Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Other application of Liouville's theorem besides thermodynamics Are there any other important practical and theoretical consequences of Liouville's theorem on the conservation of phase space volume besides the calculation of the microcanonical potential in Thermodynamics?
| 1) On a symplectic manifold $(M,\omega)$, Liouville's theorem is often stated as that every Hamiltonian vector field $X_f=\{f,\cdot\}$ is divergence-free
$$ {\rm div}_{\rho} X_f~=~0 ,$$
where the volume density $\rho$ comes from the canonical volume form
$$\Omega~=~\rho dx^1 \wedge \ldots \wedge dx^{2n}.$$
Here the c... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/56766",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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"answer_id": 0
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Quantum field theory, particle interpretations and path integrals? I am trying to find some names or models of a particle interpretation of quantum field theory which isn't a literal path integral approach? Are there any particle interpretations of quantum field theory which don't use path integrals?
| In some sense 2nd quantization is equivalent to path integral approach when introduce quantized fields. But the point is, even if you use 2nd quantization you still need to calculate things like cross sections, which is more related to generating functional of path integral. Also, many things of more advanced QFT are b... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/56811",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 2,
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Why planets are orbiting only in one plane? Since gravity is three dimensional why planets are orbiting only in one plane around sun.
| I would probably say it has something to do with the gravity or rather fabric of space if you want. E.g. take a look of the shape of our galaxy:
Do you see the similarity?
How the galaxy resembles our solar system?
It's about the fact that after a while the biggest "rotators" like the Sun or biggest planets win and ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How is parity relevant to determining angular momentum? Question:
Particle A, whose spin $\mathbf{J}$ is less than 2, decays into two identical spin-1/2 particles of type B.
What are the allowed values of the orbital angular momentum $\mathbf{L}$, the combined spin $\mathbf{S} = \mathbf{s}_1+\mathbf{s}_2$ (where $\mat... | I actually searched for a deeper understanding of how parity is linked with angular momentum for my own, but I know from Griffiths "Introduction to Elementary Particles" that the Parity for relative angular momentum l is given by (-1)^l. All particles have parity, either + or -1, which one is determined by QFT. (creati... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/57062",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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Electrical conductivity of an intrinsic semiconductor On which factor does the electrical conductivity of an intrinsic semiconductor depend? It doesn't have an excess of charge carriers in fact, does it?
| Conductivity of intrinsic semiconductor is due to their own internal charge carriers. The bonding between between two electrons of two neighboring atoms is covalent, therefor at NTP, there is no free charge carrier for conduction. When it is heated, some covalent bonds break due to heat and thus some electron get free ... | {
"language": "en",
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Will observers moving on a sphere experience time dilation? A single source of light exists at a fixed point in space relative to two observers. The two observers move on the surface of a shell with a fixed radius with the light source at its centre. They move along a circular path on the sphere. They move at different... | You write: "All observers would agree the light blinks once every 10 secs, no matter what their velocity is as long as they are on the shell."
Using their own stationary clock, no they wouldn't, because the light source is moving relative to them. Each would record the light blinking at a rate slower by a factor $\gamm... | {
"language": "en",
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How does the solar sailing concept work? Wikipedia describes solar sailing as
a form of spacecraft propulsion using a combination of light and high speed ejected gasses from a star to push large ultra-thin mirrors to high speeds.
I understand the part where ejected gasses bump into the sail pushing the spacecraft. O... | solar sailing work on the principal impulse applied on the body by a moving photon on a reflective surface. If the ratio of the force applied by the photon which is directly proportional to the area of the reflecting surface and intensity of the light to the weight of the space craft is large enough it would accelerate... | {
"language": "en",
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Initial separation of neutron star/black hole binaries? How would I go about finding the distribution of initial separations (i.e. the lengths between the centres of mass) of stars that make up binary systems. I am interested in neutron stars and stellar black holes.
This paper uses an assumption that
"The initial sep... | The paper is rather lacking in definitions, I'll give you that.
As Murphrid points out, $\Gamma$ is just the PDF for separation, and $A$ is the variable used for the separation itself. The constant of proportionality is set by requiring the total probability to be unity.
Of course, as defined $\Gamma$ is not normalizab... | {
"language": "en",
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Why does Planck's law for black body radiation have that bell-like shape? I'm trying to understand Planck's law for the black body radiation, and it states that a black body at a certain temperature will have a maximum intensity for the emission at a certain wavelength, and the intensity will drop steeply for shorter w... | Joshua has beaten me to an answer, but I'll still post this since it's written at a simpler level.
The reason you get a maximum because there are two effects that oppose each other. The number of modes per unit frequency rises as frequency squared, so as long as the energy of the modes is well below kT the energy is pr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/57561",
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What does it mean that an inspiral is 'adiabatic'? Binary systems emit gravitational radiation. This causes the system to lose energy, which results in a shrinking of the semi-major axis. I have read on countless occasions that this 'inspiral' is adiabatic (here for example). What does this mean that the shrinking is a... | I believe it's an approximation applied to that phase of the inspiral, stating that the relative change in orbital frequency over time is small with respect to the orbital frequency itself. This defines what is known as the adiabatic parameter:
$$
\xi = \frac{\dot\omega}{\omega^2}
$$
Why adiabatic? No loss or gain of h... | {
"language": "en",
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Relating generalized momentum, generalized velocity, and kinetic energy: $2T~=~\sum_i p_{i}\dot{q}^{i}$ According to equation (6) on the first page of some lecture notes online, the above equation is used to prove the virial theorem. For rectangular coordinates, the relation
$$
2T~=~\sum_i p_{i}\dot{q}^{i}
$$
is obviou... | The equation $2T=\sum_{i=1}^n p_i\dot{q}^i$ holds both in Lagrangian and Hamiltonian formalism for large classes of systems.
*
*In Lagrangian formalism, it holds for Lagrangians of the form $L(q,\dot{q},t)=T(q,\dot{q},t)-V(q,t)$, where the kinetic energy is of the form $T=\frac{1}{2}\sum_{i,j=1}^n \dot{q}^i m_{ij}(q... | {
"language": "en",
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Future light cones inside black hole In Caroll's Spacetime and Geometry, page 227, he says that from the Schwarzschild metric, you can see than from inside a black hole future events all lead to the singularity. He says you can see this because for $r<2GM$, t becomes spacelike and r becomes timelike. I don't understand... | Objects that follow timelike trajectories always have a unique timelike coordinate associated with each point on the trajectory. This is not true for spacelike trajectories, where a Lorentz transformation can render two points on the path simultaneous.
Hence, an object on a timelike trajectory within the event horizon... | {
"language": "en",
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Deriving equations of motion of polymer chain with Hamilton's equations This is related to a question about a simple model of a polymer chain that I have asked yesterday. I have a Hamiltonian that is given as:
$H = \sum\limits_{i=1}^N \frac{p_{\alpha_i}^2}{2m} + \frac{1}{2}\sum\limits_{i=1}^{N-1} m \omega^2(\alpha_i - ... | Instead of using the chain rule (although it of course gives the same answer) expand the square of the $i^\mathrm{th}$ term in the sum parentheses to obtain
$$
\alpha_i^2 - 2\alpha_i\alpha_{i+1}+\alpha_{i+1}^2
$$
differentiating this with respect to $\alpha_i$ gives
$$
2\alpha_1 - 2\alpha_{i+1}
$$
Now, from the $(i... | {
"language": "en",
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What will happen if we place salt water on a induction cooker? As we know that induction cooker works on the principal of induction of current in a conducting plate. So I just wanted to know what will happen if we place salt water in a plastic container on the induction cooker will it get hot as it is also a conductor ... | The induction cooker works by passing a rapidly changing magnetic field through the thing to be heated.
That rapidly changing magnetic field creates an EMF (Electro Motive Force) field. (Faraday's law). This is like a voltage. Current will flow, proportional to the conductivity. No conductivity, no current. Low conduc... | {
"language": "en",
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Why do we hear a higher pitched sound outside the water when we smash two stones in water? The observer is outside the water; the stones are in water (say, 1 m below the surface). This produces a higher-pitched sound for the observer than if both the observer and the stones are in air.
Is this because it takes more ene... | The higher pitched frequencies have higher energy. The path of minimal time is to the surface.
Lower frequencies naturally travel further in water despite their lower energy value. Hence the use of infrasound by whales for the purpose of long distance communication.
| {
"language": "en",
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"source": "stackexchange",
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Pendulum axes confusion Suppose I have a simple pendulum and I want to calculate its acceleration when the bob reaches the maximal angle. I usually choose my axes such that the y-axis will be parallel to the rope. Then the acceleration would be $g \sin\alpha$ (Because: $mg\sin\alpha=ma$). However, if I choose the y-axi... | The total gravitational force is $mg$ and this force is the hypotenuse of a triangle whose sides are $mg\cos\alpha$ in the direction of the rope and $mg\sin\alpha$ in the orthogonal direction. So the latter, $mg\sin\alpha$, is the force (mass times acceleration) along the circular orbit because the centripetal part of ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/58110",
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"source": "stackexchange",
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Eye sensitivity & Danger signal Why are danger signal in red, when the eye is most sensitive to yellow-green?
You can check luminosity function for more details...
| My hypothesis is that the use of red for danger signals is because we instinctively recognize red things as potentially dangerous. Aposemitism (Wikipedia) is the use of bright colors by prey to signal the presence of secondary defense mechanisms, such as toxicity. Aposematism only functions as a defense mechanism bec... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/58166",
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"source": "stackexchange",
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Will molten iron stick to a magnet? I've known for a long time that if you heat a magnet, there is a point it loses its magnetism (the Curie temperature). It isn't clear to me if this applies to induced magnetism like iron sticking to a magnet.
Will molten iron behave like a ferrofluid and be attracted to a magnet or ... | The loss of magnetism at the Curie temperature applies primarily to "induced magnetism like iron sticking to a magnet".
Ferrofluid doesn't really include a molten iron; ferrofluid is a collection of many small but mezoscopic particles, "sawdust", and its magnetism doesn't differ so much from magnetism of normal pieces... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/59280",
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"source": "stackexchange",
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Does quantum computing rely on particular interpretations of quantum mechanics? It is my understanding that quantum computing relies on quantum superposition and entanglement to work--qbits must exist in all states simultaneously before giving a particular result when observed.
Would this mean that quantum computing is... | Generally, when you make a quantum calculation, you have to make some sort of measurement of the qubits at the end of the algorithm where the result you're looking for is a very probable (but not necessarily certain) result. In any interpretation that actually agrees with the basic results of quantum mechanics, these p... | {
"language": "en",
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Why do objects accelerate as they fall? Most importantly, what must change in order for the falling object to change its speed? Is it the distance to the centre of the planet? If you pull the earth away from the object as the object falls, will the object slow down or will it keep accelerating?
| An object accelerates when a force is acting on the object. This given by the Newton's second law $F=ma$, where $F$ is the net force act on the object, $m$ is the mass of the object and $a$ is the acceleration of the object. The reason why objects accelerate as they fall is because the gravity of earth acts on the obj... | {
"language": "en",
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Proof that a spherical lens is stigmatic In geometric optics, we generally allow that, for example in the case of a convex lens, rays coming from a particular point get refracted towards another particular point on the opposite side of the lens.
How is this proven from Snell-Descartes' law? Do we need to use the paraxi... | According to an article by the Optometric Science Research Group titled Stigmatic optical systems:
"There would appear to be little disagreement on what constitutes an astigmatic system in the case of a thin lens: the cylinder is not zero. A spherical thin lens is stigmatic or not astigmatic. The issue is less clear i... | {
"language": "en",
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Why doesn't fusion contradict the 1st law of thermodynamics? I was reading up on the 1st law of thermodynamics for my Chemistry exam and I was wondering why doesn't fusion contradict the 1st law of thermodynamics?
The 1st law states that
The energy of an isolated system is constant
or that whatever is put into the s... | By that logic, a battery violates the law also.
"Look, all I did was put in enough energy to flip a switch, and now an LED keeps shining and shining! I got more energy out than I put in!"
In nuclear fusion, we are releasing some latent energy which is present in the materials, by changing the nuclear structure into oth... | {
"language": "en",
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(Re-)use of a space elevator (basic mechanics and potential energy source) It's said that if a space elevator were made then it would be much more efficient to put objects in orbit. I've always wondered about the durability of a space elevator though. I don't mean the material strength but rather what affect using th... | I suppose that for a properly designed space elevator, the counterweight is placed far enough above geosynchronous orbit height to be able to withstand both the weight of the cable and the weight of the climber (i.e. the elevator cabin and the cargo inside it). If so, there is no reason why going up in the elevator wou... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/59746",
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Galaxies moving away at the speed of light As an arts student, I really find those cosmological questions hard to understand and hence come here to seek your kind help.
The Hubble constant $H_0$ is estimated to be about 65 km/s/Mpc, where 1 Mpc (megaparsec) is around 3.26 million light-years. At what distance would gal... | That's a very, very good question! Actually, the point you are addressing is the reason why physicists coined the term "observable universe". Those galaxies moving away from us with a speed bigger than the speed of light will never be visible (in the light they emit right now) to us and are outside the so-called "Hubbl... | {
"language": "en",
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The rule breaker, emissivity + reflectivity = 1 If emissivity and reflectivity are inversely proportionate, why does glass have a high emissivity of around 0.95-0.97 as well as being very reflective for IR Radiation?
normally it works but not with glass!
Can anyone explain this?
| One has to be careful with reflection. If you take a car rear-view mirror, it might seem to be close to 100% reflectivity, but in practice may be around only 60% (this is helped partly because the inside of the car is usually darker than the outside).
If you couple this with the usual compressed, pseudo-color look up ... | {
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Special Relativity - speed of light question Just a basic question:
I know that if you are traveling at $x$ speed the time will pass for you slower than to an observer that is relatively stopped. That's all just because a photon released at the $x$ speed can't travel faster than the $c$ limit.
I want to know what happ... | The speed of light will be the same, yes. This is the fundamental tenet of special relativity - that all inertial observers see the same laws of physics, including universal constants like the speed of light.
And yes, the wavelength $\lambda$ will change. The frequency $\nu$ will also change, since after all we still m... | {
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Is lattice enthalpy positive or negative? I've learnt that the lattice enthalpy (defined as the energy change from a solid ionic lattice to separate gaseous ions) is always positive, obviously. However, I've seen it explained as the opposite other places, so it's negative.
What is correct?
| the lattice dissociation enthalpies are always positive and the lattice formation enthalpies are always negative. when 1 mole of lattice breaks down into its gaseous ions then energy is gained here hence +ve enthalpy but when gaseous constituent ions come together to form a lattice energy is released and hence enthalpy... | {
"language": "en",
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How does the freezing temperature of water vary with respect to pressure? I know when the pressure is reduced, the boiling temperature of water is reduced as well. But how does the pressure affect the freezing point of water?
In a low-pressure environment, is water's freezing temperature higher or lower than $0\sideset... | If you decrease the pressure, the freezing point of water will increase ever so slightly. From 0° C at 1 atm pressure it will increase up to 0.01° C at 0.006 atm. This is the triple point of water. At pressures below this, water will never be liquid. It will change directly between solid and gas phase (sublimation). Th... | {
"language": "en",
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"source": "stackexchange",
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Higher order covariant Lagrangian I'm in search of examples of Lagrangian, which are at least second order in the derivatives and are covariant, preferable for field theories. Up to now I could only find first-order (such at Klein-Gordon-Lagrangian) or non-covariant (e.g. KdV) ones. Also some pointers to the literature... | You can look at the Lagrangian for the galileon particles for instance in this paper. It has the property that the equations of motion remains 2nd order in the derivatives and covariant.
| {
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How does the wavelength change in relativistic limit? In the text, it reads that the momentum of a particle will change if it is moving at speed close to light speed. In the general case, the wavelength is given as
$$
\lambda = \frac{h}{p}
$$
and
$$p = \frac{mv}{\sqrt{1-v^2/c^2}}$$
when $v \to c$, $p\to\infty$, so ... | Yes. The energy-momentum equation $E^2=p^2c^2+m^2c^4$ says that a massive object's mass (relativistic mass), momentum and energy approaches $\infty$ as a particle is accelerated towards $c$. There's nothing obvious about the fact that it requires infinite energy to accelerate it to $c$. This strictly means that you can... | {
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Could a planet sized bubble of breatheable atmostphere exist? I'm reading a book (Sun of Suns by Karl Schroeder) that the main location is a planet called Virga, which contains air, water, and floating chunks of rock, and has no or a very small amount of gravity. There is a main 'sun' at the center of the planet, which... | A sun or a star is not possible to exist on this scale; to be as massive as a core of a planet, it's just not massive enough. But you didn't mention the size of it.
So if we put that aside, first of all there's no such thing as no gravity. Where there's mass there's gravity, and that gravity has to be strong enough to ... | {
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How do you tell if a metric is curved? I was reading up on the Kerr metric (from Sean Carroll's book) and something that he said confused me.
To start with, the Kerr metric is pretty messy, but importantly, it contains two constants - $M$ and $a$. $M$ is identified as some mass, and $a$ is identified as angular moment... | The flat space time refers here to the spacetime of Minkowski written with the spherical coordinates (I think one of your sign is wrong in your equation)
$$
ds^2 = -dt^2 + dr^2 + r^2 d\theta^2 + r^2 sin^2 \theta d\phi^2.
$$
where the metric is diagonal and has constant coefficients $g_{\mu \nu} = ( -1,1,1,1)$.
I woul... | {
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Whats the anti-torque mechanism in horizontal take-off aircraft? In most helicopters there is the anti-torque tail rotor to prevent the body from spinning in the opposite direction to the main rotor.
What's the equivalent mechanism in horizontal takeoff single engine propeller, and jet aircrafts, where the air or the ... | If you place two engines spinning in opposite directions equidistantly from the center of gravity, the torque is cancelled. Hence the old Air Force song:
"Don't give me a P-38, with props that counter-rotate
They'll loop, roll and spin but they'll soon auger in
Don't give me a P-38!"
Single engine planes can compensat... | {
"language": "en",
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What is baryon loading in the context of gamma ray bursts (GRBs)? I've read that with short hard gamma ray bursts (shGRBs) associated with the coalescence of NS-NS and NS-BH binaries are expected to be beamed along the axis of the orbital angular momentum (i.e. perpendicular to the orbital plane) because the "baryon lo... | The baryon load is either the number or the density of baryons. It is the amount of baryons the burst must either clear out or carry along.
It is low at the poles and high in the orbital plain because there is nothing but empty space at the poles, whereas in the orbital plane there can be an accretion disk as well a... | {
"language": "en",
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Is it possible to "add cold" or to "add heat" to systems?
Amanda just poured herself a cup of hot coffee to get her day started.
She took her first sip and nearly burned her tongue. Since she didn't
have much time to sit and wait for it to cool down, she put an ice
cube in her coffee and stirred it with a metal... | This is not an opinion based exercise. Thermal energy is generated through conversion. It is not inherent. The natural state of empty dark space is absolute zero. Stars and other celestial bodies generate thermal energy which is distributed through space and absorbed and retained by other objects. It is not possib... | {
"language": "en",
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If the moon was rapid enough would it be able to orbit the earth from a close distance? If the moon was close in orbit that it's surface was like 100 km away from the earth's surface. And it had a large enough angular velocity will it be able to hold orbit?
If this was possible, is something similar possible to exist i... | You should do some hard assumptions, as no atmosphere, but the real problem is the so called Roche Limit, that states that at this limit, the tidal forces , difference of the gravitational potential between the face facing the Earth and the one opposite, is so large that rips the body (Moon) apart.Wiki
With the Wikiped... | {
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Dimensional Regularization involving $\epsilon^{\mu\nu\alpha\beta}$ Is it possible to dimensionally regularize an amplitude which contains the totally antisymmetric Levi-Civita tensor $\epsilon^{\mu\nu\alpha\beta}$?
I don't know if it's possible to define
$\epsilon^{\mu\nu\alpha\beta}$ in e.g. $$d-\eta$$-dimensions w... | this fails since the tensor $ \epsilon ^{a,b,c,d} $ is diemnsion dependent
however in the case of zeta regularization of integrals $ \int_{a}^{\infty}dx x^{m-s} $ with 's' a regulator we can overcome this problem
| {
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Vector and Spinor Representation in Ramond-Neveu-Schwarz Superstring Theory I am learning Ramnond-Neveu-Schwarz Superstring theory (RNS theory). I often find the following notation, especially in the closed string spectrum etc.:
$$\mathbf{8}_s,\mathbf{8}_v $$
And it is noted that these are vector and spinor representat... | Yes, they're representations of $SO(8)$, more precisely $Spin(8)$ which is an "improvement" of $SO(8)$ that allows the rotation by 360 degrees to be represented by a matrix different from the unit matrix, namely minus unit matrix.
${\bf 8}_v$ transforms normally as
$$ v\mapsto M v$$
where $MM^T=1$ is the $8\times 8$ r... | {
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How does a star ignite? I remember reading that X-Rays are generated by 'braking' electrons in a Coolidge tube.
Is it fundamentally a matter that the extreme gravity immediately before a star ignites is so strong that it affects the hydrogen atoms to the point the velocity of it's components must be let-off in the form... | The nuclear fusion that powers stars has little to nothing to do with electrons. In the cores of stars, temperatures are high enough that all the electrons are stripped from the nuclei, leaving a pure plasma.
As stars contract and condense out of interstellar dust, their gravitational potential energy is converted to h... | {
"language": "en",
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Does Earth produce metallic elements in its core? Does Earth produce metallic elements in its core?
| By metal-production, I think you're mentioning nuclear fusion (like those that take place in hydrogen bombs and core of stars) by which elements can be produced. If you look at the Wiki article I've linked, you can see a quote:
to be about the same temperature as the surface of the Sun - approximately 5700 K
I don't... | {
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Interval and proper time Is the definition of $$d s^2=-d \tau^2$$ assuming that $c=1$, so that we always have $$\left({ds\over d\tau}\right)^2=-1$$?
Is there a reason for this definition?
Don't we get an imaginary ${ds\over d\tau}$?
| It depends on what convention you're using for the metric's signature. Some people use the metric signature (-+++), which is what you have there. The interval is then:
$$ds^2=-dt^2+d \mathbf{r}^2$$
On the other hand, some people use the (+---) convention:
$$ds^2=dt^2-d \mathbf{r}^2$$
In this signature $ds^2=d \tau^2$. ... | {
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Waveguides (in the ocean?) The speed of sound in the ocean is given by
$$c_s(\theta,z) = 1450 + 4.6\theta - 0.055\theta^2 + 0.016z$$
$\theta$ is the temperature in degrees celcius, and $z$ is the depth. In a simplified model, $\theta$ is constant at 10$\,^\circ $C for the part of the ocean above the "themocline". The t... | I wonder if you're mixing up the thermocline and the SOFAR channel. The speed of sound is a minimum at the SOFAR depth, so water at this depth acts as a waveguide.
I imagine sound will reflect off the thermocline, but I don't see how this would act as a waveguide unless the sea bottom acts as the lower reflector.
| {
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Poles bit in a propagator Hi I am trying to derive the K-G propagator and am stuck on the bit where Cauchy's Integral formula is needed i.e evaluating from $$\int \frac{d^{3}p}{(2\pi)^3}\left\lbrace\frac{1}{2E_{p}}e^{-ip.(x-y)}|_{p^{o}=E_{p}}+\frac{1}{-2E_{p}}e^{-ip.(x-y)}|_{p^{o}=-E_{p}}\right\rbrace $$ to $$\int \fra... | For Feynman prescription, the poles are located at $p^0=\pm(E_p-i\epsilon)$. When $x^0>y^0$, we close the counter below the positive pole such that $\Re(-ip^0(x^0-y^0))<0$; When $x^0<y^0$, we close the counter above the negative pole such that $\Re(-ip^0(x^0-y^0))<0$. According to Jodan lemma, we know that
$$\int_{|p^0... | {
"language": "en",
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In terms of the Doppler effect, what happens when the source is moving faster than the wave? I'm just trying to understand this problem from a qualitative perspective. The Doppler effect is commonly explained in terms of how a siren sounds higher in pitch as it is approaching a particular observer. I understand this i... |
The first image shows an object traveling at Mach 1 ($v=c$). The second one shows the object traveling at some supersonic velocity ($v>c$). For both the cases, the longitudinal pressure waves pile up. Say the observer is standing in the ground and the object is traveling at $c$. The observer can't hear the pitch of s... | {
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How long does a supernova last? Is a supernova over instantaneously? Or, does the (for want of a better word) explosion continue for a while? What is/are the order of timescales involved? What is the duration for which the supernova continues to release copious amounts of energy?
| I love theoretical physics, I am not capable of the math, but here's a neat comparison. This is one of many proposed solutions to the mean free path of a photon produced in the core of the sun, this one says 4000 years to travel to emission surface...pretty wild drunken walk indeed! This is due to the assumed density o... | {
"language": "en",
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What happens when a star undergoes gravitational collapse? Immediately prior to becoming a supernova the core of some types of stars may suffer gravitational collapse.
*
*What happens to any planets in orbit around the star at the instant the mass is fully collapsed?
*Assuming this sudden change would cause some ... | It depends on the nature of the system, and the explosion. If more than about half the mass of the system is lost from the central star, the planet will become unbound (interesting National Geographic article on the subject). This can be relevant even before the actually supernova - as massive stars lose a lot of mas... | {
"language": "en",
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Parabolic motion (experiment) We performed a laboratory, performing six releases of a sphere with angles $15^\circ,30^\circ,45^\circ,60^\circ,75^\circ,40^\circ$ a parabolic movement, took five distances for each angle, the initial velocity was calculated $3.025~\text{m/s}$.
Then doing 5 tosses of the sphere with an an... | I'm a little confused by one part of your question. You ask,
Why are these speeds almost the same?
If you are asking why they are almost the same, and not completely different, then the answer is that you expect them to be the same because they are caused by the same launch mechanism. But I don't think you are askin... | {
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Can the effects of a person's mass upon the local gravitational field be detected and measured remotely? As the title suggests, Can the effects of a person's mass upon the local gravitational field be detected and measured remotely?
I am aware any mass produces and effects gravity but couldn't find anything in my searc... | According to this site
http://en.wikipedia.org/wiki/Gravimetry
Gravimeters can have a accuracy of up to 0.002 mGal (= 2*10^-8 m/s^2)
The gravity of a person of lets say 100kg at a distance of one meter is approximately
G * m/r^2 = 6.7*10^-9 m/s^2
So that person would need to weigh at least 300kg to be detectable.
| {
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Joule heating due to the (slow) electron drift velocity? I understand the concept of why the signal speed is higher than the electron drift velocity, but I can't understand the concept of joule heating. If electrons move slow then how do they produce a lot of heat when they hit the nucleus. Besides my friend once tol... | The absolute velocity of the electrons actually doesn't matter for joule heating. Think about it this way, if there is no current flowing there wouldn't be any joule heating. So, even if electrons are moving quickly and randomly when no current is flowing, we know no joule heating would occur and that joule heating i... | {
"language": "en",
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When does Thevenin's theorem not apply (modelling a power source with a ohmic internal resistance) Most physics text books say that a power source can be modelled as an EMF with a internal resistance. This is also know as Thevenin's theorem or Norton's theorem. However I have read in some sources that this is not alway... | It is doubtful if Thevenin's eqv also supports transients/dynamics. Suppose the ïnternals of a battery include a resistance as is usual and also an inductance in series with it. Concept of ïmpedance does not hold as supply is DC, and the same cannot also be converted to an eqv Norton's.
If the supply is AC and the "s... | {
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Is light red shifted in optical tweezers? This is a question I put to my supervisor during my PhD many years ago, and never really got a satisfactory answer to.
In an optical tweezers, assume that a beam of light is used to move a glass bead. My question is whether the outgoing light is red-shifted. If it is not I can... | In theory, yes, the light will be redshifted. In practice, it sounds like the glass bead is too large for any measurable red shift. This is actually used in Mossbauer spectroscopy. What happens is that if your $\gamma$-ray source is a free atom, the recoil of the atom will cause the resulting radiation to be red-shifte... | {
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Voltage of open circuit
A battery with emf $\varepsilon$ and internal resistance $r$ is connected
with a resistor $R$ in the following open circuit. What is the voltage $V_{ab}=V_a-V_b$?
The answer is $- \varepsilon$. "No current. There is no voltage change across R and r.". But I don't really understand why ... I... |
But Va−Vb=−2ε ... how do I make sense of this?
It's incorrect to write $V_a = \varepsilon$. The voltage $\varepsilon$ is across the battery.
Try this: place a ground symbol on the wire between the battery and the $a$ terminal; this is your zero node or the place you put the black lead of your voltmeter.
Now, if you... | {
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Purpose of Grover's algorithm? How is the output of Grover's algorithm useful if the result is required to use the oracle? If we already know the desired state, what's the point of using the algorithm?
So can you give me a concrete example of an oracle function. For example if the indexed items in a Grover search were,... | There is a difference between finding a solution and recognizing a solution. Oracle can recognize the solution or solve a particular instance of the problem but cannot give you the solution for complete problem. Or in other words, oracles gives you a part of solution and you may need to consult oracle a number of times... | {
"language": "en",
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How can anything be hotter than the Sun? I've heard that if a space shuttle enters the atmosphere from a bad angle its surface will become so hot that it will be hotter than the surface of the Sun.
How can that be? It seems to an uneducated mind that Sun is really really hot, how could something seemingly minor such as... | It depends on many factors such as the reentry velocity of the object, its shape (cone-spherical, etc.), what the planet's atmosphere is made of, whether it enters at some shallow angle and also the altitude where there's density variations in atmosphere, etc.
Googling on this, could return you a lot of results. And, a... | {
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How can Ohm's law be correct if superconductors have 0 resistivity? Ohm's law states that the relationship between current ( I ) voltage ( V ) and resistance ( R ) is
$$I = \frac{V}{R}$$
However superconductors cause the resistance of a material to go to zero, and as I understand it, as $R \to 0$, $I \to \infty$. Does ... | Ohm's law works for ordinary conductors for a reason: the particles carrying the current (usually, but not always electrons) scatter incoherently and inelastically from features of the conductor. In the case of an electron current, at low temperature this scattering is caused by impurities in the conductor; at high te... | {
"language": "en",
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Polarization of sound Sound can't be polarized because the vibration of such type can't be polarized i.e, it can't be limited or controlled by any barriers and so polarization is not possible in them.
This is what my teacher answered me when i asked the question. But i didn't understand what did he mean by "the vibrati... | It would be difficult to imagine a polarisation of a longitudinal wave, but this certainly is true for transverse waves. The air couples weakly to transverse waves and so does your ear! Hence, we often consider sound waves (in the air) as longitudinal only, that would not be polarised.
Generally, though, sound waves c... | {
"language": "en",
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How can an asymptotic expansion give an extremely accurate prediction, as in QED? What is the meaning of "twenty digits accuracy" of certain QED calculations? If I take too little loops, or too many of them, the result won't be as accurate, so do people stop adding loops when the result of their calculation best agrees... | Suppose you're interested in computing some quantity $F(\alpha)$, like the excess magnetic moment $g-2$, which depends on the fine structure constant $\alpha \simeq .007$.
Perturbation theory gives a recipe for the coefficients $F_i$ of an infinite series $\sum_{i \geq 0} F_i \alpha^i$, which is expected to be asympt... | {
"language": "en",
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What materials focus EM radiation in the 2.4GHz range If glass and similar materials refract visible light effectively, what materials would be best for focusing lower frequencies of EM radiation, if any? If not, what other methods exist for focusing these ranges?
The thought was inspired by wondering how you might bui... | Anything that 2.4Ghz EM waves (microwaves) will pass through that has a different index of refraction than air can be used as as a lens or prism. A really common material for this is wax.
Also, you can reflect microwaves using metal surfaces. This is how a satellite dish works.
For a simplified model of your wifi rou... | {
"language": "en",
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Probability of position in linear shm? The problem that got me thinking goes like this:-
Find $dp/dx$ where $p$ is the probability of finding a body at a random instant of time undergoing linear shm according to $x=a\sin(\omega t)$. Plot the probability versus displacement graph. $x$=Displacement from mean.
My wo... | In your notation, $dp/dx$ is your probability density. $p(x)$ is your cumulative probability density, the probability that the particle is to the left of $x$ at a given time. Knowing this, there are at least three ways you can reason. As Emilio Pisanty pointed out in his answer, you can require that $p(-a) = 0$ (ie, th... | {
"language": "en",
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Microscopic picture of an inductor I have a good understanding of how inductors behave in electrical circuits, and a somewhat rough-and-ready understanding of how this behaviour arises from Maxwell's equations. However, what I don't have a good mental picture of is how electromagnetic induction works on the microscopic... | You do not need neither a coil, nor core. The vacuum is a pretty good conductor of the magnetic field. Cores and coils only complicate the things. Consider a single loop of current. Surprise: It also has a magnetic field!
Individual electrons are susceptible to the electric field, that is induced by the changing magne... | {
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Reaching the speed of light via quantum mechanical uncertainty? Suppose you accelerate a body to very near the speed of light $c$ where $v = c - \epsilon$. Although this would take an enormous energy, is it possible the last arbitrarily small velocity needed -- $\epsilon$ -- could be overcome with a minor bump in velo... | No, because the uncertainty principle operates between position and momentum rather than position and velocity. For speeds much less than $c$, momentum is just proportional to velocity: $p = mv$. But at relativistic speeds we have to use the relativistic version,
$$
p = \gamma mv,
$$
where $\gamma = 1/\sqrt{1-v^2/c^2}$... | {
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Evolution principle of the physical laws I wanted to know if there is a physical theory that considers that the laws of physics undergo an evolutionary process. That see the law of physics or the absence of them, as something dynamic, and that with time they slowly converge to something we know today. A kind of simulat... | This has nothing to do with theories of everything, but there is such a thing as quantum darwinism. I read about a long time ago and can not give a detailed answer, sorry. The link contains further reference. I remember the nature paper to be quite good.
Quantum Darwinism hopes to explain the collapse of wave functions... | {
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"timestamp": "2023-03-29T00:00:00",
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Mathematical proof of non-negative change of entropy $\Delta S\geq0$ I understand that we can prove that for any process that occurs in an isolated and closed system it must hold that
$$\Delta S\geq0$$
via Clausius' theorem. My question is, how can I prove this in a mathematical way?
| Here's an enlightening special case: Take $n$ bodies with temperatures $T_1,\ldots T_n$ and bring them together until they reach a final temperature $T$. The first law of thermodynamics tells you that $T$ is the arithmetic mean of the $T_i$. The second law of thermodynamics tells you that the change in entropy is $n... | {
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Are all points in the universe connected? Is it true that every point in the universe is connected or could be so theoretically? If so how is this mediated?
Is it through the quantum nature of the fabric of space or is it through the interrelationships of the gravity fields throughout the universe. From the gravity fie... | All points in the observable universe are "connected" in the sense that they can be acted upon by forces that have an infinite range (gravity and electromagnetism).
However, points that are outside of our cosmological horizon (due to the expansion of the universe) are no longer causally connected with points in our loc... | {
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Lookback Time & Age of the Universe Calculations I try to calculate the age of the universe with the FLRW model:
$$ H(a) = H_0 \sqrt{\Omega_{\mathrm{R},0} \left(\frac{a_0}{a}\right)^4 + \Omega_{\mathrm{M},0} \left(\frac{a_0}{a}\right)^3 + (1-\Omega_{\mathrm{T},0}) \left(\frac{a_0}{a}\right)^2 + \Omega_{\Lambda,0}}. $$
... | The total energy density is by definition
$$ \Omega_{T,0} = \Omega_{R,0} + \Omega_{M,0} + \Omega_{\Lambda,0},$$
so with the values you cite ($\Omega_{R,0}=4.8\times 10^{-5}$, $\Omega_{M,0}=0.317$, $\Omega_{\Lambda,0}=0.683$), we get $\Omega_{T,0} = 1$, or in a more common notation $\Omega_{K,0}=1-\Omega_{T,0}=0$, i.e. ... | {
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Calculating the mechanical power of a water pump Say I want to pump water from one container to another. The water levels are 3 meters apart, and I want to pump 10 litres per hour. I figure the mechanical power necessary, assuming no losses, is:
$$
\require{cancel}
\dfrac{10\cancel{l}}{\cancel{h}}
\dfrac{kg}{\cancel{l}... | The number you calculate is proportional to the flow rate you put in, so a ten times faster flow rate will require ten times more electrical power, so if you do the same calculation with a flow rate closer to what you'd get from a fountain, you'll probably get a lot closer to the right order of magnitude.
This calculat... | {
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If particles can find themselves spontaneously arranged, isn't entropy actually decreasing? Take a box of gas particles. At $t = 0$, the distribution of particles is homogeneous. There is a small probability that at $t = 1$, all particles go to the left side of the box. In this case, entropy is decreasing. However, it ... | Right, there is a small probability that the entropy will decrease. But for the decrease by $-|\Delta S|$, the probability is of the order $\exp(-|\Delta S| / k)$, exponentially small, where $k$ is (in the SI units) the tiny Boltzmann constant. So whenever $|\Delta S|$ is macroscopically large, something like one joule... | {
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North and south of magnetic field
The current I is flowing upward in the wire in this figure. The direction of the magnetic filed due to the current can be determined by the right hand rule.
Can we determine the north and the south of the magnetic field produced by the current I by using a hand rule?
| The concept of magnetic poles is only defined for localized magnetic systems, which include permanent magnets (or equivalently their surface currents) and induction coils.
The reason for this is that the north/south pole description of a magnet is, mathematically, a description of the magnetic (dipole) moment of the s... | {
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Does relativistic mass have weight? If an object was sliding on an infinitely long friction-less floor on Earth with relativistic speeds (ignoring air resistance), would it exert more vertical weight force on the floor than when it's at rest?
| "Does gravity depend on relativistic mass or rest mass?" is a rather interesting question -- Einstein's initial approach was to say "the relativistic mass", and this was the pre-general relativistic answer, but this is not satisfactory, since the relativistic mass is only one component of the energy-momentum vector (an... | {
"language": "en",
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Error in Sear's and Zemansky's University Physics with Modern Physics 13th Edition (Young and Freeman)? I was reading up on the Ideal Gas Equation in University Physics with Modern Physics by Young and Freeman when I chanced upon a seemingly illogical mathematical equation.
Can anyone rectify this error? Or is it misun... | Nice catch!
For reference here is the book page.
:
See , though it may error in printing or anything else.The final equation they get $$pV=\dfrac23K_{tr}$$ is very correct.
The correct form of $eq.(18.12)$ must be $$pV=\dfrac13Nm(v^2)_{av}=\dfrac
{\color{red}{\huge{2}}}3N\bigg[\dfrac12 m (v^2)_{av}\bigg]$$
| {
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$\langle B|A \rangle$ expressed in terms of the Partition Function Say you have an electron departing from point A and reaching poing B after a time t.
According to some helping friend, the Partition Function for that electron going from point A to B can be written as
$$Z = \int_{A \to B} [\mathcal{D}x]~ e^{iS[x]}$$
wh... | What your friend actually meant is that you can obtain all desirable correlation functions. Assuming you're talking about a non-relativistic electron, consider a source term added to your action
$$
S'[x] = S[x] + \int dt \, J(t) x(t)\,.
$$
Now you can write any correlation function as a derivative of $\ln Z$ calculated... | {
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Mercury's Orbital Precession in Special Relativity I am researching Mercury's orbital precession. I have considered most perturbations and general relativity. I am still not satisfied. I need your help.
I need a solution to Exercise 13, Chapter 6, in Ref. 1 (which is Exercise 26, Chapter 7, in both Ref. 2 and Ref. 3).
... | I think this is the Thomas precession, which is a kinematical effect that depends on the shape of the worldline and is independent of the nature of the force.
Wikipedia gives a low-speed approximation for the Thomas precession of $ω_T=av/2c^2$. For a circular orbit with radius $r$ and speed $v$, the precession per orbi... | {
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What's the physical significance of using fourier transform for diffraction? I am studying some basic idea of diffraction and there mention in far field, the diffraction pattern could be understood by Fourier transform. But I just don't understand what's the physical fact for that. And why cannot use Fourier transform ... | To give an unmathematical catchy answer, let's look at Fraunhofer diffraction in double slit experiment.
Interference at the observation plane depends on slit parameter $d$. What is the frequency of slits? E.g. $1\,\text{mm}\frac{1}{d}$: number of slits per length. Concluding frequiency in the setup. The following argu... | {
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Physical interpretation of Poisson bracket properties In classical Hamiltonian mechanics evolution of any observable (scalar function on a manifold in hand) is given as
$$\frac{dA}{dt} = \{A,H\}+\frac{\partial A}{\partial t}$$
So Poisson bracket is a binary, skew-symmetric operation
$$\{f,g\} = - \{f,g\}$$
which is bil... | If we consider for simplicity a 2d phase space (q,p), then we can interpretate the poisson bracket between two functions f(q,p) and g(q,p) as the vector product of their gradients, which are vector fields in this plane:
$[f,g]=(\nabla f\times \nabla g)\cdot \mathbf{e}_z$
where $e_z$ is a unit vector perpendicular to th... | {
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Bleaching groundstate I'm reading an article about two-dimensional infrared spectroscopy and I don't understand the following sentence.
Bleach or stimulated emission contributions yield negative signals.
What are "bleach contributions"? I have never heard of it and cannot find a suitable explanation on the Internet. ... | I feel obliged to post another answer since the first one contains a mistake.
As you deplete the ground state, you also populate the excited state, and when the photon interacts with the excited molecule, then instead of being absorbed it generates another photon through stimulated emission. The paper you cite treats t... | {
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What is our estimated running speed on Moon's surface? I was wondering if we have the chance to run on the Moon's surface, how would you expect it look like?
I expect our velocity will increase for the same work we do on Earth, but not sure if this will be multiples in term of gravity variations.
How do you think our m... | Maximum speed can be ~ (because friction etc. are slowing you down and the moon isn't a perfect sphere)
$\frac{v^2}{r} = \frac{GM}{r^2}$ $-$ $(1)$
where $r$ is radius of moon & $M$ is mass of the moon.
EDIT : Since then in this case your normal reaction is $0$ , means you are almost flying , speed up a little... | {
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Why does increasing the temperature of a thermistor decrease it's resistance? Surely, upon an increase in temperature, the atoms within the thermistor would vibrate with more energy and therefore more vigorously, hence making the electrons flowing through the electric circuit more likely to collide with one of the atom... | Thermistor with this particular temperature behavior are commonly semiconductors. In a semi-conductor, there is an energy gap between the (filled) valence and the (empty) conduction band. At zero temperature, no charges are in the conduction band and the resistance should be infinite as the system behaves basically lik... | {
"language": "en",
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Does inertia increase with speed? I have heard that when the speed of the object increase, the mass of the object also increase. (Why does an object with higher speed gain more (relativistic) mass?)
So inertia which is related to mass, increase with speed?
So, if I accelerate on a bus, my mass will increase and my iner... | I think It has more to do with acceleration than speed. What do you compare a constant speed to without knowing the inertial frame for the universe. For instance if the earth is traveling toward the constellation Leo at 390 km/s what would happen if you blasted off in a rocket in the opposite? After accelerating would ... | {
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What is the derivation for the exponential energy relation and where does it apply? Very often when people state a relaxation time $\tau_\text{kin-kin}, \tau_\text{rot-kin}$,, etc. they think of a context where the energy relaxation goes as $\propto\text e^{-t/\tau}$. Related is an approach to compute it via
$$\tau=E... | This kind of exponential decay toward "equilibrium" can be derived when one looks at a Markov process.
In this case, if we call $S_t$ the state of the system at time $t$ and $S_{t+1}$ the state at time $t+1$, one has for the evolution:
$S_{t+1} = T S_t $
where $T$ is called the transition matrix. This implies that $S_t... | {
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Comparing Static Frictions In this figure, which of the static frictional forces will be more?
My aim isn't to solve this particular problem but to learn how is static friction distributed . Since each of the rough-surfaces are perfectly capable of providing the $-1N$ horizontal frictional force but why don't they ? T... | The ground will provide all of the static friction. Imagine what would happen if the upper block contributed even a tiny amount to the static friction: It would have to move forward due to the reaction force. Having M2 inch along you pull M1 (which stays stationary) would be very strange indeed.
Static friction alway... | {
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Effective mass in Spring-with-mass/mass system Suppose you have a particle of mass $m$ fixed to a spring of mass $m_0$ that, in turn, is fixed to some wall. I'm trying to calculate the effective mass $m'$ that appears in the law of motion of the particle (suppose the system is isolated):$$m'\ddot x=-k(x-x_0).$$
I've re... | You can understand in a simple way the factor $1/3$ which gives you the approximate solution in the low frequency regime (more on this later) in the following way. Start by writing the kinetic energy of your system as:
$$K = \frac{1}{2} m \dot{\delta}(\ell)^2 + \int_0^\ell \frac{1}{2} \lambda \dot{\delta}(u)^2 du$$
wh... | {
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How can a car's engine move the car? Newton's First Law of Motion states that an object at rest or uniform motion tends to stay in that state of motion unless an unbalanced, external force acts on it.
Say if I were in a car and I push it from the inside. It won't move. So how is the engine of a car capable of moving t... | Each force causes reaction (3rd law). If move a car from the inside the car moves you as well. That's because you are pushing or pulling. However the engine does not push but converts energy in other directions, usually a rotating one (the same as riding a bicycle). This rotating force has its counter-force which is ... | {
"language": "en",
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Quantum Mechanical Operators in the argument of an exponential In Quantum Optics and Quantum Mechanics, the time evolution operator
$$U(t,t_i) = \exp\left[\frac{-i}{\hbar}H(t-t_i)\right]$$
is used quite a lot.
Suppose $t_i =0$ for simplicity, and say the eigenvalue and eigenvectors of the hamiltionian are $\lambda_i... | Without loss of generality, let's take the $|\lambda_i\rangle$ to be orthonormal. Notice that, by the spectral theorem, the hamiltonian can be written as follows:
$$
H = \sum_i \lambda_i P_i, \qquad P_i = |\lambda_i\rangle\langle \lambda_i|
$$
Each operator $P_i$ is a projectors onto the subspace spanned by $|\lambd... | {
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Why the magnetic flux is not zero? If $\vec{\mathbf B}=B\vec{\mathbf a}_z$, compute the magnetic flux passing through a hemisphere of radius $R$ centered at the origin and bounded by the plane $z=0$.
Solution
The hemisphere and the circular disc of radius $R$ form a closed surface, as illustrated in the figure; there... | The flux through the closed hemisphere is zero,
$$\Phi_{\mathrm{hemi}}+\Phi_{\mathrm{disk}} = 0.$$
This allows us to find the flux through the hemisphere knowing the (more easily calculable) flux through the disk,
$$\Phi_{\mathrm{hemi}} = -\Phi_{\mathrm{disk}}.$$
| {
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Induced current using a reference system bound with a moving charge Suppose we have a charge moving at velocity $\mathbf{v}$ in the same plane of a square wire.
If I sit in a reference frame where the square wire is still, since the charge is moving with velocity $\textbf{v}$ in this coordinate system, I will see an... | There's no contradiction (there never is in relativity problems...): a transient current flows in the square as it passes by the charge.
You're correct that the conservative electric field in the charge's rest frame means that the line integral around a square in that frame is zero, but that's not the appropriate integ... | {
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Convergence of Light on the Retina So, I've learned about lens ray diagrams-but the problem I'm having is that when ray diagrams are drawn for a point of an image, they converge to another point, but there are two problems that I see with regards to our eyes:
1) In the simplest drawn case it's at least three rays conve... | You are a bit confused.
Rays are a geometrical representation of the classical electromagnetic waves and are very good for optics situations.
The cells in the retina are in the quantum mechanical regime, because to react to light they absorb photons at specific molecular energy levels of the molecules in the cells whic... | {
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How does relativity explain gravity, without assuming gravity I have seen the "objects pull down on space-time" explanations, but they assume a "pull down" force themselves. Could anyone explain the space-time explanation without assuming gravity in the first place?
| Massive objects distort spacetime, as described by the Einstein Field Equations. In turn, this causes particles to accelerate: the GR equivalent of $\mathbf{F}=m\mathbf{a}$ are the geodesic equations:
$$
\frac{\text{d}^2x^\alpha}{\text{d}\lambda^2} + \Gamma^{\alpha}_{\mu\nu}\frac{\text{d}x^\mu}{\text{d}\lambda}\frac{\t... | {
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Stable Nuclei - Deviation from equal protons and neutrons While studying the semi-empirical mass formula for nuclei, I came across an "asymmetry term" whose function, as far as I understand, is to build in the fact that nuclei "prefer" to have equal numbers of protons and neutrons. This is explained by the Pauli exclus... | Neutrons are subject to the strong force, holding the nucleus together, but not to the electric force, which pushes only the protons apart. In that sense, it's more stable for a nucleus to have a few spare neutrons to space the protons apart and keep them stuck together.
| {
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How can the big bang occur mathematically? As we know time began with the big bang. Before that there was no time, no laws, nothing. Mathematically how can an event take place when no time passes by? How did the big bang took place when there was no time?
Note my question is not about weather big bang took place or not... | You asked for a purely mathematical answer and received a correct physical answer from John Rennie. If you want a purely mathematical answer, that purely mathematical answer has to exist within a well-defined mathematical theory. As John has explained, we don't have a well-defined mathematical theory of the Big Bang th... | {
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Why does sound move faster in solids? I know that the molecules are closer together in solids, and I know thicker springs also respond carry waves faster than thinner springs, but for some reasons I can't understand why.
The molecules will have a larger distance to move before colliding with another molecule, but in a... | Think of it this way. Elasticity is a property of material that allows it to store energy and release it without dissipating. Solids have high elasticity, therefore, they can store and release energy quite efficiently. Liquids and gases have low elasticity. They are also viscous and dissipate energy instead of transmit... | {
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Where does the extra equation come from to determine the forces from an object on a table? I have a question about basic statics but somehow I cannot manage to find the answer on my own (btw, this is not a homework. It's been so many years since school for me...).
The problem is very simple: we have an object with wei... | As you have noticed yourself, your system is simply underdetermined. In order to find a unique solution you need to add some extra constraints in addition to Newton's equations. Imagine a table with more than four legs: the more legs you add, the more unknown forces you have. But the number of equations does not change... | {
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Tensor equations in General Relativity In the context of general relativity it is often stated that one of the main purposes of tensors is that of making equations frame-independent.
Question: why is this true?
I'm looking for a mathematical argument/proof about this fact.
| What we want of a law of nature is that is has the same form for every equivalent observer.
Therefore, these laws should be construct with geometrical objects which transform into themselves up to multiplicative factors. This is also known as an homogeneous transformation under certain group (typically Lorentz or diffe... | {
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Why are the magnetic moment and the angular moment related? Why are the magnetic moment and the angular moment related? I've always read everywhere that they are related but found nowhere a satisfactory explanation of the cause
| The way I understand it, a charged particle, which has an angular momentum, will have a magnetic moment associated with it. This could be because an angular momentum is associated with some kind of rotation. For a charged particle, this rotation could be thought to constitute a current loop. And a current loop can alwa... | {
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Solving a light ray worldline with the geodesic equation I'm having trouble solving the geodesic equation for a light ray.
$$ {d^2 x^\mu \over d\tau^2} + \Gamma^\mu_{\alpha\beta} {dx^\alpha \over d\tau} {dx^\beta \over d\tau} = 0 $$
I apologise, but I'm a bit new to this, but I have the initial $x^\mu$ and initial $dx^... | $\tau$ can be seen as proper time scaled by an arbitrary factor. For the limit of approaching a null geodesic, yes $\tau$ as proper time goes to zero, but use an arbitrary factor approaching infinity, and the combination can be kept finite. Or ignore all that; $\tau$ can be any arbitrary parameterization along the ge... | {
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"S-duality" between confinement and the Higgs mechanism? I feel picked by the second to last sentence in this answer to a question about what would happen if EM and QCD were spontaneously broken, which says
"In fact, there is a sense in theoretical physics in which confinement is complementary to Higgsing – it's the s... | Experimentally there are the running coupling constants, which are being used in models like GUTS etc which aim to eventually unify all four forces, strong, weak, electromagnetic, and hopefully gravity.
Note the LEP line on the left, that is where experiments are up to now. I do not expect the LHC to improve on this, ... | {
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How is it that the Earth's atmosphere is not “blown away”? The Earth moves at a high rate of speed around the Sun, and the solar system is moving quickly around the Milky Way. How is it that the Earth's atmosphere is not “blown away”?
| I dont think @Brendon is right. Best exemple of an object moving trougth space and being blown away is a comet (blown away part is the tail).
Best answer I think si that the Earth's atmosphere IS blown away but to a lesser level due to its gravitationnal force (Keeping the Earth in one pieces).
| {
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Quantum Mechanics, Uncertainty Principle-- help understanding notes There is a section of my notes which I do not understand, hopefully someone here will be able to explain this to me. The notes read (after introducing the uncertainty operator):
If the state $\chi_A$ is an eigenstate of $\hat O_A$ then the uncertaint... | You can justify thus:
$\psi=\ Ae^{i\frac{(px-E t)}{h}}$ is an eigenstate of a free particle. The momentum $\ p$ is well defined and its in the eignestate of momentum operator (as $O_p\psi=\ -ih\frac{d\psi}{dt}=p\psi$ ) This means the probability of finding the particle with momentum $\ p$ is $\ 1$.
Operators $\ x$ ... | {
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Does potential energy in gravitationall field increase mass? I was just taught (comments) that any type of energy contributes to mass of the object. This must indeed include potential energy in gravitational field. But here, things cease to make sense, have a look:
*
*I have object at some distance $r$ from radial s... | Yes. All energy contributes to the overall mass. PBS Space Time has a really clear video on this subject: The Real Meaning of E=mc² In the video, Gabe points out that Einstein originally wrote the equation as m = E/c², and describes how all energy has the property of mass, including potential energy.
Edit to add: it's ... | {
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"source": "stackexchange",
"question_score": "11",
"answer_count": 4,
"answer_id": 2
} |
What happens when a photon hits a beamsplitter? Yesterday I read that we can affect the path and the 'form' (particle or wave) of a photon after the fact (Wheeler's delayed choice experiment). Part of what is puzzling me is the beam-splitter. Are the individual photons actually being split into two new photons of less... | A single photon is a quantised packet of Electromagnetic energy, the smallest indivisible unit imposed by boundary conditions according to quantum mechanics. In this regime I find it easier to think of the photon as a particle with a 'polarization' degree of freedom which can be horizontal $\left|H\right>$,vertical $\l... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/66498",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
"answer_count": 6,
"answer_id": 1
} |
Solving equation of motion of two massive particle exerting the gravitational force each other I'm trying to analyze the motion of the particles which exert the gravitational force each other. Let $M_1$, $M_2$ be the masses of the particles, and the equation of motion of particle $M_1$
$$
F=G\frac{M_1M_2}{r^2}=M_1\ddot... | I suggest to see the scenario physically first, and proceed from there.
Here, the gravitational force does not change the distance from the center, but it provides the centripetal force for the circular motion (or any conic section for that matter, based on initial values).
Assuming it is a circular motion for now, we... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/66568",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
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