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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Are photons massless? [closed]

If anything that has no rest mass will travel at the maximum possible speed. Hence, light being massless travels at this speed. Does this means that photons are massless?
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Working out Length Contraction

I'm having trouble reconciling the quantitative and conceptual aspects of length contraction. This example is taken out of a book: Say a particle is moving toward us at 0.99c, relative to us. If at ...
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231 views

How does EM radiation depend on the reference frame?

In special relativity, magnetism is electrostatics in a different reference frame. This is how we explain the magnetic field being produced by moving charges (aka currents). Charges that move produce ...
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42 views

Physical reasons for metric definition in special relativity [duplicate]

I am working through "General Relativity" by Wald, and am currently going through the brief section on Special Relativity. The spacetime metric is defined as $\eta_{ab} = \sum\limits_{\mu, \nu=0}^3 ...
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437 views

Derivation of force law in special relativity

I've seen force defined in special relativity as the rate of change of 4-momentum $$ {\bf{F}} = \frac{d {\bf{p}}}{dt} $$ Can anyone comment on the following derivation of that relation? Take one ...
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(Hyper)Surface of Simultaneity

How can I determine the surfaces of simultaneity if I know the metric? In particular, what are the surfaces of simultaneity for rotating disk with Langevin metric: $$ ...
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Two particles of different velocities travel through a region of time-dependant acceleration. At what time do they meet afterwards? [closed]

Two projectiles: $P_{1}$ and $P_{2}$ have velocities $v_{1}$ and $v_{2}$, both propagting in the x direction and starting at $x=0$. They propagate with constant velocity over a distance $L$ and reach ...
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1answer
164 views

How do simple two-component Fierz identities follow from a property of the Pauli matrices?

On page 51 Peskin and Schroeder are beginning to derive basic Fierz interchange relations using two-component right-handed spinors. They start by stating the trivial (but tedious) Pauli sigma identity ...
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Rest mass of phonon: is this concept definable?

Phonons are obtaied by non-relativistic quantization of the lattice vibration. The dispersion relation is given by $\omega=c_s k$ where $c_s$ is the velocity of sound. What can we say about the mass ...
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Trouble understanding spacetime and invariant interval

First, how is the invariant interval useful? How can it help us understand things around us in the universe? Second, I know that they changed time into space or better say SPACETIME in order to ...
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$F=ma$ can only be used if the relativistic mass of the object is known, true?

I have received this question "Einstein's ideas on mass mean in essence the equation $F=ma$ can only be used if the relativistic mass of the object is known. Describe in your own words to what ...
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“Constant Fermion”

I was talking to a professor in my institution which works in Lorentz Violation of various QF theories. While we talk about a SUSY lagrangian, I asked him if we could have a fermion acquiring VEV and ...
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Question about time dilation for a traveler that can reach the “edge” of the universe

I thought I understood time dilations but I feel now confused. Imagine somebody traveling in a rocket near the speed of light, close enough so that he will be able to reach the edge of the universe in ...
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236 views

Physical interpretation of distances

Suppose we have a universe with only two distinguishable particles, neglecting gravitation. These particles start off next to each-other, ostensibly "touching" each-other and at rest. If it takes ...
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1answer
55 views

Tensor notation of Maxwell's equations

Tensor notation of Maxwell's equation read So when we explicitly try to find the Maxwell's equation from the above tensor equation we only get gauss law and curl of B. The div.B=0 and curl of E are ...
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2answers
50 views

How to show invariance using the Maxwell tensor?

I want to show the invariance of $E^2-c^2B^2$ under the Lorentz transformations. The obvious way to do this is to show that $$E^2-c^2B^2=E'^2-c^2B'^2,$$ where $E'$ and $B'$ are the Lorentz ...
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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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7answers
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Is proper time a vector?

Proper time is identical with the spacetime interval of a timelike movement. A spacetime interval is the dot product of two vectors and thus a scalar. Proper time however is always pointing exactly ...
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Special Relativity and its relation to refractive index [duplicate]

As is known, light slows down (compared to vacuum) whenever it enters a medium. Also, Special Relativity effectively puts a limit on the max. speed of any body. So is it possible for a body (in a ...
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1answer
81 views

Are all diffusion-like processes described as wave-like in relativity-compatible formulations?

Citing from Wikipedia's article on relativistic heat conduction: For most of the last century, it was recognized that Fourier equation (and its more general Fick's law of diffusion) is in ...
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71 views

Speed of a particle approaching that of light relative to itself

There's a particle moving at a certain speed $v$ with respect to a reference frame $A$ through an axis I will call $x$. We thus know that for the frame of reference located at the particle itself, the ...
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2answers
39 views

Rotation matrix for aligning x-axis in an arbitrary direction

I want to align the x-axis of my coordinate system, with an arbitrary direction in space $\hat{n}$. About which axis should I rotate? Ceratinty rotation about x-axis or $\hat{n}$-axis will not serve ...
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2answers
66 views

In relativity, perpendicular motion does not show contraction… Isn't the whole concept lost?

I read in HC Verma's Concept of Physics that a body moving in direction perpendicular to length, doesn't show Length Contraction. And Length Contraction, they said, is to maintain the velocity of ...
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Time Delay in different frame of reference | Theory of relativity [duplicate]

Let suppose there is a train that travelling close to the speed of light. Alice and Bob have a watch that have same time. Alice decided to board that train and after 5 minutes of journey ( according ...
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1answer
135 views

Hafele-Keating revisited with a gravity clock

Most modern clocks use electromagnetic phenomena to measure time. There are perhaps some older clocks that involve gravity to some degree (hour glass, pendulum), but I believe they still have a ...
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1answer
333 views

Application of special relativity on sound waves

What is the difference between an electromagnetic wave and other waves that amounts to the EM wave following the Special Relativity. I have been reading about the Special Relativity for some time, and ...
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39 views

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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Performing Wick Rotation to get Euclidean action of scalar field

I'm working with the signature $(+,-,-,-)$ and with a Minkowski space-stime Lagrangian $$ \mathcal{L}_M = \Psi^\dagger\left(i\partial_0 + \frac{\nabla^2}{2m}\right)\Psi $$ The Minkowski action is $$ ...
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39 views

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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36 views

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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Special Relativity, refractive index and catching up with a wave

Einstein was partially motivated by the following: With Maxwell's equations, a plane wave is a sinusoidal wave that varies in space in time and moving with speed $c$. These variations are linked by ...
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1answer
40 views

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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Why does weak equivalence principle say gravity is equivalent to acceleration?

I am told that the weak equivalent principle, that $m_i=m_g$ (inertial and gravitational masses are equivalent) is equivalent to the statement that in a small system you can't tell whether you are in ...
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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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1answer
45 views

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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35 views

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 ...
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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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131 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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57 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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44 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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1answer
44 views

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 ...