All Questions
Tagged with conservation-laws special-relativity
166
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Apparent violation of Newton's Third Law in relativistic force transformation
In special relativity, we know that, relativistic force is defined as F = dp/dt, where p = γmv.
For forces perpendicular to the direction of relative motion, force transforms as F' = γF.
Consider two ...
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Energy of moving Sine-Gordon breather
A few days ago I stumbled across the formula for the energy of a moving breather for the sine-Gordon equation
$$ \Box^2 \phi = -\sin\phi.$$ The energy in general is given by ($c=1$)
$$ E = \int_{-\...
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Kinematics of a two-body decay [closed]
I suspect a flaw in the reasoning below, but am unable to pinpoint it: Is there something inconsistent in terms of the application of conservation of momentum and energy? Thanks for any hints in ...
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Theorem in mechanics relating energy flow and momentum
In Feynman's Lecture 27 on Vol. II it is written that
There is an important theorem in mechanics which is this: whenever there is a flow of energy in any circumstance at all (field energy or any ...
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Equations of motion for a force in special relativity seem to require a differential equation — in this context, what does Kinetic Energy *mean*?
I was faced with a situation where I suddenly realized that although Kinetic Energy in Special Relativity is defined as
$KE=\gamma m_0 c^2 - m_0 c^2$
The work energy theorem says
$\Delta KE +\Delta ...
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Threshold energy formula
In Krane's Introductory Nuclear Physics, in chapter 11, he uses the conservation of energy and momentum to derive the formula for the threshold energy of a reaction a + X → b + Y (with X being an ...
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Are the relativistic masses conserved in nuclear fission? [duplicate]
If A $\rightarrow$ B+C+ΔE, then
$M_{B}+M_{C}< M_{A}$ So, whether the masses involved were the relativistic or the rest, they aren't conserved. So, why would anyone say the rest masses, not the ...
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Unusual example of Compton Scattering (+Four-momentum approach, +nonrelativistic) [closed]
An electron of kinetic energy $k=100 keV$ (first note, doesn't this mean that its energy is much lower than $0.511 MeV$, and thus that it is a nonrelativistic electron we are dealing with?), collides ...
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Poincaré group conservation laws: 10 of 7? [duplicate]
According to the Wikipedia page about the Poincaré group, we get 10 conservation laws using Noethers theorem.
10 generators (in four spacetime dimensions) associated with the Poincaré symmetry, by ...
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Complete absortion of a photon by an atom (from the perspective of conservation laws)
It is very simple to show that an isolated charged particle cannot completely absorb a photon, since that would contradict the conservation of linear momentum or energy: consider a system where the ...
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Deriving continuity equation from 4-current of a charged particle
how can i check that following 4-current for a single charged particle
$$j^{\mu}(x)=qc\int d\tau u^{\mu}(\tau)\delta^{4}(x-r(\tau))$$
satisfies continuity equation $$\partial_\mu j^\mu = 0.$$
user391340
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Commutation of the Hamiltonian with the generator of boost
Consider the Hamiltonian $H = (\textbf{P}^2+m^2)^{1/2}$ the generators of rotation and and boost given by $$M^{0i} = tP^i-x^iH \\ M^{ij} = x^iP^j-x^jP^i$$ where $x^i$ and $P^j$ satisfy $\{x^i, P^j\} = ...
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Calculating the recoil mass of an atom after absorption of a photon [duplicate]
I'm solving a problem 4.11 in <Introducing Einstein's Relativity, Ray D'Inverno>. The problem states as follows:
An atom of rest mass $m_0$ is at rest in a laboratory and absorbs a photon of ...
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Energy conservation and Lorentz invariants [closed]
In relativistic collision theory,How can we deduce energy is conserved by using Lorentz transformation?
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Proof that if the 3-momentum is conserved then so is energy. (Weinberg's Gravitation and Cosmology)
In section 4 chapter 2 of his book "Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity", Weinberg argues that if the 3 momentum is conserved in a '...
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