Physics questions and answers


Are theta vacua topologically protected?

In discussions of Yang-Mills instantons it is often stated that one should sum in the path integral over all contributions of fluctuations around all the topologically distinct vacua labelled by winding number $n$. Usually there follows a discussion on $\theta$-vacua, which are basically a linear combination of $n$-vacua, in the ....

Jeremiah Jeremiah: 1 hour ago


How to compare the observation with the theoretically predicted result?

On the Wikipedia Article on “Geodesics in general relativity”, it says the following: “Thus, for example, the path of a planet orbiting a star is the projection of a geodesic of the curved 4-D spacetime geometry around the star onto 3-D space.” I want to know how the geodesic of ....

Alice Alice: 1 hour ago


Dyson series derivation

$$ i\hbar \frac{dU_I(t, t_i)}{dt} = \hat{V}_I(t)\hat{U}_I(t,t_i) \tag{10.32} $$ The solutions of this equation, with the initial condition $\hat{U}_I(t_i,t_i)$, are given by the integral equation $$ \hat{U}_I(t,t_i) = 1 - \frac{i}{\hbar}\int_{t_i}^t\hat{V}_I(t')\hat{U}_I(t',t_i)dt' \tag{10.33} $$ In the derivation of Dyson Series please explain why in equation (10.33) $t$ is changed to $t'$ without ....

Easton Easton: 2 hours ago


How is the relationship between the old and the new canonical variables justified?

In Classical Hamiltonian Mechanics, a canonical transformation of the phase-space coordinates $(p,q,t) \to (P,Q,t)$ is such that the general form of Hamilton's equations is followed and Hamilton's principle is obeyed: $$\delta \int_{t_0}^{t_1} \left (P_i \dot{Q_i} - K (Q,P,t)\right) \, \mathrm{d}t = 0\tag{1}$$ for some new Hamiltonian $K$ just as before ....

Leah Leah: 2 hours ago


Can we detect a photon's direction?

The question of if a photon even has a direction may be up for interpretation, but I wanted to know if it's possible for a device to absorb most light from every which direction and only detect light from one general direction, as well detect the wavelength of that photon. ....

Weston Weston: 2 hours ago


Why would a perfectly incompressible ball on a rough surface stop rolling?

We know that the force that opposes the rolling of an object exists due to the deformation of the body's surface at the point of contact which creates a decelerating torque on the body. What if the object is perfectly rigid such that it doesn't deform even a little? In ....

Gianna Gianna: 2 hours ago


Very basic question about empty universe

I'm trying to understand the empty universe model. My first textbook (which doesn't cover the empty universe) gives the Friedmann equation as $$\left^{2}=\frac{8\pi G}{3}\rho-\frac{kc^{2}}{R^{2}}$$ Am I right in thinking all I need do is put $\rho=0$ so $$\frac{dR}{dt}=\pm c$$ for $k=-1$ and then say $$R=\pm ct$$ for an expanding or ....

Amelia Amelia: 3 hours ago


What opposes a smooth motion of a rubber eraser on a glass surface?

A metal block smoothly moves on a glass surface. But a rubber eraser doesn't move very smoothly on a glass surface. In each of the cases, the surfaces are smooth at the macroscopic scale. If the latter is due to friction at the molecular level, how come a metal block ....

Matthew Matthew: 3 hours ago


Negative Magnus effect?

Supposedly, the Magnus effect, which is responsible for the curve of a curveball, and is the reason that tennis players hit their ground strokes with topspin, only acts above a critical Reynolds number ($\mathrm{Re}=Ud/\nu$, where $U$ is the velocity, $d$ is the diameter, and $\nu$ is the kinematic viscosity) of ....

Greyson Greyson: 4 hours ago