Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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What is the relationship between gravity and inertia? What is the relationship between Gravity and Inertia? Einstein told us that gravity and inertia are identical. And from the fact that two different masses fall at the same rate, I believe we can say that gravity and inertia are equal (That is, the inertia of a dro... | Well Inertia and gravity are same at fundamental level.
Inertia - A body due to its mass (energy), creates a dip of space around it. That dip makes a force be required to make a change in state of the body. Hence causes inertia.
Gravity - Same dip (curve) due to mass (energy) of the body manifests as gravity for other ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/390540",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
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What does this notation mean: $\mathrm{O}_{2} \ \ a\,{}^{1} Δ_{g} ← X\,{}^{3}Σ^{-}_{g} $? The notation (which I found in the abstract of this paper) is
$$\mathrm{O}_{2} \ \ a\,{}^{1} Δ_{g} ← X\,{}^{3}Σ^{-}_{g}. $$
Any help with this?
I understand it's talking about quantum states of the molecule but I can't find a con... | The notation is molecular term symbols and, the wikipedia article does seem to provide what you are asking for. The larger subject is molecular spectroscopy.
Lets look at the term on the right. The capitalized sigma refers to the angular momentum of this orbital along the molecular z axis, in this case it is zero. A... | {
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Formula of escape velocity While establishing relation of escape velocity and radius , I confronted a problem .
(i) $$v_e=\sqrt{\frac{2GM}{R}}$$
This states that $v_e$ is inversely proportional to the square root of radius .
(i) $$v_e=\sqrt{2gR}$$
This states that $v_e$ is directly proportional to the square root of ... | The problem is solved when you realize that $g$ in your second formula is a function of $R$: if
$$F = \frac{GMm}{r^2}$$
is rewritten as
$$F = mg$$
Then it follows that
$$g = \frac{GM}{r^2}$$
When you substitute that in your second equation, you get the first...
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/390923",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Calculating $W$ - $Z$ bosons mass difference Naively one might expect the W weak vector bosons to have slightly higher mass than the Z due to EM self-energy, while the opposite is true (80 vs. 91 Gev). Presumably due to the strong interactions and mediated by quarks since that is the only particle coupled to both inter... | No, absolutely not! Naively, one might expect $M_W=M_Z ~ \cos \theta_W < M_Z$, where $\theta_W= \arccos \frac{g}{\sqrt{g^2+g'^2}}$ is the weak mixing angle, at the heart of the logic of the standard model!
Geometrically, $M_W$ is the base and $M_Z$ the hypotenuse of the SM coupling space right triangle,
g being t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/391067",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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How is the waveform deviation from the equilibrium related to the air molecule movement? I'm not sure if this is a stupid question. I've been considering the deviation from the equilibrium reflects the air pressure, with larger deviations reflecting higher air pressure. But in Reetz and Jongman's Phonetics, it's said t... | The answer by jknappen gives the reason why one can treat are as a continuous medium instead of trying to calculate movements of molecules. One usually regards sound pressure. But there is also a longitudinal displacement of volume elements of the gas. It is less convenient to use displacement because it is further at ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/391127",
"timestamp": "2023-03-29T00:00:00",
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How to calculate a change in velocity as a result of friction? If you have an object moving at $u$ initial velocity with no acceleration, and a surface with a $$\mu_k$$ frictional coefficient, how can you calculate its final velocity after having traveled $d$ distance over this surface?
Would I also need mass $m$ to fi... | Equate work done by friction force per travel distance $d$ to the loss of kinetic energy :
$$ \mu_k mg\,d = \frac {m (u - v)^2}{2} $$
Then solve equation for $v$.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/391318",
"timestamp": "2023-03-29T00:00:00",
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Thought Experiment Spaceship Accelerating from Earth From Earth, a spaceship is observed accelerating away at a constant acceleration of $g=9.81 m/s^2$.
As the spaceship continues to accelerate, how would people on Earth see the spaceship's acceleration? Would we still see it accelerate at $g$ or will it change?
| Yes, it would change as seen by the observer, which it starts to decelerate. This is caused by the limit of causality speed $c$, and therefore you need to take the effect of time dilation and length contraction into account. You can calculate the acceleration of spaceship as seen by observers on Earth by the equation: ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/391460",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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What can be the simplest way to find the thickness of a soap bubble? Is it possible to measure the thickness of a soap bubble without using any sophisticated instruments such that anyone can do it?
| Average thickness could be determined by observing a bubble machine consume soapy water and produce bubbles. The calculations require only arithmetic and the physical science concepts of length, area, volume, and time.
$$\text{average thickness} [L] = \frac V {\frac {\pi d^2} 3 \frac {n s} t}$$
$$V = \text{volume of so... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/391563",
"timestamp": "2023-03-29T00:00:00",
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Why are spins initially coherent after 90 degree pulse in NMR? In NMR we apply a 90 degree radio frequency pulse to the sample. This causes magnetization vector to fall into transverse plane. Then the relaxation of initial phase coherence occurs. Why are the spins initially coherent?
| I know this is kinda old but I find the answer of John is actually contradicting what I learned. My intuition was as well, that the loss of phase coherence is due to spins precessing around $B_0$ at different speeds. However, why would it then be, that large molecules like proteins or polymers show quicker $T_2$-relaxa... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/391705",
"timestamp": "2023-03-29T00:00:00",
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Laws of physics and diffeomorphism covariance Up to my limited understanding, diffeomorphisms on a space-time manifold can be viewed as changes of coordinates. While studying general relativty, I read that the theory has diffemorphism covariance because it expresses its laws on a geometrical form. The same can be said ... | As for my understanding the meaning is different.
A diffeomorphism is an invertible and differentiable map between differentiable manifolds.
A diffeomorphism covariance is the invariance of the form of physical laws under arbitrary differentiable coordinate transformations. The essential idea is that coordinates are ju... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/391925",
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Are there 'closed' solution of Schroedinger equation? Are there closed solution for the wave function of schroedinger equation?
i mean solutions in the form $ \Psi (x,t)= f(x-t,y,z,t) $
that are not given by infinite series.
For example for the 1+1D wave function there is the closed d'Alambert solution
$$ f(x-vt)+ f(... | Any "nice" square-normalizable function $f(\textbf{x})$ can be a solution to the time-dependent Schrödinger equation at some point in time. To see this, consider the case of a time-independent Hamiltonian, and define the function
$$f(\textbf{x},t)\equiv e^{-iHt/\hbar}f(\textbf{x}).$$
It is clear from the functional for... | {
"language": "en",
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What is a "decade" as a unit of measure (ex. a decade of the EM spectrum)? Reading through papers and online sources about radio galaxies, I kept stumbling across a term--a "decade" of the electromagnetic spectrum. Radio galaxy emission encompasses "11 decades of the EM spectrum". Or this quote from NASA:
Astronomers ... | While many units are available for physical measurables, there are only a few that identify unitless variables, like ratios.
One is 'octave', meaning a factor of two (usually in frequency); another is 'decade', meaning a factor of ten. A third is bel, which grows
a suffix from time to time, and indicates (almost alwa... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/392508",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "31",
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Reparameterization and conformal transformation in SYK I have a simple question about SYK model.
For SYK in the IR limit, the Schwinger-Dyson equations have some so called rearamerization invariance
$$\psi_i(\tau)\rightarrow \psi_i(f(\tau))=f'(\tau)^{-\Delta}\psi_i(\tau)$$
I want to whether this transformation is relat... | You are probably thinking about higher dimensional CFTs, e.g. 2d CFT. In 2d CFT, you have two dilation operators ($L_0$ and $\bar{L}_0$ from two copies of $SL_2$), acting on left and right. One can label the eigenvalues by e.g. $h$ and $\bar{h}$ and define spin and scaling dimension by recombining them. However in the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/392631",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Do masses interact with each other or not? I want to know whether there is any interaction between masses due to gravity. To illustrate my point suppose two masses are in space. They will get attracted to each other. But is this interaction due to exchange of gravitons or there is no interaction between them but a natu... | The word interaction does not have a precise meaning in physics, but to the extent that it does have a meaning it implies an exchange of momentum. That is, if two bodies interact then they exchange momentum with each other. This implies there is an interaction force since change of momentum (also called impulse) is the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/392698",
"timestamp": "2023-03-29T00:00:00",
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radiation of rotating spherical shell with constant or changing angular speed Does a rotating spherical shell with uniform charge density radiate for both cases of constant and changing angular speed?
| Rotating spherical shell possesses magnetic dipole moment $\vec{m}={Q \vec{\omega} R^2}/{3}$. Rotation with a constant angular speed does not cause changes in the electromagnetic field of this system, so there would be no radiation.
On the other hand, if the angular speed changes, then there would be magnetic dipole r... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Newton's 3rd law of motion, related to Earth's gravity When a stone falls from a certain height above the Earth's surface, it accelerates towards the center of Earth under the influence of Earth's gravity. According to Newton's 3rd law, the stone also exerts an equal force on the Earth, but towards itself. So the Earth... | From a fundamental point of view there is nothing special about earth (or the heavier object) compared to the stone (or lighter object) here. Gravity is a force that acts between masses. You can also see this from the law of gravity:
$$F=G\frac{mM}{r^2}$$
which is completely symmetrical between the stone ($m$) and eart... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/394009",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Evaporation of BH and area theorem Just a silly question. If black holes evatorate completely due to Hawking radiation, how can the area theorem hold if no black hole is left at the end? If no black hole, no area. How is compensated the event horizon area increasing with the accepted emission of hawking radiation makin... | The area theorem makes use of the Raychaudhuri equation for a congruence of null geodesics together with the null energy condition, but exotic fields can violate this law.
Indeed the Hawking radiation stress energy tensor doesn’t satisfy the null energy condition, therefore the second law is violated and the black hol... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/394110",
"timestamp": "2023-03-29T00:00:00",
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On fluctuations of the gravitational potential? In the book "Gravitation", written by Charles W. Misner, Kip S. Thorne, and John A. Wheeler, in § 43.4, p.1192 "Fluctuations in geometry", and in § 44.2, p.1200, by analogy with electrodynamics, the following formula (43.29) is obtained for the fluctuations of the gravita... | The answer can be the following. The gravitational field performs zero-point oscillations, and the geometry associated with it also oscillates. The ratio of the circumference to the radius varies near the Euclidean value . The smaller the scale, the greater the deviations from the Euclidean geometry. Let us estimate th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/394238",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Derivative of proper time w.r.t. time? On page 86 of Theoretical Minimum (part 3 on special relativity) by Susskind, he writes:
$$\frac{d\tau}{dt}=\sqrt{1-v^2}$$
Where $v$ is the velocity of a moving reference frame relative to the restframe (which is the frame of coordinates $t,x$). He derives this from the equation (... | You don't "go from $\tau = \sqrt{ t^2 - x^2}$ to $d\tau = \sqrt{dt^2 - dx^2}$" because your starting point itself is incorrect.
Think about what $\tau$ is. It is the proper time interval between two events, $E_1$ and $E_2$. If the two events have coordinates $(t_1,x_1)$ and $(t_2,x_2)$, then the proper time interval b... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Is it true that matter and antimatter must have same mass? Consider a matter and antimatter pair having the same mass and one of the two has been accelerated by an external force or supplied with some initial kinetic energy (After big bang least one of the many formed matter and antimatter pairs may have different kine... | It should be cited that, for two equal-mass particles, even if you accelerate one to some (constant) speed, there will always be a frame of reference, called the center-of-mass frame, where the two particles will have equal momenta and energies. So if you're worried about unequal relativistic masses in a particle coll... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Why do turkey bacon slices form bubbles in the same places? Often, turkey bacon forms large bubbles when cooking. It's simply a fact of how it cooks. More interestingly however, I was making turkey bacon this morning when I noticed that all of the slices formed bubbles in nearly exactly the same place along the slice, ... | this product is probably extruded from a mixer/grinder and then sliced thinly across the extrusion direction. This makes each slice cook up similarly because the distribution of ingredients in any two slices will be similar.
there was a time when the safeway store chain sold pre-sliced swiss cheese in plastic packagin... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/394778",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Velocity of light in Galilean transformation What is the velocity of light in Galilean transformation? Is it infinity?
| The short answer to your question is: any.
The speed of light as any speed under Galilean transformation follows the usual vector sum rule. i.e., let it be $c$ the speed of light in a reference frame $R$ and $c’$ the speed of light in another frame $R’$ moving relatively to $R$ with the speed $v$. According to Galilee’... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/394890",
"timestamp": "2023-03-29T00:00:00",
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Does the mass of a bicycle directly affect stopping distance? In this answer on the cycling SE, the claim is made that adding more mass to a bicycle increases the stopping distance. I was under the impression that mass should not affect the stopping distance so long as all the other factors remain the same (balance, co... | Here is a practical answer. If you can make your tires skid, mass does not really affect stopping distance. This is another way of saying the limiting factor is road/tire friction. Thus max stopping force increases proportionally with mass and balances the F=ma equation. Most people can make their tires skid if the bra... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/394975",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
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How to compare the resistance of various elements? Resistance is a function of distance. How to compare the resistance of various materials independent of distance?
| Resistivity is the intrinsic property of a material that measures how much the material opposes the flow of current, but does not reflect the dimensions of the object made out of the material. With an object made out of the material which has a uniform cross section and electrical contacts on the two ends, the material... | {
"language": "en",
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Earth, re-radiation So Earth receives radiation from the Sun, which heats it up, but then reradiation occurs and Earth loses energy into space. Lets assume the processes are perfectly balanced, this is not about the greenhouse effect. Some of the radiation gets reflected back into space, but much of that radiation stay... | The Earth radiates the Energy because light speed is greater than Earth's escape velocity. However the light since it cannot slow down will lose a really really really tiny amount of energy to the Earth's gravitational field. Some light gets trapped by molecules like carbon dioxide which trap infrared light and that is... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/395195",
"timestamp": "2023-03-29T00:00:00",
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Why do we take the partial differntial with respect to time when calculating the particle velocity of a particle in a wave? When calculating the velocity using y=Asin(wt-kx), shouldn't we consider the change in x with respect to t instead of assuming that x is constant. Do we take x constant because in a transverse wav... | $y$ is the displacement of a particle from its equilibrium position.
That displacement can be perpendicular to the direction of wave motion / energy/momentum transfer (transverse wave) or parallel to the direction of wave motion / energy/momentum transfer (longitudinal wave).
$x$ is the equilibrium position of a part... | {
"language": "en",
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Paradox in special relativity involving capacitor In the laboratory reference frame (LRF), a horizontally moving (with constant speed) flat capacitor would have a different size of plates therefore resulting in different capacity $C'$, namely
$$
C' = \frac{1}{\gamma}C,
$$
where C is a capacity in its own reference fram... | Related: Is the inertia of light equal to the inertia of mass under $E=mc^2$?
The source of inertia of the capacitor is its stress-energy, just like the source of gravity of the capacitor is its stress-energy.
When we accelerate a box that contains light, the box must have reduced inertia, because the light has increa... | {
"language": "en",
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Different methods for measuring intensity of IR wavelengths I am proposing a teaching experiment at my university for undergraduates to learn about black body radiation and part of it will involve measuring intensities of different near - mid IR wavelengths. This is where the problem lies.
As far as I am aware there ar... | Building your own spectrometer as suggested by @ostrichCamel is not a bad idea to save cash because a grating spectrometer is rather simple, although it would take some effort to get right. Another option is these filters, which are still a little pricy, but I think they might be just what you need.
Another issue is ... | {
"language": "en",
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How did the hubble deep field took pictures of far away galaxies? Milyway has a radius of ~27K ly. Is our galaxy like a net with large holes that the light from another galaxy could pass straight through these holes and reach us on earth ? Theoretically, is it possible to shoot an arrow from earth to one of the galaxie... | The solar system, galaxies, and the universe itself is quite empty as far as opaque objects are concerned. Think of how much space there is between Earth and the moon. Most things that pass closer to Earth than the moon don't end up hitting the moon because the moon takes up a very small fraction of the spherical vol... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/396060",
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Could a tube with a serie of solenoids be used to move an iron particle? If I had a tube with electric solenoids at intervals along it, could I get small iron particles to move through the tube by turning the on the solenoids further along the tube and turning off the one the particles is closing in on?
If not, how cou... | The magnetic force that moves an iron particle is due to the gradient of the magnetic field strength. From the perspective of magnetic field lines, that means the particle experiences a force in the direction toward which the magnetic field lines are converging.
The experiment you're proposing should work just fine; t... | {
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How does holding a glass prevent it from falling? When I hold a glass of water,
$\hspace{1.5cm}$,
I am applying a force horizontally, but its weight acts downwards. Should it not fall?
How do you describe the equilibrium?
| I'm not sure exactly what you're asking, but you've used the friction tag, so you realize friction is involved.
Think about how the usual "block on a plane" friction problems work: Gravity exerts a force downward (normal to the friction surface), but if you try to move the block across the plane, friction exerts a forc... | {
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Must all periodic sound waves have harmonics? Does there exist a periodic sound wave that has partials which are not integer multiples of the fundamental frequency?
| A pure sinusoid does not have any harmonics except the fundamental.
Otherwise, if a frequency is present that is not an integer multiple of the fundamental, then you have not properly identified the fundamental.
For example, say you have a 100 Hz and a 150 Hz signal superposed. This signal will not repeat ever 10 ms, t... | {
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"url": "https://physics.stackexchange.com/questions/396718",
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Why is magnetic field zero for open circuit and electric field zero for short circuit? I read this statement in a book for a simple circuit (1 resistor connected to a voltage source). If we short out the resistor, the E field is said to be zero and if the circuit is broken (open circuit), the magnetic field is said to ... | If the resistor is shorted, then for the $E$ field since $V=IR$, if $R=0$ then $V=0$ so $E=0$.
If the circuit is open $I=0$, then for the magnetic field $B=(uI)/(2\pi r)$ and if $I=0$ then $B=0$.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/396866",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Difference between curvature and Ricci scalar curvature? I know about curvature by this notation
$$\tau=\frac{dt}{ds}$$
the change of tangent vector with respect to arc length $s$ .
I also know about Ricci scalar curvature is
$$g^{ij}R_{ij}=R$$
I know the formulas. But i want to really know about their differences ... | Your formula $\tau = \frac{dt}{ds}$ requires a correction, namely $t$ is not just any old tangent vector but is instead the unit length tangent vector. Also, that notion of curvature, which is known as "geodesic curvature", applies only to curves (1-dimensional objects) in space, the one parameter being $s$.
On the ot... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why do the Pauli matrices 'transform like a vector'? Maybe I still have trouble understanding what physicists mean when something is a vector but here is how I see it. I use the Einstein summation convention throughout.
Given a set of basis vectors $B = \{\vec{x}_i\}$ and a set of coordinates $C = \{c_i\}$, we represen... | The formulae you see in textbooks for the spin matrices are just one representation of an algebra satisfying $\sigma_a\sigma_b =\delta_{ab}I_2+i \sum_c \epsilon_{abc}\sigma_c$. This condition is preserved under the usual rotational transformation, which obtains a different representation of this algebra. The same one-a... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Entropy change between two systems Example 14.2 of Concepts in Thermal Phyiscs, 2nd ed:
"Consider two systems, with pressures $p_1$ and $p_2$ and tempreatures $T_1$ and $T_2$. If internal energy $\Delta U$ is trasferred from system 1 to system 2, and volume $\Delta V$ is transferred from system 1 to system 2, find the ... | $$dS = (1/T)dU + (p/T)dV$$
for system 1, $$\triangle S_1 = \int 1/T_1d U + \int p_1/T_1dV= 1/T_1 \triangle U + p_1/T_1 \triangle V$$
for system 2, $$\triangle S_2 = -1/T_2 \triangle U - p_2/T_2 \triangle V$$
Thus, the change of the total entropy $$\triangle S = \triangle S_1 + \triangle S_2= (1/T_1 - 1/T_2) \Delta U + ... | {
"language": "en",
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Reflection of "phone screen" light in a window I've noticed that the reflection of a phone (or computer) screen in a window (or other smooth surface) has distorted colors (towards red-purple or green-yellow), which change as the screen is rotated
I thought it had something to do with LCD screens polarizing different co... | I noticed this too. My conclusion was that it's not because of the polarizers in the screen but the viewing angle. I am not sure about LCD screens but LEDs are focused in a direction and if you view it from a different direction, that particular color could now have lower intensity as compared to other colors in the vi... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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How does the electric field produced by a battery get transferred along a relatively long wire connecting the ends of the battery together? My understanding of how the electric field produced by a battery gets transferred along the length of the wire is summarised in the following picture:
Is it correct to say that th... | When you study electrical engineering, there are two main topics: (1) fields and waves, and (2) circuits.
2 is simply a very simplified version of 1 - doing things and making things happen in ways you can 'ignore' the fields and waves (Maxwell's equations) and focus on the circuit elements, and corresponding laws (e.g.... | {
"language": "en",
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Why does the space of pure qudit states have dimension $2(D-1)$, rather than $D^2-2$? It is well known that two-dimensional states, that is, qubits, can be represented using the Bloch sphere: all pure states lie on the surface of a three-dimensional sphere, while all the mixed states are in its interior.
This is consis... | You can reach the correct conclusion starting from
$$
\vert 1\rangle=\left(\begin{array}{c}1 \\ 0 \\ 0\\ \vdots \\ 0\end{array}\right)
$$
and the simple density matrix $\rho_1=\vert 1\rangle\langle 1\vert$. Clearly, $\rho_1$ is left invariant by all transformations of the type
$$
T= \left(\begin{array}{cc}
e^{i\phi}&... | {
"language": "en",
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"source": "stackexchange",
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Gravity without force of gravity. What does it mean? As we know, the gravitation force in General Relativity is the semblant phenomenon. Let's look at this phenomenon in more detail.
A brief preface
From the Landau-Lifshitz "Volume 2. The Classical Theory of fields" (LL2)(Problem 1 in §88), we can see the equation o... | The geodesic deviation equation is $\ddot{x}^\mu=-\Gamma^\mu_{\nu\rho}\dot{x}^\nu\dot{x}^\rho$, where dots denote derivatives with respect to proper time. Speeds $\ll c$ give $\partial_t\approx\partial_\tau$ and $\dot{x}^j\ll \dot{x}^0$ so $\partial_t^2 x^i\approx -\Gamma^i_{00}$. This recovers Newtonian gravity, and e... | {
"language": "en",
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How to measure the refractive index of a lens? how to measure the refractive index of a lens? (a simple method)
I want to find a simple method to measure the refractive index of a lens.
| Use a spherometer to measure the radius of curvature of the two lens faces $r_1$ and $r_2$.
Use any standard method to measure the focal length of the lens $f$.
Use the lens makers formula $\dfrac 1f = (n-1)(\dfrac {1}{r_1}+ \dfrac {1}{r_2} )$ to find the refractive index $n$ of the lens.
| {
"language": "en",
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"source": "stackexchange",
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Maximum entropy: an assumption or a fact From what I gather (and please correct me if I'm wrong), Jaynes argues that thermodynamic and information entropy are the same since the assumption in statistical thermodynamics that the energy distribution attained is that which maximizes the ways energy is distributed is equiv... | We needn't go to QM for the moment. If you take a lecture course in classical thermodynamics, the second law is derived from informational considerations, although they typically discuss it in terms of maximising the number (typically denoted $W$ or $\Omega$) of microstates per macrostate. We can then show the second l... | {
"language": "en",
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How to prove $\{\gamma^{\mu}, \gamma^{\nu}\}$ ? (notation problem) I want to prove that $ \{\gamma^{\mu}, \gamma^{\nu} \}=2g^{\mu \nu} $ what are the indices $ \mu$ and $ \nu$ here? because I know the gamma matrices from 0 to 5 and I need to verify the anti commutation relation. but what should I put in here?
I just tr... | The gamma matrices in $d=4$ dimensions (one spatial, three temporal) in Minkowski space satisfy
$$\{\gamma^\mu, \gamma^\nu\} = 2\eta^{\mu\nu} \mathbb{I}_4$$
where $\mathbb I_4$ is the $4\times 4$ identity matrix. Recall that $\mu,\nu$ are Lorentz indices running over $0,1,2,3$. There is a fifth gamma matrix, denoted $\... | {
"language": "en",
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Rocket fuel consumption Consider a velocity change $dV$ for a rocket accelerated by an on-board thruster. Is the total amount of fuel consumed proportional to $dV$, or to $dE$, where $dE$ is the change in kinetic energy, or to some other measure, and if so, which measure?
| For this question you should consider the rocket equation:
$$v(t)-v_0 = u \ln \left ( \frac{M_0}{M(t)} \right ) - gt$$
where $v_0$ and $M_0$ are the initial speed and mass, $v(t)$ and $M(t)$ are the speed and mass after a time $t$ and $u$ is the exhaust velocity relative to the rocket body. You can ignore the $-gt$ te... | {
"language": "en",
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Connection between Weyl fermions and Fermi arcs I am looking for references (such as research or review articles) that discuss the theoretical origin of Fermi arcs in certain materials and their connection to Weyl fermion physics. In particular, how do Fermi arcs in systems with Weyl fermions differ from those that don... | You can think of a Weyl point as a magnetic monopole in the Berry connection, and the Fermi arc represents the (homology class of the) Dirac string connecting these two monopoles. Fermi arcs are impossible to realize in intrinsicly 2d band structures because bands are not allowed to end (but they are allowed to "flow" ... | {
"language": "en",
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"source": "stackexchange",
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Concept of surface tension: excess pressure inside an air bubble in a tank of water I know the expression for excess pressure inside a LIQUID DROP is :
$$
P_2 - P_1 = 2S/R
$$
where $P_2$ is the pressure just inside the liquid drop and $P_1$ is the pressure outside the liquid drop and $S$ is surface tension of water.
... | There is actually surface tension between the air particles themselves, roughly 0.076 N/m, which is the reason for $F1$.
| {
"language": "en",
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"source": "stackexchange",
"question_score": "4",
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What exactly is deterministic in Schrödinger's equation? I have read the following on Wikipedia but I can't understand it:
In quantum mechanics, the Schrödinger equation, which describes the continuous time evolution of a system's wave function, is deterministic. However, the relationship between a system's wave funct... | In the standard interpretation of quantum mechanics the time-evolution of the system and what we observe are separated (unlike Newtonian mechanics). The system, while unobserved exists in a superposition of states (all the states that satisfy the Schrödinger equation). These states (while unobserved) evolve in time acc... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "28",
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Matrix representation of spin-1/2 system Problem 1.19 from Sakurai's Modern Quantum Mechanics asks you to find $\left< (\Delta S_x)^2 \right> = \left< s_x^2 \right> - (\left< s_x \right>)^2 $ in the $S_z +$ state.
However, $S_x^2$ can be computed in its matrix form by
$$
S_x^2 = \left( \frac{\hbar}{2} \right)^2
\begi... | Your second result is a constant times the identity operator, which in matrix representation corresponds to the identity matrix.
It is a common notation practice in quantum mechanics to denote both the identity operator and the unit matrix using the symbol 1, or even drop it altogether if it is part of a product. The o... | {
"language": "en",
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A variation of the train-and-platform demonstration of relativity of simultaneity Suppose one observer is midway inside a speeding train and another observer standing on a platform as the train moves past. A flash of light is given off at the center of the train just as the two observers pass each other $t_0$.
Additio... | No, both observers will agree on what the clocks say. The reason for this is that Lorentz transformations don't change clock faces. What they won't agree on is everything else:
On the train, both clocks are synchronous--the light pulse is emitted and simultaneously stops both clocks, which read the same value (12:34 56... | {
"language": "en",
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How the current of a wire pass so quickly if it has that less drift velocity of electrons.? The rate of flow of electrons is known as current. When we switch on a light bulb, then it lights immediately. If drift velocity of electrons is so small--at least on the supply on 220V (supply of my home)--then why does the lig... | The electrons are already within the material, they do not need to travel from your power socket into the light bulb. It is rather that all the electrons in the wiring and the bulb start to move roughly at the same time. So even if all these electrons move slowly, it is a collective motion everywhere in your circuit.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Comparing work in thermodynamics with work done in mechanics Let us the consider a gas as our system enclosed in a cylinder with piston.
1st case(Expansion of gas):
Here force on the piston is exerted by the gas in upward direction and during expansion piston moves up. So, the work done here is positive(force and displ... | First you must notice that sign of work depends upon whom you consider as the work doer (energy converter). When the force transfers energy to the object(i.e., the object gains some energy) a positive work is done and when it transfers from an object (i.e., the object losses some energy) a negative work is done (imagi... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Rotational mechanics theory This is a statement given in my text book:
"The general motion of a rigid body can be considered to be a combination of (i) a motion of its centre of mass about an axis, and (ii) its motion about an instantaneous axis passing through the centre of mass. These axis need not be stationary." ... | This statement seems to be talking about several things. First, the author seems to be mentioning the fact that a barbell spinning about some kind of axis might very well be traveling through space (these axes need not be stationary). Also, they seem to be hinting at the parallel axis theorem.
Lastly, I agree that ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How do we know that bending of light around stars is due to bending of space-time and not diffraction? One question that popped up during the studies of special and general relativity (which I am forced to take unfortunately) is the following:
How do we know that this is due to the bending of space-time and not jus... | On one hand, a typical diffraction angle $\theta$ for light with wavelength $\lambda$ by a spherical obstacle with the radius $R$ of the Sun is
$$\theta~\sim~\frac{\lambda}{R}~\sim~~\frac{10^{-6} \text{ m} }{10^{9} \text{ m}}~\sim~10^{-15}\text{ rad};$$
while on the other hand, the gravitational bending/deflection of l... | {
"language": "en",
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"source": "stackexchange",
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Why doesn't calculating the de Broglie wavelength work with h in eV·s? I'm trying to calculate the de Broglie wavelength of a particle with a known momentum $p = 980.93 \,\mathrm{GeV}/\mathrm s$. The de Broglie relation is:
$$
\lambda = \frac{h}{p}
$$
but I notice that if I use the value of $4.136\times 10^{-15}\, \mat... | You're running into trouble because in order to give momentum units of energy, you're setting the speed of light equal to 1, $c=1$. If you keep the units of $c$ the momentum should be given in units of $\text{eV}/c$. By dimensional analysis you can check for yourself that eV/s does not have units of momentum (kg$\cdot$... | {
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How to get the Ricci tensor of an EM field? We have the Einstein equations $$G_{\alpha\beta}=\frac{8\pi G}{c^4}T_{\alpha\beta}\\R_{\alpha\beta}-\frac12 g_{\alpha\beta}R=\frac{8\pi G}{c^4}T_{\alpha\beta}$$
I have been asked to show that for an electromagnetic field these can be written as $$R_{\alpha\beta}=\kappa (F_{\... | EDIT: The orijinal question was completely different when I first answered, so I changed the answer for the new version.
First of all, $\kappa \equiv\frac{8 \pi G}{c^4}$ and $G_{\mu\nu} \equiv R_{\mu\nu} - \frac12 g_{\mu\nu} R$ are the definitions.
You can first express $R_{\mu\nu}$ in terms of $T_{\mu\nu}$ by taking ... | {
"language": "en",
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Active and passive pulling - is there a physical difference? Let's suppose we have two people Alice and Bob in a vacuum. The are connected by a rope.
At first, Alice pulls Bob with force $F$ and Bob only clings to the rope. Afterwards, the experiment is repeated with Bob pulling with force $F$ and Alice only clinging t... | Consider an "arm" as massless in the force diagram shown below with force $F_{\rm 1a}$ as the force on mass $m_1$ due to the arm etc.
All the forces have the same constant magnitude, $F$.
In the lower diagram the arm contracts by a distance of $x_1+x_2$.
The mass $m_1$ moves a distance $x_1$ and the mass $m_2$ mov... | {
"language": "en",
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Does a charged particle travelling with uniform velocity induce a magnetic field? Does a charged particle, an electron say, travelling with uniform velocity induce a magnetic field? I believe it doesn't. In primary school, we all learned how to induce a magnetic field into an iron nail by wrapping coils of wire aroun... | A flow of electrons makes a current and therefore produces a magnetic field.
If electrons are traveling with a uniform speed, the current they form produces a constant magnetic field.
The reason you need a coil to magnetize a nail is because the magnetic fields of individual loops in a coil add up on the inside of th... | {
"language": "en",
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EM Plane wave, the changing electric field is in all directions right? I just want to confirm this, because this type of diagram seems pretty popular.
The electric field and magnetic field actually surround in all directions orthogonal to x axis, right? It is not just 2d pointing only in the y direction and z direction... | This is a fairly common point of confusion. The arrows you see in that diagram express the magnitude and direction of the electric and magnetic fields on the $\hat x$ axis.
When you are introduced to vectors for the first time, they are usually represented as arrows which extend from one point to another. The vector ... | {
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How is comparing $|E|^2$ to $|H|^2$ relevant? I am reading one article that compares two kinds of electromagnetic surface waves, but the following figure confuses me:
Why instead of comparing $|E|^2$ and $|E|^2$ do they compare $|E|^2$ and $|H|^2$? Is it somehow better? Or maybe is it a manipulation? Or maybe it i... | They’re trying to show where the energy is located. They show H vs E for the two waves because the two different types of waves are just different.
There’s a Wikipedia article that discusses the role of the H field in surface plasmon polariton (SPP) waves, which are always transverse magnetic (TM) mode.
| {
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The Lagrangian of a free particle in Landau & Lifshitz In Landau & Lifshitz's derivation of the Lagrangian of a free particle in a galilean frame of reference one finds the following argument: the equations of motion in two galilean frames must be identical; hence the respective Lagrangians must differ by the total de... | L&L's logic is as follows:
*
*L&L demands$^1$ that an (infinitesimal) Galilean transformation should be a quasisymmetry (QS) of the sought-for action functional $S$.
*We furthermore demand that
*
*the action functional is local, and
*the position space is contractible.
*From this Phys.SE post, we then dedu... | {
"language": "en",
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"source": "stackexchange",
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balancing a weight on a table without tipping over I have a statics problem.
Here is a model for a table:
*
*a circle of radius 1.5 ft
*a pole in the center
*a base in the shape of an X.
I place a weight on the table on the edge. How much weight can the table support before it tips over?
This is from an actual ... | the table will not trip even for larger weights. since the weight of the object and the disc is exerted only on the X shaped base, unless the base is strong this will be stable, provided if the base of the table is also strongly fixed to the floor. i.e., it's just like keeping the disc on the floor and adding some weig... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is this derivation for schwarzschild radius for a black hole of mass $M$ correct? Consider a body of mass $M$.
We know that light can’t escape a black hole.
Speed of light being the highest possible could be set as the escape velocity.(??)
Then
$$\text{Escape velocity}^2=(2GM/r)$$
Solving for $r$ we get
$$r=2GM/v^2$$
S... | The problem with your derivation is that the Newtonian notion of escape velocity is not the same as the General Relativity notion of light not being able to escape.
In Newtonian gravity, if you shine a beam of light outwards from the radius $2GM/c^2$, the light will actually leave the radius and go all the way out to i... | {
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How do you interpret fluxes derived from Monte-Carlo simulations, specifically neutrino fluxes coming from the Sun I'm reading the neutrino oscillations paper from the SNO and I'm having a bit of trouble interpreting their results on page 4.
I understand that they fitted PDFs to the data to get an amount of events an... | SNO measures the number of events in three categories: $n_{CC}$, $n_{NC}$ and $n_{ES}$, which relate to the number of events per particle type $n_{\nu_e}$, $n_{\nu_\mu}$ and $n_{\nu_\tau}$:
CC works only with $\nu_e$:
$n_{CC} = \nu_e$.
NC works with all three kinds (with the same probability):
$n_{NC} = \nu_e + \nu_\mu... | {
"language": "en",
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In terms of electric charge, what does it mean to "charge a plate to five volts"? My understanding of electrostatics is based on the concept of charge and electric field. If each point in a region of space has a certain charge density associated to it, then by integrating Coulomb's law over space, we get a certain elec... | The voltage between the plates, the charges on them and the separation and medium in between are related by the following formula
$$Q = C U$$
where $Q$ is the total charge on the plate, $U$ the voltage difference and $C$ the capacitance (it depends on the plate separation and the dielectric between the plates).
From th... | {
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Current in Square loop under electric field From "Introduction to Electrodynamics" by David J. Griffiths, Example 12.13:
Consider a rectangular loop of wire carrying a steady current $I$. Picture the current as a stream of noninteracting positive charges that move freely within the wire. When a uniform electric field ... | The current in a wire loop with several sources could be calculated as a sum of currents caused by these sources acting alone. This is principle of superposition of currents that is applicable to any linear circuit.
The original, unknown, source, by itself, was causing a permanent current I.
The second, known source, t... | {
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Continuity equation and Bernoulli equation on inclined pipes I came across the following problem in Fluid Mechanics. We are asked to find the velocity in 3.
The pipe diameter from 2 to 3 is constant. I calculated the velocity in 2 using $\sqrt{2g\times50}$ and then from the continuity equation I deduced that the veloc... | Since the pipe at the bottom is open, the pressure at the bottom, $p_3$, will be atmospheric. This explains the statement $p_1=p_3$.
The water in the pipe, lacking support at the bottom, will submit to gravity and accelerate. As a result, $v_3$ will be greater than $v_2$.
So, for the continuity equation $v_2A_2=v_3A_3$... | {
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How can electrons spin if they have no volume? My understanding of electrons is that they have no volume, eg they are point particles. If this is true, how can a point spin?
| The electron spin corresponds to a classical angular momentum, but it is not related to any "rotation" of the electron. The spin of the electron is a quantum mechanical phenomenon and can only have the value of + or - $\frac {\hbar}{2}$ in a given direction. The electron is a point-like particle, it has no finite spati... | {
"language": "en",
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Question on measuring $I$-$V$ characteristic of a component When measuring the I-V characteristic of a metal wire/diode/filament light bulb , what is generally the best circuit set up?
You can
*
*Change the voltage across the component directly using a variable power supply
*Use a variable resistor to change the vo... | As long as the ammeter is in series with the device under test and has negligible resistance, and the volt meter is in parallel with practically infinite resistance, it doesn't matter which method you use. The ammeter measures the current through the device, and the voltmeter measures the voltage drop. That's all yo... | {
"language": "en",
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Physical meaning of simultaneous hyperplane If we consider a null cone and a world line $\mathcal{C}$ we can define a 3-plane $\Sigma_P^{\,}$ called simultaneous hyperplane (world line) as the set of 4-vectors in the tangent space of Minkowski that are orthogonal, according to Minkowski metrics, to the tangent 4-vecto... | The orthogonality with the worldline (the t-axis) means $t=0$ (i.e. the present) -- you can show this by calculating a trivial dot product, or just realise it's obvious, since the axes are orthogonal.
If you have trouble understanding this, you might want to step back and review some basic linear algebra. In particular... | {
"language": "en",
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Charge Distribution on Conductor - Uniform or Not? Consider a hollow conducting spherical shell S1 inside an irregularly shaped conducting wall S2 (in the figure). The sphere S1 is somehow given a charge +Q.
Will the charge distribution on S1 be uniform or not?
Here's what I've deduced till now:
*
*On the inner su... | Your points 1. and 2. are correct. But the surface charge distributions on S1 and S2 will be non-uniform. Only if S2 was a concentric conducting sphere then the surface charge distributions both on S1 and S2 would be uniform. The reason is that for a uniform surface charge you need a constant normal surface electric fi... | {
"language": "en",
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"source": "stackexchange",
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Can someone explain the concept of 'Negative Probabilities' in an intuitive manner? Can someone explain the concept of Negative Probabilities in an intuitive manner? I can't seem to understand this concept. I hope someone can explain this concept in an intuitive manner.
| this my personal interpretation of negative probabilities, it defines negative probabilities against the concept of unitarity
1 ) negative probabilities violate unitarity ( unitarity is a 'conservation law' )
2 ) consequentially negative probabilities represent disappearing or newly appearing events or possible outcome... | {
"language": "en",
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A proton's weak charge is .0719. Is this dimensionless? A ratio? A recent piece of major news in the physics world is that the proton's weak-force charge was measured to be .0719.
Is that a ratio? A dimensionless number, with no units? The articles I read didn't say.....
| The charges in particle physics are mostly dimensionless along with the corresponding coupling constants.
In particle physics, as you may notice, some universal constants are set to unity:
$$
\hbar=c=1
$$
This implies that any renormalizable term in the Lagrangian would have the charge and the coupling constant to be d... | {
"language": "en",
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Where do ultrahigh-energy particles come from? The most energetic particles that strike us from space, which include neutrinos as well as gamma-ray photons and various other bits of subatomic shrapnel, i.e the cosmic rays are sometimes so energetic, that they must be born in cosmic accelerators fueled by cataclysms of ... | The source of these UHCERs are active galactic nuclei, of energetic galaxies, powered by matter swirling into a supermassive black hole.
These rays should obey the GZK limit, 5*10^19eV. Though, there have been observations that contradict this limit, and the solutions are either that the source is nearby our galaxy or ... | {
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In what physical situations is the weak-field limit invalid? in the weak-field limit gravitation is described by a symmetric tensor field $h_{μν}(x)$ in flat spacetime. Linear theory suffices for nearly all experimental applications of general relativity performed to date, including the solar system tests (light deflec... | The standard review article on tests of relativity is Will 2014. He updates the article every 5-10 years.
Linear theory suffices for nearly all experimental applications of general relativity performed to date, including the solar system tests (light deflection, perihelion precession, and Shapiro time delay measuremen... | {
"language": "en",
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Link between integrability and soliton solutions I have been doing some research on the properties and dynamics of solitons (in particular, solitons in superfluids) and several works and papers mention the link between solitonic solutions and integrability of the non-linear differential equation describing the physical... | In the context of physics we say that a (Hamiltonian) system is integrable if it can, in principle, be solved by quadratures such as a completely separable Hamilton-Jacobi equation. It can be shown that a system with $N$ degrees of freedom is integrable if and only if it has $N$ independent conserved quantities in invo... | {
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Why is $ \frac{\vec{r}}{r^3} = \frac{1}{r^2} $? I know it's surely a beginner's question but I don't see why you can write
\begin{align}
\frac{\vec{r}}{r^3} = \frac{1}{r^2}\cdot \frac{|\vec{r}|}{r}
\end{align}
Could someone explain it please? It would help understand quite a few things ...
| What you wrote is not true. The $r$ without an arrow is only a scalar - the length of a vector. So the right-hand side is a scalar. The left-hand side is a vector $\vec{r}$ divided by its length cubed. So the result is still a vector. However, the length of the resulting vector in the left is $1/r^2$. This is because t... | {
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Potential difference across a resistor Why is potential difference across two ends of a resistor equal to the terminal voltage of the battery?
| Electric force is a conservative force (when there is no changing magnetic field). So, the net work done on a charge by electric forces when it returns to the same point after traversing a loop is zero.
Suppose, a charge $q$ falls from the positive terminal of the battery to the negative terminal of the battery, throug... | {
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What atomic forces are acting to resist me pushing an air filled bottle underwater? Yes air is less dense than water but how does the bottle know to rise or indeed to move? It's not electromagnetism I think. Does this have a relation to gravitational forces? Is it to do with the number of protons in the molecules of th... | The microscopic explanation for the macroscopic phenomenon of pressure is that momentum is transferred by electromagnetic forces from individual fluid particles (in this case, water molecules) to anything they approach closely enough, including other water molecules or the molecules of plastic that make up the bottle. ... | {
"language": "en",
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Why can a wave be expressed with a sine function? I see many expressions which express waves with the sine function like $y=\sin(kx-\omega t)$.
Waves really look similar to the shapes of a sine or cosine function, but does this guarantee that expressions that show wave-like movement are sine or cosine functions or is t... | One of the simplest ways to get waves is to have a situation where force is proportional to location: $F=kx$ for some $k$. Since force is mass times acceleration, and acceleration is the second derivative, the one-variable case gives $x'' = \frac{k}{m}x$. If $k$ is negative, then $x = \sin{\left(\sqrt{\frac {-k} m}t\ri... | {
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What is the evidence for a supermassive black hole at the center of Milky Way? Black holes cannot be seen because they do not emit visible light or any electromagnetic radiation. Then how do astronomers infer their existence? I think it's now almost established in the scientific community that black holes do exist and ... | Black holes are like your Death Metal loving neighbors who never leave their apartment: You can't see them, but you know for sure they are there.
When you state that "black holes cannot be seen because they do not emit any electromagnetic radiation" you are nominally correct: The amount of Hawking radiation the large o... | {
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Expectation Value $\langle \frac{1}{r^2} \rangle$ using Hellmann–Feynman theorem Suppose we have the hydrogen atom$$
H ~=~ \frac{p_r ^2}{2m} + \frac{L^2}{2mr^2} -\frac{e^2}{r}
\,.$$And have solved the Schrodinger equation finding $$E_n = - \frac{me^4}{2 \hbar ^2 n^2} $$ and $$ Ψ_{nlm}~=~R_{E,l}\left(r\right) Y_{lm}\lef... | Just consider the radial Hamiltonian as a hamiltonian on its own. So you want to compute an observable that depends only on the radial behaviour, vaguely speaking.
Alternatively you can always start from the full Hamiltonian, take partial derivatives on any parameter you wish and you arrive to the same answer, since t... | {
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Is there a basic/elementary mass in the universe? When speaking about electrical charges, it seems every particle either has a charge $+1$ or $-1$, in units of the electron charge. Therefore, we have a fundamental charge.
But what about mass? Is there any kind of such mass that every other mass can be seen a sum of tho... | It's a question of scale. And scale matters, this is where physicists take about effective theories where they ignore higher energy effects, or equivalently, short scale effects.
At the effective level of the atom there appears roughly to be a set of basic masses: the mass of an electron, the mass of a proton. Below t... | {
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Help with D. Tong example on Noether in QFT In this lectures, example 1.3.2 on page 14 concludes that the Noether current is
But how can the current be a two index object when it is defined in eq. (1.38), which is
as a one index object? If I apply the formula I obtain something of the form $j^\mu$. Can someone mak... | In this case you can think of left hand side as representing a vector of currents, each component of which has an index ν. So then your conservation equation applies to each component of j (that is for μ = 0,1,2...D):
$$\partial_\nu (j^\mu)^\nu = 0 ~ \forall ~ \mu$$
or $\partial_\nu T^{\mu\nu} = 0 ~ \forall ~ \mu$
| {
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Rindler motion and Horizon The Rindler coordinates are:
$$
\begin{align}
x'(\tau)&={\frac {\cosh \left( g\tau \right) }{g}} \\
t'(\tau)&={\frac {\sinh \left( g\tau \right) }{g}}
\end{align}
\tag{1}
$$
$$
\begin{align}
x'\left(\tau,\,\xi\right)&=\left( \xi+{g}^{-1} \right) \cosh \left( g\tau \right) \\
t' \left(\tau,\,\... | I simplified definition of the horizon (enough for this case, but by no means general enough) is regions of space-time where the metric becomes singular. In this setting you begin with the Minkowski metric:
$$ds^2 = -dT^2 + dX^2 + dY^2 + dZ^2$$
First you should realize the coordinates in (1) cannot be correct because t... | {
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Rigorous derivation of relativistic energy-momentum relation I wish to derive the relativistic energy-momentum relation $E^2 = p^2c^2 + m^2 c^4$ following rigorous mathematical steps and without resorting to relativistic mass.
In one spatial dimension, given $p := m \gamma(u) u$ with $\gamma(u) := (1 - \frac{|u|^2}{c^2... | I want to elaborate a little bit inspired by the comment made by AccidentalFourierTransform and how it relates to the answer by knzouh. You start from the four-velocity
$$
u = \gamma~( c, \mathbf{v}),
$$
on which you base your definition of the four-momentum as
$$
p = m_0\gamma~( c, \mathbf{v}) = ( m_0\gamma c,m_0\gamm... | {
"language": "en",
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Does a black body have a higher temperature when moving away from us at high speed? When a black body moves away from us at high speed the average velocity of its constituents will be higher. This means the body's temperature has increased. The whole spectrum of the wavelengths though will have been increased when arri... | lesnik's nice answer explains why the speed of the body does not affect its temperature.
The second part of your question has to do with the perception of a stationary observer, who, due to the Doppler's effect, will see all the wavelengths increased.
Should the observer conclude that the temperature of the body movin... | {
"language": "en",
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Redshift - How can $z$ be greater than 1? I'm having trouble understanding the equation for redshift:
$z = Δλ/λ ≈ Δf/f ≈ v/c$.
If $z = v/c$ and $c =$ speed of light,
how can $z>1$ (as nothing can exceed the speed of light)?
| $\Delta \lambda$ can be very large, much larger than $\lambda$, because the wavelength can be quite stretched out: a 21cm line earlier in the universe can be many meters now.
| {
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Potential due to line charge Is it possible to calculate the electric potential at a point due to an infinite line charge? Because potential is defined with respect to infinity.
| It is not possible to choose $\infty$ as the reference point to define the electric potential because there are charges at $\infty$. This is easily seen since the field of an infinite line $\sim 1/r$ so the standard definition of $V(\vec r)$ as the integral
$$
V(r)=-\int_{r}^{\infty}\frac{\lambda}{2\pi\epsilon R}dR
=-... | {
"language": "en",
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Can the increase in thickness of a piece of paper which can be folded infinitely surpass the speed of light? Supposing I have a piece of paper that can be folded infinitely.
*
*In the first $5 \, \mathrm{s}$, I fold it to twice its thickness.
*In the next $5 \, \mathrm{s}$, I fold it to 4 times.
*If I fold it to t... | It is a fact of nature that nothing moves faster than c, the velocity of light in vacuum.
One can imagine infinite scenaria for things moving faster than light, simpler than folding a paper. A continuous acceleration in vacuum is the simplest.
It is an observational fact that nothing moves faster than light. Innumera... | {
"language": "en",
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What is the theory concerning gravitational atoms? Imagine sometime in the distance future where the expansion of the Universe has created vast areas of empty space, light years wide.
Imagine, say, a neutron and a neutrino bound together as a gravitationaly bound atom. The "atom" in it's lowest energy state would be se... | You don't want a neutron and a neutrino, because neutrons are unstable. You could do this with, say, a carbon-12 atom and a neutrino, or with two neutrinos.
Quantum gravity is not needed for this kind of thing, e.g., people have done neutron interferometry in a gravitational field and have gotten the results you expect... | {
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How does emitting light while moving not break the law of conservation of energy? Say you have 2 identical LED monochromatic flashlights. The battery lasts exactly 1 hour. We are able to calculate the energy emitted as photons from the LED by Planck's Law: $E = h\nu$.
Now if we were to move one of our flashlights thoug... | The correct expression for the relativistic Doppler effect can be found here.
An object has a different energy when observed from a different reference frame, relativistic or Galilean. Photons are qualitatively speaking no different than tennis balls in this respect.
| {
"language": "en",
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Does potential energy affect the mass of an object? Assume a space contains one black hole and two electrons $e_1$ and $e_2$ only. The distance between the black hole and electron $e_1$ is $10^6$ km, and the distance between the black hole and $e_2$ is $10^{15}$ km (about 100 light years). Relative velocities of two el... | Potential energy certainly contributes to mass. For example the mass of the hydrogen atom contains proton and electron masses as well as their kinetic and potential energy. However an external potential energy does not contribute to the mass. Mass is simply the energy of a system at rest. The interaction with another o... | {
"language": "en",
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In QM why can wavefunctions be written as $\psi (x,t)= Ae^{i(kx-\omega t+\phi)}$? In my textbook, a wave traveling in the positive $x$-direction can be described using $$\psi(x,t)=Ae^{i(kx-\omega t+\phi)}. $$
I understand that the equation for a classical wave can be extrapolated by solving the differential equation as... | $\psi (x,t) = Ae^{i(kx-\omega t+\phi)}$ is a solution of the free particle Schrödinger equation, but $\psi(x,t)=Acos(kx-\omega t +\phi)$ is not.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Resistance of liquids What is the effect of temperature on the resistance of liquid conductors (like electrolytes)? I think that it should increase with rise in temperature, as, just like in metals, the ions would bump into each other more often but the reverse is mentioned in my textbook.
| Resistance may decrease with rise in temperature as in case of electrolytes conductance is due to ions which have interionic forces. As we increase the temperature the energy is used to weaken these forces leading to increase in mobility of these ions thus increasing conductance or decreading resistance
| {
"language": "en",
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Resolution of dipole moment into components In the derivation that involves finding the electric field due to a dipole at a general point on a plane in which the dipole lies, the following procedure is followed:
*
*Resolve the dipole moment into two components that are concentric with the original dipole moment such... | This is maybe a bit of a cheat as it's been implemented by the source you quote. In essence, it's because the electric field produced by a point dipole with dipole moment $\mathbf p$ produces an electrostatic potential
$$
V(\mathbf r) = \frac{1}{4\pi\epsilon_0} \frac{\mathbf p\cdot\mathbf r}{r^3}
$$
that is a linear fu... | {
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Molasses flood, "50 feet a second" Reading an article about the famous 'molasses flood' in Boston (Scientists finally decode the Great Molasses Flood of 1919) and read the following:
The flood began shortly after 12:40 pm local time on Jan. 15, 1919,
when a giant storage tank – 50 feet tall and 90 feet wide – colla... | This is explained in the Scientific American article The Science of the Great Molasses Flood of 1 August 2013 :
A wave of molasses does not behave like a wave of water. Molasses is a non-Newtonian fluid, which means that its viscosity depends on the forces applied to it, as measured by shear rate. Consider non-Newtoni... | {
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How strict are the boundaries that divide dimensions? Is a single-layer sheet of graphene 2D or 3D? I would like to know if there is any theory that describes a set of rules that define the boundaries of dimensions.
For example, does a single layer sheet made of graphene considered a two or a three dimensional object?
... |
For example, does a single layer sheet made of graphene considered a two or a three dimensional object?
Three dimensional , as all atoms and complex systems
Or does any object consisted of at least one atom considered by default a 3D object?
Complex systems, including protons in these, are three dimensional. In add... | {
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Is it more efficient to drive fast uphill? I know that for a rocket escaping the atmosphere, it's not efficient to travel slowly because even staying stationary consumes a lot of fuel. Does the same apply to a vehicle traveling uphill? In other words, is it more efficient for a car/bike/runner to accelerate and go over... | Generally, yes the faster you go the less energy you spend fighting gravity, but the more you spend overcoming resistance. At the vertical extreme, the faster the better. But at the horizontal extreme, the closer to the most economical cruise speed the better. For any given vehicle up any given slope, there will be an ... | {
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"answer_id": 4
} |
Why does the Anode and not the Cathode corode during eletrolysis of water into $H_2$ and $O_2$? After experimenting with the production of Hydrogen from salt water, I kept on noticing that the Anode (-) gets coroded and not the Cathode (+). Is it perhaps that water in itself is a naturaly positively charged medium and ... | Metals tend to be oxidized, not reduced. Oxidation happens at the anode (positive charged one during electrolysis, it wants electrons), thus the cathode is protected look into cathodic protection.
The long answer:
Metals tend to become positive ions thus they are easily oxidized not reduced. Oxidation happens at the an... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/409503",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
Energy of UV Light How much energy does UV light, in the atmosphere, exert?
For example, I know that CFCs were outlawed because the UV light was providing sufficient energy (BDE) to break the chlorine bonds and create chlorine radicals which wipe out ozone.
Therefore, is it possible to determine the amount of energy,... | It's need to be above UV C light, so above 10ev (see Wikipedia). So it's not from the order of kJ. Maximally it can reach around 100eV.
Namely the energy is always given by $$E=h \cdot f$$ where $f$ is the frequency and $h$ the Planck constant. So you can take frequency of the UV light and put it in. That's basically ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/409760",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
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