Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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When solving problems on linear momentum, when can external forces be neglected? I was recently solving a problem in which one end of a massless string (in vertical orientation) was tied to a block of mass $2m$ and the other end to a ring of mass $m$, which was free to move along a horizontal rod. The block is then giv... |
momentum conservation would require net external force on the system to be zero
You are correct - moment of a system is conserved when net external force equals zero, because by third Newton's law of motion all internal forces cancel. This means that there can be external forces, it is just that their vector sum must... | {
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Different formal definitions of Lorentz Transformations The formal definition for Lorentz Transformation is a matrix $\Lambda$ such that $$\Lambda^\mu_{\ \ \alpha}\Lambda^\nu_{\ \ \beta}\eta_{\mu\nu}=\eta_{\alpha\beta.}$$
In some books I have found a definition that use the transposition: $$(\Lambda^T)\eta\Lambda=\eta.... | Kontle's answer contains the main idea, but let me be a bit more specific about your example: all is about matrix notation.
Recall in general linear algebra that, given $n \times n$ matrices $X,A \in \mathbb{R}^{n \times n}$ one can write the $(i,j)$-coefficient of the matrix $B= X^TAX$ as follows:
\begin{equation}
(b_... | {
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Do the components of a force written for a purpose actually exist? On an inclined plane if you put a box, the force of gravity $mg$ is written as sum of two forces $mg\sin\theta$ and $mg\cos\theta$ where $\theta$ is the angle the incline is making with earths surface. Do these forces $mg\sinθ$ and $mg\cosθ$ actually wo... | In the case of no friction, a load cell on the incline surface measures $F_N = mgcos(\theta)$. And the box has an acceleration of $a = gsin(\theta)$, what by the Newton's second law implies a force $F_t = mgsin(\theta)$.
So, the $2$ forces are real in the meaning that they can be measured. Their vectorial sum happens t... | {
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How can they estimate exoplanet radial velocities using Doppler considering spectrograph resolving power? I read that spectrograph resolving powers, the ratio of wavelength uncertainty to wavelength are like 1000 or 10000. Plugging this into the non relativistic Doppler formula gives a velocity uncertainty like 30000 m... | Typical resolving powers for exoplanet-finding spectrographs are 50000-100000, but nevertheless, this still means a resolution element has a FWHM of 3-6 km/s. This is to be compared with the radial velocity amplitudes caused by the planets of anywhere from 100 m/s for close-in hot Jupiters, to less than 1 m/s for Earth... | {
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Does the Schrödinger equation apply to spinors? I was reading about Larmor precession of the electron in a magnetic field in Griffiths QM when I came across the equation
$$
i\hbar \frac{\partial \mathbf \chi}{\partial t} = \mathbf H \mathbf \chi,
$$
where $\mathbf\chi(t)$ is a 2D vector that represents only the spin st... | If you want to describe non-relativistic, interacting spins you need to extend the Schrödinger equation with the Pauli interaction, $H_{spin} = -\gamma {\bf B} \cdot {\bf S}$. This is the simplest of a class of hamiltonians known as spin hamiltonians. For non-translating spins, as in your case, you only need the Pauli ... | {
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Why is Avogadro constant used to calculate the number density? My book says:
The number density of particles is $nN/V$, where $n$ is the total amount of molecules in the container of volume $V$ and $N$ is Avogadro's constant.
I can do something with the concentration $n/V$, it tells me how many moles of a particle I ... | If n is the number of moles then n/V will be the number of moles per volume.
If you want to know the number of molecules per volume, you need to multiply this by Avogadro's constant.
An example:
If you measure a container's volume is 2 liters. And you know there is 2 moles of gas in this volume. Then you know there is ... | {
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Measuring radius vs diameter for a circular ring? Consider an experiment where I have to measure the radius of a circular ring diffraction (or interference) pattern (think Newton's rings).
It is advised to measure the diameter and then divide it by half instead of directly measuring the radius.
One reason for this coul... | Yes, your reasoning is correct.
| {
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Single gravitational plane wave or their interference can carry spin angular momentum? I would be grateful if anybody could tell me if I had one gravitational wave in the form of a plane wave, it still would carry spin angular momentum? We know that gravitational waves are mostly the interference between many gravitati... | I'm guessing that any angular momentum carried by a (transverse) wave would be associated with a circular (or elliptical) polarization.
| {
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Warm air syphon to cool down greenhouse I'm thinking about a very energy efficient way of controlling temperature inside a greenhouse when it's too hot.
The goal is to use the syphon effect in order to draw hot air from the top of the greenhouse to the outside, perhaps using a cooler fan as a trigger for this air motio... | This might work, but there's another way that does not need a fan- called the chimney effect, which will work for a pipe of diameter ~at least 4 to 6 inches.
Imagine a tall black pipe standing vertically in the sun, open at both ends. The sun's rays make the air inside get hotter than the air outside and the inside air... | {
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Is angular momentum just a convenience? I'm wondering whether angular momentum is just a convenience that I could hypothetically solve any mechanics problems without ever using the concept of angular momentum.
I came up with this question when I saw a problem in my physics textbook today. In the problem, a puck with kn... | Another small point, implicit in the other answers: it's not exactly that "angular momentum is essential to solve problems", but that it is a convenient concept by which to understand things.
Slightly fancier: neither Lagrangian nor Hamiltonian classical mechanics immediately give "formulas to solve problems", but, rat... | {
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What does is really mean to say that a 3-body problem is not solvable? What does it really mean to say that a three-body problem (the Sun, the earth, and the moon) is not solvable? Why is it not possible to solve the differential equations on a computer with adequate initial conditions? What's the real issue here?
| Quoting from wikipedia
The three-body problem is a special case of the n-body problem. Unlike two-body problems, no general closed-form solution exists,[1] as the resulting dynamical system is chaotic for most initial conditions, and numerical methods are generally required.
Of course, you can get a numerical solutio... | {
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Unitary Transformation Taking a 4$\pi$ Periodic Wave Function to 2$\pi$ Periodic Wave Function I am reading the following paper, which discusses Majorana fermions in Josephson junction arrays. Initially, the paper starts with a model such that the wavefunctions are $4\pi$ periodic. These satisfy the following relations... | First note (I'm assuming there are no operator ordering issues)
\begin{eqnarray}
\Omega(\phi+2\pi) &=& \Omega(\phi) e^{i(1-\hat{P})\pi/2} = \Omega(\phi)\left(e^{i\pi}\right)^{(1-\hat{P})/2} = \Omega^\dagger(\phi) (-1)^{(1-\hat{P})/2} \\
\Omega^\dagger(\phi+2\pi) &=& \Omega(\phi) \left((-1)^{(1-\hat{P})/2}\right)^\dagge... | {
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How can light produce electric and magnetic field when there are no accelerating charged particles? If we see light as a wave, especially in vaccum, there is nothing there, no particles, yet light has an electric and magnetic field. How can this be possible?
|
there is nothing there, no particles,
There is no particle there, but there is field. A charge at the rest has an associated electric field everywhere around in the space, getting smaller with the inverse of the distance squared. If we think of all existing charges, the space is full of fields.
If one of the charges ... | {
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What causes this strange noise in a pair of walkie-talkies? Let us suppose that Bob and Alice both have walkie-talkies. They are both 3m apart from one another. Alice pushes her walkie-talkie to speak but instead of speaking, she starts walking toward Bob. Both Alice's and Bob's walkie talkies are facing each other in ... | It's called feedback . Here is what happens:
When Alice presses TRANSMIT, it turns on the microphone in her radio and hence begins to transmit any noise that hits the mic. With Bob's radio on RECEIVE, its speaker is turned on and it plays out anything that it receives at that moment- which in this case is the audio sig... | {
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Why can I write $\frac{d}{dt}=\frac{d}{dt'}\frac{dt'}{dt}+\frac{d}{dx'}\frac{dx'}{dt}$? I’m dealing with a Lorentz invariance problem, and in one of the solutions I’ve seen to prove the wave equation the term above was used. However I don’t really understand why it can be written that way. Could someone provide an expl... | For a function of two variables $\displaystyle f=f( x,y)$ the total differential is given by
\begin{equation*}
df=\frac{\partial f}{\partial x} dx+\frac{\partial f}{\partial y} dy.
\end{equation*}
The function $\displaystyle f$ depends explicitly only on $\displaystyle x$ and $\displaystyle y$. It can depend on more va... | {
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Why is torque defined as $\vec{r} \times F$? Here I cannot convince myself myself that it is units because the torque is defined to be in units of Newton meter is a reiteration of the law stated above. Why was it not $r^2 \times F$ or $r^3 \times F$ or $r^2 \times F^2$ etc. The argument "in our experience how much some... | Consider a point particle of mass $m$ with velocity $\vec v$. The particle is located at some position $\vec r$ with respect to the origin $O$.
I will start with the angular momentum calculated about $O$. The angular momentum is $\vec L = I\vec \omega$, where $I=mr^2$.
Since we know $v=\omega r$, you can work out that... | {
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Why doesn’t horizon distance move exactly proportional to the height of the observer? For instance if someone is 8 inches above the surface of the Earth, they can see approximately 1 mile to the horizon. However, if someone is viewing the horizon at an eye level of 5’5 they can only see about 3 miles out. If the height... | Consider the following image showing the earth (with radius $R$)
and an observer at height $h$ above the ground.
The distance from the observer to the horizon is $s$.
The theorem of Pythagoras applied to the right triangle gives
$$R^2+s^2=(R+h)^2$$
With a little bit of algebra we get
$$R^2+s^2=R^2+2Rh+h^2$$
$$s^2=2Rh+... | {
"language": "en",
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Is the speed of signal transport via electricity as fast as light? Let us assume a time synchronization system that comprises a sender and a receiver. The sender generates and sends an encoded signal which presents the current time to the receiver periodically, and the receiver calibrates its clock according to this si... | Electrical signals propagate as electromagnetic waves. If conductors are present, the waves occupy the space around the conductors. The geometry of the conductors is designed to guide the wave.
The nature of the conductor guiding the wave (copper, aluminum, gold, ...) has little influence. The medium in which the wave... | {
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What frequency of cord shaking maintains the same vertical motion for a point on the cord after increasing the wave speed on the cord? I'm studying for my upcoming AP Physics 1 exam but can't figure out this problem
A student shakes a horizontally-stretched cord, creating waves. The graph above shows the vertical pos... | Bottom line intuitive answer: Changing the propagation speed affects the relationship between frequency and wavelength. The wave moves faster, but is correspondingly longer, and those two cancel out, leaving the frequency the same at any point on the cord.
| {
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Is it generally accepted that Field Aligned Currents are caused by Force-Free Fields? I am currently an undergraduate working on a project about FAC (Birkeland Currents) and it seems that most of the sources on the subject are very technical and hard for me to read (particularily because I am not at all familiar with p... |
Is it generally accepted that Field Aligned Currents are caused by Force-Free Fields?
In a plasma, a force-free field is one that satisfies $\mathbf{j} \times \mathbf{B} = 0$, where $\mathbf{j}$ is the electric current density and $\mathbf{B}$ is the magnetic field. One way to guarantee that the system is force-free... | {
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Two touching surfaces transmitting light: Name of effect When two surfaces are sufficiently close enough to each other, light travels through the remaining gap as if it did not exist. Effects like total internal reflection no longer occurs.
If you look at this candle picture, you can see where the wax "touches" the gla... | It sound like you are describing an evanescent wave.
| {
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Confusion with the variational operator $\delta$ and finding variations I have recently started studying String Theory and this notion of variations has come up. Suppose that we have a Lagrangian $L$ such that the action of this Lagrangian is just $$S=\int dt L.$$ The variation of our action $\delta S$ is just $$\delt... | If the Lagrangian only depends on time through $X$ or $\dot{X}$, then we say that the Lagrangian has implicit but not explicit time dependence. So in your example, we would write
\begin{equation}
L(X, \dot{X}) = \frac{1}{2} m \dot{X}^2 - V(X)
\end{equation}
even though $X=X(t)$ depends on time. Given this Lagrangian, y... | {
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In Particle Physics what does the Rest Mass notation: 95$^{+9}_{−3}$ MeV/c$^2$ mean? On the Wikipedia page for the Strange Quark, I came across the following notation for defining its mass:
95$^{+9}_{−3}$ MeV/c$^2$
Following the reference link brings me to this page, which shows a range of published values for the Stra... | It is the way the evaluation of the error for the quark masses is given in the particle data group, page 10 for the strange quark in the link.
In the corresponding figure for the up quark there is the clarification:
Values above of weighted average, error,
and scale factor are based upon the data in
this ideogram onl... | {
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Gauss' law in the presence of surface charges Assume $V$ is a volume such that $\rho=0$ in $V$ where $\rho$ is the charge density. Assume further that we have a surface charge density $\sigma$ on the surface $S$ enclosing $V$ such that the total charge $Q_S$ on the surface is $\neq 0$. If we assume that $S$ is an equip... | There are two ways of explaining this. First is that if you're considering a charge density which is concentrated on a surface, then the electric field $\mathbf{E}$ does not satisfy the hypotheses of Gauss' divergence theorem (being continuously differentiable), because if you assume $\mathbf{E}$ is continuously differ... | {
"language": "en",
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Wouldn't the cosmic background radiation (CMB) produce drag and thus create a preferential inertial frame? Because the CMB is everywhere and is isotropic, if an object would have a certain velocity, it could have a pressure differential produced by the CMB which would produce drag till it would stop with respect to the... | One thing to note is that the CMB looks different from different locations (and at different times).
So while it provides a local frame of reference for every point in space-time, that frame is not constant over larger amounts of space, and it's likely that observers elsewhere (millions of light years away) observe it ... | {
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The entropy given by stefan Boltzmann's law looks remarkably similar to the volume of the sphere; $S(T)=\frac{4}{3}\sigma T^3$ If I am not mistaken the entropy for a blackbody per unit area is given by:
$$S(T)=\frac{4}{3}\sigma T^3.$$
The volume of a sphere is given by:
$$ V(r) =\frac{4}{3}\pi r^3. $$
Is this coinciden... | It's a coincidence, as the lack of $\pi$ indicates. The entropy per surface of a blackbody in $D$-dimensional space is $\frac{D+1}{D}\sigma T^D$. (You can deduce it e.g. by generalizing this.) By contrast, the unit $D$-ball has volume $\frac{\pi^{D/2}}{\Gamma(D/2+1)}$, which decays superexponentially at large $D$.
| {
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Is it possible to visualise red shift? If a picture of a star or galaxy hurtling away from Earth is taken, does it appear red despite it being a different colour? Would a blue coloured star moving away from us appear red to us or vice versa? If so how do scientists understand if say, the red colour of a star is due to ... |
If a picture of a star or galaxy hurtling away from Earth is taken, does it appear red despite it being a different colour? Would a blue coloured star moving away from us appear red to us or vice versa?
Red shift and blue shift is a terminology meaning shifting towards lower/higher frequencies. Usually one applies th... | {
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Why is there no temperature difference in the Joule expansion experiment? The whole system is adiabatic, and no heat exchange can take place. If the volume of the gas now doubles, it should actually cool down.
That's why I don't understand $dT=0$
|
if i have a piston and i pull on it really hard and this expands the isolated gas, i have no temperature difference?
In the case of the moving piston, the molecules of the gas are striking a moving wall. The pressure of the gas creates a force and the motion of the wall means this happens over a distance. So work i... | {
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Fake Perpetual Motion Device using an Electromagnet I was watching a video of one of those fake perpetual motion machines where a ball falls down a hole and then flies off a ramp back onto the starting platform.
As suspected, the large base is hiding an electromagnet. Studying frames of one cycle it seems that the bal... | When you switch on a magnetic field in the vicinity of a conductive object, you induce an eddy current in the object. This, in turn, makes its own magnetic field. The polarity of this field opposes the polarity of the inducing field, so repulsion results.
| {
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Slope of constant pressure line on $T$-$S$ plot Is slope of constant pressure line is same or di in liquid region and super heated region for pure substance on $T$-$S$ diagram?
| $$U=T\,\mathrm{d}S-P\,\mathrm{d}V+\mu\,\mathrm{d}N$$
We want $\frac{\partial T}{\partial S}$.
We know $T=\frac{\partial U}{\partial S}$, so $\frac{\partial T}{\partial S}$ is the second derivative of the internal energy with respect to entropy.
| {
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How does the combination of lens create a sharper image? There's a line in a book which states that the combination of lens helps create a sharper image, but I don't understand how. Does more magnification mean sharper image?
| The distance between nerve endings in the retina of the eye places a limit on the sharpness of an image that you can observe. A good lens system can bring the image closer and larger. This can cause the sharpness observed to be limited by other (smaller) factors.
| {
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Different values for the Normal ordering I've come across 2 examples approaching the ordering of $a^2({a^\dagger})^2$, each reach different results:
*
*$a^2({a^\dagger})^2=\;:\!\sum\text{all contractions}\!:\;=\;:\!aaa^\dagger a^\dagger\!:+\;4:\!aa^\dagger\!:+\;2:\!0\!:$
*$a^2({a^\dagger})^2=a(aa^\dagger)a^\dagger=a... | Hint: In Wick's theorem what remains in the fully contracted term (= the double contration) is the unit-operator $\hat{\bf 1}$ not the zero-operator $\hat{\bf 0}$, so OP's 1st calculation (v3) is wrong.
| {
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Is there any end to the electromagnetic spectrum? Is there any theoretical end to the electromagnetic spectrum…
| In theory, the electromagnetic spectrum should extend indefinitely without limit.
You can create an electromagnetic wave with arbitrarily long or short wavelength, and therefore arbitrarily low or high frequency respectively, by accelerating a charged particle back and forth.
Of course the amount of energy required to ... | {
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Question about the parity violation of weak interaction Lagrangian In the textbook of A. Zee, Quantum Field Theory in a Nutshell, the author states that the following Lagrangian:
$$ \mathcal{L} = G (\overline{\psi}_{1L} \gamma^\mu \psi_{2L})(\overline{\psi}_{3L} \gamma^\mu \psi_{4L})$$
Which describes the weak interact... | $$
\gamma^0 P_L \gamma^0 = P_R, \\
\gamma^0 P_R \gamma^0 = P_L,
$$
$$
P: \qquad \psi(x) \longrightarrow \gamma^0 \psi(-x) ~~~~\leadsto \\
P: \qquad \psi(x)^\dagger \longrightarrow \psi(-x)^\dagger \gamma^0 ~~~~\leadsto \\
P: \qquad \overline \psi(x)\gamma^0\psi'(x) \longrightarrow \overline \psi(-x)\gamma^0 \gam... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Does the standing wave equation proof require $\ell=Nλ$? Consider two identical sources $S_1$ and $S_2$ of waves, separated by a distance $\ell$ (as shown in the figure).
The sources produce waves in opposite directions(and towards each other). Now, suppose we wish to derive the equation for the standing wave produced... | You did correct mathematics deriving the standing wave equation
$$y=2Acos(kx-\frac {kl}{2})sin(wt-\frac{kl}{2})$$ which comes as the superposition of
$$y_1=Asin(wt-kx)$$ and $$y_2=Asin(wt+kx-kl)$$
However the other equation of standing wave which is
$$y=2Asin(wt)cos(kx)$$
comes as the superposition of the following two... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Does the neutrino interact with the photon? I know that the straight answer is no, but in my EFT course, where we're interested in nonrenormalizable operators of the Lagrangian, things aren't so straightforward.
The non-minimal QED Lagrangian is
$$\mathcal{L}=\mathcal{L}_{ren}+\mathcal{L}_{nonren}=\bar{e}(i\hat{D}-m)e-... | Yes, the neutrino may have a magnetic moment at the 1 loop level in vacuum, cf here, e.g.
This is summarized by your unrenormalizable effective (fake tree)
dimension 5 operator, since the loop into which neutrinos can resolve involves charged leptons or gauge bosons.
Highly suppressed by the weak/EM coupling factor (F... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/709513",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Photoelectric emission at frequency less then threshold frequency If I shine an EM radiation of frequency $\nu$ on a metal surface which has threshold frequency of $\nu_o$, where $\nu < \nu_o$ then, will the emission occur by multi photon absorption?
My reasoning is this
Since there are quantised energy levels in meta... | This is the experiment that established the photoelectric effect:
Within experimental errors there are no electrons coming out when the frequency is below the threshold for the metal.
so it may happen that the incident photon excites the electron (even though the photon has not enough energy to knock the electron out... | {
"language": "en",
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Does gravitation really exist at the particle level? As I understand, we usually talk about gravity at a macro scale, with "objects" and their "centre(s) of mass". However, since gravity is a property of mass generally (at least under the classical interpretation), it should therefore apply to individual mass-carrying ... | That's exactly what we are observing when we look at the night sky and see galaxies form out of nothing but dust.
Ever wondered why we are here to ask this question? Because gravity pulled together nothing really just dust of particles in the very early universe, forming all the galaxies and solar systems etc.
As a sid... | {
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"source": "stackexchange",
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Confusion in the showing EM wave exist from Maxwell equation When deriving the mathematical description of a field, we set the current density and charge to zero in Maxwell's equations.
However, this condition is not absolutely true anywhere on earth.
Yet, we are able to apply EM waves for problems in communication, me... | Free space solutions of maxwells equations show that wave like solutions can theoretically exist. Plane wave solutions to the homogenous wave equations are not created by charges and currents, and thus these solutions don't prove that EM waves are generated by charges.
This is not the only way that we can show wave lik... | {
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Currently self-studying QFT and The Standard Model by Schwartz and I'm stuck at equation 1.5 in Part 1 regarding black-body radiation So basically the equation is basically a derivation of Planck's radiation law and I can't somehow find any resources as to how he derived it by adding a derivative inside. Planck says th... | It just a clever use of the geometrical series:
$$\frac{1}{1-q} = \sum_{j=0}^\infty q^j$$
which is valid for any real number $q<1$.
Here $q = e^{-E_n\beta} \equiv e^{-\hbar\omega_n\beta}$. As long as the energies $E_n >0$ which is certainly fulfilled, we can make use of the geometrical series. And only this. The parame... | {
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What is the instant velocity? The velocity is the variation rate of the position correct? So does it make sense to talk about velocity without time?
| Velocity is indeed the rate of change of displacement w.r.t time. You are right that it is paradoxical to consider velocity at a point, as at one point there is no change in time or a change in displacement.
For velocity for any two points in time:
$$ v = \frac {\Delta s}{\Delta t} $$ where s is displacement, and $\Del... | {
"language": "en",
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"source": "stackexchange",
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Can't understand a statement about motion From the book where I am studying motion, It says
Motion is a combined property of the object under study and the observer. There is no meaning of rest or motion without the viewer.
I know that, for an object, it can be said that 'it is moving' in one frame of reference, and ... | A non accelerating particle can always be said to have a velocity of zero in its own non accelerating frame of reference regardless of what an external viewer measures. In this manner, There is no meaning of rest or motion without a viewer of the particle in the viewers frame of reference.
| {
"language": "en",
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"source": "stackexchange",
"question_score": "4",
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Earth is spiraling away from Sun at rate of 1.5cm per year due to mass loss of Sun? How it was calculated? My physics teacher asked if we could calculate the rate at which Earth moves away from the Sun due to the mass loss of the Sun. It's very sensible for me to understand that Earth is spiraling away from Sun due to ... | If we assume$^\dagger$ the earth always takes on a circular orbit of $r$ around the sun we get the following equation:
$$\frac{mv^2}r=G\frac{Mm}{r^2}$$
We can solve this for the radius:
$$r=\frac{GM}{v^2}.$$
If we now assume the velocity is constant throughout this process$^{\dagger\dagger}$ we get that the orbital rad... | {
"language": "en",
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If the escape velocity at the event horizon is the speed of light does it mean that slower bodies won't move away at all? If we say that the escape velocity from a planet is say 10 km/s we think that a slower body will move away from that planet but will be eventually forced to fall back on the planet. In simple words ... | The people who first postulated the existence of an object like a star or planet massive enough that the escape velocity would be equal to that of light did apparently think in those terms (light struggling to leave the object but inevitably being drawn back in, or light beams hovering motionlessly in space right next ... | {
"language": "en",
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How to see that the electromagnetic stress-energy tensor satisfies the null energy condition? I am trying to show that the Maxwell stress-energy tensor,
$$T_{\mu\nu} = \frac{1}{4\pi}\left( F_{\mu\rho} F^{\rho}{}_{\nu} - \frac{1}{4}\eta_{\mu\nu}F_{\rho \sigma} F^{\rho\sigma} \right),$$
satisfies the null energy conditio... | Notice that what you are trying to show is that $k^\mu F_{\mu}{}^\nu$ is a spacelike vector (in this answer, I'm assuming the $-+++$ metric convention). Hence, let us focus on this particular vector.
Given $k^\mu$ at some point, pick a choice of Cartesian coordinates such that $k^\mu = (1,1,0,0)^\intercal$, which is al... | {
"language": "en",
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If the EM field is a self-propagating field that doesn't need a media why should space expansion make any changes to its wavelength? If the EM field is a self-propagating field that doesn't need a media why should space expansion make any changes to its wavelength? If it makes changes to the photons wavelength should i... | In general relativity it is important to separate in your mind coordinate-dependent effects from coordinate-independent effects. This can be tricky, particularly in scenarios where there is a “standard” coordinate system. In those cases it is easy to forget that the standard coordinate system is still just a coordinate... | {
"language": "en",
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Eyes shut, can a passenger tell if they’re facing the front or rear of the train? Suppose you’re a passenger sitting in one of the carriages of a train which is travelling at a high, fairly steady speed. Your eyes are shut and you have no recollection of getting on the train or the direction of the train’s acceleration... | Bumps and gaps are asymmetric.
They make the cart jump up AND BACK and then, at slower rate, return to its equilibrium speed and direction. So you will detect rapid accelerations back and slower accelerations forward.
Curve handling (both intentional turns and railroad imperfections) happens at front wheels first and n... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/711352",
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"source": "stackexchange",
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Electric potential generated by spherical symmetric charge density I know this question is pretty basic but I found a supposedly wrong formula in my notes and I'm trying to understand where this is coming from. Suppose we have a spherically symmetric charge density $\rho({\boldsymbol{r}})=\rho(r)$, then the formula I w... | The first formula is true only far away from the source. It is in fact the first term of the multipole expansion.
By using Gauss theorem, you obtain the correct result for the electric field, but if you try to compute it with the gradient, you should use the general expression for the potential of a continuous distribu... | {
"language": "en",
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Is sand in a vacuum a good thermal insulator? My reason for thinking that sand in a vacuum would be a good insulator is that heat cannot be conducted in a vacuum, and the area of contact between adjacent grains of sand is very small, which means heat would transfer between grains relatively slowly. Is this correct, or ... | It sounds reasonable. But there are a few more things to consider.
How good a vacuum are you talking about? If you mean just good enough to make a better insulator, likely yes. But if you are pulling a vacuum just to get an insulator, there are likely better ways. A vacuum thermos bottle does this. It does not use sand... | {
"language": "en",
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Why is skin depth quoted as when the amplitude has decayed by a factor of $\frac{1}{e}$ The definition of the skin depth is:
"Skin depth defines the distance a wave must travel before its amplitude has decayed by a factor of $1/e$."
My question why is the decay of 37% significant here. The EM wave will still have some ... | Because the decay of an electromagnetic wave is exponential, i.e. it decays as $A_0e^{-z/\delta}$, where $A_0$ is the initial amplitude, $z$ is the distance in the conductor, and $\delta$ is the skin depth. It feels straightforward to then write the skin depth in terms of the natural exponential function.
Of course the... | {
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Invariants of inner product in pseudoreal representation of $SU(2)$ I am reading Peskin's and Schroeder (P&S), "An introduction to Quantum Field Theory", specifically the first paragraph on page 499 in section 15.4 "Basic Facts about Lie Algebras". At some point, the authors claim that the invariant combination of two... | P&S are talking about the spinor/defining/fundamental representation $$\eta,\xi~\in~ V~\cong~ \mathbb{C}^2$$ of $SU(2)$.
*
*The expression $\epsilon^{\alpha\beta}\eta_{\alpha}\xi_{\beta}$ is $SU(2)$-invariant because the determinant of an $SU(2)$-matrix is 1.
*One can use this to show that the complex conjugate spi... | {
"language": "en",
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Why is I = $\partial Q / \partial t$ and not $I=-\partial Q / \partial t$? I was playing around the Maxwell equations and I came across this:
$$\nabla\cdot J =-\frac{\partial \rho}{\partial t}$$
$$\iiint_V{\nabla\cdot J \space \partial V} = \iint_A{J\cdot\partial A}$$
$$-\iiint_V{ \frac{\partial \rho}{\partial t} \cdot... | Where you're using the divergence theorem, surface $A$ is oriented from the inside to the outside, making it a charge loss for the system: current is positive when charges leave the system.
On the other hand, in electricity, the usual $i=dq/dt$ relies on the opposite norm: $q$ rises when the current enters the system (... | {
"language": "en",
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Wick Theorem: number of contractions I have to prove that the number of contractions in Wick's Theorem
is equal to:
$$\frac{n!}{(n/2)! \ 2^{n/2}} \ \ \ where \ \ n \ \ is \ even$$
I don't know how to start, if someone can help.
| Since $n$ is even, I prefer to work with $2n$ instead. Take the correlator $\langle \phi_1 \cdots \phi_{2n}\rangle$. Starts with $\phi_1$: it has exactly $2n-1$ contractions; once all the $\phi_1$ contractions have been taken care, consider $\phi_2$: it has $(2n-3)$ contractions; in general $\phi_k$ has $(2n-k)$ contra... | {
"language": "en",
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How does current flow in a purely inductive circuit if the net voltage is zero? Considering the equation,
$$E=−L\frac{di}{dt}$$
The negative sign in the above equation indicates that the induced emf opposes the battery's emf.
If we're talking about a purely inductive circuit, the induced emf is equal and opposite to ap... | When the source voltage is suddenly made zero then the current will be decreasing at some rate and if an ideal inductor is present in a circuit then that decaying current will cause the magnetic flux to decrease with time through the loop of that inductor.
And In accordance with faradays law if the magnetic flux throug... | {
"language": "en",
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How you calculate the age of the observable Universe if the acceleration expansion is not constant? What makes us believe that the Cosmological constant was the same in the past?
And if there is no way to prove this then could the age of our Universe be different from the current calculated value since the Universe cou... | It is, of course, possible to add dynamical fields to the theory which act as Dark Energy given an appropriate equation of state. In general, different models will indeed lead to a different age of the Universe.
In addition to its simplicity and the good agreement with a large array of observations, the cosmological co... | {
"language": "en",
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Higher order terms in Big Bang derivation You can easilty proof that an SEC fluid gives a big bang by looking at the second Friedmann equation:
$$
\frac{\ddot{a}}{a} = -\frac{4\pi G}{3}(\rho + 3P) \le 0
$$
This implies that $\ddot{a} \le 0$ and thus $a$ continues to get smaller and smaller for smaller t, so at some po... | As put by this course, when using the linear approximation to estimate the age of the universe:
"This result of 14 billion years is surprisingly close to the currently accepted value of
around 13.8 billion years. However, there is a large dose of luck in this agreement, since
the linear approximation is not very good w... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/714095",
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What actually are microscopic and macroscopic viewpoints in thermodynamics? The microscopic viewpoint of studying a system in thermodynamics is the one in which we consider the system on a molecular/atomic/sub-atomic level. (is that even right?)
The macroscopic viewpoint is the one in which we ignore the molecular natu... | A full answer to your question is simply reading a book on statistical physics.
The thermodynamic limit
There's no microscopic thermodynamics. At the microscopic level, you simply use ordinary mechanics (classical or quantum) for the particles.
But as the number of particles grow, this approach becomes both inefficient... | {
"language": "en",
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What does $\sin(a,b)$ mean in the absorber theory of radiation? I'm doing a revision of the absorber theory of radiation by Wheeler and Feynman (that you can see here: "Interaction with the Absorber as the Mechanism of Radiation" - page 161) and I have encountered the expression $-(e a/r_k c^2) \sin(a,r_k)$, where $a$ ... | It stands for sine of the angle between the two vectors in the braces, in this case, between the retarded radius vector $r_k$ and the charged particle acceleration $\mathscr{U}$.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/714857",
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Why is there still disagreement over the mass of the bottom (or beauty) quark, but none of the others? Wikipedia (among other places) lists two values for the alleged mass of the B quark, 4.18 and 4.65 GeV.
Only one of the two possible masses listed has a link to another Wiki page explaining the theoretical framework b... | Looking at the wiki article, the difference in the mass values depends on the mathematical model used to derive from the data the value of the bottom quark mass.
One of the values links to this model
In quantum field theory, the minimal subtraction scheme, or MS scheme, is a particular renormalization scheme used to a... | {
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I can't seem to figure out a way to compute a gradient without reference coordinates I'm not sure if this question is better asked here or in Mathematics but here it goes:
I'm studying electric dipoles, and this exercise I'm working on asks for the energy between 2 dipoles, given by $$U_{DD}=-\vec{p}_1\cdot\vec{E}_2\,\... | Use $\nabla\left[\frac{{\vec p}\cdot{\vec r}}{r^3}\right]$=$\frac{\nabla({\vec p}\cdot{\vec r})}{r^3}$+$({\vec p}\cdot{\vec r})\nabla\left(\frac{1}{r^3}\right)$. $\nabla({\vec p}\cdot {\vec r})={\vec p}$ since $\nabla\times{\vec r}=0.$
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/715071",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Will the potential energy is same in both the cases? Suppose there is a charge $Q$. Now bring in another charge $Q'$ from infinity to a position a distance $r$ from charge $Q$. Then the change in potential energy is equal to $kQQ'/r$.
My question is: will the potential energy will be same if the same charge $Q'$ is bro... | Short answer: Not really.
The answer is slightly different when talking about point charges vs distributons.
Given I have some charge distribution $\rho_{1}$ and some other charge distribution $\rho_{2}$ that produces a potential $V_{2}$
The potential energy between the 2 distributions [not the same thing as the total... | {
"language": "en",
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Difference between stable manifold and basin of attraction? In 'Nonlinear Dynamics and Chaos' by S. Strogatz, a distinction is made between a stable manifold and basin of attraction of a fixed point in phase space:
Here, the stable manifold of a saddle point is a line, and the basin of attraction of a stable node is a... | To some extent it's indeed a convention/definition:
*
*intuitively, if a set has a region of typical initial conditions leading to it (say, a neighborhood, a finite phase space volume, etc.), and this region is by definition its "basin of attraction" and this attracting set is called an "attractor";
*whereas invaria... | {
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How can we experimentally confirm that atoms/molecules in a solid actually "move"? The atoms in a solid are so attracted to each other that they "vibrate" and don't move past each other.
How do scientists "measure" that atomic vibration in a solid (let's say at room temperature)?
As a raw, uneducated person it is easy ... | For me, the most salient fact arising from molecular “jiggling” is simply thermal radiation. It has the advantage of being relatively easy to observe (using thermal imaging at room temperature, and just your eyes at red-hot temperatures and higher), but I suppose whether you consider it convincing evidence of molecular... | {
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Why, in this solution, acceleration is constant even when it depends on distance between two charges? I used integration of $a=dv/dt$ to solve this Why, in this solution is acceleration constant, even when it depends on the distance between two charges? I used integration of $a=dv/dt$ to solve this.
Question
Two partic... | The method used in the given solution is completely incorrect. Its only redeeming virtue is that it happens to give the correct answer through a numerical coincidence. The simplest way to solve the answer correctly would involve energy conservation, as described in Visza Sekar's answer.
To be a bit more concrete abou... | {
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The value of $g$ in free fall motion on earth When we release a heavy body from a height to earth. We get the value of $g=9.8 \ ms^{-2}$. Now, I'm confused about what it means. For example, does it mean that the body's speed increases to $9.8$ every second? Or, does it mean that the speed of the body is $9.8 \ m/s$?
| You can see that $g$ has units of acceleration, namely $\frac {m}{s^2}$ or $\frac {m}{s} \left (\frac 1s \right )$. Last form gives an easy interpretation,- speed change per 1 second. Additionally, there are couple of assumptions in use:
*
*Earth is assumed an ideal sphere, otherwise $g$ would depend on radius $R$ at... | {
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Born's Rule for states over supernumbers? For Quantum-mechanics on a Hilbert-space over the complex numbers, the usual scalar product of two states $\langle \phi | \psi \rangle$ and gives the transition amplitude between the two states. The absolute square of this quantity then gives the probability that a particular v... | In order for the Born rule of a wavefunction or an overlap to produce measurable physical probabilities $\in[0,1]$ of ordinary numbers, all supernumbers must first have been integrated out, cf. e.g. this & this Phys.SE posts.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/716897",
"timestamp": "2023-03-29T00:00:00",
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Why does the the dielectric constant of a ferroelectric increases with temperature, below $T_C$?
The above figure is taken from C. Kittel.
When a ferroelectric substance (say, BaTi${\rm O}_3$) at room temperature is gradually heated, the dielectric constant $\varepsilon_r$ first increases and then attains a peak at a ... | The response of dielectric constants to temperature is model-dependent; thus, I would say that there is no simple rule of thumb. However, in the specific case of phase transitions, the material always builds up long-range correlations between its parts and fluctuations are very intense (near the critical temperature, t... | {
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Why doesn't $dU=nC_{v}\,dT$ hold for all substances? Consider the following proof for change in internal energy of real gases, liquids and solids(assuming Non-$PV$ work $=0$):
*
*Let X denote real gases, liquids, and solids
*The First law of thermodynamics is $dU=dQ-dW=dQ-PdV$, which also holds for X
*At constant v... | For a constant volume transformation, the relation is always true: it is simply a definition of Cv !
| {
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An extension of von Neumann entropy to observables Suppose we define the "entropy" of a self-adjoint matrix $\rho$ as the real number $S(\rho)$ given by:
$$S(\rho)=-\text{tr}(\rho\log|\rho|)$$
(notice the absolute value on $\rho$, as $\rho$ may have negative eigenvalues). While clearly such an entropy function can be n... | Let $\rho=p\lvert a\rangle\langle a\rvert+(1-p)\lvert b\rangle\langle b\rvert$ , with $\lvert a\rangle$ and $\lvert b\rangle$ two orthogonal maximally entanged states.
Then, the reduced density matrices of $\rho$ are maximally mixed states, and thus valid density matrices, independent of the value of $p$.
On the other ... | {
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Heat death of the Universe in LCDM I have often read that the heat deat of the Universe occurs in cosmologies where its age can be arbitarily large, even with a cosmological constant. However the standard LCDM cosmology's conformal age is bounded, even in the arbitarily far future. It seems to me that for the Universe ... | The fact that the conformal time is bounded in the future means that there are regions in the universe which we will not be able to get information from, so particles here cannot equilibrate with particles there.
However, the form of equilibrium you reach in LCDM is not one with a bunch of particles colliding and reach... | {
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How can the Cosmic Neutrino Background (CνB) have a temperature? How can any neutrino have a 'temperature'? The word temperature usually refers to the average velocity of massive particles, correct?
And the Cosmic Microwave Background (CMB) has a 'temperature' based on the temperature of a 'black body' that would emit ... | The temperature of a gas is a parameter that reflects the distribution of energy/momentum of the particles. It is not a characteristic of any individual particle.
Before the cosmic neutrino background was formed (when the early universe was $>10^{11}$ K) neutrinos and anti-neutrinos were produced and destroyed in therm... | {
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Does dusk really remain for a shorter period of time at the equator? It is said that the dusk remains for shorter time at equator than the poles. Because, the equator rotates faster than poles. But it is also true that time is the same in every latitude, and if it's true, then the dusk should remain the same at equator... | "Dusk" is defined as "the darker phases of twilight" (in the evening), so it may be ambiguous. There are in fact 3 different twilights:
which are defined by how far the sun is below the horizon (hence the answer from @tobalt). Since the East-West speed of the sun in the sky is identical across the planet (though it do... | {
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Why doesn't the variation of resistivity with temperature go both ways? I've learnt that the variation of resistivity with temperature for a conductor is:
$\rho=\rho_0(1+\alpha (T−T_0))$
Let's consider resistivity at 0℃ and 100℃.
When heating the conductor from 0℃ to 100℃,
$ρ₁₀₀=\rho_0(1+\alpha (100-0))$
α=$\displaysty... | More broadly, it's convenient to postulate that the resistivity $\rho$ changes with temperature $T$ in differential form as
$$d\rho=\alpha(T)\rho\,dT,$$
where $\alpha$ is the (temperature-dependent) thermal coefficient of resistivity.
For the purposes of this question, though, we can idealize $\alpha(T)$ as constant. I... | {
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How does an electron move in the $p$ orbital? This is my first time learning about orbitals and I am very confused over how do electrons move around the nucleus in the
$p$ orbital.
Wouldn't it have to move out of the orbital where probability of finding an electron is low in order to complete its revolution? Maybe my u... | The electron $p$ orbitals with $\ell,m=1,\pm1$ have nonzero expectation value in a torus around the $z$-axis. As time evolves, the complex phase of the wavefunction increases clockwise or counterclockwise around the $z$-axis, depending on the sign of $m$. Your favorite intro quantum textbook has a paragraph about inter... | {
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If water is nearly as incompressible as ground, why don't divers get injured when they plunge into it? I have read that water (or any other liquid) cannot be compressed like gases and it is nearly as elastic as solid. So why isn’t the impact of diving into water equivalent to that of diving on hard concrete?
| Incompressible doesn't mean that it has to keep the same shape.
But, due to viscosity, water can be "slow" to change its shape under external influence. So when a diver arrives too fast, water can't adapt in time and behave like a brick wall for the duration of the diver's penetration.
| {
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Translating Ashcroft and Mermin's "Second Proof" of Bloch's Theorem to Dirac's Notation At the end of this post I attach Ashcroft and Mermin's proof of Bloch's theorem which is not essential per se (the proof using lattice symmetries is more general), but is key in being used later as a jumping off point for the nearly... | You need to use the fact that $U$ is periodic with the same periodicity as the lattice, which means that it can be expressed as a sum
$$U(\mathbf r)=\sum_{\mathbf G\in \mathrm{RL}}u_\mathbf G e^{i\mathbf G\cdot\mathbf r}$$
where RL is the reciprocal lattice.
Also, for what it’s worth note that since Ashcroft and Mermin... | {
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Is Newton’s third law of motion formed from Poincare symmetries? So I know that Newton's third law states that every action has an equal reaction, making a symmetry. But just like how Poincare symmetries form conservation laws, do any Poincare symmetries form Newton's third law?
(Side question: If not, what symmetry is... | The third law states that momentum is conserved. From Noether we know that momentum consrevation is a consequence of translational symmetry. The tranlations are a subgroup of Poincare. So Yes.
| {
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How is a state of $|0\rangle$ created experimentally? In the context of quantum computing, many times in textbooks and online courses, they say "we generate a state of $|0\rangle$", and then proceed to apply quantum (logic) gates.
My question is: how would we practically ensure that a generated state is actually $|0\ra... | $|0\rangle$ is typically a ground state, separated from the other (excited) states by a gap $\Delta$. One typically lowers the temperature below the gap, $k_BT\ll\Delta$ and waits for long enough to be sure that the system has relaxed to the ground state.
There have been extensive research in initialization of quantum... | {
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A cylinder rolling down an inclined plane A few questions popped into my mind while studying rotational motion.
Take a cylinder to the top of an inclined plane. Suppose there is friction. Let go of the cylinder. If it is rolling without slipping, is its acceleration constant over the time interval it is rolling down? I... | Newton's second law is stated for point objects where acceleration has no ambiguity. When you are studying a system like the cylinder which is composed of many points, the problem is to choose which point are you going to choose to calculate the acceleration. The centre of mass theorem states that the point to consider... | {
"language": "en",
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Why does the Lagrangian have $O(4)$ symmetry after Wick rotating (previously Lorentz symmetry)? Pertaining to the answer within link.
Why is it the case, that for Lorentz invariant Lagrangian $\mathcal{L}$, after Wick rotation, the $O(4)$ invariance is established, thus manifesting itself as having Euclidean metric? Is... | As long as the Minkowski action is constructed from Lorentz-covariant tensors, then under Wick rotation [where the contravariant and covariant $0$-components of the tensors are Wick-rotated in opposite ways], the corresponding Euclidean action becomes constructed from the corresponding $O(4)$-covariant tensors, cf. e.g... | {
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Functional Derivative Calculation Given the functional:
$$ F[\phi] = \int_V \frac{k_B T}{a^3}\phi\ln(\phi) \ ds = \int_V I(\phi) ds $$
I want to find the functional derivative. I believe this would result in:
$$ \frac{\delta F}{\delta \phi} = \frac{\partial I}{\partial \phi}=\frac{k_B T}{a^3}[\ln(\phi)+1]$$
However, th... | Your attempt points in the right direction, but note that the functional derivative is not the partial derivative as you're deriving with respect to a function and not a variable. Nonetheless, they are connected for certain functionals.
Take a compactly supported smooth function $\psi$, then by the definition of the fu... | {
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Why is the black body radiation independent of composition and incident radiation? There have been questions similar to this, but most of them do not explain the mechanism responsible for the phenomena but instead explain through contradiction of second law of thermodynamics, for example this answer https://physics.sta... | That is must be radiating is clear from the fact that it is absorbing energy from the environment it is in thermal equilibrium with while not heating up.
So the question becomes why this is independent of material type and why it had that particular distribution.
It is important to remember that a black body is an idea... | {
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Differential charge existing We define current by $I=\frac{\mathrm{d}q}{\mathrm{d}t}$. Here, $\mathrm{d}q$ is the infinitesimal element of charge. But again,we know that charge is quantised meaning there is a finite value to the smallest amount of charge which is $e$. Since $\mathrm{d}q$ is infinitely small, $\mathrm{d... | The same holds true for water. I presume you don't have problem using $d V/dt$ for the flow of a volume $V$ of water. Yet we know that water is ultimately discrete molecules...
The point is: the discrete nature of the water molecule or the electric charge does not manifest itself much in everyday life so it's much mo... | {
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How can you calculate how long life will last with a regular run in terms of special relativity? Imagine, John run everyday 10 km with speed 12 km/h towards the east along the equator. If he had not run, he would have died at 70 from the point of view of a motionless observer. How long will John live from the point of ... | The scenario you describes has thousands of potential variables that might play a role in the outcome, such as the weather each day, the clothes John wears each day, the route he follows on each run. However, if you ignore those, and you assume that John does exactly the same run every day, going 5km directly to the Ea... | {
"language": "en",
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Can plasmas be black bodies? I have recently heard the claim that sun can not be composed of plasma because plasma can not be a black body.
I am an uneducated layman, I've seen a lot of people (laymen) deviate from accepted scientific consensus. I am skeptical and I don't have enough knowledge about physics to argue it... | The argument is silly if the claim is that plasmas cannot appear anything like blackbodies, since there are observable examples like the Sun.
To be a blackbody, a volume of plasma needs to come into equilibrium at a reasonably uniform temperature and to be thick enough that it will absorb all radiation incident upon it... | {
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Why flapping rudder produce net thrust if one half-stroke produce thrust and second half-stroke drag? In small sailing boat like optimist is well know technique when there is no wind, rudder pupming which push boat forward.You just need push-pull rudder stick left to right with fast movement.
Rudder works complety unde... | I guess that during the forward thrust portion of the stroke the skipper pushes harder and faster creating more turbulence and drag and thus more thrust. During the reverse thrust part they slow down for more laminar flow and thus less drag and less thrust. So over one cycle the net impulse is forward.
But I also guess... | {
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Does the force between two magnetic poles ever reach zero? If we hold two magnetic like-poles together and start to move them away, would the repelling force reach absolute zero at certain point?
In that scenario, as a layman, I think that there is something paradoxical :(
We can never reach absolute ZERO in Physics. T... | Like gravity or electrostatic attraction, magnetism reduces with distance. However, while the first 2 have an inverse square law (the force diminishes with the square of the distance), the magnetic force diminishes with the 4th power of the distance, or $f\propto{r^{-4}}$. Hence it reduces much faster than electric or ... | {
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How do quantum probabilities transform under Lorentz transformations? I think I get how scattering probabilities transform under Lorentz transforms. Once the interaction phase is over, the final probabilities become time independent. Hence, every observer could describe the final state using the same probabilities.
But... | There is no universal answer here. Transformation formulas depend on the way you describe (enumerate) system states: it can be done in invariant and non-invariant way, consistent with system symmetry or not. So the only answer to your question is: they transform somehow, as some representation of Lorentz group.
ADDENDU... | {
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A nuclear fusion generating cart In an unrealistic thought experiment, suppose I had a $100$ meter track with a cart ontop that had a "pocket" on the front of the cart. Suppose further that this track and cart were in a room of hydrogen gas at 1atm.
How quickly would I need to accelerate the cart down the track so that... |
How quickly would I need to accelerate the cart down the track so that
by the end the compressed and heated hydrogen gas in the front
"pocket" of the cart has fused together (i.e. the cart has caused a
nuclear fusion reaction)?
I believe no amount of speed will suffice.
The problem is that the compression takes place... | {
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How can I know who is accelerating? – Inertial reference frames and relative motion Suppose I (observer $I$) am standing somewhere in space. I see a region in which my friend ($F$) is accelerating in some direction $\mathrm{\mathbf{\hat{u}}}$. Suppose I see everything in $F$ accelerating in the same direction.
My quest... |
how can I know if I am an inertial frame of reference or if he is (in which case I am accelerating in the −u^ direction)?
Use an accelerometer. If your accelerometer reads 0 then you know that you are inertial. If your accelerometer reads something other than 0 then you know that you are non-inertial. This is irrespe... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/722522",
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Shape of fastest spinning rod A one-meter steel rod of variable thickness is attached at one end to a spinning hub. The cross-sectional area of the rod is a function $f(x)$ of the distance $x$ in meters from the hub, x ranging from 0 to 1. My question is: how can I choose the function $f(x)$ to maximize the speed at wh... | start with this equation ?
$$F_{tu} f(x) = \int \rho \cdot x \cdot f(x) \cdot \omega^2 dx$$
heche
$$F_{tu} \frac{df(x)}{dx}=\rho \cdot x \cdot f(x) \cdot \omega^2$$
with $~f(0)=f_0~$ you obtain
$$f(x)=f_0\,e^{\frac{\rho\omega^2\,x^2}{2\,F_{tu}}}$$
| {
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How do physicists know that some of a beta ray/particle's 'missing' energy isn't lost to interference with the electron cloud surrounding the atom? Enrico Fermi and Wolfgang Pauli ultimately concluded that beta decay resulted in an electron and an electron antineutrino leaving a nucleus... BUT...
How does the electron ... | Beta particles have a typical kinetic energy of about half a million electron volts. This is plenty enough to pass through the electron cloud surrounding the nucleus and completely escape from it.
| {
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Does the intermolecular forces change during phase transition? When water is heated but not yet boiling, I understand that the intermolecular attraction does not change, but the molecules vibrate more.
But when water boils to gas, does the forces of attraction between the molecules change, or are the intermolecular for... | Intermolecular forces are never broken. What can be broken are bonds, although one should add that the precise concept of a bond is not straightforward (there are no hooks joining molecules).
From a fundamental point of view, all the interactions relevant in typical condensed matter systems are basically electrostatic.... | {
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Deriving wave equation of string without approximation When deriving the equation for a standing wave of a string, we often approximate that the tension at all points in the wave is constant. but I want to derive the equation without the approximation. I tried to derive it with lagrangian as below:
*
*kinetic energy ... | You want to derive a non linear 1 D wave equation but still assume the motion to be purely transverse: $ \overrightarrow{v}(x,t) = \frac{\partial f}{\partial t} \overrightarrow{ e_{y} } $. If the tension varies along the string you must include the horizontal component of the velocity: T(x) and T(x+dx) do not cancel ... | {
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By Jordan-Wigner transform, we can tranfer spin-$1/2$ model into fermions, then how to choose the right hamiltonian so that we can solve the model? I know that by using Jordan-Wigner transform(JWT), we can transform spin-$1/2$ systems into fermions. My problem is, for example, after JWT, we have a hamiltonian of form
$... | The example you find has a mistake. When you diagonalize the matrix $\mathcal{H}$, you are applying some unitary transformation $U$, which is a $4 \times 4$ matrix, to the vector $(c_1,c^{\dagger}_2,c_2,c^{\dagger}_1)^T$. Let the transformed vector be $(\tilde{c}_1,\tilde{c}^{\dagger}_2,\tilde{c}_2,\tilde{c}^{\dagger}_... | {
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Emf induced by a solenoid Could someone please clear my confusion regarding this concept and point out what is wrong with my argument:
Say we have a simple circuit as shown in the image:
Why is the potential difference between points b and a not equal to L*di/dt but is instead -Ldi/dt?
Since the magnetic flux through ... | Your understanding of the two currents is incorrect. There is only one current. The way the circuit is drawn the current flows clockwise. Current always enters the positive end of passive elements when they are absorbing or dissipating energy.
The voltage is placed across the RL combination such that $$V_{a}>V_{b}>V_{c... | {
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How to calculate the energy of a spring-mass system considering harmonic oscillation of the normal mode? For a spring-mass system, we know that the potential and kinetic energy are
$$E_p = \frac{1}{2}ku^2 \text{ and } E_k = \frac{1}{2}m\dot{u}^2.$$
where $k$, $m$ and $u$ are the spring constant, mass and the displaceme... | The position of a spring-mass system is real valued function of time, not complex. When you write down the normal mode, you need to specify that you are taking the real part of the complex expression:
$$
u(t) = \text{Re}\left(\hat u e^{i\omega t} \right) = A \cos(\omega t + \delta).
$$
Here, $A = |\hat u|$ is the ampli... | {
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What causes light passing through a hole to change direction? On diagrams showing light passing through a hole, the wave of light appears to change direction when it emerges from the hole.
What causes that change of direction? Is it maybe the walls of the hole imparting a pulling force or the sudden absence of light ne... | Photons, including single photons interact with single edges. The effect is more noticeable when the edge is sharp. Photons are pulled around and behind the edge But photons also scatter away from the Edge. A single slit is created with two sharp edges. Each edge is diffracting and scattering photons on their way to th... | {
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What percentage of sunlight isn't scattered by the atmosphere? What percentage of sunlight isn't scattered by the atmosphere and instead will arrive at your eyes directly from the sun.
It's been aksed here before but a proper answer hasn't been given.
I was thinking about the effects looking directly at the sun would h... | It very much depends on the wavelength, the elevation of the Sun, the altitude of the observer and what pollution is in the atmosphere.
A simple example. At zenith, the extinction in the V band (about 550 nm) is about 0.12 astronomical magnitudes at a pristine observatory site, high on a mountain. This means a fraction... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/724116",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
} |
Brightness of bulbs in Parallel When adding bulbs in parallel, the brightness is brighter than that of series. But does that mean adding bulbs in parallel will increase the brightness of the other bulbs?
My intuition is as follows: When adding a bulb in parallel the current doubles, but that current splits between the ... | You just get the brightness of two ore more bulbs, every single bulb keeps its brightness, if they are parallel.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/724239",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 1
} |
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