

I was going through a paper on De-Synchronization of 2 Clocks in Special Theory of Relativity. The author shows up number of ways clocks de-synchronize relative to 2 frames. The one I am stuck is due ...
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How to “transfer” indices from dot product to metric?

In this source, the author (Andrzej Pokraka, Solutions to problems from Peskin & Schroeder) is computing an integral related to scalar QED. In the step where the equation is labelled (29), the ...
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Simultaneity (working backwards) and absolute time [closed]

If two events happen at different times and at different places in two different reference frames (observers) couldn't the observers work backwards (considering the finite speed of light) to find out ...
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Has this group something to do with the cone of light?

Consider the group $V=(-1,1)$ with addition $+_{rel}:V\times V\to V$ defined as: $$v+_{rel}w=\frac{v+w}{1+vw}$$ This group is analogous to the relativistic velocities where the speed of light equals ...
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Observers at rest and simultaneity

Suppose we have two observers A and B and they are at rest. Observer A observes two objects falling from height H (A has same distance between the two objects). Does observer B will measure different ...
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75 views

To Be Forever Young [duplicate]

It is clear from the Lorentz Parameters, applied to Einstein's Equations, that as velocity, v approaches speed-of-light, c, the denominator (1 - [v/c]) tends to zero; when v=c, time, t=0: time stops?! ...
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independence of inner product in relativity

"Notice that the definition of a tensor does not mention components of the vectors. A tensor must be a rule which gives the same real number independently of the reference frame in which vectors' ...
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Why Didn't the Energy-Momentum Relation Work?

I am currently studying for the GRE Physics subject test by working through published past tests. My question is about problem 20 from the test GR8677: A positive kaon ($K^{{}+{}}$) has a rest ...
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Time dilation at perceived constant acceleration

Let's say that we have a spaceship. From the beginning, the ship is stationary (relative to me) and not affected by outer forces (like Earth's or Sun's gravity). Then the ship starts to accelerate at $...
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Intuition of Maxwell's Equations [duplicate]

Is there an intuitive explanation for Maxwell's equations? I know they are axioms but is there a logical understanding of why instead of mathematical. Both forms don't explicate the scientific ...
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Lavoisier law of mass conservation vs. conservation of energy

Lavoisier law states that for any isolated system, mass must be conserved over time. Also, Einstein's equation $E = mc²$ shows energy-mass equivalency. So, since mass must be conserved and energy ...
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Is it possible that “$c = 1$?” [duplicate]

Can c = 1 and if so, what does this mean for Physics? If you were to take any Physics equation, and let c = 1, will it work?
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Stellar Aberration

In Stellar Aberration Experiment how do I know there is a star above my head before doing the experiment? Reference: Special Theory of Relativity - Resnick (Section-1.7)
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Still confuse about tensor

In special relativity, a four-vector $\mathbf{x}$ in an inertial frame is related to $\mathbf{\overline{x}}$ through a Lorentz transformation $\mathbf{\Lambda}$: \begin{align} \overline{\mathbf{x}}...
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Transformation of the derivative of the scalar field in Ramond's book about QFT

In the book by Pierre Ramond about quantum field theory, he explores in chapter 1.4 (p.13) the behavior of fields under Poincaré transformations. He starts by explaining that infinitesimal ...
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What does it mean to take the tensor product of two reps of the Lorentz group? [duplicate]

If I reduce the Lorentz group to the representation $\mathfrak{su}(2)\oplus \mathfrak{su}(2)$, I can write left and right-handed Weyl spinors respectively as $\left( \frac{1}{2},0 \right)$ and $\left(...
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In special relativity is mass just a measure of all other energy than kinetic?

The energy momentum equation in special relativity is: $$E^2=(pc)^2+(mc^2)^2.$$ and it holds for a moving but not accelerating object. One special case is the massless photon: $$E=pc.$$ And another ...
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Is Lorentz transformation the only way to preserve speed of light?

Doesn't this transformation also preserve speed of light?: $B$ is moving with speed $v$ relative to $A$ in the $+x$ direction. $B$ passes $A$ at $t=0$, and $A$ shines a torch at that moment. Let $(x'...
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54 views

The Lorentz Transformation of the electric field of a moving charge

If I have a moving charge observed in frame $S$, may a Lorentz boost from $S$ in a direction not parallel to the charge's velocity in $S$ result in an electric field that has a different magnitude of ...
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Reference systems in Special and General Relativity

I am enthralled by the notion of placing observers along with standard identical clocks in a line spaced from one another according to rods of standard length when place next to one another at the ...
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How to understand $E=mc^2$?

I am trying to understand Einstein's mass-energy equation $E=mc^2$. Knowing about the atomic bomb I am inclined to believe that $E$ is proportional to the mass: $E=Cm$. For this equation to be ...
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Lorentz transformations: new actual notation for a $4$-vector [duplicate]

For the Lorentz trasformations I use this notation \begin{equation*} \left\{\begin{aligned} x&=\gamma (x'+\beta ct')\\ y&=y'\\ z&=z'\\ ct&=\gamma (ct'+\beta x')\\ \end{aligned}\right. ...
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How to explain time dilation using Lorentz transformation? [duplicate]

Suppose that a frame S' is moving along X axis with velocity $v=\sqrt{3}c/2$ relative to a frame S. Now if a clock being at rest in the frame S', measures the times $t'_1$ and $t'_2$ and clock being ...
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Are photons affected by SR time dilation (velocity) or not?

Photons are massless particles. Time dilation is caused between two observers either by the relative speed of the observers or by the observers being in different gravitational zones (stress-energy ...
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Is the value for the speed of light in vacuum irrelevant? [duplicate]

Does it matter that the speed of light, $c$, is 299,792,458 meters per second in a vacuum? Would the universe be different if $c$ were, for example, 1 meter per second? Or should things be the same, ...
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Is 'photons being massless' the reason everyone observes their speed to be the same?

When a man on a train throws a ball, the resultant velocity of the ball (as seen from ground) is the sum of the velocity of the train and the velocity imparted to the ball from the throw. However, if ...
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Has the Michelson-Morley experiment been performed while moving in relationship to Earth?

I'm currently trying to debunk some geocentrist claims the Michelson-Morley experiment proves Earth isn't moving and I'm wondering - has this experiment ever been performed while in motion relative to ...
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What is this annoying term in speed of relativistic center of mass?

Let's define relativistic center of mass in this way \begin{equation} \mathbf{r}_{cm} = \frac{\sum_i \gamma_i m_i \mathbf{r_i}}{\sum_i \gamma_i m_i} \end{equation} If system is isolated the total ...
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Motion of a charged particle in a constant and uniform magnetic field

Assuming the following relationship has been demonstrated $$r=\frac{m u_{0}\sin \theta_0}{qB\sqrt{1-\left(\dfrac{u_{0}^2}{c^2}\right)}}=\frac{p_0\sin \theta_0}{qB}$$ where $p_0=mu_0/\sqrt{1-\beta^2}$...
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Sound wave and Principle of relativity

Principle of Relativity: "An experimenter doing an experiment in an inertial frame of reference can never measure the velocity of its own frame of reference. OR a law of physics is never expressed ...
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How to derive the Galilean transformation for magnetic field B without taking help of special theory of relativity?

I have seen in some texts that the Galilean transformation of the magnetic field across inertial reference frames is given by: $\vec B'= \vec B - (1/c^2)(\vec v\times \vec E)$. Every where it is ...
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Coefficient of restitution in special relativity

It seems that all books about special relativity only include discussion about perfectly elastic and perfectly inelastic collisions. The notion of the coefficient of restitution, $e$ in classical ...
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4answers
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Astronauts in a spaceship moving close to the speed of light

There is a spaceship, moving at a speed close to the speed of light. The control room of the spaceship is in the front and the sleeping quarters are at the back. One of the astronauts, Joe, decides ...
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Zero mass Kerr metric

When mass in Kerr metric is put to zero we have $$ds^{2}=-dt^{2}+\frac{r^{2}+a^{2}\cos^{2}\theta}{r^{2}+a^{2}}dr^{2}+\left(r^{2}+a^{2}\cos^{2}\theta\right)d\theta^{2}+\left(r^{2}+a^{2}\right)\sin^{2}\...
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Why would a spinor transform under Lorentz transformations?

From my understanding of spinors, they arise as projective representations of $SO_0(1,3)$ that do not correspond to representations of $SO_0(1,3)$. But still one says here - and virtually everywhere - ...
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Motivation for the abandonment of inertial frames in general relativity [closed]

Inertial frames are at the core of special relativity. The laws of physics are supposed to be the same among them and free particles follow rectilinear paths in spacetime or simply stay at rest. Just ...
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Why maxwells speed distribution law doesn’t violet special theory if relativity [duplicate]

As per maxwells distribution law the molecule of gas will have speed across zero to infinity with some probability function. I want to know that why the speed above speed of light is possible (i know ...
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Is not length contraction a distortion of light? [duplicate]

The first picture shows how length contraction occurs. The second picture is based on the first picture, showing that the light in front of the bar reaches the observer slower than the light in the ...
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Derivation of 4-velocity - where does this equation come from?

I'm a student working through a special relativity book. In a chapter of the book, they are deriving each of the components of a 4-velocity vector in terms of ordinary 3-velocity. (Here $\vec{x}$ ...
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Do gravitational time dilation and SR time dilation always cancel eachother out - on every planet?

In the show Gravity and Me, he discusses that on Earth the bulge at the equator leads to the SR time dilation (from moving faster) to exactly equal the gravitational time dilation (from increased ...
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Relativistic Collision Mass Assumption

David Tong's Dynamics and Relativity Problem Set 4 Problem 7: A photon collides with a stationary electron of rest mass $m$. Show that the angle $\theta$ by which the photon is deflected is related ...
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A special relativity question about two platforms and a light source

Suppose that we have two platforms: A and B. Each of them has a special photon detector on them. Detectors are constructed in such a way so that only photons falling on them with 90 degrees incidence ...
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Trying proving that energy and momentum are conserved in every inertial frame

I'm trying to show, using Lorentz transformations, that if relativistic energy and momentum are conserved in $S$, then they are conserved in $S'$ too. A wrong proof Let's suppose I know that in ...
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Non-relativistic limit of the coupled Dirac equation

In Greiner's relativistic quantum mechanics textbook he has a derivation of the Pauli equation as a nonrelativistic limit of the coupled Dirac equation. Just below Eq. (2.81) he makes the following ...
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Question about $E=mc^2$

When a nuclear reaction happens, the amount of mass disappeared satisfies $E=mc^2$. However, the reaction will stop at a certain point, there is no way to make the whole thing disappear into energy. ...
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Why the velocity $v$ is taken as value and not as definition in special relativity equations?

Why the velocity $v$ is taken as a value and the definition of velocity not applied on a relativistic equations? The equations of time dilation and length contractions as we know are $$L = {L_0}{\...
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Understanding the definition of tangent basis

This question could sound silly but I though a lot about it and I'm not new to physics. Let's say I have a plane on which I use polar coordinates, it means a point $P$ can be indicated by its ...