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What does it mean to give the fields energy and momentum?

What does it mean to give the fields energy and momentum? The concept of a field in physics In physics, a field is a physical quantity, represented by a scalar, vector, or tensor, that has a value ...
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What does it mean to give the fields energy and momentum?

As you mentioned, the energy and momentum stored in the fields can be "given back" to particles. This does make it seem like we defined field energy and momentum just for the sake of it and ...
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What does it mean to give the fields energy and momentum?

Fields can exert forces on charged particles. Force by definition is the rate at which momentum changes. Meaning when the field exerts a force on charged particles it increases its momentum, this ...
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What does it mean to give the fields energy and momentum?

Perhaps the most direct consequence is radiation pressure. While small in everyday life, it's measurable on Earth with a Nichols radiometer. In space, it's a big deal, with a substantial effect on ...
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Can something have momentum but not velocity?

The idea of momentum is fundamental, even more fundamental than velocity or mass. This is not correct. At best it is a matter of opinion what is "more fundamental." In the classical ...
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Can something have momentum but not velocity?

thinking about photon, it has constant speed, so when a force, like gravity is applied to it, because there is no mass, It changes the direction of the photon, and also the frequency. so now about the ...
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Can something have momentum but not velocity?

Momentum does not require mass. For example the electromagnetic field carries momentum, the momentum density of the EM field is: $$\vec{p} = \epsilon_{0} \vec{E} × \vec{B}$$ For light: $$p = \frac{E}{...
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Potential energy in Special Relativity

In special relativity, the equation of motion in Galilean coordinates are: $$\frac{\text{d}\boldsymbol{p}}{\text{d}t} - \boldsymbol{F} = \frac{\text{d}}{\text{d}t}\left(\frac{m\boldsymbol{v}}{\sqrt{1-...
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How exactly is kinetic energy transferred between two moving objects when a force is applied?

Here is a simpler way to think about this, which may be helpful. Besides the spring between them, the colliding objects are themselves elastic- in addition to possessing mass. When acted upon by ...
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How to understand the mass in the definition of momentum in quantum mechanics?

If you continue reading, I'm sure you'll eventually find another form of the momentum expectation as $$\langle p\rangle = \int_{-\infty}^\infty \Psi^*(x,t)\left(\frac{\hbar}{i}\frac{\partial}{\partial ...
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Conflicting Change in Momentum Question

You say (after correction by another person answering) the magnitude of the change in momentum is $|\Delta \vec{p}| = |\vec{p}_f| - |\vec{p}_i|$ That's not correct. What is actually correct is $|\...
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How exactly is kinetic energy transferred between two moving objects when a force is applied?

While we often talk about energy "flowing" as if it was some sort of fluid, and sometimes it is useful to think of it that way, this can also lead to error. Energy isn't a material, it isn'...
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How does conservation of energy differ from conservation of momentum in this problem?

One way of thinking about this is that energy always has to do with "state changes". "State" is all of the measureable quantities that describe an object or system of objects. ...
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How does conservation of energy differ from conservation of momentum in this problem?

In an "inelastic collision" the KE isn't conserved (due to internal friction), so that approach would lead to a wrong result. A collision where two bodies stick together is usually called a &...
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Conflicting Change in Momentum Question

This question was poorly constructed and did not go through sufficient proof-reading and review. If the answer is A or B, then the question should have asked for "the magnitude of the change in ...
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Conflicting Change in Momentum Question

You are correct I think. The change in magnitude of the momentum, to me, would mean $|p_{2}|-|p_{1}| = 0$ The magnitude of the change in momentum would be: $| p_{2} - p_{1}| = 2mv cos(\theta)$
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Is acceleration of particle by photon a continuous process?

The problem here is thinking about electron-photon collision in classical terms, as if it were described by Newton's equations... in fact, we have a collision from a state $p=0,\hbar k$ to state $p', \...
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Momentum and energy conservation and preconditions

Short answer to your question: energy conservation does require both considering the falling body and the earth, as the gravitational potential energy is shared among the earth and the falling body (...
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Momentum and energy conservation and preconditions

Momentum is conserved in a system if there are no external forces on the system. Likewise, angular momentum is conserved in a system if there are no external torques on the system. Energy is conserved ...
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Momentum and energy conservation and preconditions

what the preconditions for applying momentum and energy conservation in mechanics are? We write the laws of physics that describe a system in the system’s Lagrangian. If the Lagrangian is not an ...
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What do you think about this particularization of the Euler-Lagrange equation that resembles Newton's 2nd Law?

Yes, one may use d'Alembert principle to rewrite Newton's 2nd Law as Lagrange equations $$ \sum_{i=1}^N\underbrace{\left(\dot{\bf p}_i-{\bf F}_i\right)}_{\text{Newton's 2nd Law}}\cdot \delta {\bf r}_i ...
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Is there an official name for "Lorentz Pairs" like energy and momentum?

What you might be looking for is the concept of Lorentz covariance. A Lorentz covariant quantity is a (finite collection of) quantities which are taken to linear combinations of themselves under ...
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Superposition principle in classical collision theory

It might help to draw a free-body diagram of the particle as it collides with the wall. Presuming a smooth wall, the force by the wall on the particle is perpendicular to the wall's surface. So, apply ...
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Newton's Third Law in General Relativity

In terms of their reduced mass $\mu$ and orbital angular momentum $\vec{L}$, the distance between two masses evolves like a Cartesian coordinate in $1$-dimensional space seeing effective potential $-\...
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I was reading a question where it asked if astronauts on space shuttle lost weight would the spacecraft velocity increase? (Assuming closed system)

To answer your first question, it is easy to see that the shape and velocity of an orbit do not depend on the mass of the orbiting object. Astronauts on the ISS regularly perform EVAs (“spacewalks”) ...
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If photons have no mass, how can they have momentum?

Something that hasn't been mentioned is the concept of electromagnetic momentum and the Poynting vector. The Poynting vector is defined as $${\bf S} = \frac{1}{\mu_0}\,{\bf E}\times{\bf B} $$ and &...
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Can you make photons without momentum?

The momentum of a photon is given by: $$ p = \frac{h}{\lambda} $$ so all photons have a momentum and there is no way to make the momentum zero. You can make the momentum arbitrarily small by making ...
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Interpretation of momentum in special relativity

The easiest way to work such problems in relativity is to use the concept of four-vectors. There is a little bit of a learning curve, but if you are going to spend any time doing relativity the ...
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Interpretation of momentum in special relativity

There are many questions here about mass in S.R. The contemporary interpretation is that there is only rest mass. Rest energy is an invariant quantity. Therefore mass, $m = E_0 / c^2$, is too. Your ...
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Action of translation operator on ket in momentum representation

The translation opertor is $T_a= \exp\{- a\partial_x\}= \exp\{-ia\hat p\}$ acts on a momentum eigenstate $|p\rangle$ by $$ T_a |p\rangle= e^{-iap}|p\rangle, \quad \langle p|T_a= e^{iap}\langle p| $$ ...
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Conservation of momentum from moving frame

The frame in which mass $M$ is at rest is not an inertial frame, because during the collision it is accelerated with respect to the ground frame (which is an inertial frame). As such, momentum isn't ...
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Lt. Joe Kenda's expertise(?) in fundamental physics

As to the observation that people tends to slump forward when they've been shot. When a person is standing upright most of of the weight of that person is carried by the forefeet. You can try that as ...
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Lt. Joe Kenda's expertise(?) in fundamental physics

While bullets travel fast, they are extremely light compared to the mass of the human body, so they barely cause any backward motion on the victim. Let's do the math. Consider a $80\text{ kg}$ target ...
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