Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Does EMR emanate in all directions? Does the wave expand like a sphere surface whose radius grows at $c$? I made a commitment to understand special relativity.
Right now I'd like to understand Electro-Magnetic Radiation. What would it "look like"if I could see it emanate. From a book (Simply Einstein) I'm told any m... | You are right; when an electric charge is forced to vibrate in all directions, it gives off electromagnetic radiation in all directions. You can think of this as consisting of a large number of photons being sprayed in all directions. That radiation then moves away through space as an expanding spherical wavefront, tra... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/403624",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Can I change solid into liquid, gas or solute by cutting again and again until it is a molecule particle? If I have small piece of solid, for example, pure iron powder, fine sand , (at room temperature) then I cut it slowly into half again and again. Every times, after I cut it, I wait for temperature back to room temp... | There is no free lunch. The mechanical breaking of bonds by cutting will take as much energy as melting or boiling and the final temperatures should also be the same. It may seem impossible to get a liquid this way, but assuming a perfectly insulated sample, it will. The act of cutting will generate higher energy molec... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/403739",
"timestamp": "2023-03-29T00:00:00",
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What would qualify as a deceleration rather than an acceleration if speed is unchanged? The instantaneous acceleration $\textbf{a}(t)$ of a particle is defined as the rate of change of its instantaneous velocity $\textbf{v}(t)$: $$\textbf{a}(t)=\frac{\mathrm{d}}{\mathrm{d}t}\textbf{v}(t).\tag{1}$$ If the speed is const... | According to this definition, "deceleration" is undefined.
| {
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"url": "https://physics.stackexchange.com/questions/403864",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
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Is it possible to break any given matter down into protons, neutrons, and electrons and then reorganize those particles into any other form of matter? I was reading about this somewhere but can't find the site now. It was talking about using 3d printers in the future that can intake any matter (dirt, garbage, etc..) an... | Yes, this is theoretically possible. In fact, it has already been done for certain transmutations. But even when turning lead into gold, at present the cost of the process (at least that process) is prohibitive.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/403993",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Ultra low level light detection: What measurement principles are used? I was reading up on how Avalanche Photodiodes(APD) are used to detect very low light levels, some are even used in "photon-counting" experiments (in Geiger mode). However, a survey of some commercial APDs such as this indicates that these sensors al... | If background is a problem, there are photomultiplier tubes. But those are bulky and delicate vacuum tubes and require high-voltage power supplies (about 1000 volts).
For solid state detectors, one can use the avalanche photodiodes in an array, where each diode has low area and low dark current. When there is a small f... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/404206",
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How fast are cyclotrons? I know this question is kind of vague, but I just want have a handle on how fast a average cyclotron can accelerate particles, and what kind of limits there are...
| The cyclotron depends on the fact that the angular frequency is a constant given by $\omega={qB\over mc}$. However, that equation is in the non-relativistic limit.
The correct relativistic equation is $\omega={qB\over mc\gamma}$, so $\omega$ is not a constant when the relativistic parameter gamma increases from its no... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/404348",
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Size of the Universe at end of recombination (~477000 years)? What was the size of the Universe at start of recombination (377000 years) when the Universe started to become transparent and release of trapped photons into what we now know as the CMB and till end of this phase (~477000 years)?
| The redshift at (re)combination is about $z=1100$. The relationship between scale factor and $z$ is $a = (1+z)^{-1}$. So the universe was about 1/1100 of the size that it is now.
| {
"language": "en",
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In an experiment, the transducer showed -1.9 Bar pressure. How is it possible? I was doing an experiment on water hammer in pipes. During the experiments, in several cases, the transducer reported negative pressure, as low as -1.9 bar gauge! But I have read that it is not possible for the pressure to practically go bey... | The sensor measures push or pull force on a plate, and, using the area of the plate, translates that into pressure. There are multiple ways to get a "pull" force on the plate without negative pressure. Inertia from moved sensor, internal pressure in the sensor,...
Sensors only perform as expected if they are used withi... | {
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Experiment - does mass of a moving body really increase or is it invariant? Suppose we have a mechanical balance, with two identical particles kept in the two sides. Now the balance does not show any deflection.
Now, one of the particles is given some constant horizontal velocity.
Will the balance show the moving part... | Your experiment doesn't actually distinguish between the two definitions, because the two definitions give equivalent dynamics.
In the "rest-mass" framework, the gravitational force between two objects, where one is stationary and the observer's frame and one is moving, is
$$F=\gamma \frac{GMm_0}{r^2}$$
where $m_0$ is ... | {
"language": "en",
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First excited state during Bose-Einstein condensate We know that the ground state is macroscopically occupied. What about the first excited state?
| I am writing this answer in continuation from my last answer on your previously related post. As described there, the macroscopic occupation of the ground state is enforced by the quantum statistics by bounding the number density of excited states. Note that consequently the first excited state is also bounded, and the... | {
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Using complex exponential to represent waves in EM Ever since we've been using exponentials to work with electromagnetic waves, I've been confused about the imaginary portion and want to confirm my thinking.
What does the imaginary portion represent? Nothing, right? It's just a side effect of using complex exponentials... | Yes, it is out of convenience and to simplify the equations. The implication is that the real part of the complex quantities is taken to get the actual physical value (which gives you some term that is a cosine with some phase).
This is analogous to the way we encode the phase of our quantities in complex alternate cur... | {
"language": "en",
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London theory, an electromagnetic description? Currently I'm reading "Introducton to Solid-State Physics" by Charles Kittel, 8th edition and about superconductivity. I'm having a bit of trouble getting the whole plot, because as far as I'm concerned, the Meissner effect is an effect closely related to superconductors (... | The first part of the argument is simply saying that the Meissner effect cannot simply be explain as a consequence of perfect conductivity. It is an independent physical phenomenon that has to be explained separately. It is not saying that the entire theory of electromagnetism cannot be applied to superconductors.
The ... | {
"language": "en",
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"source": "stackexchange",
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Confusion about condition of dark fringes in YDSE I have read that the condition for dark fringes in YDSE is when the path difference is
$$y_n = \left(n + \frac{1}{2} \right) \frac{\lambda D}{d}$$
where $D$ is the distance between the double slit pane and $d$ is the distance between the two slits. I saw a question abou... | Mathematically, both these expressions are equally valid, it only differs in terms of how you label fringes, or rather, how you start counting $n$. One can always redefine a new $n' = n - 1$, start counting from $n' = 0, 1, 2 \ldots$ instead of $n = 1, 2, 3 \ldots$. The maths doesn't change. (Actually, the $n \lambda$ ... | {
"language": "en",
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Why do really cold objects evaporate really quick? So I saw a video of LNG (liquid natural gas) and when it got in contact with water, which was room temp the LNG evaporated instantly...why?
Ice takes a while to evaporate like a sec even when hot water is dumped...why do really “cold” liquids evaporate super quick. Is... | I'll add to the answers above, (though @BobJacobson touched on this). Water has a high heat capacity. Air is very disburse and by contact area, a very very low heat capacity. (Heat capacity is usually measured by mass, not contact area, but I think contact area is important in relation to this question)
Water is ab... | {
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Change of wavefunction due to relativistic speed Imagine a spacecraft which is moving at a speed comparable to the speed of light relative to a reference frame with a hydrogen atom at it's origin. How would the probability distribution function of an electron in 1s orbit look relative to an observer inside the spacecra... | Technically, in order to incorporate special relativity with quantum theory, you need Quantum Field Theory.
The Lorentz transformation (in particular, boosts) is not unitary. This means that the wavefunction is no longer properly normalized. This is not the case with rotations, which are unitary. Trying to directly jam... | {
"language": "en",
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Electromagnetic force (EMF) example I am currently studying this example from the book "Introduction to Electrodynamics" - David J. Griffiths.
According to the solution, there is an EMF applied to the metal disk and also there is a current flowing to the resistor.
I was wondering why this happens, since dΦ/dt=0 (there... | The disc in your figure could be considered as being made up of large number of radial,conuducting ,differential elements rotating with angular velocity ω about the center of the disc.This is same as emf due to rotating rod which comes from motional emf.
Induced emf is the more general term. By Faraday's Law, you get ... | {
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Einstein field equations to the Alcubierre metric I was wondering how Alcubierre derived the metric for the warp drive? Sources have said it's based on Einstein's field equations, but how did he go from this to the metric?
| The metric for the Alcubierre warp drive was constructed by considering the properties that it should obey, and not the matter source (which is why it's fairly unphysical).
The two ingredients used in it are :
*
*A bump function, so that the warp drive is localized in a specific region (and that bump function moves... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/406012",
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How to show that apparent velocity V(app) is always greater than -c/2 for an object fleeing away from you? I am currently taking the online course on Relativity and Astrophysics provided by Cornell on EdX.
There, how the apparent velocity of an object moving at a fraction of c might sometimes be greater than c was sho... | Imagine you have a craft receding from you at basically $c$. At observer time $t$ after launch, the craft shines a light. We know where the craft is at that point in the observer frame, it's $ct$ distance away. The light returns to the observer, and provides evidence of the craft at that distance. But the light tak... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/406269",
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Inertia on a rotating disc? If I toss a ball upwards in a train moving with uniform velocity, the ball will land right back in my hand. This is because the ball has inertia and it continues to move forward at the speed of train even after leaving my hand.
Now consider I'm standing on the outer edge of a rotating disc (... | This example might help visualize your question:
Water drops are ejected from a rotating nozzle. Once a drop is ejected from the nozzle, it follows a parabolic trajectory (let's ignore air drag) in a vertical plane. The drops fall outside of the vase shape but we don't see them well.
We don't see this trajectory when ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/406384",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
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Schroedinger equation on the line with non-symmetric double well potential In the 3rd volume of the Landau-Lifschitz text book ("Quantum mechanics") problem 3 after section 50 studies the Schroedinger equation on the line with symmetric double well potential, e.g. $U(x)=g(x^2-a^2)^2$ with $g,a>0$. In particular they es... | Cute and interesting question.
What really happens is that the stable points are the global minima (if more than one) of the Hamiltonian, i.e. the states having the lowest eigenvalues.
The effect of tunneling can be seen by using the WKBJ method (just as is done when estimating the life time of alpha decays).
Thanks fo... | {
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Can air make shadows? I have read about schlieren photography, which uses the ability of non-uniform air to create shadows. Is it really possible that air makes shadows?
| If air particles are dense enough and or clustered together then yes. Shadows are not created so much as cast, kind of like looking in a mirror. The reflection is exactly that a reflection, if light can't penetrate an object it therefor casts around it. To the observer it looks like a shadow or a reflection.
Simplifie... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/406604",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is the difference between relative time dilation and absolute time dilation I know special relativity says that traveling at high speeds (or really any speed) causes time dilation; and General relativity says that gravity also causes time dilation. I was wondering if relative time dilation (where two observers eac... | Time dilation in special relativity does not depend on the distance of the two observers. It depends on their relative velocity $v$ only, according to $\Delta t'=1/\sqrt(1-v^2/c^2)\Delta t$. This shows that $\Delta t'$ is in fact delayed compared to $\Delta t$.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Harmonic oscillator in microcanonical ensemble Consider a hamiltonian of a simple classical pendulum
$$H=p^2+\omega q^2.$$
How can quantities such as $\langle p^2 \rangle$ or $\langle q^2\rangle$ can be calculated using the microcanonical measure?
| As far as I understand this average values are
$$
<p^2> = A^{-1} \iint_{-\infty}^\infty p^2\delta(p^2+\omega^2q^2-E)\ dpdq,
$$
and similar for $<q^2>$, where $E$ is fixed energy of a pendulum and
$$
A = \iint_{-\infty}^\infty \delta(p^2+\omega^2q^2-E)\ dpdq
$$
One can calculate integrals with the $\delta$-function dire... | {
"language": "en",
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Line element in Kruskal coordinates I try to calculate the line element in Kruskal coordinates, these coordinates use the Schwarzschild coordinates but replace $t$ and $r$ by two new variables.
$$
T = \sqrt{\frac{r}{2GM} - 1} \ e^{r/4GM} \sinh \left( \frac{t}{4GM} \right) \\
X = \sqrt{\frac{r}{2GM} - 1} \ e^{r/4GM} \co... | I would like to add that, contrary to the other answer, it is possible to find the metric using the Jacobian.
The transformation law for the metric tensor from Schwarzschild coordinates to
Kruskal–Szekeres coordinates is as follows:
$$g_{\bar{\alpha}\bar{\beta}}=\frac{\partial x^\alpha}{\partial x^\bar{\alpha}}\frac{\p... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/407108",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Formula for spring constant $k$ Is there a formula for the spring constant $k$ which satisfies the equation $$F=k\Delta \ell~?$$
A similar question was asked but was answered by transposition of this equation... I'm hoping for an answer addressing the physical meaning of a spring constant.
Unlike the question which is... | The elastic constant of the spring depends on the geometry of the spring. There are formulas relating spring constant to the spring dimensions for various conditions.
For a helical spring, a first approximation formula is
$$ k= \frac{Gd^4}{8ND^3} $$
where G is the shear modulus, d is the diameter of the wire, N is the ... | {
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Does Frame Dragging exert a force? Can a planet in a stable clockwise orbit slow down into a spiral if orbiting a black hole spinning counter-clockwise?
| In this context you cannot really speak about "forces", since in any case the object will follow a geodesic through the curved spacetime.
However, there certainly is a noticeable effect of frame dragging on orbits. As you may or may not know, there exist a smallest possible circular orbit around any black hole. For a n... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/407608",
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Angle in pair production Assuming a very high energy photon (energy $E$) crosses the atmosphere and produces an electron-positron pair, I would like to know what is the angle between these to leptons produced. I was trying to calculate it by applying the energy-momentum conservation and realized that in this case the a... | Momentum and energy have to be conserved in pair production. That's why it only occurs near a nucleus: in a perfect vacuum, the simple 'decay' of a sufficiently high-energy photon into an electron-positron pair doesn't conserve momentum.
The consequence of this is that the exact angle between the particles of the pair ... | {
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Why is this cloud blue? I saw these clouds on the horizon, behind a ridge (apologies I couldn't get more pixels):
Why is the front cloud darker than the cloud behind? There were no other clouds that I saw which could've been casting a shadow on the front cloud. What would cause a cloud to reflect less light?
| the cloud is "blue" because the microscopic droplets that make the cloud are bigger. Colors of clouds are determined by size of droplets, which governs the wavelengths of light they reflect. I'm sure others can post answers in more detail.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/408100",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Mossbauer effect explanation I need to understand Mossbauer effect. Is there any simple explanation? So far I know, when an atomic nucleus emits a gamma-ray photon, the nucleus must recoil to conserve linear momentum.
Consequently there is a change of frequency of the radiation due to the movement of the source the Dop... | Starting from
So far I know, when an atomic nucleus emits a gamma-ray photon, the nucleus must recoil to conserve linear momentum.
is to begin with a classical expectation.
Instead say, "When a system emits a gamma ray the system must recoil", but allow that the system could be the single atomic nucleus or if the ato... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/408241",
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Does the neutral charged object attract the positive charged object or the negatively charged object? Consider an electrically neutral object:
*
*Is it going to attract a positively charged object or the negatively charged object?
*What is the type of attraction?
*How does it attract or why does not it?
*Why the ... | Let's assume that we're talking about macroscopic objects, say particles of soot. The neutral object (call it 'O') will attract either a positively charged object ('P') or a negatively charged object ('N'). Here's why…
If P is placed near O, P will tend to pull the electrons in O towards the side of O nearest P. If O i... | {
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When is it appropriate to solve the time-independent Schrödinger equation? I am currently going through Griffiths over the summer but I am a bit confused by one point and I don't have any instructor to ask, so I was wondering if you could help clarify. In Section 2.3, the harmonic oscillator, he writes: "it suffices to... | If you can solve the time-independent case, it always suffices to do so, since the time-evolution of a stationary state is simply $\psi_n(t)=e^{i\omega t}\psi_n(0)$, and any state can be written as a superposition of stationary states.
You can be sure you are not missing anything because every self-adjoint operator$^1$... | {
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If you are ontop of a giant heavy object that is falling from the sky, is it possible to jump and roll at the perfect time to survive? I don't know if gravity or the speed of the drop would prevent us from jumping, but would something like this be possible?
If it's not possible on the ground, is it possible in the ocea... | Damage to a living being with bones, organs, tissues, in a collision
is a transfer of energy into breaking of materials. The more
energy transferred, the more breakage is possible.
So, a large (large volume) heavy object will determine the
terminal velocity of the fall (it acts as a parachute would),
but a parachute ... | {
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"url": "https://physics.stackexchange.com/questions/408657",
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Are the 7 fundamental SI units able to differentiate between all elementary particles? More specifically, can the 7 base SI units express qualities like quark strangeness (of quarks) and quark color? How do these SI units differentiate between different quarks (charm, up, top...)?
| Properties like the strangeness of a quark are just numbers with no dimension. Quark color is mostly related to a category than to a quantifiable thing, is like saying positive or negative, red or blue. The SI units may help to differentiate between different quarks by measuring the respective rest masses and electric ... | {
"language": "en",
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What gives mass to dark matter particles? Assuming that dark matter is not made of WIMPs (weakly interacting massive particles), but interacts only gravitationally, what would be the possible mechanism giving mass to dark matter particles? If they don't interact weakly, they couldn't get mass from interacting with the ... | There are various ways dark matter could acquire mass that have nothing to do with the standard model weak force. For example, there are theories involving a hidden sector- particles that do not interact with the standard model gauge bosons at all, but have their own interactions.
Note that the Higgs mechanism is not r... | {
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Potential difference across a zero resistance wire So I started off with electrostatics and everything seemed nice and mathematical and justified and then "DC circuits" happened!
I just cannot understand the model of electron flow in electrical circuits. Here are my specific doubts-:
1) If potential difference across ... | In ordinary circuit analysis (no superconductors involved) when we say the resistance of a wire is zero, we really mean it's close enough to zero that the voltage drop across it doesn't significantly affect the circuit behavior.
If you want to understand exactly how this could work, you could model each wire as a low-v... | {
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Why doesn't magnetomotive force have units of force? Why does it have units of Ampere-turns and not Newtons?
Is it a current, or turns mean metres?
| No, turns doesn't mean meters here. Unfortunately, electromagnetics uses many bizarre units. A force should be a force, not a current. The correct units of magnetomotive force are weber/m or emu/cm, which dimensionally is t/s^2 x t/s, which in a sense means force times t/s, rather than the simple t/s^2 for other for... | {
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Operators in infinite dimensions In page 64 of Shankar's Principles of Quantum Mechanics, there are a few lines that leave me doubtful:
It is worth remembering that $D_{xx'} = \delta'(x-x') $ is to be integrated over the second index ($x'$) and pulls out the derivative of $f$ at the first index ($x$).
In the above li... | Re. "What does "pulls out the derivative of f at the first index (x)" mean?"
The sifting property of the Dirac Delta distribution is
$$\int f(x)\delta(x-a)dx=f(a)$$
and for its derivative
$$\int f(x)\delta'(x-a)dx= -f'(a)$$
or
$$\int f(x)\delta'(a-x)dx= f'(a)$$
So for $\delta'(x-x')$ when its placed under the integra... | {
"language": "en",
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Symmetry of the 2d anisotropic Heisenberg model? I am getting confused about the symmetries of the 2d anisotropic Heisenberg model. The Hamiltonian is:
$$H=-\sum_{\langle i,j\rangle}(J_x S_i^xS_j^x+J_yS_i^yS_j^y)\tag{1}$$
I have read (source not publicly available) that this has symmetry $\Bbb{Z}_2$. Which although I a... | Short Answer
Yes the symmetry group is larger then $\Bbb{Z}_2$ and is $\mathbf{k_4\cong \Bbb{Z}_2 \times \Bbb{Z}_2}$. But the ground states are only related by $\Bbb{Z}_2$ and it is this symmetry the get's broken in spontaneous symmetry breaking.
Long Answer
Let us look at the individual symmetry groups mentioned in th... | {
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What is the connection between Lagrangian symmetry and particle multiplets? I am struggling to see the connection between the symmetries of Lagrangians and particle multiplets. If I had three quark fields arranged in a vector $\Psi(x) = (u(x),d(x),s(x))$, these three fields have a combined Lagrangian
$$ \mathcal{L}= \b... | In general, a lagrangian can be invariant under more than one transformation so there can be several symmetries and representations related. Specifically, the one particle states furnish representations of the Poincare Group and therefore live in an infinite dimensional space. On the other hand flavor (or color) symmet... | {
"language": "en",
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If quantum cloning was possible would entanglement enable faster than light communication? Assume quantum mechanics allowed you to clone particles. How could you use quantum entanglement to communicate faster than the speed of light?
In the 1980s a scientist proposed using quantum cloning to send information between e... | Imagine Alice and Bob share a Bell state:
$$
|\psi \rangle = |00\rangle +|11\rangle \ .
$$
Note that this state looks like this in the $X$ basis:
$$
|\psi\rangle = |++\rangle + |--\rangle \ .
$$
As you know if Alice measures her qubit in the $Z$ basis, and gets $|0\rangle$ or $|1\rangle$, Bob's qubit will collapse unto... | {
"language": "en",
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Energy conservation on expanding universe Due to the expansion of the universe, the photons emitted by the stars suffer redshift, Its mean that the energy is lowered a little bit. Does this mean that the energy is lost? Does the expansion of the universe violate some conservation principles according to Noether's theor... | Redshift happens when the wavelength of the photon is increased, or shifted to to the red end of the spectrum. Energy is never lost but transferred.
So the answer to your question is NO - No energy is lost.
| {
"language": "en",
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Why does a mirror reflect visible light but not gamma rays? Visible light (~500 THz) as well as gamma rays (~100 EHz) are electromagnetic radiation but we can reflect visible light using a glass mirror but not gamma rays. Why is that?
| Reflection is caused by electrons reacting to the electromagnetic field by oscillating at the same frequency. When they do this they emit radiation of the same frequency as the incoming light and this is observed as reflection. This works well if the EM frequency is near the eigen frequencies of the electrons. When the... | {
"language": "en",
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"source": "stackexchange",
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Why does a magnetic field "curl" around a current carrying element? From all the texts I've read, it's always stated that the magnetic field would either curl or warp around the the current flowing within a conductive element, yet, I never was clarified as to why that is. Why would the field "curl" around it? I'm curio... | If you ignore all what you learned about the B-field being a "vector" and you treat it as what really is a 3D skew-symmetric tensor then the mystery goes away. In this view the B-field is a bi-vector, a surface-like quantity whose source is the current element from which it radiates outward, so to speak. Unlike the E-f... | {
"language": "en",
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What would be the charge distribution of a conducting sphere in front of a positive point charge? What would be the charge distribution of a conducting sphere in front of a positive point charge? I mean if it's a positive charge then it should induce negative charge in the near side and positive on the other side. But ... | The answer using the method of images is for a grounded sphere, but to correct for this you simply need to add a second image charge
$$
q ^{\prime \prime} = -q^{\prime}
$$
at the center of the sphere. This gives a total "induced" charge of
$$
q_{induced} = q^{\prime}+q^{\prime \prime} = 0
$$
so you have two image charg... | {
"language": "en",
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As the universe expands, do we have any reason to suspect further separation of the fundamental forces/interactions? At some point, all four forces were one force. (another question: what exactly does that mean?). At some point gravity and the strong force separated out leaving the electroweak force. Then the electrow... |
At some point, all four forces were one force.
This is speculative. E.g., it's true in string theory, but string theory is probably wrong.
Others will probably be able to give a more definitive answer, but I think basically the reason the weak force separated out from the electroweak force is that there's a temperatu... | {
"language": "en",
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A ball attached on a moving string If there is a ball attached on a string and the string's point of hanging is accelerating horizontally at $\vec{a}$, what will be the forces exerted on the ball that is hanging? It is obvious that there will be a gravitational force downwards and a tension force, and there should be a... |
...and there should be another horizontal force on the ball in the opposite direction of the acceleration of the string, but where does that force come from? It should be from the ball's inertia, but how can that be a force?
This apparent force is known as a fictitious force. These forces are not present in an inert... | {
"language": "en",
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What is $z$ in the Bose gas? I'm studying the ideal Bose gas, and I found this equation for the average occupation number of particles at the fundamental level:
\begin{equation}
\langle n_0 \rangle = \frac{z}{1-z}
\end{equation}
There's no degeneration due to spin, and $z$ is the fugacity defined as
\begin{equation}
z ... | $\mu $ is the chemical potential and it is negative in the case of Bose gas.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Movement within a magnetic field My class went over magnetism and electricity, and my professor repeatedly mentioned how the field moves from north to south, and he would say "they" and "it." I wasn't sure if he meant that the field itself was moving, or particles within the field were moving.
If my professor was refer... | It seems that the way he was describing it is confusing you. First off, let's just clarify the assumption that we are dealing with the magnetic field from a fixed source (ie a magnet). Then:
*
*As you correctly stated, the magnetic field is stationary and is just a visual representation of how the magnetic field loo... | {
"language": "en",
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Does the Earth emit gravitational waves? We know about Bohr's model and his vague postulate challenging Rutherford regarding discrete orbits and not emitting electromagnetic waves during this.
Extending this idea to our solar system, does the Earth emit gravitational waves around its orbit of the Sun and if not why no... | Presuming general relativity is correct, yes the Earth orbiting emits gravity waves. The intensity of this emission is quite low. The intensity of the gravity field the Earth creates is small. The speed the Earth moves around the Sun is small. So the rate of energy being carried away is very small. Thus the stability t... | {
"language": "en",
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Why is voltage described as potential energy per charge? Voltage is often called an electromotive force since it causes a flow of charge. However, it is described in terms of Joules per Coulomb or Potential Energy per Charge.
Question: How does the potential energy associated with charge contribute to its effect on th... | Charges don't posses potential energy. To be more accurate a system possesses potential energy. In electrostatics, you have to distinguish between potential, potential difference and potential energy.
First of all potential energy of a system refers to the amount of energy spent in assembling the system from infinity.... | {
"language": "en",
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Sign of work done by friction In Goldstein's classical mechanics (3rd ed.) we read:
"The independence of W12 on
the particular path implies that the work done around such a closed circuit is zero,i.e.
$$\oint \textbf{F}.d\textbf{s}$$
Physically it is clear that a system cannot be conservative if friction or othe... | The force of friction, a vector, opposes the actual or impending motion, and the work done by friction can be positive or negative depending on the situation.
We are addressing the mechanical work done by friction on the system $\int_{a}^{b} \vec F \cdot d \vec s$. Typically, physics mechanics assume a rigid body for ... | {
"language": "en",
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Sound waves produced by drums I am searching for an explanation of how drums produce sound waves. What type are these waves and how do they spread in the air?
| Like all sound waves in air, the waves emitted by a vibrating drum head are called compression or longitudinal waves.
As the drum head vibrates upwards, it pushes on the air next to it, which pushes on the air next to it, and so on. then when the drum head vibrates downwards, it pulls on the air next to it, which then... | {
"language": "en",
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Newton's law requires two initial conditions while the Taylor series requires infinite! From Taylor's theorem, we know that a function of time $x(t)$ can be constructed at any time $t>0$ as $$x(t)=x(0)+\dot{x}(0)t+\ddot{x}(0)\frac{t^2}{2!}+\dddot{x}(0)\frac{t^3}{3!}+...\tag{1}$$ by knowing an infinite number of initial... | Power series expansion does not hold for all functions $f(t)$ or for all $t\in\mathbb{R}$, but only for real analytic functions and for $t$ in the radius of convergence. In particular, it does not hold at any point e.g. for functions $C^2(\mathbb{R},\mathbb{R}^d)\smallsetminus C^3(\mathbb{R},\mathbb{R}^d)$. Therefore i... | {
"language": "en",
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"source": "stackexchange",
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Relativistic mass of components gives system rest mass? To put it briefly, in the classic thought experiment of a massless box with mirrored insides containing photons, does the relativistic mass of the photons imbue the box with rest mass?
I take it that's the case, because I think that's how baryons are supposed to g... | You can only say that if the components are non-interacting.
As soon as you introduce interactions between the components the mass of the system is neither the sum of the rest masses of the components nor the sum of the "relativistic masses".
I've done a moderately thorough treatment in a previous answer.
| {
"language": "en",
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In what ways can entropy of the universe increase? So far, I have been able to come across two scenarios in which entropy of the universe increases. First, when heat flows at a finite temperature gradient and second, during expansion of air particles into a vacuum (Joule's Expansion). Is there any other way in which en... | Bird, Stewart, and Lightfoot, Transport Phenomena, in Chapter 11, problem 11D.1 (Equation of change for entropy) discuss the fundamental causes of entropy generation/irreversibility. They identify heat flows at finite temperature gradients, viscous dissipation of mechanical energy (associated with viscous stresses res... | {
"language": "en",
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What is the physics behind the movement of the split-finger fastball in baseball? A split-finger fastball, or a splitter, is a baseball pitch thrown like a fastball with an v-shaped split finger grip. When thrown correctly, it moves like a fastball, straight in the air, but suddenly drops as it approaches the home plat... | First off, there is no consistent answer to this question because there is no consistent pitcher, muscle power and slight variations in the manner in which the baseball is thrown will always produce different results from each throw.
It seems to depend on the pitcher releasing the ball closer to the end of the arc of ... | {
"language": "en",
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Where does the gravitational energy come from We know that when a mass is pulled by gravitation it's kinetic energy increases.
This is also the case when a photon is being radiated towards a massive body,its wave length decreases and it's energy increases. Since I know that energy is conserved,my question is,where does... | It comes from the potential energy from gravity arising from the configuration of the objects.
When an object gains kinetic energy due to the gravitational force, the overall gravitational potential energy of the system decreases by an equal amount.
The graviational field can be thought of as "storing" work energy. Yo... | {
"language": "en",
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In general, how are representations used in physics? I want is a basic overview, if there is one, of the meaning (and purpose) of the word representation in general terms. I have looked up sources such as Particle Physics and Representation Theory, but I can't see the general purpose of using representations, beyond i... | You're asking about "representations" in the group-theoretic sense. You can think of a representation simply as a way to make an abstract group concrete, by expressing each group element as a numerical matrix.
This may seem odd because a lot of groups in physics are defined as matrix groups... for example, SU(3) is def... | {
"language": "en",
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Can X-rays emitted due to bremsstrahlung radiation have frequency matching with other EM waves like visible ones? The continuous X-ray spectrum has x-rays of widely varying frequencies. Since an E-M wave is characterized by its frequency, is it possible for the X-rays coming out of heavy metals due to bremsstrahlung ra... | The behaviour of an EM wave as it interacts with matter is frequency dependent. X-rays have high frequencies and show greater penetrability in matter as compared to visible light of lower frequency. If the frequency of EM wave coming out of any source has that of visible light they would not be X rays but visible light... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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How to prove a set of matrices form a representation of Lie algebra? When reading Paul Langacker's The Standard Model and Beyond, I am quite confused on equation 3.29, which says with a set of fields $\Phi _a$, where $a$ goes from 1 to $n$, are chosen to be transformed to it self by Lie algebra generators $T^i$. Theref... | I have the answer now! It is explained in equation 3.36 and 3.37 of the same book.
First, take the adjoint of $\left[ T^i , \Phi _a \right] = - L_{a b}^i \Phi _b$, remember $T^i$ is hermitian, assume $L^i$ is real, which would lead to $\left[ T^i , \Phi _a^{\dagger} \right] = \left( L_{a b}^i \right)^T \Phi _b^{\dagger... | {
"language": "en",
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Why Does Amplitude Have no Effect on the Energy of a Light Particle? In my high school physics class, I was taught that the energy of light is dependent only on the frequency, as demonstrated in the equation $E = h \cdot \nu$.
My question is, why is amplitude part of the equation? As the amplitude of the light increase... | As you've said, that's the energy of a light particle, not an arbitrary light wave. As you point out, an electromagnetic plane wave with electric field amplitude $E_0$ has total average energy density $u=\varepsilon_0E_0^2/2$. The formula of energy you have given actually relates this to the number density $n$ of light... | {
"language": "en",
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Calculating an "apparent" speed of a beam in a medium While thinking about relativity, one question sparked my curiosity. If we could observe the trajectory of a light beam by using some partially opaque medium, like smoke, to make it visible, we'd not perceive light as moving at $c$. As the light rays approached the o... | This is a real effect called apparent superluminal motion, with the apparent velocity being
$$v' = \frac{v \sin \theta}{1 - v \cos \theta}$$
in units where $c = 1$. Here, $v'$ is an apparent tangential velocity, defined as $v' = r \omega$ where $r$ is the distance, $\omega$ is the angular velocity of the object in the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/415627",
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Using Helmholtz Free Energy to Calculate Liquid Density My objective is to find an equation of state (EoS) for density, i.e. density as a function of pressure, temperature and concentration, for aqueous acids, bases and salts.
A StackExchange user suggested that I look into the following paper:
1. Myers JA, Sandler SI,... | In the IAPWS 1995 Formulation, the Helmholz Free Energy is used in connection with the density of Water:
| {
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"source": "stackexchange",
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Lie derivative of a vector along itself In Tensorial form, the definition of the Lie derivative for a covariant and contravariant vector are respectively:
$$\mathcal{L}_U V^\mu=U^\nu\nabla_\nu V^\mu- V^\nu\nabla_\nu U^\mu$$
$$\mathcal{L}_U V_\mu=U^\nu\nabla_\nu V_\mu+ n_\nu\nabla_\mu U^\nu$$
At some point of a calculat... | When you take the Lie derivative of a vector, you are looking at how it changes as you move along integral curves. Now if you look at $L_UU$ you are asking how does $U$ change along its integral curves. But the point of an integral curve is that it’s tangent is always $U$. So $U$ does not change as you travel along th... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Outside electric field due to an off-center charge inside a conducting shell Suppose there is an off-center charge inside a copper conducting shell. We know that we can use the method of images to calculate the charge distribution on the inner surface. We also know that the charge distribution on the outer surface is u... | One way to explain why the field outside a conducting shell is completely defined by the charge distribution on the outer surface of the shell is to consider that the field inside the conductor is zero.
This means that there are no electric field lines going from the inside to the outside of the shell and, therefore, ... | {
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Do the wires having AC current emit EM waves? When ac current is passed through a wire, the electrons in the wire oscillate to and fro in the wire (due to change in polarity of current in the wire). If the ac current is of frequency, say 50Hz, then will the wire emit electromagnetic waves of the same frequency?
| Yes. they do produce an electric field, if we're working with $50$Hz a rough estimate is that the $\lambda$ would be $\frac{c}{f}=\frac{3\cdot 10^8}{50}\approx6000000$m which is a wavelength that's hard to make use of, but yes, em waves are produced.
| {
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"timestamp": "2023-03-29T00:00:00",
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How are high-energy detectors able to to distinguish between $m_{e}$ and $m_{\mu}$? I had a teacher pose this interesting question yesterday:
Suppose you're running a high-energy scattering experiment at the LHC. For concreteness, let's suppose it's a 2 to 2 scattering event which involves electrons and/or muons.
The t... | Particles as expected to be seen in the CMS experiment at LHC
So electrons and muons leave completely different signatures although because of high energy they may leave a similar track in the tracking detector. Electrons are absorbed in the electromagnetic calorimeter, and muons go through,their electromagnetic inte... | {
"language": "en",
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Have all three flavors of solar neutrino been measured? As far as I know that the sun exclusively produces electron neutrinos ($\nu_e$). When the flux of solar neutrinos ($\nu_e$) is measured on the earth, a depletion is observed in the $\nu_e$ flux i.e., some $\nu_e$'s have "disappeared" in their way from the sun to t... | The SNO experiment was sensitive to all three flavors of neutrinos, and hence provided definitive evidence for solar neutrino oscillations. That's why half of the 2015 Nobel prize for neutrino oscillations went to the director of this experiment, rather than the many other previous experiments.
As usual, there's a bit ... | {
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Why does this paper use 1/cm for units of frequency? Reading this paper from 1963 $^*$, they use units of cm$^{-1}$ for frequency.
Here is an excerpt:
It doesn't seem like wave number, as they clearly call it frequency. What's going on here?
$^*$ Sievers III, A. J., and M. Tinkham. "Far infrared antiferromagnetic reso... | If you suppose c=1, then 'centimetre' is the time it takes for light to cross a centimetre, and a count of cycles per centimetre is something that can be done in nature, and also relates to the frequency in cycles per second.
| {
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"source": "stackexchange",
"question_score": "1",
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Global warming and air temperature The layman's question. Is there a maximum temperature that can be reached by air on Earth due to global warming? For example, one that would prevent living organisms from functioning? I read somewhere that with the increase of the sun's brightness by 10%, the average temperature on ou... | Is there a limit? Yes and no.
No, there isn't really a maximum temperature anywhere near what we're used to. It's certainly possible to reach an average temperature of 47°C. That may well trigger a runaway greenhouse effect, when all the oceans evaporate. Look at our neighbour Venus. On Venus, the greenhouse effec... | {
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Ocean density vs atmosphere density I understand that the density of the oceans on Earth in on average constant regardless of the depth. It is 1020 kg/m^3 at the surface and 1050 kg/m^3 at deep waters.
I understand too that this is not the case with the atmosphere. The density of the atmosphere decreases with height.
... | The incompressibility of liquids is due to the fact that they are made of atoms or molecules of finite radius. The atoms in a liquid are constantly in contact with their neighbors, and increasing the density would require that atoms or molecules overlap, which they typically don't do very readily. as such, liquids have... | {
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Changin the optical depth (axial resoltuion) on an Optical Cohernce Tomagrpahy system So the axial resolution in a OCT system is given by:
$$I_c=\frac{4ln2}{\pi}\frac{\lambda^2}{\Delta \lambda}$$
My question what would you do to say increase the axial resolution, and how would it effect the image quality?
So looking a... | Moving the reference mirror does not change the axial resolution. Its action is to "bring the image in focus", so to speak. Because the light has short coherence length $\Delta\lambda$, the two beams split by the beam splitter do not interfere on the detector. They show clear interference (which is the raw signal) when... | {
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Why do materials obey Hooke's law? Why do materials extend proportionally to the force exerted on them (Hooke's law)? I thought that
*
*when materials are compressed or extended under force, their atoms become closer or further apart;
*the inter-atomic forces are essentially electrostatic;
*electrostatic forces... | When one considers a relatively small segment of a curve, most appear approximately linear when one zooms in far enough. Most materials are not truly linear when stretched a considerable distance, but for small deviations about the equilibrium some are approximately linear. This can be seen when one considers Taylor Se... | {
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Relative motion and time When someone reaches to a speed which is close to the speed of light with respect to earth, will he see the things actually moving faster than when he is in low speeds?
| In SR (special relativity) time is running at a different pace if measured in inertial reference frames in relative motion. A stationary observer (observer in its own rest frame) measures a time $t$ running faster than the proper time $\tau$ of a moving frame. The well known relation is:
$\Delta t = \gamma \Delta \tau$... | {
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Questions about shapes and the reason behind the drag coefficient differences
*
*What is the reason that a streamlined body has a drag coefficient that is lesser than the drag coefficient of a streamlined half-body, when the latter has a completely flat bottom, while the former has bulges on either side of the center... | Drag is not friction between the surface of the body and the fluid. The assumption is usually that the fluid is not moving relative to the surface at the surface itself. This is the basis of boundary layer theory. D'alembert's paradox shows that laminar flow does not produce drag. The upshot is that the drag is due to ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What does it mean if the dot product of two vectors is negative? If the dot product gives only magnitude, then how can it be negative?
For example, in this calculation:
$$W = \vec{F}\cdot\vec{r} = Fr\cos\theta = (12\ \mathrm{N})(2.0\ \mathrm{m})(\cos 180^\circ) = -24\ \mathrm{N\,m} = -24\ \mathrm{J}$$
Why is there a ne... | In your function:
$$W = \vec{F}\cdot\vec{r} = Fr\cos\theta $$
Let's assume that
$$\vec{r}>0$$
There are three cases:
*
*the dot product is 0, this means that the two vectors are perpendicular
*the dot product is >0, this means that the two vectors point approximately in the same direction, that is, their angle is ... | {
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Is the Bose-Einstein condensation a single particle phenomenon? BEC occurs for noninteracting Bosons. Can we conclude that it can be described with a single particle? What is the significance of the number of the particles?
| The Bose Einstein condensate is a QM effect of collective quantum state in which a macroscopic number of particles occupy the lowest energy state and thus is described by a single wavefunction.
All the bosons will be described by the same wavefunction.
So it is not a single particle, but all the particles (their probab... | {
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From where energy comes for the heat released when direction of electric field is changed with a dipole placed in the field
This is an example problem in my book. Forget about the values.
Initial anf final(after heat is released) conditions in this problem are same, ie, dipole moment and electric field are in same dir... | Since the direction of the field changes suddenly, the dipoles rotate quickly and, as a result, when they reach the new orientation, they have some kinetic energy, which will turn into heat, i.e., some energy will be released.
This kinetic energy is equal the difference of potential energies corresponding to the initia... | {
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How much mass is in gravitational waves? Like photons, I understand gravitational waves to have no rest mass but mass due to their energy. Are gravitational waves a significant part of total mass and what are the main components (black hole collisions, big bang etc)?
| Turning to the very useful cosmic energy inventory by Peebles and Fukugita, they estimate that gravitational radiation from massive black holes make up $10^{-7.5\pm 0.5}$ of the total energy of the universe, stellar binaries contribute the smaller $10^{-9\pm 1}$ and primeval gravitational waves are less than $10^{-10}$... | {
"language": "en",
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How does a satellite take pictures when the surface seems to be always cloudy/white? I've just opened ISS video on youtube for the first time, and I must say I'm underwhelmed. There are no oceans/landforms. It's all white everywhere. I'm a bit confused how the satellites can take pictures when the view from space looks... | The satellites (optical satellites) utilize the electromagnetic spectrum to bypass the opacity provided by the atmosphere, which are known as atmospheric windows. In these windows the Channels of the sensor can penetrate the atmosphere. For example, in the image below the atmosphere is basically transparent if the band... | {
"language": "en",
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does tension in the string affect its equilibrium? In my textbook (Sears and Zemansky's University Physics), it is written that the vector sum of the forces on the rope is zero, however the tension is 50 N. Then is tension different than the force? And if not, then why force is zero while tension is not?
A body that h... | Okay, I am a student myself so please re-read it if you don't get at once.
Your textbook says that the Sum of all forces on the rope is zero and yes it is because the rope is in equilibrium.
To understand this first answer these questions,
*
*Is the rope moving? (Hint: No)
*Is the rope pulling the wall? (Yes)
*Is ... | {
"language": "en",
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Why is Copper(I) Oxide Red? This may appear to be a chemistry problem. But, after reading the Wikipedia article on copper(I) oxide, it seems to have more to do with semiconductor-physics. For example:
… light travels almost as slowly as sound in this medium.
Is that true?
What have Kramers–Kronig relations got to do ... | Apparently $\rm Cu_2O$ has a band gap of about $2.1\ \rm eV$ (according to the linked wikipedia page). That means it'll absorb photons with a wavelength of less than $590.4\ \rm nm$ (just do the calculation with $E=hf$). For comparison, yellow light has a wavelength in the range $570-590\ \rm nm$. Hence we detect longe... | {
"language": "en",
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Can Newton’s law of gravitation be derived from Coulomb’s law? I’m casually learning physics and have noticed that Newton’s law of gravitation and the electrostatic force formulas look similar. I’ve asked this question before but would really appreciate another response. Is it possible that the two laws are related? Ca... | What if mass had a sign?
There are (let's keep it simple) Sun, Earth and Moon.
Earth goes around the Sun, so they have different signs.
What about the Moon? If it's attracted to the Earth, it would be repelled by Sun, and vice versa. This is not what happens.
| {
"language": "en",
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"source": "stackexchange",
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Zero velocity divergence for incompressible flow is derived from conservation of energy equation or conservation of mass equation? I'm a bit confused about incompressible flow definition. In many textbooks or scientific articles, they simply claim that the incompressibility condition for Navier-Stokes equation is:
$\na... | Physical meaning of divergence is rate of change of control volume per unit volume. If density is not changing then rate of charge of control volume will be zero this is directly from conservation of mass.
| {
"language": "en",
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Do photons violate the uncertainty principle, given that they have a constant speed $c$ with no uncertainty? I have a very basic understanding of quantum physics, but as I understand it the uncertainty principle says that the more precisely you know a particle momentum and the less you know the particle's position.
But... | There is an uncertainty in momentum! Because, for a photon,
$$p = \frac{h}{\lambda} = \frac{h \nu}{c}$$
where $p$ is the magnitude of the momentum, $\lambda$ is the wavelength of the photon and equivalently $\nu$ is the frequency.
So even though photons travel at $c$, their momentum can be uncertain if their frequency... | {
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Why does kinetic energy of elecron on Bohr's orbit not change if zero of potential energy changes? If zero of potential energy is not taken at infinity, total energy and potential energy of electron change but not kinetic energy. Why is that so?
| The zero of PE is at infinity actually. A charge at rest would have 0 energy at infinity. That's why bounded states have negative energy. For the hydrogen atom, the electron at its fundamental level is $-13,6 eV$, negative because it would escape if it had 0 energy, just like any orbit.
Plus, KE depends on velocity, no... | {
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In a globally-hyperbolic spacetime, does every pair of elements have overlapping light cones? Suppose we have a spacetime $(M,g)$, and denote by $J^+(p)$ the set of points that lie in the causal future of $p$, i.e. $x \in J^+(p)$ iff there is a future-directed timelike curve $\gamma: [0,1]\rightarrow M$ such that $\gam... |
In a globally-hyperbolic spacetime, does every pair of elements have overlapping light cones?
No. Standard cosmological models of our own universe are a counterexample. There are cosmological horizons, so future light cones do not all overlap, but the universe is globally hyperbolic.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/422423",
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"source": "stackexchange",
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Discrepancy in general work and pressure-volume work Consider a massless, frictionless piston fit into an airtight container containing an ideal gas. And let us say that the gas undergoes quasi-static isothermal expansion by lowering the pressure applied by the piston slowly.
The piston moves a distance, say $dr$ in an... | Work done is defined as $dW = \vec{F}.d\vec{r}$. Force on the piston is in direction of it's displacement, so according to definition of work done it will be positive. On the other hand, force on gas is opposite to the displacement of gas, so work done on gas comes out to be negative due to the $cos(\theta)$ term.
For ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/422559",
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"source": "stackexchange",
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Why do lights appear like straight lines on a windshield of a car? (becomes more prominent at sunset and night)
i think thats the Diffraction of light caused by the scratches in the glass. or the wiper blade leave a pattern of dirt and grime in an arc. i hope someone can confirm my logic.
my seconde question is why t... | The streak is caused by refraction (&/or reflection) from scratches on the glass or from streaks of oil, grime, wax, etc., on the surface. As Farcher said, it is not caused by diffraction. The reason the streaks are curved at the bottom of the windshield is because the windshield is curved, and/or because the wiper bla... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/422679",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Electric field between 2 coaxial cylindrical charged tubes Griffith's book on electrodynamics says the electric field between 2 coaxial metal tubes of charge $+q$ and $-q$ is found by using Gauss's law, where the gaussian surface is a cylinder with radius between the outer and inner tube. But that doesn't take into acc... | Gauss's law always holds. Imagine for a moment that the inner tube is the only tube present. Then, using a symmetry argument, you can calculate the electric field using Gauss's law. Now imagine adding some kind of charge distribution outside of your Gaussian volume. While the total electric flux through the boundary of... | {
"language": "en",
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Meaning of the word 'canonical' in physics I often encounter the term canonical in my study of physics. What does it mean? There is canonical momentum, canonical transformations and I have even heard the phrase 'proving something more canonically'. What does the word mean in each of these contexts?
| Even in physics, the term canonical requires a disambiguation for clarity. In the contexts you were citing, it means that it is a more general form. E.g. if you are dealing with momentum, then the canonical momentum refers to $p = p + q \bf{A}$, however, momentum in a Newtonian physics course would most certainly refer... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How can I say whether a Hamiltonian is integrable or not? The transverse field Ising Hamiltonian $$ H = J\sum_{i=0}^{N}\sigma_{i}^{z}\sigma_{i+1}^{z}+h_{x}\sum_{i=0}^{N}\sigma_{i}^{x} $$ is integrable because it can be exactly solved using Jordan Wigner transformations. But the tilted field Ising Hamiltonian $$ J\sum_... | I don't think that level spacing is "enough" to determine a system is "integrable" or not. (of course it depends on how one defines integrability.) The level spacing idea is called Berry-Tabor conjecture, and it is not proven that Poissonian distribution is intrinsic in the case of quantum integrability.
To me, the exi... | {
"language": "en",
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"source": "stackexchange",
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In a vacuum can a cooler body radiate Infrared radiation to a warmer body? I mentioned vacuum, because I want to discount the effects of conduction or convection. I simply want to know if some of the infrared radiation(IR) goes from the cooler body to the hotter body? How does each body know how much to radiate at any ... | I am agree with answers by @Ricky Tensor and @V.F., but more detailed answer is "there are several scenarios". It will depend on:
*
*How much total radiation emits each of bodies
*How much each body absorbs of enother body's radiation (how close they are, how reflective they are)
*What is the rate of cooling for e... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/423524",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
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Are all fields in the universe we know of quantum fields? Are all fields in the universe we know of quantum fields?
Do all fields that exist must be inherently quantum in nature?
How about fields that are yet to be discovered (ie. a new field like Higgs field) , do they all have to be quantum fields?
| Currently all fundamental fields are quantum, except for gravity. For this reason Quantum Gravity is a hot area of research, but the full Quantum Gravity theory has not been developed yet. Why not?
The challenge is not just technical, but conceptual. On one hand, the Quantum Field Theory cannot consistently co-exist wi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/423626",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
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Orthogonality of Scattering states The scattering states solution ($E>V_0$) to the time independent Schrodinger equation for a finite square barrier ($V_0$ ) in an otherwise free region has the form:
$$\psi(x)=\begin{cases}e^{i k x} + r(k) e^{-i k x} &\textrm{for } x<0\\
a(q) e^{i q x} + b(q) e^{-i q x} &... | If they are orthogonal, then their dot product or in this case the probability must be 0. To check whether they are orthogonal or not, just integrate it all over space. If it comes 0 then they are orthogonal.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/423820",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
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Do speakers have non-radiating nearfield? Antenna nearfield contains energy that is not radiated away,does speaker or any other acoustic device nearfield also have this non-radiating energy element that exist in space and doesnt travel away?
| In the electromagnetic case, we say that a component of the field is non-radiating if the field strength of that component decreases with distance faster than $1/r$. Since the intensity of radiation is proportional to the square of the field strength, it follows that the intensity of a non-radiating component decreases... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/423899",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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If a drop of water hits something at bullet speed, will it damage it? I can't find this anywhere. If a drop of water hits a glass for example, at the speed of a bullet, will it damage it? Or will it just make the same as a raindrop?
| Wet steam erosion is a big problem in steam turbine design, as you can see from this image:
So yes, water droplets with enough energy can certainly cause damage to even objects made of steel. With enough energy, it could certainly cause damage (or destroy) your glass.
Water jet cutting is another good example of high-... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/423999",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
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All central forces are conservative forces, but are all conservative forces central forces? I have just been introduced to the concept of central forces, and to the fact that they are per definition conservative forces. I have looked up several examples of central forces (gravity, electric, and spring), but they cover ... | Paul's answer is great. But I just found out an error in the background information you mentioned: central forces aren't necessarily conservative forces. I'm writing it down so you may have a clearer understanding of the logic relationship between a 'central' force and a 'conservative' force.
For example we may take $$... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/424205",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 4,
"answer_id": 2
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Which is more efficient in stopping a bullet, small cubes or fine grains of sand Recently, I was presented with the following problem, relating to pressure: which would be more efficient in stopping a bullet, small cubes or fine grains of sand.
Using my intuition, I would say the small cubes, since it has a larger surf... | When you hit sand, the sand has time to move out of the way. It behaves like a fluid in that regard - dipping your finger in water isn't painful. But doing a belly-flop off the high dive into the water is extremely painful, the reason being that the water has no time to get out of the way, so it behaves more like a sol... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/424338",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
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Would a conical siphon be able to lift water greater than 10.1 m? In a discussion with my father, he argued that a siphon can only pull water up to a limit of ~33 ft (10.1 m). I understand that this limit would apply to water with a density of 1.0 g/cm at sea level (101,325 Pa) being pulled with a perfect vacuum (0 Pa)... | Your father is correct in this case. The pressure of a fluid in hydrostatic equilibrium does not depend on the shape of the container, only the depth, the density, and the pressure at the surface. If a fluid is exposed to atmospheric pressure on one side and vacuum on the other side then the vacuum side will only rise ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/424709",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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