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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Dropping a ball in a train moving close to the speed of light?

Suppose a train is moving very close to the speed of light, say 0.999c relative to a stationary observer on Earth. Now a stationary observer on Earth will observe clocks on the train to tick slower ...
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Apparent velocity of an approaching object

What would be the apparent velocity of an object approaching us at an actual velocity of $v$? I know $cv/c-v$ is a possible answer but here's another argument - shouldn't the velocity be the Doppler ...
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All possible electromagnetic Lorentz invariants that can be built into the electromagnetic Lagrangian?

Given the electromagnetic Lagrangian density $$ \mathcal{L}~=~-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}~=~\frac{1}{2}(E^2-B^2) $$ is a Lorentz invariant, how many other electromagnetic invariants exists that ...
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147 views

Has QFT successfully mediated between QM and Special Relativity?

I understand that QFT is the theoretical framework for combining QM and Special Relativity, but as I understand it, though even without proof or experimental confirmations; has QFT managed to "behind ...
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A question about relativistic spin operator

The question comes from Ryder's Quantum Field Theory, 2nd edition. The author was looking for relativistic spin operator. It was concluded that it cannot be $J^2:=\mathrm{J} \cdot \mathrm{J}$, where ...
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127 views

Theoretical Upper Bound on Processor Speed?

Barring aside considerations such as heat dissipation, capacitance, etc... (aka any sort of technological issue) what is the fastest speed of a processor? I am told that at distances of 1 planck ...
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1answer
138 views

Lorentz transformation - need a little clarification

So the question states: A's and B's systems are related by the standard Lorentz transform. B simultaneously fires off two photons from transmitters distance D apart along the x' axis, and in the ...
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1answer
345 views

Minkowski Metric

Hi all I'm a little confused So I have that in special relativity time is included as a coordinate so that in 1 spatial dimension we have 2 space time coordinates. The most basic metric is the ...
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2answers
737 views

2 protons collision (both with different kinetic energies) - I don't know what to put in for $p^2c^2$

The problem statement: Two protons with kinetic energies $W_{k1}=4GeV$ and $W_{k2}=2GeV$ colide and form new particles. What is the mass of newly born particles? There are as many as possible ...
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2answers
261 views

How much faster would a Clock without gravity run?

Pardon the misleading title. It is to my understanding that moving/heavy clocks run slow. The Earth itself is under gravitational influence from many sources, and is moving. Is there a way to know ...
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2answers
6k views

Does inertia increase with speed?

I have heard that when the speed of the object increase, the mass of the object also increase. (Why does an object with higher speed gain more (relativistic) mass?) So inertia which is related to ...
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1answer
134 views

Properties of the Faraday tensor for constant fields

I'm doing a special relativity past exam paper and have got caught up with something that I hope someone can help me with! I have to show that for constant fields, the magnitude of A, the ...
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637 views

Point charge 4-current derivation

How do I derive that the 4-current of a point charge is $$j^{\mu}(x)=ec\int_{-\infty}^{+\infty}\dot{z}^{\mu}(s)\delta(x-z(s))ds$$ where $\dot{z}^{\mu}(s)$ is the 4-velocity of the charge and $s$ is ...
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1answer
163 views

Lorentz invariance of the wave equation

I want to show that the 2-d wave equation is invariant under a boost, so, the starting point is the wave equation $$\frac{\partial^2\phi}{\partial x^2}=\frac{1}{c^2}\frac{\partial^2\phi}{\partial ...
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1answer
488 views

Does special relativity unify the two phenomena at the base of Faraday's flux law (was Feynman wrong in this case)?

Consider Faraday's flux law for the EMF generated in a conductor loop: $$ \varepsilon = - \frac{d \phi}{dt},$$ where $\varepsilon$ is the EMF, and $\phi$ is the magnetic flux through the loop. ...
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Is it part of special relativity that mass possessing energy is more dense?

I was reading http://www.edge.org/3rd_culture/hillis/hillis_p2.html and it says that a charged battery weighs more than a dead one or a rotating object weighs more than a stationary one (i.e. mass ...
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1answer
1k views

Minkowski diagram, hyperbola and invariant quantity of relativity

I have heard of the invariant quantity $\Delta s$ in relativity for which I have stumbled upon an equation $\Delta s^2 = \Delta x^2 - c \Delta t^2$. This reminds me of hyperbola, which has general ...
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1answer
55 views

Testing covariance of an expression?

This is something I've been unsure of for a while but still don't quite get. How does one tell whether an expression (e.g. the Dirac equation) is covariant or not? I get it for a single tensor, but ...
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What is the relativistic calculation of travel time to Proxima Centauri?

It has already been asked here how fast a probe would have to travel to reach Alpha Centauri within 60 years. NASA has done some research into a probe that would take 100 years to make the trip. But ...
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1answer
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Is it best to look at light as a particle when trying to understand special relativity?

So my course about special relativity explains time dilation using a moving train, where one sends up (i.e. perpendicular to the direction of movement) a light pulse which gets reflected etc. (a ...
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195 views

Which new insight did $E=mc^2$ give us?

I had a special relativity course at university. Now I'm trying to extract what new insight $E=mc^2$ did give us. I mean that moving mass has/is energy (kinetic) not new. The energy merely changed ...
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513 views

Einstein Relative Motion and Time Order of Events

According to Einstein, do observers in relative motion agree on the time order of all events? I don't think they would agree on the timing of events, but I am having trouble figuring out why they ...
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761 views

How is this classical “paradox” resolved in electromagnetism?

A magnet and a coil move relative to each other. In the frame of reference of the magnet, there is a magnetic field and consequently a force acting on the charges in the coil according to the Lorentz ...
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1answer
167 views

Kinetic energy transfer in matter annihilation?

What happens to the kinetic energy of matter when it is annihilated? Is it released in the resultant explosion? In that case shouldn't it be $E=(mc^2 + \frac{1}{2} mv^2)$ ?
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Do the particles that were found to break the speed of light really break Einstein's theory of relativity? [duplicate]

Possible Duplicate: What would be the effects on theoretical physics if neutrinos go faster than light? Update: Loose cable caused faulty results Apparently, researchers at CERN have found ...
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1answer
348 views

speed of light flashlights question

This might be a silly question but I take the risk because it's been puzzling me for quite some time : If you have 2 flashlights, one facing North and one facing South, how fast are the photons (or ...
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338 views

Physical interpretation of equation for relativistic aberration

I'm working in a book on relativity. The author states that if $u$ and $u'$ are a velocity referred to two inertial frames with relative velocity $v$ confined to the $x$ axis, then the quantities ...
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32 views

Available energy in centre of mass system

The problem given is "A proton of total energy 3GeV makes a head-on collision with a 5GeV electron. Calculate the available energy in the centre-of-mass system to create any new additional particles ...
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1answer
49 views

Is there any way to justify or derive the form of the Lorentz force from relativity theory?

Lorentz force is in this form: $$\vec{F}=q[\vec{E}+\vec{u}\times\vec{B}]$$ As we know, it is Lorentz-invariant. Is there any way to justify or derive its form from relativity theory?
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Relativity of simultaneity subtle example [closed]

imagine three persons, Person A is standing next to a device these device is an AND gate if two photons(one from right and one from left) reaches the AND gate at the same time the device explodes and ...
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1answer
70 views

relativistic addition of velocities using tensor notation? [closed]

I know the way of deriving the formula using usual lorentz transformation formulas,,but is there a way out of deriving it using 4-vector notation??please help
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1answer
65 views

How can parity be meaningful in an affine space?

I've recently begun a course in QFT (within a Physics Master's), and despite (admittedly limited) reading I can't get my head round the idea of parity. Here's what I think I understand: the Minkowski ...
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Deduce time dilation from a Minkowski diagram?

Is it possible to deduce the phenomena of time dilation from a carefully constructed Minkowski diagram? For example, consider the image below. Here, Let us say the Euclidean distance between the ...
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Velocity addition rule in special relativity

I just worked out a problem showing peculiarities of the velocity addition rule in special relativity. This was the statement for the problem: "Nefarious thieves flee the scene of their bank ...
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3answers
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Justification of $P_{\text{photon}}=E/c$ in derivation of $E=mc^2$

I recently was reading up on the derivation of $E=mc^2$. Now, I came across this derivation at this link. I noticed that several lines into the derivation they throw in the equation ...
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Where does the 3-velocity live?

Imagine a four-dimensional affine space $\mathcal{M}$ with the standard metric $\eta = \text{diag} (1,-1,-1,-1)$. Let $\mathcal{C}$ be a worldline of a point particle parametrized by an affine ...
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Two sets of coordinates each in frames $O$ and $ O' $ (Lorentz transformation)

Suppose inertia frame $O'$ is moving at velocity $v$ relative to inertia frame $O$. Let the coordinate systems of $O$ be denoted by $(x,y,z)$ and the corresponding one on $O'$ be denoted by ...
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1answer
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The effects of special relativity when accounting for two reference frames

If reference frame A is travelling past reference frame B could one argue that it is in fact B that is motionless as their motion is relative to each other? If this is the case then how does one ...
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1answer
218 views

What does the ratio $\frac{x-ct}{x'-ct'}$ signify?

$(x,t)$ being coordinates of any event in an inertial frame $A$ and $(x',t')$ being the coordinates of the same event in another frame moving with uniform velocity $v$ along the same direction in ...
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1answer
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Does relativity objectively define entropy?

In his undergraduate text "Spacetime Physics", Wheeler points out that there is always a fourth component to momentum and energy interactions, because the internal motion of the objects involved will ...
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1answer
123 views

How do we know that fundamental constants don't slowly change in time? [duplicate]

Let me get one thing straight first. I am not saying that fundamental constants like the speed of light don't have the value that we know they have today. What I am asking is whether the value of a ...
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Sum according to a function - composition of velocities

An observation more than a question. Take any function $f$ (additional hypotheses may follow) and evaluate it on any two points $x_1, x_2\in\mathcal{D}_f$. Define then the sum of these two points as ...
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1answer
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Analytical mechanics with SR

Is there an analytical mechanics with SR? Of course you can write down the Lagrangian and Hamiltonian of a free particle. What about non-free? Are there any problems? To be specific: what would the ...
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277 views

What can change a photon's frequency?

I found this question: Is it possible to apply force to a light particle? As it states, gravity can change the frequency of light by changing its momentum. My question regards other phenomena that ...
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1answer
94 views

Does scale invariance imply massless or continuous mass distribution?

$\newcommand{\ket}[1]{\lvert #1 \rangle}\newcommand{\bra}[1]{\langle #1 \rvert}\newcommand{\scp}[2]{\langle #1 \vert #2 \rangle}$ In his 2008 slides (PDF), Tzu-Chiang Yuan mentions the following on p. ...
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1answer
138 views

Magnetic monopoles and special relativity

I was thinking about magnetism as a product of special relativity and the result of this approach to the magnetic monopoles. So if magnetism is a product of electricity(like electricity from another ...
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1answer
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Force on a moving charge in relative frame

Consider a particle of charge $q$ moving at velocity, $v$, enters a magnetic field $B$ which is perpendicular to its motion. Now consider two observers, one stationary and the other moving at the ...
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2answers
127 views

Does time dilation imply that events do not take place?

I take two mirrors parallel and facing each other. A light pulse is being infinitely reflected between the two mirrors $M_1,M_2$. $E_1,E_2$ are the events when the pulse is reflected by $M_1,M_2$, ...
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1answer
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Since the Earth is moving through space, do we experience time dilation?

What I mean is, the Earth orbits around the sun at around 30km/s, while I understand that this isn't a very high velocity does time dilation still occur to say a person who is completely stationary in ...
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1answer
90 views

Special relativity and Lorentz transformation

I recently learned about special relativity and different reference frames. The conversion from two inertial reference frames is given by Lorentz transformations: $$x' = ...