Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Separation between slip rings of DC generator
This is a DC generator which converts mechanical energy to Direct Current. The commutators in a DC generator are separated (as you can see in the image). It is explained in our book that it prevents the change in direction of current. But I don't understand.
Even if we don... | The direction of the current with respect to the magnets stays the same, but not with respect to the wire. Imagine that the positive terminus is on the left and the negative terminus on the right. The current starts out going $a\rightarrow b\rightarrow c\rightarrow d$, which is clockwise with respect to the magnets, ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Can entropy be equal to zero? I've searched for it but I only found contradicting answers from "scientists":
Dr. David Balson, Ph.D. states: "entropy in a system can never be equal to zero".
Sam Bowen does not refutes the following affirmation: "It is know[n] that entropy is zero when a pure crystalline substance is at... | If we use the definition of entropy $$ S=-k_B \sum_i P_i ln P_i$$ where $P_i$ is the probability of the i'th microstate, then at 0K, we know the system is certainly in the ground state, $P_0=1$ so the definition returns zero.
The only "residual motion" in the system at this state is that due to the uncertainty princip... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/47445",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
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What is the current radius of cosmological event horizon? Doing some crude calculations (using the value of $H_0$ at this point of time only, since it is time dependent but not distance dependent thanks to Johannes answer) what is the radius of cosmological event horizon at this point of time? (not looking for the chan... | The answer by Johannes is correct - the proper horizon distance in the concordance cosmology is ~46 billion light years. The reason that the answer in (1) was three times larger than that, when it should have been three times smaller, is that the value of c used was incorrect: The speed of light is $3 \times 10^5\ \mat... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/47584",
"timestamp": "2023-03-29T00:00:00",
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What is the simplest possible topological Bloch function? Kohmoto (1985) pointed out in Topological Invariant and the Quantization of the Hall Conductance how TKNN's calcuation of Hall conducance is related to topology, in which topologically nontriviality is said to be equivalent to impossiblility choosing a global ph... | Surprisingly, according to Immanuel Bloch's group (no relation to F. Bloch!), the simplest topological Bloch function is the 1D staggered lattice. The topological invariant is the Zak phase, the Barry phase accrued by walking across the edge of the Brillouin zone. The article will explain it better than I can: Direct M... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/47870",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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Don't understand the integral over the square of the Dirac delta function In Griffiths' Intro to QM [1] he gives the eigenfunctions of the Hermitian operator $\hat{x}=x$ as being
$$g_{\lambda}\left(x\right)~=~B_{\lambda}\delta\left(x-\lambda\right)$$
(cf. last formula on p. 101). He then says that these eigenfunctions... | Suppose I want to show $$\int \delta(x-a)\delta(x-b)\; dx = \delta(a-b) $$ To do that , I need to show $$\int g(a)\int \delta(x-a)\delta(x-b) \;dx \;da = \int g(a)\delta(a-b)\; da$$ for any function $g(a)$.
\begin{align}\textrm{LHS}& = \int \int g(a) \delta(x-a)\;da \ \delta(x-b) \;dx\\ &=\int g(x)\delta(x-b)\;dx \\&... | {
"language": "en",
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Do particle pairs avoid each other? Please end my musings Can you explain what happens when a particle and its antiparticle are created. Do they whiz away from each other at the speed of light or what? I suppose that they don't because otherwise they would never meet and annihilate each other, but then, if I had just b... |
Do they whiz away from each other at the speed of light or what? I suppose that they don't because otherwise they would never meet and annihilate each other,
Do you mean that you can have particles moving at speed of light? The difficulty of deaccelerating those particles what makes you thinking that renders the anni... | {
"language": "en",
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What causes the structure visible in first few milliseconds of a nuclear explosion? Following on from this question, here is a high-speed photograph of a nuclear explosion, taken about 1 ms after detonation: (source) As anna v pointed out, several similar images can be seen in a Google image search for "high speed nucl... | There is a description on Wikipedia accompanying this picture that seems to indicate the mottled surface is the leading edge of a compression shock propagating through the air. In particular, it carries the imprint of the irregularities in the casing surrounding the bomb.
I am inclined to agree. While I admit there is ... | {
"language": "en",
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Conformal Quantum Mechanics I heard the term Conformal Quantum Mechanics used today.
*
*What exactly does this mean?
*Why would one want to study this?
| Conformal groups are basically groups that preserve the angle between two points locally. SO(2,1) group is a prototype of conformal groups. Conformal field theory (theory developed from conformal groups) in zero spatial dimension is known as conformal quantum mechanics. It has applications in string theory, AdS_2-CFT c... | {
"language": "en",
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Will two trains running along the equator in opposite direction experience same wear out? Two identical trains, at the equator start travelling round the world in opposite directions. They start together, run at the same speed and are on different tracks. Which train will wear out its wheel treads first?
Will their wei... | As the question is probably more about reference frames, than actual wearing out of train wheels, i'll try to answer it.
The reference frame is not intertial, but rotating reference frame. There is an centrifugal force associated with movement of the reference frame: $F=\frac{mv^2}{r}$.
Assuming non rotating referenc... | {
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Phase difference of driving frequency and oscillating frequency Suppose a mass is attached to a spring and is oscillating (SHM). If a driving force is applied, it must be at the same frequency as the mass' oscillation frequency. However I'm told that the phase difference between the driving frequency and the mass's fre... | The oscillator frequency $\omega$ says nothing about the actual oscillator phase. Let us suppose that your oscillator oscillates freely like this: $$x(t) = A_0\cdot\cos(\omega t + \phi_0),\; t<0.$$ At $t=0$ it has a phase $\phi_0$. Depending on its value the oscillator can be moving forward or backward with some veloci... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/48589",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
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Rigorous approaches to quantum field theory I have been reading Quantum Mechanics: A Modern Development by L. Ballentine. I like the way everything is deduced starting from symmetry principles.
I was wondering if anyone familiar with the book knows any equally elegant presentation for quantum field theory. Weinberg's ... | I enjoyed Brian Hatfield's "Quantum Field Theory of Point Particles and Strings." Part 1 of the book is great IMO, Part 2 is useless. Also make sure to get the newest edition, there are many errors in the older editions, but the work is still good.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why do we weigh less when falling?
I don't want to go to science world to find out because it would be a long round-trip.
I understand that acceleration/deceleration would effect the weight and I can also imagine that someone at terminal velocity would weigh nothing but I can't get my understanding in terms of forces ... |
"I understand that acceleration/deceleration would effect the weight and I can also imagine that someone at terminal velocity would weigh nothing"
It looks like you think that only in terminal velocity we do not weight, and that's wrong. We measure weight by the normal force applied by the ground on us. That means th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/49826",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Cyclic Coordinates in Hamiltonian Mechanics I was reading up on Hamiltonian Mechanics and came across the following:
If a generalized coordinate $q_j$ doesn't explicitly occur in the
Hamiltonian, then $p_j$ is a constant of motion (meaning, a constant, independent
of time for a true dynamical motion). $q_j$ then ... | OP is right. The text has an error. A cyclic coordinate $q_j$ does not have to be an linear function of $t$.
Example: Consider two canonical pairs $(q,p)$ and $(Q,P)$ with Hamiltonian $H= p Q +P$.
Then $q$ is cyclic, and therefore $p$ is a constant of motion.
$\dot{Q} =\frac{\partial H}{\partial P}=1$, so $Q$ is a lin... | {
"language": "en",
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Do perfect spheres exist in nature? Often in physics, Objects are approximated as spherical. However do any perfectly spherical objects actually exist in nature?
| I suppose it depends on how perfect your perfect sphere is.
A drop of water in space with no other gravity effects would look spherical, but if you zoomed in enough to see edges of molecules, then it wouldn't be.
From there you can just keep getting smaller (atoms, protons and neutrons, quarks, etc.) until you get into... | {
"language": "en",
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How to get "real-time" temperature from sensor? The following is LM35 Thermal response time in air
The following is temperature reading from LM35 sensor. Horizontal axis is time in sec.
So this is not "real-time" temperature graph. The question is having thermal response graph, how to best adjust real readings from s... | You would need to know the transfer function of your sensor, but as a first approximation the graph you have from the manufacturer seems compatible with something like:
$$\frac{dT_s}{dt}=k(T-T_s)$$
where $T$ is the outside temperature and $T_s$ the sensor reading. You could then estimate $T$ as
$$T=T_s+\frac{1}{k}\frac... | {
"language": "en",
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What happens to heat waste produced by energy generation? What happens to heat waste produced by energy generation on earth that must be there according to the laws of thermodynamics? So, it never dissipates and remains on earth?
| The energy does not necessarily remain on earth. Earth maintains an energy balance with its surroundings. The sum of the energy reaching earth through radiation and the energy produced on earth must match the energy leaving earth through radiation. If the latter is too low, earth will warm up, thereby increasing its bl... | {
"language": "en",
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Construction of the supersymmetric Faraday tensor When I first learned gauge theories in my introductory quantum field theory course, I was taught that the Faraday (field-strength) tensor can be constructed by computing the commutator of the gauge-covariant derivative:
$$[D_\mu,D_\nu]=-ieF_{\mu\nu}$$
Now, I am studying... | As far as I know, it is defined in that form in order to satisfy chirality
\begin{equation}D^{\dagger}_{\dot{\alpha}}W_{\alpha}=0\end{equation}
and gauge invariance
\begin{equation}\delta W_\alpha=0.\end{equation}
I have not seen a definition by a commutator anywhere.
| {
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Force and Torque Question on an isolated system If there's a rigid rod in space, and you give some external force perpendicular to the rod at one of the ends for a short time, what happens?
Specifically:
What dependence does the moment of inertia have?
If it rotates, what is the center of rotation?
Does it matter that ... | The moment of inertia is the rotational mass of the object and it is solely a function of mass distribution - the shape. Usually it does not matter if it is rotating, but if the rate of rotation is high enough the body could deform. This is a concern in the connecting rods of high speed engines.
The MI does depend on ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why does smoke go out the window of the car - and what if there's wind blowing instead of the car moving? When driving a car while smoking with the window open (safety and legal issues aside), I've noticed that the smoke tends to go outside the window.
*
*Why does the smoke go outside?
*If the car is standing still... | The air flowing around the outside of your car near the windows will be at a reduced pressure due to the Bernoulli effect. There will also be some sort of vent letting air into the cabin, the vent intake must be located at a point in the airflow where you have higher stagnation pressure, so you get a net flow going in... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/51308",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is there a Lagrangian formulation of statistical mechanics? In statistical mechanics, we usually think in terms of the Hamiltonian formalism. At a particular time $t$, the system is in a particular state, where "state" means the generalised coordinates and momenta for a potentially very large number of particles. (I'm ... | There is a field theory version of statistical physics. The temperature is like the imaginary time. In this way we can formulate theory by path integral with action determined by Lagrangian.
| {
"language": "en",
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Spinning spheres colliding In an ideal environment with no friction, in a vacuum, what happens to the velocity of the spin of two spheres spinning in perfect parity at two different velocities when they come into contact?
| The rotating surfaces of the spheres would just slide over each other at the instant of contact: no forces perpendicular to the line connecting the centers of the two spheres would exist (i.e. no torque would exist). They would undergo a perfectly elastic collision (no loss of energy, thus no friction), thus conserving... | {
"language": "en",
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How to guarantee that a kilogram of antimatter will quickly annihilate another kilogram of matter? What I mean is, suppose we could somehow get a kilogram of antimatter and contain it safely. Now lets say we want to make a bomb using this kilogram, now, we have two ways, either store another kilogram of matter inside t... | The obvious answer, to my mind, would be to build an antimatter bomb like a fission bomb. You have a shell of matter (probably the containment unit) around the antimatter which is crushed by some kind of explosive, perhaps a nuclear explosive, creating a rapidly contracting dense shell that can partially overcome the c... | {
"language": "en",
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How do transformers work? A transformer is basically a primary inductor connected to a voltage $U_P$ which you want to transform. You also have an iron rod and a secondary inductor. So when there is a current $I_P$ the iron rods becomes magnetic. When you connect the primary inductor to AC, that means that you'll have... | According to ATL Transformers Ltd:
The transformer is based on two principles: first, that an electric current can produce a magnetic field (electromagnetism), and, second that a changing magnetic field within a coil of wire induces a voltage across the ends of the coil (electromagnetic induction). Changing the curren... | {
"language": "en",
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What is $v \, dp$ work and when do I use it? I am a little confused, from the first law of thermodynamics (energy conservation)
$$\Delta E = \delta Q - \delta W $$
If the amount of work done is a volume expansion of a gas in, say a piston cylinder instrument at constant pressure,
$$\Delta E = \delta Q - p \, dv$$
Here ... | Generally we call p dV as the displacemnt work done by a piston expanding in a cylinder containing some amount of gas. This is applicable to only NON FLOW PROCESSES. But the work v dp is applied to only flow processes or control volume processes. you can simply use the steady flow energy equation in place of this to c... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is it possible for a physical object to have an irrational length? Suppose I have a caliper that is infinitely precise. Also suppose that this caliper returns not a number, but rather whether the precise length is rational or irrational.
If I were to use this caliper to measure any small object, would the caliper ever ... | First of all, it doesn't make sense to assign an absolute number to a physical quantity like length and volume.
The number can be different with respect to different "units" of measurement.
But one can still question the ratio of two lengths, in this case:
According to the Bekenstein entropy limit(information), I guess... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
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Exact diagonalization of graphene's tight binding Hamiltonian While directly diagonalize graphene's tight binding Hamiltonian, which is numerical. We have to use a finite-sized graphene.
So how to deal with boundary conditions? The usual solutions are zigzag or armchair condition, but to make our model more realistic t... | TL;DR version: you want periodic boundary conditions with an extra twist.
You don't want straightforward periodic boundary conditions as this would be solving for a structure that is periodic. You can solve for an infinite sheet of graphene using Bloch's theorem.
I'll give a couple of details:
Find a basic finite unit ... | {
"language": "en",
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Could an ultra-relativistic particle tunnel directly through a stellar mass black hole? It occurred to me in passing that the Lorentz contraction of a black hole from the perspective of an ultra-relativistic (Lorentz factor larger than about 10^16) particle could reduce the thickness of a black hole to less than the De... | The important thing is the cross-sectional area of the horizon, and this is independent of Lorentz transformation, since the $y$ and $z$ coordinates are not changed.
Additionally, you can calculate that light will be captured by the horizon with non-zero cross section, and the geodesics ultra-relativistic particles w... | {
"language": "en",
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Can low-gravity planets sustain a breathable atmosphere? If astronauts could deliver a large quantity of breathable air to somewhere with lower gravity, such as Earth's moon, would the air form an atmosphere, or would it float away and disappear? Is there a minimum amount of gravity necessary to trap a breathable atmos... | The speed of oxygen at room temperature (293k) is 1720km per hour so if the escape velocity of the moon or planet is greater than that then at least you will have oxygen. If you want some nitrogen in the mix then you will have to google it's speed like I did for oxygen;-)
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/52527",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "14",
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Equivalence principle question I understand the equivalence principle as "The physics in a freely-falling small laboratory is that of special relativity (SR)." But I'm not quite sure why this is equivalent to "One cannot tell whether a laboratory on Earth is not actually in a rocket accelerating at 1 g".
| I'm not sure if the O.P. was satisfied with the previous answers or not but I feel that there is something that wasn't answered, at least in the way that the question asked for it. The reason why the equivalence between a free falling system and a Special Relativity Rest Frame implies the equivalence between a laborato... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/52593",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Question on Radiance equation The radiance equation is
$$
L = \frac{d}{dA} \frac{2(\phi)}{dW cos(\theta)} (watt/srm^2)
$$
where $\phi$ is the flux.
I am thinking, should not be the cosine term on the numerator instead of the denominator? Having the cosine in the denominator will make L goes to infinity if $\theta = 90$... | Generally, the radiative transfer equation is given by
$$
\frac{1}{c}\frac{\partial I_{\nu}(\vec{r},\vec{n},t)}{\partial t} +
\vec{n}\cdot\frac{I_{\nu}(\vec{r},\vec{n},t)}{\partial \vec{r}} =
\rho(\vec{r},t) \kappa_{\nu} (\vec{r},t)\left\{-I_{\nu}(\vec{r},\vec{n},t)+S_{\nu}(\vec{r},\vec{n},t)\right\}.
$$
To monochromat... | {
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How should I simulate the electric potential field from a wavefunction? I was interested in making what I thought would be a simple simulation of an electron encountering a positron by numerically solving the Schrodinger equation over several time steps, but I've run into 1 problem: the potential used in most textbook... | If you look at hwlau answer, you see that you can change coordinates from x1,x2 to the center of mass and relative coordinate. Just like you do for the Hydrogen atom.
If you work in the system of coordinates where the COM is stationary, the solution will be simple - identical to the Hydrogen atom, in fact.
My guess is,... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/52721",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Infinite square well in momentum space As we know the eigenfunctions for a particle of mass $m$ in an infinite square well defined by $V(x) = 0$ if $0 \leq x \leq a$ and $V(x) = \infty$ otherwise are:
$$\psi_n (x) = \sqrt{\frac{2}{a}} \sin \left(\frac{n\pi x}{a} \right).$$
How does the ground state wave function look l... | This question is not well-posed from scratch. There is no Momentum Operator for the problem you are considering. Your geometric space is a bounded region of the real axis, so no translation group can be defined and no self-adjoint generator of translation (the momentum observable) exists. The symmetric operator $-i\fra... | {
"language": "en",
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When do I apply Significant figures in physics calculations? I'm a little confused as to when to use significant figures for my physics class. For example, I'm asked to find the average speed of a race car that travels around a circular track with a radius of $500~\mathrm{m}$ in $50~\mathrm{s}$.
Would I need to apply t... | https://chem.libretexts.org/Bookshelves/Introductory_Chemistry/Map%3A_Introductory_Chemistry_(Tro)/02%3A_Measurement_and_Problem_Solving/2.04%3A_Significant_Figures_in_Calculations
Just revisited this in chemistry this year. You actually have to apply the correct number of significant figures based on the rules of oper... | {
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} |
What are the "loopholes" in past Bell's theorem experiments? I am intrigued by the following Phys.org article:
Researchers began using photons in 1980s to test Bell's theory and determine if Einstein's reasoning is right or wrong. Since then, researchers have used various quantum states to test the theory but continue... | The main loopholes were the detection (efficiency) loophole and the locality (or communication) loophole (http://en.wikipedia.org/wiki/Loopholes_in_Bell_test_experiments ). I don't know why or if this time it's going to be different.
| {
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Andrew's experiment In Thomas Andrew's experiment, consider the dome shaped saturation region. If we increase the pressure at constant volume until we reach the critical point, why does the density of vapours rise and the density of liquid fall? Moreover, why will the meniscus or the separation boundary of two phase sl... | Regarding your second question, it is intimately linked to the feature of scale invariance of critical phase transitions. Essentially what goes on is that a condensing vapour, within the coexistence region, forms droplets of some particular size (more precisely, a distribution of sizes with some particular scale), whic... | {
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Electrostatic charge leakage What are the ways electrostatic charged objects leak charge in humid conditions?
Can airborne particles pick up charge by contact, then be repelled hence removing charge? If so would it be a significant factor?
| There are two ways charge can leak in humid air. I'll give a basic description here, but I encourage you to Google around the area as you'll find lots of papers reporting measurements of conductivity of humid air and charge leakage in humid air.
The first leakage mechanism is that in the presence of water vapour virtua... | {
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Partition function of a gas of $N$ identical classical particles Partition function of a gas of $N$ identical classical particles is given by
$$ Z~=~\frac {1}{N! h^{3N}} \int \exp[-\beta H(p_1.......p_n, x_1....x_n)]d^3p_1...d^3p_n,d^3x_1...d^3x_n $$
in this above equation we use $N!$ as the total number of sub-systems... | Notice that the $e^{-\beta H}$ is dimensionless, while each factor of $dp$ contributes one factor with the dimensions of momentum while each $dx$ contributes one factor with the dimensions of length. Therefore each factor $dp dx$ contributes a factor with dimensions of angular momentum. Since there are $3N$ of these ... | {
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How accurate are our calculations about distant stars keeping in mind their enormous distances? Since many stars are hundreds of light years away from the Earth and therefore, what we observe of them today is really their distant past, how can we say anything with certainty about their composition, size and nature? Bet... | What we infer about stars from the light we see at the Earth is indeed "old news". However, for almost all practical purposes in stellar astrophysics this doesn't matter. The phases of a star's life last millions or billions of years and most of the individual stars that are studied are within say 30 thousand light yea... | {
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Amplitude of Probability amplitude. Which one is it? QM begins with a Born's rule which states that probability $P$ is equal to a modulus square of probability amplitude $\psi$:
$$P = \left|\psi\right|^2.$$
If I write down a wave function like this $\psi = \psi_0 e^{i(kx - \omega t)}$, I find $\psi_0$ inside.
If $\psi... | $\psi_0$ is the initial amplitude and $\psi$ is the amplitude after some amount of time (or more appropriately, the amplitude after some change in spacetime coordinates). The function you have provided: $\psi=\psi_0e^{i(kx-\omega t)}$; is a function of space and time. So it tells me that given some initial function $... | {
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What is the proof that a force applied on a rigid body will cause it to rotate around its center of mass? Say I have a rigid body in space. I've read that if I during some short time interval apply a force on the body at some point which is not in line with the center of mass, it would start rotating about an axis whic... |
What is the proof of this?
The proof of Chasles’s Theorem relating to the rotational and translational displacements of a rigid body is done in very many texts including Appendix 20A of this document produced by MIT.
In essence this shows that, if a force whose line of action does not pass through the centre of mas... | {
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Lorentz transformation of classical Klein–Gordon field I'm trying to see that the invariance of the Klein–Gordon field implies that the Fourier coefficients $a(\mathbf{k})$ transform like scalars:
$a'(\Lambda\mathbf{k})=a(\mathbf{k}).$
Starting from the mode expansion of the field
$$\phi'(x)=\phi(\Lambda^{-1}x)=
\int ... | The important insight is that it's actually the whole combination
$$
\frac{d^3 k}{2(2\pi)^3 E_\mathbf k}, \qquad E_\mathbf{k} = \sqrt{\mathbf k^2 + m^2}
$$
that forms a Lorentz-invariant measure. To see this, note that if we define $k= (k^0, \mathbf k)$ and use the identity
$$
\delta(f(x)) = \sum_{\{x_i:f(x_i) = ... | {
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Confused over complex representation of the wave My quantum mechanics textbook says that the following is a representation of a wave traveling in the +$x$ direction:$$\Psi(x,t)=Ae^{i\left(kx-\omega t\right)}\tag1$$
I'm having trouble visualizing this because of the imaginary part. I can see that (1) can be written as:$... | In short, “a wave traveling in the $+x$ direction” has nothing to do with actual motion of a wave packet. In spite of some mathematical similarities, wave function isn’t anything physically like a gravity wave on water surface. In quantum “waves”, there is no water (or gas, other 3D continuum, string, or anything else ... | {
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How do we make symmetry assumptions rigorous? I have, for instance, a problem with a spherically symmetric charge distribution. I deduce here, in order to solve the problem easily, that the corresponding electric field must be symmetric. How is this type of deduction rigorously justified?
| Let me first answer this question in a particular class of electrostatics problems.
In the case of a localized charge distribution in electrostatics (one in which the charge density vanishes outside of some ball around the origin), the general solution for a potential that vanishes at $\infty$ is
$$
\mathbf \Phi(\mat... | {
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Changes in Water Bonding Angle I heard something recently in a casual discussion, but have yet to be able to confirm it: is there any evidence that the bonding angle for a water molecule, currently defined as 104.5, has been either steadily growing or shrinking since it was first observed and measured? Is there any pos... | No, there has been no change to the bond angle of pure water,1 nor does anyone expect to measure one. The reason is this angle is set by fundamental physical constants - things like the mass of the proton and the speed of light - albeit in a complicated way. Such things are called constants for a reason. Now there are ... | {
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Usage of Schrödinger equation vs Madelung equations It is well known that Madelung formulation is alternative to the Schrödinger Formulation, cf. this previous Madelung transformation Phys.SE post. I wanted to know what makes Schrödinger's formulation superior to that of Madelung, and in particular, when does the Madel... | This is a translation from the German Wikipedia entry about the Madelung equations:
Due to their non-linearity, the Madelung-equations are difficult to use in practise. However, they show that there exist non-linear equations that are based on linear equations.
Hope this helps.
| {
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Internal/Rotational angular momentum I have some difficulties to understand the relation between the internal and the rotational angular momentum of a rigid body which is also known as König's theorem, so what physical intuition lies behind this equation? (I googled it but I can't find anything, so I will also apprecia... | König's theorem is essentially a statement of conservation of angular momentum. If you consider the angular momenta of a system of particles, they had better add up to the same value no matter what frame you consider, provided that you are computing the angular momentum about the same fixed point in space. In a fixed... | {
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Water-cooled fast neutron reactors Can anyone explain why fast neutron reactor designs use sodium/lead/salt cooling, instead of water (heavy/light)?
Is that because neutron absorption by water would not allow to break even in fuel cycle?
Will heavy water help here?
Or water slows neutrons so efficienly so that even if ... | Please see a discussion of advantages and drawbacks of sodium cooling in fast neutron reactors at http://en.wikipedia.org/wiki/Sodium-cooled_fast_reactor . You mentioned one of the advantages: neutrons slow down much less in collisions with sodium nuclei than in collisions with hydrogen nuclei of water.
| {
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What would the collision of two photons look like? Could someone explain to me what the collision of two photons would look like? Will they behave like,
*
*Electromagnetic waves: they will interfere with each other and keep their wave nature
*Particles: they will bounce like classical balls
I assume that energy o... | By time symmetry, two photons with sufficient mutual energy necessarily are capable of annihilating each other to produce an electron-positron pair, since one of the decay modes for positron-electron annihilation is the production of two gamma photons. It's just harder to arrange experimentally, since unlike the electr... | {
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Difference between torque and moment What is the difference between torque and moment? I would like to see mathematical definitions for both quantities.
I also do not prefer definitions like "It is the tendancy..../It is a measure of ...."
To make my question clearer:
Let $D\subseteq\mathbb{R}^3$ be the volume occupie... | moment is turning effect produced by a force . while torque is due to rotation of body.
| {
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Can we make images of single atoms? I was wondering how far in imaging physics had gotten. Do we hold the technology to actually take a picture of, say, an alpha particle, or even a single atom?
I realise we aren't talking about camera pictures, so what kind of imaging techniques have taken images/is most likely to be ... | We can, and have, taken "pictures" of individual atoms in materials.
One example is this image taken at IBM :
Each dot is a single atom that was placed on the substrate. You can find similar images taken by IBM here.
This image was made using a technique called "Scanning Tunneling Microscopy" (STM) which relies on qua... | {
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What happens to string theory if spacetime is doomed? What is expected to happen with string theory, if physics is reformulated according the lines hinted at by the twistor-uprising business discussed in this question and its answers for example and spacetime is doomed, as Nima likes to say?
Will it be incorporated int... | My earlier impression that Nima's slogan "spacetime is doomed" could potentially lead to a reformulation of string theory, is wrong and an overinterpretation of Nima's very enthusiastic comments. As Lumo says in his nice clarifying comments, it is rather the other way round and "spacetime is doomed" is in fact a result... | {
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Proper notation for normalized scalar? I have not been able to find a resource to tell me the standard notation for a normalized scalar value. Normalized vectors (i.e. unit vectors) are typically denoted by placing a hat over the variable, something like:
$${\bf \hat{e} = \dfrac{e}{||e||} }$$
However, does the same a... | I know in electrical engineering, particularly in power transmission fields, sometimes people use the so-called per-unit system, where quantities are normalized to the corresponding base value. Sometimes, subscript like $U_{\text{p.u.}}=\frac{U}{U_0}$ ($U_0=U_{\text{base}}$) is used. I don't think there are any proper ... | {
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Why is electric potential scalar? I can't conceptually visualize why it would be so. Say you have two point charges of equal charge and a point right in the middle of them. The potential of that charge, mathematically, is proportional to the sum of their charges over distance from the point ($q/r$). But intuitively, my... | Suppose in a equilibrium system where two negative charges is accompanied by one positive test charge in the middle. Here the resultant electric field at the centre is zero. Due to opposite and equal electric line of force from two negative charges but to bring that test charge from zero potential to the middle some wo... | {
"language": "en",
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Whistle Physics I'm looking for a simple explanation of how a whistle operates. I know that forcing air over a sharp lip can set up a wave in a resonating cavity, but how? "Most whistles operate due to a feedback mechanism between flow instability and acoustics"--yes, but what does that feedback mechanism look like?
... | Air in a chamber resonates like a spring: It has mass and springs back when compressed or decompressed. When air is blown across the opening, and slightly down, it will push the air inside down & cause a disturbance which will cause the air inside to start to resonate. As it resonates down, it deflects the air stream d... | {
"language": "en",
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How is possible for current to flow so fast when charge flows so slow? How is it possible for current to flow so fast when charge flows so slowly?
We know electrons travel very slowly while charge travels at ~the speed of light.
| It seems you are contrasting the speed of propagation of current with the speed of the individual charge carriers.
These two things are clearly separate. There are many examples. Consider sound.
A fire cracker goes off at the other end of a football field from you. You hear the sound a few 100 ms later. The air mol... | {
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How does positive charge spread out in conductors? I know that when there are excess positive charges in a conductor, for example, a metal sphere, the positive charges will spread out over its surface. However, I am confused about how this excess charge spreads out over the surface, if protons cannot move and only elec... | For a conductor to display positive charge it means that some of the electrons have been removed from it. The positive charge displayed homogeneously on the conductor's surface is the result of charge balance, between the positive stationary charges of the surface atoms and the negative charge of the electrons.
Becau... | {
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Can a black hole bounce? Is there a limit to the amount of matter that a black hole can accrete per second and if so could a certain sized black hole bounce off a dense enough surface?
| Look, there's no limit to the accretion because the blackhole simply starts growing as it accretes more mass. I don't think it can "bounce off" any surface.
Yes, if the gravitational forces are comparable, for example, if it encounters another black-hole, they can get in equilibrium, bounce off each other or simply mer... | {
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Cylindrical wave I know that a wave dependent of the radius (cylindrical symmetry), has a good a approximations as $$u(r,t)=\frac{a}{\sqrt{r}}[f(x-vt)+f(x+vt)]$$ when $r$ is big. I would like to know how to deduce that approximation from the wave equation, which is this (after making symmetry simplifications):
$$u_{tt}... | Use the following identity:
$$ r^{-\alpha} \partial^2_{rr} \left( r^\alpha f(r) \right) = f_{rr} + \frac{2\alpha}{r} f_r + \frac{\alpha(\alpha - 1)}{r^2} f $$
Now, by inspection and comparing the above equation to the cylindrical wave equation you have that
$$ u_{tt} - \nu^2(u_{rr} + \frac1r u_r) = u_{tt} - \nu^2 \left... | {
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Maxwell Stress Tensor in the absence of a magnetic field I'm having some trouble calculating the stress tensor in the case of a static electric field without a magnetic field. Following the derivation on Wikipedia,
*
*Start with Lorentz force:
$$\mathbf{F} = q(\mathbf{E} + \mathbf{v}\times\mathbf{B})$$
*Get force d... | The stress tensor is defined in such a way that taking its divergence brings you back to the force density (apart from the cross product term which corresponds to the time derivative of the Poynting vector). In the case of $\mathbf{B}=\mathbf{0}$, we take the divergence in index notation, i.e.
$$f_j=\partial_i\sigma_{i... | {
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Why is there no time dilation for frequency of a wave? Since frequency of a wave is a function of time, then for a particular ray of the wave, why would the frequency remain the same when observed from a moving reference frame? The frequency should change according to time dilation. No?
| Both the the frequency and wavelength change. Obviously so because $\nu\lambda = c$ and $c$ is a constant. If you have a specific example of where you think the frequency doesn't change update your question with the details and I'll update my answer to address it.
| {
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How does my car acquire satellite signal? I just got XM radio again after a brief period without it. A customer service rep said that the satellite needs to beam my signal to me in a six minute time window. How exactly does this happen? How does the satellite know where to find me, and how exactly does it "talk" to my ... | It doesn't find you - XM uses three (IIRC) satellites in geostationary orbit as long as you are on the right continent you should get a signal.
I'm guessing that the six minutes is something to do with ensuring your receiver is authorized . Presumably it broadcasts some sort of key that unlocks your receiver when you p... | {
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How to evaluate commutator with angular momentum? I need to evaluate the commutator $[\hat{x},\hat{L}_z]$. I believe the $L_z$ is referring to the angular momentum operator which is:
$L_z = xp_y - yp_x$
using this relationship i end up with:
$[x,L_z] = x(xp_y - yp_x)-(xp_y - yp_x)x$
my next step is substituting in for ... | I'll help you with a general solution. First, you can write the angular momentum as $L_{i}=\epsilon_{ijk}x_{j}p_{k}$. Where $e_{ijk}$ is the Levi-Civita symbol. Now write a general commutator as $[x_{l},L_{i}]$ where $l,i$ run from 1 to 3. With this you have
$[x_{l},L_{i}]=[x_{l},\epsilon_{ijk}x_{j}p_{k}]$
Now, you us... | {
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What is potential energy in special relativity? I know what is rest energy $E_0=m_0 c^2$, total energy $E=\gamma E_0$, kinetic energy $E- E_0=(\gamma-1) E_0$, and momentum $p=\gamma m_0 c$. But what is potential energy in special relativity?
| Special relativity doesn't alter the fact that interactions between particles "store energy" in the form of "potential energy," alhtough special relativity does alter the terms you listed, all of which have to do with the energies possessed by particles either by virtue of their motion, or their mass.
For example, in s... | {
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Relation between the determinants of metric tensors Recently I have started to study the classical theory of gravity. In Landau, Classical Theory of Field, paragraph 84 ("Distances and time intervals") , it is written
We also state that the determinanats $g$ and $\gamma$, formed respectively from the quantities $g_{ik}... | *
*Consider the $4\times 4$ matrix $g_{\mu\nu}$ with zeroth row $g_{0\nu}$.
*Now for $i=1,2,3$, add to the $i$'th row the zeroth row times $-g_{i0}/g_{00}$.
*This produces the following matrix
$$\begin{bmatrix}
g_{00} & g_{01} & g_{02}& g_{03} \\
0 & -\gamma_{11} & -\gamma_{12}& -\gamma_{13} \\
0 & -\gamma_... | {
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Parallel circuits - Overall resistance decreases with additional resistor Let's say that there is a parallel circuit with two identical resistors in parallel with each other. If a third resistor, identical to the other two, is added in parallel with the first two, the overall resistance decreases.
Why does this overa... |
Why does this overall resistance decrease?
A more elegant, sophisticated way to see why is through the notion of duality.
In electric circuit theory, conductance (the reciprocal of resistance) is dual to resistance. Other dual pairs are:
voltage - current
series - parallel
inductance - capacitance
Thevenin - Norton
... | {
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spectral functions Please, I would like to understand why you call the function $A(k,\omega)$ (here :The Spectral Function in Many-Body Physics and its Relation to Quasiparticles ) a spectral function? For me, as a mathematician, a spectral function is a function which writes : $F(S)=f( \lambda(S))$ where for example $... | If you perform spectroscopy on a material (be it angular resolved photoemission spectroscopy (ARPES) or scanning tunneling spectroscopy (STS) or whatever method you fancy), the quantity you measure is roughly related to $A(k,\omega)$ (with additional prefactors and matrix elements depending on your method of choice.
T... | {
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What is the effect of refractive index of an object for imaging? My Question is as follows.
What is the effect of refractive index of an object for imaging (Photographs by high speed camera) on its size and shape information incurred from image?
Lets say ,
I keep the camera focal length, aperture, distance between cam... | A while back I did an experiment imaging oil droplets in water, where we used oils of differing refractive index. Is this the sort of thing you're interested in?
If so, assuming your camera is in focus it will accurately record the size of the oil droplet so varying the refractive index will not cause the apparent size... | {
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Absolute zero and Heisenberg uncertainty principle I got to read Volume I of Feynmann's lectures. It said that at absolute zero, molecular motion doesn't cease at all, because if that happens, we will be able to make precise determination of position and momentum of the atom. We do know that Heisenberg uncertainty prin... | Motion does not cease at absolute zero if the system you are looking at has a zero point energy.
In many systems, e.g. crystals, at low temperatures the atoms/molecules behave as harmonic oscillators, and the energy of a harmonic oscillator cannot be reduced to zero: there is always some minimum energy called the zero ... | {
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A thought on definition of momentum Well, this is a simple, basic and I think even silly doubt. The first time I saw the definition of momentum as $p = mv$ I started to think why this is a good definition. So I've read the beginning of Newton's Principia where he said that momentum is a measure of quantity of motion.
W... | It's a good question! Physics is all about linking your intuition to science, so it's good that you're thinking about this. The statement that momentum should be proportional to mass and velocity is intuition. Like elfmotat says, you can choose your constant as long as it's consistent with units, I guess.
If you want ... | {
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Why is electrical energy so difficult to store? Does anyone know a general answer to these questions? (I've asked them together because they're all pretty related, it seems.)
*
*Why is it that we find electrical energy so difficult to store? Do we just find energy difficult to store generally? (...surely not, we can... | We need to create a battery that would instantly store a large amount of electricity at one time. Ex. When a bolt of lighting strikes it gives off a very large amount of power. However a battery needs time to take that energy and change it over to a chemical for storage.
Lets say a bolt of lightning is 500 gallons o... | {
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How to determine the direction of a wave propagation? In the textbook, it said a wave in the form $y(x, t) = A\cos(\omega t + \beta x + \varphi)$ propagates along negative $x$ direction and $y(x, t) = A\cos(\omega t - \beta x + \varphi)$ propagates along positive $x$ direction. This statement looks really confusing bec... | Here is (in my opinion) an easier answer. I'm sure you know that the line y = x crosses the x-axis in the origin (0, 0). Now we shift the entire line to the right in such a way that it crosses the x-axis in the point (1, 0). The consequence of this is that the function of the line changes. It becomes y = x - 1. Here is... | {
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Proof that flux through a surface is independent of the inner objects' arrangement $$\Phi=\iint_{\partial V}\mathbf{g} \cdot d \mathbf{A}=-4 \pi G M$$
Essentially, why is $\Phi$ independent of the distribution of mass inside the surface $\partial V$, and the shape of surface $\partial V$? That is, I'm looking for a mat... | Its because the divergence is undefined at the origin and 0 everywhere else. Thus as long as the volume you integrate over contains the origin, it doesn't matter what region you integrate over.
| {
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Calculating the mass equivalency of a song? I've recently become fascinated with the idea of sound energy having a theoretical equivalent mass. I've read over this thread:
Do light and sound waves have mass
I understand this part: $m_{eq}=E/c^2$ and $E=A\rho \xi^2\omega^2$
Where I am getting tripped up is the way to me... | You could also set an upper bound if you know the phone's battery capacity (usually written on the battery) and how long you get out of a full charge playing the song on repeat. You can estimate the energy required to play the song by
$$ \text{Energy per song} = \text{Battery capacity} \times \frac{\text{Song length}}{... | {
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Am I properly identifying the resistor terminal voltage?
The frequency applied to a circuit of voltage 120 V with a real coil and a resistor has a value of 50 Hz. The resistance of the resistor is 10 $\Omega$. The voltage at the resistor terminals $u_1=60V$. The voltage at the coil's terminals is $u_2=90V$.
$$\nu=50\... | Ok , it was a nice one.!
Let's consider the real inductor as a pure inductor plus resistance pair.
the value of I(rms) can be get using the Pure resistor outside this pair,
U=I(rms)*R2 ; r2=10;
I(rms)=6;
Now potential drop across real inductor Ulr (90) , across pure inductor Ul and across resistance Ur are pytha... | {
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Weak isospin and types of weak charge My understanding is that QCD has three color charges that are conserved as a result of global SU(3) invariance. What about SU(2) weak? Does it have two types of charges? What I'm getting at is:
U(1) --> 1 type of charge
SU(2) --> ?
SU(3) --> 3 types of charge
Does SU(2) have two ty... | @Michael Brown is right. The SM has 12 exactly conserved currents.
*
*All local invariances, a fortiori also imply global invariances, if you ignore (for the sake of argument) the spacetime variability of transformation parameters/angles. So SU(3) has 8, not 3 conserved charges, RG, BG, .... The group has 8 generator... | {
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Inertial Frames of Reference - Description of an Inertial Frame of Reference An inertial frame of reference is described as being a frame of reference in which the first law of Newton (the law of inertia) holds. This means that all events as described with respect to this frame of reference must have a zero net force a... |
all events as described with respect to this frame of reference must have a zero net force acting on it
This is wrong: there may exist nonzero forces in an inertial frame of reference. These have to obey Newton's laws. If the forces do not obey Newton's laws in your frame of reference, then it is not an inertial fram... | {
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Number of configurations of the universe I have read that quantum mechanics says that the amount of possible particle configurations is $10^{10^{122}}$ to be exact in the universe. Do we know this figure to be exactly true to the exact figure? Wouldn't we need to know a true theory of quantum gravity to know the exact ... | This is clearly an estimate, not an exact figure. It comes from ideas about quantum gravity (not proven but very strong conjecture) that say that the maximum entropy of a region is
$$ S = \frac{A}{4 \ell_P^2}, $$
where $A$ is the area of a surface bounding the region and $\ell_P \approx 10^{-35}\ \mathrm{m}$ is the Pla... | {
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does a rotating moving body in "flat" space curve its path because of frame dragging? I am not a physicist.
let's say we have a space with an object in it, where all other gravitational bodies are so far away that their affect on the shape of the space is negligible.
let's say the object is moving, and rotating such th... | The object doesn't move relative to fixed space--there is no fixed space per special relativity--so forget that. The question is "why is there frame dragging?": because there is normal Newtonian-like gravitational attraction, and you need the frame-dragging field to make the whole thing relativistically invariant--that... | {
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Electronic filter Can you explain, please, step-by-step how an electronic filter does work?
For example, high pass filter. I know It's a trivial things, but I can't get it completely. Don't bring me formula and etc. Just explanation in three words.
| A SIMPLE HIGH PASS FILTER: T-CONFIGURATION - no maths
For a high pass filter you can have a resistor with resistance $R$, and two capacitors with capacitance $C$, with the capacitors connected to the resistor which is grounded at one end. When a signal is entering the filter from the left, the high harmonics in the sig... | {
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Electrical conductivity of an intrinsic semiconductor On which factor does the electrical conductivity of an intrinsic semiconductor depend? It doesn't have an excess of charge carriers in fact, does it?
| Electron and hole generation takes place when a bond breaks.
Average energy of these particles under thermal equilibrium is $KT=0.026\,eV$.So when a semiconductor block sits at room temperature its average energy is KT. But to break a Si-Si bond we need 1.1eV of energy. So if we want to break a silicon bond we have to... | {
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Weyl Ordering Rule While studying Path Integrals in Quantum Mechanics I have found that [Srednicki: Eqn. no. 6.6] the quantum Hamiltonian $\hat{H}(\hat{P},\hat{Q})$ can be given in terms of the classical Hamiltonian $H(p,q)$ by
$$\hat{H}(\hat{P},\hat{Q}) \equiv \int {dx\over2\pi}\,{dk\over2\pi}\,
e^{ix\hat{P} + ik\hat... | The basic Weyl ordering property generating all the Weyl ordering identities for polynomial functions is:
$$
((sq+tp)^n)_W = (sQ+tP)^n
$$
$(q, p)$ are the commuting phase space variables, $(Q, P)$ are the corresponding noncommuting operators (satisfying $[Q,P] = i\hbar $).
For example for n = 2, the identity coming fro... | {
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How does the solar sailing concept work? Wikipedia describes solar sailing as
a form of spacecraft propulsion using a combination of light and high speed ejected gasses from a star to push large ultra-thin mirrors to high speeds.
I understand the part where ejected gasses bump into the sail pushing the spacecraft. O... | Light is an electromagnetic wave. When light arrives at a solar sail the electric and magnetic fields that make up the light accelerate the electrically charged partciles in the atoms of the sail, after all, that's what electric and magnetic fields do. If these particles are accelerated their momentum is changed and so... | {
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Cantilever Beam - Maximum Shear of the Beam
A cantilever beam $3\ \text{m}$ long is subjected to a moment of $10\ \text{kNm}$ at the free end. Find the maximum shear of the beam.
The answer is "There is no vertical load, shear is zero"
How come? The shear should be sliding upward at the end of the wall and downward t... | The answer is "no vertical load, the shear is zero" because the moment on the end of the cantilever beam only creates a bending moment on the beam which results in only a normal force on the beam and no shear force.
| {
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How can a massless boson (Gluon) mediate the short range Strong Force? I thought massless particles were mediators for long range forces such as electromagnetism and gravitation. How can the massless gluon mediate the short range strong force?
| Unlike photons, gluons carry the "charge" of the strong force (confusingly, it's called "color"). This means that, unlike photons, gluons interact with each other. The effect is that, rather than spreading out in all directions (as photons do), gluons tend to stick together and form strings. For example, two quarks ... | {
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kinetic energy of the stone Suppose we have a man traveling in an open car (roof open) with speed $v$ towards right (man faces right). He throws a stone (mass $m$) towards right, in his frame-forward with speed $V$.
In the car's frame, the total energy imparted to it was $$E=E_f-E_i=\frac{1}{2}mV^2$$
In the ground fr... | You are not wrong. The only thing that may be wrong, is the interpretation. Energy is a conserved quantity, but only within an inertial reference frame. If you change to another reference frame, the energy will also be different. This is what you calculated.
Suppose you throw two rocks with the same velocity $V$. The f... | {
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Out of phase voltage current source and resulting power Examining the following graph, I am trying to understand the power plot. The power appears to take on a negative value when the current changes direction or the voltage changes polarity. Negative power does not make sense to me. In a proper representation of the p... | Now to answer your question, first I want to point out what $V$ and $I$ should be representing. The negative values of these functions represents the change in the direction of either the electric field $E$, or the current density $J$, which is a vector with a magnitude of current per unit volume.
Now if you think abou... | {
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Why does tea rise in the pot but water doesn't? I was wondering when I boil water in a pot it only shakes too much while boiling. But I could not figure out why tea rises in the pot when we boil it. It is also a liquid but it starts rising up till it jumps out of the pot and tries to kill the flame.
I think this happe... | The phenomenon at play here is foaming. Due to the heat the water will start to boil. In normal water this will result in small bubbles that pop quickly. When you add milk, you create a mixture which has the ability to foam due to proteins and surfactants present in the milk. This foam will rise up the pan and eventual... | {
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Smaller Airy disk with another lens? Is it possible to reduce the airy disk size produced by one lens with another lens placed after the previous one? For example, parallel ray incident on first lens L1 (without aberration), then there is Airy disk on the back focal plane of L1, if image this pattern by another lens, h... | Airy disk intensity is described by
$$I(r) = \left(
\frac{ 2 \cdot J_1(v) }{v}
\right)^2
\qquad \text{ with } v= \frac{2\pi}{\lambda}r\cdot NA
$$
The Bessel function $J_1(v)$ of first kind has a first minimum at
$$J_1(3.832) = 0$$
$$ \Rightarrow r_{\text{min}}=0.61\cdot \frac{\lambda}{NA}$$
At a given wavelength, the ... | {
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Conservation of Angular momentum in the dipole selection rules If the total angular momentum J of an atom is not changing during a dipole transition, where does the angular momentum for the photon come from?
| One must distinguish two conditions: whether the eigenvalue of $|\vec J|^2$, the squared total angular momentum, is changing; and whether the whole vector $\vec J$ is changing.
The latter is guaranteed in a dipole transition: one can't keep the whole vector constant. At most, you may satisfy the former condition: the l... | {
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Will molten iron stick to a magnet? I've known for a long time that if you heat a magnet, there is a point it loses its magnetism (the Curie temperature). It isn't clear to me if this applies to induced magnetism like iron sticking to a magnet.
Will molten iron behave like a ferrofluid and be attracted to a magnet or ... | If the metal heats up the magnet above around $500^\circ\mathrm F$ the magnet will lose it magnetic characteristics, and will not regain those properties when it cools down.
| {
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Derivation of $ E=h\nu$ Is it possible to derive the relation $ E=h\nu$ from Schrodinger equation or the basic principles of quantum mechanics or is it something which is considered to be an axiom with no explanation?
| No. The Schrodinger equation tells you how the state of a quantum system evolves, this is not specific to photons, and cannot be used to derive any facts about them. I'm assuming that by "basic principles" you mean the postulates of quantum mechanics that hold for every quantum system (like Born's rule etc.) in which... | {
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Why do objects accelerate as they fall? Most importantly, what must change in order for the falling object to change its speed? Is it the distance to the centre of the planet? If you pull the earth away from the object as the object falls, will the object slow down or will it keep accelerating?
| As long as there's a non-zero net force acting on the object, it will have a non-zero acceleration and therefore it will continuously change its velocity: $$\vec{F} = m\vec{a}.$$
In the case of gravity, the force is inversely proportional to the distance between the objects squared: $$\vec{F}_G = G\frac{m_1m_2}{r^2}\fr... | {
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Third-order phase transition in Landau theory $F=\frac{a}{2}m^2+\frac{u}{4}m^4+\frac{v}{6}m^6-hm$, where $F$ is the free energy, $m$ is the order parameter, $h$ is the external field, $a=a_0(T-T_c)$, and $a_0>0,u>0$ and $v>0$.We know this free energy expansion describes a second-order phase transition. How to write dow... | Although third-order transitions are rare to see, but it is not hard to write down Landau theory for third-order transitions. Let $m$ be the order parameter, the free energy simply reads
$$F=a m^4+ b m^6+\cdots$$
with $b>0$, and $a$ is the driving parameter, which triggers a third-order transition at $a_c=0$. To verify... | {
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Indistinguishable particles in quantum mechanics If you have two particles of the same species , Quantum mechanics says that $\Phi_{m_{1},x_{1},p_{1},m_{2},x_{2},p_{2}}=\alpha\Phi_{m_{2},x_{2},p_{2},m_{1},x_{1},p_{1}}$
But I don't understand why $\alpha$ doesn't depend on $x$ , $p$ . If $\alpha$ depends on $SO(3)$ inva... | Let us step back for a moment to answer your question.
We consider a system of $n$ indistinguishable particles. What does that mean ?
Let $S_n$ be the set of all permutations of $n$ elements, and let $\sigma \in S_n$. Then if $P(\sigma)$ is the (unitary) operator representing $\sigma$ on the $n$-particles Hilbert space... | {
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Why doesn't fusion contradict the 1st law of thermodynamics? I was reading up on the 1st law of thermodynamics for my Chemistry exam and I was wondering why doesn't fusion contradict the 1st law of thermodynamics?
The 1st law states that
The energy of an isolated system is constant
or that whatever is put into the s... | To answer the question simply, $E=mc^2$.
Energy is a manifestation of mass, and mass is a manifestation of energy. In a fusion or fission process, the total "energy" of the system remains constant, it just changes shape.
By "energy" I mean the totality of the already present energy, and the bound energy of the mass tha... | {
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Elastic collision of rotating bodies How would you explain in detail elastic collision of two rotating bodies to someone with basic understanding of classical mechanics?
I'm writing simple physics engine, but now only simulating non-rotating spheres and would like to step it up a bit.
So what reading do you recommend... | I worked on a physics engine written in C# that does just this.
Here are my notes on this topic.
Objects have both translational and rotational momentum.
When two objects collide, the overall algorithm goes like this:
1> Find the total momentum of both objects. Calculate the translational and rotational momentum, the... | {
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The rule breaker, emissivity + reflectivity = 1 If emissivity and reflectivity are inversely proportionate, why does glass have a high emissivity of around 0.95-0.97 as well as being very reflective for IR Radiation?
normally it works but not with glass!
Can anyone explain this?
| The law of energy conservation certainly also applies here. What is not reflected will be absorbed. R+A=1 has to hold. And according to Kirchoff's law E=A (absorptivity is emissivity) you could write R=1-E.
If you have to consider transmission through the glass as well, then R+A+T=1 would hold.
You do not specify what ... | {
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A water balloon in vacuum: does it boil? If I put water in a vacuum it will boil. But what if I put this water inside a balloon ?
I searched for answers and fount this video: http://www.youtube.com/watch?v=9q8F3ClUuV0
It appears that the water isn't boiling but I am still not satisfied. The vacuum on the video could be... | Water boils when the pressure is less than its vapour pressure (there is a table of vapour pressure vs temperature here).
At 20ºC the vapour pressure is 2339Pa, so if your balloon exerts a pressure greater than this the water won't boil. If the pressure exerted by the ballon is less than this, the water will start to b... | {
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Special Relativity - speed of light question Just a basic question:
I know that if you are traveling at $x$ speed the time will pass for you slower than to an observer that is relatively stopped. That's all just because a photon released at the $x$ speed can't travel faster than the $c$ limit.
I want to know what happ... | Yes, every observer who makes a local measurement of the speed of light will get the same result, i.e. $c$, regardless of where the light came from.
I've used the word local because in general relativity the speed of light can differ from $c$ if it's not measured at your location. The most famous example of this is pro... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/60043",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
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How does a thermal temperature gun work? I once worked as a kitchen porter over a winter season.
We had fun with thermal temperature guns (like these) which I learned can be used for measuring the temperature of something a reasonable distance away (aside from the obvious use of laser tag), which to my mind is pretty i... | They basically measure the intensity of the infrared blackbody radiation in some wavelength region and calculate the temperature needed to give that intensity according to Planck's law.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/60115",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
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