Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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How can two charged black holes merge despite electrostatic repulsion? I have read this question:
Collision of charged black holes
And it made me curious.
I understand that the charged black holes do have negative EM charge, and they repel.
This EM interaction and repulsion between electron fields around nuclei, caus... | Two charged black holes are very much like two charged droplets: they can merge, as long as the charge is not strong enough to repel them. The result is a bigger hole with the sum of the charges. It is not like the EM repulsion goes to infinity as they approach each other: they have a spatial extent, and the surface el... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/428208",
"timestamp": "2023-03-29T00:00:00",
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Concise way to express commutators of two-qubit quantum gates I would like to calculate the commutator of quantum operations
*
*$C^{(ij)}$ (by that I mean CNOT with $i$ being the control qubit and $j$ being the target qubit; please correct me if there's a better and more common notation) single qubit operations, $\s... | Remember that $$\operatorname{CNOT}=\lvert0\rangle\!\langle0\rvert\otimes1+
\lvert1\rangle\!\langle1\rvert\otimes X.$$
Because $[1,\sigma]=0$ for any Pauli matrix $\sigma$, we immediately have
$$[\operatorname{CNOT},1\otimes\sigma]=\lvert1\rangle\!\langle1\rvert\otimes [X,\sigma],$$
which is consistent with your result... | {
"language": "en",
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Are two charges attracting each other constantly accelerating? Using Coulomb's Law: $\frac{k_eq_1q_2}{r^2}$, say we have $2$ charges of $1\ \rm C$ each, separated by a distance of $1\ \rm m$. The force would be $8,987,551,787.3681767\ \rm N$, considering $k_e = 8,987,551,787.3681767\ \rm N m^2 C^{-2}$. So if we were t... | Yes, there is a net force on the charges, so they will accelerate until they collide. The acceleration will obviously not be constant as they move toward each other, the distance is decreasing, which means that the electric force acting on them is increasing. Acceleration is directly proportional to the net force. What... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/428408",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Why does work depend on distance? So the formula for work is$$
\left[\text{work}\right] ~=~ \left[\text{force}\right] \, \times \, \left[\text{distance}\right]
\,.
$$
I'm trying to get an understanding of how this represents energy.
If I'm in a vacuum, and I push a block with a force of $1 \, \mathrm{N},$ it will move... | You have to put in the distance on which the force acts. If you release the force, there will be no work done since there is no force acting on the body.
| {
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"url": "https://physics.stackexchange.com/questions/428525",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "32",
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"answer_id": 2
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How to resolve impulse on a free-floating body into translation and rotation I have free-floating in 2D a long thin homogeneous rectangular body with the center of gravity at its geometric center. It seems to me intuitively that if an impulse is applied to the middle of a long edge, parallel to the edge, there will be... | The general motion of a planar rigid body is a rotation about a point. If you consider an impulse $\hat{j}$ that passes on a line a distance $a$ from the center of mass, then the center of rotation is going to be a distance $b$ on the other side of the center of mass as seen below
The relationship between the two dist... | {
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States created by translation operator Quantum Mechanics Volume One page 188 by Claude Cohen Tannoudji.
In $q$ and $p$ state vectov formalism.
$QS(\lambda) |q\rangle=(q+\lambda)S(\lambda)|q\rangle$, where $S(\lambda)=e^{-i\lambda P/\hbar}$.
Thus when only consider $p$ and $q$, one may effectively think $S(\lambda)|q\ra... | The properity closely related to the fact that $|q>$ in heliber space is considered as a complete set of basis(Use of 'complete' as in 'complete set of states' or 'complete basis'), that is $S(\lambda)|q>$ as a states with eigenvalue of $\lambda +q$, there is "nothing more to say" about the vector $S(\lambda)|q>$ as it... | {
"language": "en",
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Modes in optical fibers I am trying to understand the modes in step-index optical fibers and I saw that they say the electric field distribution in the core and cladding is as bellow. my question is that which component of electric field is this?
| As The Photon already pointed out, "TE" means "Transverse Electrical", which is just telling you that there is no component along the direction of propagation - $z$, in this case. See here for the distinction.
Now, if you want to find the functional form of your electric field, you have to solve the wave equation.
Sin... | {
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"source": "stackexchange",
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Which field Passes Through the Polarization Film? Why Isn’t the Perpendicular Field Stopped? When one EM field is aligned so that it can pass through a polarizing lens the other field (E or B) is 90 degrees out. Is only one of the EM fields affected by a polarizing lens or film? How is it that one field is stopped yet ... | One way of making a polarizing film is having a lot of small narrow conducting 'rods' inside it. The rods are much longer than they are wide, and are mostly oriented in the same direction. The spacing between the rods is on the order of the wavelength of light. Imagine, for lack of a better analogy, the bars on a priso... | {
"language": "en",
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Mixed canonical transformation Wikipedia and most authors denote four types of canonical transformations: $F_1(\mathbf{q},\mathbf{Q})$
, $F_2(\mathbf{q},\mathbf{P})$, $F_3(\mathbf{p},\mathbf{Q})$ and $F_4(\mathbf{p},\mathbf{P})$. However, is it possible (or necessary, perhaps) to define a transformation that mixes both... | Classical Mechanics (Third Edition), H. Goldstein, Chapter 9, Page 374:
[...]
Finally, note that a suitable generating function doesn't have to conform to one of the four basic types for all degrees of freedom of the system. It is possible. for some canonical transformations necessary, to use a generating function tha... | {
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Simple DC motor with one bar magnet https://www.instructables.com/id/The-Simple-DC-Motor/
I'm struggling to get my head around how this motor works.
Let's say for the sake of argument that the field lines are running from the LHS of the bar magnet round to the right and that current flows through the coil in a CW dire... | You are missing the fact that this simple motor has a commutator which does not allow current to flow during half a revolution of the coil so the direction of the force/torque is never reversed it just goes from being in one direction to zero to being in the same direction as before to zero etc.
Hold the loop vert... | {
"language": "en",
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Can the Earth's negative charge make negatively charged objects levitate? Since the earth's surface has a negative charge, could it repel a large highly negatively charged body? An example is an object on stilts carrying a negative charge that is heavier than air, maybe multiple tons in weight.
| The strength of the electric field near the surface of the Earth due to its negative charge is reported to be around $100 \frac V m$.
This field should easily lift an electron, since the force acting on an electron, $eE=1.6\times10^{-19}C\times 100 \frac V m=1.6\times 10^{-17}N $ is orders of magnitude greater than the... | {
"language": "en",
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What happens at the molecular level during evaporation? During boiling the liquid gets its energy from the heat source so it can break the force between molecules and turn into gas while evaporation happens at the top of the liquid at any temperature. Where does it get it's energy, I've read that when molecules bump th... | Evaporation is not simple to understand, even wikipedia omits a major factor in evaporation called entropy which is powerful force. The above explanations focus on the kinetic aspect of things but entropy is just as important. Entropy basically says that atoms and molecules will mix together and once this happens you... | {
"language": "en",
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How can velocity be a tensor? I have just begun studying general relativity and have a question.
I know that if a tensor is zero in one coordinate system, it will be zero in all coordinate systems.
So how can the $\mu$'th component of the velocity $dx^\mu/d\tau$ be a tensor?
There must be something I have misunderstood... | In your question, you ask "how can the $\mu$-th component of $\frac{d x^{\mu}}{d \tau}$ be a tensor?"
To put it simply, it is not a tensor. The thing that is actually the tensor is the four-velocity $v$. The numbers $\frac{d v^{\mu}}{d \tau}$ are the components of this tensor in some particular coordinate system $x^{\m... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/430063",
"timestamp": "2023-03-29T00:00:00",
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Equation for probability amplitude of a free particle given a mean position, a mean velocity, and the mass of the free particle? The uncertainty principle can be expressed using the equation $\sigma_x\sigma_p\geq\frac{h}{4\pi}$ with $\sigma_x$ being the uncertainty in position, $\sigma_p$ being the uncertainty in momen... | A usual definition of the wavefunction of a free particle is simply $\psi(x) = \exp(-ikx)$. This of course corresponds to a particle with definite momentum that is infinitely 'smeared out' in space ($\delta p = 0$, $\delta x = \infty$). I assume you're asking about the wavefunction of a free particle with the constrain... | {
"language": "en",
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Lorentz Velocity Transform With Tensor Notation So I'm attempting to prove the Lorentz Velocity tranform:
$${v_x}' =\frac{v_x-u}{1-v_xu/c^2} $$
using tensor notation. In this case obviously $\beta = u/c$ and $\gamma=(1-\beta^2)^{-1/2}$. The velocity transform tensor can be represented as
$$\Lambda = \begin{pmatrix}
\... | Einstein velocity addition equation in Minkowski space
\begin{align*}
&\text{I) We want to show that The velocity addition equation is:} \\
&v_g=\frac{v_1+v_2}{1+\frac{v_1\,v_2}{c^2}}\\
&\text{ We take the coordinate transformation between $(t'\,,x')$ and $(t\,,x)$ (c=1)}\\\\
&\begin{bmatrix}
t' \\
... | {
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If we push a syringe with gas in it In space , would its temperature increase permanently , Violating Boyles Law? On Earth
If we push a gas syringe very fast Inwards , work is done on the gas by
W = PV
which increases the Kinetic energy of molecules in it and since Temperature is Average Kinetic Energy thus T... | This will happen only if the container in which gas is present conducts 0 heat. This means that their is no exchange of heat from inside to outside. This will also happen on earth if we use that type of container and it is not the violation of boyle's law
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Non-acceleration and 0 force If a mass is moving at the rate of 30/ft. per minute for 5 minutes on a straight line and it strikes a second stationary mass and effects a change of position to this second mass, then we know from F=ma that the force is 0 since the acceleration is 0. Then why do we say because it is 0 that... | It appears you are mixing the force at one given time with the acceleration at a different given time.
Don't feel bad; it is a common beginner mistake to think that there is "one force" and "one acceleration" in a given problem. Part of learning physics is learning how to treat values from different times, as well as ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/431032",
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Once a black hole is formed, is there anything other than Hawking radiation which shortens its life? Hawking radiation is supposed to very slowly evaporate a black hole (terms and conditions apply :] ).
Apart from Hawking radiation, is there any mechanism or effect that can make a black hole cease to exist? Or once th... | There is speculation that a black hole which somehow manages (or is made) to rotate fast enough could turn into a naked singularity. The missing event horizon of such a speculative anomal anomaly would imply that "stuff" could escape from it.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/431175",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Why doesn't using more appliances at home decrease the electricity bill? I know that at home the electric circuits are parallel, and this explains why if one appliance (eg bulb) fails, everything else continues to work, but if more devices are added in parallel to each other, their combined resistance should decrease, ... | The power will increase .See the formula given carefully $V^2/R$. For constant voltage power is inversly propotional to resistance.As we add one more resistance in parallel overall resistance decreases and hence power increases.Or you can also think in the way if overall resistance decreases then current increases and ... | {
"language": "en",
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Symmetries in quantum mechanics I have been studying symmetries in quantum mechanics and I have come across two types:
*
*Given some transformation on a Hilbert space of states $\mathcal{H}$, an operator $U: \mathcal{H} \rightarrow \mathcal{H}$ is a symmetry operator if
$$ U^\dagger H U = H$$
where $H$ is the Hamil... | In the first definition you have not made $U$ preserve the $\mid \langle \psi \mid \phi \rangle \mid$. As an example, suppose $H=0$ (a trivial system), then you would get all operators $U$ as symmetries even if they aren't even unitary or anti-unitary. Those shouldn't have been called symmetries. You want both conditio... | {
"language": "en",
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"source": "stackexchange",
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What is the difference between reflection and emission? What is the difference between a body that simply reflects the light that falls upon it and a body that absorbs and emits it (like a black body in thermal equilibrium)?
How can one experimentally distinguish these two scenarios by simple measurements?
(I think t... | In both cases, light falling on an object is a vibrating electromagnetic field. This makes electrons in the object vibrate and may make them more energetic.
A mirror is a smooth object with free electrons. Light makes them vibrate. Vibrating electrons are accelerated. Accelerated electrons radiate. For a mirror, the r... | {
"language": "en",
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Instantaneous velocity So here’s a question I’ve been thinking of for a while. Suppose we say, “an object is having an instantaneous velocity along a particular direction ( say 10 m/s along the $x$-direction)” . Is it fair to conclude that it is traveling in a straight line along the $x$-axis? Well my opinion on this i... | In a parabola, the instantaneous velocity isn't constant or only acting in one direction while travelling through it's path. It is always tangent to the parabola.
An object which has an instantaneous velocity in one direction does not have to keep travelling in that direction as long as there are other forces acting o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/431908",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Are Minkowski and Schwarzschild spacetimes diffeomorphic? Another mathematical question, arising from GR. Some days ago I wrote, in an answer to 1, that they are. Then @magma commented they are not. He promised a proof, but none appeared. After magma's comment I have some doubts about my intuition and I would like to s... | They aren't. That is because Kruskal-Schwartzschild is diffeomorphic to $S^2 \times R^2$, while Minkowski is $R^4$. This is roughly similar to the difference between a 2D cylinder $S^1\times R$ and $R^2$.
The formal reason is that pointed out by G. Golfetti in a comment above: the second homotopy groups are differe... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/432035",
"timestamp": "2023-03-29T00:00:00",
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What is Chirped Pulse Amplification, and why is it important enough to warrant a Nobel Prize? The 2018 Nobel Prize in Physics was awarded recently, with half going to Arthur Ashkin for his work on optical tweezers and half going to Gérard Mourou and Donna Strickland for developing a technique called "Chirped Pulse Ampl... | As an addendum to @EmilioPisanty’s excellent review, I’d just like to mention one more application of CPA lasers, which may be overlooked from a theorist’s perspective:
Ultrafast Spectroscopy
Sometimes lower-order nonlinear processes like second-harmonic generation are enough; you just need them done efficiently for pr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/432137",
"timestamp": "2023-03-29T00:00:00",
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What happens on the atomic level that allows us to see objects that have the same order of magnitude as visible light's wavelength? By virtue, human eyes can only see EM waves in the visible light region. From my understanding of 'why we see things', it is because light reflects off an object, and the lights' diffracti... |
the wavelength of visible light is too long for light to interact effectively with individual atoms and molecules
That's some extremely clumsy wording on the part of your text. The wavelength of visible light is indeed much, much longer than the characteristic sizes of atoms and molecules (half a micron to half an an... | {
"language": "en",
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Time evolution of eigenstates superposition If a system is in a state $\psi$ which is superposition of, let's say two, energy eigenfunction, namely $\psi_1$ and $\psi_2$, so that $$\psi(t)=\psi_1e^{-i\omega_1t}+\psi_2e^{-i\omega_2t}$$ (I am omitting normalization constants for simplicity) then $$\left|\psi(t)\right|^2=... | Your notation is ambiguous so it's not quite clear what you're actually asking. If by $\psi_1$ you mean the position basis-wavefunction $\psi_1(x)$, then as the other answers point out, only the integrals of the cross-terms with respect to $x$ vanish, not the pointwise products. If by $\psi_1$ you mean the basis-indepe... | {
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Speed of EM waves differ from GWs? I understand that light travels at speed c in vacuum, when measured locally. This speed has an exact value, not an approximation, because it is defined as 299 792 458 m / s.
It is an exact value, because the meter is defined as the distance that light travels in a 1/299 792 458th of... | Because GR is just one of the many models of gravity. From the observation of gravity's long range, classical GR is based upon masslessness of graviton. GR is the unique theory of massless spin 2 particles.
But you can give up masslessness and study the ensuing consequences of such a modified theory of gravity. Such mo... | {
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Confusion with regards to uncertainty calculations Let’s say we have a scenario of a ball being released from the top of the building. This can be modeled simply with the kinematics equation $S=ut +\frac{1}{2}at^2$, which reduced to $S=\frac{1}{2}at^2$. We are given $\Delta t, t, \Delta S, S$, are we are to find $a, ... | So I am pretty sure the difference between your two equations depends on what you actually measured and what you are calculating from those measurements.
Think of it this way: One of your two equations (before your addition to the question), tells you how to calculate an uncertainty from the uncertainties of your measu... | {
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Why the rubber ball bounced higher than the glass ball? For a teaching degree we did the following experiment:
Drop a rubber and a glass ball of approx. same size from approx. same height onto laminate flooring.
As we expected, the rubber ball bounced higher than the glass ball.
Our explanation: The rubber ball is mo... | There is a property of materials called the coefficient of restitution that is given by the relative velocity after a collision divided by the relative velocity before the collision. This coefficient is often denoted by e and comes from "Newton's Law of Restitution". This number is proportional to the height of an obje... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Reverse engineering a time dilation problem Consider the following problem
A rocket with a clock moves at $0.8c$ relative to the earth. An observer A on the rocket measures a time interval of 6 seconds. With respect to an observer B on the earth, the time interval is $$\frac{6}{\sqrt{1-(0.8)^2}}=10$$ seconds.
I got c... | $\let\D=\Delta \let\g=\gamma$
Your question (and your misunderstanding) is recurring over and over. Your first application of time dilation formula is right, the second is wrong. Why?
Simply because some simple points must be kept, referring to reference frames and events.
You have two frames, say A (the rocket) and B ... | {
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How is momentum conserved in this example? Suppose a sticky substance is thrown at wall. The initial momentum of the wall and substance system is only due to velocity of the substance but the final momentum is 0. Why is momentum not conserved?
| You should also consider what the wall is attached to. And obviously it is the Earth. If we assume the Earth's velocity is zero after the substance is thrown, since there is the force that slow down the substance at the moment of impact, there is also the reaction force on Earth with the same magnitude and opposite dir... | {
"language": "en",
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Why do we use the RMS but not the fourth root mean quad? Why do we use the power of $2$? What is the relation between this and having the same heat energy in both AC and DC?
|
what is the relation between this and having the same heat energy in
both AC and DC?
First, the context here is the voltage across and current through a resistor. The power delivered to a circuit element is the product of the voltage across and current through. So, for a resistor (only), the instantaneous power i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/433726",
"timestamp": "2023-03-29T00:00:00",
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Is the dark matter present only around the galaxies? Dark matter is believed to give galaxies its shape and prevent them from flying apart.
Is dark matter present only on outer edges of the galaxy or is it present throughout the galaxy?
| In order to explain the rotation curves of galaxies, the dark matter would have to be distributed throughout the galaxy and not only in the outer edges. More detail below:
The basic experimental results that lead to the discovery of dark matter is the rotation curve of galaxies. The rotation curve is basically a graph ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/433941",
"timestamp": "2023-03-29T00:00:00",
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Question on convective heat transfer Why is the following formula used when we define heat transfer due to convection on a flat plate?:
$$ q=h(T_s-T_\infty)$$
Where $T_s$ is the temperature of surface at a particular location and $T_\infty$ is the temperature of fluid flowing with free stream velocity.
Why are we using... | The way I think about $t_\infty$ is that we could pick it by going to extremes: $t_\infty$ should either be the temperature of the fluid right above the plate or it should be the temperature of the fluid far away from the plate. I will argue that it is way more useful to choose the temperature of the fluid far away fro... | {
"language": "en",
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Conceptual question in thermodynamics about isothermal processes If a process is isothermal then Δ U is zero. So ΔQ is non zero. But isn't ΔQ=nCΔT. Implying that ΔQ is zero. Where am I wrong? (Considering ideal nature)
| The thing is that the relation $\Delta Q = nC\Delta T$ is true for some particular processes -- in an ideal gas, for instance, it is true when the system passes through a process at constant pressure (in which case $C = C_p$) or in constant volume (in which case $C = C_V$), but this is not true in general. In an adiaba... | {
"language": "en",
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Why position and momentum operators are both continuous spectrum while angular momentum is discrete? We know that position $\hat{r}$ and momentum $\hat{p}$ are both continuous spectrum operators, i.e.
$$\hat{r}|r'\rangle=r'|r'\rangle, \quad \hat{p}|p'\rangle=p'|p'\rangle.$$
But the angular operator $\hat{L}=\hat{r}\tim... | One possible answer: boundary conditions.
If we think of the classical to quantum transition to be from point-like particles to waves which describe probability densities, then the position and momentum of a free particle does not have any explicit boundary conditions. That is, there is no restriction on the specific ... | {
"language": "en",
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Problem regarding finding work done This problem is given in my physics book. How much work will be done if anyone wants to stack up 12 bricks? Given that each brick is $10 cm$ high and each brick's mass is $2 kg$. ($g=9.8$)
Now in finding my answer I used the mass and height of all the bricks. But in my book they used... | We are supposed to stack 12 bricks on one another. One brick is unmoved. The centre of mass of 11 bricks is 60 cm or 0.6m above initial level after stacking.
Now, the work done against the force of gravity is:
$W = mg \Delta h = 2(11)(9.8)(0.6) = 129.36J $
Another method is to calculate work done individually
$W = m... | {
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Why does the Boltzmann equation deal with single-particle phase space density? Why does the Boltzmann equation deal with single-particle phase space density $\rho_{1}(\textbf{r}_1,\textbf{p}_1,t)$ rather than the N-particle phase space density $\rho(\{\textbf{r}_i,\textbf{p}_i,t\})$? How'll deal with Boltzmann equation... | That's the whole point. Rather than dealing with the complicated N-particle distribution we try to find an equation of motion for the 1-body distribution
$$
f_1(r_1,p_1,t)=\int d\Gamma_2\ldots d\Gamma_n\, f_N(r_1,p_1,r_2,p_2,\ldots).
$$
Boltzmann brilliantly guessed an equation for $f_1$, and standard textbooks try to ... | {
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Pressure on side walls of container My textbook mentions the standard derivation of finding pressure at a depth of a liquid by considering a cylindrical portion of liquid an then using the equilibrium of forces and hence pressure comes out to be $$hdg$$.What I want to ask is that the above method is correct but then ... | Pressure at a depth in a liquid is equal to the pressure exerted by the liquid on a surfce at that depth in the liquid.Because pressure at a point is the same in all directions and if the liquid particles exert a pressure on each other then they exert the same pressure on any other surface immersed at that depth.
| {
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Orientation of momentum of a virtual photon Picture a wire with current directed out of the page. The electrons in the wire emit virtual photons in all directions which mediate the produced magnetic field. What is the orientation of the momenta of the emitted virtual photons, or are they randomly oriented?
| I disagree with the other answer. If the electrons are moving with a constant velocity (i.e. not accelerating), then there are no real photons emitted.
In the rest frame of the moving electrons, the electrons will set up an electric field (in this case a field that will point inwards and drop like a log of the distanc... | {
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Why naturalness is an issue in particle physics? It is not in fluid dynamics I have often heard that naturalness is a strong argument in favor of Supersymmetry. They say that there must be energy scales not too far away the EW-energy so that the quantum corrections of the heavy particles (Higgs, top quark, etc) do not... | I think that this is a misguided example. In isotropic turbulence the mean vorticity is zero (by rotational invariance), but the mean square vorticity is not. This means that there is indeed a symmetry that ensures that the mean vorticity is much smaller than the root mean square vorticity. This is precisely what natur... | {
"language": "en",
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Confusion while deriving kinetic-molecular theory of gases
How many of the molecules will collide within a given area A of the
wall normal to the x-direction in some fixed time interval Δt ? On average half the molecules have a positive x-component of velocity. Therefore half the molecules c... | A simple way of thinking about this is to think about the motion of particles through an imaginary plane somewhere inside the fluid. The number of particles crossing the plane from one side to the other must be the same as the number of particles crossing in the other direction. This must be the case because first of a... | {
"language": "en",
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Is extracting energy via the Penrose Process only possible with Kerr black holes? I have been learning about extracting energy via the Penrose Process. Everything I read mentions leveraging the ergosphere of a rotating black hole.
But the ergosphere and the mechanisms of extracting energy sound a lot like frame draggin... | Energy extraction from Kerr black holes is possible not only through Penrose process, but from a variety of other processes. Penrose process is also not astrophysically feasible because it has been shown by Bardeen that for Penrose process to occur, the relative velocity of the split should be around $c/2$, i.e., the p... | {
"language": "en",
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What part of special relativity is factored in in relativistic redshift velocity equations? While doing research into redshift equations (doppler redshift and cosmological redshift), both types of redshift had two equations for finding recession velocity: a 'non-relativistic' equation and a 'relativistic' equation. I l... | Speaking of Special Relativity, there are three basic relativistic effects: time dilation, length contraction, and relativity of simultaneity. Of those three the relativity of simultaneity is the most difficult for new students to understand, and it is the source of most of the errors that new students make in relativi... | {
"language": "en",
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What is the meaning of $PV^\gamma=$ constant in an adiabatic process? In an adiabatic process, heat transfer doesn't occur and hence $\Delta U=-W$ (an increase in internal energy due to work done on the system or a decrease in internal energy due to work done on the surrounding).
My textbook then says (for monatomic ga... | You are correct in saying that, in an adiabatic reversible process, the pressure, volume, and temperature are changing in tandem. However, the temperature is changing in such a way that, along the process path, the equation $PV^{\gamma}=const$ is always satisfied. And, in an adiabatic process, the parameter $\gamma$ ... | {
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How do charges lose electrical potential energy when going through a resistor? I can understand that the charges need to do work against the resistance - which transfers energy to forms such as light, heat, etcetera - using the electrostatic force provided by the battery terminals. But how does this result in a loss of... | The charges lose potential energy by moving from a higher potential energy to a lower one. In the mean time they are accelerated and scattered. The result is an equilibrium drift speed, while the excess kinetic energy is transformed into heat.
| {
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Why are tall block stacks so hard to make? Consider a stack of wood chips: each 0.5cm thick and 2x2 cm in length and width. There are 200 of them all stacked on each other. For some reason they all instantly fall. Evwn though their centre of gravity is at the centre of the stack and they have the extra added help of ... | First, let's assume the tower is a single solid rod. The tower will fall over when the center of mass extends past the base. For a longer tower, a smaller angular displacement is needed for this. This is because we want the horizontal displacement of the center of mass to be
$$x=\frac 12 H\sin\theta<\frac 12 w$$
where ... | {
"language": "en",
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Is the relative speed of light really invariant, irrespective of the motion of the observer? If 3 observers are on a planet which 100 light years from a star, and the star goes supernova, if one observer moves towards the star and one moves in the opposite direction, each observer will see the explosion at a different ... | You are reasoning in the frame of the observers and while the speed of light is the same in that frame, the distance to the supernova is different in the frame of the moving observer so they are not all "100 light years away" at the time (on the observer clock which is different for the 3 observers) the light is emitt... | {
"language": "en",
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What is the most useful to learn out of complex analysis and differential equations for undergraduate studies in physics? Next year I'm planning to start on my bachelor's in physics, however, I have already started taking some undergraduate courses in mathematics and next semester I will have to choose between complex ... | Complex analysis is unlikely to be of any use at all in undergraduate physics classes. Differential equations are used constantly. All of physics is expressed in terms of differential equations, such as Maxwell's equations and the Schrodinger equation.
| {
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Work done by a gas In the expression for work done by a gas,
$$W=\int P \,\mathrm{d}V,$$
aren't we supposed to use internal pressure?
Moreover work done by gas is the work done by the force exerted by the gas, but everywhere I find people using external pressure instead of internal pressure.
| At the interface with the surroundings, by Newton's third law, the force per unit area exerted the gas on its surroundings is equal to the pressure of the surroundings on the gas. But, in an irreversible expansion or compression process, the pressure of the gas may not be uniform within the cylinder. So the pressures... | {
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Does measurement with unknown outcome transform a pure superposition state into a mixed state? $\def\+{\!\!\kern0.08333em}$
Say I have a spin-1/2 particle in a general, pure superposition state
$$
|\psi\rangle=\alpha|\+\uparrow\rangle+\beta|\+\downarrow\rangle,
$$
or equivalently
$$
\rho=(\alpha|\+\uparrow\rangle+\beta... | Yes, this reasoning is correct.
| {
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Is the mass of Tachyons real or imaginary? I have always considered quantities like mass, charge, momentum etc. to be real quantities as them being imaginary doesn't make much sense to me.
But for tachyons to exist, they should have imaginary mass compatible with special relativity. Or their rest mass should be imagina... | First let's clear up the possible confusion about rest mass and mass. All working physicists these days define mass to be the same thing as what used to be referred to as "rest mass" back in the 1950's. The modern convention has slowly filtered down into textbooks and is now a universal standard except in popularizatio... | {
"language": "en",
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Are uncertainties higher than measured values realistic? Whenever I measure a positive quantity (e.g. a volume) there is some uncertainty related to the measurement. The uncertainty will usually be quite low, e.g. lower than 10%, depending on the equipment. However, I have recently seen uncertainties (due to extrapolat... | Something which has an exponential distribution (so positive) with expected value $\mu$ also has standard deviation $\mu$ - there are other distributions on positive values where the standard deviation can be many times the size of the expected value
By a vague recollection from the normal distribution, you might naiv... | {
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Perfect Vacuum Beneath an Object Recently I became interested in how suction cups work by creating a region of space with lower pressure than their surroundings, thus sealing the suction cup to the contact surface. Extrapolating this idea further, does this mean that a cube resting on a perfectly flat surface would be ... | Even though real objects cannot be perfectly flat, they could be flat enough to stick together pretty well.
Common examples are two pieces of glass or gauge blocks wrung together (video). Besides vacuum action, other forces, like molecular attraction (adhesion) may play a significant role.
| {
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Can any body be uniform in the universe? If I take any body in the shape of a rod and stretch that, after it reaches breaking stress it breaks at one point.
Even though we apply the same the stress on each and every part of the rod it broke at one point. If it's uniform it should break at all points because breaking st... | Uniform bodies are idealizations like frictionless surfaces or no air resistance. They make the work easier. In reality there will be slight deviations in material properties (such as density, tensile strength, etc.) along various parts of the body. In your example these deviations become more and more important and ex... | {
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Faxen's Law Proof Been working on this for a couple weeks and have had no dice. Does anyone know of a nice way to prove Faxen's law (force on a sphere in a fluid flow)? Particularly using the reciprocal theorem? Here is the link to what Faxen's law is: https://en.wikipedia.org/wiki/Fax%C3%A9n%27s_law
In particular the ... | The most straightforward development I've seen of the Faxén laws, at least for the first one you mention, is in Kim and Karrila's book which precisely uses the Lorentz reciprocal theorem.
Although I won't reproduce it exactly, I'll mention the key conceptual aspects and you can take it from there:
*
*Consider the ge... | {
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Color and the absorption of light in quantum mechanics In an answer to a another question, the poster states without sources the following:
From a quantum mechanical perspective, all light scattering is a form
of absorption and re-emission of light energy. Photons don't bounce
off a surface.
If this is true, what... | The fundamental theory that described the interaction between light and matter is quantum electrodynamics (QED). It has been exhaustively tested and found to be in excellent agreement with experimental observation.
According to QED the fundamntal interaction is given by a vertex with three legs: two for the charged fe... | {
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How can a particle in circular motion about a fixed point accelerate, if the point doesn't too? When a particle is performing uniform circular motion attached to a string about a fixed centre, at any instant of time its acceleration is directed towards the centre but the centre has no acceleration. But I was taught in ... | To distill (previous answers are correct, but perhaps unnecessarily long if I understand your point of confusion):
For a rigid system moving without rotation, all points in the system move with the same acceleration.
In any other case (i.e. if there is any change in orientation of the system) this is no longer true.
| {
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How does Newton's corpuscular theory explain the speeding up of corpuscles when entering a denser medium? I can't find an explanation for this anywhere. Intuition would imply that the corpuscle would slow down. I mean a person running at a constant speed enters a crowd of people or a forest. The presence of obstacles w... | In order to explain the refraction of light in going from air into a medium Newton assumed that the medium applied an attractive force on the corpuscles which was perpendicular to the surface.
This force accelerated the corpuscles as they entered the medium in a direction which was perpendicular to the surface of the m... | {
"language": "en",
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BB84 protocol with cloning I am taking a Quantum Information course and I stumbled onto this problem, which I am unsure about. The situation assumes BB84 protocol, but with Eve doing a cloning operation (let's assume that she's doing it in states $|+>$ and $|->$ which are orthogonal) instead of the measurement. She kee... | Cloning an arbitrary quantum state is forbidden. See here for a proof https://en.wikipedia.org/wiki/No-cloning_theorem
It is not clear what you mean by "assume she does it (cloning) in the $\vert +\rangle, \vert -\rangle$ basis" but she is unable to measure (as that is detectable) and unable to clone as that is forbidd... | {
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Can someone explain why there is water in this vacuum chamber? I work at a water treatment plant that uses a vacuum system to pull the water into the filters and backwash the filters. In the middle of the vacuum system there is the vacuum chamber. What I don't understand is why is there water in the bottom of the chamb... | The vacuum process in the drawing is configured in a way that allows you to "pull" a low vacuum by opening the appropriate valve, and it allows you to "pull" a high vacuum by opening a different valve, and you can get these two different vacuum settings from the same vacuum pumps. A high vacuum setting will pull water... | {
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Why are bend losses higher at higher wavelengths in fiber optic cables I have been reading about fiber optic cables for the past few months, specifically about bend losses. It is often mentioned that bend losses are higher at longer wavelength light and indeed this is the case, but I am curious as to why this is so. In... | An intuitive explanation for why this occurs is as follows. If you think of the wavelength of the light as the limiting length scale for it to resolve changes in the guiding structure then as the wavelength increases resolution decreases. Since the resolution has decreased the bend in the guide appears to become more ... | {
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Why does gauge invariance in electrodynamics mean that there are redundant degrees of freedom? It is possible to choose different gauges in electrodynamics. I am familiar with two of them: Coulomb gauge and Lorenz gauge. Let us stick to the Coulomb gauge. It sets $$\nabla\cdot\vec{A}=0.$$ The wisdom is that with this c... | Gauge invariance just happens to be the technical term people chose to indicate that redundant electromagnetic degrees if freedom. I guess that answers the question in the title.
In your example you as they say fixed the gauge by choosing $\vec \nabla \times \vec A=0$. That is all there is to it.
| {
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Relativistic space rocks. Are they possible? I was thinking that the Universe is full of extreme events. Colliding galaxies, exploding stars, colliding planets (like in one of models of our Moon formation), colliding black holes...
Can it be possible, that such event would accelerate some rocks to let's say $0.1c$ ?
D... | The most likely way for a rock to reach that speed a long distance from any stars would be as a result of a close encounter with a close binary system - or even better, with a pair of black holes in close orbit. Think of the rock as a baseball and one of the pair of black holes as a baseball bat. The rock could fal... | {
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How do we know quantum entanglement works no matter the distance? It is said quantum entanglement works regardless of distance. 2 particles can be entangled and information is shared instantaneously, even if they are lightyears away from each other.
But how do we know this still works with such a vast distance between ... | Personally I would like to say the statement is not exact or at least not clear so far. If generally we believe the structure of spacetime is closely related with entanglement, then we should be very careful to talk about 'distance/time/velocity' in a case when entanglement is involved.
My opinion is that when we are ... | {
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How many eyes are needed to see a four-dimensional world? If a four-dimensional world were to exist, how many eyes would a creature minimally need to see it (in three dimensions)?
Three? Four?
(Bonus question: how should these eyes be spatially configured?)
| One eye would be enough. (Try closing one eye and you can experience the result for a 3-D world).
But I guess you had in mind what is the value of $N$ such that $N$ eyes give geometric info not available with $N-1$ eyes.
First suppose that in the 4D world, an eye has a 3D volume into which it projects whatever light a... | {
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What would happen to 2 separate photons on an uninterrupted path So I am a middle schooler and from what i understand, photons can interact with surrounding particle via gravity. If this is true, would 2 photons on an uninterrupted and completely isolated path eventually gravitate towards each other and pass each other... | That is an insightful question. To answer the first part fully would require a LOT of math. Your basic thought is right: photons would attract each other gravitationally. However, the attraction would be very small; much too small to observe or measure using any instrument currently imagined. The second part of you... | {
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Is there a traditionally accepted threshold probability at which highly unlikely becomes impossible? Many events which by any practical definition are impossible have extremely low but nonzero probability of occurrence. For instance, the positions of oxygen molecules in a room are basically random and independent, but ... |
Is there a traditionally accepted threshold probability at which highly unlikely becomes impossible?
No, there isn't. People will in practice set certain probability thresholds that are specific to certain applications. For example, suppose a drug company is doing an automated trial of 10,000 new substances in vitro ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/439909",
"timestamp": "2023-03-29T00:00:00",
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What is the $\,\phi=0\,$ gauge called? In electromagnetism textbooks, the gauges most often talked about are the Lorenz gauge and Coulomb gauge. Sometimes it's convenient to work in a gauge in which there is only the vector potential $\vec{A}$ but no scalar potential $\phi$. The following gauge transformation transform... | Your specified gauge is actually incomplete. In general, though, any gauge with $\phi = 0$ is a Weyl gauge.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why isn't the emissive power of a black body 1? My text book has a question which says that the emissive power of a black body isn't one but the answer states that the absorptive power is 1, considering that $$e=a \tag{Kirchoff's law}$$
and a black body is defined as an object which has $$e=1$$ Then why isn't $a=1$
... | For blackbody $a=e=1. a=1$ implies that the blackbody absorbs all radiation falling on it. For anything that is not a blackbody, $0≤e=a<1$
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/440304",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Energy density in magnetic field If an electric field $\mathbf{E}$ exists at a point in free space then the energy density in that point is $\frac{1}{2} \epsilon_0 |\mathbf{E}|^2$.
When a field with same magnitude $|\mathbf{E}|$ exists in a material with relative permettivity $k$, the energy density becomes $\frac{1}{... | Inside a dielectric, an externally-applied electric field is reduced. Therefore, a higher energy density is required to generate a given electric field inside the dielectric. This means that for a given electric field inside a dielectric, the associated energy density will be larger than in the vacuum; intuitively, you... | {
"language": "en",
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Is it possible to suggest a physical experiment in which measurement errors are dramatically increasing? (due to the accumulation of errors) Is it possible to suggest a physical experiment in which measurement errors are dramatically increasing? (due to the accumulation of errors)
Maybe some magnetic field can be used ... | Here is a simple experiment which will demonstrate this effect.
You can buy a device called a pedometer, which measures how far you have walked on a hike by detecting each time you take a step. The pedometer has a calibration procedure in which you tell it how many inches there are in one of your steps, and it then add... | {
"language": "en",
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"source": "stackexchange",
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What would happen if light was completely blocked from an object? Here's the scenario:
There's an object that has been cased with a device that shoots off an 'anti-light' wave (complete reverse of light waves, destructive interference). Say, you have it set up to automatically detect and fire upon a a light wave in tha... |
There's an object that has been cased with a device that shoots off an 'anti-light' wave (complete reverse of light waves, destructive interference). Say, you have it set up to automatically detect and fire upon a a light wave in that proximity so that no light wave reaches that object.
You've just described a layer ... | {
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Relation of Hydrogen orbitals to its spectral series? I'm looking for the link between the Rydberg formula for hydrogen spetcral series
$$\frac{1}{\lambda_{\mathrm{vac}}} = R\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$$
and this image.
Is it right to say that the Balmer Series is created by all transitions from (x, _... | The 'link' is, in short, the Schrödinger equation.
The orbitals plotted in the image ─ the wavefunctions $\psi_{n,l,m}(r,\theta,\phi)$ ─ are the hydrogenic solutions to the hydrogen Schrödinger equation,
$$
\left[
-\frac{\hbar^2}{2m}\nabla^2 - \frac{e^2}{4\pi\epsilon_0} \frac{1}{r}
\right]\psi_{n,l,m}(r,\theta,\phi) = ... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Can we enhance evaporation rate with a vacuum pump? First, consider having water at 100C and 1atm and a heat source. If more heat added to water, we have more evaporation rate according to the following formula:
$$Q_{in}=m_{vapor}*h_{fg}$$
THEN
Consider having water at 100C and 1atm and a vacuum pump.
Can we change the... | I dont quite see the purpose of the vacuum pump if you stay at the same 1 atm pressure. With a simple fan though you will accelerate evaporation because the air is never saturated
| {
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Use of generating function in canonical transformation In the theory of Canonical transformations, initially we use the fact that the new and the old system of $(q_i, p_i)$ with the Hamiltonian $H$ satisfy the modified Hamilton's principle. Now here, the use of the theory of generating functions makes sense. But after ... | In canonical perturbation theory, the generating function (of the $F_2$-type) is determined order by order from the perturbative term, i.e. if
$H(q,p,t)=H_0(q,p)+\epsilon H_1(q,p,t)$ then one can write a series expansion
$$
S= qP+ \epsilon S^{(1)}(q,P,t)+\epsilon^2 S^{(2)}(q,P,t)+\ldots
$$
and determine $S^{(1)}$ give... | {
"language": "en",
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Why can't the collision be elastic if after the collision the two objects move together with the same velocity? I don't quite understand why two bodies can't 'stick' together in elastic collision. I have found several sources that say that if two objects collide and end up moving at the same velocity their collision is... | By definition, elastic collision is one in which total mechanical energy is conserved. That means kinetic energy of the system before and after collision will be same.
Other way to look at it is using coefficient of restitution. If coefficient of restitution is 0, there is zero recoiling (bouncing back) and the collisi... | {
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Will a warm object in a vacuum cool more quickly than a warm object surrounded by an atmosphere containing CO2? I have gotten stuck on an endless thread about Global Warming, in which skeptics sometimes make the claim that an object surrounded by a "heat absorber" like CO2 will cool more quickly than one not surrounded... | Depends on the situation!
If you have a thermos flask setup, where your warm object is surrounded by some medium and then by air, then the carbon dioxide cools it faster. This is because there's better thermal contact - the carbon dioxide molecules collide with the warm object and carry away some energy, whilst if ther... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/441349",
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Why we can't take torque equation for the mid point of the ladder in the question **Source IIT JEE 2005 PHYSICS** Question (Source IIT JEE 2005 Physics)
Two identical ladders, each of mass M and length L are resting on the rough horizontal surface as shown in the figure. A block of mass m hangs from P. If the system is... | The left ladder presses the right ladder at point P. This is a force you need to include as a torque unless you select P as your axis of rotation.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/441578",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Why gas molecules move with different speed at a given tempreture? As per my understanding we know that molecules of an ideal gas are identical in all aspects (size, shape, mass). Since collisions are elastic in nature, they don't lose their kinetic energy. That means that kinetic energy of each molecule doesn't change... | Here is the misunderstanding:
Since collisions are elastic in nature, they don't lose their kinetic energy
Only in the center of mass of two colliding particles the collisions have equal and opposite energy , not in the laboratory frame of the containing box. When one puts all the "identical molecules of an ideal gas... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/441735",
"timestamp": "2023-03-29T00:00:00",
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What is the difference between the voltage in the electrical circuit and electrostatics? In electrostatics it depends on the distance from the charges, should it also be in the circuit? But in practice, the voltage depends on the resistance, for example on a resistor. And the distance itself does not play any role. Why... | I'm not quite sure, what do you actually mean. Voltage is voltage, it does not "know" where it comes from. Also in case of induced electricity. Ohm's law (a relationship between voltage, resistance and current) remains in force in both cases too.
The main difference is that although a static voltage can be quite high,... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/442017",
"timestamp": "2023-03-29T00:00:00",
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Will the SI units need redefining ever again? Up until recently, there were obvious problems with the SI definitions of fundamental units, like bits rubbing off the kilogram prototypes (or mercury vapour absorption), and the water used for the kelvin definition being only found in Switzerland.
From wikipedia: "On 16 No... | One possible redefinition that is foreseen, is that the second may be redefined. Currently, it is defined in terms of a radio frequency of the Cesium atom. However, there are many optical clocks (clocks based on some optical frequency of some atom) that can measure time intervals more accurately. Perhaps in the future,... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/442359",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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Focusing Sunlight with Flat Mirrors- solar barbecue Say somebody had 48 1sqft glass mirrors (almost 4.5 sq.m total), because these tiles cost about $1 each.
If mirrors are all tediously aligned to redirect sunlight onto a Weber BBQ, the air temp inside the BBQ quickly rises to 260F (400K), and the irradiated surface (i... | Considering the discussion to date- it's looking like I'll need both more mirrors and to improve the receiver.
It sounds like I'll need at 10-15 square meters of mirror to rival the "BTU rating" of a similar gas grill.
It sounds like the BBQ desperately needs to insulated on the backside. Also, I should probably scuff... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/442584",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Inner product in QFT When we write inner product in QM for example $\langle\psi\rvert x \psi\rangle$it means (in position space) $\int\psi^*(x,t)x\psi(x,t)dx$. But when we write, in QFT, $\langle0\rvert0\rangle=1$ what does it mean? As $\rvert0\rangle$ stands for vacuum state and since there is no particle as of now (s... | In the standard treatment of quantum field theory, states are treated as abstract vectors in a large Hilbert space (specifically, a Fock space), and no "wavefunction" interpretation is given to them like it is in 1D quantum mechanics.
For applications to black hole physics (and other areas of quantum gravity), however,... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/442713",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Why is $E=mc^2$ and not $E=m\frac{c^2}{2}$? Kinetic energy for a moving object is the integral of force with respect to distance, often given as:
$$E=m\frac{v^2}{2}.$$
This would imply that for mass moving at the speed of light, the kinetic energy would be:
$$E=m\frac{c^2}{2}.$$
This puts it off from the Einstein resul... | $E=mc^2$ isn't supposed to be the body's kinetic energy. In that equation, $c$ is the speed of light, but in the formula for kinetic energy, $c$ (or preferably $v$ is the velocity of the body. Furthermore, there's no body which can be accurately described as having kinetic energy $E=\frac{1}{2}mc^2$, because that impli... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/442916",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 1
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Killing vectors - Schwarzschild metric Given the Schwarzschild metric, $$\mathrm{d}s^{2}=-\left(1-\frac{R_s}{r}\right)\mathrm{d}t^{2}+\left(1-\frac{R_s}{r}\right)^{-1}\mathrm{d}r^{2}+r^{2}\mathrm{d}\theta^{2}+ r^2 \sin^{2}\theta\mathrm{d}\phi^{2},$$ I'm asked to show that $$K^{\mu}=\left(1,0,0,0\right),\; R^{\mu}=(0,0,... | Your equation for $R_\mu$ reads $$\nabla_\mu R_\nu + \nabla_\nu R_\mu =\left(\partial_\mu R_\nu -\Gamma^\lambda_{\mu\nu} R_\lambda\right) + \left(\partial_\nu R_\mu - \Gamma^\sigma_{\nu\mu}R_\sigma\right)=\partial_\mu R_\nu + \partial_\nu R_\mu -2\Gamma^\phi_{\mu\nu} R_\phi.$$
If you use $\mu=r$ and $\mu=\theta$ (the o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/442983",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Can we say that bosons attract each other? We know that bosons donot follow Pauli exclusion principle, thus they can occupy the same state. But is it equivalent to say that bosons attract each other?
| Using a statistical physics approach, you can indeed show that the properties of bosons and fermions result in an effective potential that is attractive for bosons and repulsive for fermions:
In a statistical mechanics framework, you can construct the partition functions for both classical, interacting particles in a p... | {
"language": "en",
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Easiest Way to understanding coefficient of friction? So I am having issues understanding how to find the coefficient of friction, I should have understood this couple chapters ago but I couldn't. I am not understanding the difference between the static coefficient and the kinetic coefficient (I know static is not movi... | The coefficient of friction is just the proportionality constant between the normal force and the friction force magnitudes between two surfaces: $f=\mu N$
Kinetic Friction
This is, in my opinion, the easier one to understand. If the two surfaces are moving relative to each other, then kinetic friction will be the forc... | {
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"url": "https://physics.stackexchange.com/questions/443484",
"timestamp": "2023-03-29T00:00:00",
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Why can't we see images reflected on a piece of paper? Why can't you see a reflected image on a piece of paper? Say you put a pen in front of the paper, even when light rays are coming from other sources, hitting the pen, reflecting back, and hitting the paper, there is no reflection.
What's wrong with the following "... | You will not see a real image of the pen forming on the paper, nor will you see a virtual image from the reflection of the pen from the paper.
The reason you will not see a real image forming on the paper is that the light scattering from the pen is diverging, and in order to see an image all rays from a single point o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/443586",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "72",
"answer_count": 9,
"answer_id": 5
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Derivation of 2nd law of Thermodynamics from ergodicity assumption In Wikipedia it is claimed that:
Assumption of the ergodic hypothesis allows proof that certain types of perpetual motion machines of the second kind are impossible.
Since perpetual motion machines are machines which would violate the 2nd law, shouldn... | Ergodicity is a property used to allow the use of ensemble averages in place of time averages. As such, it is only indirectly related to the second law.
In order to provide a statement equivalent to 2nd law, statistical mechanics has to show that the relevant fundamental equation (entropy, Helmholtz free energy, grand... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/443676",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Mathematical question on Mathisson-Papapetrou-Dixon equations I am studying about Mathisson-Papapetrou-Dixon equations which govern the motion of a test particle around a central massive object in the pole-dipole approximation.
Given that $S_a=-\frac{1}{2}\epsilon_{abcd}V^bS^{cd}$ I want to prove that $S^{cd}=-\epsilon... | So what you basically mean following your notation is that $\epsilon_{abcd}\epsilon^{aijk}=-$$\begin{vmatrix}
4 & \delta_b^a & \delta_c^a & \delta_d^a \\
\delta_a^i & \delta_b^i & \delta_c^i & \delta_d^i\\
\delta_a^j & \delta_b^j & \delta_c^j & \delta_d^j \\
\delta_a^k & \delta_b^k & \delta_c^k & \delta_d^k\\
\end{vma... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/443795",
"timestamp": "2023-03-29T00:00:00",
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Can I apply the standard Runge Kutta 4th order method to the Langevin Equation? If I have a Langevin Equation with an external force term (which may be time dependent), is it possible for me to apply the standard 4th order Runge Kutta algortihm to solve it numerically?
Edit:
I would like to mention the use case for th... | No, you cannot directly apply a deterministic method such as 4th order Runge-Kutta to the integration of stochastic differential equations, in general. This is only possible, in the way described by alephzero, if the stochastic Langevin force can be considered a very weak perturbation compared to the deterministic part... | {
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Two People Pushing Off of Eachother, Newton's Third Law, and Unbalanced Force Different versions of this question have come up all over the internet. Usually it deals with tension in a rope or two people pushing on each other with the same force. I am trying to understand 2 people pushing each other with different forc... | The human body is terrible laboratory for Gedanken experiments, and this problem proves it. What exactly does pushing with 70N mean? Is it active? Is it passive? Nothing feels correct.
This is why Newton's Laws are quite often imagined with masses and springs, which is the only way to save this problem from comments ex... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/444396",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How to do dimensional analysis? $$mgh = \frac{mc^2}{\sqrt{1-(v/c)^2}}-mc^2.$$
In dimensional analysis do we just ignore the square root? Or do we solve what’s inside first then we do the square root? Do we say $(v/c)^2$ is 1 as dimensions cancel? Then say each term now has the same dimension, so this is correct? I’m s... | Since:
$$ \beta = \frac v c $$
and
$$ \gamma = \frac 1 {\sqrt{1-(\frac v c)^2}} $$
are both dimensionless, that are not amenable to dimensional analysis.
In fact, their lack of dimension makes them great "scale factors" telling you how relativistic your system is. $\beta$ goes from $\epsilon$, or Newtonian mechanics, u... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/444504",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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If there is no atmosphere on a planet that is rotating on an axis and a rocket is launched "Straight up" from its surface, If there is no atmosphere on a planet that is rotating on an axis and a rocket is launched "Straight up" from its surface, won't the rocket still have an angular/orbital velocity because the planet... | It all depends on what "straight up is", and also the location of the launch complex. Let's put it on the equator on a prograde planet. A the rocket rises, the guidance will have to account for the Coriolis force pushing the rocket westward in order to keep it above the launch pad. That will require increasing the east... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/444608",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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"answer_id": 1
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Time taken by a Magnifying Glass to heat Metal I would like to know how long would it take for a small or medium sized mag. glass to heat a black painted metal particularly aluminum since I can't do the maths.
| In your comment, you say you are trying to heat the following object...
a soda can tightly selaed and painted black at the bottom ... inside the can is water.
using a 70mm magnifying glass.
In this case, the magnifying glass will probably not raise the average temperature of the can at all! The magnifying glass focu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/444824",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
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Are photons and electromagnetic waves the same thing? I have a little bit of confusion: From my understanding (which could be totally wrong), photons are the same as electromagnetic waves but are called photons because their frequency is in the realm of what we can see.
Seems too simplistic. Can anyone enlighten me?
|
are photons and electromagnetic waves the same thing?
Photons are quantum mechanical entities, a particle in the standard model of particle physics. Light is perfectly modeled as an electromagnetic wave with classical Maxwell equations , so they are not the same. They are related similar to the way bricks are relate... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/444917",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
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What is the function of this complicated tensioning system? I saw this arrangement for tensioning overhead cables from my train window (schematic below). Why not just have one pulley wheel leading directly to the weights? What function do the additional pulleys serve? For that matter, what are the cables for? They're c... | Railway overhead electrification is a complex business, I am far from an expert but this is my simplified understanding.
There will normally be at least two wires, a "contact" wire which runs horizontally to make contact with the train's pantograph and a "catenary" wire which supports the contact wire. An appropriate t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/445062",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "25",
"answer_count": 5,
"answer_id": 1
} |
How do we know that light cannot travel faster than it does? We assume the speed of light in vacuum is its maximum speed but can we not assume that it could be faster, or slower?
| Light can be treated as an electromagnetic wave. Electric and magnetic fields have some properties: if electric field changes the magnetic field appears around, if magnetic field changes - electric field appears. There are accurate mathematical formulas which describe these laws (Maxwell's laws). There are some constan... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/445225",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
} |
Why is torque defined as $r × F$ and not $F × r$? Is it merely due to popular convention or does it supply any special clarification regarding other physical quantities?
| Maybe we can make a quick comparison of both.
Let us define the torque $\boldsymbol M = \boldsymbol r \times \boldsymbol F$. Let us further consider $\boldsymbol r$ and $\boldsymbol F$ lying in a plane and $\boldsymbol M$ facing upwards. The absolute value of $\boldsymbol M$ becomes $M=r\cdot F\cdot \sin\theta$ with $r... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/445322",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 5,
"answer_id": 3
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