Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Are neutrons an actual particle? I'm a senior student in high school and we are learning about Particle Physics in Physics. I wanted to ask a question about neutrons. Is there a possibility that neutrons may not even be a particle, just a bond, relationship or pairing between electrons and protons? Can neutrons just be... | If I understand your thoughts correctly, and you had a typo when you said "Could the 6 neutrons (you wanted to say electrons) and 6 protons cancel each other", you expected a carbon atom to have the same number of protons and neutrons. If you know that there are carbon 13 (which has 7 neutrons) and carbon 14 (which has... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/617053",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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If radio signals attenuate when travelling through space, then what kinds of emissions are we looking for when searching for extraterrestreal life? My understanding is that radio waves travel forever, like ripples in a pond, but attenuate with distance. They get mixed with other signals and become cosmic noise.
I'm loo... | Electromagnetic waves are still the best bet and distances are huge but we’re reasonably good at sending and detecting weak signals, and constantly improving at that job. We are still communicating with the Voyager probes, even if they
have both reached the interstellar region, and signal strengths have energy 20 bill... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/617251",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Does AdS/CFT correspondence take place only near black holes? Is it related to black holes or is AdS/CFT a separate thing itself?
| While the AdS/CFT correspondence is related to black holes and a tool for studying them, it is a much broader framework. Generally speaking, it concerns a correspondence between a quantum field theory defined on anti de Sitter space and conformal field theory.
Anti de Sitter space is the maximally symmetric, Lorentzian... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What are these geometric patterns on ice? In a winter day, I noticed the water frozen inside a canal in our building. As you see there are very nice geometric patterns formed by the ice, with specific angles. What is the physical interpretation of these patterns? Are the giant cristals? The only physical inputs that I ... | They are crystals of ice which grow outward from nucleation sites, where the freezing process prefers to start. Those crystals expand until they hit an edge of the container, or another crystal as it grows.
This effect is exploited in a process called directional casting, in which a gas turbine blade can be grown as a ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/617497",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Why does general homogenous solution of differential equations modelling circuits die off after a long time? I was reading this answer in Elecronic engineering stack exchange which said that when solving the linear second order differential equation modelling circuits having ac source. We only need to account for parti... | When you apply power to a circuit, there is a transient response (such as when you connect an RC circuit to a battery) followed by a steady-state behavior. I would assume that the homogeneous part refers to the transients.
| {
"language": "en",
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"source": "stackexchange",
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$\gamma^5$ rotation of chiral fermion in (1) Peskin&Schroeder, (2) Weinberg, or (3) Srednicki The theta angle due to the chiral gamma^5 rotation of chiral fermion results in the phase alpha(x) that has different + or - sign for
(1) Peskin&Schroeder, (2) Weinberg or (3) Srednicki.
Here
*
*Peskin&Schroeder does a psi' ... | The gamma matrices that Peskin & Schroeder work with are $$\gamma^0 = \begin{pmatrix}0 & 1\\ 1 & 0\end{pmatrix},\quad \gamma^i=\begin{pmatrix}0& \sigma^i\\ -\sigma^i & 0\end{pmatrix}\tag{3.25}$$
On the other hand, for Weinberg, the gamma matrices are $$\gamma^0=-i\begin{pmatrix}0 & 1 \\ 1 &0\end{pmatrix},\quad \gamma^i... | {
"language": "en",
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Two bubbles attract or repel? I have this weird thought that bothers me, but unfortunately, I know little physics and I thought I can get help to mentally settle it.
Here we go:
Let's say you have infinite sand or at least a vast quantity of it. And no gravity.
Just sand, tight in a vast container
You manage to inflate... | Let's suppose a big container, but not so big that gravitational effects become relevant. When the baloons are inflated, the sand is forced to be more compact in the neighborhood. But unlike a fluid, the pressure is not evenly distributed to all container. It is like a pile foundation, that compact locally the soil, bu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/618926",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Definition of the probability current I know that the definition of probability current is given by
\begin{equation}
J\sim \psi^*\frac{\partial \psi}{\partial x}-\psi \frac{\partial \psi^*}{\partial x}
\end{equation}
However, some papers are using this definition:
\begin{equation}
J\sim \psi^*\frac{\partial H}{\parti... | Ok, I think I get it and would like to share in case any additional input.
So in general the probability current can be written as
\begin{equation}
J=\frac{-ie\hbar}{2m} [\psi^*(\nabla\psi)-(\nabla\psi^*)\psi]
\end{equation}
knowing that the momentum operator is $\bf p=-i\hbar\nabla$, we get
\begin{equation}
J=\frac... | {
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How do charge conjugate fields transform under $SU(2)$ and $SU(3)$? I am trying to derive the gauge transformation for the charge conjugate field of a quark doublet (left handed quark) such that its field $Q$ transforms under $SU(2)$ and $SU(3)$ as:
$SU(2):$ $Q \rightarrow \exp\left[ \frac{i}{2}\theta^{a} \sigma^{a}\ri... | The gamma matrices act on spinor indices while the $SU(2)$ and $SU(3)$ matrices act on group indices, for one is like the others do not exist. Therefore they commute.
| {
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Does the magnetic field produced by a current carrying wire, exert a magnetic force on the wire itself? I have to calculate the pressure on a current carrying wire. Since there is a pressure on the wire, there must be a force on it, which is a magnetic force. Does the magnetic field produced by the wire, exert a magnet... | The answer is: no.
The 'magnetic force' on the wire is due (indirectly) to magnetic Lorentz forces acting on the moving electrons in it. It is true that there will be attractive magnetic forces between electrons moving in parallel paths at different points in the wire's cross-section (for example between electrons at o... | {
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Conjugate momentum notation I was reading Peter Mann's Lagrangian & Hamiltonian Dynamics, and I found this equation (page 115):
$$p_i := \frac{\partial L}{\partial \dot{q}^i}$$
where L is the Lagrangian. I understand this is the definition of conjugate momentum, but I wanted to know if there is a particular reason for ... | Usually, you would write your Lagrangian in some sort of form like:
$$L = {\dot q}^{i}{\dot q}_{i} = g^{ij}{\dot q}_{i}{\dot q}_{j}$$, because the lagrangian itself is a scalar. Then, if you took a variation with respect to the "downed" version, you'd be left with
$$\frac{\delta L}{\delta {\dot q}_i} = 2 g^{ij}{\dot ... | {
"language": "en",
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Can the Hamiltonian be interpreted as the "speed" of unitary evolution? The Schrodinger equation
$$i\hslash \frac{d}{dt} \psi = H \psi$$
means a quantum state $\psi(t)$ evolves unitarily, that is,
$$\psi(t) = \exp(-\frac{i}{\hslash} H t) \psi(0)$$
where $\psi(0)$ is the initial state at time $t = 0$.
Suppose if we sca... | To paraphrase @Qmechanic in more mundane language: Hamiltonian is the generator of unitary evolution, i.e., the rate of infinitesimal change. In this sense it can be called speed.
Note however, that the Hamiltonian appears in the exponent, and we do not have here a physical quantity, the derivative of which we could ca... | {
"language": "en",
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Why voltage is same across parallel circuit if it is work done per unit charge? Suppose we have the following circuit:
If voltage is work done per unit charge, why voltage is same across each resistor if the charge has to do more work in resistor R2 than in resistor R1?
| The work is the same. Both resistors would require the same work per coulomb to move a test charge through the resistor. One way to get an intuition for why this is true is from a physical picture. This won't be true always, but let's imagine the reason why the resistor $R_2$ has double the resistance is because it's t... | {
"language": "en",
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What is our time-size in spacetime? Are we spaghetti or flat blobs? In special and general relativity time is treated as a dimension ($ict$, being $t$ a real number). Computations usually revolve around describing world lines, and events (crossings of world lines).
But objects can't physically be time-lines. Future unf... | Although in the geometric picture of general relativity time is pictured as a dimension this is not how Einstein viewed the matter. He was against interpreting physics in a purely geometric fashion which began with Minkowski interpreting special relativity with a Lorentz metric. In fact, he saw general relativity as th... | {
"language": "en",
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Field strength tensor This question seems very simple however I'm stuck:
given the following:
How can we find those components? And how can we check the antisymmetry of $F$?
The equations are from Nakahara, Geometry, Topology and Physics.
$$
\mathcal A_\mu=A_\mu{}^\alpha T_\alpha \quad \mathcal{F}_{\mu\nu}=F_{\mu\nu}{}... | The easiest way to check the antisymmetry of $F$ is to write it as
$$
\mathcal{F}_{\mu \nu} = \partial_\mu \mathcal{A}_\nu - \partial_\nu \mathcal{A}_\mu + [ \mathcal{A}_\mu , \mathcal{A}_\nu]
$$
This is manifestly antisymmetric, because the commutator is antisymmetric. Note then that
\begin{align}
[ \mathcal{A}_\mu , ... | {
"language": "en",
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Singularity in Robertson Walker metric with flat spatial slices In Sean Carroll's GR book, pg. 76, a special case of the Robertson-Walker metric, where the spatial slices are flat is given by
$$ds^2=-dt^2+a^2(t)[dx^2+dy^2+dz^2].$$
It was said that $t=0 $ represents a true singularity of the geometry (the 'Big Bang') an... | Carroll mentions that in the solution under consideration, the scale factor $a\rightarrow 0$ as $t\rightarrow 0$. Since the metric must always be non-degenerate, this represents a singular point. Operationally, if the metric is degenerate than the dual metric $g^{\mu\nu}$ becomes undefined.
| {
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Spherical Lens Instead of Parabolic Lens I know that using the paraxial approximation, spherical lenses behave like parabolic lenses.
It seems that there is no reason to use spherical lenses instead of parabolic (because they are used in the same way, and parabolic lenses do not required paraxial approximation) apart f... | Spherical reflectors have the outstanding advantage over parabolic reflectors in that by moving the feedpoint/receiver off-center above the spherical surface, the beam aperture can be steered without having to steer the entire antenna. This principle was used in the design of the radio telescope at Arecibo, PR which re... | {
"language": "en",
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"source": "stackexchange",
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Why voltage is not the same for the capacitors in series?
In this picture, there are two capacitors C1 and C2 joined in series and connected to a battery. We know there are two terminals in a battery, a positive terminal and a negative terminal.
The potentials of the positive and negative terminals are +P and -P respe... | This is an important point which is commonly overlooked. The crux is that the voltage drop on each capacitor is not necessarily the batteries voltage. Let's work out the ideas step by step.
Firstly, to find the charge on capacitor system let us take equivalent capacitance. When we replace the two with an equivalent one... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What is a simple example illustrating the concept of "commensurate" and "incommensurate" order in condensed matter physics? In a wide range of contexts in condensed matter physics, e.g this paper, the concepts of commensurate and incommensurate orders are invoked to describe particular ordered phases. I think I have so... | I am very new at this and have seen these two terms come up in various topics within CM physics so the answer depends on what you are talking about. I'll provide an answer in different words than what was stated in the previous answer.
Commensurate means integer multiple of the crystal lattice constant.
Incommensurate ... | {
"language": "en",
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Newton's Laws of Motion, Pulleys, Rope and tension I was solving some questions to apply my concepts, and I came across the atwood machine and pulley block problems.
Consider the following for example:
The pulley is massless and frictionless, string, too, is ideal.
Why does the book say that the tension in the green s... | If pulley had mass $M_{pulley}$ and it is in equilibrium in the frame in which you are working, then assume that tension in string is $T_{g}$
$$\sum \vec{F}_{net,pulley}=0$$
$$T_{g}-T-T-M_{pulley}g=0$$
$$T_{g}=M_{pulley}g+2T$$
If pulley is ideal, then $M_{pulley}=0$, so, $T_{g}=2T$.
If there is friction in pulley and s... | {
"language": "en",
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What does $\rm kg m^{-2}$ mean in simple terms? I'm reading a research paper on fish stocking density and they measure the density in terms of $\rm kg m^{-2}$ (i.e. stocking density is 1.27 $\rm kg m^{-2}$). I've googled it but still don't have a good grasp on what a kg m is. Is kg m just an alternate way of writing ... | it is density of kg per unit area.
m^-2= 1/m^2
aka kg/m^2
| {
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What is a simple way to slow down this cart? What can I do to slow the wheels down and make this 4 wheel cart harder to push? I'd prefer a fairly straight forward solution. It will be used for exercise. I am very naïve when it comes to physics.
| We do not know how much slow down you need, but I can propose a scalable method over a wide range.
I expect it may not be practical for your case, but it could be.
You could make the wheels roll on a layer of a sticky and highly viscous fluid.
You could vary the viscosity, but also the layer depth.
Drive through honey.... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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How does the Bohm interpretation/pilot wave theory explain particles getting spontaneously created and destroyed? Pilot wave theory says that classical particles are riding on waves.
Quantum field theory says that particles are the excitations of a field.
Both of these descriptions seem like essentially the same thing,... |
if we equate pilot waves with quantum fields. What are the differences?
The fields of quantum field theory are not associated with a specific particle, they are generic over space and time, like a coordinate system , on which creation and annihilation operators operate to create a given particle. The pilot waves are ... | {
"language": "en",
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Using Christoffel symbols to derive formulas for div, grad, curl In Sean Carroll's GR book, pg. 1oo, it was said that in flat space, the Christoffel symbols vanish in Cartesian coordinates. However, in curvilinear coordinates, they do not vanish. For example, for plane polar coordinates
$$ds^2=dr^2+r^2 d\theta^2$$
the ... | In an arbitrary coordinate system on a manifold, the grad, div and curl are defined using covariant derivatives:
$$\nabla\phi=(\nabla_a\phi)\textbf{e}^a$$
$$\nabla \cdot \textbf{v}=\nabla_av^a$$
$$(\text{curl} \textbf{v})_{ab}= \nabla_av_b -\nabla_bv_a$$
where $\phi$ is a scalar field, $\textbf{v}$ is a vector field an... | {
"language": "en",
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Creating a Bouyancy Force Generator How much energy is needed to maintain boiling water? (I'm assuming $1400~\rm W$). With that said, when air is added to an object to decrease its density, does the strength of its buoyant force increase? Can it be enough to create/maintain $1400~\rm W$?
| No.
At a temperature of $100^\circ~\rm C$ and a pressure of $1~\rm atm$, the heat of vaporization is $2257~\rm kJ/kg$. The more power you put in, the faster the water boils. It also generally decreases with higher temperatures and increases with higher pressures.
If this water vapor is used to displace water in an obje... | {
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Is the many-worlds interpretation really just an interpretation? Is the many-worlds interpretation just a different interpretation to quantum mechanics or does it contain some different predictions?
In other words, is it possible theoretically to conduct an experiment that checks the many-worlds interpretation?
| Actually, there is one experiment documented that could just prove this. It is based on proving that communication exist between the proposed parallel worlds. They basically isolate a particle in an ion trap. Then they make a quantum measurement on another system (with two discrete outcomes), creating two parallel worl... | {
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"question_score": "20",
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Mesoscopic Bose-Einstein Condensate Bose-Einstein condensates of molecules of a few daltons have been already created, so I was wondering: would making a Bose-Einstein condensate on a system of Quantum Dots, due to their properties, cause the system to display any different effects?
| Bose-einstein condensate is a state of a multiparticle boson system. It is not clear in which sense QDs can be viewed as particles. Otherwise, condensates of cold atoms and excitons are mesoscopic. So are superfluidity and superconductivity - since they are characterized by a macroscopic order parameter.
One quantum-d... | {
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How do I find the approximate surface area of a chicken? I'm working on building a chicken army and I'm trying to find out how much metal or kevlar (still deciding) I need to make armor for the chickens. this measurement does not need to be exact I'm just trying to get an estimate for how much I will need. You will be ... | Assume a spherical chicken, of some radius $r$. The surface area of said bird would then be $4\pi r^2$, which would be a good approximation of the amount of metal required to cover it completely.
If you assume $r\approx 30\text{ cm}$, that would come to an area of around $$A \approx 1\text{m}^2/\text{chicken}.$$
If the... | {
"language": "en",
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"source": "stackexchange",
"question_score": "13",
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Understanding a Poynting vector equation I'm reading this section in the Griffiths Introduction to Electrodynamics book.
I trying to understand where equation 9.57 comes from (the middle part of the equation at least; I see where the $cu\;\hat{\mathbf{z}}$ part on the right comes from).
Does it come directly from calcu... | A monochromatic plane wave in $z$-direction has the fields
$$\begin{align}
\mathbf{E}&=E_0\cos(kz-\omega t+\delta)\ \hat{\mathbf{x}} \\
\mathbf{B}&=\frac{1}{c}E_0\cos(kz-\omega t+\delta)\ \hat{\mathbf{y}}
\end{align}$$
I guess you find these a few pages earlier in your book.
Or you can check that these fields actually ... | {
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Is no acceleration a cause or consequence of no net force? If a body is moving with constant velocity, or is at rest, then the net force on it must be $0$. If the net force on a body is $0$, then it must be moving with constant velocity or must be at rest.
Is $0$ net force a consequence of being at rest or moving with ... | It may be a matter of opinion, but based on Newton’s first law. I would lean towards the latter.
This is Newton’s first law. It states if a body is at rest or moving at constant speed in a straight line it will remain at rest or continue move in a straight line unless acted upon by a net force. The law begins with the... | {
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Normalization of squeezed vacuum for QFT in the black hole background (Hawking radiation) In the context of BH evaporation, one can represent an initial vacuum as the final state containing particles, following Polchcinski (2016, page 9)
$$|0\rangle_{a}=\mathcal{N} \exp \left(\int_{0}^{\infty} \frac{d \omega}{2 \pi} e^... |
is that state actually normalizable...?
Yes. To see this, start with the state $U|0\rangle$ with
$$
\newcommand{\ra}{\rangle}
U =
\exp\left(
\int_0^\infty\frac{d\omega}{2\pi}\
f(\omega)\left(b_\omega\tilde b_\omega
- b_\omega^\dagger\tilde b_\omega^\dagger\right)
\right)
\tag{1}
$$
for some real-valued fu... | {
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Which is the centripetal term here? In spherical coordinates the acceleration can be written as
$$\textbf{a} = \dot{\textbf{v}} = \ddot{r} \hat{\textbf{r}} + \dot{r} ( \dot{θ} \boldsymbol{\hat{\theta}} + \sin θ \dot{\phi} \boldsymbol{\hat{\phi}}) + \dot{r} \dot{θ} \boldsymbol{\hat{\theta}} + r \ddot{\theta} \boldsymbo... | The two negative terms combine to give a resultant, -r$ω^2$.
| {
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"timestamp": "2023-03-29T00:00:00",
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How would velocity of sound, the fundamental frequency and wavelength of sound vary when the temperature of an organ pipe is increased? Here is my approach to this:
neglecting any thermal expansion of the pipe:
By the Laplace formula for the speed of sound,
$V=\sqrt{\frac{\gamma P}{\rho}}$ where P is the pressure, $... | HINT: Sound waves in an organ pipe are examples of standing waves. The allowed wavelengths of a standing wave on (for example) a string are not arbitrary, but are instead determined by the length of the string.
| {
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Force on the bottom of a tank full of liquid - Hydrostatic Pressure or Gravity
Imagine a tank filled with water that has some height $h$ and at the bottom area $A$ but as it goes up, for example at height $h/2$, it's area is now $A/2 $. What's the correct way to calculate the force at the bottom of the tank? (Let's ig... | I would like to point out that the question you encountered poorly defines how the cross-sectional area is related to the height at which it is being observed.
Is it like:
*
*Area(x) = (x/h)*A, x being the distance from the bottom, h being the total height, A being the area at the bottom.
*The way parsa639 describes... | {
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Understanding renormalizability I want to understand when a given theory is renormalizable and how to find renormalizable theories for different dimensions (the latter will become clearer later on).
To do so, we work through an example: the following real scalar field theory in $d$ spacetime dimensions
\begin{equation*... | Your statement (*) is valid only for $d > 2$ (you have to take care when dividing an inequality by a non-positive number). Based on the original formula for $[\lambda_n]$, renormalizability holds for all $n$ if $d \le 2$.
You are correct that the "simplest" (free) scalar field theory is renormalizable for all $d$.
| {
"language": "en",
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Why is the constant of integration zero when solving the Friedmann equations? I'm confused regarding relating the Hubble constant H$_0$ to current age of the universe $t_0$.
I'm looking at solutions for different epochs of the Friedmann equation, which I've got in the general form
\begin{align}
\frac{a}{\sqrt{\Omega_va... | I'm not sure where the confusion is; this seems straightforward.
An arbitrary solution to $a\dot a= H_0$ for constant $H_0$ satisfies
$$
a^2(t_1)-a^2(t_2)=2 H_0 (t_1-t_2)\qquad (\ast)$$
for any $t_1,t_2$. For fixed $H_0$, $a^2(t)$ is uniquely specified by the single initial condition at some time $t'$, as 1st-order ODE... | {
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What do angle have to do with waves? Why do we use trigonometric functions to model waves? I've just learned SHM and I'm not able to understand why "phi" (initial phase) is an angle. Why are angles used in SHM?
| The solution to the differential equation of a harmonic oscillator involves rotation.
If you specify your position and velocity as the real and complex components of a complex number $z$, then the solution of the differential equation is $z k^t$ where $k$ is some complex number, which is just rotation and scaling.
If y... | {
"language": "en",
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Standard boost for one-particle states in Weinberg's QFT chapter 2 Weinberg's approach to QFT starts with particles which are not necessarily more fundamental than fields but are known more for certain. A particle of a particular species can have different momenta $p$ in different frames but its internal degrees of fre... | I had some difficulty understanding a fair amount of chapter 2 because Weinberg’s book on QFOT (which you appear to be describing) sometimes skips some of the logic (like what are the “sigma’ degrees of freedom). I managed to find a set of videos that helped me a lot - much is filled in to Weinberg’s terse presentation... | {
"language": "en",
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Angular momentum commutation relations The operator $L^2$ commutes with each of the operators $L_x$, $L_y$ and $L_z$, yet $L_x$, $L_y$ and $L_z$ do not commute with each other.
From linear algebra, we know that if two hermitian operators commute, they admit complete sets of common/simultaneous eigenfunctions. The way I... | Commuting operators do not necessarily share ALL eigenstates, just some set.
An eigenstate shared by $L^2$ and $L_x$ will not be the same as that shared by $L^2$ and $L_y$
| {
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What is light, a wave or a particle or A wave-particle? What is light?
And how do we know that light is an electromagnetic wave?
I asked my teacher and he said that when you place a compass in light's path, the needle of the compass rotates. Which I think is not a valid answer and thats not what actually happens when w... | Your instructor is wrong, and you are right. Placing a compass needle in a light beam will not cause the needle to turn, the way it certainly will if you place that compass near a magnet or a piece of wire carrying an electrical current. This is because light beams do not generate electrical current flow or magnetic fi... | {
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Bosonic coherent state normalization In the paper arXiv:1208.3469 (equation (85)) it is stated that the coherent state for two bosons with corresponding annihilation operators $a,b$ can be written as:
$$|\Psi_\lambda \rangle = \sqrt{1-|\lambda|^2} e^{-\lambda a^\dagger b^\dagger}|0\rangle,$$
where $|0\rangle$ is the va... | You forgot a factor of $1/n!$ in your exponential expansions, and then forgot to use the geometric series. The correct set of steps are:
$$\langle \Psi_\lambda |\Psi_\lambda \rangle = (1-|\lambda|^2)\langle 0|e^{-\lambda^\star ab} e^{-\lambda a^\dagger b^\dagger}|0\rangle = (1-|\lambda|)^2 \sum_{m,n=0}^\infty \frac{\la... | {
"language": "en",
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What is the strongest result that has subsequently been shown to just be a statistical glitch? While reading up on the $g-2$ result, I noticed that the authors stopped short of announcing a definitive result because they only had 4.2 sigma of confidence rather than the 5 that is the standard for confirmation. That got ... | There are lots of unexplained >5-sigma results out there, and the only way establish that one of them was a statistical glitch would be to prove that it had no systematic errors. This is impossible. There is a well-known aphorism that "all models are wrong", and all real measurements have inherent systematic errors. We... | {
"language": "en",
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According to general relativity planets and Sun bend the spacetime (explaining gravity), but does this hold true for smaller objects? According to general relativity planets and the sun bend spacetime, and that is the explanation of gravity. However, does this hold true for smaller objects, like toys, pens, etc.? Do t... | As explained in the other answers, yes. Its so hard to tell because, compared to the other forces, gravity is very, very, very, very, very, very, very, very, very, very weak. Only when a whole lot of matter gets together does it become significant.
For example, the Earth is 6,000,000,000,000,000,000,000,000 kg of matte... | {
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Why is there a volumetric dimension to pressure-volume work? This concept was a bit hard to grasp, because I'm bad at seeing the real-world implications of multiplication. Division makes sense, but multiplication is harder for me. Pressure-volume work is measured in $1$ Pa $\times$ m$^3$. It says that $1$ Pa $\times$ m... |
Basically saying that either the volumetric quantity or the pressure quantity has a 1/1 relation with the energy of the work (J), meaning the other quantity is equal to 1.
The definition of mechanical pressure-volume work is the integral of the external pressure times the differential change in volume of the system $... | {
"language": "en",
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Why do images not appear inverted when looking directly through a pinhole camera? I understand that the way light takes through a pinhole creates an inverted image on a surface behind the pinhole. I remember this effect from school experiments, it's also described in this wikipedia article. I punctured a piece of paper... | Has the OP just reduced the size of his pupil by adding another aperture (the pinhole) in front of his eye?
A smaller aperture of the will make the scene seem dimmer and if the OP requires corrective lenses their vision will improve as the "stopped down" aperture improves depth of field.
| {
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Hyperfine Splitting What does Hyperfine Splitting exactly mean?
I am having a bit of trouble understanding the concept of hyperfine splitting.
I solved the problem of including hyperfine interaction for the ground state of Hydrogen and I found the eigenvalues. However, I can't understand the physical meaning.
What I th... | The ground of hydrogen atom in the Coulumb potential is
$$
E_0 = - 13.6057 eV.
$$
Its wavefunction
$$
\psi(\vec{r}) = \mathbb{N} \exp\left(-\frac{r}{a_B}\right).\,\,\,\text{ where } a_B = 0.529177 \dot A
$$
The degeneracy of the ground state is two electron spin states: $\vert \uparrow \rangle$ , and $\vert \downar... | {
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Is it possible to stir the tea so that it cools more slowly? I recently learned that stirring the tea with vertical movements speeds up the cooling process. As a result, I had a question, and whether it is possible to stir it so that it cools down, as slowly as possible. Conditions: the spoon is an aluminum tea spoon, ... | There are more factors involved here.
Stirring in a way than causes turbulence does not have the same effect as stirring in circles, creating a vortex. Moreover, heat loss due to evaporation and surface radiation may or may not exceed heat loss due to wall contact, depending on environmental conditions and the choice o... | {
"language": "en",
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Do all Joukowski aerofoils violate no-penetration condition at trailing edge? In our fluids course we calculated the velocity distribution around a completely symmetric Joukowski aerofoil (as shown below) and used the Kutta condition to ensure that the velocity was not infinite at the trailing edge. However, even after... | As @alephzero and @Chiral Anomaly said, the Joukowski mapping produces a cusp at the trailing edge of the aerofoil which doesnt have a defined normal to the surface, therefore it's less that the no-penetration condition is violated there, but that a direction normal to the surface from which to apply the no-penetration... | {
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If a polarized light wave is indistinguishable from its original self after being flipped 180°, why doesn't a photon have a spin of two? The spin of a photon has a counterpart in classical physics, it's polarization, right?
And if you spin a polarized light wave by 180°, (or pi radians), it is now the same as before, c... | If you rotate a polarized classical electromagnetic wave by 180° about its axis of propagation, you don't get the same wave back; you get the same wave phase-shifted by half a cycle. You need to make a full rotation of 360° to get the same classical wave solution back, so by your logic, the photon should indeed have ... | {
"language": "en",
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What motivated Einstein to formulate general relativity? I never really fully understood what motivated general relativity or why the Newtonian concept of gravity was considered problematic.
One thing I always hear is that it is because it doesn't address what causes two masses at a distance to be attracted. Maybe qua... | Einstein came up with General Relativity because he recognized that Special Relativity was not a good description of the universe (he couldn't make gravitation work sensibly within it).
He came up with Special Relativity because Newtonian physics had failed to accommodate light in any useful or consistent way.
| {
"language": "en",
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How can you measure the polarization of a single-photon without destroying it? In Quantum Key Distribution, namely the BB84 protocol, Alice creates single-photons in the horizontal/vertical basis or the (45 degree rotated) diagonal basis which she then sends to Bob over a transmission line.
Now if an eavesdropper Eve t... | In general, if you want to know the polarization of light experimentally, you need to make a series of measurements in different bases/directions using a different filter each time. Each measurement indeed will destroy a single photon, so in order to fully know the polarization of light you need to measure an ensemble/... | {
"language": "en",
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Analysis of a state vector $\,|\psi\rangle\,$ in the basis of eigenvectors of a $4\times 4$ Hamiltonian matrix I have the following matrix
\begin{equation}
A=
\begin{pmatrix}
0 &1 &0 &0 \\
1 & 0 &0 &0\\
0 &0&0&1\\
0&0&1&0
\end{pmatrix}
\end{equation}
The eigenvalues of this matrix is $\left\{1,1,-1,-1\right\}$. We s... | You have found the eigenvectors in the 1-eigenspace to be
$$
|\psi \rangle = \alpha
\begin{pmatrix}
1\\
1\\
0\\
0
\end{pmatrix}
+ \gamma
\begin{pmatrix}
0\\
0\\
1\\
1
\end{pmatrix} = \alpha |v_1\rangle + \gamma|v_2\rangle,
$$
where $\alpha$ and $\gamma$ are any complex numbers constrained by $|\alpha|^2 + |\gamma|^2 =... | {
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Why is the half-wave dipole the most used antenna design? When producing em waves using a dipole antenna (of length L), you could theoretically use any L and adjust the frequency of the oscillating voltage to get the desired wavelength. Then why are most antennas half a wavelength long? I'd also like to know why it's u... | An antenna, in general, is NOT a resonator (contra @oliver). The purpose of the antenna is to be a direction dependent impedance transformer that matches the wave impedance of the transmission line connecting the transmitter/receiver to space (air) having impedance $\sqrt{\frac{\mu_0}{\epsilon_0}}=377\Omega$ in all dir... | {
"language": "en",
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What is the proof of $C_{V} = \frac{fR}{2}$? I came across this formula in thermodynamics. Please give me a rigorous proof to this formula. My teacher did not even give any proof neither do any of my books. The formula is :
$C_{V}=\frac{fR}{2}$ where $C_{V}$ is the molar heat capacity at constant volume, $f$ is the tot... | This is the so called equipartition theorem, that says that each degree of freedom contributes with $\frac{k_BT} {2} $ to the average energy, or using mol $\frac{RT} {2} $.
More precisely, each degree of freedom in the Hamiltonian that is quadratic contributes for $\frac{k_BT} {2} $.
If we can write the energy:$ E = \s... | {
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Commutation relations inconsistent with constraints In section $9.5$ of Weinberg's Lectures on Quantum Mechanics, he uses an example to explain the clasification of constraints. The Lagrangian for a non-relativistic particle that is constrained to remain on a surface described by
$$f(\vec x)=0\tag{1}$$
can be taken as
... | Would an example suffice? If so, consider the case $f(\vec x) = x_1$. Then (1) says $x_1=0$, which is already inconsistent with the commutation relation, and (3) says $p_1=0$, which is again inconsistent with the commutation relation. If $x_1$ or $p_1$ is zero, then we can't have $[x_1,p_1]\neq 0$.
| {
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Heisenberg uncertainty principle at relativistic velocities Would the Heisenberg uncertainty principle, the energy of h-bar in particular, be affected by the Lorentz factor at relativistic velocities from an external pov?
If a rocket were to speed by at relativistic velocities and if we could see inside it, or if we co... | Planck constant $h= 6.62607015\times 10^{−34}$ Js (i.e. Joules times second and not Joules per second) in SI units. See here. As such it has the units of action. Although energy transforms as a result of Lorentz transformations, the Planck constant does not. There may be some interesting effects of special relativity (... | {
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Can a body float in the middle of a fluid? Let's say we have a cubic body of side $a$ and made of a material with density $\rho$ and we measure its immersed height in a fluid of density $\rho_f$ by the variable $y$. Then, its potential energy (and considering a gain of potential due to buoyancy) can be written as:
$V =... | An object can remain at a fixed depth, fully submerged as long as the buoyant force equals the weight. This will generally require monitoring and adjustment. A submarine can adjust the amount of compressed air in a tank which admits outside water. A scuba diver can adjust the amount of air in an inflatable vest.
| {
"language": "en",
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Why are constant volume and constant pressure heat capacities basically the same for solids? Are degrees of freedom involved? I knowv that $C_V=\frac{\frac{f}{2} Nk_B}{m}$ and $C_P=\frac{(\frac{f}{2} +1)Nk_B}{m}$. Since for solids their values are very close to each other, I would assume $\frac{f}{2} +1$ is very close ... | Although changing the temperature of a solid under constant volume conditions can cause extremely high pressures, the corresponding volume changes under constant pressure conditions are very small, so the amount of work that a solid can do while expanding when heated, is also very small. It is this work that makes the ... | {
"language": "en",
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In special relativity, how do we know that distance doesn't change in the direction perpendicular to velocity? In the theory of special relativity it is said that the distance in the direction of the speed changes by a factor of
$$\gamma=\frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$$
How do we know that the distance perpendi... | We can simply derive this from the Lorentz transform. With the $x$ direction parallel and the $y$, $z$ directions perpendicular the Lorentz transform is: $$t'=\gamma \left(t-\frac{vx}{c^2} \right)$$ $$x'=\gamma (x - vt)$$ $$ y' = y$$ $$z' = z$$ For an object with a length $L$ in the $y$ direction at rest in the unprime... | {
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How to find the falling time of an object when acceleration is not a constant? Let's say we are throwing an object from the surface of the earth, this object reaches 70,000km with initial velocity of $10713 \mathrm{m}/\mathrm{s}$ until it reaches the peak high , the g value at 70,000km is $0.068 \mathrm{m}/\mathrm{s}^2... | I will only outline an answer for now.
The object is on a suborbital trajectory. Classically this just means the objects or it is a 2 body gravitational orbit like earth and moon except the periapsis is lower altitude then the surface of the earth. Describing orbital characteristics is the same.
Now there is usually no... | {
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"source": "stackexchange",
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How can parallel rays meet at infinity? I found that in every book (till my 12th) it is written that, in concave mirror, when object is at focus, then reflected rays will be parallel and they meet at infinity to form a real image.
But, as we know, parallel rays never meet. Then, does this mean that all books are wrong ... | The books are just suggesting that as the object distance approaches the focus (from outside of the focus), the image distance will approach infinity.
| {
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Does Einstein's Equivalence Principle ignore time dilation? It seems Einstein's equivalence principle is neglecting time dilation. If an observer is at rest in an inertial reference frame, free of any gravitation, she will experience time flow at the "native" rate of a universe empty of mass and energy. However, an obs... | Not only is the equivalence principle not ignoring time dilation, you can actually use the equivalence principle to derive gravitational time dilation.
The issue that you are running into is probably the most common issue in applying the equivalence principle. That is that the equivalence principle is strictly local. I... | {
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Mathematical proof of charging by induction If we bring a positive charge +Q near a neutral conductor , we know that the surface near the source gets-Q and opposite to it gets +Q, but why do these induced charges have to be equal in magnitude to source charge, why isn't a charge distribution such as -7Q on surface ne... | In the equilibrium situation any free charge inside the conductor has no prefered direction to travel.
If a charge Q is near the conductor, and 7Q of opposing changes at its surface, clearly a free charge would have a prefered direction.
As the are plenty of free charges in a conductor, eventually (and very quick indee... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/631150",
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Distinguishing between static and dynamic pressure in fluids I read about the difference between static and dynamic pressure in fluids in the mechanics textbook (part 2) by BM Sharma. It explained me by using a Pitot tube and an ordinary pipe attached to the same main pipe. I applied Bernoulli's theorem at point $A$ an... | $$\underline{\textit{Analysis}}$$
Let $P_A=P_0$, $P_B=P_0$ and $P'_A$, $P'_B$ denote the static pressures at the points $A$, $B$, and their vertical projections $A'$, $B'$, on the datum line respectively. Let $v_A=0$, $v_B=0$ and $v'_A$, $v'_B=0$ denote the horizontal velocity components at the points $A$, $B$, and the... | {
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Problem understanding what densities of states represent I understand that the one particle partition function for a particle in a box can be written as: $$Z_1 = \sum_{k_x} \sum_{k_y} \sum_{k_z} (2s+1) e^{- \beta \epsilon( \vec k) } $$
My first question is that I'm not sure why we can also write it in the following way... | Maybe it would help to look at a simple finite-dimensional example. Consider the hamiltonian
\begin{align}
H = \begin{pmatrix}
\varepsilon & 0 &0\\
0 & 3\varepsilon &0\\
0 & 0 & 3\varepsilon
\end{pmatrix}
\end{align}
The partition function in the canonical ensemble is
\begin{align}
Z &= \text{Tr}\,e^{-\beta H}\\
&= e^{... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Why force between charges increases when it moves, instead of decreasing? Imagine two positive charges in a space ship moving with a velocity,v with respect to an observer on earth.
according to the person in the spaceship,the electrostatic force between the charges is $F'=(\frac{1}{4π\epsilon_0})\times \frac{q_1q_2}{r... | A common class of error, in these sorts of problems, is getting the transformation backwards and putting $\gamma$ where you should have $1/\gamma$. That's what's happened to you here.
To see this intuitively, consider a pair of opposite charges instead of same-sign charges. Released from rest, the opposite charges will... | {
"language": "en",
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Why is the power of a car limited? As an introduction this is what's written in my textbook:
$Power=\frac{work\ done\ by\ driving\ force}{time}$
$=\frac{Driving\ force×distance}{time}$
(as distance over time = speed)
$= Driving\ force×speed$
Note: If the power is constant and the body is accelerating then the speed is... |
Yet why does the power have to be limited to a certain range?
Aside from the power limits of car itself, as stated in @silverrahul answer, power is limited because there is an upper limit to the driving force on the car equal to the maximum possible static friction force between the tire(s) of the drive wheel(s) and ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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If I pull a metal bar for long enough with a constant small force, will it eventually break? Let's say I have a strong metal bar. I pull it apart with a very small constant force -- obviously it doesn't break. However, this would disturb the internal configuration. If I let go, then eventually the internal configuratio... | Lots and none at all.
Clearly not usefully, anyway.
Is it not obvious that if what you Ask were true, every screw or bolt holding any shelf would eventually break?
You might fall back on "if… long enough" meaning that the experiment should continue beyond the corrosion life of the screw (or bolt) and if you do, are the... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is there an intuitive way to view the concept of momentum? Ideas like distance, velocity and force are very intuitive to understand because you can "see" their real-world applications and so one can come to understand them without having any knowledge of their mathematical formulas.
Momentum as it is defined is the pro... | Imagine two large iron rolling balls, one larger than the other. Imagine they are moving at the same speed.
Imagine trying and stopping them. Which would be easier? The lighter one, of course. And if the balls are the same size, their speed is what matters.
So basically momentum is the property of the object that makes... | {
"language": "en",
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Is friction always opposite to velocity? Let's say an object is sliding on a slope and is the object has a velocity of $(0,0,5)$. The friction would be acting in the opposite direction of motion, being $(0,0,-1)$.
However, gravity is also affecting the object on the slope. The gravity is exerting a force of $(-1,-1,0)$... | A better phrasing is:
Friction always pulls in the direction that prevents sliding (often called relative motion).
Remember, there are two types of friction:
*
*Kinetic friction when the object slides. To prevent sliding (to stop sliding), kinetic friction pulls exactly opposite to the velocity. Regardless of any f... | {
"language": "en",
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How to know the true value of the measured quantity from an interferometer phase? For an interferometer, the measured signal will oscillate as a function of the accumulated phase $\phi(x)$ as a sinusoid or cosine, where $x$ is a quantity we are trying to measure from the interference. The signal will have the same prop... | This is a great example why physical theories are necessary a priori for interpretting the results of any experiment. One must first have an idea of the magnitude of the effect they are trying to measure before really being able to ascertain its value. When we are talking about a physical rotation, perhaps all that mat... | {
"language": "en",
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Why 2nd Shell can have 8 electrons? I recently watched this video:https://youtu.be/INYZy6_HaQE
and understood why 1st orbital can have only 2 electrons: According to Pauli's exclusion principle, two electrons cannot have the same quantum states.In the first energy level,all other quantum states are same except for the ... |
In other words, why the 2nd shell can have 8 electrons?
I do not know just how deep and detailed of an answer you are looking for.
In very simple, not deep at all terms, 2nd shell can have 8 electrons, because 2nd shell has 4 orbitals, and each orbital can have 2 electrons.
1st shell has only 1 orbital, hence 1st she... | {
"language": "en",
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Do electromagnetic fields also have thermal fluctuations? As far as I know electromagnetic fields have vacuum fluctuations. But can electromagnetic fields also have thermal fluctuations and can they induce current in coils? If the answers are positive. How does one model a fluctuating electromagnetic field inside the c... | Not only can this happen, but what you are describing is essentially why you hear static on your radio or see it on your TV.
Thermal radiation (eg from the sun) follows a blackbody spectrum. Thermal radiation can interact with a resonant circuit consisting of an inductor (coil), as well as a capacitor, tuned to amplify... | {
"language": "en",
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Does universal speed limit of information contradict the ability of a particle to pick a trajectory using Principle of Least Action? I'm doing some self reading on Lagrangian Mechanics and Special Relavivity. The following are two statements that seem to be taken as absolute fundamentals and yet I'm unable to reconcile... | There are typically an infinite number of solutions to Lagrange equations, corresponding to one starting point and an infinity of end points. If the system starts out on one trajectory, its end point is determined. The system does not "know" in advance what its endpoint is, but the physicist who has advance knowledge... | {
"language": "en",
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"source": "stackexchange",
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Why don't evanescent waves give rise to electromagnetic waves? I'm reading about evanescent waves for the first time. I understand that even thought no electromagnetic wave is transmitted across the boundary, an electric field is transmitted which decays exponentially into the material.
As far as I understand this is s... | An evanescent wave is a superposition of the incident (penetrated) wave and the medium reaction to this incident wave (a radiated everywhere wave). The interference is "destructive" in the medium direction and "constructive in the opposite direction.
You must consider all sources of a wave to understand its behaviour.
| {
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Expressing acceleration in terms of velocity and derivative of velocity with respect to position we know that
$$a = \dfrac{dv}{dt}$$
dividing numerator and denominator by $dx$, we get $$a=v\dfrac{dv}{dx}$$ provided that $dx$ is not equal to zero or instantaneous velocity not equal to zero
when I questioned my teacher t... | What is wrong is assuming that dv/dx is finite when v=0. Try this for motion with uniform acceleration. For example, for object thrown upwards with some initial velocity. At the top turning point the expression fir dv/dx tends to infinity.
| {
"language": "en",
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Coaxial Cable acts as differentiator In order to determine the characteristic impedance of a coaxial cable, I put a resistance on the one end and connected the other end of the cable to a signal generator and an oscilloscope.
This worked fine when using a sine signal as I just had to find the resistance, for which the ... | The dominant characteristic of a piece of coax is its parallel capacitance per foot of length. This effect is significant and must be included in a model of the cable along with its series inductance (small) and series DC resistance (very small) per foot.
| {
"language": "en",
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Velocity is relative, which means acceleration is relative, which further implies that forces are relative as well So how would we know whether a force truly exists or not. I can be accelerating a car my 5 meters per second squared but another car accelerating with the same acceleration would think that my car is at re... |
I can be accelerating a car my 5 meters per second squared but another car accelerating with the same acceleration would think that my car is at rest relative to them
That is not true.
When we consider just velocity, it’s simple because there are no forces involved.
But in accelerated motion we have to consider pseud... | {
"language": "en",
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Why $\frac{1}{E-H_0+i\eta}|n\rangle \stackrel{?}{=} \frac{1}{E-E_n+i\eta}|n\rangle$? A Hamiltonian $H_0$ is diagonalized in $\{|n\rangle\}$ i.e. $H_0|n\rangle=E_n|n\rangle$. Why can we write
$$\frac{1}{E-H_0+i\eta}|n\rangle \stackrel{?}{=} \frac{1}{E-E_n+i\eta}|n\rangle$$
$H_0$ is in denominator, how come we can apply ... | Whenever you see weird manipulations of operators, like $\sqrt{\mathcal{O}}$, $\frac{1}{\mathcal{O}}$, or $\log{\mathcal{O}}$, they are always defined by just doing those operations to the eigenvalues. Now, if the operators aren't diagonalizable in an eigenbasis, then it is more complicated to define these operations,... | {
"language": "en",
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Is there an alternative to radio waves that can go through metallic objects? Radar can pass through materials such as paper, wood, glass, brick, and concrete, but it reflects off of metal. Is there an alternative to radar that can pass through metal substances? If not, is it likely that we will ever find such a wave?
| As pointed out in another answer, ultrasound is an option for detection of objects behind sheet metal. Actually developing such a system is very difficult, of course.
The rear doors of the Tesla model X are wing doors (referred to by Tesla as 'falcon wing doors'). These wing doors are moved by electric motors, control... | {
"language": "en",
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Physical interpretation of relativistic synchrotron radiation When an electron approaches the speed of light, the emission pattern is sharply collimated forward, in the direction of motion. I can see how this is mathematically true from taking the relativistic limit of the angular distribution of the radiated energy (a... | The Bremsstrahlung diagram is used for a decelerating electron.
It could equally apply to an accelerating one, (instead of a nucleus, just the accelerating field). Feynman diagrams are in the center of mass system of the input and output particles
The collinearity comes because the whole diagram should be Lorentz tra... | {
"language": "en",
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Kinematic behavior of a flat, a closed, an open universe
according to An Introduction to Modern Astrophysics, 1263p, there is explanation about evolution of scale factor.
“ For the early universe($R<1$) there is little difference among the kinematic behaviors of a flat, a closed, an open universe because the early u... | This answer is based on the Figure 5 you added to your question. I believe that the concept of "kinetic behavior" in this context means the mathematics of the expanding universe based on the cosmological model related to Figure 5. The "early flat universe" refers to the similarity between the three assumed models (open... | {
"language": "en",
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Why is there no kinetic term in the Hamiltonian of the Ising model? I am used to the Hamiltonian formalism in the context of (quantum) field theory, where as far as I can remember it always has the form of a kinetic term + a potential term. For me the absence of kinetic terms means a theory without dynamics. In Wikiped... | In classical statistical mechanics (as opposed to quantum stat-phys), the dynamical (kinetic energy) part of the Hamiltonian decouples from the interaction (potential) part, since both momentum and position are independent. The same is true for classical spin systems: their thermodynamics is independent from the dynam... | {
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Shouldn’t the Lorentz force acting on an electron increase it’s tangential speed? I know some of you might be tempted to just answer “No, the Lorentz force acting on a particle is in every point perpendicular to the velocity vector” but please help me with my doubt.
Let’s say we have an electron that for some undefined... | If the radius is going to stay the same as you require (which is fine), the centripetal force needs to stay the same. The initial force that was the agent of that centripetal force will change if some force is added or subtracted in that direction.
If (for simplicity) a string was supplying $F_C$, then you add a magnet... | {
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Where does the kinetic energy of a spaceship in flight go, when it is stopped by firing thrusters in the opposite direction? Where does the kinetic energy of a spaceship in flight go, when it is stopped by firing thrusters in the opposite direction?
If you stopp a driving car, the kinetic energy is converted to thermal... | The kinetic energy of the spacecraft is carried off by the exhaust gas from the rocket engines that are being fired to stop its motion.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/635285",
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In a semiconductor, how exactly do electrons move into the conduction band? From what I know, electrons that are excited can move into the conduction band, but how and what causes electrons to be excited? Heat/light seem to make sense as to something that can 'excite' the electron, but I am not completely sure.
Does th... | There are many processes that may excite electrons into the conduction band:
*
*light (even if we do not illuminate the semicodnuctor, there is usually some background radiation)
*strong electric field (Zener tunneling)
*collisions with other electrons, in which they may exchange energy
*scattering particles, such... | {
"language": "en",
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Does this research paper prove that warp drives are impossible? Does this preprint prove that warp drives are impossible?
J. Santiago, S. Schuster and M. Visser, "Generic warp drives violate the null energy condition"
It states that the NEC (Null Energy Condition) is violated in this paper and many others: E. W. Lentz,... | It proves that warp drives violate an energy condition that many physicists think is reasonable. The universe of course has no obligation to be reasonable.
The NEC states roughly that the energy embodied in tension or negative pressure cannot be larger than the density of mass-energy somewhere. That is very extreme: no... | {
"language": "en",
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Earths electric charge: is it neutral? Is the whole earth electric neutral? I know about the negative charge of the earths surface and the positive charge of the ionosphere, but i wonder if the whole earth (including its atmosphere) has an equivalent number of electrons and protons.
It could be measured by some space p... | No, I won't say that.You answered it yourself the atmosphere is constantly being irradiated by ionizing radiation and some of the charged particles might leave the earth's atmosphere and hence would make the earth a charged object at least on a very small scale.
This question has been asked before, you can find a more ... | {
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How do you differentiate this differential equation? I have to differentiate this equation (Gravitational force between N-Bodies)
$\begin{align}
\frac{d^2}{dt^2}\vec{r_i}(t)=G
\sum_{k=1}^{n}
\frac
{m_k(\vec{r}_k(t)-\vec{r}_i(t))}
{\lvert\vec{r}_k(t)-\vec{r}_k(t)\rvert^3}
\end{align}$
where $\vec{r_{i/k}}(t... | The right hand side of your equation is an explicit function of $r_{i}$ and the $r_{k}$s. One just needs to apply the chain and product rules from introductory calculus. The expression will be super-ugly, and will have explicit $\dot r$'s in it, but I don't see what difficulty you're having with the computation.
Perh... | {
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Why does the intensity of the bright fringes decrease as we move away from the central maxima in Young's Double Slit Experiment? I studied that in Young's Double Slit Experiment the variation of intensity ($I$) of the fringes on the screen with respect to the phase difference ($Φ$) is given by :
$I = 4I_{0} \cos^{2}\fr... | In your formula, $I_0$ is the intensity of wave from either one of the sources, at the point of consideration. Now, as we move further from Central Bright Fringe, $I_0$ decreases too, varying as $I \propto \frac 1r$, if we consider line source (and hence cylindrical wavefront). Hence bright fringes become dimmer.
| {
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Non-constant wavelength of particles Is it possible for a particle's wavelength to change with respect to time? I'm thinking of a massless particle like a photon, but as it evolves through time its wavelength changes. I'm aware photons wavelengths do change from the expansion of spacetime, but I'm thinking on a smaller... | The photon wavelength may vary for a photon propagating in a non-uniform medium - with variable $n(\vec{r})$, the frequency being constant.
| {
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Since the speed of light is constant and also the speed limit; would you, in your reference frame, have no upper bound on your speed? Let us imagine you are in a vacuum and after having maintained a speed of 0 km/s (standing still) you accelerate to 297,000 km/s (99%). You know this is now your speed because you have a... |
You know this is now your speed because you have a speedometer telling you so.
This is precisely where you hit a (metaphorical) roadblock.
A speedometer must use something outside of your reference frame to measure your speed, as speed inside your frame is either 0 or meaningless (take your pick).
It's measuring the... | {
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An algebra step in the Quantum Partition Function for the Harmonic Oscillator On page 183 of Altland Simons, we are told:
$$ \prod_{n = 1}^{\infty} \Big[ \Big( \frac{2\pi n}{\beta} \Big)^2 + \omega^2 \Big]^{-1} \sim \prod_{n = 1}^{\infty} \Big[ 1 + \Big( \frac{\beta \omega}{2\pi n} \Big)^2 \Big]^{-1} \sim \frac{1}{\sin... | They are dropping an $\omega$-independent factor. Such factors are often dropped as they have no physical effect.
| {
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"timestamp": "2023-03-29T00:00:00",
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Wave propagation through conductors During wave propagation through conductor, why is the current density out of phase with electric field ?
When the oscillating electric field applies a driving force on the free electrons, they will start oscillating. Then the current density should be in phase with electric field , i... | The effect is identical to that of a harmonic oscillator. The electric field accelerates the electrons similar to how the spring accelerates the mass at the end. In the harmonic oscillator, too, the velocity is the highest when the force is lowest, i.e. when the displacement is zero.
If I have to guess at the origin of... | {
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What happens to entropy when half the particles are removed? Curiosity question. What happens to entropy in the following situation?
A gas fills an entire container and is in equilibrium. Suddenly all particles are removed from half the container. As such, there are now 1/2 the original number of particles, but all ... | The question is ambiguous, since talking about entropy we have to say entropy of what we discuss. In most cases "what" is omitted, since the answer is obvious, but not here. More specifically, assuming that initially we had $2N$ molecules:
*
*One can discuss the entropy of the $2N$ molecules after half of them was re... | {
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Why is $kx−ωt$ a constant for a travelling wave? In my physics textbook, there is a statement like this:
The motion of a fixed phase point on a progressive wave is given by
$kx−ωt$= a constant.
What does this mean? Why is it a constant?
Does fixed phase point mean that it is a particle of the medium always at the same ... | This relation pretty much defines a travelling wave:
$$
\mathbf{k}\mathbf{x}-\omega t=const \Rightarrow \mathbf{x}=\mathbf{v}t+\mathbf{x}_0,
$$
i.e., the wave front (or the surface pf constant phase) of a wave $v(\mathbf{k}\mathbf{x}-\omega t)$ moves with a constant velocity (where $v(\phi)$ is an arbitrary shape).
| {
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What is the force pair for the normal force? Clarification on Newton's 3rd Law In the process of trying to wrap my head around Newton's 3rd law I've come across 2 definitive statements.
*
*Forces must occur in pairs
*Forces must act on different bodies
This is confusing to me when applied to the classic box on a fl... | I find that Newton's 3rd law is often written in a way that makes it easy to get confused.
Here's how I like to write it:
If object A exerts a force on object B, then object B exerts a force on object A that has the same strength but opposite direction.
This makes it clear that you will never ever find two forces fro... | {
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"answer_id": 1
} |
How to measure the speed of an electric current? We all know that the definition of a current is the amount of charge flowing per second, that is often expressed by the equation $i=dq/dt$. But is it possible to measure the speed of an electric current in m/s? And also how can we measure such speed?
| Let's say that you have a wire with cross section $S$. Denote by $v$ the average speed of charge carriers, whose density is $n$. Assuming also that each charge carrier has charge $e$, it is clear that
\begin{equation}
J=e v n S
\end{equation}
From here you can find $v$
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/637532",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 2
} |
How do you understand stall in terms of Newtonian mechanics (i.e. without Bernoulli's Principle)? Okay, so. I understand how a wing generates life using Newtownian mechanics, to wit: the air molecules crash into wing, which is at an angle to the air molecules. As a result, the air molecules are deflected downward and... | The way to think about is in term of the ratio of lift and drag.
Wing design is optimized for good lift/drag ratio. (Provided, of course, that the pilot maintains the optimal angle of attack for the wings and the speed of the aircraft.)
Aircrafts that are designed for aerial acrobatics have flat wings, giving the pilot... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/637625",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 3
} |
Why the mass of initial particle has to be greater than the sum of masses of final particles? Suppose we have a decay of a rest particle $A$ into other particles $a_1,...,a_n$
\begin{equation}
A \rightarrow a_1+a_2+\cdots+a_n
\end{equation}
It is always stated that in order to this particle decay to be possible, the ma... | At the most fundamental level [in terms of the structure of special relativity],
the reason that
"the parent mass is greater than the sum of the daughter masses" (always the invariant masses)
is the same as
"the Clock Effect (which I will describe analogous to the above by: the proper time of the inertial path from O... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/637721",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
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