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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Relativity on a universal scale

Imagine there was a clock on a planet the same size as earth, travelling at the same speed through space, and that this planet was at the most distant part of the universe from earth. If we had a ...
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49 views

Why does $k^z/E$ have dimensions of inverse velocity rather than velocity?

I'm studying quantum field theory and I want to prove the cross section. In Peskin's book, equation 4.77 says that: $$ \frac{1}{\left | \frac{k_{A}^{z}}{E_{A}}-\frac{k_{B}^{z}}{E_{B}}\right |}=\frac{...
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74 views

Special relativity: is this a known paradox, or one at all?

Two ships of the same proper length $L$ move towards each other, as in the diagram below (which shows it in the reference frame where the ship at the left is at rest). The fronts (noses) are pointing ...
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33 views

Lorentz contraction (or not) of an accelerated electron bunch

It's a well-known fact from special relativity that moving objects are subject to a length contraction: an object with a proper length $L_0$ moving at a high velocity $v$ will appear to a stationary ...
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1answer
28 views

Anti-commutator relation of supercharges

Reading mutiple references on SUSY (e.g. Baer and Tata's Weak Scale SUSY and A SUSY Primer by S.P. Martin, arXiv:hep-ph/9709356), there seems to be different anti-commutation relation conventions for ...
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Does $E=mc^2$ mean that an object with mass $m$ travels at the speed of light in empty space? [closed]

I cannot wrap my head around this (Im new to physics), and this concept is troubling me. I think no, but im not sure why?
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1answer
62 views

If we traveled at almost the speed of light would objects appear the same?

We see objects with our eyes as object emits/reflects light. Say if we travel at almost the speed of light can we see the objects normally?
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1answer
111 views

Is there a physical upper limit on how fast a physical object can rotate?

Objects can not travel faster than the speed of light. Angular velocity is $\omega = \frac{s \times v}{|s|^2}$ It seems to me that for infinitely small objects (like electrons) there is no limit on ...
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1answer
164 views

The norm of the vector sum of two 4-momentum vectors before and after pair production

Two photons traveling along the x-axis (in a lab frame of reference) of different frequencies are about to collide. Their 4-momentum vectors are (h$\nu_1$/c , h$\nu_1$/c , 0, 0) and (h$\nu_2$/c , -h$\...
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2answers
68 views

Difference between KE “relativistic” mass and heat mass

I have been told in several answers that the term "relativistic mass" is no longer considered adequate wrt. the mass/energy increase in KE. Yet, I read that 1 Kg of gold's mass ingreases by 10^-14 Kg ...
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1answer
144 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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50 views

Difference between space of reference and system of coordinates

In the book "The meaning of the relativity" by A. Einstein, it is referring to two different concepts: space of reference and system of coordinates. What it is the difference? It says: "we ...
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3answers
96 views

What is meant by rest in rest-mass?

As far as I know only photons are considered to have no rest-mass. In common words when it doesn't move it 'disappears'. Electrons and quarks should have a rest-mass. But are they really at rest? ...
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2answers
75 views

The criteria of light

My question is regarding if the "speed of light" 299,792,458 m/s should only apply to certain frequencies of light/colors/amplitude and most the medium in which it travels at 299,792,458 m/s . Shouldn'...
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2answers
63 views

Time dilation: time shortest where events occur at same place?

In his book Simply Einstein Richard Wolfson describes time dilation this way: "The time between two events is shortest when measured in a reference frame where the two events occur at the same place." ...
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1answer
41 views

Observer travelling near speed of light observing a laser pointer seeing photons at speed of light?

I'm a little confused by the following classic example about the speed of light being constant for all observers (paraphrasing): Jack and Jill are both travelling at a significant portion of the ...
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53 views

How do I draw the Minkowski diagram of a event in two inertial systems when t=t'=0?

An Introduction to Mechanics" by David Kleppner & Robert Kolenkow, 1st Edition, 12.1 Assume that v= 0.6c . Find the coordinates in S' of the following events: a). x=4 [m], t= 0[s] b). x=4 [m], ...
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What is relationship between electromagnetic mass and rest mass?

Is there a direct equation which compares rest mass $m_°$ and electromagnetic mass $m_{em}$? Nothing on web I found. $m_{em} = \frac{4 E_{em}}{3c^2}$ 4/3 problem The final solution of the ...
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2answers
164 views

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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1answer
163 views

Relevance of spinor in relativistic (classical) electrodynamics

I'm following a course about relativity and electrodynamics (not the "quantum" one), and the lecture notes introduces the concept of spinor by a map between an orthogonal basis in Minkowski spacetime ...
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2answers
108 views

Is the speed of light constant in all directions?

Consider the shape of the waveform emitted by a moving source: (with the horizontal axis "x" and the vertical axis "y"). According to the stationary observer, the wavefront of a short pulse ...
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Presentism: doesn't everything exist at the same moment? [closed]

The Help Center recommends I 'fix' this question: (original question) "It seems self-evident that everything exist in the Now. Notwithstanding time-dilation and different rates of the passage of ...
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26answers
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Do we know why there is a speed limit in our universe?

This question is about why we have a universal speed limit (the speed of light in vacuum). Is there a more fundamental law that tells us why this is? I'm not asking why the speed limit is equal to $c$...
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2answers
126 views

Special Relativity: Verifying a general boost matrix is in the Lorentz group

I'm attempting the problem shown below. Using the hint, I have so far found: \begin{align}B^T \eta B &= \begin{pmatrix}\gamma & -\gamma\beta^j \\ -\gamma \beta_k & \delta_k^j+\frac{(\...
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If photons can exert a change in momentum when being reflected, what leads us to conclude they have zero mass? [duplicate]

It is well known that gravity affects light. It is also known that light can impart a change in momentum to objects when being reflected. This leads me to think that photons have momentum and ...
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343 views

Time-reversed twin paradox

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
111 views

Action of a massive free point-particle in relativistic mechanics

I was reading about the formulation of mechanics in special relativity and found that the action for a massive free point-particle as $$ S = -mc\int_a^b ds $$ So, I did a few observations, ie. $$ S =...
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Are gravitational time dilation and the time dilation in special relativity independent?

There are two kinds of time dilation: One because the other clock moves fast relative to me (special relativity). Another one because the other clock is in a stronger gravitational field (general ...
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Is Young's Modulus a Lorentz Scalar?

If a spring is at rest and lies along $X$ axis in a frame $O$ with a spring constant $k_{0}$ then its spring constant in a frame $O'$ which is moving with a speed $v$ at an angle $\theta$ with the $X$ ...
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1answer
258 views

Is it possible to determine maximum frequency of a disc using a relative circumference?

On Wikipedia there is an article that shows how to calculate the relativistic effects on a rigid spinning disc, I am referencing the formula under the "Ehrenfest's argument" section in the link. The ...
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3answers
309 views

Speed of Dark experiment, does it *really* travel faster than light? [duplicate]

I have seen many folks doing this Moon shadow experiment concluding that shadow from point A on the Moon can travel to point B on the Moon faster than light. What I fail to understand here (and I am ...
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Can't reach speed of light, but relative to who?

Imagine a stationary person (with respect to a spaceship) floating in space and looks at a clock on the spaceship going 0.5c and sees it's clock ticking slower than his own, and concludes that it is ...
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Were the Michelson-Morley results a surprise?

How unexpected were the Michelson-Morley experiment results? Did physicists have theoretical reasons to predict that the speed of light would result to be invariant?
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Spacetime and quantum mechanics

In special relativity, the particle has a fixed world line in spacetime. So its whole trajectory is determined. But how can we represent the world line of the particle in spacetime when we take ...
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37 views

A photon lives life as a flat-lander? [duplicate]

Think length contraction... I was thinking about going close to the speed of light the other day, and I was thinking about the idea that, if you went close to the speed of light, time would slow down ...
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Why are usually 4x4 gamma matrices used? [duplicate]

As far as I understand gamma matrices are a representation of the Dirac algebra and there is a representation of the Lorentz group that can be expressed as $$S^{\mu \nu} = \frac{1}{4} \left[ \gamma^\...
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1answer
52 views

Why shift in fringe is expected in Michelson Morley Experiment?

When I (beginner) learnt Michelson Morley experiment, it was expected that there should be a shift in the fringe pattern when the setup was rotated by 90 deg if the presence of ether is true. But why ...
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1answer
35 views

Is an extended spring gain mass from potential energy? [duplicate]

Is it true that when a spring is extended, potential energy is stored in spring and result in gain of mass of the spring?
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1answer
90 views

SR and a rotating observer [closed]

What if an observer took a particle placed it some distance away from himself and began to circle the particle approaching the speed of light. Would the observer himself observe that the circle is ...
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97 views

Conservation of linear momentum (classical mechanics and special relativity)

How did Newton deduce the law of conservation of linear momentum? Can it be derived only by Newton's laws, or does it follow from practical experiments? If the law of conservation of linear momentum ...
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0answers
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A question from “The meaning of the relativity, by A.Einstein” - Lorentz transformations [duplicate]

Let $K$ and $\bar K$ be two cartesian co-orditate systems in $\mathbb{R}^3$. The element: $$s^2=(\Delta x^1)^2+(\Delta x^2)^2+(\Delta x^3)^2$$ is an invariant in all co-ordinate system. I want prove ...
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How does the speed of light affect energy? [duplicate]

According to Einstein's theorem E=mc2, energy equals to product of mass and speed of light. How does the speed of light affect energy? If it is so, then why is the specific value for the speed of ...
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2answers
53 views

Electric field around a moving charge

A moving charge has magnetic field around it. Is it just increased electric field in relativistic frame? If yes, does a moving charge has more electric field around it?
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1answer
46 views

Lorentz transformation and symmetries of the Lagrangian [duplicate]

Since the Lagrangian of our quantum field theories is covariant under Lorentz transformations I'm asking myself if there is any link to some symmetries (like that we get from gauge transformations ...
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2answers
91 views

Relativistic Rocket Fuel Requirements

I am trying to reconcile two different calculations of fuel for a 1g constant acceleration/deceleration trip to Alpha Centauri. One found here (http://math.ucr.edu/home/baez/physics/Relativity/SR/...
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1answer
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Wave operator applied to electromagnetic field tensor

I'm trying to understand an argument in "An introduction to general relativity" by Hughston and Todd (p37). Let $F_{ab}$ be the electromagnetic field tensor, I'm trying to show: $$\Box F_{ab} = -4 \...
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Relativity paradox with mirrors and light pulses

Consider two very short light pulses emitted from the centre (C) of two mirrors A and B (as shown in the diagram). From the point of view of the lab frame, the apparatus is all moving to the left at ...