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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The link between GR and SR

I have studied a bit of Newton Cartan theory recently, the geometrised version of Newtonian gravity in which gravity is due to the curvature of spacetime, but is Newtonian (simultaneity is absolute). ...
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Why is Lorentz force linear in velocity?

I am working on the derivation of the Lorentz force. (I know that Lorentz force is in some sense definition of fields, but still, there is nontrivial dependence on velocity) I want to derive that ...
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Special Relativity - Simultaneity of events

For the discussion below, consider only 1-space dimension, x Let E1 and E2 be two physical "events". Let S ans S' be two IRFs. Let the coordinate of E1 be (x1,t1) w.r.t to S and (x1',t1') w.r.t to S'...
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Looking for physical intuition into the Electromagnetic Tensor:

I have done some work with the electromagnetic tensor and I'm fairly good at manipulating it and using it to transform the Maxwell Equations into tensored forms. Admittedly though, I have no physical ...
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How can I show that the speed of light in vacuum is the same in all reference frames?

I have regularly heard that the Michelson-Morley experiment demonstrates that the speed of light is constant in all reference frames. By doing some research I have found that it actually demonstrated ...
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A charge accelerating while confined to an equipotential surface

Suppose I had the following in Cartesian $(x,y,z)$ space, where $x$ is horizontal, $y$ is vertical, and $z$ is depth: A negligibly thin conductive rod extending from $(0,1,0)$ to $(0,+\infty,0)$. An ...
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What has general relativity got to do with special relativity?

What has general relativity got to do with special relativity? Arguably, special relativity is encompassed in the requirement that the dynamical laws of physics be Poincare invariant (as opposed to ...
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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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1answer
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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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1answer
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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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1answer
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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

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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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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1answer
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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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2answers
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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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Why is Non-relativistic quantum mechanics not consistent with relativity? [closed]

The Answer of this question is discussed in almost all good books on Quantum Field theory. For example,it is shown in Lancaster Blundell's "Quantum Field Theory for the gifted amateur" that the ...
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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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Acquiring Solution Manual and Resource Recommendations

I am currently preparing a course on special relativity. I want to include some exercises and problems. So I am searching for solved problems references on special relativity. Could anyone recommend a ...
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Minkowski space and Rindler spaces, What's relation?

To describe the dynamic of a qubit one can use the Minkowski cordinates, But when that qubit is accelerated with Unruh acceleration we need Rindler cordinate . So, what is UNRUH acceleration ? and ...
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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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If (a possible explanation for gravity) objects are attracted to the slowing of time, then wouldn't free floating objects tend to speed up? [closed]

One theory of gravity is that objects are attracted to the slower time at a mass. See this quote: "According to the Least Action Principle, stuff is "lazy" and moves to where energy is lower. Time and ...
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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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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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Measuring the speed of a relativistic particle

The time dilation principle shows that when measuring the time of a moving object, we find it bigger than the proper time. So, if we measure the time for a particle to move a certain distance and then ...
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2answers
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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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1answer
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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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6answers
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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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Time dilation, but not in space [closed]

What if you accelerate in the speed of light, but in Earth, no in space, will time also stop? Einstein said that as you move faster in space, you move slower in time, but what if you move faster like ...
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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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1answer
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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}\...