Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
What is the entropy change of the universe for a rock if it falls from a height into a lake? The rock and the lake are at the same temperature According to my textbook, the entropy change of the universe is $+mgh/T$. I'm confused about why this happens.
after falling (without air resistance), wouldn't the rock possess ... | The lake absorbs part of heat through the friction between the rock and the water's mulecules. At the same time, the internal energy of rock is changed accordingly. Therefore, this process (heating up the lake) is irreversible. So the total entropy increases.
| {
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"timestamp": "2023-03-29T00:00:00",
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Why does increasing tension in a string increase the speed of travelling waves? We know that $$ v = \sqrt\frac{T}{\mu} $$ meaning that increase in the tension of a string increases the velocity of the traveling wave. But how exactly does this happen? If we consider that the travelling wave is just a certain amount of e... | Increasing the string tension effectively reduces the remaining elastic capacity.
A "wave" or mechanical signal (such as a force or impulse) propagates through a perfectly rigid material at the speed of sound. If the material is not rigid but elastic, then for each particle along the string, that particle first must mo... | {
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Differences between observations of light versus gravity for a satellite traveling by the sun A satellite travels in a geodesic by the sun with sufficient velocity to escape the sun's orbit. The distance of closest approach is 100 light seconds when the satellite's velocity is perpendicular to the sun as observed by l... | Answer from Safesphere's link: https://arxiv.org/abs/gr-qc/9909087v2, "Does eqn. (2.4) imply that gravity propagates instantaneously? ...it clearly does not...Indeed, the vector (2.5) does not point toward the “instantaneous”
position of the source, but only toward its position extrapolated from this retarded data...In... | {
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Elastic collision with one moving object hitting a stationary object In an elastic collision, I understand that momentum is conserved and kinetic energy is conserved. If billiard ball of silver (with velocity $v_{(Ag)}$ impacts a stationary billiard ball of aluminum, I am trying to calculate the velocity of the aluminu... | You say...
After an elastic collision, the impactor is at rest and the impactee has the motion.
That is only true if the masses of the two balls are equal. Clearly they will not be equal if one is made of silver and the other aluminium.
| {
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Why does phase conjugation not result in superposition? I'm reading about phase conjugations in optics here while this is more extensive but it's in German. Nevertheless, the image might visualize it quite well:
I wonder why such a reflected phase conjugated wave, which travels back to its source (?!) doesn't add to t... | The outgoing (phase conjugated) wave will interact with the incoming wave (from the bottle; the interaction isn't visible in the picture though, just for clarity I guess). Just as two opposite traveling pulses on a rope will interact. When the pulses on the rope have traveled "through" one another, they will continue t... | {
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Operator Product Expansions using the stress energy tensor I'm reading "String Theory Demystified" by David McMahon. On p.111 of the book, it is asserted that:
One operator product expansion of particular interest involves the energy-momentum tensor. In the complex plane: $$T_{zz}(z)= \ :\eta_{\mu \nu} \partial_z X^\m... | Ok, so it seems that this just Wick contracting the normally ordered fields with those that are not. So we obtain two possible contractions, which give the expressions in my question.
| {
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Since the speed of light is constant and also the speed limit; would you, in your reference frame, have no upper bound on your speed? Let us imagine you are in a vacuum and after having maintained a speed of 0 km/s (standing still) you accelerate to 297,000 km/s (99%). You know this is now your speed because you have a... | You do not need a speedometer; as long as you have fuel to "burn" you can add another $\delta v$, and so continue to accelerate. Eventually you will run out of fuel.
| {
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What is the distinction between work done by torque and force about an axis other than centre of mass? Suppose a point particle is undergoing circular motion about a fixed point such that a tangential force is accelerating its speed continuously. Now I believe that I can calculate the work done on this particle either ... | In the circular motion case we only have a particle, so the centre of mass itself is not defined. Since force is tangential, $dW=F ds$, so that $W=F s$ considering constant force. If you apply apply torque method you get $W=\tau \theta =F r\theta =F s$. Thus they are the same result. You can apply method (1) about any ... | {
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Why is it said that antiparticles are a result of combining SR with Quantum theory? I did understand the historical reasons for the discovery of antiparticles in this context. But are antiparticles really a 'consequence' of combining special relativity and quantum theory? Why isn't it better to say that the existence o... | This is a very interesting question. Galileo once stated that "our Universe is a “grand book” written in the language of mathematics".
But are antiparticles really a 'consequence' of combining special relativity and quantum theory
Yes, they are, in that the relativistic mathematical formulation of quantum theory sugg... | {
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What would you see dropping a sufficiently strong chain with substantial length into a black hole? Here's a visual representation of the scenario
Here you can see we have a black hole on the left. The event horizon is the edge of the black hole. You are far away from the event horizon, and a chain is passing you by fa... | because at the even horizon light cant escape we will see that end disappear as there is no more light for us to see so it is still going into the black hole we just can't see it, as for it looking like it slows down that is just the was space-time has distorted the light, not from the physics being applied to the chai... | {
"language": "en",
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Equipotential as a circle
I just dont understand how with this configuration there could exist a equipotential as a circle. For the assumption that $R>>$ dipole size I think it is there for the approximation of potential due to a dipole $p$ at a distance $r$ $$V=\frac{pcos{\theta}}{4\pi \epsilon_{o} r^{2}}$$
This is a... | for the circle to be equipotential the electric field at every point should be perpendicular to it.
i've turned the diagram 45 degrees just so it is easy to understand.See the diagram carefully while reading so that you can understand the solution clearly.(dia 1)
as the net electric field should be perpendicular to the... | {
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Will a massive particle be attracted to an infinitely long beam of light? I was attended to Bonnor beams. A Bonnor beam is the general relativistic exact solution for the spacetime surrounding an infinitely long straight beam of light (it includes also the spacetime including the interior of the beam, but I'm mainly in... | Looking at the original paper by Bonnor, he finds that geodesics of particles are affected by the beams, not just through gravitational attraction but a Coriolis-like force along them:
Note that this is velocity-dependent: a particle at rest would not start drifting along the beam. However, it is hard to avoid this si... | {
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What is the role of the dilaton in Jackiw-Teitelboim 2D gravity? I read that the Einstein Hilbert action is topological in 2 dimensions. (What does that mean?). To write down a non-trivial action one introduces the dilaton field in JT gravity. Does this field have a physical interpretation?
I read some references but d... | For the following, I refer to https://arxiv.org/abs/1711.08482
Dilatonic gravity models often originate from some higher dimensional parent theory. For example, the following action
\begin{equation}
I = \frac{1}{16 \pi G_N} \int d^2x \sqrt{-h} \left[\Phi^2 R_h + \lambda (\partial \Phi)^2 - U \left( \frac{\Phi^2}{L^2} \... | {
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Tensor product of wavefunctions In a system of two non-interacting particles in a one-dimensional infinite square well, we represent the eigenstate of the whole system as the tensor product of the eigenstates of the individual particles: $|n_1,n_2\rangle=|n_1\rangle \otimes |n_2\rangle$, since both kets belong to diffe... | I'd say that it is merely for historical and cultural reasons. Mathematically there is an isomorphism
$$
L^2[{\mathbb R}^3]\simeq L^2[{\mathbb R}]\otimes L^2[{\mathbb R}]\otimes L^2[{\mathbb R}],
$$
but we customarily use the first form for a single particle moving in 3d.
| {
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What is the $y$-axis in an electromagnetic wave? Apologies if my question is unclear, any help to clarify it along the way is most welcome.
I'm confused about what we mean when we say electromagnetic 'waves' (say visible light). In the usual mental picture we have of a simple sine wave, what does the y-axis correspond ... | Maybe this will help
Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. This 3D animation shows a plane linearly polarized wave propagating from left to right. The electric and magnetic fields in such a wave are in-phase with each other, reaching m... | {
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Wave packet in quantum mechanics? When we talk about light waves or EM waves, we simply say that the wave packet is the superposition of other waves of different wavelengths. In quantum mechanics, we say the same thing; the superposition of many waves associated with electron form a wave packet. I don't understand this... | The state of a particle is given by the wave function (state vector $\psi$), which we get by solving the Schrödinger's equation. This wave function can be written as the superposition of many other simpler wave functions analogous to Fourier decomposition. Hence, the superposition of those simpler wave functions gives ... | {
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Why don't electrons accelerate in a circuit? In a circuit, electric field exerts force on electrons, so they must accelerate. Every text book I have read, points that electrons move with a constant drift velocity. How can this happen? Does Newton's law not apply there?
| Newton's law does apply but the electrons in the circuit aren't moving in a straight line like a car on a straight road for example. The motion of the electron is rather chaotic, they bounce around in the crystal and their average velocity is considered to be proportional to the Electric field.
| {
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Multiple spin measurements in the same direction What will be the outcome of the experiment during which charged particles will go through the set of Stern Gerlach apparatus aligned in the same direction (say Up)?
[SG Up] < ?1
[ Source ] -> [SG Up] <
[SG Up] < ?2
H... | The Stern-Gerlach apparatus creates what is known as spin-path entanglement – ie. the particle's spin and its position become entangled. More specifically, if a particle flies from a SG apparatus up, then we are sure that its spin is also up, and vice versa.
If we measure spin along an axis and the incoming particle is... | {
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Weightlessness and free fall on oil drop experiment Suppose I have an oil drop which is negatively charged placed in a box with the bottom of the box negatively charged. When this box and oil drop is placed on a table where the box is stationary, the oil drop is stationary in the middle of the box. Hence, we can conclu... | Simple answer is, the oil droplet will slowly move upwards. Because, the oil droplet is floating in the middle of the box for electrostatic repulsion. 'The droplet can't start it's free fall until the box's surface or the box move downwards'— What does it mean? It means that that box starts it's free fall before the oi... | {
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Is Landau theory for phase transitions valid only for "order to disorder" phase transition? In the Landau theory we assume order parameter that is equal to zero at $T>T_c$ and none zero at $T<T_c$ which is valid only for order to disorder phase transition according to my understanding.
So that is mean that I can't use... | Away from the critical point, the liquid-gas phase transition is a first order phase transition, so you must use a theoretical description that treats it as one. The standard formulation of the Landau theory does not treat first order phase transitions, but it can be modified so that it does.
The liquid-gas phase trans... | {
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Why is power transmission carried out at low current high voltage? My textbook states that power is transmitted at high voltage and low current since $P=I^2R$ and as the current has a small magnitude, the heat dissipated across the transmission lines is less than when we carry it out at high current and low voltage. Bu... | When we talk about high voltages we do not mean a high potential difference between the two ends of the wire. In any case we want to minimise the potential difference across the wire as this obviously means a loss of potential in the wire( the thing that is needed to power things)
in the equation
P=v^2/r
v is the poten... | {
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Solving the Schroedinger equation with the initial condition as an energy eigenstate I was studying quantum mechanics by watching a video lecture series. In the lecture https://youtu.be/TWpyhsPAK14?list=PLUl4u3cNGP61-9PEhRognw5vryrSEVLPr&t=2784 , the professor tries to solve the Schroedinger equation with the initial c... | By equation 2, $\psi$ at some infinitesimal time $\epsilon$ will be in the same state, multiplied by a phase $e^{-iE\epsilon/\hbar}$. Since it's the same state, you can use equation 1 again. And you can keep doing this forever.
But I feel like there should be a cleaner answer than this.
| {
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Friction between two horizontal rotating discs Let's say we have two rotating disks and one disk is given some angular velocity. As one disk rotates, due to friction the other disk should rotate as well. The two disks are completely identical (radii, mass etc). The two disks are lined up next to each other horizontally... | Initially, there is a relative motion between the two discs. So, the frictional force is given by $ F_{fr} = \mu_k N $, where $N$ is the normal force, and $\mu_k$ is the coefficient of kinetic friction. At one point, the relative velocity between the two discs becomes 0. At this stage, the frictional force also be 0.
H... | {
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Why is 4-velocity not defined as the covariant derivative of position instead of the regular time derivative? The geodesic equation is usually written as
\begin{equation}
D_\tau u^\mu = 0
\end{equation}
where $D_\tau= u^\mu \nabla_\mu$ is the covariant proper time derivative and $u^\mu=\frac{dx^\mu}{d\tau}$ is the 4-ve... | Because position is not a vector.
| {
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Why doesn't current flow through an open branch? I know that current doesn't flow through open branch because current can't flow through air due to its high resistance .But i was thinking , what's the problem if current flows through an open wire (assumed 0 resistance for matter of circuit solving). I mean, isn't there... | Voltage is the driving force .
If you have a real ( non ideal) wire and connect it across a battery, due to its non zero resistance, there will be a continuous drop in voltage. If the battery is 5 V rated, the potential at one end of the wire is 5, dropping down to 2.5 V at its mid length and all the way to zero at the... | {
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EM wave power dependency on frequency Does a (classical) radio wave with a given amplitude carry more power if that wave is at a higher frequency than at a lower frequency?
| Energy density in EM field is given by
$$
u = \frac{1}{2} \epsilon_0 E^2 + \frac{1}{2 \mu_0} B^2
$$
and energy flux (energy crossing unit area per unit time is)
$$
{\bf S} = {\bf E} \times {\bf H}
= \frac{1}{\mu_0} {\bf E} \times {\bf B}
$$
where the second version applies in vacuum.
It follows that the answer to your ... | {
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A clarification on acceleration and velocity This is one of those questions which require an answer that does not take practical limitations into account. It is a theoretical physics question, perhaps. If there are any loopholes used, please explicitly state them.
If the position is known as $x(t)$ from t=0 to t=1 seco... | Strictly speaking, the velocity at the end points is not defined, since you cannot determine either the left-hand or the right-hand limits to the change in position at those times as the time interval gets arbitrarily smaller.
Since velocity is the time-derivative of the position, $$v(t) = \frac{dx(t)}{dt}.$$ For this ... | {
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What does an $x$ Watt bulb actually means? Let's say I have a 11W bulb in my home, connected to a 220V power supply. What exactly does it mean that this bulb is 11W? As far as I know, the Wattage is determined by the formula $W = V * I$, so it really depends on the voltage and the current. The current is determined by ... | $11 W$ means the bulb uses 11 watts of power when it's operating at the rated voltage. If you run it for an hour for example, it will cost $0.011 kWh$, and your power company will bill you for ___ (check your local electricity prices).
You can also calculate how much current the bulb will draw since you know the voltag... | {
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If lower gear generates more torque at the wheel, why does it generate less acceleration/speed of the car compared to higher gear? If lower gear generates more torque (compared to higher gear) at the wheel, that would presumably mean the wheels can exert more force on the floor to propel the car forward. Thus, why does... |
Thus, why does lower gear generate less acceleration/speed of the car
compared to higher gear?
The wheels RPM depends on the motor RPM and gear ratio. $N_w = \frac{N_m}{i}$. The acceleration is the derivative with respect to time: $\frac{dN_w}{dt} = \frac{\frac{dN_m}{dt}}{i}$.
So, for smaller $i$ (higher gear), the (... | {
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Does a lens always act as a Fourier transform? I understand that putting a lens behind an aperture at the distance 1f, it will "get" the diffraction pattern to appear in the back focal plane. In this case the FT of the aperture plane happens within the realm of using Fraunhofer diffraction.
Does a lens generally Fourie... | An ideal lens takes a point source that is located on its focal plane, say $\mathcal {F}$ emitting monochromatic homocentric rays/spherical waves and transforms them into parallel rays/plane waves whose direction (propagation phase) depends on the location of the point source in the focal plane relative to the symmetry... | {
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How to generate electric current without a permanent magnet? The question is pretty simple:
Can we build a device that coverts mechanical work in electric current1 without employing a permanent magnet and without access to any external source of current?
The restrictions in place seem to rule out the possibility of c... | You have a lot of ways to convert other forms of energy to electricity without permanent magnets, you might be using one right now, batteries, wich uses chemical energy (Unless it is recharged)
Here is a list of what i can think of:
*
*Solar power
*Chemical reactions (A good example for that is batteries)
*Static e... | {
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Direction of propagation of electromagnetic waves I have a differential equation for an electromagentic wave propogating in the z-direction and oriented alone the x-axis:
$$\frac{d^2 E_x}{d z^2}+\omega^2 \mu \epsilon E_x=0$$
and if I say $k^2= \omega^2 \mu \epsilon$
the solution to the differential equation yield the f... | Your equation is incomplete and is not an electromagnetic wave equation. Any wave function $f$ has to depend on both position and time:
$$f = f(x,t)$$
as well as satisfy the wave equation
$$\frac{\partial^2 f}{\partial x^2} = \frac{1}{c^2} \frac{\partial^2 f}{\partial t^2}$$
Sinusoidal solutions to the wave equation wi... | {
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How to identify series and parallel connections of capacitors in complex circuits? Like for this question (picture attached) how to identify if capacitors are in series or in parallel?
| Those batteries and capacitor are all in series. The current will follow through them one after each other.
If they were in parallel, the current could take two different paths (hence the parallel part).
Keep in mind that if you were to extend the circuit, this would change. But as it is, from the viewpoint of each bat... | {
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Is pseudo force just an ad hoc number to explain motion in non-inertial frames? Consider an observer in a non-inertial frame $S$ who observes a particle's motion with a relative acceleration $\vec a_s$ and further calculates (or was told by his fellow observer in an inertial frame) the net real forces acting on it as $... |
In other words, is pseudo force just an arbitrary constant that arose out of our desperation to explain non-inertial motion?
Suppose we have a motion happening somewhere in space, now we can either observe it with a frame attached to the person in motion or one which is outside and is inertial. According to newton's ... | {
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How do I normalise the wavefunction of a hydrogen 1s orbital to obtain the normalisation constant? The wavefunction I've been given for a 1s hydrogen orbital is:
$$ \Psi = A e^{-r} $$
And I need to normalize this to find the value of A. I understand to normalise this I would inset this wave function into:
$$\int_{-\inf... | In 3d spherical coordinates, the integration is
$$
\int_0^\infty dr r^2 \int_0^{\pi} \sin\theta d\theta \int_0^{2\pi} d\phi \vert\psi(r,\theta,\phi)\vert^2
$$
since
\begin{align}
\int_{-\infty}^\infty dx \int_{-\infty}^\infty dy\int_{-\infty}^\infty dz
\to \int_0^\infty dr r^2 \int_0^{\pi} \sin\theta d\theta \int_0^{2\... | {
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I am moving right and rain is falling vertically down.Why should I hold umbrella at an angle? This is related to relative velocity.I get that, from my moving frame of reference rain is making an angle.But still... it doesn't make sense to hold umbrella at an angle when rain is falling vertically down.
| I guess you're asking for an intuitive explanation, because it seems to be mathematically clear.
Well, imagine a set of three columns of raindrops, each row containing three drops. Let's call columns A B C and rows 1 2 3, because they fall orderedly. You first encounter drop 1, then the second, then the third.
For a ... | {
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Does bitcoin mining take work? I'm neither a professional in cryptocurrency nor physics, but an interesting idea occurred to me. Bitcoin involves mining, which generates a lot of heat as waste.
Is the amount of heat produced by a computer mining bitcoin the same as a traditional heater, if they have the same input powe... | I wouldn't say it is organising information
Bitcoin uses one thing called Proof of Work (PoW), which consists in varying some numbers until the hash function matches a target number of zeros.
You're not generating information differently than solving a numerical equation. The energy used in the PoW comes from the power... | {
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Indistinguishability of Quantum States and its Consequences In the book Quantum Computation and Quantum Information, there is a discussion about how if states are not orthonormal then there is no quantum measurement capable of distinguishing the states.
I am interested in the consequences of this. What does this mean p... | I'm not sure if this will help but a very sharp former colleague once posed this question.
You have two boxes. The first contains 1000 horizontally polarized photons and 1000 vertically polarized photons while the second contains 1000 left circularly polarized photons and 1000 right circularly polarized photons. How do... | {
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When I walk down the stairs where does my potential energy go? When I leave my room I walk down three flights of stairs releasing about 7kJ of potential energy. Where does it go? Is it all getting dispersed into heat and sound? Is that heat being generated at the point of impact between my feet and the ground, or is it... | This is easily tested experimentally. If you walked down a longer staircase, such as subway escalator, as fast as possible, you would feel that most of the energy have been be dissipated as heat in shin muscles and tendons. Then it rapidly moves with blood flow into the rest of your body.
Energy consumption for 5km/h w... | {
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Mechanical energy in a body moving upwards Why is it that mechanical energy is always conserved, I mean when an object is thrown in air, why does the kinetic energy convert to potential energy and not any other form of energy?
| Mechanical energy is not always conserved. If you throw the object up hard enough to hit the ceiling then suddenly its remaining kinetic energy is converted into heat, sound waves and deformation energy, and it is left with just potential energy. When it falls back down and hits you on the head, same thing happens agai... | {
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Anomalous Dimension and Infinitesimal Transformation In the theory of Renormalization Group (RG) transformations I ended up with the following equation
$$\left( \frac{Z(\mu)}{Z(\mu / s)} s^{d-2}\right)^{1/2} = 1+\left(\frac{1}{2}(d-2)-\gamma_{\phi}\right)\delta s$$
where $Z(\mu)$ is the wave function renormalization, $... | Expanding the LHS=$\left(\displaystyle \frac{Z(\mu)}{Z(\mu/s)s^{d-2}} \right)^{1/2}$ in $s=1+\delta s$ to first order in $\delta s$ goes as follows:
*
*$\displaystyle \frac{\mu}{s}=\frac{\mu}{1+\delta s} \sim \mu (1-\delta s)$
*$Z(\mu/s) \sim Z(\mu (1-\delta s))\sim Z(\mu) - \displaystyle \mu \frac{dZ(\mu)}{d\mu} \... | {
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What is the definition of a magnet or a magnetic field? Electric forces are the forces which come about between two types of charges, positive and negative. Gravitational forces are the forces between matter. Nuclear forces are the forces which act on the atomic scale and are quantum mechanical forces, they act between... |
Electric forces are the forces which come about between two types of charges, positive and negative.
Gravitational forces are the forces between matter.
Nuclear forces are the forces which act on the atomic scale and are quantum mechanical forces, they act between nucleons.
To finish your list, magnetic forces are th... | {
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If a compass is placed near the middle of the magnet, where will the compass needle point? If we're thinking about a case where bar magnet is placed on a flat surface, with its N-pole on the right and a compass is placed just above the middle of the magnet, in which direction will the compass needle point? Will it go i... | Mark H's answer is good, but I just want to add some clarity to what a compass does and what Earth's north and south mean, magnetically, and it's easier to do that with a picture, hence using an answer rather than a comment.
A compass in Earth's magnetic field points North, and a compass points in the direction of the ... | {
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What are the physical principles at play when a glass is stuck to a wet table? I've decided to write a relatively detailed paper on the following situation, but I'm finding the topic quite hard-to-google. Imagine a glass table with water spilled onto it. Once a drinking glass is placed on top, it becomes quite difficul... | Many glasses have a concave bottom, and there is likely to be some air trapped underneath. In any case, when you try to lift the glass, the pressure under the glass drops and you are working against the air pressure from above. Adhesion and surface tension may also play a roll. As you lift, water flows in from the edge... | {
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Is it possible to convert a normal force into a vertical force of a moving object into the direction of travel? I have read some questions here about normal forces applied to moving objects but I still can't find an answer to the following scenario:
So there is an object with a constant velocity and on its way the obje... | *
*You can imagine some kind of "regenerative damping" whereby the damping mechanism would store the energy of the shocks rather than dissipate it (actuating a magnet along a coil, etc.)
*However, since the energy of the shock is by definition a consequence of (and hence borrowed from) the kinetic energy of the body... | {
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Unexpected different results from Newton's second law Please don't ban me. I read through Homework-like questions and I know they should ask about a specific physics concept and show some effort to work through the problem. I hope the question is ok.
I recently came across a mechanic basic problem which I wanted to sol... | In the section "torques relative to the right edge of the bar:"
The torque from the $N$ should be included...best of luck getting the two ways to match.
| {
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Is it necessary to use a collimated light beam when using a polarizer? I am using two polarizers (one for an halogen light source and one for a camera) to measure light reflected in parallel and perpendicular polarization setups. Should the light source used along with the polarizer be a collimated light beam or can it... | Yes, you should collimate your beam. The reason for this is that polarizers work well at the angles of incidence they were designed for, and increasingly worse at other angles. The reason for this is that they rely on optical reflectivity (and interference for thin film polarizers) of the two orthogonal polarizations, ... | {
"language": "en",
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Why doesn't the double-slit experiment violate the uncertainty principle? In the double-slit experiment, when an electron reaches the detector after passing through the holes, it has a certain momentum which we can measure with arbitrary accuracy.
From this data, we can calculate what momentum the electron had when it ... | The narrower the slits ($dx$), the broader the expected (measured and/or calculated) distribution of momentum ($dp$) of the photons passing said slits, so the product ($dx.dp$) cannot get arbitrarily small, therefore the Heisenberg principle ($dx dp \geq \hslash$) is respected in the double slit experiment.
| {
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Why is Hartree-Fock considered a mean-field approach? In studying the Hartree-Fock method for solving systems of interacting particles, I have often found that the method is referred to as a mean-field approach. Wikipedia's page for instance says that the mean-field approximation is implied. I don't see why this is the... | In HF we assume that we can separate the wavefunction into a product ansatz
$$
\Psi(r_1, r_2, ...)\Psi^*(r_1, r_2, ...)=|\Psi(r_1, r_2, ...)|^2=\rho(r_1, r_2, ...)
$$
$$
\rho(r_1, r_2, ...)\approx\rho_1(r_1)\rho_2(r_2)\cdots
$$
$$
\rho_1(r_1)=\psi_1(r_1)\psi^*_1(r_1)
$$
This allows us to define single particle potenti... | {
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Why does the electron not spin? The goto answer to that question is that the electron is a pointlike particle and cannot spin.
The electron is not pointlike though. It is described by a wavefunction. One can prepare the wavefunction to describe a very small electron, but not a point-like electron.
Is there a genuine an... | Particle physicists usually use the term "spin" to denote intrinsic angular momentum, which for a charged particle can give rise to a magnetic dipole moment. In this sense, the electron has spin, even though it is an elementary particle and, as far as we know, has no internal structure.
| {
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Why aren't all quarks clumped together in one giant hadron? As far as I am aware, the strong interaction is attractive only, and its carrier, the gluon, is massless meaning it has unlimited range. If this is the case, how come we only observe quarks in pairs and triplets? What's preventing every quark in the universe f... | In quantum chromodynamics, the theory that describes quarks, there exists a quantum number called color charge or just "color", and all stable hadrons need to have neutral or "white" color.
All hadrons need to have this zero total color charge because of color confinement or quark confinement, such that the color force... | {
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Antiunitary operators and compatibility with group structure (Wigner's theorem) From Wigner's theorem, we get that a physical symmetry can be described either by a unitary or antiunitary operator, eventually with a phase factor, as in here.
However we have to respect the group structure, so we need to have:
$$O(f)\circ... | I am not sure to understand the problem. What it is clear is that a (unitary or projective unitary) representation is not possible if it is made of antiunitary operators only. That is because, just in view of the representation rules, some operators should be antiunitary and unitary simultaneously as you point out. (... | {
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Why is everything not invisible if 99% space is empty? If every object is $99$% empty space, how is reflection possible? Why doesn't light just pass through?
Also light passes as a straight line, doesn't it? The wave nature doesn't say anything about its motion. Also, does light reflect after striking an electron or at... | Frame challenge: Yes, each atom is mostly empty space, but there are very many of them in the path of an idealized classical light ray, and even a small amount of obstruction in each adds up.
Even if electrons were little classical spheres with a radius equal to the "classical electron radius" (which is around 5 orders... | {
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If air is a bad conductor, how does fire heat up a room? If air is a bad heat conductor, how does fire heat up a room?
Could someone help me, as I really don't get this?
| Probably the most important heat transfer mechanism in the development and spread of a fire in room is radiation which can raise the temperature of the materials in the room to their ignition point. The main role of the air in the room is to provide oxygen to enable ignition and self-sustained combustion.
Hope this hel... | {
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Double Slit Interference pattern - horizontal or vertical? What determines whether in a double slit experiment the interference pattern will be horizontal or vertical for example? Is it mostly seen horizontal because the slits are small enough horizontally for interference pattern to be seen? Also, I sometimes see a "r... | If the slits are vertical, the light will diffract left and right, creating a horizontal pattern.
| {
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Do $2s$ and $2p$ orbitals have same energy? While solving the Schrodinger equation for the H atom, we get $E_n$ depending exclusively on $n$ (actually on $\frac{1}{n^2}$). Then I thought 2s and 2p orbitals must have the same energy.
But while reading Molecular orbital theory in Atkin's Physical chemistry book, I found ... | The hydrogen 2s and 2p orbitals do not have the same energy. They are separated by the tiny Lamb shift, which is only 1057 MHz or 4.3714 10$^{−12}$ eV. The origin of this energy difference lies in radiative (QED) corrections to the degenerate Dirac result.
Note that there is also hyperfine splitting due to interaction ... | {
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Entanglement in 2D Harmonic Oscillator system Let's assume a 2 dimensional harmonic oscillator system with the Hamiltonian $\hat{H} = \frac{1}{2} p_x^2 + \frac{1}{2} p_y^2 + \frac{1}{2} \omega_x^2 x^2 + \frac{1}{2} \omega_y^2 y^2$ with the solution of the ground state being simply the product of the the ground state of... | To add to @ZeroTheHero answer: one usually talks about entanglement in a narrower sense, as a state of two or more particles, since what we have here can be described as a superposition of one-particle states (whatever is the basis).
| {
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Experimental result of the atomic nucleus volume by scattering alpha particles from the atomic nucleus. Investigation of the electron volume by what? Rutherford's alpha particle experiments marked the beginning of the determination of the volume of the atomic nucleus.
How were the experiments conducted that led to the ... | To enlarge slightly on Anna V's answer, here is what we mean by scattering experiments.
Let's imagine a tight beam of electrons zooming through a vacuum, aimed at a target consisting of a simple sort of atom, and separated into bunches of electrons. So... we are going to "machine-gun" the target atom with "bullets" con... | {
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Uniqueness of the definition of Noether current On page 28 of Pierre Ramond Field theory - A modern primer the following is written:
"we remark that a conserved current does not have a unique definition since we can always add to it the four-divergence of an antisymmetric tensor [...] Also since $j$ [the Noether curre... | I can give you an example:
$$
S=\int dt \left(\dot x^+\dot x^--x^+ x^-\right)
$$
has a conserved current associated with $x^{\pm}\rightarrow e^{\pm\rho} x^{\pm}$ given by
$$
j=x^+\dot x^--x^-\dot x^+
$$
This means that the current above will be conserved if the equations of motion are satisfied. Now if we add to this c... | {
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Why does running spend more energy than walking? The study energy expenditure of walking and running concludes that running spends more energy than walking.
My understanding is that although running makes one feel more tired, that only indicates that the power was higher (since the time of displacement was shorter), bu... | A common stumbling block pointed out in the other answers and the comments is the inappropriateness of modeling a runner as a point-like object (a spherical runner in vacuum), as is done in simple classical mechanics. Indeed, kinematic or dynamic (in terms of Newton laws) description of a runner may require more comple... | {
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Does real life have "update lag" for mirrors? This may sound like a ridiculous question, but it struck me as something that might be the case.
Suppose that you have a gigantic mirror mounted at a huge stadium. In front, there's a bunch of people facing the mirror, with a long distance between them and the mirror.
Behin... | This is a simple distance problem the distance from your eye to the mirror and the distance of the man from the mirror added together. The size of the mirror makes NO difference at all in speed of light but some in how far the object is away and the prior answer was correct except he was using the speed of light in a ... | {
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Center-of-mass and relative coordinate integral transformation Assuming I have a function $f(r_s,r)$ where $\vec{r_s}$ is the center-of-mass- and $\vec{r}$ the relative-coordinate of a two particle system and I perform the following integral in spherical coordinates (assuming the function is only dependent on the absol... | It looks like you have a pair of 3D integration variables in spherical coordinates, albeit ones in which you've integrated out the angular coordinates. You might have to undo that and put those back in to the integral. Once you do, you can use a Jacobian (or a pair of Jacobians, depending on how you look at it) to conv... | {
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Can we cool Earth by shooting powerful lasers into space? In a sense, the climate change discussion revolves around the unwanted warming of the earth's atmosphere as a whole.
It seems a bit too obvious to be true, but could we cool the atmosphere by simply shooting that unwanted energy somewhere else?
Energy might be c... | Your idea to cool the Earth by shooting photons off into space is actually what already happens now! However, instead of a laser, the Earth cools itself by blackbody radiation. The Earth radiates a $\mathrm{\approx 300~^\circ K}$ (room temperature) black body spectrum with a peak at $\mathrm{kT=\frac{1}{40}eV}$ which... | {
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Does an electron have multiple positions BEFORE being observed? I realize that an electron can only ever be detected at a single location in space when it is observed. That is, post-detection, an electron can only ever be at a single position in space. But prior to the detection, when the probability distribution of fi... | An electron existing at different positions in space would raise more interpretation questions than those it is intended to reduce.
Here a partial list of difficulties.
If a full electron coexisted with its clones at different
positions, we would go into troubles with conservation laws:
*
*charge and spin conservatio... | {
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About virtual displacement
Thornton Marion
The varied path represented by $\delta y$ can be thought of physically as a virtual displacement from the actual path consistent with all the forces and constraints (see Figure above).
The varied path $\delta y$, in fact, need not even correspond to a possible path of moti... | First of all, the first statement is wrong, the condition of being consistent with forces should be eliminated, retaining the consistency with constraints. Because if it is not eliminated, then the first statement is basically saying that the varied path is kinematically admissible, or in your phrase, possible path, wh... | {
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Proton Electron Merger Can somebody explain what would happen if an electron & a proton, very close to each other are left to "fall" to each other in a straight line?
|
Can somebody explain what would happen if an electron & a proton, very close to each other are left to "fall" to each other in a straight line?
One of the three solid evidences that classical electrodynamics and mechanics could not describe electrons, protons and atoms was exactly the fact that in classical electrody... | {
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Addition of velocities vs. Addition of forces Imagine two strings tied to a box.
Case 1: Two strings are pulled with the same $u$ velocity. The box will also move with velocity $u$.
Case 2 : Tension along $\text{a}$ string is $T$. Therefore total force acting on the box is $T+T=2T$. (Box is accelerating)
I think my... | Sorry for my poor english. French is my native language.
To define a vector, it is necessary to specify the vector space on which it is defined. In general, for a manifold, we have a tangent vector space at each point. In classical physics, space has an affine flat space structure and we define at each point a tangent ... | {
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How to know the direction of the unit normal vector to an open surface? For an open surface shape (assume surface $x=4$) there is 2 possibilities for the unit normal vector direction either $(+î)$ or $(-î)$. so how can we know what direction it is supposed to be (ie $.. - î$ or $+î$)?
| The unit normal vector is part of the definition of a surface. To completely define a surface you must give (choice) its unit normal vector. Consequently you must be careful using it for calculations. For example the flux of a vector function for one choice would be the opposite of that of the other choice etc.
In Fig... | {
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Eigenvalues of antiunitary operators I have sometimes come across the statement that antiunitary operators have no eigenvalues. For example, on page 34 in the book "Topological Insulators and Topological Superconductors" by Bernevig and Hughes, it is stated that
The preceding ( $T i T^{-1} = -i$ ) makes it clear that ... | Your fine link has the answer for you in its section 2.2, illustrating that some antiunitary operators, like Fermi's spin flip, lack eigenvectors, as you may easily check.
But the counterexample you chose is of the $\vartheta ^2={\mathbb I}$ variety, and so $\vartheta$ does have the obvious eigenvectors: that's the poi... | {
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Why is the gravitational potential energy lost not subtracted from the required work done in the given problem?
An elastic string of natural length $l \;\text{m}$ is suspended from a fixed point $O$. When a mass of $M \;\text{kg}$ is attached to the other end of the string, its extension is $\frac {l}{10} \;\text{m}$.... | The issue here is that energy of the spring-mass system is not conserved. The initial state of the system is the mass at rest and attached to the unstretched spring. If we release it, the mass will begin to gain kinetic energy and oscillate. It will never reach the final state of equilibrium where $mg=kx$. Therefore yo... | {
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Why the phase shift of an electromagnetic wave or light after reflection is smaller than 0, being in the range $[-\pi, \pi]$? In some reports, the phase shift becomes in the range $[-\pi, \pi]$, for instance on this website. However, Wikipedia gives the range as $[0, \pi]$ instead. Which one is correct?
| The first link you quote is about Fresnel equations in general, which may describe both transmission or reflection off a boundary. In this case, the deflection angle is $\theta \in [-\pi, \pi]$ with respect to the boundary, with the negative angles being the transmitted (refracted) part, that is above the boundary. The... | {
"language": "en",
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Why doesn't charge escape from capacitor? A charged spherical capacitor kept in air do not loose charge because air is a bad conductor and increase in charge results in Corona Discharge. Is it because the nucleus of air molecule repels the charge in sphere and after a limit the repulsion is less than the attraction by ... | If the charge of an object does not change, it means the net flux of charges to and from it is zero. It all depends on the environment and the object itself. It is normal that an object has some charge even in the near vacuum of space. Sunlit surfaces for instance become charged positively due to ultraviolet radiation ... | {
"language": "en",
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Does gravity get stronger the higher up you are on a mountain? So I saw this article stating that gravity is stronger on the top on the mountain due to there being more mass under you however I have read some questions other people have asked and most of the responses state that the mass is concentrated at the middle o... | I looked at the link you gave, I think it may not mean to say the higher up you go on a mountain, the stronger the gravitational field.
The link's meaning, I suppose (because they mentioned it is measured by satellites, I suppose it was measuring gravity fields at the altitude of the satellites, which supposedly stayed... | {
"language": "en",
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In 2D space, how to calculate the direction to hit a moving projectile from a position? Imagine a 2D space. A is where our missile is, and B is where our target is currently moving with a velocity of $v_{2}$. B will come close to A in a certain time and then move away like a comet to earth. Our missile can travel at a ... | So we have $\vec A, \vec B, \vec v_2$ and $|\vec{v_1}| = s_1$. We can represent the vector $\vec{v_1}$ as follows:
$$
\vec d = \vec B - \vec A \\
\vec B + \vec v _2 t = \vec A + \vec v _1 t \\
\vec v_1 = \frac{\vec d + \vec v_2t}{t} \\
\vec v_1 ^2 = |\vec v_1|^2 = v_1^2= s_1^2\\
$$
Where t is the time after which the ... | {
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Why does water contract on melting whereas gold, lead, etc. expand on melting? My book mentions that water contracts on melting, but the book doesn't give any reason why it does so. It is mentioned that:
$1\,\mathrm g$ of ice of volume $1.091\,\mathrm{cm}^3$ at $0^\circ\mathrm C$ contracts on melting to become $1\,\ma... | It's because of the crystal structure of the solids. When water freezes, the molecules form various structures of crystals which have empty gaps that cause the solid to be about 9% larger in volume than the liquid was. Metals usually form crystals when they freeze too, but they're often simpler crystals, if you will, a... | {
"language": "en",
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Why does twisting a cork make it easier to remove from a bottle? When we want to remove a cork from a bottle first we turn the cork. Turning in one direction makes it easier to remove in the axial direction.
Does anyone know something more about this?
| The initial twisting step is just ergonomically easier than the initial pull it would be require to get the cork moving. For this you have to overcome the static friction between cork and glass. Also there may be van der Waals forces that need to be broken before the cork starts moving. Once the cork moves the friction... | {
"language": "en",
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Why can't the speed of gravitational waves be greater than the speed of light if the universe can expand faster than the speed of light? Since the expansion speed of the universe can be greater than the speed of light, why can't gravitational waves, which also uses space as the medium, travel faster than the speed of l... | Gravitational waves propagate at the same speed as light and in a similar manner. The point here is that the speed $c$ is only measured locally. The speed of objects with mass is also only limited to be $\lt c$ locally. The relative speed of two objects separated by great distance is not well-defined. See this post for... | {
"language": "en",
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Is time taken by light to travel any distance 0 or finite? According to relativity, Light does not experience any time. So it must travel any distance in no time.
But, we know that light has finite speed $c$. So it should take finite time.
| Speed is measured with respect to some reference frame. Relativity does not allow for a reference frame that is comoving with a photon, so there's no sense within the theory talking about the time or speed "experienced" by the photon in "its own frame". From any valid frame, the speed of light is $c$.
The statement t... | {
"language": "en",
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Why don't we use absolute error while calculating the product of two uncertain quantities? I've found a rule that says, "When two quantities are multiplied, the error in the result is the sum of the relative error in the multipliers."
Here, why can't we use absolute error? And why do we've to add the relative errors? W... | You get the best intuition if you just take two easy numbers with a possible error and multiply it. Choose 100±1 and 200±4 the relative errors are 1/100 or 1% and 4/200=2%.
Now multiply and you get for the positive error 101*204=20604=20000+604 or an error of about 3%. Multiplying the absolute error would give you 1*4 ... | {
"language": "en",
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Why do little chips break off so easily from strong neodymium magnets? I have some strong toy neodymium magnets. Typically after a while little chips start breaking off, unlike from most other small metal objects, like in this image.
It could of course be that neodymium is more brittle than metals used for other objec... | The Neodymium magnets that you use are not actually made from solid chunks of metal, but are rather made by compressing a large amount of powder into blocks through a process called sintering. This is the reason they are so brittle, which is not helped by the fact that they are also so strong!
Furthermore, such magnets... | {
"language": "en",
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The faster you move, does it take more and more energy to increase your speed at the same rate? I'd like to confirm this somewhat counterintuitive result. Starting with the definition of kinetic energy:
$$E = \frac{1}{2} mv^2$$
Assume a vacuum, no external forces, and starting from rest. Adding some energy $E$ to the s... | Yes, that's right, you can also differentiate both sides of
$$\frac{1}{2} mv_1^2 = \frac{1}2 mv_0^2 + E$$
with respect to time and putting $\frac{dE}{dt} = P$, the power supplied, you get to
$$mv\frac{dv}{dt} = P$$
so for a given power $\frac{dv}{dt}$ is inversely proportional to $v$
| {
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Proving that flux contribution due to rotation is zero for a triangular loop welded to infinite wire set up
Consider a triangular loop attached at the vertex to an infinitely long wire which has time varying current flowing in the +x direction
Adapted from JEE advanced paper-1 2016
One may find that the contributio... | Since then magnetic field produced by a current in the long wire forms circular loops around the wire, a rotation of the triangle around the wire would not result in a change in the flux.
| {
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How to understand the ambiguity of vector resolvation? When we solve problems where there is a pendulum suspended using a tight, inextensible string and the question asks about the tension developed in the string at the highest point of the bob's swing. The following is the conventional approach to solve the problem.
... | Newton's Second Law is $\vec{F} = m \vec{a}$. In terms of vector components, this becomes
$$
F_x = m a_x \qquad F_y = m a_y.
$$
Depending on how we set up our coordinates, we may have one or both of $a_x$ or $a_y$ non-vanishing. But we can use our freedom to pick our coordinate axes however we want to simplify our l... | {
"language": "en",
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Kinematics of Scattering Amplitudes in $\left(2, 2\right)$ Signature within the Amplituhedron I am just working my way through the concepts of Amplituhedron and often stumble across the phrase
[...] in $\left(2,2\right)$ signature $\lambda$, $\tilde{\lambda}$ are real and independent [...]
in various references (Jaro... | The main points are:
*
*There is bijective isometry from the split-signature space $(\mathbb{R}^{2,2},||⋅||^2)$ to the space of $2\times 2$ real matrices $({\rm Mat}_{2\times 2}(\mathbb{R}),\det(⋅))$,
where
$$\begin{align} ||p||^2~=~&(p^0)^2-(p^1)^2+(p^2)^2-(p^3)^2~=~\det(P), \cr
p~=~&(p^0,p^1,p^2,p^3)~\in~\mathbb{R... | {
"language": "en",
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What are clover fermions? I've seen the term been used quite a lot when reading about lattice gauge theory calculations. So far what I've gathered is the following, from this source [1].
Lorentz invariance of the action is broken on a discretized lattice. When calculating any quantity on the lattice, the continuum limi... | A clover fermion is a fermion described by the Wilson fermion action plus the clover-term. Clover fermion is just a short-hand version of Wilson clover fermion. Other terms which describe the same fermion discretization are clover-improved Wilson fermion or $\mathrm{O}(a)$ improved Wilson fermion.
| {
"language": "en",
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"source": "stackexchange",
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Why does dispersion occur? In a vacuum, electromagnetic waves of all frequencies travel with the same phase speed, so they propagate with a fixed shape once determined. In a dispersive medium, waves of different frequencies travel with different phase speeds and this causes the wave packet to change shape when propagat... | Electromagnetic field induces polarisation and magnétisation in the media, which are not an instantaneous response. This results in k-vector being frequency-dependent, hence the group velocity,
$$
v_g=\frac{d\omega}{dk}=\left(\frac{dk}{d\omega}\right)^{-1}
$$
is different from the phase velocity
$$
v_{ph}=\frac{\omega}... | {
"language": "en",
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Amount of force required it to tip over a cone Say I have a cone of height $h$, radius $r$, and mass $m$.
How can I determine the amount of force required to tip it over (to have it fall completely to the other side), say exerted (horizontally) at the top of the cone? And in addition, how does the position at which I ... | For rotational static equilibrium, all torques about the CG must balance. Whatever amount of force is required to make the normal vector be applied at the rim of the cone is the load required for tipping.
| {
"language": "en",
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Why would partial derivatives not commute inside an axionic cosmic string? In this 1985 paper by Callan and Harvey, Eq. $11$ seems to claim that in the presence of an infinitely extended string-like topological defect, partial derivatives do not commute on the string:
$$
[\partial_x, \partial_y]\, \theta = 2\pi \delta(... | The integral
$$
I_\gamma=\oint_\gamma d\theta= \oint (\partial_x\theta dx +\partial_y \theta dy)= \oint\nabla \theta \cdot d{\bf r}
$$
is $2\pi$ if the loop $\gamma$ encloses the origin and zero if it does not. Now use Stokes' theorem
$$
I_\gamma = \int_\Omega \nabla\times (\nabla\theta) d^2r , \quad \partial \Omega... | {
"language": "en",
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Can a metal sheet roof be vibrated at audio frequencies? So I'm renting a cheap place for now due to certain circumstances. Problem is outside noise is excessive because there is no ceiling and the roof is only a metal sheet... Lately I play white noise to get some peace but it's not as effective as I want it to be... ... | If you plan to stay there for long it's probably best to add a ceiling inside the metal sheet. In-between put a thick layer (20cm or more) of sound absorbing material such as Rockwool.
If you use the right material it'll act as a heat insulator in winter. Living spaces lose most heat through the ceiling.
| {
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Why does the normal force do no work in the falling stick problem? I'm studying the next problem what I found in a book.
A stick of length $l$ and mass $M$, initially upright on a frictionless table,
starts falling. The problem is to find the speed of the center of mass as
a function of the angle $\theta$ from the vert... | The bottom of the stick, the part in contact with the table, is moving only horizontally. The normal force is applied vertically to the bottom of the stick. Therefore, the dot product of the velocity of the bottom of the stick and the normal force is 0, so no work is done.
| {
"language": "en",
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"source": "stackexchange",
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Torques acting on a unicyclist When a unicyclist rounds a bend, he or she has to tilt in order to generate a frictional force, the friction acting as the centripetal force constraining the unicyclist to a circular path. However, this tilting causes the combined weight of the unicyclist and the unicycle to have a torque... |
On the other hand, if the torque remains unbalanced, the unicyclist will eventually crash to the floor
Not quite. An unbalanced torque must mean that angular momentum is changing. But angular momentum can be expressed in many different ways, not just rotation.
In the case of the unicyclist if we look at the point o... | {
"language": "en",
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Electric field above a ring of charge To find the electric field at a point $p$ which is at a distance $h$ above the center of a ring of total charge $q$ with radius $r$, one can integrate the charge density over the circumference of the ring and get:
$$E = \frac{qh}{4\pi\epsilon_o(r^2+h^2)^{\frac{3}{2}}}$$
Another app... | What you miss in the second method is that the vertical component of the field is not equal to the total magnitude of the field. As you said, the horizontal components cancel out so you have to sum the vertical components only. You can tell that the second formula is wrong with no calculation. The field in the center o... | {
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Conservation of Angular Momentum when potential energy is function of position I have read that the angular momentum $(L)$ of a body is conserved if its potential energy is a function of solely its position vector. For example, the motion of planets on their orbits. I have two questions regarding this concept:
*
*How... | The conservation of angular momentum is due to the symmetry of some physical systems under rotation, and is a special case of Noether's theorem.
To understand this, consider the Euler-Lagrange equation for a system:
$$\frac{\partial L}{\partial q_i} - \frac{d}{dt} \frac{\partial L}{\partial \dot{q}_i} = 0$$
Where $q_i$... | {
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Local decrease of entropy, does it require life? Universal entropy can decrease only locally at the expense of bigger increase elsewhere.
Can this occur in a lifeless environment or does it necessarily require living organisms to do it?
Can this occur spontaneously or does it have to be an intentionally arranged proces... | It happens about 50 times in a second in any internal combustion engine, including cars. Without life. Life has no specific meaning in thermodynamical sense.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/659544",
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"source": "stackexchange",
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Is space really expanding? In a book called "Einstein, Relativity and Absolute Simultaneity" there was this sentence by Smith:
There is no observational evidence for a space expansion hypothesis. What is observed are superclusters of clusters of galaxies receding from each other with a velocity that is proportional to... | According to its Introduction, Einstein, Relativity and Absolute Simultaneity is a volume of essays “devoted, for the most part, to arguing that simultaneity is absolute” (as the title suggests). This is not mainstream physics. Since the book’s editors (William Lane Craig and Quentin Smith) are/were philosophers rather... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/659661",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "32",
"answer_count": 8,
"answer_id": 2
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How can spacetime be expanding faster than the speed of light? How can spacetime be expanding faster than the speed of light when the speed of light is the speed limit of the universe?
| The idea that space expands faster than c is a fundamentally flawed concept. The expansion of space is measured in units of m/s/Mpc. A quantity measured in those units cannot be compared to a quantity measured in m/s. There is no sense in which a greater than or less than comparison is even valid between such incompati... | {
"language": "en",
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Does electron physically move in an interband transition? How does electron move say from ground state energy level to first excited state? Is there any actual displacement in terms of motion?Is there a way to logically think about this by the help of creation and annihilation operators?
I know this is a quantum mechan... | Energy levels are eigenstates of the Hamiltonian, so their probability density remains constant in time. But a superposition of two (non-degenerate) Hamiltonian eigenstates has time-dependent relative phase, which makes the density change with period $\propto E_1-E_2$. Speaking classically, this means something like an... | {
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"source": "stackexchange",
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Conceptual: Pressure change in closed very long pipe Let's say I have a very long pipe with a very small diameter with one closed end and a tight fitting piston.
If I pull the piston to increase the volume and/or push the piston to reduce the volume, will the pressure change be felt throughout the volume or only in the... | As you are pushing the piston, there will be a greater pressure (or lower pressure, if you pull it backward) in the region in front of the piston, and the pressure in the whole pipe will equalize after a time depending on how long the pipe is once you stop pushing.
The pressure will be the same throughout the volume af... | {
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Issue about rotational and translational kinetic energy of a pendulum Let’s say we have a pendulum that consist of a light string hanging a disk-like object. It is allowed to undergo simple harmonic motion with small oscillations.
My question: Is the energy of the disk pendulum at anytime written as
*
*(a) $$E_\text{... | The kinetic energy of a rigid body is invariant (does not change) with the location where it is measured if the parallel axis theorem is used to transfer mass moment of inertia from point to point.
For your example, consider the following two locations
*
*About the center of mass the object has mass moment of inerti... | {
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Where does pseudo force act at? It is known that, to apply Newton's laws in a non-inertial frame, we use the concept of pseudo force. We also know that force is a bound vector. Hence, is there a general way to determine where the pseudo force vector would be located at?
| In a linearly accelerated reference frame the same pseudo force acts uniformly (at any given instant) on all particles in an extended body. This set of pseudo forces can be replaced by a single force acting at the body’s centre of mass.
In a rotating reference frame the pseudo forces will not be uniform, so you have to... | {
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"question_score": "9",
"answer_count": 4,
"answer_id": 2
} |
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