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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Intuitive picture for Mandelstam $t$

In tree-level electron-positron scattering one has two possible channels corresponding to Mandelstam variables $s$ and $t$. The $s$-channel ist fine, there $\sqrt s$ is just the center of mass energy ...
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Rotating magnet and magnetic field intensity change?

if magnetic disc is rotating on it's axis super fast and electric field is produced(because of time varying magnetic field),does this means that in the frame of non moving observer magnetic field no ...
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Help needed for Simple derivation for duality of matter

A teacher told showed me a way to derive an equation which shows the duality of matter. We know, $E=hc/\lambda$. and $E=mc^2$ So, $hc/\lambda=mc^2$ We get, $p$ ( momentum ) = $h/\lambda$. How ...
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Time variable in Lorentz transformations

When an object goes with a speed near from the light celerity, it inflates in the direction of its speed. The inflation rate is given by Lorentz transformations as follows: $x'= γ(x-vt)$ where $v$ ...
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Staggered Indices ($\Lambda^\mu{}_\nu$ vs. $\Lambda_\mu{}^\nu$) on Lorentz Transformations

I have some open-ended questions on the use of staggered indices in writing Lorentz transformations and their inverses and transposes. What are the respective meanings of $\Lambda^\mu{}_\nu$ as ...
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How do electromagnetic waves/light travel at the speed of light?

When something reaches the speed of light, then time is said to stop, or at least is perceived to have stopped. The reason is that at that speed, the object become infinitely heavy and requires ...
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Norm of the momentum 4-vector

The norm of the momentum 4-vector is $\mathbf{P}.\mathbf{P}$ $= (\gamma mc, \gamma mv).(\gamma mc, \gamma mv) = \gamma mc^2 - \gamma mv^2$ But why is $\gamma mc^2 - \gamma mv^2 = mc^2$?
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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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4answers
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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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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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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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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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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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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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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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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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Why define four-vectors to be quantities that transform only like the position vector transforms?

A four-vector is defined to be a four component quantity $A^\nu$ which transforms under a Lorentz transformation as $A^{\mu'} = L_\nu^{\mu'} A^\nu$, where $L_\nu^{\mu'}$ is the Lorentz transformation ...
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Is time dilation based on the formula for period of a pendulum?

The theory Albert Einstein put forward about special relativity mentions a possibility for time dilation, in which he states gravity has a considerable effect on time. And in high school physics we ...
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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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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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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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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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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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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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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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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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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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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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Why magnetic field lines and force are not orthogonal with magnets?

The below explanation why magnetism exists is superb in this video. The explanation about magnets is also great in this video. A magnet has atoms with unpaired electrons forming mini magnets. The ...
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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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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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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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Is the rate of light emissions actually the frequency of the light?

I am confusing with the concept of frequency in the context of Doppler effect studying SR. The Schutz says, if the source emits pulses more frequently, then the observer would see the lights not only ...
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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 ...
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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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Point charge 4-current derivation

How do I derive that the 4-current of a point charge is $$j^{\mu}(x)=e\int_{-\infty}^{+\infty}\dot{z}^{\mu}(s)\delta^4(x-z(s))ds$$ where $\dot{z}^{\mu}(s)$ is the 4-velocity of the charge and $s$ is ...
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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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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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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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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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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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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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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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Proving that interval preserving transformations are linear

In almost all proofs I've seen of the Lorentz transformations one starts on the assumption that the required transformations are linear. I'm wondering if there is a way to prove the linearity: Prove ...
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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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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 ...