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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Information, entanglement and EPR

I'm currently trying to understand why superluminal information transport is not possible. Therefore, I would like to get some help concerning the definition of information or the general setting. ...
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When particle number can change in quantum physics?

Let me write a paragraph from D.Tong lecture notes on QFT-chapter2 when he is talking about non-relativistic limit of scalar quantum field theory : A related fact is that the conserved charge $Q=\...
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675 views

How can we show that the speed of light is really constant in all reference frames?

I had a debate with a friend who cannot believe that the speed of light is constant. He said something like: so what if in the Michelson-experiment the moving apparatus simply added a constant ...
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Composition of Lorentz Transformations

If a particle is moving in the $x$-direction with velocity $c/2$, then the Lorentz transformation $\Lambda = \begin{pmatrix}\gamma & -\beta \gamma & 0 & 0 \\ -\beta \gamma & \gamma &...
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Where are all the slow neutrinos?

The conventional way physicists describe neutrinos is that they have a very small amount of mass which entails they are traveling close to the speed of light. Here's a Wikipedia quote which is also ...
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213 views

What's the max speed a man-made satellite can travel in space before its circuitry stopped working?

Assume it could withstand extreme temperatures in either direction. I'm mainly curious what would happen to its circuits as it approached the speed of light.
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71 views

Four Vectors in SR and QFT

I'm covering both special relativity and quantum field theory in the summer. I'm currently using Spacetime Physics by Taylor and Wheeler to cover SR. Since I'm covering SR on the side with QFT, I'm ...
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345 views

Why Do Glueballs Have Mass, When Individual Gluons Are Massless?

From Wikipedia Glueballs Glueballs are predicted by quantum chromodynamics to be massive, notwithstanding the fact that gluons themselves have zero rest mass in the Standard Model. Glueballs with ...
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1answer
152 views

Invariance in Euclidean and Minkowski spaces

Consider Wick's rotation from Minkowski to Euclidean space in QFT. What is the connection between O(4) invariance in Euclidean space and Lorentz invariance in Minkowski space? If we define a quantity ...
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Is it possible that all “spontaneous nuclear decay” is actually “slow neutrino” induced?

This thought was inspired by a comment from the current leading answer, by @Sentry, to the question Where are all the slow neutrinos? This [slow-neutrino induced nuclear decay] will still be an ...
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1answer
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In Einstein's “relativity of simultaneity” thought experiment, would not the passenger on the train see a dimmer signal? [closed]

This is the updated, more precise question--is this a paradox?: Suppose a rocket traveling close to the velocity of light which emits a single photon from its midpoint at point A, illustrated ...
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3answers
298 views

How is time not a constant?

I am a visual person, so it's hard to imagine the information I keep getting, but shouldn't time be a constant? If you were traveling at the speed of light and your able to cover $299{,}792{,}458$ ...
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Why did Einstein retain the hypothesis of length contraction?

Why did Einstein retain the hypothesis of length contraction, which Lorentz introduced to save his æther theory, yet Einstein had no need to accept length contraction because he rejected the æther?
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Relativistic effects

When are relativistic effects justifiably negligible? (I know that that is true for 'small velocities', but how small is 'small enough'?) 0.1c, 0.01c, etc.? And how does one properly justify that? I ...
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1answer
110 views

What does it look like for a ball falling to the event horizon observed by distant static observer?

Here is the picture used in susskind&Lindesay's book ''An Introduction to Black Holes, Information and String Theory Revolution'' I understand very well that the ball will be contracted at the ...
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1answer
140 views

Does speed in space really matter?

This is about validating the science from a science fiction novel. My understanding is that speed is all relative. So while I am in a car on the freeway my speed relative to another passenger is ...
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1answer
37 views

What exactly were the “asymmetries which do not appear to be inherent in the phenomena” in Einstein's 1905 SR paper?

The first ¶ of Einstein's "On the Electrodynamics of Moving Bodies" says (my emphases): It is known that Maxwell's electrodynamics—as usually understood at the present time—when applied to moving ...
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1answer
352 views

Time-reversed twin paradox [closed]

This started with wondering about the nature of certain physical quantities under time-reversal - chiefly, that acceleration retains its magnitude and direction at a given time regardless of the '...
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1answer
73 views

What is the meaning of a (1/2, 1/2) representation?

A spin-1 representation is equivalently a (1/2, 1/2) representation of the Lorentz group. Does this mean we are summing together two irreducible representations labelled by the 'quantum number' a 1/2 ...
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5answers
806 views

With respect to what can't we travel at the speed of light? [closed]

According to theory of relativity the speed of light in vacuum is ultimate. But since objects move relative to each other, with respect to what can't we travel at the speed of light?
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Space travel and time dilation

I want to know how long it takes, from an observer in a spaceship moving at constant velocity $v=\beta c$, to cover a distance $d$. From a stationnary observer outside, the spaceship goes at a ...
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0answers
122 views

Why does the clock work slowly at higher speed? [duplicate]

I know nothing about relativity but I cannot accept that there is a phenomenon called time dilation. However I have no problem with it because of mathematics behind it. I have no problem if time is ...
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1answer
39 views

Why we assign a rotation transformation and not any other when we derive Lorentz factor

I can't truly understand why when we derive Lorentz factor we should assume that the transformation of coordinates is rotational one. In the book "Relativity demystified" they say that: "In some ...
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1answer
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What happens in this collision? [closed]

First, I describe a simple contraption. Second, I describe a simple collision. Third, I replace a box in the collision with the contraption and ask whether, "What happens after the collision?"-i.e., "...
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What is the matrix representation of the momentum operator (generator of translations) that is used in the commutators of the Poincaré Group?

So the commutators of the Poincareé group are given by \begin{eqnarray} [J_{i},P_{j}]=i\epsilon_{ijk}P_{k}, \quad [J_{i},J_{j}]=i\epsilon_{ijk}J_{k}, \quad [J_{i},K_{j}]=i\epsilon_{ijk}K_{k}, \quad [...
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268 views

Doppler effect of matter waves

We all know that the relativistic mass of a moving object in Special relativity increases for an observer who is measuring it for a moving object. We also know the the concept of particle-wave ...
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1answer
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Conceptual interpretation of the left- and right-handed spinor representations of the Lorentz group

I understand mathematically that the Lorentz group's Lie algrebra $\mathfrak{so(3,1)}$ (given by eqns. (33.11)-(33.13) in Srednicki's QFT book) is isomorphic to $\mathfrak{su(2) \times su(2)}$ (given ...
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Relative speed of two space ships moving at speed of light [duplicate]

If two space ships sped away from each other at the speed of light, would they be moving at twice the speed of light away from each other?
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3answers
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Isn't the “constant speed of light” postulate valid also for sound waves?

The second postulate of Special Relativity says: As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the ...
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Atomic Weight and Time Dilation

So, this might sound kind of ridiculous but I was thinking about Relativity and since Gravity is a warping of Space-Time, or Time Dilation, why don't we measure Atomic Mass in Units of Time Dilation? ...
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1answer
42 views

Two-dimensional momentum

Suppose a particle travels with velocity $v$ in both the $x$ and $y$ direction. Its velocity along the $x$-$y$ line is $\sqrt{2}v$. Its momentum along the $x$-$y$ line is $$p_{xy} = \frac{\sqrt{2}v}{\...
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Can relativistic mass be treated as rest mass?

In what real sense does the mass of an object increase with its speed? When we learn that the mass of an object increases according to the equation, $$m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}$$ We ...
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Derivation of force law in special relativity

I've seen force defined in special relativity as the rate of change of 4-momentum $$ {\bf{F}} = \frac{d {\bf{p}}}{dt} $$ Can anyone comment on the following derivation of that relation? Take one ...
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Time Dilation of one frame wrt other

Suppose A and B are two objects , with B travelling at some constant velocity v wrt A. After B covers some distance, A(the person in A) notes in his clock as 30sec elapsed. Then from A's perspective, ...
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Why doesn't the relativistic formula for momentum appear consistent with collisions?

The relativistic formula for momentum is $$p = \frac{mv}{\sqrt{1 - \dfrac{v^2}{c^2}}} \,.$$ In the following example, I apply the formula in the most basic way possible to the addition of velocities. ...
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1answer
165 views

Why do we add gamma to derive the Lorentz transformation?

As set up and described by Professor Shankar, I was trying to derive the Lorentz transformation with his equations... $$\frac{t'}{t} = \frac{c-v}{c},\qquad \frac{t}{t'} = \frac{c+v}{c}$$ After adding ...
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What is the resolution of this Lewis-Tolman like paradox?

Though my question stands on its own, here is a brief overview of a well-explored question which I think might be helpful in finding the resolution to my question. The Lewis-Tolman Lever Paradox has ...
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2answers
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Is measure relative velocity the same for both observer n particle

A particle is moving at velocity v. A stationary observer tries to measure its velocity. From the observer reference frame, he will measure a shorter distance travel as compared to what the particle ...
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1answer
72 views

What do things move relative to?

When someone says that a spacecraft in otherwise empty space is traveling at a constant velocity of 10 km/h (for the sake of convenience) then what is the reference point for which this measurement ...
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1answer
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Can molecules/atoms/any subatomic particle cause space time curvature?

Space-time curvature is caused by huge objects in space like black holes, merging black holes, or planets. This curvature is what causes gravity. Can molecules cause at least a really tiny curve ?
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Lorentz Invariance of Entropy

So I am working on Relativistic Thermodynamics and I have skimmed through a few papers by Hamity, Callen, etc. People are not in agreement as far as I know, but I don't understand why people don't ...
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One particle states in an interacting theory

Question: What is the general definition of one particle states $|\vec p\rangle$ in an interacting QFT? By general I mean non-perturbative and non-asymptotic. Context. 1) For example, in Weigand'...
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92 views

Reciprocal Time Dialation in Special Relativity [duplicate]

I'm trying to understand theory of special relativity, but there is one thing that really makes me confused which is reciprocal time dilation in special relativity. In special relativity, the time ...
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3answers
63 views

Why is speed defined as coordinate derivative over proper time rather than observer's time in STR?

In special theory of relativity, why is 4-velocity defined as: $$ u^\mu = \frac{dx^\mu}{d\tau} $$ and not as $$ u^\mu = \frac{dx^\mu}{dt} $$ where ${\tau}$ is proper-time and t is time in some ...
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Idea of Covering Group

$SU(2)$ is the covering group of $SO(3)$. What does it mean and does it have a physical consequence? I heard that this fact is related to the description of bosons and fermions. But how does it ...
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195 views

Plane curve transform to moving inertial system coordinates

As a non-phycisist I hope my question makes sense and is understandable. It deals with special relativity. I suppose there is a e.g. plane curve ( e.g. a circle ) given in the x-y plane of of an ...
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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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Construction of vector bundles of relativistic fields by Mackey's method of induced representation

I recently stumbled on Sternberg's book on group theory and physics. The ideas expressed in the book are really great, but the detailed reasoning is very hard to follow, I find. I am kind of stuck ...
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Does the use of $\gamma=\left(1-v^{2}/c^{2}\right)^{-1/2}$ automatically assume a (+ - - - ) metric? [closed]

In Special Relativity, does the use of $\gamma=\left(1-v^{2}/c^{2}\right)^{-1/2}$ automatically assume a (+ - - - ) metric convention? For introductory textbooks, the Lorentz factor is is always ...