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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Why helicity for massless particles is Lorentz invariant?

By definition helicity is projection of spin onto the 3 momentum. $$h={\bf J} \cdot {\mathbf{P }} $$ where ${\mathbf{P }}=(P_1,P_2,P_3)$ is the momentum operator and ${\mathbf{J }}=(J_1,J_2,J_3)$ ...
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Is relativistic channeled electron catalyzed fusion possible?

A few words first  about muon catalyzed fusion.  You can see this question sigoldberg1 answer, and  this link. "The muon may bump the electron from one of the hydrogen isotopes. The muon, 207 ...
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74 views

The Proof of $\cos\phi=\gamma$ Equation in Special Relativity [closed]

In the Introductory Special Relativity book, by W. G. V. Rosser, page 182, Section 7.3, the author is defining the 4-vector methods using complex numbers. In his derivation, he writes the following ...
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Question about the travel time of a ship “using” a warp drive metric

I - The Warp Drive metric: The Warp Drive is a geometry in a spacetime $(\mathcal{M},g)$ given (in geometrized coordinates $c=G=1$) by the following metric tensor: $$ ds^{2} = -dt^{2}+ (dx-v_{s}f(...
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Think of a boost as a deformation of the underlying spacetime manifold or a change of coordinates?

I am new to relativity, but I have some familiarity with differential geometry. If I ask a mathematician what the difference is between a change of coordinates (or basis) on a vector space and an ...
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46 views

Which Frame of Reference is Correct?

I am reading a lot about the theory of special relativity, but I have a very basic question about this theory I still don't understand. Consider a particle in two inertial reference frames $\Sigma$ ...
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182 views

A best definition of proper acceleration

In this link of Wikipedia https://en.wikipedia.org/wiki/Hyperbolic_motion_(relativity) there is a definition of proper acceleration: The proper acceleration to a particle is defined as the ...
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1answer
49 views

Relative velocity from space-time diagram

Consider two frames of reference, with velocities V1 and V2 relative to an initial ground frame. I have made the space-time diagrams for the three frames (Time represented on Y-axis). As far as I ...
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Relativistic doppler effect vs cosmological redshift

If these two would interfere what would happen? consider two bodies away from each other at certain distance which one is source of a light ray and other is receiver. and they have relative speed of v ...
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61 views

Why there are the hyperbolic (not harmonic) functions in Rindler coordinates

Usually the Rindler coordinate transform is written as $$T = \frac{1}{a} \sinh(at) \tag{1}$$ $$X = \frac{1}{a} \cosh(at) \tag{2}$$ where $a$ is the uniform acceleration. The transforms lead to the ...
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Proof that entanglement “speed” can not exceed the sped of light?

Is there a mathematical proof, if any, in the quantum mechanics formalism, proving that "entanglement" can not be used to send information to speed greater than light? Remark (related): can the speed ...
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High speed and low speed photons (hypothesis - difference/relation)

In this question I found an interesting answer with the source. Quotation: A telescope viewing a supernova from over 16 billion light years away recently clocked the low energy photon arriving 5-...
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Force on a moving charge in 2 frames

The following simple problem seems to lead to a contradiction when analyzed in different frames. Consider an infinitely long stationary wire with positive line charge density $\lambda_0$ and ...
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48 views

Solving relativistic free EOM

Consider a relativistic free particle of rest mass $m$. From Goldstein's Classical Mechanics, it's Lagrangian is $$\mathcal{L}=\frac{1}{2}mV^{\mu}V_{\mu},$$ where $V^{\mu}=\frac{\mathrm{d} x^{\mu}}{\...
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76 views

Orthochronous indefinite orthogonal group $O^+(m, n)$ form a group

My question is based on Qmechanic's answer here which proves that $O^+(m, 1)$ forms a group -- that if two Lorentz transformations have positive time-time co-ordinate, so does their product. The key ...
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81 views

Relative speed when getting close to the speed of light

I was thinking about the relative speed of an observation reference frame and an object which has been accelerated to a speed close to the speed of light. I'm by no mean an expert and the last physics ...
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Two ships, one year apart, travelling from earth to a distant planet. What is the time difference of arrival? [closed]

If a ship set off at a significant percentage of the speed of light, and landed on a distant planet, and then a second ship set off a year or so later, what would the time distance be at the ...
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Relative simultaneity and time going backwards as someone accelerates

I have an observer on Earth with an atomic clock, let's call this the unprimed frame with space coordinate x=0 and t. Universe is one dimensional. I have a rocket ship sitting stationary in empty ...
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Law of cosines in Time dilation formula derivation [duplicate]

In my book, Bob takes off on a spaceship with a light clock so that the direction of motion of his spaceship is perpendicular to the direction of motion of light in the light clock. As a result, ...
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42 views

Lorentz Transformation Derivation

So I'm going through The Einstein Theory of Relativity by Lillian R. Lieber, and I cannot for the life of me figure out where she got this equation. I will attach pictures of the relavent page. We ...
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Why is relativistic beaming/ Doppler beaming occur at non-relativistic speeds

The reflexive motion of a binary star system causes the host star to occasionally wobble towards and away from an observer on Earth, which gives rise to an effect called relativistic beaming. This is ...
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Motion of an object “halfway in” a gravitational field

As a thought experiment, imagine a very long girder, moving at a constant velocity through space. At some point, it passes close to a black hole, such that one end of the girder is experiencing time ...
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108 views

Do virtual particles follow worldlines (spacelike, timelike, lightlike)?

When we talk about static force fields, we use virtual particles to describe the interaction of such fields with other particles. These virtual particles are not real particles, they are a ...
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Relation of time dilation with Biological clock

I have completely understood the time dilation topic along with its mathematical derivation and consequences. And we know due to time dilation a person's biological clock slows down.So I am not ...
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Does light emitted in opposite direction hit equally distant objects at different times?

I am a physics student just learning about special relativity for the first time, and was wondering what would happen if you emitted two photons of light from the center of a boxcar in opposite ...
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What causes the Sagnac effect?

Wikipedia explains the Sagnac effect as a result of the rotating disk, which moves the target so that one of the light beams has farther to travel and consequently, will arrive later than the other ...
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Relativistic beaming/ Aberration effect derivation

I'm researching applications of relativistic beaming and I want to derive a formula for the aberration effect but I am stuck (I am off by a factor of 1/c). Here's what I have: Consider a star in its ...
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Effectively Lorentz-invariant interacting Lagrangians in solid state?

Are there any known examples in solid state physics when an essentially non-relativistic system in certain regime may be described by a relativistically invariant Lagrangian with an interaction? ...
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Simplified general relativity simulation

I've been thinking how massive space battles might play out when vessels travel at significant portions of the speed of light (e.g. 0.01c-0.2c). I wondered if it was possible to simulate such actions ...
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Components of speed of light

I'd like to start off by saying this may be totally wrong; thus I would like some help clarifying this. Suppose you are in a vacuum, and a beam of light is travelling at, say, a N$45°$E bearing. The ...
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What is the radiation field of a black body with temperature $T$ translating at speed $v$?

Suppose I have a spherical black body at temperature $T$ with radius $R$. When stationary in a vacuum at zero Kelvin, it produces an incoherent radiation field according to Planck's law $$ B_\nu = \...
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Variable acceleration relativistic rocket

I was wondering how a realistic fusion-or-something rocket would fly... More specifically, I wonder about the time dilation that would be experienced (say in the classic example of two twins). So, of ...
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The meaning of the 4-divergence of the 4-magnetic field?

In special and general relativity, the magnetic field is defined as $$B^\mu = F^{*\mu\nu}u_\nu, \label{tag1}\tag{1}$$ where $F^{*\mu\nu} = \frac12 \varepsilon^{\mu\nu\rho\sigma}F_{\sigma\rho}$, and $...
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What do spacelike and timelike intervals represent? [duplicate]

I've understood that with timelike intervals all observers agree on the order of events and with spacelike intervals the order of the events can be changed with the reference frame. However, I wanted ...
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185 views

Why is the equation $E=mc^2$?

The equation $E=mc^2$ never made any sense to me. c is a constant (speed of light), therefore c squared is also a constant. We're not specifying any units so surely the equation should be reduced to ...
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Free-float frames and inertial frames [duplicate]

In the book Spacetime Physics by Taylor and Wheeler, a free-float reference frame is defined as a reference frame where every free particle initially at rest with respect to that frame remains at ...
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Are there good reasons why special relativity should motivate geometrised gravity in a way that Newtonian mechanics does not?

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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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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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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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?! ...