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 do we use the complexification of the Lorentz group?

I do understand why we are using the double cover, but why exactly do we make the transition to complex Lorentz transformations? Where and why are they needed? To be precise: The double cover of ...
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Trying to rhyme Peskin and Schroeder with Weinberg

This is a follow up question of this one. In the Vol 1, Weinberg derives how a unitary operator $U(\Lambda)$ acts on one-particle states, which is given by equation (2.5.2): \begin{equation} ...
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Question about Weinberg's derivation of a one-particle states under the Poincare group

I'm reading QFT: Vol 1 by Weinberg and I have a (perhaps trivial) question about a statement he makes on page 63. I can follow him to his derivation of equation (2.5.2): \begin{equation} P^\mu ...
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Spinor formalism in QFT

We can describe fields by two formalisms: vector and spinor. This is the result of possibility of representation of the Lorentz's group irreducible rep as straight cross product of two $SU(2)$ or two ...
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Why does Lorentz factor not hold for relativistic mass when we apply it to photons? [duplicate]

We know that the photon itself is massless particle $m_0=0$. But we also know, that the mass of the objects does increase with their energy. And we know that under certain circumstances (gravity, ...
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Relativistic Doppler effect derivation

This is about a step in a derivation of the expression for the relativistic Doppler effect. Consider a source receding from an observer at a velocity $v$ along the line joining the two. Light is ...
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Special Relativity - speed of light question

Just a basic question: I know that if you are traveling at $x$ speed the time will pass for you slower than to an observer that is relatively stopped. That's all just because a photon released at the ...
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114 views

particle accelerator in space

I'm attempting to learn special relativity and i'm having trouble calculating velocity and momentum for each part of the system after interactions. I wanted to know how fast a linear accelerator and ...
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Why is energy-momentum 4-vector so much easier to explore/observe than spacetime 4-vector

I have read that spacetime 4-vector is quite difficult to observe/explore and that energy-momentum 4-vector is much more appropriate for CERN etc. Why is that? Could anyone give me a brief ...
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deriving a Lorentz transfomation for velocity vector components

If $S'$ and $S$ are two different inertial reference frames and $S$ moves along the $x$ axis of $S$ in a standard configuration, then the Lorentz transformation will be: $$x'=\gamma(v)[x-\beta ct]$$ ...
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Time dilation $t'=(1-\frac{v}{c})t$ instead of $t'=\frac{1}{\gamma} t$

Suppose we have a train moving. When the origin of train's frame coincides with the origin of observers frame; the the time is set to zero. At that very instant, a photon is emitted from train towards ...
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An accelerating and shrinking train in special relativity

Suppose when a train is at rest, it has a length of $L$. Let the position of the back of the train at any time be $A$, and let the position of the front of the train at any time be $B$. Now assume ...
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Does the sign of $\Delta x$ matter in this time dilation calculation?

I cannot for the life of me figure out what I am doing wrong with this problem: If a high speed particle travels a distance of 39 Km with a half life of 1 micro sec, what must its speed be to travel ...
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Lorentz Invariance of Maxwell Equations

I am curious to see a simple demonstration of how special relativity leads to Lorentz Invariance of the Maxwell Equations. Differential form will suffice.
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Einstein's Famous Thought Experiment Contradiction

Putting Special Relativity into the General Relativity category as is current practices submerges important aspects of Einstein's 1905 paper, which I recently read in a 1952 Dover paperback (The ...
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Do we need a quantum theory of gravity in order to describe photons blueshifted past planck energy?

If yes, then how does this accord with relativity: the laws of physics are the same in all reference frames? We can move from a reference frame in which the photon has near zero energy density, to a ...
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How to theoretically define a concrete operation to perform in order to measure the length of an object?

EDIT: Some answerers pointed out that the title of this question is in contrast with what is actually been asked in the body of the question, so I changed the title accordingly. The original title was ...
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If the vacuum is not “emptiness” why the speed of the electromagnetic wave is independent of the frame of reference?

If the vacuum were "emptiness" it were easy to accept that there is no "preferred frame of coordinates" and the light velocity is the same in any inertial frame of coordinates. But the vacuum is an ...
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Energy-Time Uncertainty Principle and Photons

Heisenberg's uncertainty principle states that: $$ \Delta E \cdot \Delta t \ge \frac{\hbar}{2} $$ It is clear that this has nothing to do with the accuracy of our measurements, but rather is a ...
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When talking about atomic mass, how is $E=mc^2$ factored in? [duplicate]

When talking about atomic mass in the periodic table of elements, is this number the mass of the element at rest? If I understand correctly, the (relativistic) mass of an element will increase as the ...
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Mathematical Definition of Locality

What is the mathematically precise definition of principle of locality in physics for a continuous space-time in the sense that an object is only directly influenced by its immediate surroundings?
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131 views

Magnetic force as a relativistic effect?

There is something I am confused about when it comes to the force between two parallel wires carrying current, specifically why when they carry current in the same direction the wires are always ...
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82 views

How does EM radition depend on the reference frame?

In special relativity, magnetism is electrostatics in a different reference frame. This is how we explain the magnetic field being produced by moving charges (aka currents). Charges that move produce ...
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Does a moving object really shrink due to length contraction? [duplicate]

Is length contraction an optical illusion? Does object really shrink? Though measurements say yes, does it really happen? Or I have to say object is really measured to shrink?
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Timelike curves in Special Relativity

I have a question that probably might sound silly to most of you. We know that a natural Lorentz-invariant parametrization of a timelike curve is provided by: $$\tau$$ the Lorentz-invariant proper ...
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Special Relativity Question: Doppler shift

Imagine an observer watching a moving rocket carrying on it both, a light source and a clock. If on the rocket the clock is synchronized with the frequency of the light being emitted then will not a ...
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108 views

Coulomb's Law- Why the Coulomb's law is valid only for point and static charges?

Why the coulomb's law is valid only for point and static charges? Is there is any definite reason?
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Inertial frames

I'm just starting my study of relativity, and I have a rough understanding of the connection between inertial frames, newton's laws, and galilean transformations, but I'd probably benefit more if ...
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Would an object lose physical mass if it accelerated to a relativistic speed (would an object burn it's own mass)?

First of all, I have read other questions, and seen how an object gains mass just by gaining a lot of speed. But here, I am talking about losing some of that mass to convert the value into kinetic ...
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44 views

What is the status of massless photons traveling through a medium?

Photons in vacuum have no proper time, and they are not considered as observers and not as reference frame. But what about photons travelling through matter? Their velocity is lower than light speed, ...
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Verification of the Poincare Algebra

The generators of the Poincare group $P(1;3)$ are supposed to obey the following commutation relation to be verified: $$\left[ M^{\mu\nu}, P^{\rho} \right] = i \left(g^{\nu\rho} P^{\mu} - g^{\mu\rho} ...
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GPS Satellite - Special Relativity

I'm going through an old relativity assignment, and I've been asked to calculate the time dilation for a satellite which orbits the earth in 12 hours at 26000km from the surface, and travels at a ...
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Light cone and order of events?

If one event lies outside the light cone of another, can the events to some observers appear in a different order in one reference frame compared to the other, and is this the only time when this is ...
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Tensors in special relativity [duplicate]

I'm trying to understand tensors, but I've come across the following question: Let $T^{\mu\nu}$ by a $(2,0)$ tensor. Give the definitions of $T_\mu^{\,\nu}$, $T_{\mu\nu}$, and ...
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Arguments for finite speed of physical processes

When beginning a study of the special theory of relativity, one discovers that the theory of special relativity has as an axiom that the laws of physics are invariant with respect to transformations ...
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Why does the light intensity increase as I approach a distance light source?

Analogy: assume that I have constant rain fall and I have a water bucket to collect this rain. If I am rest relative to the earth, I will catch a certain amount of rain. However, if I now move towards ...
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Help with Special Relativity velocity addition formula

While looking for question about speed of light I saw this Physics.SE question where I found this: $$v_\text{rel} = \frac{v_1 - v_2}{1 - \frac{v_1v_2}{c^2}}.\tag1$$ But in another answer there was ...
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Do hot objects moving at relativistic speeds slow down as they emit radiation?

In an astrophysics class I learned about the Poynting-Robertson effect, by which grains of dust orbiting a star slow down and eventually fall into the star. Every source that I have been able to find ...
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Integral Over Hypersurface Simplification

How does one see it as obvious that $$\int_S \frac{\partial A_i}{\partial x^j} dS^{ji} = \int_S\frac{1}{2}(\frac{\partial A_j}{\partial x^i} - \frac{\partial A_i}{\partial x^j})dS^{ij}$$ where $d ...
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Distance Between Two Photons Calculated in Different Inertial Frames

I am a self-studier. This is a question from a text I am studying: The distance between two photons traveling along the $x$-axis of an inertial frame, $S$, is always $l$. Show that in a second ...
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324 views

Relativistic Elastic Collision

I am having trouble getting my head around the transfer of energy in a relativistic elastic collision. My understanding of a relativistic elastic collision is one in which the total rest mass on each ...
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Learning the stress-energy tensor

I am learning dynamics in special relativity and come across the stress-energy tensor. I have real trouble understanding it. I would love answers on How to motivate the definition of this tensor. ...
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Units in time dilation calculation

I am currently working through Brian Greene's "World Science U" course on special relativity, and I have a question regarding one of the calculations performed for an exercise on time dilation (MODULE ...
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127 views

Does the light speed change in media? [duplicate]

Does the light speed change? The Theory of Relativity says that the speed of light in vacuum is the same and unchangeable, while I read that the speed of light in glass is lower than in air, and that ...
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140 views

Is time dilation an illusion? Variation on the twins paradox [duplicate]

Consider the twins paradox with a slight variation: Twins A and B are in separate space ships both capable of going at the speed of light instantly (i.e. without any acceleration). Both ships are ...
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Understanding the operation of Thomas precession

How can we physically understand the operation of Thomas Precession? This modifies the effective energy of coupling between the spin and the orbital angular momentum of the electron by an extra factor ...
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Does the speed of light in different mediums affect the lorentz transformation?

We know that the Lorentz transformation is derived using the speed of light in vacuum. But if we were to use it in water, would it change since the speed of light in water should also remain constant ...
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Time dilation and relativity

We've just started with relativity and I got a question regarding an exercise we got. A spaceship passes by earth on its way to planet X, at the moment it passes by Anna is born on the spaceship. Can ...
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Because position is relative, is it possible to see a star orbiting a planet? [duplicate]

Position is relative, as it depends on the reference frame. We usually visualize the sun at the center of the solar system. BUT, we can also visualize the Earth at the center of the solar system, ...
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Lorentz boost matrix in terms of four-velocity

As I understand it, the value of a 4-vector $x$ in another reference frame ($x'$) with the same orientation can be derived using the Lorentz boost matrix $\bf{\lambda}$ by $x'=\lambda x$. More ...