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Physics | |homework-and-exercises|rotational-dynamics|angular-momentum|momentum|energy-conservation| | Very interesting case, where energy is not conserved? | <p>Your analysis is correct. The initial energy in the system of particle plus disc is the kinetic energy of the particle, <span class="math-container">$(1/2) m v^2$</span>. The final energy in the system of particle plus disc is the kinetic energy of the disc, which has a contribution <span class="math-container">$(1/... |
Physics | |electric-current|capacitance| | Current and infinite coils/resisotrs/capacitors | <p>In order to simplify these types of arrangements of components you need more advanced methods than simply combining series and parallel components. One such method is called the "Pi to Tee" conversion, also known as the "Delta to Wye" conversion. See the figure below.</p> <p>After making appropriate conversions the ... |
Physics | |electromagnetism|electrostatics|charge|gauss-law| | What exactly does charge density mean in Gauss's law? | <p>The charge density in Gauss' law is simply a scalar function that specifies the distribution of charge in a region of space. The region may be 1, 2, or 3-dimensional as the case demands. Essentially, <span class="math-container">$\rho$</span> specifies the nature of the source of the electrostatic field, in terms bo... |
Physics | |classical-mechanics|oscillators| | Double Pendulum Cannot Flip | <p><strong>Preliminaries.</strong></p> <p>First, let's clarify: the "solid black line" is not very clearly visible in this image, but the article provides a bigger image from which it's clear that it refers to the boundary of the central white region (excluding the two mushroom-shaped protrusions).</p> <p>Now, getting ... |
Physics | |quantum-mechanics|resource-recommendations|quantum-interpretations|wavefunction-collapse| | Relationship of the do-operator in do calculus and the notion of the collapse of wave a function | <p>You make an interesting point, although not a popular one (at least not yet). Far more common is to interpret the wavefunction collapse as Bayesian updating (upon learning new information). See for instance <a href="https://arxiv.org/abs/1107.5849" rel="nofollow noreferrer">Leifer and Spekkens</a>, and arguably all ... |
Physics | |quantum-mechanics|energy|magnetic-fields|schroedinger-equation|linear-algebra| | Landau levels in symmetric gauge, what is the constraint on the quantum numbers? | <p>I have looked at this problem in the context of the Weyl equation. Below is a word-for-word extract from my notes, so it is not <em>exactly</em> what you want, but the square of the Weyl operator is the Schroedinger equation and my last paragraph relates to the physical meaning of the ranges of various integers. Thi... |
Physics | |fluid-dynamics|aircraft|propulsion| | Why is accelerating more air slower more efficient than less air faster? | <p>One of assumptions in the answer that you linked to is that the purpose of accelerating the air is to use the reaction force to lift an object off the ground. Force is change in momentum per unit time. So to generate a given force <span class="math-container">$F$</span> we have to accelerate a mass <span class="math... |
Physics | |newtonian-mechanics|experimental-physics| | Breaking the rock using eggs | <p>Easy, if you allow for relativistic speed. At a few tens of kilometers per second (about earth's orbital speed), minor forces like chemical bonds or electrostatic attraction between electrons and nuclei already cease to play a role. Egg and stone would simply turn into a mixed plasma for an instant, and the plasma w... |
Physics | |quantum-field-theory|lagrangian-formalism|dirac-equation|charge-conjugation|cpt-symmetry| | Charge conjugation is a symmetry for the quantized free Dirac action? | <p>Charge conjugation leaves spacetime coordinates and Dirac matrices alone, and acts only on the spinor structure of <span class="math-container">$\Psi$</span>, meaning that <span class="math-container">$$ {\cal{C}}\left(i\gamma^\mu\partial_\mu\right)\Psi{\cal{C}}^\dagger=\left(i\gamma^\mu\partial_\mu\right){\cal{C}}\... |
Physics | |speed-of-light|time|speed| | Northern lights / aurora borealis "pre-warning" - how does this work w.r.t timing and different particle / wave speeds? | <p>You are roughly correct, although the first thing isn't really a material thing that is "ejected" by the Sun. The prediction is usually first done by satellites directly observing the Sun (indeed "light travelling at light speed"), most notably the <a href="https://en.wikipedia.org/wiki/Solar_and_Heliospheric_Observ... |
Physics | |waves|electromagnetic-radiation| | What exactly qualifies something to be a transverse wave? | <p>Statement D is not true because there are transverse waves that require a medium to be vibrated and so do not travel in vacuum. Transverse waves on a rope is an example.</p> <p>By a process of elimination I think C is the expected answer. You can form a "stationary" wave (I think this must mean a standing wave) from... |
Physics | |quantum-field-theory|quarks|protons|gluons| | Why so much kinetic energy inside a proton? | <p>The simplistic answer is that a proton is very small. The quarks are not free, but are confined to a small region. By the uncertainty principle a small uncertainty in the position of the quarks implies a large uncertainty in their momentum. The expectation of the momentum is zero, but the uncertainty is large. To ca... |
Physics | |thermodynamics|water|fluid-statics|phase-transition|density| | Does having a liquid (less dense than ice) above a floating (in water) ice cube, change the fact that the water level remains constant when ice melts? | <p>Without the second liquid above, the ice displaces a volume of water exactly equal to its own weight. After it melts, the ice becomes the same weight and volume of water, which is why the water level remains constant.</p> <p>However, the upper liquid layer provides some buoyancy, so less of the ice cube is in the wa... |
Physics | |newtonian-mechanics|forces|rotational-dynamics|friction|rigid-body-dynamics| | How does rolling without slipping happen physically? | <blockquote> <p>"<em>What is the mechanism that assures the equality v=Rω, and under what conditions does it work?</em>"</p> </blockquote> <p>The condition when the friction force at the interface between the wheel's edge and the ground never exceeds the the (maximum) static friction. Because if it does, that's when yo... |
Physics | |newtonian-mechanics|vectors|velocity|collision|speed| | In this conservation of momentum problem, where is the sign error coming from? | <p>You have a choice of you keeping track of the vertical direction, or the math keeping track.</p> <p>Since you know one particle is going "up" and one particle is going "down", you can set the magnitude of their vertical momentum equal to each other. That's what you've done with the final equation. That works because... |
Physics | |electromagnetism|special-relativity|causality| | How do you make self-consistent initial values? | <p>Knowing the initial position and momenta of all charges, plus the analogous quantities for the electric and magnetic fields, at one initial time, is sufficient to determine the motion of the charges and fields at all later times (using the <a href="https://en.wikipedia.org/wiki/Green%27s_function#Advanced_and_retard... |
Physics | |oscillators|dissipation|linear-systems|coupled-oscillators| | How to demonstrate in a simple way that this system of differential equations form a damped harmonic oscillator? | <p>The standard technique to solve this system of linear differential equations <span class="math-container">$$\begin{align} \dot x &= -\alpha_x x - \omega y \\ \dot y &= -\alpha_y y + \omega x \end{align}$$</span> is to write it in matrix form: <span class="math-container">$$\frac{d}{dt}\begin{pmatrix}x \\ y \end{pmat... |
Physics | |thermodynamics|energy|thermal-radiation|thought-experiment| | Fundamental principles for simple radiative heat transfer problems | <p>The first thing to note is that the properties of the gray plate are such that it is for all intents and purposes a blackbody with respect to its absorption from the brown plate and its emission to space, but it is completely transparent to the radiation from the hot source. For example for a temperature of 300K a b... |
Physics | |newtonian-mechanics|newtonian-gravity|orbital-motion|celestial-mechanics| | Orbiting body around a star | <p>That equation relating the mass, orbital speed, radial distance, and semi-major axis is known as the <a href="https://en.wikipedia.org/wiki/Vis-viva_equation" rel="nofollow noreferrer">vis-viva</a> equation. Its standard form is</p> <p><span class="math-container">$$v^2 = \mu\left(\frac2r - \frac1a\right)$$</span></... |
Physics | |quantum-mechanics|quantum-field-theory|operators|harmonic-oscillator|second-quantization| | Ladder operators and creation & annihilation operators - different between $a$, $b$ and $c$ | <p>When we talk about the quantum harmonic oscillator, <span class="math-container">$a$</span> and <span class="math-container">$a^{\dagger}$</span> are usually used.(<span class="math-container">$a$</span> may stands for "annihilation".) Note that we have not discuss second quantization here, so <span class="math-cont... |
Physics | |electromagnetism|electric-circuits|electricity|electric-current|potential| | Why doesn't charge accumulate in a loop? | <p>It depends on how this potential difference is applied to the conductor. The first case seems to correspond to a conductor placed in an external electric field. Then the charges would move to the ends of the conductor and build up a counteracting electric field so that the field and potential difference and thus the... |
Physics | |forces|fluid-dynamics|drag| | Difference between Drag force and virtual force | <p>F.W. Bessel introduced the concept of 'added mass' or 'virtual mass' when he observed that the period of a pendulum moving in a fluid differs from that in a vacuum.</p> <p>Consider an object of mass <span class="math-container">$m$</span> connected to a spring of spring constant <span class="math-container">$k$</spa... |
Physics | |quantum-field-theory|lagrangian-formalism|renormalization|feynman-diagrams|dimensional-analysis| | Difference between renormalizable and super-renormalizable theories | <ul> <li><p>It should stressed be that Peskin & Schroeder are here using the old Dyson definitions of renormalizability. For a more general derivation of eq. (10.13), see e.g. <a href="https://physics.stackexchange.com/q/481249/2451">this</a> Phys.SE post, which also answers several of OP's questions.</p> </li> <li><p>... |
Physics | |quantum-field-theory|lagrangian-formalism|path-integral|quantum-chromodynamics|ghosts| | Ghosts in QCD Lagrangian | <p>It's conventional to specify the classical Lagrangian, which does not include ghost terms. (Ghosts only contribute at loop level).</p> <p>One reason not to write ghost terms, when one is speaking generically about the classical Lagrangian of QCD, is that the ghost terms depend on your gauge fixing procedure, so it d... |
Physics | |cosmology|space-expansion|redshift| | Why are physicists not more concerned that there are too many explanations for redshift in the universe? | <p>One of the difficult concepts for people starting in general relativity is that we can and often do use radically different coordinates to describe the same physical system. It often appears that we are using different physical theories when really it is the same theory (GR) just in different coordinates.</p> <p>In ... |
Physics | |quantum-mechanics|wavefunction|potential|schroedinger-equation|quantum-tunneling| | Why is probability outside the infinite square well zero? | <p>If the well is sufficiently deep to bind the particle, the wavefunction decays exponentially outside the well. The rate of exponential decay depends on the depth of the well. For an infinitely deep well, the decay is infinitely fast, so the amplitude is zero outside the well.</p> |
Physics | |special-relativity|coordinate-systems|acceleration|speed-of-light| | Rindler coordinates and objects possibly exceeding the speed of light | <p>I will use the more standard Rindler coordinates (<span class="math-container">$a=1$</span>): <span class="math-container">$$ \begin{align} t &= X\sinh T & x &= X\cosh T \end{align} $$</span> with <span class="math-container">$t,x$</span> inertial coordinates and <span class="math-container">$T,X$</span> your accele... |
Physics | |thermodynamics| | How do we know that we only need three second derivatives to represent all the second derivatives of a thermodynamic system? | <p>In the context that your thermodynamical system has 3 independent variables this is true. Because any other derivative along some direction in parameter space can be expressed as a linear combination of these. But in general, e.g. if you have like 200 particle species with all different chemical potential, I'm not s... |
Physics | |radiation| | Beta decay in Au-198 element | <p>Here is the decay chart from the <a href="https://pripyat.mit.edu/KAERI/" rel="nofollow noreferrer">KAERI website</a> which shows that your data was missing one of the possible <span class="math-container">$\beta^-$</span> decay modes.</p> <p><a href="https://i.stack.imgur.com/f23Zt.jpg" rel="nofollow noreferrer"><i... |
Physics | |general-relativity|energy-conservation|gravitational-waves|stress-energy-momentum-tensor|linearized-theory| | How do gravitational waves carry energy when gravitational energy cannot be localised? | <p>Suppose some matter A emits gravitational waves, and some matter B absorbs those waves, and the spacetime does not have further dynamics apart from this. In such a process the <span class="math-container">$0,0$</span> component of the energy momentum tensor <span class="math-container">$T_{\mu\nu}$</span> integrated... |
Physics | |quantum-field-theory|renormalization|interactions|effective-field-theory|non-perturbative| | Triviality of $\phi^4$ theory, is it settled now (2024)? | <p>It sort of depends on what exactly you mean by "settled". Up to physics standards, the question is definitely settled: it has been understood, for many decades now, that <span class="math-container">$\phi^4$</span> in <span class="math-container">$d=4$</span> is trivial. The only open question is to prove this in a ... |
Physics | |rotation| | Rotation of disc on smooth surface | <p>It is possible for an object to be on a frictionless surface and have both translational and rotational motion, i.e. rolling with slipping.(now, if you launch a rotating disc onto a frictionless surface with the right initial conditions, you <em>can</em> have rolling without slipping) In the case of pure rotation th... |
Physics | |statistical-mechanics|temperature| | Can energy be any energy in canonical ensembles? | <p>When we consider the canonical ensemble (so constant temperature <span class="math-container">$T$</span>) we have that given that the system consists of a set of energies <span class="math-container">${E_i}$</span>, the probability of finding the system in energy <span class="math-container">$E_j$</span> is proporti... |
Physics | |homework-and-exercises|newtonian-mechanics|forces|orbital-motion|propulsion| | Applying 1 gram-force for 1000 seconds to 1kg mass | <p>According to Newton’s laws F=ma. If a net force is applied to a body it <em>will</em> accelerate. With no net force the body remains in a state of constant motion, either at rest or with constant velocity in a straight line.</p> <p>When a body is accelerated its velocity will be a*t plus any initial velocity v_0. In... |
Physics | |tensor-calculus|group-theory|representation-theory|lie-algebra| | Multiplying two $SO(3)$ representations | <p><strong>Question 1</strong>. I don't have that text, but Tony is "cheating" by reminding himself that adding spin 2 to spin 1, your 5⊗3, he gets a spin 3, and a spin 2, and a spin 1, your more tasteful 7⊕5⊕3. His (2⋅3+1)=7 reminds you spin 3 is a septuplet, is all.</p> <p>Response to <strong>Question 2</strong> and ... |
Physics | |electromagnetism|magnetic-fields|isotopes|cold-atoms|ion-traps| | Ultracold magnetic traps for uranium enrichment | <p>In principle yes: One can enrich elements with magnetic traps. Even other traps are in principle feasible to enrich elements (Magneto-optical traps).</p> <p>HOWEVER (this is a big however!) typically, magnetic traps can trap only very few atoms (e.g. ~10^8 for rubidium).</p> <p>Trapping 10^8 uranium atoms (which is ... |
Physics | |classical-mechanics|lagrangian-formalism|conventions|notation| | Why do we multiply the Euler-Lagrange equations by negative one? | <p>If you were to prefer one over the other, perhaps you could argue for</p> <p><span class="math-container">$$\frac{\partial L}{\partial q_k} - \frac{d}{dt} \left( \frac{\partial L}{\partial \dot{q}_k} \right) = 0.$$</span></p> <p>since that's what directly follows from the condition that the integrand must be 0 in th... |
Physics | |electromagnetism|magnetic-fields|electric-current| | Does a single moving charge produce magnetic field in an empty universe? | <p>According to our current understanding of electromagnetism, a single moving charge in an empty universe would not produce a static magnetic field in the reference frame where the charge is at rest.</p> <p>Here's why:</p> <p>Magnetic field arises from relative motion: Magnetism is a consequence of the theory of relat... |
Physics | |waves| | Wavefront of concentric Water Waves | <p>In a water wave, molecules travel in a circle as the wave passes. The crest of the wave is where the molecules are at the top of their circle.</p> <p>The surface where all molecules are at the top is a wavefront. You could also pick any other phase: at the bottom, or at <span class="math-container">$37^o$</span>.</p... |
Physics | |electromagnetic-radiation|wavelength| | Emission spectrum of a fluorescent lamp | <p>the emission lines you detect are only those that make it all the way through the phosphor coating on the inside of the CFL tube. Those phosphors are designed to absorb as much of the spectral output of the ionized mercury as possible and convert it into a mixture of red, green and blue light that your eye interpret... |
Physics | |general-relativity|black-holes|kerr-metric| | Perimeter of Kerr's event horizon | <p>Horizon is a <em>null hypersurface</em>, the metric induced on it is degenerate, so it does not matter how you define hypersurface <span class="math-container">$t=\mathrm {const}$</span>, circumference of the equator would not change.</p> |
Physics | |optics|experimental-physics|laser|interferometry|fiber-optics| | Why fiber optic Sagnac interferometers don't produce multiple interference fringes | <p>The fibre is a single mode fibre and the phase is therefore associated with the mode as a whole varying along the longitudinal direction. The interference thus only determines which output port gets how much of the wave. There is no transverse phase variation.</p> |
Physics | |quantum-field-theory|operators|quantum-interpretations|observables| | Dictionary between interpretations of field operators | <p>Assuming that you are interested in the physical interpretation of the hermitean field operator of a free <em>relativistic</em> scalar theory in the Heisenberg picture, its Fourier decomposition (omitting the hat indicating the operator) is given by <span class="math-container">$$\begin{align} \phi(t, \vec{x})&=\int... |
Physics | |thermodynamics|energy|temperature|entropy| | Does the notion of temperature depend on the zeroth law of thermodynamics? | <p>Yes, there are different notions of temperature and they are not the same.</p> <p>The notion of temperature arising from the zeroth law is that you can assign some number to objects describing the direction of heat flows. This is not sufficiently precise to lead to a unique quantity temperature – even beyond the pro... |
Physics | |quantum-mechanics|hilbert-space|wavefunction|mathematical-physics|quantum-states| | When do two state functions represent the same quantum state? | <p>The set of wavefunctions which corresponds to the same state as <span class="math-container">$\psi$</span> is just the set of multiples of <span class="math-container">$\psi$</span> by a non-zero complex number (respectively, a complex number of absolute value <span class="math-container">$1$</span>, if you consider... |
Physics | |condensed-matter|solid-state-physics|dispersion|ferromagnetism|domain-walls| | Derivation in a Landau-Lifshitz ferromagnetism paper | <p>As you wrote, the expression is for the energy <em>density</em>, so its dimensions are [Energy / volume]. Meaning that <span class="math-container">$\alpha$</span> has dimensions of <span class="math-container">$[E a^2 s^{-2} a^{-3}] = [E s^{-2} a^{-1}]$</span> as they have in their formula</p> |
Physics | |classical-mechanics|rotational-dynamics|angular-momentum|definition| | Why is angular momentum defined so? | <p>The concept of angular momentum has a precursor: Kepler's law of areas. In retrospect: Kepler's law of areas is an instance of conservation of angular momentum.</p> <p>Isaac Newton showed in his work 'Principia' that Kepler's law of areas generalizes to <em>any</em> central force.</p> <p>There is a 2022 answer (by m... |
Physics | |general-relativity|metric-tensor|perturbation-theory|klein-gordon-equation|qft-in-curved-spacetime| | Dervation of the first-order Klein-Gordon equation | <p>In your case, one has <span class="math-container">$$ \sqrt{-g}=\sqrt{a^8(1-2\Phi)(1-2\Psi)^3}\approx a^4\left(1-\Phi-3\Psi\right). $$</span></p> |
Physics | |newtonian-mechanics|rotation| | Understanding the relationship between the angular velocity and angular acceleration vectors | <p>So my understanding is that you are always finding the direction of the angular velocity and calling that the <span class="math-container">$z$</span>-direction, such that <span class="math-container">$\boldsymbol{\omega} = \omega \boldsymbol{k}$</span> where <span class="math-container">$\boldsymbol{k}$</span> is th... |
Physics | |thermodynamics|entropy|reversibility| | Change in entropy in reversible and irreversible process | <blockquote> <p>But to prove it we used the fact that in reversible process <span class="math-container">$dS=\frac{\delta Q_{rev}}{T}$</span>. How is that logically possible?</p> </blockquote> <p>I think you misunderstand. The entropy change is <em><strong>defined</strong></em> for a reversible transfer of heat, but ap... |
Physics | |homework-and-exercises|rotational-dynamics|reference-frames|work|rigid-body-dynamics| | Doubt in rotational work-energy theorem | <p>There is no such thing as "rotational work" or "translational work". Work is work and energy is energy. In fact, we can go further - "work" and "energy" are just two names for the same thing.</p> <p>The horizontal force <span class="math-container">$F$</span> moves through a horizontal distance <span class="math-con... |
Physics | |magnetic-fields|magnetic-moment| | Confusion regarding magnetic moment | <p>Imagine if you have two dipoles that are right next to each other pointing in opposite directions. Such a configuration has no dipole moment, and at long range the field is a "quadruple" field. That's the next term in the multipole expansion.</p> |
Physics | |general-relativity|field-theory|resource-recommendations|vortex|cosmic-string| | Metric of a rotating Cosmic String | <p>The "Catalogue of Spacetimes" review of exact solutions to Einstein's equation, <a href="https://arxiv.org/abs/0904.4184" rel="nofollow noreferrer">Mueller & Graves (2009)</a>, is the first place I would look. And sure enough section 2.22 might be what you are looking for. They pulled that metric from <a href="https... |
Physics | |newtonian-mechanics|rotation| | A drum is rolling down a hill - is the force of friction with the surface a constant? | <p>Yes, <strong>friction must be static</strong> because the point that is in contact with the ground at a particular instant is in rest (wrt ground).</p> <p>Yes, the <strong>frictional force is constant</strong>.</p> <p>mgsin(θ) - ƒ = ma</p> <p>ƒR = {m(r^2)/2}* (α)</p> <hr /> <p>m = mass of drum r = radius of drum θ =... |
Physics | |forces|rotational-dynamics|work|rigid-body-dynamics| | Rotational work by a force | <blockquote> <p>If we have an object which is acted upon by a force which which produces both translational and rotational motion of body then would the total work done by the force be the sum of its translational and rotational work?</p> </blockquote> <p>There may be semantic issues here and it would perhaps to cleare... |
Physics | |general-relativity|black-holes|astrophysics|polarization|frame-dragging| | Is this an actual photo of frame dragging? | <p>It is not frame dragging, it is a visualisation of the linear polarisation present in 230 GHz light emerging from the vicinity of Sgr A* at the centre of the Milky Way. But getting an answer took some detective work...</p> <p>The press release links to a paper by the <a href="https://iopscience.iop.org/article/10.38... |
Physics | |quantum-mechanics|fermions|dirac-delta-distributions|grassmann-numbers|coherent-states| | Grassmann variables and orthogonality of coherent fermionic states | <ol> <li><p>Bosonic (Grassmann-even) and fermionic (Grassmann-odd) <a href="https://en.wikipedia.org/wiki/Coherent_state#Mathematical_features_of_the_canonical_coherent_states" rel="nofollow noreferrer">coherent states</a> are <em>overcomplete bases,</em> that are <em>not</em> orthogonal.</p> </li> <li><p>One may show ... |
Physics | |homework-and-exercises|special-relativity|relative-motion| | Calculating relative velocity: What am I doing wrong? | <p>The mistake is in making differences between positions as they were scalars, while they are vectors.</p> <p>Consider the vectors <span class="math-container">$\vec{r}_1$</span>, <span class="math-container">$\vec{r}_2$</span>, and <span class="math-container">$\vec{r}_3$</span> corresponding to the position of <span... |
Physics | |electromagnetism|magnetic-fields|electric-fields|electromagnetic-induction| | How do Electric and magnetic fields generate each other (mathematically)? | <p>Linked differential equations <em>may</em> reinforce one another leading to unbounded exponential growth - but they do not have to.</p> <p>For example, the linked equations</p> <p><span class="math-container">$\displaystyle y = \frac {dx}{dt} \\ \displaystyle x = \frac {dy}{dt}$</span></p> <p>with initial conditions... |
Physics | |quantum-mechanics|wavefunction|schroedinger-equation|boundary-conditions| | Question about Griffiths' proof that $\Psi$ stays normalized | <p>The proof by Griffiths relies in fact on stronger (implicit) hypotheses about the behaviour of <span class="math-container">$\psi$</span> at infinity. These hypotheses could be justified by requiring (as in Giorgio's answer of the other question) that the used <span class="math-container">$\psi$</span> also belongs ... |
Physics | |electromagnetism|electrostatics|electric-circuits| | Why Don't Electrons "Try" to Flow in an Open Circuit? | <p>An open switch can be thought of as a capacitor with a very small capacitance with air as the dielectric. As such opposite sign charges can reside on the two sides of a switch wand there will be a potential difference across the switch. Thus there will be a time when current flows along the wires until the capacitor... |
Physics | |quantum-field-theory|feynman-diagrams|correlation-functions|self-energy|1pi-effective-action| | Understanding $W^{(n)}$, $\Gamma^{(n)}$, and $\Sigma$ in Feynman diagrams | <ul> <li><p>The connected <span class="math-container">$n$</span>-point function <span class="math-container">$$\langle \phi^{k_1}\ldots \phi^{k_n}\rangle^c_{J=0}~=~\left(\frac{\hbar}{i}\right)^{n-1} W_{c,n}^{k_1\ldots k_n}$$</span> is the sum of connected Feynman diagrams with <span class="math-container">$n$</span> e... |
Physics | |quantum-mechanics|electromagnetism|entropy|physical-chemistry|electrochemistry| | Can a Transformer Last until the Heath Death of the Universe if Made with Inorganic Insulation? | <p>Your transformer will last nowhere near the heat death of the universe. The heat death of the universe is a really really really really really really really really really really really really really really really really really really really really really really really really really really long time away. And to be p... |
Physics | |classical-mechanics|lagrangian-formalism|harmonic-oscillator|action| | Directly integrating the Lagrangian for a simple harmonic oscillator | <ol> <li><p>Well, if we know the classical solution <span class="math-container">$q_{\rm cl}:[t_i,t_f] \to \mathbb{R}$</span> (which we do for the harmonic oscillator), we can plug it into the action functional <span class="math-container">$S[q]$</span> and obtain the on-shell action function <span class="math-containe... |
Physics | |electromagnetism|magnetic-fields|electric-fields|electromagnetic-induction| | Induced Electric field due to magnetic field in Faraday experiment | <p>To start with question 3), the case where there is no coil but just a magnet that you move through empty space, as <a href="https://physics.stackexchange.com/users/161019/user1245">@user1245</a> asked in question<a href="https://physics.stackexchange.com/questions/343447">questions/343447</a>: is there a force oppos... |
Physics | |fluid-dynamics|pressure|fluid-statics|flow|bernoulli-equation| | Bottle with a hole, with straw through the lid | <p>It is clear that the water tap works by regulating the air supply through bubbles in the red straw, but how it does that is interesting.</p> <p>The bubble formation only happens at a threshold pressure. Since water pressure has a linear vertical gradient, he can control when this threshold is crossed by moving the s... |
Physics | |general-relativity|astrophysics| | What is the energy density on the surface of a polytropic gas sphere? | <blockquote> <p>Where is my fallacy?</p> </blockquote> <p>The “fallacy” is in the choice of matter model. If you want a solution of Einstein equation with a distinct boundary between matter and vacuum then you have to choose matter that allows nonzero density with zero pressure. But <em>polytropic gas</em> has equation... |
Physics | |newtonian-mechanics|angular-momentum|rotational-kinematics|angular-velocity| | Understanding the meaning of the directions of $\vec\omega$ and $\vec{L}$ | <p>It sounds like you got if figured out. The direction of <span class="math-container">$\vec \omega$</span> is always perpendicular to the plane defined by <span class="math-container">$\vec r\times \vec v$</span>. Further, <span class="math-container">$\vec \omega$</span> is always parallel to the axis of rotation wh... |
Physics | |newtonian-mechanics|fluid-dynamics|kinematics|vectors| | What is the locus of the velocity vectors of a boat navigating in the sea under the presence of some force? | <p>We know from Newton's second law that</p> <p><span class="math-container">$\displaystyle \vec F = \frac {d(m \vec v)}{dt}$</span></p> <p>and as long as the mass <span class="math-container">$m$</span> of the boat is constant we can conclude that</p> <p><span class="math-container">$\displaystyle \vec F = m \frac {d ... |
Physics | |electromagnetism|poynting-vector| | Confusion in Poynting's theorem | <p>Whenever you have a conflict between some established principle and the concept of a classical point charge, the issue is the classical point charge. They lead to all sorts of oddities like infinite energy, weird self-forces, and other such things.</p> <p>Poynting's theorem follows directly from Maxwell's equations.... |
Physics | |newtonian-mechanics|forces|free-body-diagram| | Tension while hanging from a bar | <p>You are correct. <span class="math-container">$T = \frac {mg} {2 \cos(x)}$</span> where <span class="math-container">$x$</span> is <em>half</em> the angle between the arms. When <span class="math-container">$x=0$</span> (arms vertical below the bar) we have <span class="math-container">$T = \frac {mg} 2$</span>. As ... |
Physics | |quantum-mechanics|fourier-transform|heisenberg-uncertainty-principle|dimensional-analysis|physical-constants| | How does the Planck constant enter into the uncertainty principle? | <p>Notice that the kernel of the transform from position to momentum representations is <span class="math-container">$$ e^{- i x p / \hbar}. $$</span> Thus, comparing with your definition of Fourier transform, you need to have <span class="math-container">$$ \xi = \frac{p}{h}, $$</span> while you used <span class="math... |
Physics | |thermodynamics|fluid-dynamics|temperature|everyday-life| | What is the difference between heating and cooling, fundamentally? | <p>Heating and cooling were originally thought to be different things. The equations for them were derived differently. Eventually it was discovered that they are the same mechanism, but in opposite directions. (James Maxwell)</p> <p>What you describe, however, is more than <em>just</em> heating or cooling. When you ta... |
Physics | |general-relativity|reference-frames|acceleration|time-dilation|equivalence-principle| | On the equivalence principle | <p>These considerations about the principle of equivalence fall in the category of cases where there is a tension between local assessment and global assessment.</p> <p>Example:<br /> Locally any part of the Earth's surface is - as far as the naked eye can tell - flat, but globally the shape of the Earth is (to a very ... |
Physics | |electromagnetic-radiation|wavelength|doppler-effect|gravitational-redshift| | How is wavelength defined when it's changing continuously? | <p>Those are good ways. Though you can't make the time interval infinitesimal because you then can match any sine wave.</p> <p>If the function is slowly varying, the frequency doesn't change fast. You get a good estimate of the frequency at a given time from the wave in the near future and near past. So average over an... |
Physics | |hamiltonian-formalism|phase-space|constrained-dynamics|poisson-brackets| | Why do we need a Poisson bracket structure? | <p>The simplest way to motivate the Dirac bracket is to consider a situation where two second-class constraints <span class="math-container">$f_1,f_2$</span> have constant non-zero Poisson bracket <span class="math-container">$\{f_1,f_2\} = c \neq 0$</span>, e.g. when we have a system where one pair of position and mom... |
Physics | |cosmology|perturbation-theory| | Expression for $k_\mathrm{eq}$, the wavenumber entering the horizon at matter-radiation equality | <p><span class="math-container">$$H(a_\mathrm{eq})=H_0 \sqrt{\Omega_\mathrm{m}a_\mathrm{eq}^{-3}+\Omega_\mathrm{r}a_\mathrm{eq}^{-4}+\Omega_\Lambda}.$$</span> But <span class="math-container">$\Omega_\mathrm{m}a_\mathrm{eq}^{-3}=\Omega_\mathrm{r}a_\mathrm{eq}^{-4}$</span> at matter-radiation equality, by definition: th... |
Physics | |quantum-mechanics|experimental-physics|interference|diffraction|wavelength| | What is the upper limit of size for diffracting an object? | <p>As far as I know the largest object that has been successfully diffracted is a oligoporphyrin molecule with a molecular weight of about <span class="math-container">$25000$</span>. This was done on 2019 and is reported in <a href="https://www.nature.com/articles/s41567-019-0663-9" rel="nofollow noreferrer">Quantum s... |
Physics | |homework-and-exercises|differentiation|error-analysis|statistics| | Question regarding error analysis of focal length of a lens | <p>There are two separate issues here. Firstly you're asking how differentiation is being used here, and secondly you correctly point out that errors should be added in quadrature.</p> <p>Let's take the second issue first: you are correct that if the errors are normally distributed and if our equation is:</p> <p><span ... |
Physics | |thermodynamics|energy|differential-geometry|entropy| | How to understand the relationship between Weinhold geometry and Ruppeiner geometry in thermodynamic geometry? | <p>You have to provide more background information, with more-accessible references.</p> <p>From a Google search, these seem relevant and more-accessible</p> <ul> <li><a href="https://en.wikipedia.org/wiki/Ruppeiner_geometry" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Ruppeiner_geometry</a></li> <li>(presu... |
Physics | |kinematics|velocity|differentiation| | How to calculate the final position of a particle under variable accelaration and its instantenous velocity? | <p>The time shown on the screen(4 mins) is also instantaneous and based on the speed of the train. That's why ETA decreases when you reach closer to the destination. So, <span class="math-container">$d=V(inst) × t = 11.73 km$</span></p> <p>No need of calculus here it seems. About your second part, the relation of <span... |
Physics | |general-relativity|reference-frames|acceleration|centrifugal-force|equivalence-principle| | Would objects really be at rest relative to each other in orbit? | <p>From a Newtonian perspective the objects free-floating inside the spaceship are subject to (almost) exactly the same gravitational acceleration as the spaceship and travel on similar orbits. The walls of the spaceship do not "shield" them from gravitational attraction. Hence there is no apparent centrifugal or corio... |
Physics | |quantum-field-theory| | Orthonormality condition of polarization four-vectors | <p>The choice that you propose is not possible. You can change the sign of all <span class="math-container">$\zeta$</span>, which is a matter of taste.</p> |
Physics | |electromagnetism|electrostatics|energy|acceleration|propulsion| | Are there very high voltage very low amperage electromagnetic/electrostatic launchers? | <p>In a launcher, force comes from the magnetic field. The magnetic field comes from the current. So they are designed for high current and low voltage. High current comes with high resistive heating.</p> <p>There is no simple way around it. Use the strongest, lowest resistance material you can.</p> <p>Superconductors ... |
Physics | |special-relativity|tensor-calculus|linear-algebra| | Determinant of Rank-2 Tensor using Levi-Civita notation | <p>Levi-cevita symbol which is defined as <span class="math-container">$$ \varepsilon_{\mu\nu\rho\sigma}= \begin{cases} +1&\text{if}\,{\mu\nu\rho\sigma} \rm \, is\,an\,even\,permutation\,of\,0123 \\ -1&\text{if}\, {\mu\nu\rho\sigma}\rm \,is\,an\,odd\,permutation\,of\,0123\\ 0&\text{otherwise} \end{cases} $$</span> is a... |
Physics | |homework-and-exercises|quantum-field-theory|integration|causality|propagator| | Exponential decay of propagator outside lightcone | <p>Such asymptotic behaviour are typically calculated using the Laplace method (which is generalised to the saddle point method). It's worth looking into in depth, you'll use it again and again in QFT. You want to estimate (setting <span class="math-container">$m=1$</span> to fix the energy scale): <span class="math-co... |
Physics | |thermodynamics|energy|ideal-gas| | Internal energy of a gas under motion | <p>If you also consider the motion of the system, then you have to use a more sophisticated formalization of the thermodynamical system, proper of the <em>theory of continuum thermo-mechanics</em>.</p> <p>There, the work done on the system is responsible for both thermodynamical effects (together with the heat entering... |
Physics | |electromagnetism|charge|potential| | Is there any finite charge distribution the potential of which doesn't decay with $\frac{1}{r}$ at infinity? | <p>If the charge distribution is finite in it's spatial extension and it is simple in the sense that it is composed of all positive or all negative charge, then the potential will always look like <span class="math-container">$1/r$</span> at far distances. However, if you have more complicated distributions, for exampl... |
Physics | |mathematics|dirac-delta-distributions| | Manipulation of functions inside a Dirac Delta function | <p>This is pretty grotesque.</p> <p>You need to first know a property of the Dirac delta distribution. It is stated as <span class="math-container">$$\tag1\delta[g(x)]=\frac{\delta(x-x_0)}{|g^\prime(x_0)|}$$</span> on Wikipedia, say, for any function <span class="math-container">$g$</span> that has a simple isolated ro... |
Physics | |quantum-mechanics|wavefunction|schroedinger-equation|scattering|s-matrix-theory| | Scattering Matrix and the Lippmann-Schwinger equation in QM | <blockquote> <p><strong>However, is there a formula that relates the S-matrix elements and these states <span class="math-container">$\psi^{(+)}$</span> and <span class="math-container">$\psi^{(-)}$</span>?</strong></p> </blockquote> <p>You have not provided a sufficiently detailed description of what exactly the <span... |
Physics | |electromagnetism|antennas|waveguide| | Phasors and propagating modes in a waveguide | <p>In a homogeneous waveguide, both propagating TE and TM waves, modes, can be derived from the scalar Helmholtz equation. Let <span class="math-container">$\partial \mathcal B =0$</span> denote the metal boundary of the cross section. Denoting the wavenumber in the guide by <span class="math-container">$\beta$</span> ... |
Physics | |homework-and-exercises|kinematics| | Doubt regarding Velocity-Time graph with Constant Accleration | <p>Initial velocity is not 0 in condition C and E.</p> |
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