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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Minkowski Metric Signature

When I learned about the Minkowski Space and it's coordinates, it was explained such that the metric turns out to be $$ ds^{2} = -(cdx^{0})^{2} +(dx^{1})^{2} + (dx^{2})^{2} + (dx^{3})^{2} $$ where $ ...
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Potential energy in $E_f^2=(mc^2)^2+(pc)^2$?

Let's consider $$E_f^2=(mc^2)^2+(pc)^2$$ where the $mc^2$ is the rest energy due to the rest mass -- in Finnish "lepomassa". $$ \sqrt{(mc^2)^2+(pc)^2} - mc^2~=~(\gamma-1)mc^2$$ is the kinetic ...
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Lay explanation of the special theory of relativity? [closed]

What is Einstein's theory of Special relativity, in terms a lay person can follow?
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What happens when relativistic effects stop?

I'm currently learning special relativity in high school and we only primarily deal with what happens when an object is moving at constant relativistic speeds. But what if the object slowed back down ...
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Is Minkowski space usually a vector space or an affine space?

When I visited Wikipedia's page on Minkowski space, it seemed to offer two definitions. The first defined Minkowski space a vector space. Then, in a later section, it says The section above ...
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Does the discreteness of spacetime in canonical approaches imply good bye to STR?

In all the canonical approaches to the problem of quantum gravity, (eg. loop variable) spacetime is thought to have a discrete structure. One question immediately comes naively to an outsider of this ...
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Why is the space-time interval squared?

The space-time interval equation is this: $$\Delta s^2=\Delta x^2+\Delta y^2+\Delta z^2-(c\Delta t)^2$$ Where, $\Delta x, \Delta y, \Delta z$ and $\Delta t$ represent the distances along various ...
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Are Classical Field Theory and Quantum Mechanics of a single particle (nonrelativistic or “classical”) limits of Quantum Field Theory?

Recently I talked about QFT with another physicist and mentioned that the Quantum Field Theory of a fermion is a quantisation of its one-particle quantum mechanical theory. He denied this and ...
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How does $E=mc^2$ put an upper limit to velocity of a body?

How does $E=mc^2$ put a upper limit to velocity of a body? I have read some articles on speed of light and they just tell me that it is the maximum velocity that can be acquired by any particle. How ...
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Reconciling Minkowski and 3+1 view of special relativity

I am having some trouble reconciling the Minkowski (4-dimensional) and the pre-Minkowski (3+1-dimensional) approach to special relativity. Let me describe (how I interpret) the Lorentz transformations ...
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Is there any theorem that suggests that QM+SR has to be an operator theory?

UPDATE To make my question more precise, I'll define what I mean by an operator theory: An operator theory is a theory in which the dynamical objects are operators, i.e., the equations of motion ...
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Boosts are non-unitary!

The boost transformations are not unitary unlike rotations, the boost generators are not Hermitian. When this induces transformations in the Hilbert space, will those transformation be unitary? I ...
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Why don't electromagnetic waves require a medium?

As I understand it, electromagnetic waves have two components which are the result of each other, i.e., when a moving electric charge creates a changing magnetic field at point X then a changing ...
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Why is pseudorapidity defined as $-\log \tan \theta/2$

Why the log? Is it there to make the growth of the function slower? As this is a common experimental observable, it doesn't seem reasonable to take the range from $[0,\infty)$ to $(-\infty,\infty)$ ...
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The Euler-Lagrange equation in special relativity

How can I derive the Euler-Lagrange equations valid in the field of special relativity? Specifically, consider a scalar field.
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Distance in relativistic circular motion in invariant spacetime

I understand that the closer something travels to the speed of light, that time will stretch by a factor, and distance will compress by the same factor. My question is, if something travels in a ...
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The Lagrangian in Scalar Field Theory

This is perhaps a naive question, but why do we write down the Lagrangian $$\mathcal{L}=\frac{1}{2}\eta^{\mu\nu}\partial_{\mu}\phi\partial_{\nu}\phi - \frac{1}{2}m^2\phi^2$$ as the simplest ...
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Maxwell's Equations using Differential Forms

Maxwell's Equations written with usual vector calculus are $$\nabla \cdot E=\rho/\epsilon_0 \qquad \nabla \cdot B=0$$ $$\nabla\times E=-\dfrac{\partial B}{\partial t} \qquad\nabla\times ...
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Is acceleration relative?

A while back in my Dynamics & Relativity lectures my lecturer mentioned that an object need not be accelerating relative to anything - he said it makes sense for an object to just be accelerating. ...
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Relativistic centripetal force

The thought randomly occurred to me that a circular particle accelerator would have to exert a lot of force in order to maintain the curvature of the trajectory. Many accelerators move particles at ...
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Is causality a formalised concept in physics?

I have never seen a “causality operator” in physics. When people invoke the informal concept of causality aren’t they really talking about consistency (perhaps in a temporal context)? For example, if ...
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The choice of measurement basis on one half of an entangled state affects the other half. Can this be used to communicate faster than light?

It is often stated, particularly in popular physics articles and videos, that if one measures a particle A that is entangled with some other particle B, then this measurement will immediately affect ...
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Identification of the state of particle types with representations of Poincare group

In the second chapter of the first volume of his books on QFT, Weinberg writes in the last paragraph of page 63: In general, it may be possible by using suitable linear combinations of the ...
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Vector spaces for the irreducible representations of the Lorentz Group

EDIT: The vector space for the $(\frac{1}{2},0)$ Representation is $\mathbb{C}^2$ as mentioned by Qmechanic in the comments to his answer below! The vector spaces for the other representations remain ...
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The equivalent electric field of a magnetic field

I know that Lorentz force for a charge $q$, with velocity $\vec{v}$ in magnetic field $\vec{B}$ is given by $$\vec{F} =q \vec{v} \times \vec{B}$$ but there will exist a frame of reference where ...
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Rigorous definition of frame of reference

I'm looking for a mathematical definition of frame of reference. Most of the textbooks I have seen take it for granted and they just refer to some set of spacetime coordinates. A more mathematical ...
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Can a spinor be defined as any quantity which transforms linearly under Lorentz transformations?

Recently I’ve come across a few papers from China (e.g. Xiang-Yao Wu et al., arXiv:1212.4028v1 14 Dec 2012) that make the following statement: ...any quantity which transforms linearly under ...
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Is there a relativity-compatible thermodynamics?

I am just wondering that laws in thermodynamics are not Lorentz invariant, it only involves the $T^{00}$ component. Tolman gave a formalism in his book. For example, the first law is replaced by the ...
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Understanding the “$\pi$” of a rotating disk

Let us say you are in an inertial reference frame with a circular planar disk. If you take your meter measuring rods (or perhaps tape measure) you can find the diameter and circumference of the disk. ...
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What are the consequences of relativistic angular velocities?

If I take a rod of some radius $r$ and length $L$, and I spin this rod with angular velocity $\omega$. How would the geometry of the rod appear to an observer as one converges to $c$? What are the ...
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The origin of the value of speed of light in vacuum

Meaning, why is it the exact number that it is? Why not 2x10^8 m/s instead of 3? Does it have something to do with the mass, size or behavior of a photon? To be clear, I'm not asking "how we ...
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How does Newtonian gravitation conflict with special relativity?

In the Wikipedia article Classical Field Theory (Gravitation), it says After Newtonian gravitation was found to be inconsistent with special relativity, . . . I don't see how Newtonian ...
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Could any object have zero mass? [duplicate]

Energy and mass are interrelated. As everything has energy could any object be massless? For example a photon is a packet of energy but still it is considered to be a massless particle. Why is it so?
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Is there a fourth component to the electric field and magnetic field?

The Question If the three vector electric and magnetic fields come from the four component four-potential, then is there a fourth component to the electric and magnetic field? Related Question I ...
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Is a photon “fixed in spacetime”?

From what I've read, according to relativity, a photon does not "experience" the passage of time. (Can we say there is no past/present/future for a photon?) Would it be better to say a photon is ...
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What does it mean when physical theories are inconsistent?

I am hoping that someone can explain in layman terms why Newtonian mechanics and Maxwell's equations are inconsistent. Wikipedia says that this inconsistency is what led to the development of ...
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Why is the ratio of velocity to the speed of light squared in the Lorentz factor?

Why is the ratio of velocity to the speed of light squared in the Lorentz factor? $${\left( {{v \over c}} \right)^2}$$ My only guess is the value must be positive.
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Why does the Lorentz transformation in special relativity have to be like this?

Basically I think Albert Einstein (A.E.) was trying to find a transformation that: Always transform a constant-velocity movement into a constant-velocity movement. Always transform a ...
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Can something travel faster than light if it has always been travelling faster than light?

I know there are zillions of questions about faster than light travel, but please hear me out. According to special relativity, it is impossible to accelerate something to the speed of light. However, ...
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Why isn't there a limit for a Euclidean rotation, as for a Minkowski rotation?

From invariance of the Minkowski scalar product, we get the Lorentz transformations. In addition, we get a constant $c$ preventing space-like and time-like intervals being rotated into one another. ...
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Generators of Poincare Groups

How can I determine the generators of the Poincare Group, $P(1,3)$ explicitly? Here $P(1,3)$ means a matrix Lie group.
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Do you encounter more photons (per unit time) when moving forwards at a constant velocity?

Let's say you have rain hitting you evenly on all sides (not very realistic, I know). If you were to move forwards at a constant speed, there would be more droplets of rain hitting you per second on ...
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Time travel outside of light cone without causality violation

If one is able to travel into the past but at a spatial distance that puts him outside of his own past light cone would this be considered a causality violating trip? Looking at a Minkoski diagram, it ...
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Lorentz Invariant Integration Measure [closed]

When we canonically quantize the scalar field in QFT, we use a Lorentz invariant integration measure given by $$\widetilde{dk} \equiv \frac{d^3k}{(2\pi)^3 2\omega(\textbf{k})}.$$ How can I show that ...
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Deriving the action and the Lagrangian for a free point particle in Special Relativity

My question relates to Landau & Lifshitz, Classical Theory of Field, Chapter 2: Relativistic Mechanics, Paragraph 8: The principle of least action. As stated there, to determine the action ...
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Help Me Gain an Intuitive Understanding of Lorentz Contraction

I'm having a hard time getting an intuitive understanding of Lorentz Contraction. I understand what it is by definition but I don't 'get it.' I'm not a physicist, just an amateur, so sorry if this ...
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Poincare group vs Galilean group

One can define the Poincare group as the group of isometries of the Minkowski space. Is its Lie algebra given either by the equations 2.4.12 to 2.4.14 (..as also given in this page - ...
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Is Einstein's Special Relativity completely inclusive of Newton's 3 laws of motion?

Relativity has always been explained to me (in books I've read, etc) as a superset of newton's laws - that is; it encapsulates all of Newton's mechanics in addition to other effects (observer effect, ...
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Has relativity of simultaneity been directly observed?

I know that thought experiment about trains when a flash of light in the middle reaches the both end simultaneously for a passenger but different times for the bystander. So were there (non-thought) ...
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Why is the stress-energy tensor symmetric?

The relativistic stress-energy tensor $T$ is important in both special and general relativity. Why is it symmetric, with $T_{\mu\nu}=T_{\nu\mu}$? As a secondary question, how does this relate to the ...