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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A point on a disc travelling at the speed of light [duplicate]

This might be a duplicate of this. I had an interesting thought experiment: suppose that you have a disc of a 1 m radius, where a point P2 inside the disc travels at the speed of light. You have a ...
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Rotations acting on quantum states

Suppose I have a free relativistic massive particle described by a state $|p,\sigma\rangle,$, with $p^\mu=(p^0,0,0,p^3)$, so that $P^3|p\rangle=p^3 |p,\sigma\rangle$ and $J_3|p,\sigma\rangle=\sigma|p,\...
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86 views

If photons travel at the speed of light how can they ever be destroyed? [duplicate]

If photons travel at the speed of light than due to relativity they must experience no time frame in which to be destroyed in the first place so they must be immortal which is silly. So, clearly I am ...
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What type of fields are continuous spin representations?

Continuous spin representations (infinite dimensional representations of the Lorentz group) are pretty rarely discussed, and usually not in that much mathematical details. And usually it is done in a ...
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Deriving Fizeau's velocity equation with special relativity

I can't get to the equation Fizeau found experimentally, $u = \frac{c}{\mu} + v(1-\frac{1}{\mu^2})$, Using special relativity. In particular, where does that minus sign come from?! I have done: $$ \...
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46 views

special relativity mirror experiment

There's an experiment in special relativity that involves a light source and a mirror, both placed in a moving object. It is used to derive the time dilation equation. I'm having serious doubts about ...
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2answers
61 views

How can photon have wave properties if they travel at the speed of light? [duplicate]

I am not a physicist so please excuse me if this is a dumb question. As far as I understand Relativity, as observer (in this case a photon) travels at the speed of light, time stops. So how can the ...
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Can we produce energy from pure substance having considerable mass? [closed]

According to Einstein's formula, $E=mc^2$. Any substance which has mass can be converted into energy or energy is also existing in the form of mass. So I am very much interested to build a machine ...
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If E= hv then E= mc2 then h=mc2/v! [closed]

E= pc (1) = hv (2), p= mc (3) From (1) and (2): c= hv/p (4) We put (4) in (3): p=hv/p.m => p2=hvm (5) If we use E=hv in (5) we will get: E= p2/m (6) We use (3) in (6) we will get: E= mc2 From ...
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1answer
86 views

Derivation of Lorentz Transformations

How can I derive the Lorentz transformations? I don't want to use hyperbolic functions and the fact that the light waves travel by forming spherical wavefronts. Is there a way to derive the Lorentz ...
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2answers
89 views

How can we know that the speed of light is constant?

Science say that within a constant time frame the light travels a constant distance. But if time is relative how can it be possible to use it as a reference to say that something is constant?
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1answer
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Do we have rest mass according to quantum physics? [closed]

I know wave must be in motion and resonant waves are actually in motion. So I don't understand what is a rest mass of a particle. If a particle is just a wave in a particular field, it should be ...
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1answer
47 views

4-Gradient Lorentz Transformation

I am currently studying the behavior of a scalar field $\phi$ under a Lorentz transformation $\Lambda$. However I am having trouble understanding why the following holds true: $$\partial_{\mu}\left(\...
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0answers
7 views

Head-on collision near lightspead [duplicate]

Assume two objects moving near light-speed (for this experiment let's say $0.9c$) towards each other. The speed is measured from an observation platform at the collision point (as I understood ...
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1answer
44 views

Does momentum scale linearly with time, assuming a constant nonzero net force, even at relativistic speeds?

I would expect it to, since you'd think the loss of velocity due to relativity would be made up for by the gain in relativistic mass. I'd like this to be confirmed, though. and if so, in whose ...
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1answer
31 views

Differences in notation of momentum 4 vector

I have noticed three ways to write the 4 momentum vectors: $P = (E/c, \vec{p})$ $P = (E, \vec{p})$ $P = (E, c\vec{p})$ I know how to derive equation 1, and as far as I know, one can use the ...
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Dark Matter vs. Mass from Kinetic Energy

I was thinking about dark matter, and was wondering if the extra mass due to kinetic energy has been taken into account. Here's what I mean: let's talk about any cosmological object that is known to ...
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1answer
87 views

If photons end up having a tiny mass, say $10^{-54}~\rm kg$, what would be the universal speed of massless particles?

First, I'm no expert so sorry if I get anything confused but I tried to research as much as could before asking this. So while it is pretty much accepted that photons are massless (Despite this ...
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1answer
133 views

Obtaining the temperature from Bose-Einstein and Fermi-Dirac distribution

Lets say you are given a distribution function $f(p)$ and you want to define a temperature, $T_f$, for this distribution. (I assume $\mu = 0$.) It is then natural to define a temperature the ...
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1answer
119 views

Parallel axes between inertial frames in Special Relativity

In "CLASSICAL ELECTRODYNAMICS" by J.D.Jackson, 3rd Edition , $\S$ 11.3, the author gives in equation (11.19) a generalization of Lorentz transformation as follows : If the axes in K and K' remain ...
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1answer
36 views

Is proper time and proper length relative or absolute in relation to two events?

This question concerns with a problem encountered when doing a question on special relativity. A scenario in which the question is based will be described and the problem will be explained. Scenario: ...
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2answers
229 views

How is 4-current a 4-vector?

I am looking at Jackson sec 11.9, where he states that the $\rho,\bf{J}$ form the 4-current $$J^\alpha=(c\rho,\bf{J})$$ Jackson says this is from the invariant of the 4-divergence $\partial^\alpha ...
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119 views

How to interpret Hermann Minkowski's comments on the construction of spacetime

What did Minkowski mean by his statement: "The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are ...
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Applications of octonions in special relativity?

According to the Wikipedia article on octonions: Octonions [...] have applications in fields such as string theory, special relativity, and quantum logic. However, I couldn't find any ...
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Fierz identity for chiral fermions [closed]

First of all I define the convention I use. The matrices $\bar{\sigma}^\mu$ I will use are $\{ Id, \sigma^i \}$ where $\sigma^i$ are the Pauli matrices and $Id$ is the 2x2 identity matrix. I will use ...
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Is the time dilation experiment for real?

A popular experiment is described in books on special relativity, that claims that an atomic clock was flown at high speed and later compared with a similar atomic clock on earth, and it was found ...
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What particles travel near the speed of a photon? [closed]

I know photons travel at the speed of light. How does the size of a particle determine its maximum velocity? Phonons, Preons, Electron ect. Is there a scale in from the smallest particle's maximum ...
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2answers
95 views

Why does Special Relativity apply to more than just light?

It is my understanding that time dilation is derived from the constancy of the speed of light in vacuum. I would assume this implies that the quirky consequences would therefore apply only to light. ...
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Relativistic Mass and Potential Energy

In the chapter 16–4 of the Feynman Lectures, Feynman employs a thought experiment to explain why "if two particles come together and produce potential or any other form of energy; if the pieces are ...
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2answers
58 views

Pole and Barn Paradox w/ Spacetime Interval

I'm having trouble with a pole and barn paradox problem. The problem is as follows: A pole vaulter is running with a pole at $ v=\frac{\sqrt3}{2}c $. Her pole has a proper length of $L$. She runs ...
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Colliding beams vs static target

In this problem I need to find the threshold energy of a positron-electron collision that creates a Z boson (the reverse of the following picture; Z mass 92 GeV) in two distinct cases: collision ring ...
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Am I just some energy traveled at light speed? [closed]

I don't understand $E=mc^2$ very well, and here is my question: Does this equation mean masses are just condensed energy? And does this mean that the extra energy an object has when traveling at ...
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1answer
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Einsteins theory of relativity and formula of kinetic energy [duplicate]

After seeing both Einstein's theory of relativity ($E=mc^2$) and the formula of kinetic energy (K.E=$\frac{mv^2}{2}$), I noticed that that they are mostly the same, with the only difference that ...
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Is the helicity of photon Lorentz invariant? [closed]

If the helicity of a photon is $+1$ in an inertial frame, then is the helicity of this photon $+1$ in another inertial frame? The helicity operator is $$ h=\mathbf{S}\cdot\hat{\mathbf{p}} $$ with $$ ...
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1answer
76 views

Where is the mistake in the following rationament [duplicate]

Well... kind of hard to translate in English so bare with me :). Let's consider a wheel that spins in the void. Each point of the wheel has the speed $v = ω r$. That means that for any $ω$, there is ...
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Nature of light in Special Relativity

What is the nature of light in the context of Special Relativity? Is it a photon, or an electromagnetic wave, or something else? I have doubts, because a photon seems to me a quantum mechanical ...
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69 views

Is time a coordinate or a parameter in Newtonian mechanics?

In classical (Newtonian) mechanics we only ever seem to consider 3-dimensional space, with physical quantities being represented by 3-vectors. My understanding for this is because in classical (...
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2answers
51 views

Motivation for usage of 4-vectors in special relativity

I understand that if one considers a 4-dimensional space-time from the outset then 4-vectors are the natural quantities to consider (as opposed to 3-vectors as in Newtonian mechanics), since the ...
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1answer
67 views

Relativistic correction to Hydrogen atom - Perturbation theory

Given the relativistic correction $$ H_1' = - \frac{p^4}{8m^3 c^2} $$ to the Hamiltonian (i.e. a perturbation), what does it mean when $[H_1', \mathbf{L}] = 0$? The book I'm reading says this implies ...
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63 views

Galileo's ship experiment with a laser pen instead of a rock

Ship's mast experiment with the boat moving at speed v: If a rock is dropped from the mast, then for an observer inside the boat they will see this: For an observer outside the boat and on the ...
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Speed of the Coulomb Field Measured To Be “Infinite”

The paper "Measuring Propagation Speed of Coulomb Fields" by R. de Sangro et al points out that: ...the Lienard-Weichert retarded potential leads to the same formula as the one obtained assuming ...
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1answer
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Momentum equation of a beam hitting a stationary target to create antiprotons

I'm struggling with the solution of a physics exercise which is to calculate the minimum energy needed to create antiprotons when a proton beam scatters on a stationary proton target: $$p + p \...
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Zeroth component of 4-momentum and relativistic energy-momentum relation

As I understand it one is forced to use 4-vectors since we require objects that transform as vectors under application of Lorentz transformations and 3-vectors do not (technically they do under ...
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1answer
81 views

Homogeneity and isotropy and derivation of the Lorentz transformations

In deriving the Lorentz transformations I have found (from reading a few different sets lecture notes) that it is argued that they must be linear and thus there general form must be $$x'=Ax+Bt,\quad t'...
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31 views

Inertial coordinate systems [duplicate]

In Newtonian mechanics, by the following two assumptions: (i) The time is absolute. (ii) The length is absolute. it is easy find the relations betweem two coordinate systems with uniform motion ...
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Definition of the Lorentz transformations [closed]

Until very recently I believed that the Lorentz transformations were defined as "the transformations that carry one inertial reference frame into another". In Wikipedia's page we find something along ...
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Path integral (sum over paths where $v>c$) [closed]

The path integral formalism is used to get for example the propagator of particles. In this formalism we integrate over all mathematically possible paths (and weight them with the non-relativistic ...
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2answers
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How do we determine if a certain physical quantity is a vector?

For instance in Newtonian physics we treat position of objects, displacements, velocities, forces, momenta, angular velocities etc all as vector quantities (little arrows in space which have a certain ...
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3answers
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Frames of reference, relativity, and a ball thrown in the air

Ever since my high school physics days I found relativity fascinating but I don't think I have great insight even into special relativity. For example, in almost every lesson or video they give an ...
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5answers
503 views

Can one deduce absolute motion through magnetism? [closed]

I am trying to understand forces in relativity: Suppose there are two electrons A , B travelling side by side at 1 cm distance at .99 c (in space or at lHC, ignoring all other factors). I know that ...