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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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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Why does an object with higher speed gain more (relativistic) mass? [duplicate]

Today, in my high school physics class, we had an introductory class on electromagnetism. My teacher explained at some point that an object with a very high speed (he said it started to get somewhat ...
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Why a hole in the Dirac sea can be seen as having opposite energy?

In the Dirac's old attempt of relativistic quantum mechanics, a hole in the $E'$ level of the Dirac sea was interpreted as a particle of opposite charge and positive energy. I do get why it can be ...
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148 views

How does it seem to be that space/time always equals $c$?

Given the way objects move, they seem to be going all the same "velocity" so to speak, that velocity being the speed of light. Except, velocity is displacement/time, so if something goes faster, the ...
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How is the Photoelectric Effect affected by Blue-Shifting

I was thinking about the Photoelectric Effect and Blue-Shifting when I came up with a thought experiment that I couldn't think of an answer for. The thought experiment is as follows: A metal plate is ...
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Poincare invariant Lagrangians

The Lagrangian density of a Poincare invariant theory should not depend explicitly on the space-time coordinates. Does this mean $$ \partial_\mu \mathcal{L}=0~? $$ If this is the case doesn't the ...
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685 views

Why magnetic field lines and force are not orthogonal with magnets?

The below explanation why magnetism exists is superb in this video. The explanation about magnets is also great in this video. A magnet has atoms with unpaired electrons forming mini magnets. The ...
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Is it okay to Wick rotate to give the negative of the Euclidean metric? Also, could we make the space-like coordinates imaginary instead?

There are 2 parts to my question: 1) Say we choose the metric signature to be (-+++), as in the Wikipedia page. Then the invariant interval in Minkowski space is written: $ds^{2} = -(dt^{2}) + ...
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Show: Lorentz-invariance of solution of Klein-Gordon equation [closed]

Assume $\psi$ is a solution of the Klein-Gordon equation (KGE). Let $\Lambda$ be a Lorentz transformation. Show: $\phi = \psi(\Lambda^{-1} \cdot )$ is also a solution of the KGE. I try to ...
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Special relativity and massless particles

I encountered an assertion that a massless particle moves with fundamental speed c, and this is the consequence of special relativity. Some authors (such as L. Okun) like to prove this assertion with ...
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Why does weak equivalence principle say gravity is equivalent to acceleration?

I am told that the weak equivalent principle, that $m_i=m_g$ (inertial and gravitational masses are equivalent) is equivalent to the statement that in a small system you can't tell whether you are in ...
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How fast must Nadia travel so that she is the same biological age as her twin upon returning to Earth? [closed]

Two twins, Nadia and Aidan, decide to have an adventure when they turn 21. Aidan chooses to travel to a distant star 10 light years away at a speed of 0.8c. Nadia decides to travel to a closer ...
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Electromagnetism in flat space

I want to get a deeper understanding of how Electric and Magnetic fields transform under Lorentz transformation. That is how to start from gauge transformation of Electric and Magnetic fields $$E= ...
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53 views

First variation of the action in relativistic notation - Landau & Lifshitz “Classical theory of fields”

In Landau & Lifshitz's book, Classical theory of fields, the action for a free particle is defined as: $$\tag{8.1} S= \int ^b _a {-mc \ \text d s}=0,$$ where $$\text d s=c\,\text d ...
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The variation of the Lagrangian density under an infinitesimal Lorentz transformation

I'm trying to introduce myself to QFT following these lectures by David Tong. I've started with lecture 1 (Classical Field Theory) and I'm trying to prove that under an infinitesimal Lorentz ...
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152 views

Nature of Fields in QFT

I'm not exactly an expert in quantum physics, but this seems to be a simple question, and I can't find an answer anywhere! There are specific types of fields used in physics: scalar fields (i.e. as ...
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Relation involving the Lorentz transformation and the inverse of its transpose

The relation I was referring to in the title is $${\Lambda_a}^b= \eta_{ac} {L^c}_d \eta^{db}$$ where ${\Lambda_a}^b$ is the inverse transpose of $L$, the Lorentz transformation. I was wondering ...
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In QFT, why do fermions have to anticommute in order to insure causality?

I have seen this question and I believe I understand the answer to it. However, AFAIK, only for bosons the causality condition is a vanishing commutator. For fermions we expect the anticommutator ...
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A whole lot of doubts on Lorentz representation

Can someone tell me in layman's language how the $(1/2,1/2)$ represents a vector field and $(0,1/2)$ or $(1/2,0)$ represents spinors and $(0,0)$ represents scalar field. Please don't be pedantic on ...
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Time dilation confusion

I'm just starting to learn about special relativity, and I'm a little bit confused about something. Take the example of an observer in $S$ on the ground observing a train move at constant velocity $v$ ...
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Navigating a Time Machine

Notes: The background for this question is working out details of a sci-fi story. Answers to the effect of "time travel isn't possible" or "FTL isn't possible" are therefore not helpful. I'm looking ...
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Rotational symmetry in integration

Can someone please tell me why $$4\int d^4x \, x^\mu x^\nu ~=~\int d^4x \, g^{\mu\nu}x^2 $$ by some rotational symmetry argument?
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Time Dilation Problem [closed]

I'm having some trouble using the time dilation formula. Say an astronaut leaves Earth for 10 years, at 0.85c. How much time has passed according to an observer on Earth? I tried using the ...
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Should I abandon my thought experiment about time?

I'm trying to think about special relativity without "spoiling" it by looking up the answer; I hope someone can offer some insight - or at least tell me I'm wrong. Suppose I have an ordinary clock ...
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Does time dilation correct for the Doppler effect?

Knowing that a body in motion experiences time dilation, "also" knowing when two objects travel at a great speed away from one an other, both observers experience the others clock as moving slower ...
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Lightspeed (invariance) measurement methods

I would like to know, how measurements of the speed of light are conducted these days, especially in the context of the invariance of $c$. Do all the methods involve mirrors to redirect the photons ...
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Is the energy of momentum stored physically? [closed]

While an object is moving, relativity will say it weighs more, especially so as it approaches light speed. The increase in energy is then easily sensed as an increase in mass (Almost as a rock in ...
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How can one always be standing still when compared to the speed of light?

I was thinking if I built a device with 7 clocks, synchronized to each other, one in the middle, one up, down, left, right, behind and in front of me, say 1 meter away, and I fired a laser from the ...
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460 views

What happens if someone travelling just under the speed of light makes a telephone call?

Apart from the possibility that radio transmission will not work, what would happen if someone travelling fast enough relative to another individual to experience significant time dilation made a ...
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Can the equivalence principle be shown to follow from special relativity?

Einstein showed in various papers that the energy content of a body was a measure of its inertial mass. If you increase the internal energy of a system while keeping the center of energy at rest, its ...
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Is special relativity a special case of general relativity, qualitatively?

Since Einstein name his theory Special Relativity and General Relativity, there should be some expected relationship between them, particularly "Special Relativity" being a special case of the more ...
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368 views

Special Relativity, 2nd Postulate — Why? [duplicate]

As a lowly physics undergrad who has been chewing on this 2nd postulate of special relativity for a year or more, I simply can't wrap my head around reasons why it is true or how Einstein might have ...
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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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Energy-Momentum Tensor under Lorentz Transformation

In relativity, the symmetric energy-momentum tensor is given by $$ T^{ij}, $$ where $T^{00}$ is the energy density and $\frac{1}{c}T^{10}$ is the momentum density. Thus: $$ \left(\frac{1}{c}T^{00}dV, ...
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Spin in relativity

Mass and spin of the particle are used in classification of elementary particles. The mass is defined to be a Lorentz invariant quantity. On the other hand, the spin is a spacelike 4-vector and cannot ...
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Is Kinetic Energy stored as mass?

I know that if some object acquires potential energy, it also gains mass- is it the same for kinetic energy?
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Why is there a controversy on whether mass increases with speed?

Some people say that mass increases with speed, some people say that the mass of an object is independent of its speed. I understand how some (though not many) things in physics are a matter of ...
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Is it possible for information to be transmitted faster than light by using a rigid pole?

Is it possible for information (like 1 and 0s) to be transmitted faster than light? For instance, take a rigid pole of several AU in length. Now say you have a person on each end, and one of them ...
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What problems with Electromagnetism led Einstein to the Special Theory of Relativity?

I have often heard it said that several problems in the theory of electromagnetism as described by Maxwell's equations led Einstein to his theory of Special Relativity. What exactly were these ...
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Do photons change velocity instantaneously?

Any object traveling at c is observed as traveling at c in all reference frames. When a photon travels through a vacuum at c, all reference frames observe it traveling at c. When a photon passes ...
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Can acceleration feel like constant gravity for indefinitely long?

So here's the setup: I'm in a spaceship, without windows as always, and the ship is accelerating upwards at a constant rate of $1\,\text{g}$. So inside the spaceship it feels like I'm being pulled ...
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4-vector velocity to Newtonian?

The four-vector condition for a particle free of forces is: $\frac{du}{dτ} = 0$ and the equivalence of this to the statement of newton's first law follows from the expression for four-velocity: ...
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Relativistic Conservation laws [closed]

Conservation of Relativistic mass and thus energy is easily proven by considering an inelastic collision of two bodies while invoking the conservation of momentum. As such the momentum law appears ...
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Status of experimental searches for tachyons?

Now that the dust has settled on the 2011 superluminal neutrino debacle at OPERA, I'm interested in understanding the current status of experimental searches for neutrinos. Although the OPERA claim ...
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Is negative mass for a bound system of two particles forbidden?

Is there any theorem that forbids the bound system of two massive particles to have negative mass?
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Why are objects at rest in motion through spacetime at the speed of light?

I read that an object at rest has such a stupendous amount of energy, $E=mc^2$ because it's effectively in motion through space-time at the speed of light and it's traveling through the time dimension ...
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106 views

Refractive index of dielectric in different frames of reference

The setup A transparent isotropic dielectric medium moving in the negative $x'$ direction at speed $v$ in frame $S'$ is stationary in frame $S$, where it has refractive index $n$. In other words, ...
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Minkowski spacetime vs Euclidian space

Two questions marked in bold: What is the magnitude of a Minkowski spacetime four velocity? I'm deducing that it is c for all observers, but I'd like it confirmed. In Euclidian space, a velocity ...
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Are Lorentz transformations linear transformations? [duplicate]

My textbook says that Lorentz transformations are linear transformations and present them as matrices. Lorentz transformations relate different coordinate systems with each other. It seems that ...
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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?