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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 do u get Eq3 from Eq2&Eq1 [on hold]

I keep getting the wrong results by subbing eq1 into eq2 It’s from Kleppner’s an introduction to mechanics 2nd edition
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2answers
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Why does electric field $E^i = E_i$ instead of $E^i = - E_i$?

Let us consider the Minkowski spacetim. Generally, we know that when we lower or raise the index of the convariant or contravairant tensor, we need to use the metric $\eta^{\mu \nu}=\eta_{\mu \nu}=(+,...
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Tangent space of pseudo-Euclidean manifold

My textbook says (without any justification that I can see) that "since Minkowski spacetime is pseudo-Euclidean, the tangent space $T_P$ at any point $P$ coincides with the manifold itself". My ...
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Question about Relativity and Proper Reference Frames [duplicate]

If your in a space ship moving at relativistic speeds in reference to an observer on Earth, time would have to be going slower on the space ship and faster on Earth. However, wouldn't the Earth be ...
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Conservation of Energy and Momentum - Special Relativity

I am confused as to how we can assert that energy and momentum are conserved in special relativity. I was attempting a problem on the elastic collision of two particles and came across this. I have ...
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What does the line of constant space time (interval) represent?

In this diagram, what do the hyperbola represent. I understand that for a given hyperbola t^2-(x/c)^2 is constant, but in an answer given to this question: What spacelike, timelike and lightlike ...
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Minkowski diagram

I have not well understood the picture of geogebra regarding the angle of time (t') that is inclined compared to (t) of 26.57°angle . In the picture we see that the velocity is setted at 0.5c, for ...
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Does the fact that we can only measure the two-way speed of light undermine the axiom of invariance?

When we measure the speed of light we get the same answer in all directions. This is taken to undermine the aether or absolute motion hypothesis and give support to the proposal that the speed of ...
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A charge moving relativistically in electric field [on hold]

I need help in the following question: At $t=0$ a charged particle is moving at some speed $u$ in the X direction,and enters a constant electric field E in the direction of Y (all measured in lab ...
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0answers
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Flux through a ball of a moving relativistic particle [on hold]

I have been struggling with the following question for so long that I decided to give up and ask you, the professionals. It seems that the relativistic idea of the question is not the problem, but the ...
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2answers
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Lorentz-transformation

I don't understand how to derive the matrix representing the Lorentz-transformation given two systems S and S': $$x' = \Lambda x$$ these transformations do not leave the differences $\Delta x^\mu$ ...
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How can a vertical beam of light move sideways with an interferometer? [duplicate]

The picture is of the Michelson Morley Interferometer. How can the upward, vertical beam of light move sideways with the interferometer? This brings me to the conclusion that "Aether are attracted ...
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Voyager spacecrafts life span and theory of relativity

The Voyager spacecrafts are moving with an approximate constant speed of 16 to 17 km/s. As per Einstein's theory of relativity, time passes more slowly for them compared to us. Then, is it possible ...
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Antiparticles travelling backward through time [duplicate]

Could someone please explain to me Feynman and Wheeler's theory of waves acting forward and backward in time? I have read about their idea of an antiparticle behaving as a particle travelling ...
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1answer
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From relativistic equation to find Dirac matrices

Is this possible and then how? $$((\gamma \otimes \mathbf\sigma)\bullet\mathbf p)(\gamma^\prime\otimes\mathbf 1_2) = \gamma\gamma^\prime\otimes\sigma \bullet \mathbf p $$ where $\gamma$ and $\gamma^\...
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Why can't we rule out other synchronization procedures?

According to what I've read, it is generally regarded that Einstein's choice to have the speed of light equal in every direction is only a convention, and since there is no way to measure the one-way ...
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3answers
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Four-velocity vector of light

Please note that my question is not a duplicate, it is not about the speed of light, my question is only technical about the four velocity vector for light, its definedeness, value and constantness. ...
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1answer
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Combining two Lorentz boosts

Is it possible to express two Lorentz boosts $A_x(\beta)$ and $A_y(\beta)$ along the x/y-axis as one boost described by $A(\overrightarrow \delta)$? To answer this, I start by defining $\theta \equiv ...
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Do synchronized clocks retain the same time delta between two inertial frames? [on hold]

Let's say we have a device made of a succession of clocks (red squares in the scheme) which are synchronised, in the device inertial reference frame, using Einstein synchronisation. Each clock is ...
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3answers
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Separating the topics of general and special relativity

So, I have managed to confuse myself beyond the point of repair. I am not a physics student, so my physical knowledge is limited. Anyway, there are a few topics of relativity, which I can not seem to ...
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3answers
194 views

Write electromagnetic field tensor in terms of four-vector potential

How can we know that the electromagnetic tensor $F_{\mu\nu}$ can be written in terms of a four-vector potential $A_{\mu}$ as $F_{\mu \nu} = \partial_{\mu} A_{\nu} - \partial_{\nu} A_{\mu}$? In the ...
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A book for relativistic quantum mechanics

What is the best book to learn relativistic quantum mechanics at first time? I would like a book that also talk about the representations of the Lorentz group and the Poincaré group.
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Is it possible to derive $2\times 2$ Lorentz transformation matrix from only eigenvectors?

As a preface, I am somewhat familiar with year 1 linear algebra but not too familiar with how one makes the connection to Lorentz transformation matrices so I apologize if the answer is obvious. One ...
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Static charge in an accelerated frame

In special relativity the metric of an accelerated frame is $$ds^2= (1-2 a_j x^j)dt^2 + 2 \Omega_{m j}x^j dx^m dt + \eta_{ml}dx^m dx^j$$ where the sums over latin indices go from 1 to 3. Let's suppose ...
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Connection between gauge invariance and Lorentz invariance

This question is presented in the context of Weinberg's QFT book treatment, in particular considering the electromagnetism chapter. It begins in chapter 5 where Weinberg argues that in order to have ...
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2answers
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Special Relativity; 3 Momentum Conservation

In SR, I understand you can use 4 momentum conservation, but what are the special cases where you can use 3 momentum/energy conservation? An example I have seen is with $$P_1=(M_1, 0) \\ P_2=(M_2,0) \...
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2answers
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Factorising a 4D Dirac delta function in a rest frame

I'm working through a QFT problem and at one stage in the solutions we have this step: $$\delta^{(4)}(p - q_1 - q_2) = \delta(E_1 +E_2 - M)\delta^{(3)}(\bf{q_1} - \bf{q_2}).$$ We are working in the ...
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What physical laws differs in non inertial frame

For me physical laws should be observers independent, what should be depend on the observers are measurements. But one of the postulates of Special relativity is that all laws of physics should be ...
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1answer
51 views

Momentum anti-Hermitian in RQM?

So in any book that discusses the Dirac equation in Relativistic Quantum Mechanics (For example you can check Bjorken and Drell, Greiner, or Ashok Das), whenever they take the dagger of the Dirac eq., ...
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1answer
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Momentum average on phase space for free particle

I'm studying from Greiner statistical mechanics, and he uses an approximation which I don't really understand. On averaging over many phase-space points we have $$\langle\vec{p}^2\rangle=3\langle ...
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0answers
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In special relativity, what will happen to miserable Schoedinger's cat?

In special relativity would the life of the Schroedinger's cat be observerd same by two observer? Two lights emit at the same time from each end of the train heading in the right direction whose ...
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2answers
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Interpretation of finite proper time of fast-accelerating objects for infinite coordinate time

Say we have an object with velocity in earth's frame that accelerates quickly. For example, suppose we have some object that accelerates very quickly, and has speed $v$ in earth's frame of the form ...
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1answer
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Showing that light bends twice as much as newtonian gravity predicts with special relativity

Light bends twice as much due to gravity as Newtonian theory predicts as discussed in this related question. The argument couched in general relativity, quote from here. Since most objects move ...
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1answer
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Would an observer going faster than the speed of light in a vacuum be able to observe photons that they emit? [closed]

If I could exceed the speed of light in a vacuum, would I be able to see photons that I previously emitted? Would this be theoretically possible?
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Question about path integral step of the rindler decomposition

In most papers where I've read about Rindler decomposition and the Unruh effect ( see for example [1] or [2]) they start by saying that they want to find the wavefunction of the vacuum state in the ...
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1answer
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Relativistic Subtraction of Speeds

The formula for relativistic addition of speeds is well-known; say, if you were to have two objects travelling at each other at speeds of $v_1$ and $v_2$ (as measured by an outside observer), the ...
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1answer
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Tensor index in special relativity?

I'm studying special relativity and I have some difficulties with tensor index. Take for example the Lorentz matrix, whose elements are written as $\Lambda^\mu{}_\nu$. $\Lambda^\mu{}_\nu(v) = \...
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2answers
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Derivation of the Electromagnetic Stress-Energy Tensor in Flat Space-time

I am working on deriving the electromagnetic stress energy tensor using the electromagnetic tensor in the $(-, +, +, +)$ sign convention. However, I have hit a snag and cannot figure out where I have ...
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2answers
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A book on special special relativity covering covariant and contravariant tensors [duplicate]

I am really confused about the use of tensors in special relativity. I'm not sure if I understood what is a covariant and a contravariant tensor and vector. I am looking for a book of relativity that ...
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1answer
45 views

Necessity to consider the square of Four Momentum

Why do we often need to consider the square of four momentum transfer $Q$ in scattering experiment or particle physics/cosmology instead of just the $Q$ itself?
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Unique eigenvectors of the EM energy-momentum tensor

This is a two-part question: 1) I understand that every tensor in a Minkowski 4-space has four eigenvectors, of which only one is timelike. Under what circumstances, if any, does an EM energy-...
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1answer
108 views

In what sense do photons exist?

In a photon's frame of reference travel is instantaneous, so presumably a photon cannot exist in its own frame of reference. I am not aware that a "beam" of photons interacts via gravity despite ...
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2answers
96 views

Photons’ Speed (light speed) in vacuum [duplicate]

In a vacuum, are photons always traveling at 100% light speed? Can photons go any slower in vacuum? They have no mass which means they can go at 100% light speed, but do they have to?
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6answers
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Lorentz invariance of Maxwell's equations in matter

I know that Maxwell's equations of electromagnetism are Lorentz invariant in a vacuum. But what about in a generalized medium, e.g. a metal, a rubber, a dielectric, a magnet? I have read it comes down ...
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6answers
204 views

Twin paradox - is acceleration relative? [duplicate]

The usual answer to the twin paradox is that the twin who undergoes acceleration is the one who finds the other has aged more, because the trajectory of the 'travelling twin' does not amount to a ...
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Light clock and wrist watch

The example of the light clock that bounces between two mirrors placed on a train and observed from the point of view of an observer on the train and from an observer stopped on the quay is evident. ...
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1answer
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What is the 4-momentum of a moving photon with a certain energy in natural units?

If a photon is travelling along the x-axis with an energy $E$ then the 4-momentum of the photon in natural units is: $$\begin{pmatrix}E \\E\\0\\0\end{pmatrix}$$ I don't understand why the first ...
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1answer
42 views

Properties of Dirac delta function in Integral

I was reading commutation relation of canonical momentum in KG Field from Lectures of Quantum Field Theory by Ashok Das. In page 179, He has used Integration to derive the result where he expressed ...
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0answers
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Is the speed of Magnetic field infinite?

My real question is: From Amperes law we know that there is no magnetic field outside of the coaxial cable because the magnetic field generated by the inner wire and outer shell are equal but in ...
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1answer
133 views

Why does time slow down ONLY for objects travelling at high speeds?

Today in physics class, we learned about the theory of relativity and how it relates to time dilation. We were given the example of two photon clocks- one stationary relative to the Earth, and the ...