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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Twin Paradox, calculating spacetime intervals from both perspectives

I've very recently started to try to understand special relativity. I'm want to get a decent understanding of the twin paradox. I'll post what I've done so far and highlight what's gone wrong for me. ...
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Velocity of an object undergoing homogenous acceleration

So I was considering the following problem within the context of Special Relativity: Given an object O, with initial velocity v, undergoing constant acceleration at a rate of a, I want to express the ...
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Why is ${\partial^i}{\partial_i\phi}$ = ${\partial^i {\phi}}{\partial_i{\phi}}$?

This notation can be found on page 254 of Victor Stenger's Comprehensible Cosmos and in David Tong's Lectures on QFT (Equation 2.4 http://www.damtp.cam.ac.uk/user/tong/qft/two.pdf), and in EDIT: on ...
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Is there a subtlety to the Lorentz transformations one needs to be aware of?

Playing around with the four acceleration $$\left(\gamma^4_u \frac{\vec a\cdot\vec u}{c^2}\vec u +\gamma^2_u\vec a,\, \gamma^4_u\frac{\vec a\cdot\vec u}{c}\right)$$ I found the time part for frame' ...
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Muon demonstration of time dilation

Looking at the second paragraph of page 120 here. Is the half life given measured in the rest frame of the muon? Then the calculation shows that the time to reach sea level from the muon's perspective ...
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What is the universal speed limit relative to? [duplicate]

If all speeds are relative, then what "governing" force is that speed limit relative to? Is there some sort of fixed or absolute grid with locations everything is compared to? Does this also mean ...
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A neutrino has rest-mass and travels at (near) $c$, why isn't its mass/ energy (nearly) infinite?

If the total energy of all three types of neutrinos exceeded an average of 50 eV per neutrino, there would be so much mass in the universe that it would collapse. This limit can be circumvented by ...
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Energy definition in special relativity

I'm going through the early homework assignments for my special relativity course and I've got myself a little confused about energy. I've got a basic understanding of what the 4-momentum is, having ...
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How do we know that photons are exactly massless and travel exactly with speed $c$ in vacuum?

I know that this question may sound stupid, but what I mean is that photons have some energy and no mass, yet the mass and energy are said to be equivalent (or maybe I got that part wrong). In an ...
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Why does a Lorentz scalar field transform as $U^{-1}(\Lambda)\phi(x)U(\Lambda) = \phi(\Lambda^{-1}x)$?

This problem is from Srednicki page 19. Why $U^{-1}(\Lambda)\phi(x)U(\Lambda) = \phi(\Lambda^{-1}x)$? Can anyone derive this? $\phi$ is a scalar and $\Lambda$ Lorentz transformation.
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Deriving the Electromagnetic Tensor

The electromagnetic tensor is given as: \begin{equation} F_{\mu \nu} = \partial_\mu A_\nu - \partial_\nu A_\mu \end{equation} How do you derive this? And how come there is a partial derivative in ...
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Does an accelerating spaceship move backwards due to length contraction?

Let's assume I have a spaceship in front of me let's say at 1000000km distance. Now let's assume I have also a stationary wall just behind the spaceship at 999999km. Initially the spaceship's speed is ...
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A relative time dilation paradox.

Let us assume that there are two astronauts A and B who are floating in space. A sees B passing by and vice versa. A sends signals to B every minute. According to A since B is moving his clock will be ...
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Special relativity version of Feynman's “Space-Time Approach to Non-Relativistic Quantum Mechanics”

I'm looking for an article that sets up the framework described by Feynman in Space-Time Approach to Non-Relativistic Quantum Mechanics, but in Special Relativity.
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How do I describe the order of events in spacetime?

In Newtonian mechanics, we have 3-space and time. Time allows us to order events. For example, I hold a ball in the air at time $t_0$. Then I drop it at some later time $t_1 > t_0$. Finally it hits ...
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Can length contraction really be derived from time dilation? Does speed equal speed?

I am referring to Wikipedia: "Length contraction can also be derived from time dilation." with the following proof which seems to be the result of a circular reasoning. The proof uses only one and ...
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Can lightly-ionized atoms be accelerated to relativistic speeds with current technology?

I know there're lots of various particle accelerators, which can accelerate particles to TeV's of energy, but it seems they all work on electrons or nuclei or other elementary of tightly-bound ...
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Considering the theory of special relativity: Is torque still a vector?

Considering the theory of special relativity: Is torque still a vector? In classical mechanics it is easy: You have 3 axes and thus 3 planes. Every plane has its own torque so torque has 3 ...
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Conservation of 4-momentum in special relativity

I understand that the inner product of two 4-vectors is conserved under the Lorentz transformations, so that the absolute value of the four momentum is the same in any reference frame. This is what I (...
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Does Contraction at High Speeds Happen in Any Dimension Besides Length?

I'm not sure if this is a duplicate. Whenever physics buffs talk about Einstein's relativity (I forget which kind) at high speeds, they always talk about "length contraction", or shortening of the ...
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Challenge: Answer this gedanken (PFP - Perpendicularly Fired Photon)

I'm challenging anyone who can answer the following question objectively: As usual, imagine a railway station and trains which are equipped with single photon sources (one each in the platform and ...
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Why is causality preserved in special relativity?

PART 1: I was reading the article Relativity of simultaneity Wikipedia. I couldn't understand this line: "if the two events are causally connected ("event A causes event B"), the causal order is ...
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Lorentz invariance of the action for free relativistic particle

I tried to check the Lorentz invariance of the standard special relativity action for free particle directly: ($c=1$) $$ S=\int L dt=-m\int\sqrt{1-v^{2}}dt $$ Lorentz boost: $$ dt=\frac{dt^{'}+udx^...
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If time slows down when you move faster, does this give you an “effective speed” different from your proper speed?

Suppose you're travelling at 0.9c toward the sun, and you tag past the Earth and start a clock. Would Lorentz contraction/time dilation cause you to get to the sun faster than (about) 9 minutes (...
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The real meaning of time dilation

Is this true or false: If A and B have clocks and are traveling at relative velocity to each other, then to B it APPEARS that A's clock moving slower, but A sees his own clock moving at normal speed. ...
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Special Relativity: Transforming Maxwell's equations

I'm working through Einstein's original 1905 paper*, and I'm having trouble with the section on the transformation of Maxwell's equations from rest to moving frame. The paper proceeds as follows: ...
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What is the relativistic action of a massive particle?

all Lorentz observers watching a particle move will compute the same value for the quantity $$ds^2 = -(c \, dt)^2 + dx^2 + dy^2 + dz^2,$$ $$ds^2 = g_{\mu\nu}dx^{\mu}dx^{\nu},$$ and ''ds/c'' is then ...
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Is there any law that prevents an object with mass to become massless?

I got into a discussion with my physics teacher about the speed of light and I asked What if an object with mass was to lose mass as it gained speed-- would that allow for an object to eventually ...
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Minkowski diagram and length contraction

The length contraction means that an object is the longest in the frame in which it is at rest. Lets assume i have a meter stick with length $\Delta x$ in my rest frame which is $x,ct$ and i want to ...
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Stanford: “Objects in spacetime all move at constant speed $c$.” Are they right? [duplicate]

In this Stanford University lecture on Relativity, it is stated: Likewise, objects in spacetime all move at constant speed c in spacetime but if you change its direction, say by moving at speed v in ...
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Why light moves sideways?

Greatings! I'm trying to understand special relativity and have one question bugging me. In almost every book or video about the subject there is a thought experiment with moving light clock. I hope ...
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Photon Emission/Absorbsion from the Photons Perspective [duplicate]

First some assumptions. 1) Photons travel at the speed of light. 2) From the photon's reference spacetime is contracted to 0 length in the direction of photon travel. 3) From the photon's reference ...
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Faster than light signals and the price to be paid if we accept them : a very simple protocol

Some physicists currently understand entanglement as transferring information instantaneously, yet not violating causality. Is this really a satisfactory explanation, or should be look for something ...
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Are virtual particles limited by the speed of light? [duplicate]

I have recently been reading about Quantum Electrodynamics which I found very interesting, but even more confusing. I understand photons mediate the electromagnetic force and interactions between ...
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How does a single charge produce magnetic field?

I have studied in Introduction to electrodynamics (Griffiths) that magnetic field is actually due to effects of relativity unequal Lorentz contraction of the positive charge and negative lines, a ...
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Consider relativity. If a stick accelerates from a stationary state, how will it look like during the acceleration?

I mean how it will be shortened in the sight of an observer in a stationary coordinate system. It seems I was not clear enough. If the stick becomes shorter, then while this is happening, the ...
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How much could one slow down aging using existing spacecraft?

Imagine that I board a spacecraft and head away from the Earth at top speed until I've aged twenty years, then I turn around and come back. How much younger will I be than the unexciting folk who hung ...
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Is it ok to have two events $A$ and $B$ so that for one person $A$ occurs before $B$ but for another $B$ preceds $A$

Imagine two laser beams A and B are released at the same moment to bounce between two mirrors, A was moving and B was at rest, doing the calculations I found that for a person at rest B would reach ...
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Time dilation formula and example

What is the time dilation formula by constant velocity? Is the right formula $$t'=t\times \sqrt{1-v^2/c^2}$$ or is it $$t'=\frac{t}{\sqrt{1-v^2/c^2}}$$ ? And can someone show me a computational ...
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Relativistic transformation of the wave packet length

Let us suppose we have an excited atom at rest. It has a certain mean lifetime $\tau_0$. If we wait sufficiently long time $t>>\tau_0$, we will find a deactivated atom and a (spherical) ...
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whats the rate of energy increase required for constant acceleration between 0.0c and 0.99c?

I was wondering how much energy would be required to accelerate 1000kg to 0.99c at 1G. What I don't understand is what the rate of increase of energy is required as velocity increases. I was looking ...
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Why is travelling around the speed of light a problem?

I don't fully understand what would happen if we could travel at the speed of light. But I saw somewhere here that it would mean events happen out of order. But why is this a problem. It is said that ...
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Why $x=-ct$ line in a spacetime diagram?

I can understand why the $x=ct$ line is needed as follows: If $c \Delta t \geq \Delta x$ then the event can be causally related to your current position, so the event could not appear in reverse ...
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Why is the Mixed Faraday Tensor a matrix in the algebra so(1,3)?

The mixed Faraday tensor $F^\mu{}_\nu$ explicitly in natural units is: $$(F^\mu{}_\nu)=\left(\begin{array}{cccc}0&E_x&E_y&E_z\\E_x&0&B_z&-B_y\\E_y&-B_z&0&B_x\\E_z&...
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Is this a Lorentz-scalar? How do I tell?

I'm struggling to identify whether a scalar is a Lorentz-scalar. E.g: $$\partial_i A^i \quad i \in {1,2,3}.$$ How do I determine if this is a Lorentz-scalar or not? If got the same problem with ...
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Massless particle that have momentum not equal to 0

I saw some problems in special relativity that use conservation of total energy and momentum and the conclusions are spectacular. My problem is the following: how can a massless particle like neutrino ...
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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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Why does the Michelson-Morley experiment only contradict the aether?

This question is related to Validity of Maxwell's equations with no aether or relativity? (so please read this first). In this question, the answers seem to suggest that getting rid of the aether ...