Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Can particles smaller than Planck Length be detected? It is my understanding, that anything smaller than a Planck Length cannot interact with photons, because photons with such small wavelength are massive enough to collapse into a black hole (source). Particle of such size would not interact with electromagnetic force... | Counter-question: what does "smaller than the Planck length" even mean, leave alone, can such particles even exist in the first place?
"smaller than the Planck length" is ill-defined precisely because of the meaning of the Planck length: at the latest at those scales, our concept of space and time (even if warped) will... | {
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Why can basis vectors change direction? I thought that basis vectors were of magnitude one and located at the origin and were each linearly independent, so how in things like polar coordinates can the basis vectors be moving?
| The only requirements for basis vectors is that they must be linearly independent and they must span the vector space. There is no requirement that they be normalized nor that they be orthogonal to each other.
Now, when you speak of basis vectors moving in polar coordinates what you mean is that you have some manifold ... | {
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Isn't it possible for a matter to have mass of an electron but opposite charge? I read that "Positrons" have the same mass as of an electron but it is oppositely charged but we don't call it a normal matter we have given a special name to it "anti matter". But why ? Why can't a matter particle have those properties ? W... | All particles have an associated anti-particle. Note that some particles, a.o. photons, are identical to their antiparticle. Which one of these are called particle and which antiparticle is based on natural abundance. Positrons, antiprotons, antineutrons are hardly found in nature so are termed antimatter. An electron ... | {
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Physical interpretation of Klein-Gordon Equation conserved charge In the Klein-Gordon Equation the conserved charge is: $$\rho = \frac{i \hbar}{2m} (\psi^* \frac{\partial \psi}{\partial t} - \frac{\partial \psi^*}{\partial t} \psi) $$
rather than the conserved (probability) density in the Schrodinger equation:
$$\rho =... | The answer is in the question: it is the charge density although a factor $e$ is missing.
| {
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The uniqueness of primitive vectors in a Bravais lattice I am reading Chapter 4 of Ashcroft and Mermin (A&M) in which the basic definitions of a Bravais lattice (BL) -- as considered as a purely mathematical entity -- are being laid down. One of the definitions of a BL given by A&M goes something like the following:
A... | As long as you have a 3-by-3 matrix ${M^a}_{b}$ with integer entries, and such that its determinant is unity (so that its inverse is also an integer matrix) you can use this to change the Bravais basis set to
$$
{\bf e}'_a = {\bf e}_b{M^b}_{a}
$$
and the set
$$
n_1 {\bf e}'_1+n_2 {\bf e}'_2+n_3 {\bf e}'_3
$$
is the s... | {
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Is electromagnetism caused by curved spacetime? They talk about gravity being due to the curvature of spacetime. Does this also apply to electromagnetism, if so why and if not what's the difference?
| The short answer is no. It's possible to have a theory of gravity with a curved spacetime without electromagnetism, and it's possible to have electromagnetism on a flat spacetime without gravity. Electromagnetism is simply associated with a different field than the gravitational field.
However, there are ways in which ... | {
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The effect black holes have on light We all know that light loses its energy when it is moving through expanding space and time. And sense a black hole can be summed up to a super compressed space time, shouldn't that mean that a photon gains energy when it enters a black hole because it is experiencing the opposite ef... | From the perspective of an observer far from a mass:
Light gains energy (increasing in frequency) when it goes from farther away from a mass to closer to a mass. Energy is conserved: the increase in the energy per photon is equal to the decrease in gravitational potential energy caused by bringing the mass-energy of th... | {
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Why do accelerating electrons not emit electromagnetic radiation? I've read at many places that accelerating charged particles emit electromagnetic radiation, but on this article on Bohr's hydrogen atom, at the end part, it's written under Limitations of the Bohr Model that:
The Bohr Model does not account for the fac... | The Bohr model was invented so as to explain the spectrum of light from the Hydrogen atom,. By classical theory the spectrum should be a continuous radiation and the electron should fall on the proton and neutralize it, thus no atoms. With his quantization of angular momentum postulate the model reproduces the spectru... | {
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Can a material generally score or cut itself by hand? I'm wondering if a given solid material can, in general, score or cut the same material, when applied by (at most) human muscular strength.
I've tried searching for this online, but it seems like a difficult-to-express search target. For example, the site Answers.co... | The mineral diamond can scratch diamonds.
There's no further elaboration or justification at that site.
My question differs from prior somewhat-related questions on SE Physics, because those answers all end up addressing cases where the cutting material is accelerated to very high (possibly relativistic) speed. The pr... | {
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Long-range correlations in transverse field Ising model The transverse field Ising model in 1+1d has two phases: a symmetric "disordered" phase and a symmetry-breaking "ordered" phase. Both of these phases have a finite excitation gap. In the symmetry-breaking phase, there is long-range order, that is $\langle Z_i Z_j\... | If you look at the paper by Hastings and Koma, https://arxiv.org/abs/math-ph/0507008, they claim to prove the following:
When two observables commute with each other at large distance, the connected correlation function decays exponentially under the gap assumption.
The key word here is "connected." For the $Z_i$'s (... | {
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Energy not conserved? Let us suppose a stone of $4$kg mass falls from $5$ meter above upon an iron rod of the same mass which was entering the ground. Consequently the rod entered $10$ cm more deep into the ground.
Now considering the head of the iron rod as reference level total energy initially is that of the stone w... | Part of the energy was turned to heat another part to deforming energy. You call this not energy loss but energy depreciation, in most cases of energy conversion partor all of the energy ist depreciated. If you go with your car for some instance and return home, all the energy in the fuel is first turned to kinetic en... | {
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What shape the Earth would have to be for an object in free fall to follow a straight line trajectory? I was explaining to my 8 year old daughter that objects in free fall follow an elliptical trajectory instead of the commonly believed parabolic one (source: https://www.forbes.com/sites/startswithabang/2020/03/12/we-a... | An object in free fall is accelerated towards the centre of gravity of the Earth. That means that its trajectory will be a straight line if and only if , it has no component of velocity normal to the line between it and the centre of the Earth. Off the top of my head, I imagine that to hold true regardless of what shap... | {
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Solution to two-dimensional PDE (wave/Klein-Gordon type equation) I'm cross-posting from the Math SE as more people might have relevant knowledge here. I was playing with an optimization problem and ended up reducing it to solving the following PDE:
$$ a^2 xy \frac{\partial^2 f}{\partial x \partial y} + f = -axy(y+2ax)... | First define $=\ln||$ and $=\ln||$ and then use and to define and as you did. In this way you should obtain exactly the KG equation with source.
| {
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Why do microwaves penetrate flesh when visible light does not at the same intensity? I understand why microwaves penetrate flesh, it has been answered before here, but in the most answers it was mentioned that although microwaves have less energy per photon when compared to visible light, at high intensities only do th... |
Why exactly if microwaves have less energy per photon, with visible
light at the same high intensity, would they be more capable of
penetration?
The short answer is it is the frequency not the intensity of the electromagnetic wave that determines the mechanism of absorption (e.g., molecular rotation, vibration, elect... | {
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Infinitesimal Ampère-Maxwell for (special/symmetric) current induced B field In a static magnetic field $\mathbf{B}$, which is induced by a static current density $\mathbf{j}$ the current density shall be zero for all points on the $z$ axis ($\mathbf{j}(0,0,z)=\mathbf{0} \; \forall z\in\mathbb{R}$) and obey a symmetry ... | In your problem you have set a very specific restriction on your magnetic field, that it has only $z$ component, and you have required it to be true in the whole space (at least near $xy$ plane).
If you have a surface current, the component of the magnetic field parralel to the surface is guaranteed to be discontinuous... | {
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Going from 2D dispersion relation to density of states If one was to have a 2D dispersion say: $$\varepsilon(k)=k_x^2-k_y^2$$
We know the dispersion relation generally can be written as:$$ D(\varepsilon)=\sum_{k_x}\sum_{k_y}\delta(E-\varepsilon(k_x,k_y)$$
which as can be seen in many different pieces of literature (e.g... | That integral denotes that you want to integrate $1/|\nabla \epsilon(k)|$ over all wavevectors that satisfy $\epsilon(k) = \epsilon$ for any given $\epsilon$ which is taken to be a constant. Unless you find some convenient parametrization of these constant-energy surfaces, this is a hard to do analytically and one need... | {
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How did physicist calculate times like $10^{1500}$ and $10^{10^{76}}$ years? If protons don't decay, iron stars are expected to form via quantum tunneling after $10^{1500}$ years, and they are expected to all have become neutron stars or black holes after $10^{10^{26}}$ to $10^{10^{76}}$ years. How did physicists calcu... | The key is to estimate tunnelling timescales by the WKB approximation. Your quoted figures are taken from Eqs. (41) and (47) in Dyson 1979 (this version is easier to search). While Eq. (41) follows from Eqs. (30) and (40) (the former summarizes usage of the aforementioned approximation), Eq. (47) follows from Eqs. (30)... | {
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Does a magnetic dipole spins in a uniform magnetic field Till now I believed that every magnet has a magnetic moment vector associated with it and that if that magnet is put in a uniform magnetic field its magnetic moment vector tries to align itself with the magnetic field vector but I came across a question while stu... | The field creates a torque on the dipole if it is not aligned. This accelerates the dipole.
When it is aligned, torque is zero, but the rotational speed is non-zero. So it moves past the alignment orientation. It oscillates the same way a pendulum does.
No, unless it is given extra energy, it would not be expected t... | {
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Concept of Gravitational potential energy Change in Potential energy corresponding to a conservative force is defined as $$\Delta U = U_f - U_i=-W_f$$ and gravitational potential energy is $$\Delta U = U_f-U_i = -W_g $$ Suppose a mass $m_1$ is kept at a fixed point $A$ and a second mass $m_2$ is displaced from point $B... | If you let $r_1$ go to $0$ with nonzero $m_1$, you've defined a region with positive mass and zero volume, hence infinite density. That's a gravitational singularity. Whether such things exist or not is anyone's guess, but if they did, they would be the centers of black holes.
While Newtonian gravity won't accurately d... | {
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Clarification for textbook diagram on electric potential energy and work From the textbook I'm reading about the potential energy and work on a positive vs negative charged particle in a uniform E field, for the diagram (b) on the positive charged particle moving from a to b against the E field, since the work is the n... | For the top two digrams assume that $\hat y$ points upwards, $\vec E = E\,\hat y$ so $\vec F = q_0\,\vec E = -q_0\, E\, \hat y$ and the displacement from $a$ to $b$ is $\Delta \vec y = \vec y_{\rm b} - \vec y_{\rm a}= (y_{\rm b} -y_{\rm a})\,\hat y$.
The work done by electric field in moving a charge $q_0$ from $a$ to ... | {
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Differece between torque $\tau$ and angular velocity $\omega$ The title is a weird question, i know. But hear me out: Take the equation that relates the tangential velocity $\vec v$ and the angular velocity $\vec \omega$ of an object moving on a circle with radius $r$.
$\vec v = \vec \omega × \vec r$
If we want to know... | Here's one way to think about why they transform seemingly oppositely. Force and velocity form a pair in the sense that when multiplied you get power:
$$W = \int F \cdot v\,dt.$$
The same is true for torque and angular velocity:
$$W = \int \tau \cdot \omega\,dt.$$
So if to go from force to torque we multiply by $r$, we... | {
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How do we measure time? I'm having a little trouble trying to put to words my problem and I apologize in advance for any causation of trouble in trying to interpret it.
We define periodic events as those events that occur over equal intervals of time. But, don't we use periodic events themselves to measure time (like a... | Yes, we measure time as multiples of periodic events, such as the ticking of a clock, the rotation of the Earth, or the period of radiation from caesium, and we assume that each of those events has an unvarying duration. In a thought experiment, you might imagine whether it was possible for time to expand or contract, ... | {
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Do Tadpoles Contribute to Self-energy? In evaluating contributions to the two-point function in say $\phi^3$ theory to:
$$\langle 0|\phi(x)\phi(y)e^{-i\int d^4z\frac{\lambda}{3!}\phi^3(z)}|0\rangle,$$
at $\mathcal{O}(\lambda^2)$, one of the possible contractions is the usual tadpole diagram. However, the literature oft... | *
*Yes, in general the self-energy $\Sigma=G_0^{-1}-G_c^{-1}$ may contain tadpoles$^1$ even though they are not 1PI.
*However, if one imposes the renormalization condition $\langle \phi \rangle_{J=0}=0$, then one may show that the self-energy only contains 1PI diagrams, and hence no tadpoles, cf. my Phys.SE answer h... | {
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What is faster? Pure rolling or rolling with slipping? So we know that a ball will slide down an incline when there is no frictional force. Once you say there is static friction it causes a angular momentum which in turn causes a torque and makes the ball roll. Lets say the ball number one does pure rolling, where the ... | For a reasonably long slope rolling is usually the faster option.
Lets say that we have a slope of a fixed height. We know once as the object has slid or rolled down the slope the potential energy of gravity is lost. This energy ends up split between three places: (1) The linear kinetic energy of the ball. (2) The rota... | {
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Second Kepler's law explanation What is the explanation for the second Kepler's law? Why is the law valid?
Is it that the total energy of a planet equals to the kinetic energy plus the potential energy?
| The area of a sector is $A = \frac{1}{2}r^2 \theta$ and for small changes in time (where the distance of the planet to the sun is assumed constant), the rate that the area is swept out is $\frac{dA}{dt} = \frac{1}{2}r^2 \omega$
For orbits the angular momentum is constant, so $mr^2\omega$ is constant and that means that... | {
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How is time dilated in a gravitational field? I picture a box that contains a particle that travels back and forth at the speed of light. One round trip is a unit of time. We place this box on the surface of a large planet. The particles run upwards and down, perpendicular to the surface.
If the speed of light is const... | A simple and reasonably accurate approach: Consider a photon rising in a gravitational field. It gains gravitational energy (with m = hf/$c^2$) and loses kinetic energy (hΔf). A distant observer would say that the emitting atom was vibrating atom was vibrating at a lower rate.
| {
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Does the track do work? (second try) When a ball rolls without slipping down a track, it seems like static friction from the track does rotational work on the ball. As explained in this post:
Is work done in rolling friction?,
this work is exactly the same as the work done by gravity around the pivot point. But shouldn... |
But shouldn't the track also do linear (i.e. translational, not rotational) work on the ball? After all, the ball is moving.
when a block is sliding down a slope, the friction force $F$ does work and slows the block down. Work is done on the block because the force is acting parallel to the velocity.
For the ball, i... | {
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Abuse of notation in GR? $f(x)$ vs. $(f \circ \psi^{-1})(x)$ I see some GR books write $f(x)$ (or even $f(x^\mu)$) when talking about a function on a manifold. But with $f: M \to \mathbb R$ and coordinates defined by a chart $\psi: M \to \mathbb R^n$, shouldn't the notation rather be $(f \circ \psi^{-1})(x)$ when evalu... | It's an abuse of notation. If the chart is given by $(U,x)$ with $x:M\rightarrow \mathbb R^n$ the chart map, then for each $p\in U\subseteq M$ we have
$$f(p) = \bigg(f\circ x^{-1}\bigg)\big(x(p)\big) \equiv f_x\big(x(p)\big)$$
where $f_x :\mathbb R^n \rightarrow \mathbb R$ is the local expression of $f$ in the chart $... | {
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Time averages of complex quantities If an electric field $E$ oscillates as $E_0\sin(ωt)$ then the average value of $E^2$ over one period of oscillation will be
$$E_0^2\left< \sin^2(ωt)\right>=E_0^2/2$$ since the average value of $\sin^2(ωt)$ is well known to be $1/2$.
However if we write $E$ using complex numbers as $E... | When you use the complex representation of the electric field, you have to modify the way you calculate the intensity. Instead of calculating $\langle E^2 \rangle$ you need to replace it with $1/2 \langle E E^* \rangle$, where $E^*$ is the complex conjugate.
| {
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Spring-damper in series I have a spring-damper system like so:
When $x_1$ is the length of the spring and $x_2$ is the length of the damper.
The forces are given by:
$$ \\ x=x_1+x_2\\F_d=-\sigma\ \frac{dx}{dt}\ , F_k=-k(x_1-x_0)$$
Which means that the damping force depends on the velocity of the mass.
From Newton we g... | This is the FBD
From here you can obtain the equation of motion, you should get second order differential equation plus first order differential equation.
Edit
$$m_1\,\ddot x_2=F_\sigma$$
and put dummy mass between the spring and the damper
$$m_d\,\ddot x_1=F_k-F_\sigma$$
with $~m_d=0~$ and
$$F_k-F_\sigma=0\quad,F_\si... | {
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Galvo angle of rotation to distance convertion I have a galvomotor with a specified maximum rotation of $20^o$, say $\pm10$. It's specified to rotate 1 mechanical degree per $0.5$ V. I shoot a red laser at the scanner mirror, the laser is then reflected to a target located at distance of 175.064 mm (focal length) from ... | $x$ mm per volt is from $x=175.064 \times \tan 2V ^\circ$
An approximation to this is 6.1mm per volt, but it's only accurate for small angles. That means 1mm corresponds to about 0.16V.
If you want it more accurate do $\frac{1}{2} tan^{-1}(\frac{1}{175.064})$, about 164mV for 1mm, although the relation won't be linear... | {
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Electric field and magnetic field from dipole radiation The electric field and magnetic field from dipole radiation given in my book is:
$$\overrightarrow{E}=\frac{\overrightarrow{r}\times(\overrightarrow{r}\times \overrightarrow{\ddot{d})}}{4\pi \varepsilon_0 r^3 } $$
$$\overrightarrow{B}=\frac{ \overrightarrow{\ddot{... | Hint: 1) these relations are deduced with a delay time: https://en.wikipedia.org/wiki/Li%C3%A9nard%E2%80%93Wiechert_potential
with : $\vec{B}=\vec{\nabla} \times \vec{A} = \vec{\nabla} (t-|\vec{r} -\vec{r}_{s}|/c)\times \vec{\dot{A}}=-\frac{\vec{r}}{r}\times\vec{\dot{A}} $
(.) derivation with respect to $\; t_{r}$
*... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/677277",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
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Passive transformation, pseudo vectors and cross product Let's consider the passive transformation i.e. inversion only of the basis vectors (coordinate axes) and all other vectors remaining the same and check if the cross product is a pseudo vector.
After the inversion using a passive transformation a vector $a$ remai... | . . . inversion only of the basis vectors (coordinate axes) . . .
$\hat x \to \hat x' = -\hat x,\, \hat y \to \hat y' = -\hat y$ and $\hat z \to \hat z' = -\hat z,$
Rotate the new coordinate axes by $\pi$ about the z-axis.
Now $\hat x' = \hat x,\, \hat y' = \hat y$ but $\hat z' = -\hat z$ so the new coordinate axes are... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/677386",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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High school physics problem - having trouble understanding This is a fairly straightforward problem which doesn't require the usage of more than one or two formula but I find it hard to grasp the concept behind this.
Let's say we have two trains, one which moves at the speed of $45 \frac{km}{h}$ and the other at the sp... | Great question. In fact, for this question, there are many ways to solve it, all of which anyways end up with the same answer. I am going to explain in my way. First let's see what we know. Here, we have two trains, say train A and train B, train A moving at a speed of $45\frac{km}{h}$ and train B moving at a speed of ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/677589",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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"answer_id": 5
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Energy loss in a circuit during critical damping I would like some intuitive explanation regarding impedance in an $RLC$ circuit.
So far, my understanding has been limited to underdamping situations where both resistance and reactance are present.
Suppose the resistance is big enough to cause critical damping and even ... | Only use the real components of the values. This means $X_C$ isn't in the equation and thus $Z$ is solvable. :)
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/677702",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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A 10th grade physics problem regarding the velocity of a wave There is a question in one of my textbooks:
Frequency of vibration in a wire is $500Hz$ and distance covered by the wave in $1s$ is $20cm$. Find the velocity of the wave.
The options are:
(a) $150ms^{-1}$ (b)$10000 ms^{-1}$ (c)$1000 cms^{-1}$ (d)$100 ms^{... | Judging by their answer, there may be a typo, and they meant "20 cm in 1 cycle".
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/677854",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
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Conservation of mass from material derivative Let the mass be $m=\rho \text{Vol}$, where $\text{Vol}$ is the volume of the domain and the velocity is $u$.
Applying the material derivative, then
$$\frac{Dm}{Dt}=\frac{\partial (\rho \text{Vol})}{\partial t}+ u \cdot \nabla (\rho \text{Vol})=0$$
Since the volume is consta... | What is wrong is your assumption that Vol is constant. What is constant is the mass within the volume "Vol". This is $M=\rho\, {\rm Vol}$. So as $\rho$ increases ${\rm Vol}$ decreases.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/678104",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Newton's Shell Theorem Our physics teacher was teaching us about gravitation.
He said that the force of gravity in a uniform solid sphere is due to the mass of the smaller sphere inside
(On whose surface it sits)
And that the effect of
Force due to the ring/shell outside is zero
And thus the formulas
$$gd = 4/3 × πρ × ... | If you trust gauss law for gravitation which relates the closed flux integral of the gravitation field g to the mass enclosed by my surface
$\int g \cdot da = -4\pi GM$
where M is mass enclosed
For a shell of radius R centre 0,0,0 , of some surface mass density
If I choose my gaussian surface to be a sphere of radius r... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/678460",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Does the Slavnov-Taylor identity still hold for scalar Yang-Mills? I want to renormalize the minimally-coupled scalar Yang-Mills theory:
$$\mathcal{L}_{YM\phi}=(D_\mu\phi)^\dagger(D^\mu\phi)-\frac{1}{4}F_{\mu\nu}^a{F^{\mu\nu}}^a-\frac{1}{2\xi}(\partial_\mu {A^\mu}^a)^2-\bar{c}^a\partial^\mu D_\mu^{ac}c^c$$ to find the ... | *
*Yes, the Slavnov–Taylor (ST) identities are generalized Ward identities for non-Abelian Yang-Mills theory with or without matter. (If there's matter the ST identities contain more terms.)
*More generally, any anomaly-free gauge theory can in principle be given a BRST formulation with corresponding generalized War... | {
"language": "en",
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Can I apply Kirchhoff's current law to two separate nodes which are connected only by an ideal wire?
Suppose there are 2 nodes A and B in the above circuit. If A has 2 incoming currents $I_1$, $I_2$, and B has 1 incoming currents $I_3$, $I_4$, is it correct to write the equation of whole nodes and circuit as $I_1+I_2-... | For (truly) distinct nodes in a Kirchhoff circuit network, it is not appropriate to formulate the Kirchhoff current law taking in the currents from separate nodes and mixing an incomplete set from both.
For the specific circuit in your question, however, the "nodes A and B", as you have described them, are not actually... | {
"language": "en",
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Can we measure the one-way speed of anything at all? I know the one-way speed of light question has been exhausted, and I'm sorry for the naive question, but I would like to understand one thing. Can we measure the one-way speed of anything at all? If we "truly" can, why can't we synchronize that thing and an emission ... | I would say no. One of the most fascinating things in physics is time dilation. The speed of light is always the same but the speed of time varies. Not only may A and B be in different time frames as illustrated by others but also at different rates of time change. One way to visualize this is here on earth. It is scie... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/679026",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
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Stefan–Boltzmann law applied to the human body The average person consumes 2000 kcal a day, which is equal to ~100 W. Furthermore, if one uses the Stefan–Boltzmann law to calculate how much someone loses heat due to radiation, it can be seen that it equals
$$Q=\sigma T^4 \varepsilon A$$
$$Q\approx1000\ W$$
Considering ... | I'll tell you more.
Not only the radiative heat loss of the human body is way above the available heat power, the radiation is clearly not the only mechanism available for losing heat.
Contact heat exchange, air convection (natural and forced), water evaporation from skin and lungs - all these mechanisms work and are i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/679165",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "16",
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Why doesn't a parallel circuit violate conservation of energy? Let's imagine a hypothetical circuit where there are a large number of wires placed in parallel to each other, hooked up to a simple power source.
We know that voltage at each wire would be equal $V_{total}=V_1=V_2=...=V_n$ where $n$ approaches a large numb... | The work done by the battery would have to be equal to (or greater than) your final formula.
The Work done by the battery is the E.M.F. of the battery multiplied by the charge passing through it, but many $1C$ charges would pass through the battery, $1C$ for each parallel wire.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/679464",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Normalizable wavefunctions for bound states In my quantum mechanics book I read the following sentence:
If we want the wavefunction to be normalizable, one must impose boundary conditions:
$$\lim_{x \to \pm\infty} \psi(x)=0.$$
My question is as follows:
From what I understood by reading other answers on this forum, a... | Just a small tangential comment to add to what others have said here. The wave function DOES indeed need to be continuous. Otherwise, expectation values involving derivatives of the wave function such as the momentum and the kinetic energy would be undefined at the discontinuity. The derivative of the wave function ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 3,
"answer_id": 2
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What is the expression for the single-particle energy of an orbital of a nucleus? Consider the level $p_{3/2}$. In the case of atomic physics, we know the energy of the orbital is
$$E_{J=\frac{3}{2}}=\dfrac{a}{2}\left\{ J\left( J+1\right) -L\left( L+1\right) -S\left( S+1\right) \right\} \hbar ^{2}$$
But in nuclear phys... | The term "orbital" comes from the word "orbit", found in the original semi classical Bohr model. It describes the quantum mechanical space distribution for measuring an electron at (x,y,z,t) for a given nucleus given by the probability distribution calculated with the wavefunction. Even for the simple hydrogen atom,... | {
"language": "en",
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"source": "stackexchange",
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Why is snow white? There is one question that has been bothering me sometimes the last couple of years that I want to share.
There are two statements that I believe are true.
A) snow's natural color is white
B) snow of white color melts under sun the slowest.
This, to me, seems like something that cannot be a coinciden... | Sunlight is made up all of the colors. Sunlight is also known as white light. White color is a mixture of all the colors. As sunlight hits on the snow, it is it's natural property of reflecting all of the sunlight, and not absorbing any colors. As it has reflects most of the colors, it has basically reflected back whit... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/679837",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 2,
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Christoffel symbol metric connection Suppose that you are given an arbitrary metric $g_{\mu\nu}$ such that you want to calculate all of the Christoffel symbol $\Gamma^{\lambda}_{\mu\nu}$. The equation for a Christoffel symbols are $$\Gamma^{\lambda}_{\mu\nu}=\frac{1}{2}g^{\lambda\sigma}\left(\partial_{\nu}g_{\sigma\mu}... | You sum over all $\sigma$, because it's a repeated index. It's called contraction. For example,$$\begin{align}\Gamma_{22}^3&=\frac12g^{30}(\partial_2g_{02}+\partial_2g_{02}-\partial_0g_{22})\\&+\frac12g^{31}(\partial_2g_{12}+\partial_2g_{12}-\partial_1g_{22})\\&+\frac12g^{32}(\partial_2g_{22}+\partial_2g_{22}-\partial_... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How are torques determined in equations of motion for multibody systems? In classical mechanics of multibody systems, one often ends up with equations for $n$ torques for $n$ links:
$$\tau_i= A_{ij}\ddot{\theta}_j + B_{ijk} \dot{\theta}_j \dot{\theta}_k + C_i ,$$
with certain quantities $A$, $B$, and $C$ which can be ... | You need a simulation loop which integrates $\ddot{\theta}$ to get $\dot{\theta}$ and $\theta$ at a later time.
So at each time steps follow these steps
*
*Known vectors of joint speeds and angles $\dot{\boldsymbol{\theta}}_n$ and $\boldsymbol{\theta}_n$ at time $t_n$, or initial conditions for the first step. Calcul... | {
"language": "en",
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"source": "stackexchange",
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Vector Addition of velocity
In the arrangement shown in figure, the ends P and Q of an inextensible string move downwards with uniform speed u. Pulleys A and B are fixed. The mass M moves upwards with what speed?
I tried to solve this problem with the following way-
Let the upward speed of the mass M be x.
Then,
$$x=\... | It's a similar issue to that addressed here Help me in understanding use of vector in this problem
The questioner wondered why the speed that the lower block slid along the table wasn't $5\cos53$
Instead it's $\frac{5}{\cos53}$
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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How does speed of sound change when you extract air out of the experiment? So I understand that pressure and density cancel each other out so speed of sound is mostly related to the temperature of the gas.
But I was wondering what exactly, experimentally happens with the speed of sound while you are extracting air out ... |
So I understand that pressure and density cancel each other out
so speed of sound is mostly related to the temperature of the gas.
You are right. In air the speed of sound is given by
$$v=\sqrt{\gamma\frac{p}{\rho}}$$
where $p$ is the pressure, $\rho$ is the density,
and $\gamma$ is the adiabatic constant of air ($=1... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/680623",
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Standard Model Particle Properties Basic question about the Standard Model: Is it accurate to say that all of the particles defined by the SM can be categorically distinguished entirely by discrete properties (eg, spin, color, charge units, interaction type, etc), as opposed to also requiring continuous properties (eg,... |
Is it accurate to say that all of the particles defined by the SM ...
The standard model is a quantum field theoretical model. The elementary particles of the standard model are axiomatic, they are not defined by the model, but constrain the model:
There is nothing continuous in the definitions in the table, the par... | {
"language": "en",
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Does capacitance between two point charges lead to a paradox? Is it possible to have a capacitance in a system of two point charges? Since there is a potential energy between them and they both have charges then we can divide the charge by the potential and get capacitance.
However, capacitance is supposed to depend on... | In most common cases, the concept of capacitance was used to describe the system where two sets of conductors are separated by vacuum or some dielectric medium.
For these cases, the charge is assumed to distribute (or be trapped) on the surfaces of the conductors.
If we assume that the charge is continuously distribute... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "12",
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Would a projectile launched with the escape velocity reach a final velocity of 0 as time approached infinity? I just wanted to check my understanding of escape velocity.
If a projectile was to launch and have the exact velocity as the escape velocity of the earth,
it would have a final velocity of 0 correct?
And this f... | Your understanding is correct, if we make the assumption that the Earth is the only object with mass (i.e. there is no Sun, no Milky Way, no Virgo Cluster, etc).
Note that the often-quoted escape velocity of the Earth, ~11 km/s, does not actually suffice to escape the Solar System since you need a faster speed to escap... | {
"language": "en",
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If you were invisible, would you also be cold? If you were invisible, would you also be cold? (Since light passes through you, so should thermal radiation.)
Additionally, I'd like to know if you were wearing invisible clothes, would they keep you warm? In my understanding, the heat radiation from the body would pass th... | Although the premise of this question is, well, questionable, I’ll answer because invisibility cloaks do exist. Of course, as of now, they work imperfectly, in impractical ways, and for only a narrow spectrum of light. And this last part is the key. Just because something bends light of one color does not mean it will ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/681335",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "24",
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Functional derivatives on position and momentum spaces I'll first give some context for the problem I'm having, but the essence of it seems to be related to only what is in the title.
I've been working with the Wetterich equation for the Functional Renormalization Group. In this technique, we often need to compute func... | After a while, I noticed that, if we set $\varphi(x) = \varphi_0$, the last term of Eq. (2) can be written as
$$
\begin{align}
\frac{\lambda_k}{2 (2\pi)^{12}} \int \tilde{\varphi}(r)\tilde{\varphi}(-p-q-r) \textrm{d}^4 r &= \frac{\lambda_k}{2 (2\pi)^{12}} \int \tilde{\varphi}(r)\tilde{\varphi}(s) \delta^{(4)}(p+q+r+s) ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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When a block slides down an incline, why does the incline move back, if the work is done by an external force (gravity)? If I put a point mass on the top of the incline, and if all surfaces are frictionless, I heard, that the incline is going to move back a little (depending on the mass difference), because momentum is... | I think you might be considering a special case. If the ramp itself is supported on frictionless rollers at its base, then I can see that what you describe would happen.
However, this is a special case. If the ramp is rigidly fixed to a table which itself cannot move relative to the Earth and is itself rigid then it wi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/681725",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Fundamental Interactions in the Standard Model The elementary particles of the Standard Model seem clearly enumerated and distinguished, totaling 17 (6 quarks, 6 leptons, 4 gauge bosons, and the Higgs). Is there a similar enumeration of the variety of fundamental interactions found in nature according to the Standard M... | The text Particles and Fundamental Interactions (2009) by Braibant, Giacomelli, and Spurio states that there are a total of 61 elementary particles in the Standard Model (p 314). The total consists of 24 fermions + 24 antifermions + 12 vector bosons + 1 Higgs boson.
Considering only fermion-fermion interactions then gi... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What does GR get right that QFT gets wrong, and vice versa? I wondering what precisely it was, in terms of predictions of observations, that General Relativity gets right, that QFT cannot explain. And what QFT gets right, that GR cannot explain.
I'm assuming GR cannot predict quantum effects, like wave-particle duality... | General Relativity (GR) is a theory of space and time, necessary to model large masses and energies. Quantum Field Theory (QFT) is an extension of quantum mechanics to many particle outputs, and is based on the postulates of quantum mechanics.
Though the gravitational interactions can be predicted using the formulae o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/682234",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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Two electrons moving along infinite charged sheet Two electrons move along an infinite charged sheet of positive surface charge density $\sigma$, one at each side, moving with the same velocity $v$, both at a distance $a$ from the sheet.
The question is for what value of $\sigma$ will the electrons be at a constant di... | I would have thought it easier to work in the stationary frame of the charge sheet.
It is easy enough to work out the combined Lorentz force on one electron due to the other. It is just the force between the electrons in their stationary frame, reduced by a factor of $\gamma$. You then just need the charge sheet to hav... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Having hard time computing generalized forces Suppose we have a rigid body and point $O$ is fixed. It is clear then that it has three degrees of freedom and so we can choose Euler angles $\phi,\psi,\theta$ as generalized coordinates to describe its position.
But how to compute $Q_{\psi},Q_{\phi},Q_{\theta}$ -- generali... |
The rotation matrix $~\mathbf R~$ is a function of the Euler angles $~\phi~,\theta~,\psi~$
from here you obtain the angular velocity
$$\mathbf \omega=\mathbf J_R(~\phi~,\theta~,\psi~)\,\mathbf{\dot{q}}$$
where $~\mathbf{\dot{q}}=[\dot\phi~,\dot\theta~,\dot\psi]^T~$ and $\mathbf J_R~$ $~3\times 3~$ distributor matrix
t... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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If $\mathbf{F}_{net} = m\mathbf{a}$ then how is $m\mathbf{a}$ not a force? The question is in the title: If Newton's second law says that the sum of the forces acting on a body in a given direction is the same as the mass of the object times its acceleration in that direction, then how is $m\mathbf{a}$ not a force? Eve... | What you are missing is that forces appear to be vectors in Newtonian mechanics. Newton's Principia had a pair of corollaries to his three laws of motion that essentially said that forces are vectors, without calling them out as vectors (the concept of vectors postdates Newton's laws of motion by about 200 years). Newt... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Does light have mass or not? We know light is made of photons and so it should not have mass, but light is a form of energy (light has energy) and has velocity ($c$), so according to $E=mc^2$, light should have mass... So what is correct?
| This the complete Einstein equation:
\begin{equation}
E^2=m^2c^4+p^2c^2
\end{equation}
Photons don't have mass but they still carry energy due to their momentum.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/683919",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 4,
"answer_id": 0
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Behaviour of light in air vs water Why does the red color travel the farthest in air but least in water.
I mean we have danger signals red so that they can be spotted from farthest distance but in water as we go just 30ft down the blood turns green because red light couldn't reach even 30ft to bounce off the blood. Why... | The wavelength dependence is different because the mechanisms are different. In air, the transmission of light is mainly limited by Rayleigh scattering. For this effect, the scattering strength is an inverse fourth power of wavelength, so blue light is scattered and lost from the transmission path, much more rapidly th... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Bloch sphere representation - rewriting a state If a quantum state can be represented as
$$|\psi\rangle=\alpha|0\rangle+\beta|1\rangle$$
Then
Because of $|\alpha|^2+|\beta|^2=1$, we may rewrite Equation (1.1) as $$|\psi\rangle=e^{i\gamma}\left(\cos\frac{\theta}2|0\rangle+e^{i\varphi}\sin\frac{\theta}2|1\rangle\right)$... | The key observation is that cosine and sine are bijections, i.e. one-to-one functions, between the set $[0,1]$, where $|\alpha|$ and $|\beta|$ reside, and the set $[0,\frac{\pi}{2}]$, where $\frac{\theta}{2}$ resides.
Bijection argument
First, write $\alpha$ and $\beta$ in polar form
$$
\alpha=re^{ia}\quad\beta=se^{ib}... | {
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Is the electron a pointlike particle? And if yes, how is that possible, because the energy then would diverge, wouldn't it? My problem is that I read (besides others in this post Why are electrons and quarks 0-dimensional?) that the electron is a point-like particle. My question is on the one hand whether that is true ... | A point particle is a mathematical concept, so in a way your question does not make sense. However, what we know is that with all experiments that have ever been performed, there is no indication that an electron would have a certain size/volume or substructure. Theoretically we know that there is something we don’t y... | {
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Why is kelvin used for Energy Separation in atoms? I have been reading a 1974 paper on the anisotropy of Sm$^{3+}$ ions, in which the authors say the following:
IN THE series of trivalent rare-earth ions, Sm$^{3+}$ is unique in the sense that the energy separation between the ground J 5/2 multiplet and the first excit... | Sometimes this is done to give an idea of the temperature above which an excited state is likely to be found occupied just by thermal agitation. The environment can in fact provide some energy to the system by means of thermal fluctuations, whose amplitude is of the same order of magnitude as $k_BT$ ($k_B$ being the Bo... | {
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Do gravitational redshift depends on reference frames? I just want to know is the effect of redshift depending on the frames of reference or the photon really does lose energy when it escaped from a gravitational well? Imagine a spaceship is shooting a laser at a specific wavelength is caught in a gravitational well, w... | It does, If you know the expression for shift
$$\frac{\nu_R}{\nu_E}=\frac{p_0(B)}{p_0(A)}\left[\frac{g_{00}(A)}{g_{00}(B)}\right]^{1/2}$$
See General Relativity: An introduction to Physicists Appendix 9A for the proof.
It's clear from here that different observers have different $p_0$, and therefore have a different s... | {
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At what speed do newly created protons move after a proton-proton collision? I read that when 2 protons travelling at near the speed of light collide with each other, they create 3 protons and 1 antiproton.
At what approx. speed those 3 new protons usually move once they are created after the collision?
| Proton proton collisions belong to particle physics and are studied with the mathematical tools of quantum mechanics and special relativity which are very successful in describing experiments at the particle level and predicting new interactions.
I read that when 2 protons traveling at near the speed of light collide... | {
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Does Newtonian mechanics work in polar coordinates? Our teacher suggested that Newtonian Mechanics only applies in cartesian coordinates. Is this true?
He gave this example.
Suppose there a train moving with constant velocity $\vec{v}=v_0\hat{x}$, with initial position vector $\vec{r}=(0, y_0)$, where $v_0,y_0$ are con... | I think your teacher wanted to refer to the fact that by using polar coordinates, $\mathbf{F} = m \mathbf{a}$ will not hold generally (component-wise). Of course, physical laws hold in any coordinate system, but writing the acceleration is tricky in terms of polar coordinates.
Consider the above example with the train.... | {
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Is thermal conduction really radiation? I have no doubt thermal conduction is a useful model for heat transfer, wherein kinetic energy is transferred between particles when they collide. However, according to explanations that I believe are canonical, two molecules collide due to electromagnetic repulsion (and possibly... | You are correct that virtual photons are not photons; what we refer to as radiative heat transfer is mediated by the latter. Conductive heat transfer occurs through physical contact and is not radiation.
| {
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Is it better to line dry inside or outside a house? On a winter night (so no radiation from the sun), my house is 10°C warmer than outside. Both temperatures are above freezing. I measured the humidity and found out it to be the same both outside and inside.
*
*Is it true that it is better to line dry the clothes ins... | In general, evaporating water out of clothes happens faster when it is warmer, when the relative humidity is lower, and when the air is moving.
In the wintertime, the relative humidity inside a heated house is usually quite low (this is why your skin gets dried-out and crinkly in winter) so the best place to dry clothe... | {
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What is the amplitude of current in LC oscillations Since there is no resistance in an LC circuit (not attached to an AC source), what's stopping the current from rising to infinite. And if resistance is provided by the inductor by self induction, then why does the current become infinite when an AC source is added to ... | The wiki entry is a tolerable intro to LC circuits.
https://en.wikipedia.org/wiki/LC_circuit
You will also want to read about Lenz's law here.
https://en.wikipedia.org/wiki/Lenz%27s_law
In an LC circuit, the inductor attempts to decrease changes in current according to Lenz's law. So as the current rises the inductor t... | {
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NMR/EPR with an RF electric field Is it possible to perform NMR/EPR spin alignment with an oscillating electric field instead of a magnetic field (so with a sample inside the RF electric field of capacitive plates rather than a RF magnetic field of a coil)? In other words, can an electric field align nuclei or does it... | Spin vs. electric dipole moment
NMR end EPR couple to spin, i.e., to the magnetic moment of nuclear and electrons respectively. Direct transposition of this mechanism to electric field would require manipulating electric dipolar moment of some particles. While such situations can be artificially designed, they are rath... | {
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In the Double Slit Experiment, what is the longest time $T$ recorded between shots of particles, electrons, photons, etc.? How can we be certain that electrons fired do not leave some kind of residual interference for the next shot?
What is the longest time recorded between shots?
| In the typical double slit experiment the electron source is a cathode , even for single electrons at a time, and thus an incoherent beam, so your "residual interference" cannot be from the incoming beam. In your comment you explain:
I just mean how can we be certain that a particle fired doesn't have an impact on its... | {
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How do we determine the order of the degeneracy of silicon bands? In an exercise on intrinsic semiconductors, I was asked to compute the effective state density in conduction and valence bands of Silicon (resp. $N_c(T)$ and $P_v(T)$), at $T=300$K. Those can be expressed as:
\begin{equation}
N_c(T) = \frac{1}{4} \left( ... | Problem solved! This page gives a comprehensive explanation on the origin of heavy & light holes in semiconductors, while this one demonstrates the 6-fold degeneracy of the conduction band of silicon : "The six-fold degeneracy of the valleys arise due to the symmetry of the lattice along the [100], [010], and [001] dir... | {
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Falling to Earth from Orbit Suppose we ascend to a height $h$ away from the surface of the earth and drop an object. High school physics tells us that it will accelerate at a speed of $9.8 \frac ms$ and will hit the ground in $\sqrt{\frac h{4.9}}$ seconds. However, if we ascend high enough, the gravitational force from... | Since you're a math major, the way to think about this is that Newton's Second Law is an ODE. If $h$ is the distance between the object and the center of the Earth, the force on the object is (as you have shown)
$$
F = - m g \frac{r^2}{h^2}
$$
where $r$ is the radius of the Earth. (Note the minus sign, since the forc... | {
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Confusion regarding the derivation of commutator relations using the radial ordered contour integrals in 2D CFT I am a little confused about the way commutators are derived in the radial quantization of a 2D CFT. I am trying to derive the relation $$\int_w \mathcal{R} \left(a(z)b(w)\right)dz = \left[A,b(w)\right]$$ whe... | The OPE $${\cal R} a(z)b(w)~=~\ldots$$ is often a regular function for $z\neq w$, so then the contour in OP's Fig. 4 is zero. In fact the OPE is typically a truncated Laurent series in $z$ around $w$, cf. Ref. 1.
References:
*
*P. Di Francesco, P. Mathieu and D. Senechal, CFT, 1997; subsection 6.1.2 and eq. (5.72).
| {
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Is energy really Conserved in rolling motion? Energy is conserved in pure rolling motion. Then why does the ball stops its motion after some time. I think it's not the case of air drag only. Does all work gets Transferred to surrounding in the form of heat?
| Energy is conserved when a real wheel or a real ball rolls along a real surface, but purely mechanical energy is not conserved. Some of the mechanical energy is converted to heat, which is considered to be another form of energy.
One important mechanism of energy conversion is hysteresis. No object is truly rigid. A ro... | {
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Electrons remaining in an orbit and the emission of photons? Electrons are not stationary around a nucleus, even if it remains in the same excitation state / in the same 'orbit'.
As moving electrons should stir the EM field, they should be creating EM waves/light as well? But that couldn't be as it would mean electrons... | The reason quantum mechanics became necessary was because classical mechanics and classical electrodynamics could not explain the black body radiation, the photoelectric effect and, the spectra of atoms.
The classical picture of electrons orbiting around the nucleus has the problem of radiation and neutralization so no... | {
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Yukawa Theory Peskin and Schroeder On page 116 of Peskin and Schroeder, the Yukawa theory Hamiltonian is given by
$$H=H_{Dirac}+H_{Klein Gordan}+\int\,d^3x g\overline{\psi}\psi\phi $$
and we are considering the fermionic scattering reaction
fermion($p$)+fermion($k$)$\rightarrow$ fermion($p'$)+fermion($k'$)
I have sever... | 1, 2: Yes. Putting aside issues of whether the Hilbert space of the interacting theory is well-defined, you can think of the Hilbert space here as the tensor product of the two Fock spaces. For example, the noninteracting vacuum is the state with no fermions, antifermions, or bosons.
3: No. Remember that $\phi$ has the... | {
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Why same force acts on two different strings? Let us take two different strings and arrange them vertically. The first string is attached to the ceiling and connected in series with the second string and a mass $m$ is connected at the bottom of the second string. Why does the same force $mg$ act in both strings?If we ... | A force (actually a pair of forces) is a measure of interaction between two objects. There is no interaction between the top rope and the block so there are no forces between these two. Of course there is the gravitational interaction between them but here you don't consider this, just contact forces, right? At least n... | {
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What research in theoretical physics could a high school student do? I already know what I want to conduct my research on (topic: magnetic monopoles), the problem is just that I don't know what to investigate or analyze. What are some research methods you would recommend? What are some easily applicable concepts? Pref... | If I were you , I would search colleges and study for good grades in High School which would put me in a good college instead of doing research on my own in physics.
But if you want to do research on your own I suggest before the research to study the basics about the subject of research.I would probably pick somethin... | {
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What causes this frost pattern on my windshield? I was walking back to my car yesterday when I noticed the frost on the back windshield formed these long "straight" lines:
The temperature was about -10C and I was wondering what the mechanism behind these lines was (the horizontal lines I can guess have to do with the ... | Patterns like this are most often caused by scratches in the glass surface that are too small to see with the naked eye, but which act as nucleation centers for the deposition of frost from supercooled (and supersaturated) air.
This happens because a glass surface tends to get a monolayer of water molecules adsorbed in... | {
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What will happen if both electrons and positive charges got ability to move inside the conductor? Let's consider a conductor which has a potential difference across its ends.
And let's say that the electrons which already have tendency to move inside the conductor, by all of a sudden if positive charges (not protons be... | The sort of situation you're thinking about is basically what happens in an saline solution. Both the positive and negative ions can migrate in response to an applied electric field, and the total current is the sum of the current due to the negative ions and the current due to the positive ions. To calculate the ove... | {
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The electric field formula $E=F/q$ If we follow the formula $E=F/q$ it says that when the force is bigger the electric field is bigger as well but if the charge on which the force is being exerted to bigger the electric field is somehow smaller? How does this make sense?
| The electric field definition uses E = F/q as you show, but you are missing the rest of the definition, namely that it is the ratio of F/q in the limit as q -> 0. This is done so that the test charge does not disturb the charge distribution that is creating the electric field.
| {
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What is the direction of angular momentum? Are Torque and angular momentum same? I just started learning in my class 11 physics book, where I find Torque and angular momentum. After reading the definition, I am confused about are Torque and angular momentum are same? If not what is the difference between them? Lastly w... | As we are aware about the force. It's same with the torque, unofficially we can call it as a Rotational Force for better understanding. Which is equal to
$τ = I × α $
Where I is moment of inertia and α is angular acceleration.
let's take an example if you will try to rotate the spring vertically about it's axis let's s... | {
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Am I correct in saying "falsifiability is the feature of a scientific theory to be tested"? Falsifiability is usually defined as "the extent to which a scientific theory can be proven wrong". Does this mean that falsifiability is basically the extent to which a scientific theory is testable?
| Although they sound similar, I would not say that falsifiability is testability. The whole point of falsifiability, at least as it was originally introduced by Popper, was to avoid what he believed was a logical fallacy that arose from verificationism (where a theory is meaningful if it can verified). This is because g... | {
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What is the connection between mechanics and electrodynamics that makes it necessary for both of these to obey the same principle of relativity? Mechanics obeyed Newtonian relativity (faithful to Galilean transformations) before Einstein.
Einstein formulated Special relativity (faithful to Lorentz transformations), and... |
Mechanics obeyed Newtonian relativity (faithful to Galilean transformation) before Einstein.
This isn't just wrong, it's exactly backwards. Mechanics do not obey any man-made law or equation, the various laws describe mechanics. Newtonian and Galilean equations adequately described most of the observed mechanical int... | {
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Is formation of a black hole thermodynamically favourable? Isn't it like that the black hole is just swallowing suns and other parts of cosmos, and thus continuously absorbing matter. I know that it emits radiations also, which should be negligible in terms of the absorbed matter and thus energy. If the net internal en... | Intuitively, it might seem that black holes have low entropy, but that is not correct. Their entropy is in fact gargantuan. For example, as mentioned in the Scholarpedia entry for the Bekenstein–Hawking entropy,
Note that a one-solar mass Schwarzschild black hole has an horizon area of the same order as the municipal ... | {
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Why displacement is not used to calculate average potential energy in SHM? We know that the average potential energy of a body executing simple harmonic motion (SHM) is
$$\frac{1}{4}KA^2$$
where $K$ is the spring force constant and $A$ is oscillation amplitude. This was derived using potential energy as a function of t... | Neither is "correct", or "incorrect". They are simply two different averages with different interpretations. One is the average over space and one is the average over time. We can measure the first by looking at the potential energy of the oscillator when it passes through a series of equally points and taking the aver... | {
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Why was the strongest reactivity in the bottom of the reactor during the Chernobyl accident? I can't seem to find anything addressing this.
We know that while the control rods were fully removed, the graphite extensions were fully inserted. Therefore, the reactor must have been more active in the bottom of the core to ... | The vertical distribution of the power in the corevwas initially double humped, with the power concentrated towards the top and bottom at 01:23 when the accident started. In fact the maximum was near the top. From IAEA INSAG-7
I suppose before the accidental loss of power at 00:28, the middle of the reactor was indeed... | {
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Is a single photon a wave plane or a wave packet? According to the definition a photon is monochromatic, so it has a unique frequency $\omega$ and thus it can be expressed as
$\psi(x,t)=\exp i(kx-\omega t)$.
This suggests that a photon is a plane wave which occupies the whole space at the same time.
But why we can say ... | Mode expansion of the EM field usually uses modes that are delocalized in space. Photons are basically* quanta of amplitude of corresponding modes. This means that they indeed correspond to delocalized excitations of the EM field.
Just as with electrons in quantum mechanics, we can localize a single photon to a wave pa... | {
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If gravity can accelerate a photon by bending its trajectory why doesn't it slow down a photon? If gravity can accelerate a photon by bending its trajectory why doesn't it slow down a photon? This looks like magnetism effects on particles(changes direction but not magnitude of the velocity) ...
| Gravity does change the energy of photons, and it can both increase or decrease that energy depending whether the photon is going in or out of the gravitational well. That's called gravitational red- or blue shift. Of course photons still always travel at the speed of light.
| {
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The location of the exact center of the observable universe If simultaneously in every direction, I were to precisely measure the distance to the edge of the observable universe (not: the physical universe), then would I find myself exactly in the center with zero error tolerance? Would it make a difference if I were a... | Anna V is exactly right. Here is another way of thinking about this which might be of some additional help.
If the big bang is true (lots of evidence indicates it is) but the universe did have a center, then that point would represent the point of origin of the big bang. This means that instead of originating out beyon... | {
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Twin paradox on opposite sides of the Earth The earth is rotating at about 460m/sec at the equator, so relative to me, someone on the other side of the earth is travelling at about 920m/sec. This means that their clock is running slower than mine due to special relativity. Of course, to them I am moving at 920m/sec so ... | You don't need a twin halfway around the world to address this issue, because you yourself spend a lot of time halfway around the world (if you happen to live on the equator) or at least halfway around your circle of latitude.
At noon every day, you will say (using your current instantaneous frame) that your own clocks... | {
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Why are heat and work path functions but internal energy is a state function? I had found a statement given in my textbook which said that heat and work are path functions, but the sum of the two according to the first law is internal energy difference.
How is it that two path functions add up to give a state function?... | One way to define work and heat is as energy transfer on macroscopic and microscopic levels. There are many ways how one can repartition the same energy between macroscopic and microscopic degrees of freedom, that is many paths for changing the internal energy.
| {
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Classically measuring position without disturbing the momentum Let's assume that the world is classical.
We have an electron somewhere in a room.
I am trying to understand how one can experimentally measure the position or the momentum of this electron without disturbing the other.
At the moment of measuring its positi... | Classically, you don't need to interact with a particle at all to measure its position. The particle has a well-defined position value at all times. You just place a ruler on the ground and look down on it from above to measure its position in one dimension, for example - this may be practically infeasible for somethin... | {
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} |
Can the conduction band get completely filled? I have just started studying basic solid state physics and I got to know that filled or empty bands do not conduct. Is this only the case for valence band or also conduction band.
Is there any case that I can excite so many electrons to the conduction band that it becomes ... | One uses term valence band for the last completely filled band (at zero temperature), and conduction band for the first not fully filled (or empty) band. So, by definition, conduction band is not fully occupied - otherwise it would be a valence band.
Note however that things are not always so clearly cut: see figures h... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/690903",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
} |
What exactly is mass? I was looking for a definition of mass and most of the time what I got was that "it is the amount of matter". Now that is very vague. And the way we define matter is "anything that has "mass" and occupies space". so... what exactly is mass?
Can you please answer it to the level where a highschool ... | Physics isn't mathematics. Physical quantities are defined by the methods used to measure them. So, mass may be defined by what a balance measures: given two bodies, they have the same mass if they balance. Put them together, and balance an object of twice the mass. By this means you measure gravitational mass.
Once yo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/691147",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "20",
"answer_count": 9,
"answer_id": 6
} |
Height of a table: what's the uncertainty? I would like to introduce high school students to error analysis with a simple experiment: find $g\pm \Delta g$ by measuring the time a ball takes to fall from a table, repeating many times.
Uncertainty of time of fall $\Delta t$ is determined statistically (standard error), s... | I think that one should show that the error on the height of the table, between many measurements is considerably smaller than the error on the time of fall, which, of course, should be done first, to have an order of magnitude of $\Delta t/t$
Then one should measure $\Delta h/h$ for many measurements, find that it is ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/691520",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 4,
"answer_id": 3
} |
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