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16605 | What is lepton number? | What exactly is a lepton number of a particle? With the charge (eg proton is just 1, not the exact charge), I can understand because it's a physical property, put a particle with charge + next to another particle with charge + and they will repel. What is the lepton number in similar terms? Or is it just a convention t... | What is the lepton number of an electron, and how does it compare to the lepton number of a proton? Additionally, explain how lepton number conservation plays a role in particle interactions. | 6,803 | cqadupstack-physics |
16339 | Force as gradient of scalar potential energy | My text book reads > _If a particle is acted upon by the forces which are conservative; that is, > if the forces are derivable from a scalar potential energy function in > manner $ F=-\nabla V $._ I was just wondering what may be the criteria for force to be expressed as negative gradient of scalar potential energy and... | What are the necessary conditions for a force to be classified as conservative, and how can we mathematically demonstrate that it can be expressed as the negative gradient of a scalar potential energy function? | 22,843 | cqadupstack-physics |
39400 | About turbulence modeling | I have some questions about this paper: > Lagrangian/Hamiltonian formalism for description of Navier-Stokes fluids. R. > J. Becker. _Phys. Rev. Lett._ **58** no. 14 (1987), pp. 1419-1422. After reading the paper, the question arises how far can we investigate turbulence with this approach? With all the mathematical mac... | What are the implications of using Lagrangian density to analyze turbulence in Navier-Stokes fluids, and how can it potentially aid in understanding the energy dissipation rates in turbulent flow? | 35,173 | cqadupstack-physics |
71395 | Electric field at the centre of a charged disc of uniform charge density | The electric field at any point at a finite distance z from the centre of a charged disc of uniform charge density along the axis of the disc is given by the equation:  According to this equation, at z=0, the electric field is : ![el... | Given a uniformly charged disc with charge density \(\sigma\) and radius \(R\), derive the expression for the electric field \(E\) at a point along the axis of the disc at a distance \(z\) from its center. Additionally, calculate the electric field \(E\) at the center of the disc (when \(z = 0\)) and explain why it is ... | 22,252 | cqadupstack-physics |
19703 | What makes up a resonator of radio? | I was reading this article about resonators. **Quote** : > The sine wave that matches that particular frequency will get amplified by > the **resonator** , and all of the other frequencies will be ignored. As far as I know, in picture below, the capacitor and inductor below makes up an **oscillator circuit** which osci... | What is the relationship between the frequency of an oscillator circuit composed of a capacitor and inductor, and the resonant frequency at which a resonator amplifies a sine wave? If the inductor has a value of 10 µH and the capacitor has a value of 100 nF, what is the resonant frequency of the circuit? | 10,702 | cqadupstack-physics |
45588 | Cosmology questions from a novice | These ideas/questions probably represent a lack of understanding on my part, but here they are: 1) Cosmologists talk about the increasing speed of expansion of the universe and talk of dark energy as the cause. But, I keep thinking that the farther out we observe, is farther back in time and the light we observe is fro... | What evidence supports the theory that the universe's expansion is accelerating, and how do cosmologists account for the effects of distant objects not being in their current state but rather at their positions and velocities billions of years ago? | 14,853 | cqadupstack-physics |
26945 | Gauge invariance for electromagnetic potential observables in test function form | This is a reference request for a relationship in quantum field theory between the electromagnetic potential and the electromagnetic field when they are presented in test function form. $U(1)$ gauge invariance becomes a particularly simple constraint on test functions for smeared electromagnetic potential operators to ... | What conditions must the test function \( f^\rho(x) \) satisfy in order for the smeared electromagnetic potential \( \hat A_f \) to be a \( U(1) \) gauge invariant observable, and how does this relate to the properties of the commutator for creation and annihilation operators associated with the electromagnetic potenti... | 3,749 | cqadupstack-physics |
65947 | Deriving the Angular Momentum Commutator Relations by using $\epsilon_{ijk}$ Identities | I've been trying to derive the relation $$[\hat L_i,\hat L_j] = i\hbar\epsilon_{ijk} \hat L_k $$ without doing each permutation of ${x,y,z}$ individually, but I'm not really getting anywhere. Can someone help me out please? I've tried expanding the $\hat L_i = \epsilon_{nmi} \hat x_n \hat p_m$ and using some identities... | Can you derive the commutation relation for the angular momentum operators, specifically showing that $$[\hat L_i, \hat L_j] = i\hbar \epsilon_{ijk} \hat L_k$$ using the definition of angular momentum in terms of position and momentum operators, and without resorting to the individual permutations of ${x,y,z}$? | 33,837 | cqadupstack-physics |
89532 | Feynman propagators for scalar fields | If there are few massless scalar field, are the propagators of those different massless scalar fields indistinguishable? | If there are multiple massless scalar fields in a quantum field theory, how do their propagators interact, and can we distinguish between the propagators of different scalar fields based on their mathematical properties? | 3,105 | cqadupstack-physics |
72128 | classical understanding of an atom | A problem in Bohr's day was understanding why an orbiting electron does not continuously radiate an EM field. An orbiting electron is a moving charge and according to Maxwell, this should generate an electric and magnetic field. Bohr said that photons (packets of EM energy) are only emitted when an electron jumps from ... | In Bohr's model of the atom, if an electron transitions from the n=3 quantum state to the n=2 quantum state and emits a photon with a wavelength of 656 nm, what is the energy difference between these two states, and how does this relate to the energy levels described by the Rydberg formula? | 20,116 | cqadupstack-physics |
109780 | Expectation value of Hamiltonian in different pictures of quantum mechanics | We start with the familiar Schrodinger equation: $$ i\hbar \frac{\partial \left|\psi_S\right\rangle}{\partial t} = \hat{H}_S \left|\psi_S\right\rangle $$ As we switch to a different picture than Schrodinger picture with a unitary transformation $\hat U$: $$ \left|\psi_S\right\rangle = \hat{U}\left|\psi_P\right\rangle $... | In the context of quantum mechanics, if we transform from the Schrödinger picture to an arbitrary picture using a unitary transformation, we find that the expectation values of the Hamiltonian and other observables are not necessarily equal in the two pictures. Given the expression for the Hamiltonian in the arbitrary ... | 35,840 | cqadupstack-physics |
119393 | Local fermionic symmetry and GS action | I have a trouble understanding an argument which I think has a simple answer but I am not getting it. The question is that if you don't impose local fermionic symmetry the GS action has only one term and one of the equation of motion looks as $Γ\cdot p\partial_0\psi=0$, where $\psi$ is a Majorana-Weyl spinor in 10 dime... | If the operator \( \Gamma \cdot p \) is such that \( (\Gamma \cdot p)^2 = 0 \) for the on-shell condition, what can we conclude about the eigenvalues of the operator \( \Gamma \cdot p \) and how many of them must be zero? Please provide a detailed explanation of the mathematical reasoning involved. | 33,541 | cqadupstack-physics |
93124 | Divergent Series | Why is it that divergent series make sense? Specifically, by basic calculus a sum such as $1 - 1 + 1 ...$ describes a divergent series (where divergent := non-convergent sequence of partial sums) but, as described in these videos, one can use Euler, Borel or generic summation to arrive at a value of $\tfrac{1}{2}$ for ... | Given the divergent series \( S = 1 - 1 + 1 - 1 + \ldots \), how can we show that its Cesàro sum converges to \( \frac{1}{2} \)? Please explain the reasoning behind this result in the context of summation methods for divergent series. | 28,443 | cqadupstack-physics |
16998 | Duality and Fourier Transforms | I read that $(FF(f))(x)=2\pi f(-x)$, where $F$ is the Fourier transform _and_ $F(f(x-a))(k)=\exp(-ika) X(k)$ where $X(k)=F(f(x))$ _implies_ $F(\exp(iax)f(x))(k)=X(k-a)$. But I don't see how that is done... I am quite happy with getting $F^{-1}X(k-a)=\exp(iax)f(x)$ by brute force calculation. I would like to see how to ... | How can you derive the relationship \( F(\exp(iax)f(x))(k) = X(k-a) \) using the properties of the Fourier transform, specifically through the concept of duality, rather than through direct calculation? | 10,139 | cqadupstack-physics |
66064 | Can anyone please explain Hawking-Penrose Singularity Theorems and geodesic incompleteness? | Can anyone please explain Hawking-Penrose Singularity Theorems and geodesic incompleteness? In easy to understand plain English please. | What are the implications of the Hawking-Penrose Singularity Theorems on the existence of geodesic incompleteness in the context of general relativity, and can you provide a quantitative example illustrating these concepts? | 9,246 | cqadupstack-physics |
46292 | Rough, easy DIY method of measuring magnetic field strength | How to easily, using standard DIY equipment measure the strength of magnetic field generated by a permanent magnet? Narrowing down the "loose language" of the above: strength of magnetic field: either flux density **B** at given point relative to the magnet or magnetic flux ΦB over area enclosed by a loop made of wire ... | What is a simple method to measure the magnetic flux density **B** at a point 5 cm from a permanent magnet using common household items and basic tools, while allowing for an error margin of up to 50%? | 20,004 | cqadupstack-physics |
131246 | Can refraction of the atmosphere be so high that the surface of a planet seems concave to its inhabitants? | In their novel Inhabited Island by brothers Strugatsky, the inhabitants of a planet think they live on the inner surface of a giant sphere because the refraction of the atmosphere makes the surface appearing concave. At the same time, the atmosphere is suitable for a human to breathe. I wonder whether it is actually po... | Given the scenario of a planet's atmosphere creating a concave appearance, calculate the minimum density of the atmosphere required to provide a refraction index such that light entering the atmosphere from space bends sufficiently to give the inhabitants the illusion of living on the inner surface of a giant sphere. A... | 8,916 | cqadupstack-physics |
65908 | The quickest 6-3 play in baseball: to bounce or not to bounce? | What's the quickest way the get the ball (say from shortstop) into the first- baseman's glove, given some fixed initial (throwing) speed? Directly or with one bounce? I'm fairly sure that the answer depends on the initial throwing speed, but where's the cut-off point (roughly)? * * * PS 1: Numbers, _if needed_ : > Unde... | Given a fixed initial throwing speed, calculate the maximum distance from the shortstop position to first base (36 m) where a baseball can be thrown directly to first base without bouncing, and determine the threshold initial speed at which it becomes faster to throw the ball with one bounce off the clay surface. Assum... | 14,567 | cqadupstack-physics |
13106 | Circulate smoke in a closed system | Hey i am by no means a scientist but i have a idea for a art work using smoke. Basically what i want to know is whether it is possible to circulate smoke by means of a pump through a transparent box. If the box is completely sealed will the smoke disappear within time? When the smoke is pumped out and back in again, wi... | If smoke is circulated through a sealed transparent box using a pump, what factors will affect the visibility and concentration of the smoke over time, and will the smoke maintain its original properties after being pumped out and back in? | 15,838 | cqadupstack-physics |
115126 | Magnetic flux density a small distance off axis from a current loop | I'm currently studying physics at University and struggling with the problem mentioned, it's on a past paper I'm trying to do. I have calculated the B field on axis as (sorry don't know how to format this yet) $$B = \mu \frac{Ia^2 }{2(a^2 + z^2)^{3/2}}$$ In the $z$ direction. The question then asks: > At a small distan... | Given the formula for the magnetic field on the axis of a circular current loop, $$B = \mu \frac{Ia^2 }{2(a^2 + z^2)^{3/2}}$$, where \( \mu \) is the permeability of free space, \( I \) is the current, \( a \) is the radius of the loop, and \( z \) is the distance along the axis from the center of the loop, how do you ... | 16,392 | cqadupstack-physics |
44430 | Momentum And Energy Problem | The information to the question is, "A $59.0~kg$ boy and his $38.0~kg$ sister, both wearing roller blades, face each other at rest. The girl pushes the boy hard, sending him backward with a velocity $3.00~m/s$ toward the west. Ignore friction." The specific question I am working on is, "How much potential energy in the... | Given that a $59.0~kg$ boy moves backward with a velocity of $3.00~m/s$ after being pushed by his $38.0~kg$ sister, what is the total kinetic energy of the boy after the push, and how much potential energy from the girl was converted into this kinetic energy, assuming no energy losses to friction? | 34,361 | cqadupstack-physics |
45792 | fitting van der waals law on real data | For an examples class on thermodynamics, I would like to fit Van der Waals law on data of real gasses, say $CO_2, H_2O_2, CH_4$. I want to set out measurements of pressure and volume at constant temperature in a P-V diagram, and make a fit to determine the van der Waals parameters a and b. Only I have no idea where to ... | What are the values of the van der Waals parameters \(a\) and \(b\) for the gases \(CO_2\), \(H_2O_2\), and \(CH_4\), and where can I find reliable experimental data for their pressure and volume measurements at constant temperature to fit Van der Waals law? | 24,568 | cqadupstack-physics |
61540 | Induced charge on sphere | I have a conducting sphere ($radius = a$) at potential $V_0$. It is enclosed by another thin shell ($radius = b, b > a$) which has a charge density $\sigma (\theta) = \sigma_0 \cos(\theta)$ for the polar angle. I'm supposed to find the potential everywhere, noting the field discontinuities at $r = a$ and $r = b$ (this ... | What is the electric potential at a distance \( r \) for the region inside the conducting sphere, between the conducting sphere and the thin shell, and outside the thin shell, given the surface charge density \( \sigma(\theta) = \sigma_0 \cos(\theta) \) on the thin shell? Additionally, how do you calculate the surface ... | 11,428 | cqadupstack-physics |
19298 | In the dual-slit experiment, can the time it takes for a photon to arrive reveal the path it took? | It seems like this experiment is possible: 1. Fire a photon, and start a timer 2. The photon travels through the slit(s) 3. The photon strikes a plate -- the timer is stopped. Based on where on the plate the photon struck, the time it took, and the speed of light, it seems possible to deduce through which slit th... | If a photon is fired from a source toward a double slit apparatus and strikes a detection plate located 2 meters away, and the timer indicates that it took 6.67 nanoseconds to reach the plate, can we conclusively determine through which slit the photon passed based on its impact location on the plate? What assumptions ... | 4,872 | cqadupstack-physics |
102223 | Can a long pipe stop the flow of a liquid from a pump? | If a pump is discharging a fluid into a pipe, is it possible to add a long enough pipe such that the flow of the liquid will be stopped and none will come out of the open end of the pipe? | If a pump is discharging a fluid with a flow rate of 5 liters per minute into a vertical pipe that is 10 meters long, what minimum length of horizontal pipe is needed to completely stop the flow at the open end, assuming the pipe is full of liquid and factors like friction and viscosity are negligible? | 24,282 | cqadupstack-physics |
61241 | Physics Applications of Fredholm Theory: | I find Fredholm theory beautiful, especially the Liouville-Neumann series for solving Fredholm integral equations of the second kind. There seems to be a consensus that these equations are quite useful for physicists, but all I have read is "these are useful in physics but we don't have time for that here . . . blah, b... | Can you provide an example of a physical problem that can be formulated as a Fredholm integral equation of the second kind, suitable for advanced undergraduates, and explain how it relates to the concepts of compact operators or Banach spaces? | 22,309 | cqadupstack-physics |
54141 | Stresses in asteroid during close flyby | The acceleration of an asteroid (such as 2012DA14) as it approaches earth is proportional to the reciprocal of distance $r$ from earth center, squared. the derivative of the acceleration, or jerk, is then proportional to the cube of the reciprocal of distance $r$, and the speed $v$. Thus the jerk is rapidly increasing ... | Considering an asteroid approaching Earth with acceleration \( a \) proportional to \( \frac{1}{r^2} \), where \( r \) is the distance from the Earth's center, and knowing that the jerk \( j \) is proportional to \( \frac{v}{r^3} \), calculate the jerk experienced by the asteroid when it is at a distance of 20,000 km f... | 5,847 | cqadupstack-physics |
98489 | Breaking the simultaneity | I have expressed my self in a detailed way. I've labeled the points to which I want an answer. * * * I have doubt in the Einstein's rail experiments which he mentioned in his book. In this experiment we preassume events A and B are simultaneous with respect to the embankment. The observer $M$ observes the events $A$ ... | In a thought experiment involving a moving train, two events, A and B, are observed by two different observers: M, who is stationary outside the train, and M', who is inside the moving train. If M observes events A and B as simultaneous, but M' perceives A occurring before B, how would the timing of events A and B diff... | 31,420 | cqadupstack-physics |
74296 | Many-worlds interpretation vs 'just' randomness? | I have this question about MWI I always wanted to ask but never dared to! It could be that I just don't know enough physics to understand the answer, or the question! Anyway, here goes: What is it that differentiates MWI from a physical theory (let's call it 'pure random') which is equivalent but where, in every instan... | What are the observable or measurable differences between the Many-Worlds Interpretation (MWI) of quantum mechanics and a hypothetical "pure random" theory in terms of predicting outcomes of quantum experiments, particularly in relation to phenomena like quantum entanglement? | 2,891 | cqadupstack-physics |
80696 | Rabi oscillations and two level dynamics | I'm currently looking at Rabi Oscillations, and not I have a look at the following equations: $$W = \sqrt{\Omega^2+\delta^2}.$$ The amplitude: $$\frac{|\Omega|^{2}}{\delta^{2}+|\Omega|^{2}}$$ Now, I see that if the detuning $\delta = (\omega - \omega_{0})$ is large, the two level approximation is bad, since the ratio b... | In the context of Rabi Oscillations, explain why the two-level approximation becomes invalid when the Rabi frequency \(\Omega\) is large relative to the detuning \(\delta\), and provide a quantitative analysis involving the equations \(W = \sqrt{\Omega^2+\delta^2}\) and the amplitude \(\frac{|\Omega|^{2}}{\delta^{2}+|\... | 18,083 | cqadupstack-physics |
67285 | Why no fundamental force from the Higgs? | I wish to ask whether I understand the following correctly. This universe seems to have six fundamental elementary bosons namely photon $(\gamma),\ W$-bosons$(W^+,W^-),$ gluon$(g),\ Z$-boson $(Z)$, Higgs boson$(H^0)$ and graviton$(G)$. Each fundamental force field of nature is mediated by the interaction of each of the... | What is the role of the Higgs boson $(H^0)$ in the Standard Model of particle physics, and how does its mechanism contribute to the mass of elementary particles without mediating a fundamental force like the other bosons? | 14,808 | cqadupstack-physics |
7462 | Fourier transform of the Coulomb potential | When trying to find the Fourier transform of the Coulomb potential $$V(\mathbf{r})=-\frac{e^2}{r}$$ one is faced with the problem that the resulting integral is divergent. Usually, it is then argued to introduce a screening factor $e^{-\mu r}$ and take the limit $\lim_{\mu \to 0}$ at the end of the calculation. This al... | What is the Fourier transform of the Coulomb potential $$V(\mathbf{r})=-\frac{e^2}{r}$$ when a screening factor $e^{-\mu r}$ is introduced, and how does the limit $\lim_{\mu \to 0}$ affect the result? Please calculate the transform and describe the mathematical implications of this procedure. | 8,435 | cqadupstack-physics |
55425 | Reality error and relative velocity | Suppose a person is walking in rain carrying an umbrella. He is tilting his umbrella at some angle with the vertical so as to protect himself from the rain. But a neutral observer who is standing still will find it really absurd because he will find the rain falling vertically downward, how come there are two realities... | If a person walking in the rain tilts their umbrella at an angle of 30 degrees from the vertical while moving forward at a speed of 2 m/s, and the rain is falling vertically at a velocity of 5 m/s relative to the ground, at what angle does the rain appear to fall relative to the person holding the umbrella? | 745 | cqadupstack-physics |
122258 | What is equation to find force of magnetic attraction | I was wondering as a student, when I was playing with magnets I thought like Gravitational force equation of Newton's Gravitation Theory, can we also calculate force of an magnetic attraction on an para-magnetic object\material as it can help me learn more about how big an magnet needs to be to create this much pull or... | What is the equation to calculate the magnetic force of attraction on a paramagnetic material when it is placed in a magnetic field, and how can this force be quantitatively expressed in terms of the magnet's strength and the material's properties? | 1,077 | cqadupstack-physics |
13783 | Can spin and macroscopic angular momentum convert to each other? | Suppose an isolated system with a number of particles with parallel spins. Can the macroscopic angular momentum of the system increase at expense of the number of particles having parallel spins (that is by inverting the direction of the spins of some of them) or by converting all particles into spinless ones? Converse... | In an isolated system with a fixed number of particles having parallel spins, if you invert the direction of the spins of a certain percentage of the particles, how does that affect the macroscopic angular momentum of the system? Provide a quantitative analysis of the relationship between the number of particles whose ... | 862 | cqadupstack-physics |
114634 | Gauge invariance of Rarita-Schwinger action in curved spacetime | The Rarita-Schwinger action in curved $n$-dimensional spacetime is $$ \int \sqrt{g} \overline{\psi}_a \gamma^{abc} D_b \psi_c $$ Here $g = \det(g_{\mu \nu})$, and the indices $a, b \dots$ are 'internal' indices that transform under e.g. $\mathrm{SO} (3,1) $ in $3+1$ dimensions. $\gamma^{abc} = \gamma^{[a} \gamma^{b} \g... | In the context of the Rarita-Schwinger action in curved spacetime, can you quantify the number of degrees of freedom of a spin-3/2 field as compared to a spin-1/2 field in flat spacetime? Additionally, at which level—classical or quantum—do inconsistencies arise due to the absence of the symmetry under the covariant de... | 7,406 | cqadupstack-physics |
109287 | Why do clouds fly? | I know it's probably the most stupid question there is, but why do they fly are the clouds lighter than air? What's keeping those tiny ice structures floating miles about the ground? I've been looking all over the internet and I can't find acceptable answer to this basic physical question. Can you please help me? This ... | What is the mechanism by which tiny ice crystals form clouds and remain suspended in the atmosphere despite being denser than the surrounding air? | 23,621 | cqadupstack-physics |
97836 | Neglecting mass at asymptotic spacelike momenta | What is the rational/reason for neglecting masses at asymptotic non- exceptional space-like momenta. I have come across this as a first fix for being able to extract information from the Callan-symanzik and Gell-Mann-Low methods. Is it purely physical, or is it both physical and mathematically sound reason? All respons... | Why can we neglect particle masses when considering asymptotic non-exceptional space-like momenta in quantum field theories, and how does this simplification impact the application of the Callan-Symanzik and Gell-Mann-Low methods? | 34,709 | cqadupstack-physics |
111892 | What causes a heat generating source to stabilize at a certain temperature? (Answered by myself, I think) | For example, we out a heat sink on a microprocessor to keep it cooler. I understand that if we run 100 watts of electricity through the microprocessor, it will generate 100 watts of heat, or 100 Joules per second. If the temperature of the CPU stabilizes at 50 degrees Celsius, how do we calculate the heat flow of the h... | What is the rate of heat transfer from a microprocessor with a stable temperature of 50 degrees Celsius to a heat sink in ambient air at 30 degrees Celsius, given that the microprocessor dissipates 100 watts of power? | 16,904 | cqadupstack-physics |
80230 | Solve a problem of work and energy | > A man pulling sled of his daughter by a massless rope, climbing a snowy hill > whose slope is equal to 15 °. Considering that the mass of the sled is > $4Kg$, the girl's $26Kg$ and $\mu _c = 0,25$, calculate the work done by the > tension of the string after walking with constant speed a distance of $130m > \Delta x$... | A man is pulling a sled with his daughter up a snowy hill with a slope of 15°. The sled has a mass of 4 kg and the daughter weighs 26 kg. Given the coefficient of kinetic friction between the sled and the snow is 0.25, what is the total work done by the tension in the rope after he pulls the sled a distance of 130 m at... | 35,845 | cqadupstack-physics |
7158 | By what mechanism do quantum effects become observable in normal life at the macroscopic level? | By what mechanism do quantum effects become observable in normal life at the macroscopic level? For instance, when two molecules "collide" is the momentum a probabilistic event wherein the end state is not unique? Another example, during a chemical reaction, it is a probabilistic event at the quantum level whether or n... | What is the probability of a specific molecule within a solution interacting with another molecule during a chemical reaction, given the presence of N total molecules and an average collision cross-section σ? | 19,699 | cqadupstack-physics |
55629 | Solving the diffusion equation | I am trying to clarify the relation between random walk and diffusion, and the source book proposes the following which I can't get. Starting from the diffusion equation $$ \frac{\partial C}{\partial t} = D \frac{\partial^2 C}{\partial x^2}, $$ how can this be solved to get $$ C = \frac{A}{\sqrt{t}} \mathrm{e}^{-x^2 / ... | How can you derive the solution \( C = \frac{A}{\sqrt{t}} \mathrm{e}^{-x^2 / 4 D t} \) from the diffusion equation \( \frac{\partial C}{\partial t} = D \frac{\partial^2 C}{\partial x^2} \) using appropriate methods in mathematics? Please outline the steps involved in the derivation. | 2,411 | cqadupstack-physics |
13321 | Can I measure the Reynolds number or the heat transfer coefficient | Suppose I have a flow of hot air around a cold and unevenly shaped object with holes and tunnels (think about it as a bed packed with some objects). I would like to know the Reynolds number of this flow and its convective heat transfer coefficient. The definition of the Reynolds number contains a "characteristic length... | How can I design an experiment to measure the Reynolds number of hot air flowing around a cold, unevenly shaped object with holes and tunnels without directly measuring the temperature of the object, and can the Reynolds number be determined using simple pressure drop readings? | 4,623 | cqadupstack-physics |
86328 | Acceleration on an inclined rail | I have to use $\vec{P}+\vec{R_N}+\vec{F_f}=m\vec{a}$ with $\|\vec{F_f}\|=\mu\|\vec{R_N}\|$ to express the acceleration as $$a_{x'}=g\sin\alpha(1-\frac{\mu}{\tan\alpha})$$ The configuration is (sorry about the poor image) :  I'm totally lost. How... | Given the equation of motion $\vec{P} + \vec{R_N} + \vec{F_f} = m\vec{a}$ and the relationship $\|\vec{F_f}\| = \mu\|\vec{R_N}\|$, derive the expression for acceleration $a_{x'}$ when the incline angle is $\alpha$ and the coefficient of friction is $\mu$. What is the value of $a_{x'}$ in terms of $g$, $\alpha$, and $\m... | 29,545 | cqadupstack-physics |
89828 | Oscillation Question |  Now normally (if it was a block not rotating) all you would have to do is use $w^2 = k/m$ and $E= \frac12k(A\cos(2wt+\theta))^2 + \frac12m(Aw\sin(wt+\theta))^2$ or in other words the translational kinetic and spring potential. But here I don't even kno... | A block is attached to a spring with a spring constant \( k \) and is set into oscillation with an amplitude \( A \). If the mass of the block is \( m \) and it is displaced so that the angular frequency is given by \( w^2 = \frac{k}{m} \), derive the expression for the total mechanical energy of the block-spring syste... | 8,508 | cqadupstack-physics |
77185 | Equivalence of Bogoliubov-de Gennes Hamiltonian for nanowire | I'm trying to show that the Hamiltonian for a nanowire with proximity-induced superconductivity $$ \hat{H} = \int dx \text{ } \left[\sum_{\sigma\epsilon\\{\uparrow,\downarrow\\}}\psi_{\sigma}^{\dagger}\left(\xi_{p} + \alpha p\sigma_{y} + B\sigma_{z}\right)\psi_{\sigma} + \Delta\left(\psi_{\downarrow}^{\dagger}\psi_{\up... | How can I verify the equivalence of the two Hamiltonian formulations for a nanowire with proximity-induced superconductivity, specifically that $$ \hat{H} = \int dx \left[\sum_{\sigma \in \{\uparrow,\downarrow\}}\psi_{\sigma}^{\dagger}\left(\xi_{p} + \alpha p\sigma_{y} + B\sigma_{z}\right)\psi_{\sigma} + \Delta\left(\p... | 5,482 | cqadupstack-physics |
32311 | Black hole Cyg X-1 doesn't seem dense enough | According to wikipedia, here are the Cygnus X-1 vital stats: Mass 14-16[7] M☉ Radius 20–22[8] R☉ A radius of 10 R☉ means a volume of 10^3 = 1000 Sols. Divided by 16 M☉ that means that Cyg X-1 is 60 time _less_ dense than Sol. So how could it be a black hole? | What is the average density of Cygnus X-1 if its mass is taken as 15 M☉ and its radius is 21 R☉, and how does this compare to the density of our Sun? | 21,766 | cqadupstack-physics |
61340 | One-loop $\phi^4$ theory in $d = 3$ | I'm trying to calculate the 1 loop correction to the propagator in massless $\phi^4$ theory, in $d = 3$, just for fun. The diagram just looks like a straight line with a circle touching tangently to it. I'm not sure whether to take $ m = 0$ straightaway or to compute it for $m > 0$ before taking $m \to 0$, because the ... | In a massless $\phi^4$ theory in $d = 3$, consider the one-loop correction to the propagator represented by the integral \( I(m) = \int d^3k \frac{1}{k^2 - m^2} \). If you compute \( I(m) \) for \( m > 0 \) and find that it is proportional to \( (m^{2})^{1/2} \sim \Gamma(-1/2) \) as \( m \to 0 \) yielding 0, while dire... | 15,783 | cqadupstack-physics |
107557 | Anti-symmetric forms on Dirac spinors | In order to describe invariant forms on Dirac spinors $S$ one can find trivial subrepresentations in $S \otimes S$. If we use $S \cong (1/2, 0) \oplus (0, 1/2)$ then \begin{multline} [(1/2, 0) \oplus (0, 1/2)] \otimes [(1/2, 0) \oplus (0, 1/2)] =\\\ (0, 0) \oplus (1, 0) \oplus (1/2, 1/2) \oplus (1/2, 1/2) \oplus (0, 1)... | What is the total number of invariant forms that can be constructed from the Dirac spinors as predicted by representation theory, and how does this number compare to the forms \( D_1 \), \( D_2 \), and \( D_3 \) identified in the analysis? | 7,947 | cqadupstack-physics |
4537 | Can a single classical particle have any entropy? | recently I have had some exchanges with @Marek regarding entropy of a single classical particle. I always believed that to define entropy one must have some distribution. In Quantum theory, a single particle can have entropy and I can easily understand that. But I never knew that entropy of a single rigid classical par... | Is it possible to define a verifiable concept of entropy for a single classical particle, and if so, how is it related to temperature in thermodynamic terms? | 17,967 | cqadupstack-physics |
1681 | What kind of systems of black holes satisfy the laws of black hole thermodynamics? | I've come across black holes thermodynamics multiple times recently (both at this site and elsewhere) and some things started bugging me. For one thing, first law bothers me a little. It is a reflection of the law of conservation of energy. This is fine when the space-time is stationary (as in Kerr solution) and is con... | What are the necessary conditions for a system of multiple black holes to achieve thermal equilibrium, allowing the laws of black hole thermodynamics to apply, despite their motion and the emission of gravitational waves? | 29,241 | cqadupstack-physics |
28111 | Why did Feynman's thesis almost work? | A bit of background helps frame this question. The question itself is in the last sentence. For his PhD thesis, Richard Feynman and his thesis adviser John Archibald Wheeler devised an astonishingly strange approach to explaining electron- electron interactions without using a field. Their solution was to take the ever... | What quantitative relationship can be established between the effective range of the Feynman/Wheeler retarded/advanced photon model and the scale at which vacuum polarization effects become significant in quantum electrodynamics (QED)? | 21,649 | cqadupstack-physics |
108582 | woven appearance of water-streams by the side of the street | It's pretty rainy in Boston now, and there are streams of water by the sides of the street. Why do they have a 'woven' appearance? What's the formal name for this kind of fluid flow? With lots of diagonals criss-crossing each other. And is there a good way to simulate it? | What is the formal name for the type of fluid flow that exhibits a 'woven' or meandering appearance, often seen in streams of water on rainy streets, and how can this flow pattern be simulated mathematically? | 34,043 | cqadupstack-physics |
11064 | BCS wave function in Neutron stars | I've heard mentioned in various classes that neutron stars, like superconductors, are described by BCS theory. I know that in superconductors a key element in forming cooper pairs is a net attractive force between the electrons which would normally repel one another. That attractive force is accounted for via lattice v... | What is the mechanism that provides the attractive force between neutrons in a neutron star, and how can one verify that neutron stars exhibit BCS theory behavior? | 17,247 | cqadupstack-physics |
127409 | Metric tensor in special and general relativity | I'm having trouble understanding the metric tensor in general relativity. What I've understood so far has come from my course lecture notes used in conjunction with "The Road to Reality" by Roger Penrose. **Problem 1** I know that in special relativity, the matrix $\eta_{ab}= \left( \begin{array}{cccc} 1 & 0 & 0 & 0\\\... | Given a four-dimensional spacetime with the metric tensor \( g_{ab} \) represented by the matrix:
\[
g_{ab} = \left( \begin{array}{cccc}
1 & 0 & 0 & 0 \\
0 & -1 & 0 & 0 \\
0 & 0 & -1 & 0 \\
0 & 0 & 0 & -1 \\
\end{array} \right)
\]
Calculate the quantity \( ds^2 \) for an infinitesimal displacement given in terms of t... | 1,854 | cqadupstack-physics |
71423 | Hydrogen cloud at the universe's beginning? | What prevented all of the hydrogen at the universe's start from coalescing into one gigantic star? | What factors caused the hydrogen in the early universe to remain dispersed rather than coalescing into a single massive star? | 8,322 | cqadupstack-physics |
59832 | Math for Thermodynamics Basics | I am studying Statistical Mechanics and Thermodynamics from a book that i am not sure who has written it, because of its cover is not present. There is a section that i can not understand: ${Fj|j=1,..,N}$ $S= \sum_{j=1}^{N} F_{j}$ $<S>=< \sum_{j=1}^{N} F_{j}> = \sum_{j=1}^{N} <F_{j}>$ $\sigma^{2}_{S} =<S^{2}>-<S>^{2}$ ... | In statistical mechanics, if we have a set of independent random variables \( F_j \) representing the forces acting on \( N \) particles, how can we derive the relationship \( \sigma^2_S = \sum_{j=1}^{N} \sigma_{j}^{2} \) starting from the expression \( \sigma^{2}_{S} = <S^{2}> - <S>^{2} \) and the definitions of the e... | 2,651 | cqadupstack-physics |
126132 | Existence and Uniqueness of spurious states in Bosonic String Theory | Green, Schwarz and Witten introduce so called spurious states $\phi$, that fulfill $$ (L_0 -a )\phi = 0\quad \text{and} \quad (\phi,\psi)=0 \text{ for all physical states }\psi $$ where the $L_n$ are the Virasoro generators, that can be expressed through the exitation creation/annihilation operators of the String: $$ L... | Given the condition for spurious states defined by \( (L_0 - a)\phi = 0 \), where \( L_0 \) is expressed as \( L_0 = \frac{1}{2} \alpha_0^2 + \sum_{n=1}^\infty \alpha_{-n} \cdot \alpha_n \), how do we determine the number of unique solutions \( \chi_n \) that satisfy \( (L_0 - a + n) \chi_n = 0 \) for a specific non-ne... | 10,196 | cqadupstack-physics |
132105 | Centrifugal force affecting satellite | I'm trying to explain the behaviour of a geostationary satellite using different frames of reference. 1. **Inertial frame:** The satellite has a circular motion with angular velocity $\omega$. The centripetal force $F$ required for this motion is created by the gravitational pull of Earth. Earth itself rotates around... | In a rotating frame of reference with angular velocity $2\omega$, if a geostationary satellite appears to have an angular velocity of $-\omega$, how can we account for the forces acting on the satellite, considering both the gravitational force and the centrifugal force due to the frame's acceleration? What condition m... | 34,629 | cqadupstack-physics |
123295 | Can special relativity be extended such that the frame of a photon makes sense? | Suppose I want to know what the universe looks like from the perspective of a frame of reference moving at $c$ relative to my current frame. As discussed at length in various other questions on this forum, from the perspective of the current established theory of special relativity, the notion of such a frame is more o... | Is it mathematically possible to define a frame of reference for a photon such that the principles of special relativity still hold, and if so, what implications would this have for our understanding of spacetime dimensions? | 1,691 | cqadupstack-physics |
72607 | A Rolling Quarter | A U.S quarter is rolling on the floor without slipping in such a way that it describes a circular path of radius $R=4 \text{cm}$. The plane of the coin is tilted at an angle of $\theta=45^{∘}$ with respect to the horizontal plane. Find the coin's period $T$ in seconds, that is, the time it takes for the coin to go arou... | What is the period \( T \) in seconds for a U.S. quarter, which has a radius of \( r = 1.2 \text{ cm} \), to complete one full revolution around a circular path of radius \( R = 4 \text{ cm} \), while rolling without slipping at a tilt angle of \( \theta = 45^{\circ} \)? | 14,357 | cqadupstack-physics |
67980 | The relation between spectral function and band structure | I am confused by the wavevector in spectral function A(k,w). How to understand this k for a periodic structure? And how is it related to the k (in first Brillouin Zone) we use in the band structure? If there are multibands, then in band structure for the same k we have several energies. To roughly reproduce spectral fu... | How can the spectral function \( A(k, \omega) \) be understood in relation to the wavevector \( k \) for a periodic structure, specifically regarding its peaks corresponding to multiple energies in the band structure, and do these peaks indicate that the same \( k \) value can show several energies in \( A(k, \omega) \... | 5,731 | cqadupstack-physics |
27660 | Solution to the Schrodinger equation for periodically time dependent Hamiltonians | I have a Hamiltonian which is time dependent but possesses periodic symmetry: $H(t+t_0)=H(t)$. Is there any clever techniques to exploit this? Edit: In particular, I would like a practical method to simulate the dynamics of such a system (as opposed to naive time-slicing). | Given a time-dependent Hamiltonian \( H(t) \) that satisfies the periodic symmetry \( H(t + t_0) = H(t) \), derive an expression for the time evolution operator \( U(t) \) over one period \( t_0 \) and discuss how the Floquet theory can be applied to simulate the dynamics of this system efficiently. | 30,949 | cqadupstack-physics |
61012 | Graphene +1 extra carbon bond | I'm not a physicist just a curious mind, so please go easy! I was just watching a BBC Horizon Documentary that featured a piece on the recently discovered material Graphene. One of the facts mentioned on the documentary was that a sheet of graphene, despite being a lattice of carbon atoms just one atom thick, could hol... | Could a theoretical square lattice configuration of carbon atoms exist, and if so, how would its tensile strength compare to that of graphene's hexagonal structure? Additionally, under what conditions might such a square lattice form, if at all? | 36,562 | cqadupstack-physics |
54661 | Lagrange-Euler equations for a bead moving on a ring | > _A bead with mass $m$ is free to glide on a ring that rotates about an axis > with constant angular velocity. Form the Lagrange-Euler equations for the > movement of the bead._ Solution: Let us introduce the generalized coordinates $\theta$ to determine the beads position. $$\Rightarrow L=L(\theta, \dot\theta)=K-P$$ ... | How do you derive the expression for the velocity \( v \) of a bead of mass \( m \) gliding on a rotating ring of radius \( a \), given angular velocity \( \omega \) and a generalized coordinate \( \theta \)? Specifically, what are the equations for the \( x \) and \( y \) components of the bead's velocity? | 28,815 | cqadupstack-physics |
127668 | Massless particles and the speed of light - New? Theories of existence | "The best understanding we have is that it [light] is a disturbance in the electromagnetic fields of charged bodies." http://einstein.stanford.edu/content/relativity/q212.html This is a link to the most recent report I could find for experiments attempting to observe or measure a photon without destroying it. http://ww... | What is the theoretical speed of light in a vacuum, and how does it differ from the speed at which electromagnetic waves travel in our physical universe? | 24,123 | cqadupstack-physics |
8607 | Temperature vs AC energy consumption | I'm need to understand the following: to keep the room at confortable temperature (70 degree, for example), how does the amount of energy consumed by the AC grow as the outside air temperature rises in the summer over the same length of time (a day, say)? Is it more or less linear? quadratic? exponential? or anything e... | How does the energy consumption of an air conditioning unit change in response to increasing outside temperatures when trying to maintain a constant indoor temperature of 70°F? Is the relationship between outside temperature and energy consumption linear, quadratic, or exponential over the course of a day? Please provi... | 20,295 | cqadupstack-physics |
88132 | What is the sense of introducing generating functional to the summands of expansion of S-matrix? | Let's have generating functional $Z(J)$: $$ Z(J) = \langle 0|\hat {T}e^{i \int d^{4}x (L_{Int}(\varphi (x)) + J(x) \varphi (x))}|0 \rangle , \qquad (1) $$ where $J(x)$ is the functional argument (source), $\hat {T}$ is the chronological operator, $\varphi (x)$ - some field. I want to understand the reasons for its intr... | What is the physical interpretation of the terms in the generating functional \( Z(J) \) and how does it contribute to calculating the S-matrix, particularly in relation to vacuum expectation values versus contributions from external states? Additionally, can you explain the significance of the term \( \int \frac{J(p)d... | 36,280 | cqadupstack-physics |
73373 | Are there solid materials with controllable porosity? | In analogy to piezoelectric materials, where the application of an electrical field creates mechanical deformation in the material, I have the following question. Are there solid materials whose porosity can be altered or controlled? Of course, I have googled this. This lead me to a lot of websites where _controllable ... | Are there any solid materials whose porosity can be dynamically altered in response to an external electric field, and if so, what are some examples of these materials and the mechanisms by which their porosity changes? | 25,361 | cqadupstack-physics |
106135 | How are anti-matter atoms created? | What is the reaction, or reactions that make anti-matter? I don't understand how anti-matter is created by CERN if interaction with normal matter causes annihilation. | What specific particle collisions at CERN lead to the creation of antimatter, and how do these processes differ from the annihilation that occurs when antimatter interacts with normal matter? | 1,539 | cqadupstack-physics |
68510 | Need an intermediate resistivity part/material | I need a part or material for a planned experiment (the experiment is similar to those described in my articles http://arxiv.org/abs/1208.0066 and http://arxiv.org/abs/1109.1626 ). The problem is that the required resistivity (about 0.3 Ohm-cm or of the same order of magnitude) is much higher than that of metals and mu... | What materials can be used to create a cylindrical part with a resistivity of approximately 0.3 Ohm-cm that is suitable for use at a frequency of 25 GHz, while also possessing decent mechanical properties for strain application? | 33,153 | cqadupstack-physics |
44262 | Integral representation of Thomas-Fermi Equation | The Thomas-Fermi equation with dimensionless variables is identified as; $$ \frac{d^2\phi}{dx^2} = \frac{\phi^{3/2}}{x^{1/2}} $$ with the boundary conditions as $$ \phi(0) = 1 \\\ \phi(\infty) = 0. $$ There are many series approximation solutions available to this equation. I am interested in finding the integral repre... | Can you provide the integral representation for the solution of the Thomas-Fermi equation given by $$ \frac{d^2\phi}{dx^2} = \frac{\phi^{3/2}}{x^{1/2}} $$ with the boundary conditions $$ \phi(0) = 1 $$ and $$ \phi(\infty) = 0 $$? Additionally, are there any recommended literature sources that discuss this topic? | 14,261 | cqadupstack-physics |
110478 | Unknown Mass Spring Problem | A student conducts an experiment to measure the motion of two unknown masses (A and B) along a smooth table. A constant force of 1 N was applied by means of a string connected by a falling weight. A motion sensor recorded the position (measured from the start line) of each mass at regular time intervals as they slid al... | Based on the motion data recorded in the experiment, calculate the acceleration of each mass (A and B) and determine which mass experiences a greater acceleration. | 7,812 | cqadupstack-physics |
82597 | Why is momentum (instead of something else) the canonical conjugate of position? | Why did nature decide to make conjugate of position to be momentum? Since energy and position do not commute, why not energy? What determines the pairing of time with energy and momentum with position? | What is the relationship between position and momentum in quantum mechanics, and how is this relationship quantitatively expressed through the Heisenberg Uncertainty Principle? | 25,139 | cqadupstack-physics |
96646 | Is it true that Macrorealism can be shown false? | http://en.wikipedia.org/wiki/Leggett-Garg_inequality As you can see by the link above, it claims that if the violation of the Leggett–Garg inequality can be demonstrated on the macroscopic scale, it would challenge the notion of realism that the moon is there when nobody looks. How is that even possible given that when... | How does the Leggett-Garg inequality challenge the principles of macrorealism in large-scale systems, and what experimental evidence has been collected to demonstrate such violations using superconducting quantum interference devices? | 34,279 | cqadupstack-physics |
13495 | How do I solve for the phase constant given the amplitude and the angular frequency? | > A piston (with mass M) in a car engine is in vertical simple harmonic motion > with amplitude A. The engine is running at a period T. Suppose a small piece > of metal with mass m were to break loose from the surface of the piston when > it (the piston) is at the lowest point z and velocity is v. At what position > in... | A piston with mass M in a car engine undergoes vertical simple harmonic motion with an amplitude A and a period T. If a small piece of metal with mass m detaches from the piston when it is at its lowest point (z) and moving with a velocity v, how high does the piece of metal rise (in meters) before it loses contact wit... | 15,755 | cqadupstack-physics |
114767 | Simple General Relativity Relation | Given the identity $$\nabla_a(R^{ab}-\frac{1}{2}R g^{ab})=0,$$ how do I then show that $R_{ab}=0$ implies $$\nabla_a R^a_{\space \space \space bcd}=0$$ | Given the identity $$\nabla_a(R^{ab}-\frac{1}{2}R g^{ab})=0,$$ if we assume that the Ricci tensor $R_{ab}$ is equal to zero, what must we conclude about the covariant derivative of the Riemann curvature tensor, specifically that $$\nabla_a R^a_{\space \space \space bcd}$$ is equal to zero? Provide a step-by-step justif... | 27,919 | cqadupstack-physics |
7008 | Long time deviations from exponential decay in radioactivity | Are there any examples of common substances whose decay is not exponential? We're used to thinking about radioactivity in terms of half-lives. This is a concept that makes sense only for a decay that is exponential. However, there are plenty of physics articles on the subject of non exponential decay. It seems to be th... | What are some specific examples of substances or systems where the decay does not follow an exponential law, particularly at long times, and what might explain these deviations? | 9,852 | cqadupstack-physics |
92776 | Kähler and complex manifolds | I was woundering if anyone knows any good references about Kähler and complex manifolds? I'm studying supergravity theories and for the simplest $\mathcal{N}=1$ supergravity we'll get these. Now in the course-notes they're quite short about these complex manifolds. I was hoping someone of you guys might know a good (qu... | What are the main properties of Kähler manifolds that are relevant to supergravity theories, and can you provide a specific example of a Kähler manifold used in an \(\mathcal{N}=1\) supergravity model? | 21,245 | cqadupstack-physics |
106975 | Correspondence principle and quantum computers | I just read this article at https://medium.com/the-physics-arxiv- blog/7ef5eea6fd7a about the work of a physicist called Bolotin, that states that P!=NP (from computer science) implies that large quantum mechanical objects are not possible. The author starts by explaining the Schrodingers cat thought experiment. He the... | What is the significance of the correspondence principle in explaining the behavior of quantum mechanics on macroscopic scales, and how does it relate to the P vs NP problem in computer science? | 27,518 | cqadupstack-physics |
9799 | Do and can phone signals come inside AC car which is glass-packed | Can phone signals penetrate glass, so can I expect phone signals to come if I am sitting inside a closed AC car. Thanks, | What is the percentage of phone signal attenuation when a mobile device is used inside a closed AC car, considering the type of glass used in the vehicle's windows? | 33,111 | cqadupstack-physics |
113485 | Is there a conveniently small unit of volume for talking about molecules? | When discussing energy transformations on the molecular scale, we usually use electronvolts as the energy unit. This is handy because chemical bond energies are a few electronvolts in magnitude. I had an idea to go through some thermodynamic tables and convert them into molecular-scale units (energy in $\mathrm{eV}$, e... | What unit of volume, commonly used in scientific contexts, is suitable for quantifying the average volume change per molecule and falls within the range of approximately \(10^{-31}\) to \(10^{-27}\;\mathrm{m^3}\)? | 17,893 | cqadupstack-physics |
59828 | Hyperbolic, parabolic, elliptical PDE related to under-, critical- and overdamped in harmonic osciallation | A damped harmonic oscillator has three cases for the damping: underdamped, critically damped and overdamped. With partial differential equations, I know the hyperbolic wave equation, the parabolic heat equation and the elliptical Laplace equation. Since underdamping means oscillation and therefore waves and the heat di... | How do the damping characteristics of an underdamped harmonic oscillator compare to the solution behavior of a critically damped system when modeled by their respective differential equations? Quantify the differences in terms of oscillation frequency and response time. | 26,814 | cqadupstack-physics |
23224 | How can time be relative? | I don't understand how time can be relative to different observers, and I think my confusion is around how I understand what time is. I have always been told (and thought) that time is basically a measurement we use to keep track of long it has been since an objects inception. If that is even somewhat true, how can tim... | How does the concept of time dilation explain the difference in aging between two observers moving at different speeds, and what experiments or observations have demonstrated this effect? | 24,712 | cqadupstack-physics |
72664 | How many seconds is a temporal meter? | Is there a proof that time is a 4th dimension? If it is, then why not measure it in units of the previous three? Logical right? How many seconds is a temporal meter? | If time is considered the fourth dimension, how many seconds correspond to a hypothetical "temporal meter," assuming it is defined as the distance light travels in one second? | 33,777 | cqadupstack-physics |
131044 | Does lever needs gravitation to work? | Simple question - Does lever needs gravitation force to work or it just needs fulcrum and could work in vacuum as well? | In a vacuum where there is no gravitational force acting on objects, can a lever still operate effectively if it has a fulcrum? Provide a theoretical explanation and any conditions necessary for its function. | 1,070 | cqadupstack-physics |
70509 | Naturalness arguments and dimensional regularization? | How do issues of naturalness arise when regularizing QFT using dimensional regularization? I can only recall ever seeing naturalness arguments (hierarchy problem, cosmological constant problem, etc.) phrased in terms regularizing with a cutoff, where naturalness issues arise when physical quantities are quadratically d... | What are the implications of using dimensional regularization on naturalness issues in quantum field theory, particularly in comparison to cutoff regularization, and how do the renormalization group equations play a role in addressing these issues? | 26,774 | cqadupstack-physics |
66746 | Origin of motion and relative speed of bodies in the universe | Charged particles can hit the earth at relativistic speeds. But it seems that all large bodies have fairly low relative speed. Of course, speed can increase considerably when a body orbits close to a massive object, but then it will not travel very far, and it can be discounted by averaging the speed over a long enough... | In the context of the observed motions of celestial bodies, what is the average velocity of galaxies in relation to their mass, considering that the speed formula is given by \( v = \sqrt{\frac{G \cdot M}{r}} \)? Specifically, how does this velocity vary with the size and density of the structures involved, and what im... | 27,835 | cqadupstack-physics |
104367 | The formula used to calculate electrical potential energy |  Sorry for the ugly picture but it makes my question more understandable. The $\Delta V$ from $A$ to $B$ is calculated by$$\int_A^B E \, \mathrm{d}r$$ where $r$ is the distance between $A$ and $B$. The curve line is the real path the charge take going f... | Why is the expression for the work done on a charge moving in an electric field, given by \(\int_A^B \vec{E} \cdot \mathrm{d}\vec{r}\), equivalent to \(\int_A^B \vec{E} \cdot \mathrm{d}\vec{l}\)? Is this because \(\mathrm{d}\vec{l}\) represents the infinitesimal displacement along the actual path taken by the charge, a... | 15,629 | cqadupstack-physics |
110108 | Falling metal cylinders more devastating than a nuke? | I just saw _G.I JOE - Retaliation_. In the movie the bad guys (spoiler alert) > destroy London by dropping a large metal cylinder from space onto the city. Could this device cause more destruction than a nuclear weapon? If so, how? | If a large metal cylinder were dropped from low Earth orbit onto London, what would be the estimated impact energy, and how does it compare to the yield of a typical nuclear weapon in terms of destruction potential? | 12,368 | cqadupstack-physics |
26802 | Characters of $\widehat{\mathfrak{su}}(2)_k$ and WZW coset construction | I am currently studying affine Lie algebras and the WZW coset construction. I have a minor technical problem in calculating the (specialized) character of $\widehat{\mathfrak{su}}(2)_k$ for an affine weight $\hat{\lambda} = [k-\lambda_1,\lambda_1]$. Given the generalized theta function $$\Theta_{\lambda_1}^{(k)}(z,\tau... | How can I properly evaluate the limit of the quantity $$\chi^{(k)}_{\lambda_1} = \frac{\Theta^{(k+2)}_{\lambda_1+1} - \Theta^{(k+2)}_{-\lambda_1-1}}{\Theta^{(2)}_1 - \Theta^{(2)}_{-1}}$$ as \( z \) approaches \( 0 \) when both the numerator and denominator vanish at that point? | 14,829 | cqadupstack-physics |
7166 | Unstable energy levels | Well, reading about "Raman Effect" I saw that when the electron absorb some energy, with frequency $ \omega_{abs} $, that is different from $ \omega_{n} - \omega_{n-1} \neq \omega_{abs1} $, it go to an "virtual energy level" that is unstable, but nevertheless we could measure its lifetime. And more, the electron could ... | In the context of the Raman Effect, if an electron absorbs energy with a frequency of \( \omega_{abs1} \) and transitions to a virtual energy level, what is the maximum lifetime of the electron in this unstable state before it must transition to a stable energy level, given that the uncertainties in its energy can be c... | 296 | cqadupstack-physics |
93192 | Divergent issue of Madelung's constant | This is a question triggered by this post Madelung's constant is defined to the coefficient of electrostatic potential energy in a ionic crystal. In the example of $NaCl$, \begin{equation} M = \sum_{ijk}{}^{'}\frac{(-1)^{i+j+k}}{\sqrt{i^2+j^2+k^2}} \end{equation} is conditionally convergent. > _Since this sum is condit... | What is the experimentally measured value of Madelung's constant for a perfect spherical sample of NaCl, considering that the series for expanding spheres diverges? Is the value you obtain finite and meaningful despite the divergence of the series? | 12,179 | cqadupstack-physics |
75727 | A ballpark figure on physicists | 1) Out of the 7 billion+ people alive today, around how many have earned a PhD in physics? 2) Around how many physicists are working today? 3) Around how many physicists are being added to the work force yearly? | Based on the global population, what is the estimated proportion of individuals who have earned a PhD in physics, considering there are over 7 billion people alive today? Additionally, how many physicists are currently active in the workforce, and what is the annual rate of new physicists entering the field? | 2,593 | cqadupstack-physics |
65025 | Why distinguish between row and column vectors? | Mathematically, a vector is an element of a vector space. Sometimes, it's just an n-tuple $(a,b,c)$. In physics, one often demands that the tuple has certain transformation properties to be called a vector (as opposed to e.g. a pseudovector). Sometimes its not a tuple, but e.g. an element of a hilbert space. In all cas... | In the context of general relativity, consider the metric tensor \( g_{\mu\nu} \) which raises and lowers indices of vectors. If we have a contravariant vector \( A^\mu \) and its corresponding covariant vector \( A_\nu \), define a physical situation where both vectors represent the same physical quantity. Can you pro... | 35,584 | cqadupstack-physics |
114314 | Does the conservation of energy not contradict Newton's $3^{\text{rd}}$ law? | Suppose "ball A" is flying with force F. The ball makes contact with "ball B" that has force 0. If the force applied to ball B is equal to the force that is applied to ball A then isn't there a total force of 2F? Doesn't that contradict the conservation of energy? | If ball A exerts a force F on ball B, which initially has a force of 0, what total force is felt by ball B after the collision if the force applied to it is equal to F? Additionally, how does this scenario illustrate the principle of conservation of momentum? | 25,974 | cqadupstack-physics |
101510 | Relative motion and how to calculate magnitude and velocity of objects relative to different given objects | A canoe has a velocity of 0.550m/s southeast relative to the earth. The canoe is on a river that is flowing at 0.540m/s east relative to the earth.  Alright so I attempted many different things an still do not understand the nature of the question nor d... | Determine the magnitude of the canoe's velocity relative to the river (Vc/r) and express the direction of the canoe’s velocity relative to the river as an angle measured south of west. | 28,722 | cqadupstack-physics |
57078 | Does universal wave function exist? | Does universal wave function exist? What the science tells us? | What is the mathematical representation of the universal wave function in quantum mechanics, and how does it differ from other wave functions used for individual systems? | 20,010 | cqadupstack-physics |
126226 | Problem on speed of light | As I was reading special relativity, my book says the speed of light is $c$ with respect to any other thing. Does that mean the speed of an individual photon is $c$ even with respect to another photon? I mean, shouldn't the relative velocity be zero? | If two photons are traveling towards each other in a vacuum, what is their relative speed as measured from an observer moving at a significant fraction of the speed of light relative to one of the photons? Is this relative speed equal to the speed of light, and why or why not? | 36,879 | cqadupstack-physics |
114487 | How does a unique electron probability distribution correspond to one wavefunction? | I'm reading the Wikipedia article on DFT, and it says that there is a one-to- one correspondence between the ground state particle density $$n_0(\vec{r}) = N \int \text{d}^3 r_2 \int \text{d}^3 r_3 \cdots \int \text{d}^3 r_N \Psi_0^{*}(\vec{r}, \vec{r}_2, \ldots, \vec{r}_N) \Psi_0(\vec{r}, \vec{r}_2, \ldots, \vec{r}_N)... | How can the ground state particle density \( n_0(\vec{r}) \) uniquely determine the ground state wavefunction \( \Psi_0(\vec{r}, \vec{r}_2, \ldots, \vec{r}_N) \) in the context of density functional theory, given that different wavefunctions can have the same squared amplitudes due to varying phases? | 2,739 | cqadupstack-physics |
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