Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
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 ... | In the standard model (as in all traditional relativistic quantum field theory), particles are pointlike. All experimentally available facts about microphysics seem to be consistent with the standard model. This is the (fully sufficient) reason for believing that particles in Nature are pointlike.
Pointlike is a techni... | {
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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... | It's true that at the speed of sound, you will have a huge amount of drag. The reason is that the air in front of you has to move out of the way, and if you are moving at the speed of sound, the pressure wave that pushes the air out of the way is moving at exactly the same speed as you. So in the continuum mechanics li... | {
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Is the Schwarzschild black hole unphysical? To obtain the Schwarzschild metric from Einstein equations of general relativity, we suppose that the energy density is a distribution :
$$ \rho (\vec{r}) = M \delta(\vec{r})$$
The Schwarzschild radius, corresponding to the horizon, is $R_s = 2 M$, in units $G=c=1$.
A physic... | My take is that the Schwarzschild black hole is indeed physical in the following sense. The S-metric has a timelike Killing vector, which indicates that the solution is symmetric with respect to time, hence, the "static" solution.
In GR, I generally interpret physically real objects to be scalars, that is, quantities ... | {
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Where do the high order rainbows appear? This site shows locations of the high order rainbows up to sixth order. My thought is that, There should be even higher order bows like 7th, 8th, etc. (Though they would be practically impossible to observe.)
So, Where would they appear on sky?
| Wiki says that It's possible to observe higher order rainbows up to 200 in Labs using Laser beams. But, Sky observations imply the existence of first, second & rarely third but no further add-ons.
During rainbow events, both refraction & reflection occur in a raindrop. It should also be noted that reflection takes plac... | {
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Moving along friction surfaces If a particle moves along a one dimensional surface with constant friction. As the particle moves from point $A$ to point $B$ it loses an amount of energy equals $E(A,B)$. Consider that the particle returns back to point $A$. It loses another $E(A,B)$ units of energy so it loses total $2*... | This is a simple sign error. The force of friction always opposes the direction of slippage between two surfaces (thanks to @JoeH for this correction). Therefore, when the particle changes its direction of motion, the direction of the force from friction also changes.
The work done against friction in moving the partic... | {
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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... | One shouldn't expect to have a "good" formula for the local isometric embeddings of a constant negative curvature surface in Euclidean $\mathbb{R}^3$. This is due to a little theorem proved by David Hilbert around 1901:
Theorem There does not exist a smooth immersion of the hyperbolic plane into Euclidean 3 space.
The... | {
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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?
| Let's consider a mug filled with water immersed in a bucket full of water. Water exerts force on sides of the mug as well as on it's top and bottom. the sideways forces exerted on water on the mug are equal and opposite, therefore they cancel out. As the top of the mug is at a lower depth in water it experiences less f... | {
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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?
| There is a basic difference, because mass is the actual amount of material contained in a body and is measured in kg, gm, etc.
Whereas weight is the force exerted by the gravity on that object mg.
Here m=mass in kg,gm,.. $g=9.8m/s^2$ (acceleration due to gravity)
Note that mass is independent of everything but weight ... | {
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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... | *
*Several authors (in particular Itzhak Bars) have written papers about two-time-physics that should help build intuition for the topic.
*Infinitely many 'times' appear in integrable systems.
*F-Theory, which is a 12 dimensional theory, has been described as having extra temporal dimensions, however see Wikipedia... | {
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How does the specific frequency of EM Radiation relate to displacing electrons from their orbits? I've only a general grasp on how all this works, so it could be I'm asking this poorly or misunderstanding what happens. With that said:
The energy of EM radiation is a function of its frequency. With enough energy (a high... | The problem with using a chunk of iron is that in a metal the sharp orbital energies that you get in isolated atoms spread out to form energy bands. Typically when you shine light on an iron surface nothing will happen until the energy exceeds 4.5eV (275nm so that's in the near uv), at which point it will eject photoel... | {
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Dirac equation as Hamiltonian system Let us consider Dirac equation
$$(i\gamma^\mu\partial_\mu -m)\psi ~=~0$$
as a classical field equation. Is it possible to introduce Poisson bracket on the space of spinors $\psi$ in such a way that Dirac equation becomes Hamiltonian equation
$$\dot{\psi}~=~\{ \psi,H\}_{PB}~?$$
Of c... | It is possible to construct a Hamiltonian. In fact this is the way how Dirac initially wrote his equation. For that the time and space coordinates have to be treated differently. In the Schrödinger picture, the Hamiltonian generates the time dynamics via ($\hbar =0$)
$$i \partial_t \psi = H \psi.$$
We see that we can o... | {
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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 ... | If you're taking into account the curvature of the Earth you presumably also have to account for the change in gravitational acceleration with distance from the Earth. In effect your object is in orbit and travelling in an ellipse. It just happens that the ellipse intersects the surface of the Earth. So your problem re... | {
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More than one time dimension We know that space-time dimensions are 3+1 macroscopically, but what if 2+2?
Obviously it is tough to imagine two time dimensions, but mathematically we can always imagine as either having two parameters $t_1$ and $t_2$ or else in Lorentz matrix
$$\eta_{00} = \eta_{11} = -1$$ and, $$\eta_{... | The causality issues relevant to including a second dimension of time owe their incoherence to the controlling assumption that space is contiguous and time is continuous. A formulation that understands two dimensions of space and two of time works well when the spatial dimensions are considered separated by time and th... | {
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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?
| The von Neumann entropy is the analogue of the Boltzmann entropy in quantum mechanics. It really is exactly the same thing. Any density matrix $\rho$ can be written as $\rho = \sum_i p_i |i\rangle\langle i|$, where $p_i = \mbox{probability}(\mbox{state}_i)$ is a probability distribution on state vectors. The von Neu... | {
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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... | It is true that the spreading depends on the mass as @twistor59 has already noticed, but the more important fact is that the basketball is an open system and interaction with its surrounds makes that (due to decoherence) the state of the basketball is not described by quantum wavefunction theory [*]. Using the Wigner-M... | {
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What does superposition mean in quantum mechanics? What does superposition mean in quantum mechanics?
When I say $A+B=C$ (forces). I can mean push something with force $A$ + force $B$ together, and that is same as I push it with force $C$.
But when I say wavefunction $A$ + $B$ is also a solution of Schrodinger equation... | Steven,
Mathematically (as I think you already know) superposition means that if I evolve the quantum state $|c\rangle =|a\rangle + |b\rangle$, the result will be the same as separately evolving $|a\rangle$ and $|b\rangle$,and adding the results. That is due to the linearity of the Schroedinger equation.
This means t... | {
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If superposition is possible in QM, why do we often assume systems are already in their eigenstates? My understanding is that an arbitrary quantum-mechanical wavefunction can be written as a linear combination of eigenfunctions of some Hermitian operator, most commonly the Hamiltonian; when a measurement corresponding ... | In the case of the Hydrogen atom at room temperature, we expect the superposed state to rapidly decohere and collapse to the ground state emitting a photon. We'd only expect to find Hydrogen atoms in a superposition of the ground and excited states if some mechanism was continually injecting energy into them.
If you he... | {
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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?
| In general, $\psi$ will be a complex valued function. And so $|\psi(x)|^2$ will be not equal just $\psi(x)^2$ but it is $\psi(x)$, multiplied by its complex conjugate: $|\psi(x)|^2=\psi(x)^*\psi(x)$.
| {
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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 ... | Not, always .. many times they used un mathematical models like 'dimensional regularization' or use some 'curve fitting' for some properties in several branches of physics or use 'conjectures' so the things fit
| {
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How to detect radiation on the metal (coin)? I've got metal coin : http://www.worldpeacecoin.org/
Ruble/dollar, a coin of disarmament with certificate. But, I am very spleeny person, I fear of it's radiance level and I don't know if I can trust it or check it somehow.
That could look weird but my fears feels realistic.... |
actual skin of a Soviet R-12 (SS-4) nuclear missile
So it's made from aluminium from the outside of a rocket - a long way from the radioactive end.
Even assuming a warhead was ever loaded into this missile. I don't know if the USSR routinely kept warheads installed in missiles or fitted them before launch, most sovi... | {
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Can you put a magnetic ball into a hollow magnetic sphere? if all magnets have to have two poles(one north one south), is it possible to construct a hollow sphere where the inside face of the sphere was one pole, and the outside face another pole?
is it also possible to make a magnetic sphere (not hollow) where the out... | I believe if you start with a flat magnet then press it into a semi sphere, I say semi because you want a hole in it, the hole you will role in on itself to form an inner lip creating a third semi sphere effect. As long as you have that hole I figure it will weaken the inner pole enough to give you a mono pole effect.... | {
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Question on Section 9.1.3 in "Conformal Field Theory" by Philippe Di Francesco et. al Question on Section 9.1.3 in "Conformal Field Theory" by Philippe Di Francesco et. al.
The basic idea of the Coulomb-gas formalism is to place a background charge in the system, making the $U(1)$ symmetry anomalous. This has the effe... | The non-compact $U(1)\cong \mathbb{R}$ symmetry, which the book Conformal Field Theory by Philippe Di Francesco et. al. is referring to, is the translation symmetry
$$\varphi\to\varphi+a, \qquad a\in \mathbb{R},$$
of the main boson field $\varphi$ of the Coulomb-gas formalism, reflecting the zero-mode of the $\varphi... | {
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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... | First, one thing to be clear on is that relativity assumes merely that there is a speed which is the same in all reference frames. The fact that light (or anything else) travels at that speed is mostly irrelevant.
Now, can you formulate a consistent theory in which there is no speed that is the same in all reference fr... | {
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How to determine whether a large container is air-tight? In constructing a kitchen-waste digester at home, I use a 50 Litre HDPE drum. The base of the drum is holed with a plug fitted to allow drainage when necessary.
The top has two openings - one for inlet, the other to act as outlet for the generated fluid CO2/CH4.... | If the container is airtight, it should get more and more difficult to pump air into it. If this difficulty (i.e. the pressure in the tank) does not rise at all or flats out after a short time, you can be sure that there must be a leak somewhere.
However, take care not to increase the pressure too much, as that might b... | {
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What does Metric Transitivity Mean? Jaynes In his paper "Information theory and Statistical mechanics" says
"Previously, one constructed a theory based on equations of motion, supplemented by additional hypothesis of ergodicity, Metric transitivity, or equal a priori probabilities, and the identification of entropy wa... | It is explained on the first page of
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1076959/pdf/pnas01784-0023.pdf
''If E is any invariant measurable set, then either E or its complement
is of measure zero.'''
| {
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Does matter with negative mass exist? Or does it exist mathematically?
Is it really inconsistent with a common-sense, mathematics or known physical laws?
As far as I understand, if it exists, it must be far away from the "positive" matter because of repelling force, so it explains why there is no observations of such... | So far no particle with negative mass have been discovered.
And scientific theories based on what we observe and meant to describe what we observe.
We can plug in the numbers for negative mass but what we get doesn't mean it would make physical sense. It would be mere speculation.
The problem with negative mass that ... | {
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Velocity vs Time Bounce Could someone please explain the trajectory of the ball that is bouncing in this picture...
The vertical component of the velocity of a bouncing ball is shown in the graph below. The positive Y direction is vertically up. The ball deforms slightly when it is in contact with the ground.
I'm not ... | At $t_0$=1s, the ball bounces in a perfectly elastic manner and there is no loss of momentum. Therefore, $v(t=t_0+dt) = - v(t=t_0)$. If the recording had a finer resolution in time, this would show up as a vertical jump but here you have a milder slope since it is recording only every 0.1 s. Between the bounces, gravit... | {
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Hamiltonian in position basis Let $ H = \frac{-h^2}{2m}\frac{\partial^2 }{\partial x^2}$. I want to find the matrix elements of $H$ in position basis. It is written like this:
$\langle x \mid H \mid x' \rangle = \frac{-h^2}{2m}\frac{\partial^2}{\partial x^2} \delta(x -x')$.
How do we get this? are we allowed to do $\l... | Indeed, the operator H is the sum of the kinetic energy operator and the potential energy operator. The kinetic energy operator is $$ T =\frac{P^2}{2m}
$$ other part, the operator $P$ in the x basis is $$
\langle x|P^2|x' \rangle = -\hbar^2 \frac{d^2}{dx^2} $$
| {
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What's the difference between two Hydrogen atoms? If we are given two Hydrogen atoms, would the only difference between them would be their quantum state (Energy level or eigen value, and the corresponding Orbital or eigen state) and their location (say you are the origin and each of the Hydrogen atoms are located an a... | The difference is that when two hydrogen atoms are up nice and close to one another, their $1s$ orbitals can appreciably mix to generate bonding and antibonding orbitals. The occupied $\sigma$ bonding molecular orbital of $\mathrm{H}_{2}$ (formed by the addition of the $1s$ orbitals) has a negative energy with respect ... | {
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Mechanics Problem I'm trying to follow Feynman's lecture. Unfortunately I'm a bit stuck on a small piece, so if you could show me what I'm doing wrong then I'd greatly appreciate your help. I want to exactly know how Feynman came up with $W_{ac} = \int^c_a \bf{F} \cdot d \bf{s} = F s \cos \theta$ when this implies $\bf... | I think Feynman is simply integrating the dot product of the constant force, $\mathbf{F}$ and $d\mathbf{s}$, rather than working this out from first principles per se.
$W_{ac} = \int^c_a \mathbf{F} \cdot d\mathbf{s} = Fs\cos\theta$
This can be derived from $\delta W = \mathbf{F}\cdot\mathbf{v}\delta t$ but I'm not su... | {
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Physical intuition for higher order derivatives Could somebody give me an intuitive physical interpretation of higher order derivatives (from 2 and so on), that is not related to position - velocity - acceleration - jerk - etc?
| The smoothness of acceleration and thus applied and reactive forces is related to the higher derivatives (i.e. jerk, snap, crackle and pop).
So a physical interpretation would be if you are standing in a bus, and the driver brakes with constant deceleration up to the point the bus stops at which point you feel like you... | {
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Will I recieve a shock if I charged a capacitor, then I touch the 2 poles in same time? What happens if I charged a capacitor, then I touch the 2 poles in same time?
| I experienced touching two capacitors together, when i was a child in the 1960s.
My older brother was studying Electronics at a Catholic Technical HS. I picked up capacitors from his work area and touched them together out if curiosity. The resulting shock was huge. My arms flung apart, throwing the capacitors hard an... | {
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Given Newton's third law, why are things capable of moving? Given Newton's third law, why is there motion at all? Should not all forces even themselves out, so nothing moves at all?
When I push a table using my finger, the table applies the same force onto my finger like my finger does on the table just with an opposin... | When you say ,i apply force ,on match box,and match box apply force on me, so forces cancel out ,these.forces are on two different bodies,they have different acceleration .for match box to remain at rest,forces on him should be cancel out,you can think this using newton formulas, suppose match box has mass of 5kg and... | {
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How exactly does static discharge work? Assume I have built up a pretty high charge by rubbing the floor or something. I want to understand these situations:
*
*I almost always get shocked when I touch a metal doorknob with my bare hand.
*I occasionally get shocked if I touch the wooden door first, then touch the m... | You are quite right about the origin of the charge. You can build up a very high charge that way. But it doesn't take many electrons to build a high charge.
Now when you touch a conductor (wood should not cause a shock) that charge is discharged by a current running from your body down to your finger. However the ac... | {
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"url": "https://physics.stackexchange.com/questions/45828",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Why don't we use the concept of force in quantum mechanics? I'm a quarter of the way towards finishing a basic quantum mechanics course, and I see no mention of force, after having done the 1-D Schrodinger equation for a free particle, particle in an infinitely deep potential well, and the linear harmonic oscillator.
... | In QM instead of force there is an operator of force in the momentum operator equation: $$\frac{d\hat{\vec{p}}}{dt}=\hat{\vec{F}}.$$ Operator (ordinary) equations for canonical variables are coupled and are difficult to solve for time-dependent non commuting variables. The infinite-size matrices are also generally diff... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/45869",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "12",
"answer_count": 5,
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How did we find out the shape of our own galaxy without going out of it? As far as I know, scientists have been able to see a lot of differently shaped galaxies in our visible universe through modern age telescopes. But I was wondering how it was possible to know how our own galaxy looks like without going out of it to... | We have utilized a huge number of tools to determine the shape of our galaxy over our existence on this planet... the simplest of which is just looking up. It is clear that the milky way (that grayish streak through the sky) is flat, and because we know this blotch is caused by millions of distant stars and all the d... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/45927",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 2,
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Canonical Commutation Relations Is it logically sound to accept the canonical commutation relation (CCR)
$$[x,p]~=~i\hbar$$
as a postulate of quantum mechanics? Or is it more correct to derive it given some form for $p$ in the position basis?
I understand QM formalism works, it's just that I sometimes end up thinking... | You can either accept it as a postulate (in which case it is often more convenient to postulate the CCR and CAR for creation and annihilation operators) or you can derive the relation in the position basis with
$$ \hat x = x \wedge \hat p = -i \hbar \nabla \Rightarrow [ \hat x , \hat p ] = - i \hbar x \nabla + i \hbar ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/46110",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
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Why can't one see tidal effects in a glass of water? Why can't one see the tidal effect in a glass of water like in an ocean?
| A very sensitive device would be required to measure the minuscule change in the water depth along the glass walls, because the differences in the strength of the gravitational field between each side of the glass are essentially zero. Because of this the force exerted on the glass is the same, but due to the small vol... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/46157",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "14",
"answer_count": 5,
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Terminology for opposite null lines Is there a name for two null lines that lie on the opposite sides of the null cone? Each line can be obtained from the other by reflection in the axis of the null cone (the time-axis). In terms of world-lines, this corresponds to two photons moving in the opposite directions. If ther... | To expand on Qmechanic's point, we can demonstrate how null directions get moved around even in flat space by Lorentz transformations:
Given a Lorentz vector $X^a$ you can construct a 2x2 Hermitian complex matrix $$X^{AA'} = \frac{1}{\sqrt{2}}\left(\begin{array}{cc}X^0+X^3 & X^1+iX^2 \\ X^1-iX^2 & X^0-X^3\end{array}\ri... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Superconducting nanowire in a parallel magnetic field Consider a nanoscopic wire (with radius $R$) of superconducting material. The wire lies along the $z$-axis and a magnetic field $\mathbf{H}_a = H\mathbf{e}_z$ is applied. The magnetic field is too weak to destroy superconductivity or to induce vortices and we assume... | Since you have a magnetic field along the $z$-axis, you can choose the associated potential vector to be purely radial and $\rho$-dependent (the $\mathbf{A}$ field turns around your wire, and decays as $r^{-1}$ if I remember my electromagnetism. That is, $\mathbf{A}=A_{\varphi}\left(\rho\right)\boldsymbol{\varphi}$ onl... | {
"language": "en",
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How does a warp field interferometer work? Assume I have a solid grasp of undergraduate physics. From what I've read the warp field interferometer is supposed to be a sort of Michelson interferometer, except instead of adjusting the displacement of one mirror, you have a toroidal capacitor that... somehow expands space... | The mentioned NASA paper have the answers, but it's too brief and may be difficult to follow. I recommend to read White' earlier paper http://dx.doi.org/10.1063/1.2169323 It has a nice explanation along with mathematics.In short it applies the Chung-Freese metric to the Alcubierre solution. The result is that the toroi... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Non-Degeneracy of Eigenvalues of Number Operator for Simple Harmonic Oscillator
Possible Duplicate:
Proof that the One-Dimensional Simple Harmonic Oscillator is Non-Degenerate?
I'm trying to convince myself that the eigenvalues $n$ of the number operator $N=a^{\dagger}a$ for the quantum simple harmonic oscillator ar... | I don't just use operator algebra here, so you probably already know the following, but just in case it helps:
*
*Eigenstates of the number operator are eigenstates of the Hamiltonian, since $\hat{H}=\hbar\omega\left(\hat{N}+\frac{1}{2}\right)$.
*Bound states in one dimension are non-degenerate (see e.g. http://arx... | {
"language": "en",
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"source": "stackexchange",
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The meaning of imaginary time What is imaginary (or complex) time? I was reading about Hawking's wave function of the universe and this topic came up. If imaginary mass and similar imaginary quantities do not make sense in physics, why should imaginary (or complex) time make sense?
By imaginary I mean a multiple of $i... | I will add to twistor59 answer. Hawking liked the concept of imaginary time $\tau=\mathrm{i}t$ because it transforms a Lorentzian metric
$$ds^2 = -c^2 dt^2 + dx^2 + dy^2 + dz^2$$
into a four dimensional like Euclidean metric
$$ds^2 = +c^2 d\tau^2 + dx^2 + dy^2 + dz^2$$
Hawking and others believed that a quantum gravity... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/46798",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Production of electricity from atmosphere I read the electric field intesity at the surface of earth is 100v/m. Then why can't we keep two metallic sheets at different heights and produce a continuous current by connecting these two sheets via a electric cable?
| In the 1970s Dr. O. Jefimenko experimented with balloon-lofted antennas and foil-plastic motors. Rather than employing flat plates, he reduced the high resistance of the air by using arrays of needles which spew plumes of positive ions upwards. Air which contains mobile ions is a conductor.
If we could fire a KMs-lo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/47015",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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If we charge a capacitor can we discharge it into a battery? I have read that we can charge a capacitor using a battery, but can the vice versa happen? My project needs to show a battery being charged through a fully charged capacitor.
| James Tipton is correct. You don't need ultra caps or super caps. Regular standard electrolytically will do just fine. The key is to charge the cap higher than the battery and then discharge the cap into the battery This must be done continuously and there must be no load on the battery. Batteries have this nasty... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/47077",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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Magnetic monopoles in Halbach array? I am a bit confused by the description of Halbach arrays. It is said that the line of magnets aligned in a certain way results in cancellation of magnetic field on one side of the array, and amplification on the other side.
And there is a schematic distribution of magnetic flux:
I ... | No wonder you are confused, because the diagram is a cheat! If you take the picture of the arrangement, with the labels of top and bottom, and turn it by $180°$, you get exactly the same arrangement but either displaced by 1 period, or simply with the magnetic lines in opposite direction, but now suddenly the strong f... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/47185",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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experimental technique for measuring temperature of an ant I am taking a course on thermodynamics. I have a question from my text(halliday & resnick,physics-1). They asked me to measure temperature of an ant or an insect or a small body,like a small robot. If I build a thin thermometer then it is probable that surface ... | Alternatively I would look around the lab for an infrared thermometer. There exist in the market close focus ones that go down to 6mm in close focus option ( so as not to advertise, google space accurate infrared thermometers microscopes where I found the number in a one of the first hits).
I would choose a large ant,... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
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Limitations on how far one can travel in the universe Someone once incorrectly told me that, given the speed of light is the speed limit of the universe, aliens would have to live for hundreds of years if they are to travel distances of hundreds of light years to reach Earth.
In a "special relativistic" and non-expandi... | Your question can be translated into "if right now we would send a powerful omnidirectional light pulse from earth into space, would there be galaxies that never see this light pulse?"
The answer is "yes". Due to the accelerated expansion of the universe, as described by the lambda-CDM model, only galaxies currently le... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/47368",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "19",
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Is the superposition principle universal? In David J. Griffiths' Introduction to Electrodynamics, he claims that the superposition principle is not obvious but has always been found to be consistent with the experiments. So I was wondering have we found some physics quantities which do not follow superposition principl... | Superposition principle is normally valid for weak fields. It is implemented in the Maxwell equations that are linear in fields with constant (field-independent) coefficients.
Deviation from linearity occurs for strong fields (non-lienar equations due to field-dependent coefficients). For example, a dielectric breakdo... | {
"language": "en",
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"source": "stackexchange",
"question_score": "9",
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When you apply the spin operator, what exactly is does it tell you? The example I'm trying to understand is:
$ \hat{S}_{x} \begin{pmatrix}
\frac{1}{\sqrt{2}}\\
\frac{1}{\sqrt{2}}
\end{pmatrix} = 1/2 \begin{pmatrix}
\frac{1}{\sqrt{2}}\\
\frac{1}{\sqrt{2}}
\end{pmatrix} $
My interpretation of this is that the vector show... | $$ \frac{1}{\sqrt{2}} \begin{pmatrix}
1\\
1
\end{pmatrix} $$ is the eigenvector of $\hat{S}_x=\frac{\hbar}{2}\sigma_x$ with eigenvalue $+\frac{\hbar}{2}$. $$ \frac{1}{\sqrt{2}} \begin{pmatrix}
1\\
-1
\end{pmatrix} $$ is the eigenvector of $\hat{S}_x=\frac{\hbar}{2}\sigma_x$ with eigenvalue $-\frac{\hbar}{2}$.
So f... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/47519",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Entropy and the principle of least action Is there any link between the law of maximum entropy and the principle of least action. Is it possible to derive one from the other ?
| As Joannes says, the two principles belong to two different theories:
*
*the least action principle is a principle about the (conservative) laws of motion and a proposition about the paths actually followed by the degrees of freedom of mechanical bodies
*the maximum entropy principle refers either to thermodynamic... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/47581",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "30",
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Why is the colour of sunlight yellow? I was going through the preliminary papers of other schools and found a question that I did not know. It was "Why sunlight appears yellow?". Can anyone answer it?
| Color of Sunlight as seen on Earth's surface during day is yellow due to Rayleigh Scattering.
Our Sun is actually white (mixture of all wavelengths of visible spectrum) if we see it from outer space or high-altitude airplanes. Our atmosphere scatters shorter to bigger wavelengths color from sunlight when the white ligh... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/47694",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
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Deviation from Earth's orbit How much orbital deviation is required for the Earth to get knocked out from current orbit so it either moves away from Sun or towards the Sun?
| An orbit isn't a fragile balance, where some small deviation can knock an object out of orbit. For an object at a given distance from a central body (the sun for the Earth, the Earth for an Earth satellite), any velocity less than the escape velocity results in an elliptical orbit...Earth won't spiral in or out because... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/47805",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Adiabatic process of an ideal gas derivation I am working through the derivation of an adiabatic process of an ideal gas $pV^{\gamma}$ and I can't see how to go from one step to the next. Here is my derivation so far which I understand:
$$dE=dQ+dW$$
$$dW=-pdV$$
$$dQ=0$$
$$dE=C_VdT$$
therefore
$$C_VdT=-pdV$$
differenti... | $$dU =\frac f2 NKBdT$$
$$dW= pdv$$
$$d(pv) =pdv +vdp$$
$$pdv +vdp =NKBT = - \frac 2f pdv$$
$$1+\frac 2f pdv +vdp =0$$
$$ˠ= 1 +\frac 2f$$
So,
$$ˠpdv +vdp = \text{constant}$$
$$ʸIn (dv2/v1) – In (d p2/p1)$$
$$ˠIn (d v2/v1) = In (d p2/p1)$$
$$(v2/v1)ˠ = (p2/p1)$$
Now take the exponent on both sides:
$$(p1v1ˠ) = (p2v2ˠ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/48010",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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First and Second Moment of Mass I recently came across the definition of the Center of Mass of a system as the point about which the first moment of mass is zero.
Further, it defined Moment of Inertia as the second moment of mass.
My question is, What is this 'moment of mass'?
| Given some distribution or density $\rho(x),$ a moment is the 'expectation value' of some power of $x \in \mathbb{R}$. To be precise, the $n$-th moment $M_n$ is given by
$$M_n = \int_{\mathbb{R}} x^n \rho(x) \mathrm{d}x.$$
In the mechanics case, $\rho(x)$ is simply the mass density.
You can extend this to vectors in $\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/48068",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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Banach Space representations of physical systems I think most physicists mostly model physical systems as some kind of Hilbert space.
Hilbert spaces are a strict subset of Banach spaces.
Questions:
*
*Can physical systems really have non-compact topologies, as a Banach
space has?
*Does anyone have an example of ph... | (Classical) field theory lives naturally in more general spaces than Hilbert (and even more general than Banach). The space of smooth sections of a fiber bundle is a Fréchet manifold (if the basespace is compact).
If this fiber bundle thing is new to you, you can consider your fields just as smooth functions $\psi: \te... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/48192",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Is Invisibility possible according to physics? Is Invisibility possible according to physics? Is there any backing theory to prove it true or false?
| This is an active area of research in both optics and acoustics using diffractive elements.
You can think of these diffractive elements as guiding all the incoming light around them, thus reproducing the input radiation at the output, resulting in invisibility. The are often referred to as "cloaks."
The current reason... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/48240",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
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charge density in a wire If we have a infinitely thin and infinitely long straight wire on the $z$-Axis with given current $I(t)$, how can I compute the charge density?
I figured out that the current-density is given by $\vec{j}(\vec{r},t)=I(t)\delta(x)\delta(y)\vec{e_z}$.
But how can I compute the charge-density? I th... | Localized charge density may change e.g. Surface charge, but volume charge density does not in any way depends on Current or voltage. Charge density is same whether wire is lying in backyard or being used in Light bulb. Charge simply moves, one electron goes forward right then new electron enters from left in the area ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/48333",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Measuring the quantum state of light A clarification please
The following scheme to measure linear polarization states (a single polarizing beam splitter and two photo counters) orientation (as $arctan \sqrt{\frac{v}{h}}$) of coherent light pulses cannot discriminate two states which make the same angle with the measur... | Of course you can build such a detection setup. The only question is what it will do.
To get a grip of things, let us consider three pairs of input states - horizontal/vertical (H/V), diagonal/anti-diagonal (45/-45 degrees, D/A), and circular left/right-handed (L/R) polarization. With H/V polarization on the HV detecto... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/48460",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Ideal distance of eye from a lens I observed that when I keep constant distance between object and lens but I move my eye, I get different magnification. When I am closer to lens I can see large image of the object. But if I go away from the lens I can see inverted image.
So while making my own binocular/telescope (for... | The fact that the image size changes when you move your eye towards or from the lens means that the rays leaving the lens are divergent or convergent (see top image). Telescopes are, however, constructed in such a way that they transform bundle of parallel rays to parallel rays (see bottom figure). So the image size it... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/48525",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Where and how is the entropy of a black hole stored? Where and how is the entropy of a black hole stored?
Is it around the horizon? Most of the entanglement entropy across the event horizon lies within Planck distances of it and are short lived.
Is it stored near the singularity? How can you pack so much information i... | This is a very profound question in physics. Given that a black hole has an entropy which scales as $$S_{BH} \sim \frac{A}{4}, $$ the question is how does this relate to $S_{Boltzmann} = K_B \ln W$. As in, what are the microstates of the theory which hold the information in the black hole. This was answered in part by ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/48585",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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( Legendre Generating Function) Off axis Electric Potential from an insulated disk
An insulated disk, uniform surface charge density $\sigma$, of radius $R$ is laid on the $x,y$ plane. Deduce the electric potential $V(z)$ along the z-axis. Next consider an off axis point $p'$, with distance $\rho$ from the center, Mak... | Your formula for the generating function is wrong in a crucial sense. The formula you are after reads
$$
\frac{1}{|\mathbf{r}-\mathbf{r}'|}=\sum_{l=0}^\infty \frac{r_<^l}{r_>^{l+1}}P_l(\cos\theta).
$$
Note that the numerator and denominator of each term are powers of the lesser and greater, resp., of $r$ and $r'$. For ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/48661",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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How come vibrations? We all know that sound sensation is produced only when sound waves reach upto us. We all know that sound waves are disturbances propagating in air, Vibration is necessary for the generation of sound, but it always forces me to ponder that how was it known or deduced that vibration is necessary for... | Physical sound is a mechanical wave caused by the motion (vibration) of air molecules.
The source of a sound wave does not necessarily need to persist in 'vibrating' itself (like a violin string) to initiate a sound wave. A single very sudden (i.e. step function) displacement of an object in air could generate a sound... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/49751",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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What is the covariant expression for action of the Lorentz force density on charge-current density? In a continuous medium the Lorentz force density is known to be written in the form:
$f_\alpha = F_{\alpha \beta} J^\beta$,
where $F_{\alpha \beta}$ is an electromagnetic field tensor, and $J^\beta$ is a charge-current d... | As as been pointed out, four-force (density) has to be the derivative of four-momentum (density) with respect to proper time.
Now, in a charged fluid, what is the relationship between four-momentum-density and four-current-density? Well, if the fluid has a constant charge-to-mass ratio, then they ought to be proportio... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/49821",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
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Quantum superposition of states: experimental verification How can somebody demonstrate the quantum superposition of states directly by other means than the double slit experiment?
And why can't macroscopic objects like a pen be in superpostion of states? Will it ever be possible to have an object like a pen to be in s... | In my opinion, the concept behind the famous Schroedinger's cat is exactly this: to Schroedinger, it appeared paradoxical that a macroscopic object -- even a living being -- could be in a superposition of states.
However, cases in which the radiation inside a cavity was prepared in a superposition of two macroscopicall... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/49865",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 5,
"answer_id": 3
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How does the evaporation of a black hole look for a distant observer? Let's assume an observer looking at a distant black hole that is created by collapsing star.
In observer frame of reference time near black hole horizon asymptotically slows down and he never see matter crossing event horizon. So black hole is visibl... | Considering that the field of quantum gravity is a huge questionmark, there might be some effects we don't know about. However, let us assume that there are there are no surprises, and a black hole gradually evaporates until there is nothing left of it. If it does so in finite proper time, then the cause of the "freezi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/49944",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What geological properties of the earth could we deduce by measuring magnetic field strength and direction? I wonder if it is of any use for a geophysicist, if we measure the magnetic field strength and direction of the earth.
Could we make valid statements about the composition of the the earth, earth crust or core?... | Magnetic surveys are used for prospecting for oil or minerals.
On top of the earth's magnetic field there are small contributions form magnetic materials in the surface rocks, especially granites.
You can use this to either find large bodies of volcanic rock that migth have minerals or diamonds - or alternatively you c... | {
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Gravity in other than 3 spatial dimensions and stable orbits I have heard from here that stable orbits (ones that require a large amount of force to push it significantly out of it's elliptical path) can only exist in a three spatial dimensions because gravity would operate differently in a two or four dimensional spac... | I assume this is talking about Newtonian gravity (i.e., not relativity). Let's consider the effective potential:
$$V_\text{eff}(r) = \frac{L^2}{2mr^2} + V(r)$$
where $V$ is the ordinary potential energy, and $L$ is the angular momentum. First, you may ask why the effective potential has this form. Remember that for ... | {
"language": "en",
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Is 't Hooft's Determinism based on the holographic principle? Does 't Hooft's determinism work need the holographic principle in order to work or is it just an extension of his work?
| It has been proved in [3] that a holographic description of extra-dimensional dynamics is equivalent to a semiclassical description of quantum behavior of elementary 4D fields, in agreement with AdS/CFT. In the holographic description the modes associated to the extra dimension turns out to describe quantum excitations... | {
"language": "en",
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Does the Earth have a semi-solid body at its core because of lower pressure at the center of the Earth? I have read that the Earth has a semi-solid iron body at its core, even though that object is surrounded by liquid magma.... I'm wondering if this is because of a pressure (and resulting temperature) differential --... | 1) Maximum pressure is in Earth's mass center. As, you say, all gravity forces cancel each other out at the center since the mass of Earth is symmetrically distributed around you. But the pressure in one point does not just pedpend on gravity in that point. Pressure is due to the weight of everything above you, and in ... | {
"language": "en",
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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... | It is called Venturi Effect.
The increase in speed of the air surrounding your vehicle comes with a decrease in pressure. That explains too why a chimney works better in windy days.
The Venturi effect is explained by applying the Bernoulli Equation (say, the conservation of energy of a small piece of fluid that moves w... | {
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What is the nature of the correspondence between unitary operators and reversible change? Why does the formalism of QM represent reversible changes (eg the time evolution operator, quantum gates, etc) with unitary operators?
To put it another way, can it be shown that unitary transformations preserve entropy?
| The fact that evolutions of quantum mechanics are unitary after finite periods of time can be proven from the Schrödinger equation, and hinges on the characterization of unitary operators as those linear operators which are norm-preserving.
Recall the Schrödinger equation:
$$ \frac{\mathrm d}{\mathrm d t} |\psi\rangle ... | {
"language": "en",
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Shape of a string/chain/cable/rope/wire? The height of a string in a gravitational field in 2-dimensions is bounded by $h(x_0)=h(x_l)=0$ (nails in the wall) and also $\int_0^l ds= l$. ($h(0)=h(l)=0$, if you take $h$ as a function of arc length)
.
What shape does it take?
My try so far: minimise potential energy of the... | The 2D problem of a cable hanging over a span $S$ with end-point height difference of $h$ is solved with the following shape:
$$ y(x) = y_c + a \left( \cosh \left( \frac{x-x_c}{a} \right) - 1 \right) $$
Where $(x_c,y_c)$ is the lowest point on the catenary and $a$ the catenary constant ($a = \frac{H}{\lambda\,g}$, $H$ ... | {
"language": "en",
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What is the current through the lamp? We have the following circuit:
A neon lamp and a inductor are connected in parallel to a battery of 1.5 $V$. The inductor has a 1000 loops, a length of $5.0 cm$, an area of $12cm^2$ and a resistance of $3.2 \Omega$. The lamp shines when the voltage is $\geq 80V$.
*
*When the... | When you close the switch the inductor "charges", gaining magnetic energy and hence an associated flux. When you open the switch, there is a potential energy associated with the inductor, and hence it will "discharge", generating a current in the circuit. So under the assumption that all the flux discharges, then $\Del... | {
"language": "en",
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Confused about magnetic and geographic north I'm slightly confused about the "north-seeking" pole of a magnet: does it point towards magnetic north, or is it towards geographic north?
I ask because I've been finding different explanations in different places.
| A north-seeking pole will point towards the Earth's magnetic north pole. What might have confused you, however, is that Earth's magnetic north pole is itself a south-seeking pole.
Opposite poles of a magnet attract each other, and since Earth's magnetic north pole attracts north-seeking poles, it itself is a south-seek... | {
"language": "en",
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What exactly are we doing when we set $c=1$? I understand the idea of swapping from unit systems, say from $\mathrm{m\ s^{-1}}$ to $\mathrm{km\ s^{-1}}$, but why can we just delete the units altogether?
My question is: what exactly are we doing when we say that $c=1$?
| One conceptual reason for setting $c = 1$ is to make certain symmetries more apparent. For example, consider the relativistic relationship $E^2 = (|\vec{p}|c)^2 + (mc^2)^2$ with quantities expressed in SI units, as shown. If we set $c=1$ it becomes $E^2 = |\vec{p}|^2 + m^2$, which indicates that energy, momentum, and m... | {
"language": "en",
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Is Schrödinger’s cat misleading? And what would happen if Planck constant is bigger? Schrödinger’s cat, the thought experiment, makes it seem like as if measurement can cause a system to stop being in a superposition of states and become either one of the states (collapsed).
So does a system always exist in a superposi... | In principle everything exists in a superposition of states. However everything interacts with it's environment, and this collapses the superposition through a mechanism called decoherence. In the particular case of Schrodinger's cat there is a brief discussion of this here. Also search this site for decoherence as the... | {
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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 ... | Sankaran is correct in that the magnitude of the net reversible shaft work $\delta w$ is $vdP$, but he is incorrect in ascribing to this quantity a positive sign. In reality, the shaft work done by the system must be $-vdP $, here's why...
If, by definition, a differential change in enthalpy $dh = TdS + vdP$, then for... | {
"language": "en",
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The viscous force between the layers of liquid is same, then why there is variation in the velocities of its layers? I have learned in my textbook that when the liquid flows the bottom layer of the liquid never moves because of friction, but the upper layers move with increasing velocities how it is possible if the vis... | In newtonian fluids, the viscous force is proportional to the difference in velocity - double the difference in v., doublöe the force.
Now the force between all layers is the same, so there's a little bit of velocity to add with each layer - roughly put.
| {
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Could negative dimension ever make sense? After some quick check I found that negative dimensions are not used. But we have negative probability, negative energy etc. So is it so likely that we won't ever use negative dimension(s) ?
Update
I understand there're also dimensions that are not integers e.g. dimension 1½ (?... | Using modules (e.g. vector spaces), or abelian groups, or any object which has a notation of rank / dimension, there is yet another concept of negative dimension, not in the original spaces but in their Homology.
Take a "mixed complex" of both traditional (forward) and reverse sequences of chain maps. A sequence $M_0 ... | {
"language": "en",
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How is energy transferred between atoms in a collision? Consider two bare protons. One (A) is stationary (relative to some arbitrary massless observer); the other (B) is approaching A at 1 m/s. When they collide, I assume that they bounce.
What is the precise mechanism by which energy is transferred from A to B?
For ... | You are asking for the whole theory of scattering developed the past 80 years.
Please have a look at this lecture which covers proton proton scattering.
In a nutshell, any scattering transfers momentum and energy between target and incoming with the exchange of a virtual gauge boson and possibly other allowed by quan... | {
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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 ... | From the point of view of measure theory, the probability of measuring a rational length is actually zero.
Consider, without loss of generality, the interval $[0,1]$. Using the standard Lebesgue measure, the measure of this set (its length) is 1. If we consider the subset which consists of all the rational numbers ... | {
"language": "en",
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What does it mean to find acceleration in terms of g? I'm having trouble understanding what a problem I have is seeking.
To simplify the problem:
A particle reaches a speed of 1.6 m/s in a 5.0 micrometer launch. The speed is reduced to zero in 1.0 mm by the air. Assume constant acceleration and find the acceleration i... | $g$ denotes the local acceleration due to gravity near Earth's surface. $g = 9.8 \, \mathrm{m}/\mathrm{s}^2$. Whatever acceleration you find, you should express it as a multiple of this value.
Example:
$$54 \, \mathrm{m}/\mathrm{s}^2 = 54 \, \mathrm{m}/\mathrm{s}^2 \times \frac{1g}{9.8 \, \mathrm{m}/\mathrm{s}^2} = 5... | {
"language": "en",
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Representations of Lie algebras in physics Why is an invariant vector subspace sometimes called a representation? For example in Lie algebras, say su(3), the subspace characterized by the highest weight (1,0) is an irreducible representation of dimension 3 of su(3).
However, a representation of a Lie algebra is a Lie ... | Concerning a Lie algebra representation $\rho: L \to {\rm End}(V,\mathbb{F})$, where $L$ is a Lie algebra, where $\mathbb{F}$ is a field (typically $\mathbb{F}=\mathbb{R}$ or $\mathbb{F}=\mathbb{C}$), where $V$ is a $\mathbb{F}$-vector space, and where $\rho$ is a Lie algebra homomorphism, be aware that physicists refe... | {
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Differentiation and delta function Need help doing this simple differentiation.
Consider 4 d Euclidean(or Minkowskian) spacetime.
\begin{equation}
\partial_{\mu}\frac{(a-x)_\mu}{(a-x)^4}= ?
\end{equation}
where $a_\mu$ is a constant vector and the indices are summed over since one really doesn't need to bother about up... | *
*In a $d$-dimensional Euclidean space (with positive definite norm), one has
$$\tag{1} \vec{\nabla} \cdot \frac{\vec{r}}{r^d}
~=~{\rm Vol}(S^{d-1})~\delta^d(\vec{r}), $$
cf. the divergence theorem and arguments involving either test functions and integration by parts, or $\epsilon$-regularization, similar to method... | {
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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... | I guess the devil is in the details. For example, if the celestial body in question is far from its star, so its temperature is very low, it is easier to retain low-temperature air around the body. On the other hand, very cold air is not breathable anyway. There is another way though. If the astronauts can bring so muc... | {
"language": "en",
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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".
| Say there were two identical rooms with no windows, one on earth and one on a spaceship accelerating at 9.8 m/s^2 (acceleration due to gravity on earth.) You are in one of them, and can conduct any mechanical experiment you like as long as it does not involve peeking outside of the room in any way shape or form.
Unfor... | {
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Theoretical power limit of nuclear bomb Is there any limits of power or power to mass (or any other) limits for nuclear bombs?
I found this wiki article: Nuclear weapon yield: Yield limits. Is the information provided is correct? If yes, from where this limits come from?
| Nobody really knows.
The Tsar Bomba was a 50 megaton explosion, weighing 27,000 kg
https://en.wikipedia.org/wiki/Tsar_Bomba
It was scaled down from a 100 megaton design to reduce the fallout created.
The blast did damage up to 900 km away, and despite detonating 4200m above surface, caused seismic disturbance greater t... | {
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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... | You should always find an answer that is a formula, and then only apply significant figures once you get to the one final step of substituting your numbers back into the problem in place of variables.
Avoid multiple intermediate steps of substituting numbers at all costs. Not only will this save your pencil a lot of... | {
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Dark Matter 'Stars' I'm aware that the Milky Way has a dark matter 'halo' around it, presumably a spherically symmetric distribution.
But I'm completely ignorant regarding the theories explaining dark matter... Is there any reason to not expect a star-sized object to also be made of dark matter?
I know they'll be extre... | See Is dark matter really present around the sun? and the links in the comments to the question.
It's hard to make a star from dark matter because there isn't any way for the infalling particles to lose their kinetic energy. Ordinary matter can shed energy as EM radiation, but dark matter doesn't feel the EM force.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/52877",
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"source": "stackexchange",
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How to get "complex exponential" form of wave equation out of "sinusoidal form"? I am a novice on QM and until now i have allways been using sinusoidal form of wave equation:
$$A = A_0 \sin(kx - \omega t)$$
Well in QM everyone uses complex exponential form of wave equation:
$$A = A_0\, e^{i(kx - \omega t)}$$
QUESTION... | You asked about the second equation. See below:
$e^{ix}{}= 1 + ix + \frac{(ix)^2}{2!} + \frac{(ix)^3}{3!} + \frac{(ix)^4}{4!} + \frac{(ix)^5}{5!} + \frac{(ix)^6}{6!} + \frac{(ix)^7}{7!} + \frac{(ix)^8}{8!} + \cdots \\[8pt]
{}= 1 + ix - \frac{x^2}{2!} - \frac{ix^3}{3!} + \frac{x^4}{4!} + \frac{ix^5}{5!} - \frac... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/53005",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why does gravity assist transfer twice the planet's velocity? In orbital mechanics and aerospace engineering a gravitational slingshot (also known as gravity assist manoeuver or swing-by) is the use of the relative movement and gravity of a planet or other celestial body to alter the path and speed of a spacecraft, typ... | The emergence of the factor of 2 is easy to be seen from the celestial body's vantage point (in its reference frame).
Before the maneuver, the spaceship is moving by the velocity $\vec v-\vec u$ – the relative speed of the two objects – in this frame. The celestial body is largely unaffected so after the slingshot mane... | {
"language": "en",
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Compressible fluid flow through a branched pipe junctions Backdrop: Designing a dust extraction system (LEV) with a branched junction.
What principles allow for the calculation of volume flow rate and pressure at the inlets if the volume flow rate and pressure is known at the outlet using a compressible fluid?
I am f... | Though the answer to the respective principles behind compressible fluid flow through a pipe still interests me, it transpires that one can treat air as incompressible at speeds below the velocity of sound.
As such continuity (mass conservation), momentum and Bernoulli equations are all applicable in this situation.
| {
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What is the mathematical background needed for quantum physics? I'm a computer scientist with a huge interest in mathematics. I have also recently started to develop some interest about quantum mechanics and quantum field theory. Assuming some knowledge in the areas of topology, abstract algebra, linear algebra, real/c... | I would read Richard Feynman's lectures on the subject. Specifically the book QED. If you are striving to learn some general concepts, a knowledge of the math is not necessary but is helpful. The extremely basic Quantum Physics topics use differential equations and complex variables and equations. (The standard Schrodi... | {
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How to comoving volumes depend on the evolution of the Universe? I'm reading a paper which states that
Neutron star binary merger rate at redshift $z$ per unit observer time
interval per unit volume is $\dot{n}_{m} = \dot{n}_{0} (1+z)^{2}
(1+z)^{\beta}$, where $\dot{n}_{0}$ is the local neutron star binary
merger... | Have a look at this paper. The authors are concerned with modelling gamma ray bursts from neutron star binaries, but the same argument will apply to gravitational waves emitted from the mergers. The point is that the rate of neutron star formation has varied since the big bang, and the population at any particular red ... | {
"language": "en",
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Reflection of a circularly polarized wave off a denser medium As one observes an clockwise (cw) circular polarized electromagnetic wave which is reflected off a denser medium or metal interface it is changed to a counter-clockwise (CCW) polarized em wave plus a phase of PI. A counter clockwise polarized wave which is r... | The important change is not the change of the reference frame but the change of the momentum of the photons or the direction of the electromagnetic radiation.
If two waves move in different directions, calling their polarizations "the same" or "different" is somewhat similar to comparing apples and oranges. Polarizatio... | {
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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... | A very simple reason would be that if the body rotated about some point other than the center of mass, the center of mass in the ground frame would be in circular motion.
Now we know that the motion of the center of mass is governed by EXTERNAL FORCES ONLY, and in case of a force applied for a short time, there is no... | {
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Why is ski jumping not suicidal? At least on television, ski jumpers seem to fall great vertical distances before they hit the ground - at least a few dozen meters, though I couldn't find exact distances via a quick search. And yet they almost always land on their feet as if they just fell two or three meters. (Here's ... | This is related to the angle of the slope they are landing on. There is a good article that discusses the specific mechanics of the landing so I won't repeat it here. However, since there is a considerable amount of the momentum directed in the forward direction, the velocity vector associated with the skier is not po... | {
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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:$... | What if I told you the wave equation was given by:
$$\Psi(x,t)=A \cos(kx-\omega t)\tilde{i}+A\sin(kx-\omega t)\tag2\tilde{j}$$
where $i$ and $j$ represent the unit vectors in the x and y directions?
If so, you could think about the wave oscillating in two separate spatial dimensions.
Now the wave equation is actually ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/53608",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
"answer_count": 5,
"answer_id": 0
} |
Solution of motion in hamiltonian formalism I have these canonical equations:
$$\dot p = - \alpha pq$$
$$ \dot q =\frac{1}{2} \alpha q^2$$
I have to find $q(t)$ and p$(t)$, considering initial conditions $p_0$ and $q_0$.
I thought to simply integrate with respect time both members of the equations, but something must... | The $q$ equation is a separable ODE that can be directly integrated. To do this, note that it can be written as
$$
\frac{dq}{dt} = \frac{1}{2}\alpha q^2
$$
so that multiplying both sides by $dt$ and integrating from $t_0$ to $t$ gives
$$
\frac{2}{\alpha}\int_{q_0}^{q(t)}\frac{1}{q^2}dq = \int_{t_0}^t dt'
$$
which ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/53671",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
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