Questions tagged [conservation-laws]

The statement that a property of a system does not change if the system is isolated.

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According to the standard model, if the universe were not expanding and treated as a single, closed system, would energy be conserved?

It is said that energy conservation requires the reversibility of time, but space expanding breaks that condition. If the universe was not expanding and treated as a single, closed system, is energy ...
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Incompressible fluid flow in tilted pipe setup - Continuity Equation, Flow Rate, Mass Conservation

Say that we have water flowing horizontally in a pipe of constant diameter. The continuity equation for incompressible fluids, which is a statement of mass conservation, guarantees that the flow rate ...
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How do we visualise multiplication and division (reciprocal multiplication) in physical equations?

All formulas have terms generally multiplied or divided to represent another physical quantity. Like $F=ma$, $I=Q/t$, $W=F.s$ etc. Technically this is so because of ratios and proportionalities, the ...
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Continuity equation for charge density

Let $\rho$ be the charge density and $M_i$ the momentum density. The article I am reading states that the continuity equations for this system are given by, \begin{equation} \frac{\partial \rho}{\...
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Local conservation of charge does not imply global conservation of charge?

In order for a set of $\rho, \vec{J}$ functions to conserve charge locally. $$\nabla \cdot \vec{J} = - \frac{\partial \rho}{\partial t}$$ Consider $$\vec{J} = x \hat i$$ Does this have a valid ...
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Proof that conservation of momentum is Lorentz invariant

In classical mechanics, if $$\frac{\mathrm d}{\mathrm d t}\sum_i m_i\vec{v_i}=0$$is true for one frame of reference, then it is easy to prove that this is true for all frames (since different frames ...
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How to determine the flow of a conserved vector quantity?

I know that if $F$ is a conserved quantity, then the Hamiltonian is invariant under the flow $\psi^{\lambda}(q^{\alpha},p_{\alpha})=((q^{\lambda})^{\alpha}(p,q), (p^{\lambda})_{\alpha}(p,q)) $, that ...
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Conservation of momentum flux

When is momentum flux conserved in a fluid? How do these conditions compare to the conservation of momentum? What is an example when momentum flux is conserved, and momentum not?
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Why Electron Quantum Field Wants Little Energy But Photon Field Doesn't

In this Quora post: https://qr.ae/pv5tac, it states that the electron quantum field "wants" to reduce the energy it has, so when a particle and an anti-particle interact and the charges ...
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What is conserved under spacetime translation?

Is it the energy momentum tensor: $$T_{\mu \nu}$$ Or the four momentum: $$P_{\mu}$$ I know they are essentially the same thing, but it seems that one is the outcome of spacetime translation invariance ...
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Transfer of momentum at quantum level

The clack of two billiard balls signifies the transference of their momentum and the mathematics of resulting vectors is fairly straight forward. At the quantum level, I understand that the transfer ...
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Time dependent Quantum Generators

We know a space-translation generator can be written as: \begin{equation} T(\textbf{r}_{0})|\alpha\rangle=e^{-i\frac{\textbf{p}\cdot\textbf{r} _{0}}{\hbar}}|\alpha\rangle=|\alpha'\rangle. \end{...
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Euler-Lagrange Equation, $\dot{P_{\alpha}}\neq\partial_{q_{\alpha}}L$

We know \begin{equation} \frac{d(\partial_{\dot{q}_{\alpha}}T) }{dt}=\partial_{q_{\alpha}}(T-U) \\ \partial_{\dot{q}_{\alpha}}U=0 \rightarrow\dot{P_{\alpha}}=\partial_{q_{\alpha}}L \end{equation} ...
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Physical interpretation regarding heat equation [closed]

I have included image of a problem from Oxford ( from a Math course). I was able to do the question. However, i am stuck at the last part which asks about the physical interpretation. I don't have a ...
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How to show that the Hamiltonian $H$ is invariant under flow generated by $F$?

I know usually if I have a transformation of phase space $Q(p,q), P(p,q)$ it is defined to be canonical if and only if its Jacobi matrix is part of the Symplectic Group or equivalently $\{Q^{i}, P_j \}...
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How to find speed and acceleration before and after the loss of vehicle parts? [closed]

Suppose that we have a vehicle of mass $M$ such that $$M=\sum_{i=1}^Nm_i$$ If the total sum of lost objects is $M'=m_1+m_2+\cdots +m_i$ with $i<N$ during a races, unnecessary objects that impede ...
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Do neutrons change their wavelengths when diffracted?

Both neutrons and X-rays are used in diffraction. In XRD, the diffracted beam is of the same wavelength of the incident beam. The reason is that X-rays are EM waves which cause electrons to vibrate. ...
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What is the Lie derivative of the field describing the change of mass?

I'm trying to understand Ch. 3.2 of the paper On Bubble Rings and Ink Chandeliers by Padilla et al.. I'm trying to understand the derivation of equation (15). Right now I'm stuck at the point where ...
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Why did Noether use the Lagrangian for her conservation of energy theorem?

So I know that for Noether's conservation of energy theorem, the Lagrangian is used. However, I know that the Lagrangian doesn't always equal energy. So why did she use the Lagrangian and not other ...
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Why are the residual protons and electrons equal in the Universe?

The Universe today is believed to be charge neutral and since nearly all the Standard Model content is protons, electrons, neutrons, neutrinos and photons; this requires #protons = #electrons. However ...
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A spin-1/2 particle A undergoes the decay $A \to B + C + D $, where it is known that B and C are also spin-1/2 particles

The complete set of allowed values of the spin of the particle D is? Now the answer that I am getting is: 'Spin of the left side and combined spin of the products must be same to conserve the spin ...
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Could gravity be used to cool down matter?

Thermal energy being the movements of particles, could we have a system that could use gravity to reduce the thermal energy of particles? For example, if we imagine: A box containing Argon in its ...
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What happens to velocity if mass changes, in uniform velocity motion of a body? [closed]

If a body is in motion with some constant velocity, but its mass is decreasing as it is moving forward, what will happen to its velocity? Does it stay constant, why?
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Conservation of momentum in quantum mechanics

Let $P_x=P_{1x}+P_{2x}$ be the operator for the total linear momentum of an isolated system of two particles labeled 1 and 2. The questioned asked to show that $\langle P_x \rangle$ remains constant ...
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Conservation of gauge charge

According to the semiclassical Wong equations (see page 14 of this paper), the motion of a point particle inside a gauge field theory is described by: $$ m \frac{\text{d}p^\mu}{\text{d}\tau} = gQ^a F^{...
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Is there an infinite amount of conserved currents for a given finite symmetry?

Let's say we have a field $\phi(x)$ that gets transformed to $\phi(x, \epsilon)$ under some finite transformation. We also define $\phi(x,0)=\phi(x)$. If we Taylor expand our transformation we get: $$\...
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Is Newton’s third law of motion formed from Poincare symmetries?

So I know that Newton's third law states that every action has an equal reaction, making a symmetry. But just like how Poincare symmetries form conservation laws, do any Poincare symmetries form ...
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Is there a specific case for the kinetic energy of a particle to be conserved while angular momentum is not conserved?

This is from a question from one of my country's undergraduate entrance exams, so the usual considerations of not taking extraordinary cases apply. The question is, in quotes "A particle moves ...
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What about $CT$ or $PT$ violations?

In particle physics, $CPT$ is a universal conservation law. This implies that any combination of only two of them should be violated in some processes. The only one I heard of so far is the $CP$ ...
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Does the intermediate axis theorem violate angular momentum conservation?

According to the intermediate axis theorem, an object rotating about its intermediate axis with a very slight perturbation will undergo periodic flips in its orientation in the absence of external ...
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Punchline of Liouville's Theorem

Reif's Fundamentals of Statistical and Thermal Physics, pages 627-628, presents Liouville's theorem. I do not understand the punchline. Starting with Hamilton's equations, they derive $$\frac{\partial\...
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Can an elementary particle truly be destroyed?

Much like the title above, can they be created (from absolute nothing) or destroyed (into absolute nothing), with nothing in this case being nonexistence. Taking into account the idea of quantum ...
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Conservation laws in probability and statistics [closed]

Most of my research is confined to the field of continuum fluid mechanics, where conservation of mass, momentum, energy, etc. are commonly discussed. Often the variables under consideration represent ...
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Are all asymptotic symmetries and their meaning known?

Beyond the Standard Model and the General relativity invariant groups, recently we have met (again) the BSM groups of asymptotic symmetries given by the Bondi-Metzner-Sachs (BMS) or the extended BSM ...
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Do Magnetic forces obey Newton's Third Law? [duplicate]

If we have two magnets and one is brought towards the other, the north of the former magnet is facing north of the latter. Now the other magnet is repelled which is obvious and Newton's third law is ...
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What will be the velocity of the truck after 50 minutes? [closed]

This question came in the Rajshahi University admission exam 2019-20 Q) A truck of 5 metric ton filled with sand was moving with a velocity of $20ms^{-1}$. A hole was created in the truck through ...
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Threshold energy for pair production from proton-electron collision

In this undergrad nuclear physics problem I am asked to find the kinetic energy threshold for an electron colliding with a still proton to create an electron-positron pair. So in short: $$e^- + p^+ \...
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How to interpret the conservation of mass equation?

I want to know that the difference is between the following equations: $$ \frac{\delta h_d}{\delta t} = -\nabla.(\vec{v_s} h_d) = -u_s(\frac{\delta h_d}{\delta x}) -v_s(\frac{\delta h_d}{\delta y}) - ...
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Can kinetic energy be transferred between two objects even if they are not in contact?

This question is better explained with a thought experiment. It is inspired by this answer, stating that the amount of work done depends on the inertial frame. Consider a one-dimensional space with ...
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Some questions related to the energy of a viscoelastic bar

Let's consider a problem of free longitudinal vibrations of an one dimensional infinitely long elastic relaxing bar (Maxwell material) with constant cross section. The bar's displacement $u$ and ...
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Effective field theory odd dimension operators

In the Standard Model Effective Field Theory, $$L_{EFT} = L_{SM} + \sum_{d=5}^{\infty}\sum_{i} \frac{c_i^{(d)}}{\Lambda_{i}^{d-4}} \mathcal{O}_i^{(d)},$$ typically, the odd dimension terms are omitted ...
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Can a (conservative) four-force be derived from a scalar potential?

In special relativity, the four-force is the derivative of the four-momentum with respect to proper time (a Lorentz scalar): $$f^\mu = \frac{\text{d}P^\mu}{\text{d}\tau} = c \frac{\text{d}P^\mu}{\text{...
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How is there energy and charge in the universe? [closed]

According law of conservation of charge "the total electric charge in the universe is constant and charge can neither be created nor be destroyed" so how did the existing charge came. I f it ...
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Singularities/infinities of continuity equation in polar coordinate

I encountered a bit of a difficulty in solving the continuity equation for polar coordinates. For a "fluid" or density of particles moving radially outwards with constant velocity, its flux ...
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Momentum non-conservation while on-shell condition is satisfied

There are two particles $\it{N}$ and $\pi$ with masses $m_N$ and $m_\pi$ associated with Hermitian scalar fields $\phi_N$ and $\phi_\pi$. The matrix element for the process $N\rightarrow N'\pi$ is $$...
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The divergence of the stress-energy tensor vanishes; is this statement sufficient to derive the Einstein field equations?

Can one derive the Einstein field equations from this statement alone? $$0 = T^{\mu\nu}{}_{;\nu} = \nabla_\nu T^{\mu\nu} = T^{\mu\nu}{}_{,\nu} + \Gamma^{\mu}{}_{\sigma\nu}T^{\sigma\nu} + \Gamma^{\nu}{...
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Momentum and energy conservation and preconditions

I'm reading Susskind's Classical Mechanics: The Theroretical Minimum and I also like to restrict my question to classical mechanics: In chapter 4, momentum conservation is shown for a set of particles....
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How to find distance between colliding objects?

Consider an object A with mass m with velocity v collides with another resting object B with mass M. After colliding we know that after some time both the objects will gain same velocity. But a ...
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Does conservation of charge has anything to do with phase?

I was watching youtube lecture link and professor says that "the independence of that phase leads to conservation of charge" in the following equation. $$\vec{\nabla} \cdot \vec{J} + \frac{\...
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Newton's 3rd law and rocket nozzles

For a given solid propellent charge the energy given off by the charge is equivalent in all cases. Yet by varying the throat of the nozzle, the rocket velocity will be different for each individual ...
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