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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The Lagrangian in Scalar Field Theory

This is perhaps a naive question, but why do we write down the Lagrangian $$\mathcal{L}=\frac{1}{2}\eta^{\mu\nu}\partial_{\mu}\phi\partial_{\nu}\phi - \frac{1}{2}m^2\phi^2$$ as the simplest ...
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What are relativistic and radiative effects (in quantum simulation)?

I'm reading about Quantum Monte Carlo, and I see that some people are trying to calculate hydrogen and helium energies as accurately as possible. QMC with Green's function or Diffusion QMC seem to be ...
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558 views

Velocity of electron in electrostatic field. Does radiation matter?

There's a voltage difference of 1000 Volts between two points 2 meters apart. An electron starts at the point of lower potential and is left to travel alone in a straight line until it reaches the ...
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Einstein's special relativity beyond the speed of light

Could someone with access to this paper which claims to have new transformations between frames with relative motion faster than light which are supposedly consistent with special-relativity, say what ...
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A clock devoid of motion

My understanding is that every clock mechanism we have depends on motion of something w.r.t the observer. From atomic transitions to clockwork gears. So, does this property/constraint makes every ...
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Special relativity paradox and gravitation/acceleration equivalence

One of the features of the black hole complementarity is the following : According to an external observer, the infinite time dilation at the horizon itself makes it appear as if it takes an ...
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Newton's gravitational constant $G$, the reduced Planck constant $\hbar$, the speed of light $c$: the Dream Team of moderators?

The three great constants of Nature are well known: the speed of light $c$ (special relativity), the reduced Planck constant $\hbar$ (quantum mechanics), Newton's ...
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What are $\partial_t$ and $\partial^\mu$?

I'm reading the Wikipedia page for the Dirac equation: $\rho=\phi^*\phi\,$ ...... $J = -\frac{i\hbar}{2m}(\phi^*\nabla\phi - \phi\nabla\phi^*)$ with the conservation of probability ...
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Explanation of equation that shows a failed approach to relativize Schrodinger equation

I'm reading the Wikipedia page for the Dirac equation: $\rho=\phi^*\phi\,$ ...... $J = -\frac{i\hbar}{2m}(\phi^*\nabla\phi - \phi\nabla\phi^*)$ with the conservation of probability ...
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Rotating hoop in Relativity

What does a rotating hoop, with each point moving at a velocity close to the speed of light, appear like with respect from a stationary observers perspective. For example how does the shape of the ...
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403 views

Resolution of twin paradox using Lorentz velocity addition

In the following lecture, starting at minute 29:00 and going further, the professor resolves the Twin Paradox using Lorentz velocity addition. I have a question about this: Isn't the figure given ...
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263 views

What is the 'quantum-developed' or 'relativistic-developed' equation of the electrostatic force?

Quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics that is the first theory where full agreement between quantum mechanics, special relativity and ...
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The necessity of the B field

It is fairly easy using basic special relativity to arrive at the conclusion that the magnetic force effect on nearby charges of wires carrying currents on nearby charges is only due to the length ...
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What would a length contracted object look like?

I have multiple sub-questions but they are related. What would the object look like if in were passing by? What would a star look like if we were traveling near $c$? Would the perspective be a a ...
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457 views

Is it possible to reduce speed of light? [duplicate]

Possible Duplicate: What really cause light to appear slower in media? This came to me as a question from one of my friend while I was convinced that the answer is NO. But I have read in ...
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Calculating the commutator of Pauli-Lubanski operator and generators of Lorentz group

The Pauli-Lubanski operator is defined as $${W^\alpha } = \frac{1}{2}{\varepsilon ^{\alpha \beta \mu \nu }}{P_\beta}{M_{\mu \nu }},\qquad ({\varepsilon ^{0123}} = + 1,\;{\varepsilon _{0123}} = - ...
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Faster Than Light Communication Using Gravity?

Suppose two parties $A$ and $B$, some distance apart and at rest relative to each other both had control of one massive local object each. If party $A$ lifted their local object upward relative to ...
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1answer
297 views

An accelerating and shrinking train in special relativity

Suppose when a train is at rest, it has a length of $L$. Let the position of the back of the train at any time be $A$, and let the position of the front of the train at any time be $B$. Now assume ...
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170 views

Does the sign of $\Delta x$ matter in this time dilation calculation?

I cannot for the life of me figure out what I am doing wrong with this problem: If a high speed particle travels a distance of 39 Km with a half life of 1 micro sec, what must its speed be to travel ...
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Lorentz transformations for sine wave in random direction

Hello i have been struggling to derive Lorentz transformations for a sine wave, which is traveling at random direction. I started by prooving that phase $\phi$ is invariant for relativity and that ...
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Does special relativity make magnetic fields irrelevant?

I've heard that special relativity makes the concept of magnetic fields irrelevant, replacing them with relativistic effects between charges moving in different velocity frames. Is this true? If so, ...
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Length Contraction And Simultaneity

I wanted to derive length contraction from the Lorentz transformation, but I keep getting stuck on problems with simultaneity in my derivation. At some point, I came across Wikipedia's article on ...
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Interaction between a Pair of Particles

We consider a particle, A receiving energy from a second one,particle B in a one dimensional collision. $$E^2=p^2+m_0^2$$ $$EdE=pdp$$ For particle A: $$E_AdE_A=p_Adp_A{\;\;\;\;\;\;}(1)$$ For ...
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Deriving the action and the Lagrangian for a free point particle in Special Relativity

My question relates to Landau & Lifshitz, Classical Theory of Field, Chapter 2: Relativistic Mechanics, Paragraph 8: The principle of least action. As stated there, to determine the action ...
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Reaching the speed of light, rockets [duplicate]

Possible Duplicate: Double light speed Someting almost faster than light traveling on something else almost faster than light Well I've been wondering quite a long time about this ...
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1answer
487 views

Does the Earth's revolution around the Sun affect radioactive decay?

Premises: The radioactivity is either hastened or slowed inside a fast moving aircraft. Speed of fastest aircraft: 3,529.6 km/h. The earth's revolution is: 107278.87 km/h. The earth's ...
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Stroboscope-and-telegraph problem

Narrative: Consider, in a suitably flat region, two straight lines which don't necessarily intersect. Let vector $\mathbf{x}$ point along one line, and vector $\mathbf{y}$ point along the other. Let ...
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Show the Lorentz Transformation Matrices Have an Inverse

Assume the Lorentz transformations obey the relationship $$g_{uv}\Lambda^u_{p}\Lambda^v_\sigma = g_{p\sigma},$$ where $g_{uv}$ is the metric tensor of special relativity. How can one show, under that ...
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Spooky action appears to contradict Relativity of time order of multiple events

It is well known that in special relativity observers can disagree on the time ordering of two events. It is also well known that entangled particles exhibit so called spooky action at a distance. ...
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Relativistic Doppler effect

If i have 2 coordinate systems (CS) which are travelling one towards another. CS $xy$ with an observer in its origin and CS $x'y'$ with a source in its origin. Correct me if I am wrong, but i think ...
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Measure absolute speed

Currently I'm 17 years old, going to secondary school. So, my ideas might be totally wrong... I know that everything is relative. In the example of speed, the earth moves, and the galaxy moves, etc. ...
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Is the commutation of all possible operators sufficient to identify a spacelike interval?

It has been claimed (e.g. here) and apparently already been established, that the interval $x - y$ being (called) "spacelike" implies that $\bigl[\hat O (x),\, \hat O' (y)\bigr]=0$ for any two (not ...
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454 views

Space expansion looking like time dilation

Space looks like time depending on the motion of the observer so I was going to ask if space expansion was the same as the unfolding of time, but this was asked on physics.stackexchange before and the ...
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249 views

Wavefronts and phase velocity faster than $c$

Lets assume we have parallel wavefronts in a glass of water: and we put an inclined rod on the water surface: related to a very small inclining, Vy velocity is greater or much greater then Vx ...
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How to prove that proper orthochronous Lorentz transformations form a group?

Proper orthochronous Loentz transform are Lorentz transforms that satisfy the conditions (sign convention of Minkowskian metric $+---$) $$\det \Lambda=+1, \qquad \Lambda^0{}_0 \geq +1.$$ How to prove ...
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Relativistic contraction for a wave packet and uncertainty on momentum

Consider an electron described by a wave packet of extension $\Delta x$ for experimentalist A in the lab. Now assume experimentalist B is flying at a very high speed with regard to A and observes the ...
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Magnetic paradox in relativity?

Let 2 electrons A and B be moving parallel with constant velocity $c/10$ in (near) vacuum without a strong gravity field (where $c$ is speed-of-light). A and B create an electromagnetic field that is ...
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Relativistic drift velocity of electrons in a superconductor?

Is there a formula for the effective speed of electron currents inside superconductors? The formula for normal conductors is: $$ V = \frac{I}{nAq}$$ I wonder if there are any changes to this ...
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Maxwell equations invariant under Lorentz transformation but not Galilean transformations

Why Maxwell equations are not invariant under Galilean transformations, but invariant under Lorentz transformations? What is the deep physical meaning behind it?
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Information relationship to Special Relativity

How do we write mathematically that "information" cannot go faster than light? And along a similar line of thought, how do we relate "information" with special relativity. Lastly, what is the ...
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Derivation of the Lorentz transformation

I have been reading Young's book called: University physics with modern physics and on page 1284 author states that we can derive Lorenz time transformation by eliminating two equations for Lorentz ...
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Discarded by Relativity [closed]

Both the General & Special Relativity discarded Newtonian mechanics of absoluteness. According to Einstein's view, Time, Mass, Length and Space are interdependent. So, Did Relativity discarded ...
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Increased mass from signals traveling close to the speed of light

As you travel close to the speed of light, it is to my understanding you gain mass. Does this also apply when the brain sends electrical signals to the muscles? Do the signals (that are traveling at ...
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3 inertial frames compared in STR

Suppose an event is observed in 3 inertial frames K, K' and K''. The coordinates in K are $(x,t)$ in K' are $(x',t')$ in K'' are $(x'',t'')$. The K' and K'' coordinates are then Lorentz-transformed to ...
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Is there a strong force analog to magnetic fields?

In special relativity, magnetism can be re-interpreted as an aspect of how electric charges interact when viewed from different inertial frames. Color charge is more complex than electric charge, but ...
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Causality without light

Related to my prior question: Would a species insensitive to light have developed special relativity? Imagine a species insensate to light and other em radiation. They are very attuned to sound ...
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Would it be possible to develop special relativity without knowing about light?

My understanding of special relativity is that it is fundamentally based on the constancy of the speed of electromagnetic radiation - that this speed is a physical law (or derivable from physical laws ...
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Darwin term and Zitterbewegung

I've noticed that in the discussion of the fine structure of Hydrogen atom standard QM texts claim that the Darwin term, which corrects energy of $\ell=0$ (or $s$-) states only, is related to the ...
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What happens when a photon hits a mirror?

When a photon of light hits a mirror does the exact same photon of light bounce back or is it absorbed then one with the same properties emitted? If the same one is bounced back does it's velocity ...
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Time slowing down problem

When someone moves, time slows down for him. Let, a man standing still and another moving very very very fast, this happens for an hour (as measured by the standing man). Time has moved slower for the ...