Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
What is a good introductory book on quantum mechanics? I'm really interested in quantum theory and would like to learn all that I can about it. I've followed a few tutorials and read a few books but none satisfied me completely. I'm looking for introductions for beginners which do not depend heavily on linear algebra o... | OK.
First, you need a some comfort in Linear Algebra.
Go to the MIT Open Courseware site and watch the Linear Algebra lecture (videos) by Strang. These are great.
Next, watch the "Theorectical Minimum" videos by Leonard Susskind . They represent the theoretical minimum that you need to know about quantum mechanics. (i... | {
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Must all symmetries have consequences? Must all symmetries have consequences?
We know that transnational invariance, for example, leads to momentum conservation, etc, cf. Noether's Theorem.
Is it possible for a theory or a model to have a symmetry of some kind with no physical consequences at all for that symmetry?
| If there is a continuous symmetry of the action, it is necessary to take the quotient by the symmetry--gauge fix it--when quantizing. One way to see this is to just consider perturbation theory. The quadratic coupling in the Lagrangian will be constant along the flow of the symmetry, so it will be have degenerate deriv... | {
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Electrial Conductivity of Thin Metal Films What is the best way to find specific/electric conductivity which is dependent of very thin film thickness?
| Your problem is that the conductivity depends on the film structure. Back in the dawn of time (mid 1980s!) I spent a happy three years studying reactions of silver films, and one of the techniques used was to measure the resistance of the film. As the silver reacted the film thickness went down and the resistance went ... | {
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What's up in this SPAWAR video? Here is a video presentation of infrared recordings of anomalous heating in a deuterium palladium cell: ( youtube video) (see also this presentation if you want more detail, and have time). There are two papers referenced in the link, which give more detail. You can see with your own eye... | Without knowing anything about the experiment nor the camera, I would suggest that what is shown in the video is a combination of shot noise and aliasing due to a poor choice of gradient mapping. Note that the gradient bar at the bottom of the frame jumps from a fairly deep red (actually darker than precedent tones) to... | {
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Understanding Tensors I don't seem to be able to visualize tensors. I am reading The Morgan Kauffman Game Physics Engine Development and he uses tensors to represent aerodynamics but he doesn't explain them so I am not really able to visualize them. Please explain in very simple ways. I just want to understand the basi... | Following @peter4075, Fleische's book, A Student's Guide to Vectors and Tensors is a gold mine of clear, useful, practical explanation, by someone who clearly knows their topic. Highly recommended. I got it through my local library interlibrary loan program and am loathe to surrender it.
Good luck!
| {
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References for nuclear masses, mass deficits, decay rates and modes Where can I find the base data for computing the energy release of nuclear decays and the spectra of the decay products?
My immediate need is to find the energy release by the beta decay of Thorium to Protactinum upon receiving a neutron:
$$\mathrm{Th... | In addition to the LBL interactive table of the isotopes that John mentions in the comments, I get a lot of use1 out of their associated radiation search tool and the TUNL Nuclear Data Evaluation Project site.
In general there are several major efforts to collect and collate nuclear data that go under the heading "eva... | {
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Bound states in QCD: Why only bound states of 2 or 3 quarks and not more? Why when people/textbooks talk about strong interaction, they talk only about bound states of 2 or 3 quarks to form baryons and mesons?
Does the strong interaction allow bound states of more than 3 quarks?
If so, how is the stability of a bound s... | As a quick explanation: all bound states are color-neutral. The intuitive reason is that the strong interaction is so strong that it would pull any color-charged particles together. (Because the strong force increases with distance, you can't get around this by spreading out the charged particles, as you can with the E... | {
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Problems in the modern semiconductor/electronics technology? From what I have read, the problem with modern semiconductors/electronics seems to be quantum tunnelling and heat. The root of these problems is the size of the devices. The electrons are leaking out, and currents are causing active materials to melt.
How far... | The main solution is to give up Silicon altogether since it is very inefficient, compared to some of the compound semiconductors(such as GaAs). However, GaAs will eventually reach the same limitations. In any case, you can't really make a transistor from half an atom, therefore there are some physical limits as to how ... | {
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Is it safe to study from MIT and Berkeley course series, or they contain wrong information? After surveying most of the universities introductory physics courses, I found none is using Berkeley physics books or MIT physics books as textbooks. All are using Halliday, or Serway and the like.
What is the reason behind not... | It is a mistake to assume that the books that are standardized are the ones that are superior, or have fewer mistakes. Generally, they have fewer typos, because they get more exposure, but the rate of typos and errors in most undergraduate books is roughly constant across the board.
If you find that a school is using a... | {
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How to charge an object with electricity I know this is a rather basic question, but how do you charge an object? Not a battery, an object. I'm guessing it involves static electricity, but I'm not sure. Some resources I've been reading talk about charging two objects with opposing voltages, and I am trying to figure ou... | Are these not examples of static electricity charging?
*
*Combing dry hair with comb, the comb gets charged.
*A sweater worn for sometime...
| {
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Special Relativity Second Postulate That the speed of light is constant for all inertial frames is the second postulate of special relativity but this does not means that nothing can travel faster than light.
*
*so is it possible the point that nothing can travel faster than light was wrong?
| From a purely theoretical point of view, the Special Relativity (SR) is based on a space-time metric $$\eta=\begin{bmatrix}+&0&0&0\\0&−&0&0\\0&0&-&0\\0&0&0&-\end{bmatrix}$$
The most general transformation to preserve metric $\eta$ is global Poincaré group which is the limit of the de sitter group with sphere radius $R... | {
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mathematical explanation for UV divergences and $ \delta ^{(n)}(0) $ is there any mathematical explanation for the UV divergences ??
i have read that in the framework of Epstein-Glser theory :D these UV divergences appear from the product of distributions
anyone does the numbers (divergences) of the form $ \delta ^{(n)... | I think it's best to start from the works of Wilson and Kadanoff on the renormalization group of effective field theories with an ultraviolet regulator. They find the coefficients can be classified as relevant, marginal and irrelevant. UV divergences are what you get when you run the RG in the other direction.
| {
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What law of electro-magnetics explains this? I took my son to a science museum where they had a solenoid oriented vertically with a plastic cylinder passing through the solenoid. An employee dropped an aluminum ring over the top of the cylinder when there was no current going through the solenoid. Then they turned on ... | This sounds like a Thompson's Jumping Ring setup.
Turning on the solenoid creates an increasing magnetic field B. Maxwell's (Faraday's Law) tells us
$$\frac{-\partial B}{\partial t}=\nabla \times E$$
So the increasing B field produces an azimuthal E field "curling" around the aluminum ring and since the aluminum is a c... | {
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Applying velocity Verlet algorithm I want to implement a simple particules system using the velocity form of the Verlet algorithm as integrator.
Initial conditions at $t=0$ for a given particule $p$:
*
*mass: $ m $
*position: $\overrightarrow x(t=0) = \overrightarrow x_0$
*velocity: $\overrightarrow v(t=0) = \over... | I think you all your steps are correct, I would suggest adding units though, otherwise adding $\vec{x}$ and $\vec{v}$ can be misleading.
For step 3. You can just calculate $a = F/m$, where $F$ can either be gravitation $F=m g$, so it does not depend on $x$, or for example for a spring dependent on $x$, so $F = -k x$, h... | {
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Tips on teaching Dimensional Analysis? What's a good way to explain dimensional analysis to a student?
Here's a simple question which this method would be useful:
Let's say a truck is moving with a speed of 18 m/s to a new speed of 13 m/s over a distance of 48 meters. How long did it take for the truck to break to its ... | Since I could not figure out how to write a comment on your post, I will post it as an answer, even if it's just a link:
You can find some inspiring dimensional analysis examples here:
https://particlephd.wordpress.com/2008/12/08/dimensional-analysis-for-animals/ (see also the comments)
| {
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Hawking radiation and black hole entropy Is black hole entropy, computed by means of quantum field theory on curved spacetime, the entropy of matter degrees of freedom i.e. non-gravitational dofs? What is one actually counting?
| There are a multiplicity of ways of deriving the Hawking formula for black hole entropy. Some techniques, like Bekenstein's argument, do equate the entropy of matter falling into the hole with the entropy of the hole. Some actually count gravitational microstates in various quantum gravity schema. The result $S\prop... | {
"language": "en",
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How much does electromagnetic radiation contribute to dark matter? EM radiation has a relativistic mass (see for instance,
Does a photon exert a gravitational pull?), and therefore exerts a gravitational pull.
Intuitively it makes sense to include EM radiation itself in the galactic mass used to calculate rotation cur... | I found it surprisingly hard to find an authoritative statement of the density of the CMB. According to this article it's about $5 \times 10^{-34}\mathrm{g\ cm}^{-3}$, and since the critical density is somewhere in the range $10^{-30}$ to $10^{-29}\mathrm{g\ cm}^{-3}$ photons don't make a significant contribution.
Phot... | {
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The observation of a non-SM resonance at 38 MeV Was reported here. Of course if this is real it is very exciting. It leads me to the question: given that it took so long to find this resonance at a meager 38 MeV, is it possible that all SUSY particles are hiding down in the MeV or KeV range (or lower)?
| The paper has been retracted.
Due to non ordinariness of the obtained results (standing out of The Standard Model) and at the request of co-authors the first version of the article is withdrawn for further verification and more detailed description of the experiment and data analysis. The second version is being prepa... | {
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Why isn't Hawking radiation frozen on the boundary, like in-falling matter? From the perspective of a far-away observer, matter falling into a black hole never crosses the boundary. Why doesn't a basic symmetry argument prove that Hawking radiation is therefore also frozen on the boundary, and therefore not observable?... | Evaporating black holes behave qualitatively differently from static ones if you allow an infinite amount of time to pass. In particular, there is no event horizon for an evaporating BH, only an apparent horizon. Furthermore, if you stack the apparent horizons of a shrinking black hole plus time, the resultant surfac... | {
"language": "en",
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Why does heterodyne laser Doppler vibrometry require a modulating frequency shift? On the wikipedia article (and other texts such as Optical Inspections of Microsystems) for laser Doppler vibrometry, it states that a modulating frequency must be added such that the detector can measure the interference signal with freq... | The 'heterodyne' is based in the same principle used by the 'nonio' also called 'vernier' invented by the portuguese Pedro Nunes to increase the precision of measures of lengths. The principle is widely used also in telecomunications .
A visualization.
edit add:
If you ommit the Bragg Cell the Photo Detector, shou... | {
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What is the significance of action? What is the physical interpretation of
$$ \int_{t_1}^{t_2} (T -V) dt $$
where, $T$ is Kinetic Energy and $V$ is potential energy.
How does it give trajectory?
| The only real physical interpretation of this quantity is in quantum mechanics. This is the phase of a contribution from a path that goes from $t_1$ to $t_2$ along the path $x(t)$. The two terms then are relatively clear, when you exponentiate this to make a phase and make time a lattice:
$$ e^{i \int_{t_1}^{t_2} (T - ... | {
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Can double entanglement preserve correlations? We have 2 EPR experiments running in parallel, with Alice having one leg of each (a1,a2) and Bob the other leg of each (b1,b2). Thus (a1,b1) are anticorrelated, as are (a2,b2). Thus also (a1,a2) are uncorrelated as are (b1,b2). Now Alice locally entangles (a1,a2), and Bob ... | It's clear from no signalling--- by entangling $a_1$ and $a_2$, Alice uses local operators which necessarily commute with the spin operators on $b_1$ and $b_2$, so the reduced density matrix for $b_1$ and $b_2$ stays completely random. It makes no difference what method Alice uses, unless it involves mucking around wit... | {
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Why is current not 0 in a regular resistor - battery circuit immediately after you closed a circuit? In regular open circuits with either a capacitor or inductor element, (when capacitor is uncharged) with a battery, when a switch is closed to complete the circuit the current is said to be 0 because current doesn't jum... | This is really a footnote to user1631's answer: even in the absence of any inductance the current obviously can't change instantly because no signal can propagate faster than the speed of light. In typical circuits the increase in current propagates somewhere between $0.1c$ and $c$.
| {
"language": "en",
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Black-holes are in which state of matter? Wikipedia says,
A black hole grows by absorbing everything nearby, during its life-cycle. By absorbing other stars, objects, and by merging with other black-holes, they could form supermassive Black-holes
*
*When two black-holes come to merge, don't they rotate with an in... | I would imagine it would be a solid. Gas = atoms that are connected loosely fluid = connected more than gas but still loose solid = compact and held together I would imagine that since the gravity well and escape velocity being so high that not even light can escape, that it has traits of a very dense solid. Hence Sing... | {
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The Hermiticity of the Laplacian (and other operators) Is the Laplacian operator, $\nabla^{2}$, a Hermitian operator?
Alternatively: is the matrix representation of the Laplacian Hermitian?
i.e.
$$\langle \nabla^{2} x | y \rangle = \langle x | \nabla^{2} y \rangle$$
I believe that $\nabla^{2}$ is Hermitian (if it was ... | In general, one needs to write down the integrals for $\langle\phi|\Delta\psi\rangle$ and $\langle\Delta\phi|\psi\rangle$ and transform them into each other using integration by parts.
Hermiticity does not depend on the basis (matrix representation) used.
But it depends on the boundary conditions imposed, as one needs ... | {
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Where can I find hamiltonians + lagrangians? Where would you say I can start learning about Hamiltonians, Lagrangians ... Jacobians? and the like?
I was trying to read Ibach and Luth - Solid State Physics, and suddenly
(suddenly a Hamiltonian pops up. and then a wave equation and then $H_{aa}\ and\ H_{ab}$?
| Well, for solid state physics, you should know quantum mechanics first, which will teach you about Hamiltonians. So pick up any standard undergrad quantum text. Lagrangians don't come into undergrad QM too much, unless you happen to get an introduction to path integrals, so if you want to learn about those I'd suggest ... | {
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Why does observation collapse the wave function? In one of the first lectures on QM we are always taught about Young's experiment and how particles behave either as waves or as particles depending on whether or not they are being observed. I want to know what about observation causes this change?
| Towards a better picture of the duality
On Young's double-slit experiment the wave-particle duality (one by one photon) is more a problem of "picture of the model" than a philosophic one: see Y. Couder interpretation, by your self (!),
Youtube Couder experiments
The quantum particle HAVE a location, there are only a ... | {
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Why does the aligning of magnetic dipoles in a material cause its heat capacity to decrease? This is with regards to adiabatic magnetisation.
| If the magnetic dipoles in a material are ordered, the material has a lower entropy because there are many fewer ways how the spins may be oriented if most of them (or all of them!) are required to be aligned.
Such an alignment also reduces the heat capacity because before the dipoles got aligned, the orientation (dire... | {
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Gravitational inverse-square law I was looking at the gravitational inverse-square law:
$$
F_G = G \frac{Mm}{r^2}
$$
This law comes from some experimental data? Why it is an exact inverse-square law? Could it be
$$
F_G = G \frac{Mm}{r^{2.00000000000000001}}
$$
or there is a mathematical method to find exactly this law?... | To answer your question of whether or not there is experimental data, here is one of what I am sure are many papers regarding the classical definition of the gravitational force: http://www.physics.uci.edu/~glab/papers/HoskinsPaper.pdf
Nothing in physics is ever exact, but considered an approximation to the reality of... | {
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Numerical renormalization is there a numerical algorithm (Numerical methods) to get 'renormalization' ?? i mean you have the action $ S[ \phi] = \int d^{4}x L (\phi , \partial _{\mu} \phi ) $ for a given theory and you want to get it renormalized without using perturbation theory .. can this be made with numerical meth... | The answer to this question is a resounding YES. Lattice field theorists do their computations entirely numerically. As a result, they must resort to numerical (and hence, nonperturbative) renormalization (by extrapolating down the lattice spacing).
They would not deal with counterterms, but rather deal directly with... | {
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Do we live in a world with 4 or more dimension? A NOVA show have told the audience that we are live in 3 dimensional world, the world we lived in is compose by 3 element: the energy, matter, space. By the time Einstein have invented the 4-dimensional model including the time element, why no one claim that we actually l... | Victor,
This is a good question. Probably one of the greatest tragedies surrounding modern science in popular literature is the portrayal of dimensions and our understanding of them.
Many popular shows are inconsistent in when they talk about dimensions, in some cases they refer to the 3 spatial and 1 time dimension... | {
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Increased mass from signals traveling close to the speed of light As you travel close to the speed of light, it is to my understanding you gain mass. Does this also apply when the brain sends electrical signals to the muscles? Do the signals (that are traveling at the speed of light) cause the body to weigh more?
| The signals travelling from your brain along your nerves travel at much much less than the speed of light. The maximum speed is about 100 m/sec.
In any case what travels down the nerve is a change in the sodium and potassium ion concentration not some mass, so there isn't anything to gain relativistic mass.
| {
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A problem of missing energy when charging a second capacitor A capacitor is charged. It is then connected to an identical uncharged capacitor using superconducting wires. Each capacitor has 1/2 the charge as the original, so 1/4 the energy - so we only have 1/2 the energy we started with. What happened?
my first though... | Indeed, there will be at least some losses in the superconducting wires: first, as far as I know, losses in superconductors only vanish for zero frequency, second, initial high current can exceed the critical current of the superconductor.
| {
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the difference between the operators between $\delta$ and $d$ In classical mechanics, when talking about the principle of virtual work, what is difference between $\delta r$ and $dr$? e.g. $W=\int \overrightarrow{F} \cdot \delta \overrightarrow{r} $ and $W=\int \overrightarrow{F} \cdot d \overrightarrow{r} $ .
Why ... | They are not different, they are the same, but "dr" is ossified notation, meaning the integration differential, and physicists often think about infinitesimal increments, so they use different letters to indicate smallness. You sort it out from context.
| {
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Complete set of observables in classical mechanics I'm reading "Symplectic geometry and geometric quantization" by Matthias Blau and he introduces a complete set of observables for the classical case:
The functions $q^k$ and $p_l$ form a complete set of observables in the sense that any function which Poisson commute... | Blau's definition is a classical analog of the Schur's lemma. The
reasoning behind this definition is the requirement that under a faithful
quantization map which carries functions on the phase space to operators
on some Hilbert space, the representation of the algebra of the quantum
observables is irreducible. The irr... | {
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"timestamp": "2023-03-29T00:00:00",
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Sinusoidal Wave Displacement Function I am learning about waves (intro course) and as I was studying Wave Functions, I got a little confused.
The book claims that the wave function of a sinusoidal wave moving in the $+x$ direction is $y(x,t) = A\cos(kx - wt)$.
However, I see a drawing of the wave and they always seem t... | Since
$$\cos\left(x-\frac{\pi}{2}\right)=\sin x,$$
using $\cos$ or $\sin$ does not matter, it depends on the choice of initial conditions.
In addition, in general, there will be a initial phase $\phi$, so sinusoidal wave is written like
$$ y(x,t)=A \cos(kx-\omega t+\phi).$$
| {
"language": "en",
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How does the Sun's magnetic field continue to exist at such high temperatures? The temperature at the surface of the Sun is apparently well above 5000 C; I'm assuming the layers beneath the surface may be even hotter.
At school, we learned that heating a metal beyond a certain temperature, specific to each metal, would... | If the sun's internal plasma was at rest (the sun would have to stop rotating and other factors would need to occur), then I believe the magnetic field would dissipate and dissolve, essentially being 'demagnetized'.
However, because the star is rotating, and different layers of it at varying rates, the churning of the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/36182",
"timestamp": "2023-03-29T00:00:00",
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Reason for the Gaussian wave packet spreading I have recently read how the Gaussian wave packet spreads while propagating.
see:
http://en.wikipedia.org/wiki/Wave_packet#Gaussian_wavepackets_in_quantum_mechanics
Though I understand the mathematics I don't understand the physical explanation behind it. Can you please ex... | The explanation is really very simple to understand intuitively, and very beautiful.
Imagine that a particle an uncertainity in its velocity $v$ of $\delta v$. Suppose at $t=0$ we have $x=x_{0}$. After $t=T$, the location of the particle will be given by the range $(x_{0}+Tv-T\delta v,x_{0}+Tv+T\delta v)$, because we ... | {
"language": "en",
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"source": "stackexchange",
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What are distinguishable and indistinguishable particles in statistical mechanics? What are distinguishable and indistinguishable particles in statistical mechanics? While learning different distributions in statistical mechanics I came across this doubt; Maxwell-Boltzmann distribution is used for solving distinguishab... | On the deepest level, particles are indistinguishable if and only if they have the same quantum numbers (mass, spin, and charges).
However, in statistical mechanics one often studies effective theories where there are additional means of distinguishing particles. Two important examples:
*
*In modeling molecular fl... | {
"language": "en",
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Why is the partition function called ''partition function''? The partition function plays a central role in statistical mechanics.
But why is it called ''partition function''?
| First, recall what a partition is. A partition of a set $X$ is a way to write $X$ as a disjoint union of subsets: $X=\coprod_i X_i$, $X_i\cap X_j=\emptyset$ for $i\neq j$. When the elements of the set $X$ are considered undistinguishable, what matters are the cardinals of the set only, and we have a partition of an int... | {
"language": "en",
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What is a virtual photon pair? When describing a black hole evaporation in the hawking black body radiation it is usually said that is due to a virtual photon pair, is it this what happens? And what is virtual photon pair, does the photon has anti particle or it is its own ?
I am not looking for a deep theory, just the... | As Anna says, while it's commonly stated that Hawking radiation is due to one member of a particle anti-particle pair falling through the event horizon, this is nothing more than a metaphor and it's not actually what happens.
I actually answered this question is some detail in Black holes and positive/negative-energy p... | {
"language": "en",
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Misaligned Mirror on Michelson Inferometer If one of the outer mirrors on a Michelson interferometer was to be misaligned by a small angle of theta, what would be the shape of the interference pattern in the detector plane? What would happen to this pattern as the other mirror moves?
| Misaligning one of the end mirrors will produce a set of vertical or horizontal fringes at the detector plane (depending on the misalignment of the mirror).
The number of fringes is proportional to the misalignment angle of the mirror and inversely proportional to the wavelength of the light. When first setting up the... | {
"language": "en",
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How do I figure out the probability of finding a particle between two barriers?
Given a delta function $\alpha\delta(x+a)$ and an infinite energy potential barrier at $[0,\infty)$, calculate the scattered state, calculate the probability of reflection as a function of $\alpha$, momentum of the packet and energy. Also ... | Hints to the question(v5):
*
*OP correctly imposes two conditions because of the delta function potential at $x=-a$, but OP should also impose the boundary condition $\psi(x\!=\!0)=0$ because of the infinite potential barrier at $x\geq 0$.
*There is zero probability of transmission because of the infinite potential... | {
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Total momentum of the Universe What is the total momentum of the whole Universe in reference to the point in space where the Big Bang took place?
According to my reasoning (and a bit elementary knowledge) it should be exactly equal to 0 since the 'explosion' and scattering of the matter throught the space would not cha... | There is no point in space where the big bang took place. It happened everywhere, simultaneously. Centered on Earth, since everything is moving away from us with a uniform velocity (or is stationary with respect to the CMB, if you prefer), the net momentum of the universe is approximately zero.
| {
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Is Heisenberg's matrix mechanics or Schrödinger's wave mechanics more preferred? Which quantum mechanics formulation is popular: Schrödinger's wave mechanics or Heisenberg's matrix mechanics? I find this extremely confusing: Some post-quantum mechanics textbooks seem to prefer wave mechanics version, while quantum mech... | If you do a "physics for non-physicists" course (in my case as part of a Physical Chemistry degree) you'll almost certainly be taught the Shrodinger equation because it requires less mathematical sophistication to use. For most chemical applications it's also a lot easier to use.
I'm not sure if anyone uses matrix mech... | {
"language": "en",
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2D Ghost CFT and two-point functions For some reason I am suddenly confused over something which should be quit elementary.
In two-dimensional CFT's the two-point functions of quasi-primary fields are fixed by global $SL(2,\mathbb C)/\mathbb Z_2$ invariance to have the form
$$\langle \phi_i(z)\phi_j(w)\rangle = \frac{d... | 1) Everything OP writes(v1) above his last equation is correct. The $bc$ OPE reads
$$ {\cal R}c(z)b(w) ~\sim~ \frac 1{z-w} ,$$
where ${\cal R}$ denotes radial ordering.
2) To calculate the two-point function
$$\langle c(z)b(w)\rangle $$
(which as OP writes must vanish if the conformal dimensions for $b$ and $c$ are d... | {
"language": "en",
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Why is the solar noon time different every day? If you check the local time for solar noon is different every day. Why is it so? Is it because Earth doesn't make a complete rotation in exactly 24 hours?
The following is an example of the solar noon differences (also sunrise and sunset), computed by the Python Astral mo... | Solar noon becomes earlier and then back again more than once a year; it moves 18 minutes earlier from about Feb. 10th until May, then 12 minutes later by July , then back 23 minutes earlier by late October/early November, then forwards again by half an hour by Feb tenth. So the biggest change in Solar noon occurs betw... | {
"language": "en",
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"question_score": "12",
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Magnitude of New Comet C/2012 S1 (ISON) A new comet (magnitude 18.8) has been discovered beyond the orbit of Jupiter.
Comet ISON will get within 0.012 AU of the Sun by the end of November 2013 and ~0.4 AU from of Earth early in January 2014. It may reach very welcome negative magnitudes at the end of November 2013. F... | OR maybe comets aren't "dirty snowballs", rather highly charged asteroids projected into space, as a result of an impact of charged plasma to an interstellar planetary body. The tail composed of plasma and not dirt and ice.
| {
"language": "en",
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How to make something charged using electricity? If I had a piece of metal and i wanted it to be negatively charged.
How can I do that?
| There are many ways to charge a piece of metal, but they tend to be variations on the principle used by a Van de Graaff generator. When you run two materials together you will usually transfer electrons from one to the other. Which way the electrons go depends on where the two surfaces are in the triboelectric series. ... | {
"language": "en",
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Newton 2nd Law: Does vertical force (mass) affect the horizontal acceleration? I learnt before that if 2 forces are perpendicular to each other, they should not affect each other. However in a recent experiment setup (asked in another question):
I believe the theoratical equation by newton 2nd law is
$$\begin{aligne... | What the diagram doesn't show is the force on the pulley:
It's the vector sum of this force and the force due to the weight that gives a horizontal force on the cart.
The tension in the string must be constant, because if it varied along the string the string would strtech or contract until the tension was constant, s... | {
"language": "en",
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What's driving the bucket up? Just saw this cool video from Plymouth University, which I actually found through Matthen's blog.
They fill a plastic bottle with liquid nitrogen, screw the cap on, drop it in a bucket full of warm water, cover it with ping pong balls, and when the heated, expanding gas bursts the bottle, ... | I'm with Dmitry on this one. Note that before the bottle explodes there are some ping pong balls lying on the floor next to the bin, and when the bottle explodes those ping pong balls fly up (though not as much as the bin).
The explosion deforms the floor below the bin, and when the floor rebounds it flings the bin int... | {
"language": "en",
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Determining the center of mass of a cone I'm having some trouble with a simple classical mechanics problem, where I need to calculate the center of mass of a cone whose base radius is $a$ and height $h$..!
I know the required equation. But, I think that I may be making a mistake either with my integral bounds or that $... | The volume element is $ (dr)*(rd \phi)*(dz) $. Hence, the extra r in your integrand should be eliminated.
| {
"language": "en",
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What does $\psi_j(r_i)$ mean? I have a mean-field Hamiltonian for N electrons. The mean-field potential felt by electron $i$ at position ${\bf r}_i$ is given by
$V^{(i)}_{int}({\bf r}_i)=\sum_{j\ne i}|\psi_j({\bf r}_i)|^2$
I can understand why this is the case. However, I need to clear up my understanding of the term... | The key idea in the mean field approach is taking into account the contribution, to the potential(the cause; see below) at each point ${\bf r}$, of the complete electronic configuration. By electronic configuration, we mean the probability density distribution of each of the one electron states $|\psi_j({\bf r}^')|^2 $... | {
"language": "en",
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What does the term liquid mean in condensed matter physics? In condensed matter physics, people always say quantum liquid or spin liquid. What does liquid mean?
| gas = particles are so little packed that they can easily move.
liquid = particles are fairly dense packed but can move over long distances.
solid = particles are so densely packed that they are confined to small vibrations araound an equilibrium position (site), and larger moves (site changes) are quite rare. In many ... | {
"language": "en",
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Is a volumetric rate frame-invariant in general relativity? Imagine that I have a radioactive material with a long half life. The atoms in this material decay at a certain rate $R$. The rate is the decay constant times the number density $R = \lambda N $. It has dimensionality:
$$ \left( \frac{ \text{decays} }{m^3 ... | I don't know whether it applies to all physically possible metrics, but the volumetric decay rate you define does stay constant in a Schwarzschild metric. Well, it does if the box is small compared to the curvature i.e. the time dilation etc is constant thoughout the box. I would need to think more about what happens i... | {
"language": "en",
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Resolution of twin paradox using Lorentz velocity addition In the following lecture, starting at minute 29:00 and going further, the professor resolves the Twin Paradox using Lorentz velocity addition. I have a question about this:
Isn't the figure given below (taken from a slide in the lecture, at time 37:50) referrin... | Briefly skimming the video, it seems like he's trying to resolve the paradox by having the twins meet up again somewhere else than their initial position (see 35:55). Basically, the traveling twin keeps going, and then the stationary twin tries to overtake her, starting at a later time. The velocity addition rule is us... | {
"language": "en",
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Schrödinger and thermodynamics I heard that Schrödinger pointed out that (classical/statistical) thermodynamics is impaired by logical inconsistencies and conceptual ambiguities.
I am not sure why he said this and what he is talking about. Can anyone point some direction to study what he said?
| The following source discusses some inconsistency of quantum statistical mechanics indicated by Schrödinger (see the reference there): http://jvr.freewebpage.org/TableOfContents/Volume5/Issue2/Beretta4BdQProceedings%5B1%5D.pdf
The explanation is long and cannot be outlined here. I cannot be sure that Schrödinger did no... | {
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What is predicted to happen for electron beams in the Stern-Gerlach experiment? The Stern–Gerlach experiment has been carried out for silver and hydrogen atoms, with the result that the beams are deflected discretely rather than continuously by an inhomogenous magnetic field. What is theoretically predicted to happen f... | Electron beams cannot be split by a stern Gerlach apparatus, because the spin splitting and the orbital splitting cannot be practically separated. The orbital splitting in a constant magnetic field is exactly of the same magnitude as the spin splitting, meaning that the spin anti-aligned electron in a given Landau leve... | {
"language": "en",
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Optics Paradox? Imagine we have two lens, one convex and one concave, spaced in such a way that the convex lens is before the concave lens. Now each lens has its own focus length and both are spaced such that the concave lens focus is to the right of the convex's. Furthermore, imagine that an arrow with a real length (... | I suspect you're worrying about the appearance of infinities in the equations. For example the equation for the concave lens with the object at the focal point $f$ gives:
$$ \frac{1}{f} + \frac{1}{v} = \frac{1}{f} $$
and therefore $v$ = infinity. This leaves you wondering how to calculate the magnification for the seco... | {
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Proof of equality of the integral and differential form of Maxwell's equation Just curious, can anyone show how the integral and differential form of Maxwell's equation is equivalent? (While it is conceptually obvious, I am thinking rigorous mathematical proof may be useful in some occasions..)
| Well, as the people said in the comments, the Theorems of Green, Stokes and Gauss will do the job, and are about as mathematically rigorous as you could hope for here!
The two different sets of formula follow directly.
I don't want to write all four of them out, you should be able to do them yourself, but for example, ... | {
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How does this problems are solved (modeling/simulation)? Can somebody guide me in what to read and learn in order to be able to solve or understand how to solve the following types of problems:
*
*The modeling/simulation of the bullet, shot into the water container, at the bottom of which there is a glass cup
*Auto... | Learn about Finite Element Methods. For crash dynamics Smooth Particle Dynamics is good.
Computer codes
*
*LS-DYNA
*OpenFOAM
*DEAL.II
Book
Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena- Ya. B. Zel'dovich & Yu. P. Raizer
| {
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Why do physicists think that the electron is an elementary particle? When we first discovered the proton and neutron, I'm sure scientists didn't think that it was made up of quark arrangements, but then we figured they could be and experiments proved that they were.
So, what is it about the electron that leads us to be... | Believe you me, people have devoted a lot of time to coming up with composite models of the electron, without much to show for it. For example, see the preon.
High energy scattering experiments have shown that the charge radius of the electron is very small, and yet the rest mass of the electron is also very small. I... | {
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Calculating force required to stop bungee jumper Given that:
*
*bungee jumper weighs 700N
*jumps off from a height of 36m
*needs to stop safely at 32m (4m above ground)
*unstretched length of bungee cord is 25m
Whats the force required to stop the jumper (4m above ground)
First what equation do I use?
$F = m... | As others here have pointed out, the force of the bungee cord would vary, increasing as it is stretched.
So your question is not well posed. If this is an actual homework problem I would guess that you misread it and you are actually being asked to find the force constant of the bungee cord (assuming, as I will below,... | {
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Differences between classical, analytical, rational and theoretical mechanics Can you explain me what are the differences between the four following subjects?
*
*analytical mechanics
*rational mechanics
*classical mechanics
*theoretical mechanics
| Analytical mechanics is a branch of classical mechanics that is not vectorial mechanics (original Newton's work). Analytical mechanics uses two scalar properties of motion, the kinetic and potential energies, instead of vector forces, to analyse the motion. Analytical mechanics includes Lagrangian mechanics, Hamiltonia... | {
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What are some of the best books on complex systems and emergence? I'm rather interested in getting my feet wet at the interface of complex systems and emergence. Can anybody give me references to some good books on these topics? I'm looking for very introductory technical books.
| An Introduction to Complex Systems is a recently published (2019) book by Tranquillo that has been very well reviewed in the Nov. 2019 Physics Today issue:
The text provides a useful overview of complex systems, with enough detail to allow a reader unfamiliar with the topic to understand the basics. The book stands ou... | {
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From how high could have Felix Baumgartner jumped without disintegrating like a shooting star? Today Felix Baumgartner jumped from 39 kilometres high and reached the earth safely.
Just considering friction, from how high can a human jump?
I expect that from a certain height, he would have reached a speed so high that h... | He "only" flew at the maximum speed of 370 m/s or so which is much less than the speed of the meteoroids – the latter hit the Earth by speeds between 11,000 and 70,000 m/s. So he was about 2 orders of magnitude slower. The friction is correspondingly lower for Baumgartner.
Note that even if he jumped from "infinity", h... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why are synthetic elements unstable? So far 20 synthetic elements have been synthesized. All are unstable, decaying with half-lives between years and milliseconds.
Why is that?
| The artificial elements are artificial because they're rapidly radioactive, and not regenerated through decay. 81 of the first 83 elements, as well as #90 (thorium) and 92 (uranium) can practically be considered stable for most purposes. The exceptions are technetium (43) and promethium (61). Some other elements are ra... | {
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"timestamp": "2023-03-29T00:00:00",
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Distribution of charge on a hollow metal sphere
A hollow metal sphere is electrically neutral (no excess
charge). A small amount of negative charge is suddenly
placed at one point P on this metal sphere. If we check on
this excess negative charge a few seconds later we will find
one of the following possibilit... | B, Since the sphere has no charge the negative charge would distribute evenly across the surface as like charges repel the push themselves away from each other.
| {
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What are the reasons for leaving the dissipative energy term out of the Hamiltonian when writing the Lyapunov function? I have a problem with one of my study questions for an oral exam:
The Hamiltonian of a nonlinear mechanical system, i.e. the sum of the kinetic and potential energies, is often used as a Lyapunov fun... | I am not quite sure what "dissipative energy term" means, but I do know that you can't add anything proportional to $\dot{x}$.
To see why, just take a point close to the $(x, \dot{x})=(0,0)$ point. In a neighbourhood of this point the $\dot{x}$ term will dominate over $\dot{x}^2$ and either the point $(0,\epsilon)$ or ... | {
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"timestamp": "2023-03-29T00:00:00",
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How do I integrate $\frac{1}{\Psi}\frac{\partial \Psi}{\partial x} = Cx$ How do I integrate the following?
$$\frac{1}{\Psi}\frac{\partial \Psi}{\partial x} = Cx$$
where $C$ is a constant.
I'm supposed to get a Gaussian function out of the above by integrating but don't know how to proceed.
| Sorry, I can't comment in the right place due to low rep.
@Killercam, you never need to ''treat this [the partial derivative] as an ordinary derivative''. Doing so ignores the possibility of other variables, and doesn't find the most general solution.
The only change in Killercam's derivation, is that $\kappa$ should... | {
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Why does bad smell follow people (assuming they are not the source)? When you are sitting in a room where there is a source of bad smell, such as somebody smoking or some other source of bad smell, it is often a solution to simply move to another spot where bad smell is not present. Assuming you are not actually the so... | From a fluid dynamics standpoint, as a body moves through a fluid, a small region of fluid is dragged along with it. This is what forms the boundary layer. In the near-body region, odor will be dragged along with the body.
Likewise, behind a moving person is a turbulent wake and a low pressure region. The low pressure ... | {
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What is the difference between a spinor and a vector or a tensor? Why do we call a 1/2 spin particle satisfying the Dirac equation a spinor, and not a vector or a tensor?
| A four-vector transforms under the Lorentz-Group $SO(3,1)$, i.e. a "standard Lorentz transformation". The Lorentz transformation for a spinor is under $SU(2)\times SU(2)$ (to be exact the representation $2 \times \bar 2$) which is locally isomorph to $SO(3,1)$ but not the same. To get a better understanding, you could ... | {
"language": "en",
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Does infinite energy imply Infinite mass (and vice versa)? If some kind of source was able to supply an infinite amount of energy, does that imply that it also must have an infinite mass? Is the contrary also true?
| It is very dangerous to talk about infinity in physics, especially when talking special relativity.
To your question: Yes the object would need an infinite amount of mass.
E.G. Take a battery that would have an finite amount of energy inside.
Then you would have
$M_{\text{Total mass of the battery}}=M_{0,(\text{the us... | {
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Will the siphoning effect help a system pump water upwards if the water's entry and exit points are at the same height? I am looking to pump water from a pool up to a roof for solar heating (black plastic tubing) and then back into the pool with the original source water. Does the gravitational force of the water flowi... | "I have been told that the strength of the pump needed would have to be the same regardless of the exit point's height."
This is false. You would want to bring the pipe exit to the same inlet height as the pump or you are adding required head. As long as it's not over ~33 feet (from pump center line to the highest poin... | {
"language": "en",
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The earth's magnetic field This might sound like a silly question. Is it possible for the earth's magnetic field to actually destroy or harm earth? (implosion, crushing etc.)
| I'd say a big NO for that...
Perhaps, the real truth is that "Without the magnetic field of Earth, we'd face a lot of awful things than just Greenhouse effect & Global warming..."
The magnetic field protects Earth from most of the charged particles (based on Lorentz force) in Cosmic rays and Coronal mass ejections (Not... | {
"language": "en",
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Free falling objects My teacher and I are in the middle of an argument because she says that if you were to drop two objects at the same time and the same height, but with different initial velocities, both of them would hit the ground at the same time. She also said this was proven by Galileo's unregistered experimen... | If we are throwing two objects directly to the ground you are right.
So from our kinematic equations:
$$V_f = V_i + at$$
I would ask your teacher. What happens to the $V_f$ if $V_i=0$? Then Follow it up with what would $V_f$ be if $V_i$ was very large?
The initial velocity DOES have an effect here.
HOWEVER: Make sur... | {
"language": "en",
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Minkowski diagram and time dilation After i figured out how to show length contraction in this topic. I tried to use a similar way to show time dilation in Minkowski diagram. Time dilation means that time interval between two events is the shortest in the frame in which those two events happen in same place. We call th... | We want to find the (coordinate) elapsed time between two events.
Let those two events be the origin and $ct=1, x=0$. Clearly, these two events are co-located in the unprimed coordinate system and so, the unprimed coordinate elapsed time is equal to the proper elapsed time between these two events.
To find the coordin... | {
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Why do green lasers appear brighter and stronger than red and blue lasers? This is mostly for my own personal illumination, and isn't directly related to any school or work projects. I just picked up a trio of laser pointers (red, green, and blue), and I notice that when I project them, the red and the blue appear to b... | Its because human eyes are more sensitive to green light than other colors. Here's a reference:
http://www.physicsclassroom.com/class/light/u12l2b.cfm
I also heard from a friend, although I can't find a reference, that traffic lights display red at a higher intensity so that it appears just as "bright" as green light d... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/41624",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "14",
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Why do physicists believe that particles are pointlike? String theory gives physicists reason to believe that particles are 1-dimensional strings because the theory has a purpose - unifying gravity with the gauge theories.
So why is it that it's popular belief that particles are 0-dimensional points? Was there ever a ... | I had been preparing an answer to the question made duplicate .
there were more questions than in the question above, so I am answering here:
Elementary particles are like mathematical points?
In the standard model of physics they are assumed so.
Does make sense in quantum mechanics and standard model think this way... | {
"language": "en",
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Is it possible to travel at precisely the speed of sound? I've been talking to a friend, and he said that it's impossible to travel at exactly the same speed as the speed of sound is. He argued that it's only possible to break through the sound barrier using enough acceleration, but it's impossible to maintain speed ex... | No, this is not true. Unlike the speed of light, for example, there isn't anything particularly special about the speed of sound that would prevent you from traveling exactly at it. There isn't really anything else I can explain about it without knowing what reason your friend gave for making his argument.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/41721",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why do birds sitting on electric wires not get shocked? When we touch electric wires, we get shocked. Why don't birds sitting on electric wires not get shocked?
| A simple googling would've provided you an answer. We won't get a shock if we fly or when we aren't grounded... Because, Current flows only in closed circuits (Maybe in Plasma "as an open"). A bird sitting in the wire doesn't form a complete circuit in order for the current to flow. In other words, Birds have their fee... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "16",
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Why do we need more power to do a job fast? Let's assume we have two identical electric trains. One has a big electric motor (high power) and the other has small motor (low power). Let us assume the electric motors are of the same brand and the power of the motor is directly proportional to the size. Now, the two trai... | In physics, the average power $P$ is defined as the amount of work done per unit time interval, i.e., $P = \frac{\Delta W}{\Delta t}$. So, a greater $P$ implies a smaller $\Delta t$ for the same amount of work. This answers the first part of your question. As regards whether you can measure time in terms of kg of coal,... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What are the fields in this problem? In problem 3 of chapter 2 of Landau Lifshitz "Mechanics," I don't understand the meaning of the fields as defined in the following statement:
Which components of momentum and angular momentum are conserved in motion in the following fields?
(a) the field of an infinite homogeneous ... | Yes, that is what Landau and Lify are getting at. I don't really see another interpretation. I mean, are momentum and angular momentum conserved under the following applied potential fields? I think that is a reasonable interpretation. Haven't looked at Landau and co. Mechanics in a bit, but this seems reasonable.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Equation of the saddle-like surface with constant negative curvature? What is the equation for the saddle-like 2d surface (embeded in 3d Euclidean space with cartesian coordinates x, y and z) with constant negative curvature frequently used to illustrate open universe (for example in the following image is taken from W... | I don't think you can embed a surface of constant negative curvature in Euclidean space. However you can embed it in Minkowski space. See http://en.wikipedia.org/wiki/De_Sitter_space for details. If you have Minkowski space defined by:
$$ ds^2 = -dx_0^2 + dx_1^2 + dx_2^2 + dx_3^2 $$
then the corresponding surface is:
$... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/43056",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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Cause of buoyant force? Can you explain to me what causes the buoyant force? Is this a result of a density gradient, or is it like a normal force with solid objects?
| One can think of buoyancy as the same force that lets you stand on the ground without sinking into it. When you are standing on the ground, the earth's gravity exerts a downward force equal to your weight, and the ground offers a normal reaction of equal magnitude in the upward direction which balances out your weight.... | {
"language": "en",
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What is the difference between weight and mass? What is the difference between the weight of an object and the mass of an object?
| To elaborate on John Rennie's answer - As he said, the mass is the inertial mass of the body, which isn't the same as the weight.
The weight is typically defined in context to a gravitational field.
No doubt you know that the acceleration due to gravity on the earth's surface is $9.8 m/s^{2}$ (on average). So if your ... | {
"language": "en",
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Intuition for multiple temporal dimensions It’s easy, relatively speaking, to develop an intuition for higher spatial dimensions, usually by induction on familiar lower-dimensional spaces. But I’m having difficulty envisioning a universe with multiple dimensions of time. Even if such a thing may not be real or possible... | Theories can be formulated in any number of space-time dimensions. Examples of multidimensional theories:
*
*F-theory, 12d theory with two times.
*S-theory, 13d theory with three times.
*Kalitzin's relativity with r-times or even infinite-dimensional times (the latter much less developed) was studied.
Indeed, I t... | {
"language": "en",
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Why do diamonds shine? I have always wondered why diamonds shine. Can anyone tell me why?
| Diamond is one of the hardest material. We know that it's an allotrope of carbon. A diamond (crystalline in nature) has a three dimensional arrangement of carbon atoms linked to each other by strong covalent bonds. What you've shown a round brilliant cut diamond.
Actually, the secret that's rattling inside a diamond is... | {
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"timestamp": "2023-03-29T00:00:00",
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Wheatstone bridge galvanometer error We had to measure the resistance of $R_x$, we balanced the Wheatstone bridge and did calculations. My question is: we didn't include galvanometer error into calculations. Why is that? I read that it's very precise, but that doesn't seem like a good enough explanation in exact scienc... | What it means by very precise is that the error from the galvanometer is significantly less then the error within your system. The Wheatstone Bridge calculations do not require serious precision; the galvanometer are the least of your concerns. IF you were using this device in some type of research environment that req... | {
"language": "en",
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Minimal Maxwell's Demon I would like to understand where the waste heat is generated in the Maxwell's demon problem. To this end I've come up with the simplest scenario I can think of. If my scenario is workable I am hoping someone will be kind enough to apply the right math to it to show what is going on and why it do... | The dimensionality is not relevant. The commonly-believed "solution" of the Maxwell's demon puzzle utilizes the fact that the demon must store information as measurements are made. To bring the demon back to its initial state, that memory must be erased. According to Landauer's theorem, erasure of each bit of informati... | {
"language": "en",
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Projectile motion along the earth Suppose a projectile is launched from the Earth's surface with initial velocity $v_0$ well below speed of light and initial angle $\theta_0$ with respect to the vertical line perpendicular to the Earth's surface. Omitting Earth's rotation, but knowing that Earth is not flat (as in the ... | I do not have the book you mentioned, but I could find something in my notes from last year's Classical Mechanics lecture.
Firstly, if your projectile reaches escape velocity, then it will of course travel away from the Earth forever, which answers your question with $\infty$. When does this happen? The potential energ... | {
"language": "en",
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Definition of Fine-Tuning I've looked in and out the forum, and found no precise definition of the meaning of fine-tuning in physics.
QUESTION
Is it possible to give a precise definition of fine-tuning?
Of course, I guess most of us understand the empirical meaning of the phrase... but it seem so ethereal, that's the r... | All we can do precisely is give a probability for some physical quantity to have its observed value. For example (subject to various assumptions!) the probability of the cosmological constant having it's observed value is around 1 in $10^{120}$. Since this is absurdly low we say it's fine tuned.
But where you draw the ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Current in series resistors and voltage drop in parallel resistors When we have resistors in series, the current through all the resistors is same and the voltage drop (or simply voltage) at each resistor is different.
Question 1: It is fine that voltage drop (potential drop) across each resistor is different because e... | To be clear, current is charge passing through a certain area per unit time. This does not imply a second parameter in the denominator of the formula for current $\frac{dq}{dt}$; just a guideline for how to measure $dq$. The larger the cross sectional area, the larger the perceived current will be. This is why resis... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/43782",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 5,
"answer_id": 3
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The definition of entropy in quantum mechanics I have seen entropy with several different definitions. Like Von Neumann entropy and Rényi entropy, etc.
So I am curious why there are so many different definitions in quantum mechanics while only one in classical mechanics named after Boltzmann?
| All the quantum entropies that you cite have a classical analogue. E.g. the Von Neumann entropy $\langle S \rangle = -k_B \mathrm{Tr} (\hat{\rho} \ln \hat{\rho})$ is the quantum version of the Gibbs entropy $\langle S_\mathrm{cl} \rangle = -k_B \int \mathrm{d}p \mathrm{d}x (\rho \ln \rho)$ used in classical statistica... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/43816",
"timestamp": "2023-03-29T00:00:00",
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If wave packets spread, why don't objects disappear? If you have an electron moving in empty space, it will be represented by a wave packet. But packets can spread over time, that is, their width increases, with it's uncertainty in position increasing. Now, if I throw a basketball, why doesn't the basketball's packet s... | Spreading the wave packet does not mean spreading and disappearing the electron.
If a basketball has initially uncertainty $\Delta V$ of its velocity, then with time the ball position uncertainty will grow as $\Delta V\cdot t$.. With time this uncertainty gets so large that the ball disappears from your sight (I mean y... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/43860",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How to compute the expectation value $\langle x^2 \rangle$ in quantum mechanics? $$\langle x^2 \rangle = \int_{-\infty}^\infty x^2 |\psi(x)|^2 \text d x$$
What is the meaning of $|\psi(x)|^2$? Does that just mean one has to multiply the wave function with itself?
| About your other question, the meaning of $|\psi(x)|^2$ is that of a density of probability, with $[|\psi(x)|^2 \mathrm{d}x]$ giving the probability that the particle is found between $x$ and $x + \mathrm{d}x$.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/44147",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 4,
"answer_id": 1
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Is physics rigorous in the mathematical sense? I am a student studying Mathematics with no prior knowledge of Physics whatsoever except for very simple equations. I would like to ask, due to my experience with Mathematics:
Is there a set of axioms to which it adheres? In Mathematics, we have given sets of axioms, and ... | Since you are a student of mathematics with little knowledge of physics, I strongly urge you to take a few courses in modern physics before you finish your mathematics education (General Relativity and Quantum Mechanics the very least). This is a must if you are specializing in geometry/topology.
Having said that, the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/44196",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "21",
"answer_count": 10,
"answer_id": 5
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Poincare Patch covers half of the hyperboloid of AdS We start with the general case of $AdS_{p+2}$ i.e AdS space in $p+2$ dimension.
\begin{equation}
X_{0}^{2}+X_{p+2}^{2}-\sum_{i=1}^{p+1}X_{i}^{2} = R^2
\end{equation}
This space has an isometry $SO(2,p+1)$ and is homogeneous and isotropic. The Poincare Patch is given ... | It can be shown by conformal compactification of the spacetime, i.e. using coordinates which allow you to draw a penrose diagram. After you have done so, you can analytically continue the geometry and discover the other half (see chapter 2 of this) . Regarding differences in topology: I don't see any reason for this to... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/44335",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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Photon energy - momentum in matter $E = h\nu$ and $P = h\nu/c$ in vacuum.
If a photon enters water, its frequency $\nu$ doesn't change.
What are its energy and momentum: $h\nu$ and $h\nu/c$ ?
Since part of its energy and momentum have been transferred to water, it should be less.
If water's refractive index is $n$, are... | It's a non-trivial problem, which also involves how you define a photon in a medium - as a interacting particle and treating excitation of medium separately, or as a "dressed particle", including the interaction.
From Abraham–Minkowski controversy Wikipedia page:
The Abraham–Minkowski controversy is a physics debate c... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/44509",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
"answer_count": 3,
"answer_id": 0
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Could we have assumed the speed of light to be different in different reference frames? Ptolemy's model of universe assumes that our earth is the static center of universe and everything else move relative to it (ref: The grand design ch:3). This model would give us a consistent picture of universe the only complicatio... | The given answer is in fact not complete. While aether construction is trivially knocked down, yet another construction must be used to get rid of the remaining theory in which this set up works, that is light takes some convenient reference frame relative to its emitter or collector.
The problem must be solved (again)... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/44568",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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