Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
How big of a neutron star would be needed to form a quark star inside of it?
A quark star is a hypothetical type of compact exotic star composed of quark matter. These are ultra-dense phases of degenerate matter theorized to form inside particularly massive[citation needed] neutron stars. -Wikipedia
If you add enough... | This article might be of interest to you! :)
Extract from Quark Stars
Vuorinen joined forces with Aleksi Kurkela at ETH Zurich in Switzerland and Paul Romatschke at the University of Washington in Seattle to examine how the pressure of strange quark matter depends on its density – a relationship described by the star'... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/275744",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
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Estimate the reaction force on each leg of a 4-legged table Assume you have a table with four legs with a weight placed somewhere inside the boundary created by the legs. The task is to determine the reaction force at each leg. Here are the problem constraints...
*
*The sum of the four reaction forces must equal t... | To solve this problem make the legs elastic, but nearly rigid. The reaction force on each leg is going to be a spring force. There are three degrees of freedom: a) two tilt angles and b) Overall height.
Let's assume each leg attachment is at $(x_i,y_i,z_i)$ where $z_i$ is the unknown "lift" of the table leg from the ho... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/276007",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
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Increasing water pressure to shower head I have a 200 liter water tank 3 meters above a shower head.
The tank and head are connected directly by a relatively small pipe.
The shower head has an intake with a diameter the same size as the pipe leading from the tank.
The water pressure coming from the head is too low.
I a... | What you want is increased water flow I suppose. Pressure difference between your shower head and water tank located above is a constant (approximately, if height of water in tank is much less than the height at which tank is located). So if you want greater flow rate you need to reduce the resistance to flow, and maxi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/276104",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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What would happen if a charge could travel at $c$? We know that an electron can move at sublight speed, but can we figure out what would happen if a charge moved at $c$, surfing the wave of the electric field it has produced? There does not seem to be anything that prohibits charged particles from moving at light speed... | The electron has mass. Particles that have mass cannot move at velocity c. There are no charged massless particles, thus no charged particles can move at c.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/276291",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 2,
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Is an EMF more/same/less in an insulator than in a conductor? Is an EMF (electromotive force) more/same/less in an insulator than in a conductor?
For example: A loop of copper and a loop of plastic in a changing magnetic field.
In which will the emf be the greatest?
| The part of net emf due to external magnetic field is the same. However, net emf in the case of conductor includes also contribution due to self-induction when current is changing in time. In plastic this should be negligible. So net emf will be different if current is changing in time in the copper ring.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is the physical meaning of the Schwarzschild radius for objects that aren't black holes? Earth has a Schwarzschild radius of a little less than a centimeter. What does this mean for the matter of Earth's core that is within this radius?
A related question comes up for what happens when an almost black hole accret... | (1) The Schwarzschild radius for an object that is not a black hole is the size down to which you would need to compress the object before it becomes a black hole.
(2) By the equivalence principle, absolutely nothing special happens locally at the event horizon—there's no (local) way to even tell that you've crossed it... | {
"language": "en",
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How is heat represented on a quantum level? Heat is just a form of kinetic energy for molecules, because as temperature rises, the heated molecules are "shake" and "vibrate" more and more. But how does that show up on a quantum scale? What element actually carries the kinetic energy: the heated molecule as a whole, its... | Heat energy, at a microscopic level, is stored in the degrees of freedom of atoms and molecules. These degrees of freedom are translational, rotational and vibrational. They all store different amounts of energy, depending on the geometry of the atom.
Translational degrees of freedom are the atom or molecule moving ar... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/276724",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Laser spectrum range What are the spectrum limits in which a laser can be produced? Also can you focus other electromagnetic waves (microwaves, radio waves, ect…) into a laser like beam?
| Actually, the first "laser" (1954) was emitting microwaves. Charles Townes wanted to produce a microwave source with a very narrow linewidth and came up with the idea to separate ammonia molecules residing in the upper component of the inversion splitting from those residing in the lower component using a hexapole. In ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/277070",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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How does curved spacetime affect gravitational waves? How differently will a LIGO detector detect a gravitational wave which came directly to it with a detector which happened to have a black hole between it and the source?
| Gravitational waves will scatter off strong gravitational fields. You'd expect that just from the equivalence principle, as Lawrence Crowell states. It's basically like light lensing. You can also have more sophisticated estimates of how much.
The arxiv article from 2008 calculates scattering, absorption and reflectio... | {
"language": "en",
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"question_score": "3",
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Solving first order perturbation exactly in this situation I have this homework problem in QM Perturbation Theory
The Hamiltonian of a system is given by $$H_0 = A L^2 + B L_z$$ where
$A$ and $B$ are constants. If a perturbation $V = C L_y$ is added to
the system (where $C \ll A, B$ , find the lowest order correct... | (I assume all coefficients are real obviously.) Define $N=\sqrt{B^2+C^2}$. Using a unitary transformation $U$ representing in the Hilbert space a certain rotation, the one rotating $$\left(0,\frac{C}{N} ,\frac{B}{N}\right)$$ to $$(0,0,1)$$ which therefore leaves $L^2$ invariant, you have $$U(AL^2+BL_z+CL_y)U^∗=AL^2+NL_... | {
"language": "en",
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The symbol $\gtrsim$ versus $\ge$ in physics Currently I am going through Thermodynamic cost of computation, algorithmic complexity and the information metric by W. H. Zurek. In the introduction, he mentioned a relationship between the change in entropy and the difference between the length of a program and its output.... | There's not going to be a rigorous definition; this is how I would read it as a working physicist. Usually $\sim$ means "of about the same size," often in an order of magnitude sense. So if we say $v \sim 1$ in means that $v$ might be like, 5. But probably $v < 10$. This kind of symbol would often appear in a calculati... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/277798",
"timestamp": "2023-03-29T00:00:00",
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Similarities between light and other frequencies of EM waves This may be a ridiculous question, but I'll learn something from it! Let's say there's a TV transmitter transmitting at 100kW. I can receive the station just fine 20 miles away. The antenna is 300m in the air. If I replicate this but with light (put a 100... | Technically speaking, if there is no decay of EM waves of any particular frequency, you can measure the signal in the configuration you are describing. It all depends on how sensitive the measuring instrument (antenna, eye) is to the power under consideration. This of course being true for some large values of EM wave ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/277892",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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For lattice, what are the Goldstone bosons for the broken rotation symmetries? In $1$ dimension, we know that lattice breaks continuous translational symmetry into discrete translational symmetry, which generates $1$ Goldstone boson, i.e. $1$ longitudinal phonons.
In $d$ dimensions, if there are only $1$ type of atoms... | The Wikipedia article on "Goldstone boson" says
In general, the phonon is effectively the Nambu–Goldstone boson for spontaneously broken Galilean/Lorentz symmetry. However, in contrast to the case of internal symmetry breaking, when spacetime symmetries are broken, the order parameter need not be a scalar field, but m... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/278249",
"timestamp": "2023-03-29T00:00:00",
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How does the size of the magnetic field vary with the wavelength of a photon? I tried a search and could not find it in a simple format. Like if the wavelength halves than the magnetic field falls off like $~\frac{1}{\lambda^2}$.
I mean the maximum value of the sinusoid for a single photon. I have read about this some... | The size of the magnetic field for a photon wouldn't depend its wavelength. The amplitude of the fields do not depend on the frequency or wavelength, it depends on the number density of photons (and then there is the distinction between coherent and incoherent sources to consider).
| {
"language": "en",
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Number of degrees of freedom of the coupled pendulum problem In Chapter 4 from the book Theoretical Mechanics of Particles and Continua by A. L. Fetter and J. D. Walecka, it is solved the problem of a coupled pendulum system while considering small oscillations.
There, they say the number of degrees of freedom needed t... | If the spring were perfectly rigid it would reduce the number of degrees of freedom as a constraint. Because it is not, you need the positions of both pendulums to calculate the stretch of the spring.
$$\begin{align}d &= \sqrt{l^2(\cos\theta_1 - \cos\theta_2)^2 + (l\sin\theta_1 - l\sin\theta_2 + d_0)^2} \\
&\approx l(\... | {
"language": "en",
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"source": "stackexchange",
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Why does increasing resistance decrease the heat produced in an electric circuit? If $H=\frac{V^2}{R}{t}$ ,then increasing resistance means decreasing the heat produced.
But, isnt it that the heat in a circuit is produced due to the presence of resistors? Moreover metals with high resistances are used as heating elem... | Consider analogy with fluid flow. When there flow in a pipe say, due to friction, energy of motion is dissipated away into heat. Therefore for dissipation into heat to occur two things are necessary: flow, and resistance to flow. In the absence of either of them there is no dissipation into heat. Same is true of curren... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/278530",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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At what pressure does the helium undergo phase transition at room temperature? At what pressure does the helium undergo phase transition at room temperature?
I can not find phase diagram at room temperature.
| From Chemicool
At normal atmospheric pressure helium does not solidify. At 25 atmospheres of pressure helium is a solid at 0.95 K. As the pressure rises, the temperature at which solid helium exists also rises. Helium can be made solid at room temperature if the pressure rises to about 114 thousand atmospheres: that is... | {
"language": "en",
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How does the law of conservation of energy explain magnetism? The law of the conservation of energy describes that energy cannot be created nor destroyed however in fact only changes form.
How does this law explain the energy transferred by magnetic fields?
| Magnetic fields work like springs.
So for permanent magnets one can align the magnetic dipole moments of the involved subatomic particles and "freeze" this state. But themagnet is than under iner pressure and it is not advised to drop the magnet, it will explode in pieces and the contributed energy will be released.
In... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Entropy and reversible paths I'm a little bit confused about calculating entropy changes along irreversible paths by integrating over a reversible path. When using the central equation I can understand the argument, entropy and all the quantities we use to calculate the entropy change are state functions that have well... | For an irreversible path, the integral of dQ/T is not equal to $\Delta S$. To get the change in entropy between the two end points of an irreversible path, you need to devise a reversible path between the same two end points, and calculate the integral for that path. It doesn't matter what reversible path you choose;... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Formula for lens periscope I want to build a periscope.
To my great surprise even after intense googling I could find little relevant information about periscopes anywhere on the internet.
Let's say I want to build a periscope with height h, apparent height h1, diameter d and viewing angle v. What other variables shou... | Assuming the two prisms are planar reflectors, there's no significant effect from them. If you do your refractor-telescope calculations by measuring the distances along the center of the light path, including the right angle bends, it should all work out. Then you put in the right-angle, planar reflectors (prisms or mi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/278940",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Does Gravity Depend on Spatial Dimension? Consider a line containing two point masses, $m$ and $M$. The line is a $1D$ space.
What's the gravitational force between the two masses?
Newton's formula for the gravitational force $F$ between two masses $m$ and $M$ in 3D space is
$$F=\frac{G M m}{r^2}$$
where $G$ is a cons... | The reason why the gravitational force is in $r^{-2}$ is because it has zero divergence in void — its flux is conserved through a close surface encompassing matter is conserved.
Let's take the example of a massive point, the flux of the gravitational force through a sphere of radius $r$ centered on the point is:
$$ \Ph... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/279054",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Showing that pseudorapidity equals $\ln \left(\frac{\sqrt{p_z^2 + p_t^2}+p_z}{p_t}\right)$ I found one method to calculate pseudorapidity, $\eta$, using the formula
\begin{equation}
\eta = - \ln \tan \frac{\theta}{2}
\end{equation}
And I know how we can get to this point from Lecture 7 - Rapidity and Pseudorapidity i... | Oh Maybe I have found,
Another formula for the pseudorapidity $\eta$ is :
\begin{equation}
\eta = \ln \frac{p+p_z}{p-p_z} \\
\eta = \ln \dfrac{\sqrt{p_x^2+p_y^2+p_z^2}+pz}{\sqrt{p_x^2+p_y^2+p_z^2}-p_z} \\
\eta = \ln \dfrac{\sqrt{p_x^2 +p_y^2 + 2 \times p_z^2}}{\sqrt{p_x^2+p_y^2}} \\
\end{equation}
So We can find :
\beg... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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How do we prove or disprove that a particle has no internal structure? In many pop physics books I have read that an electron has no internal structure.
How do we know that and how can we rigorously prove that it has no such structure at all?
| The electron has a magnetic dipole moment and an intrinsic spin. Both phenomenon need an extend and a structure and hence the electron has to have an internal structure.
That until know we haven't found this structure has to do with our capabilities to build the right instrument.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/279338",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "15",
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Why doesn't electric charge immediately leak off charged objects? I will focus my question with a particular example: a metal sphere, surrounded by vacuum, is given a negative charge. I know that when this charge is great enough, electrons will be emitted from the sphere, but why is the threshold for this so high? As I... | As an electron makes its way outside a metal surface, there is immediately
an image charge (positive virtual charge) on the other side of that surface
that attracts it back. The 'work function' is the kinetic energy that the
free electron needs if it is to escape to a large distance, and has
to include both surface-b... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/279431",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How can the work done in bringing a charged particle from infinity to a grounded conductor be zero? Suppose we have a grounded conducting sphere (potential of sphere = 0) and we bring a charged particle to its surface.
Since work done by us would be equal to the change in potential energy of the charge, it will be equa... | Lets proceed like this. The surface of the sphere S1 being grounded is at a potential we are labelling as V1 and an imaginary system boundary S2 at infinity is as V2(imagine a colossal spherical surface S as the boundary, this S2 is basically the sphere of influence of the grounded sphere.) WHen we start bringing a pos... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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If you are vacuuming your carpet and you wrap the cord around your body do you become a magnet? If you wrap an active electric cord around your body, do you become an electromagnet?
| The answer is no, because the electric field of each wire cancels the field of the other wire. But even if you wrap yourself many times with one wire and connect the ends to electric power, you will not become a "measurable" electro-magnet. The reason for this is that the amount of ferromagnetic material in your body... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/279783",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why does this planet (J1407 b) and Saturn's ring center on its equator? Why is the material in J1407 b's or Saturn's rings stay in a disk not scattered? Is it the gravity and/or magnetic field that causes this? Does it differ with other large bodies that might not have a electromagnetic field?
| Saturn's rings are rather interesting. From what I've read, the different layers of dust and rocks have been formed over millions of years, by a phenomenon known as orbital resonance. Orbital resonance is something like an increased(or decreased) gravitational effect due to 2 bodies moving with certain time periods. Th... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Combination of more than two lenses? I know the formula that when two lenses are separated by a distance $d,$ then the resultant focal length is given by :-
$$\frac 1f = \frac1f_1 + \frac1f_2 - \frac d{f_1\cdot f_2}$$
However , there are two doubts that arise in my mind.
1) My book says that a combination of two thin l... | *
*A thick lens is a more complicated device than a thin lens. Theoretically, it is defined by the curvature radius of each of the two sides of the lens, the thickness and the refractive index of the material (4 variables). Note that your equivalent thick-lens is under-constrained: 4 variables > 3 parameters. By playi... | {
"language": "en",
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"source": "stackexchange",
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Calculating Centripetal Acceleration of Sun about Galaxy This is a question from my Mechanics book:
Calculate the centripetal acceleration relative to the acceleration due to gravity of:
c) the Sun in its rotation about the center of the galaxy (the radius of the Sun's orbit about the center of the galaxy is $2.8 * 10^... | Can't seem to work out how the book got that answer either and my conclusion would be that the answer is wrong or that the question is poorly worded/explained. I also computed about $1.8(6)*10^{-11}$ but did notice some lack of optimisation in your approach...
Note that the centripetal acceleration can be calculated us... | {
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Are electric fields produced by static electric charges different from those produced by time-varying magnetic fields? I came across an interesting yet perplexing statement in my physics textbook:
However, we hasten to add that electric fields produced by static electric charges have properties different from those pr... | $$\begin{array}{|c|c|} \hline\textrm{True in Statics} &\textrm{True in General}\\ \hline \mathbf F ~= \dfrac1{4\pi\varepsilon_o}~ \dfrac{q_1q_2}{r^2}~\mathbf{\hat r} & \mathbf F= q(\mathbf E+ \mathbf v\times \mathbf B)\\ \hline \nabla \cdot \mathbf E = \dfrac{\rho}{\varepsilon_0} & \nabla \cdot \mathbf E = \dfrac{\rh... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/280787",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Lagrangian and finding equations of motion I am given the following lagrangian:
$L=-\frac{1}{2}\phi\Box\phi\color{red}{ +} \frac{1}{2}m^2\phi^2-\frac{\lambda}{4!}\phi^4$
and the questions asks:
*
*How many constants c can you find for which $\phi(x)=c$ is a solution to the equations of motion? Which solution has the... | You have a minor error from a missing minus sign here:$$\frac{1}{2}\Box\phi+m^2\phi-\frac{\lambda}{6}\phi^3-\frac{1}{2}\Box\phi.$$ It should be (after combining terms):
$$-\Box\phi+m^2\phi-\frac{\lambda}{6}\phi^3.$$
Now, for finding the Hamiltonian you might find it easier to integrate the term $\phi \Box \phi / 2$ by ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/280904",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Solder Phenomenon I recently saw an interesting phenomenon. I was soldering a piece of electronics and once I was at the end of my wire I could simply let go and the (small) solid piece of wire would be sucked in to the molten solder blob.
I am curios what causes this force. Perhaps it is pressure difference?
| This is due to surface tension. This effect is exploited in reflow soldering of surface-mount (SMT) devices on printed circuit boards (PCBs)
*
*Example video, look at R2 at 0:13
*Example video
*Discussion of undesirable effects
*University of Bristol
Don’t worry if the components aren’t prefectly aligned at this... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Space bends relative to what? We all are aware of gravitational waves, as it bends space and time, black hole squeeze space, but the squeezing, bending, expanding happens reference to what? Since the observable universe is the universe existing within itself, so it bends in reference to whose perspective?
| This is a fundamental question explored in non-Euclidean geometry. Here are two easy to imagine consequences of the bending of space-time, imagined as just effects on space.
First, as is used in the expanding universe model, the size of the universe, it's scale factor, can change with time. In that scenario the wavelen... | {
"language": "en",
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"source": "stackexchange",
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Understanding tension based on assumptions of pulley system If we consider a simple pulley system with two masses hanging on each end of a MASSLESS and INEXTENSIBLE string around a MASSLESS and FRICTIONLESS pulley, how then can one reason that the tension at each end of the string must be the same?
My own reasoning:
MA... | What we mean by a frictionless pulley is that the friction in the bearings of the pulley is negligible, and the pulley is free to rotate without any resistance. We don't mean that the friction between the string and the pulley surface is negligible. In fact, we assume that there is enough static friction between the ... | {
"language": "en",
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What does the constant $(\mu)$ mean in the formula $B=\mu(N/L)I\,?$ In the formula $B=\mu (N/L)I,$ what is the number of the constant $\mu$ for copper?
I need to know because I did an experiment where we created an electromagnet and changed the diameter of the wire. We measured the magnetic field using a Pasco sensor. ... | In this case, $\mu$ is a stand-in for $\mu_0\,k$. Here $\mu_0$ is a constant $4\pi\times10^{-7}\:\mathrm{T/(A\:m)}$ and $k$ is the relative permeability of the material used for the core of the solenoid.
For example, with Fe, it is around $200\:\mathrm{N/A}^2$. Whatever material your core is, just look up the relative... | {
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Help needed with applying pseudo force I have read in my book that to apply a pseudo force,
We make sure that the object ( our reference frame ) is accelerating and then we add the negative of it's acceleration vector to the object that we are trying to apply the pseudo force at.
Now take a look at this picture whe... | I think your basic confusion starts when you say
... the object ( our reference frame ) ...
The "object" and "the reference frame" are two different things. Pseudo forces are "caused" by acceleration of the reference frame, not the acceleration of the objects themselves.
In general, the objects can also be moving a... | {
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Energy dissipated when two charged capacitors are connected in parallel The question at hand is:
"Two capacitors of capacitances $C_1$ and $C_1$ have charge $Q_1$ and $Q_2$. How much energy, $\Delta w$, is dissipated when they are connected in parallel. Show explicitly that $\Delta w$ is non-negative."
I'm confused abo... | loss of energy when 2 capacitors are connected in parallel( -ive terminal with
-ive terminal of capacitors and +ive terminal with
+ive terminal of capacitor)
let, C1 capacitor is charged up to V1 potential.
C2 capacitor is charged up to V2 potential.
Q=CV
initial total charge on the capacitors= (C1*V1)+(C2*V2)
... | {
"language": "en",
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Time dilation for a clock in orbit Suppose that we want to compute the total time dilation for a clock located in an orbiting satellite relative to the clock in our cell phone on the ground.
Consider two different approaches below.
*
*Use special relativity and compute time contraction due to the relative velocity. ... | Following on from @ProfRob's method, instead of considering the SR and GR "time dilations" separately, we can work directly from the Schwarzchild metric.
(Using signature $+,-,-,-,-$)
$$\boxed{ds^2 = c^2\left(1-\frac{r_s}{r}\right)dt^2 - \left(1-\frac{r_s}{r}\right)^{-1}dr^2 - r^2\sin^2\theta\,d\phi^2 - r^2d\theta^2}$$... | {
"language": "en",
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Average Velocity: $( v_1+v_2)/2$ While searching for the answer regarding, why acceleration is needed to be constant for using the formula $(v_1+v_2)/2$ , I found many simple and easy proofs regarding this, here in this Physics.SE website, one of which is ,
But can anyone come up with a daily life simple explanation... | Here's one way to think of it that might help.
If the acceleration is not constant you could have a case where something moves at a slow velocity for a long time and then accelerates briefly at the end of its motion to a higher velocity. Intuitively the average velocity should be closer to the initial slower velocit... | {
"language": "en",
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Why does the cross section for Compton scattered photons decrease with increasing energy of incident photon? The cross section is independent of energy for energies less than electron's mass, but for greater energies the cross section of compton scattered electrons decreases, why?
| Think about what happens as you increase the photon energy, you begin to move away from merely dislodging an electron to an energy regime in which pair production becomes more predominant.
As you probably know, in the pair-production reaction, we need a third body for momentum conservation. Not surprisingly, that h... | {
"language": "en",
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Could the universe be shrinking? It is thought the universe is expanding because of the red shift of most galaxies but if all the matter in the universe was actually falling into a massive black hole wouldn't most galaxies still be red shifted because the black hole would accelerate every galaxy and every galaxy that w... | The red shift is in all galaxies regardless of direction. If the galaxies were falling into a black hole the red shift would happen, but considering the fact that all of them are red shifted, and all are moving away from us, the black hole would need to have the structure of a spherical shell of enormous radius or the... | {
"language": "en",
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How would you include gravity in a momentum problem?
Say you have a big ball of mass $m_1$ and a little ball on top of that of mass $m_2$ (assume they are a small distance apart, like $1~\mathrm{mm}$). Now lets drop these from a height of $h$ so that the big ball will bounce off the ground and collide into the little ... | Since both balls suffer same acceleration due to gravity, their relative acceleration is zero. This means that to analyse relative motion of balls you may pretend that there is no gravity. This is equivalent to switching to a free-fall frame, which incidentally is not an inertial frame, but that does not matter so far ... | {
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Equations of motion for a free particle on a sphere I derived the equations of motion for a particle constrained on the surface of a sphere Parametrizing the trajectory as a function of time through the usual $\theta$ and $\phi$ angles, these equations read:
$$ \ddot{\theta} = \dot{\phi}^2 \sin \theta \cos \theta $$
$$... | In case the particle is not subject to any external forces except those maintaining the constraint, there is no need to write and solve the equations of motion in particular system of coordinates. The particle will move with constant speed around some great circle on the sphere. Which circle it will be and the speed of... | {
"language": "en",
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Concentric Circular Loops We have two concentric circular wire loops. The inner loop has a stable, clockwise current. The outer loop does not have current. If the current of the inner loop increases, what is the direction of the current of the outer loop?
My first thought was "counter-clockwise" using the RHR, increasi... | Yes the area in between the outer and inner loop will be large, but the magnitude of the magnetic field inside the inner loop will more than compensate. (1) magnetic fields near a wire are larger than at points farther away from the wire, and (2) the points inside the inner loop are receiving nearly-aligned magnetic fi... | {
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What can Maxwell's Equations tell us about permanent magnets/ how are permanent magnets and electromagnets related? It makes sense that Maxwell's equations tell us that there are no monopoles, but can the equations tell us anything else about the magnetic fields of permanent magnets on their own, i.e. without interacti... |
but can the equations tell us anything else about the magnetic fields of permanent magnets on their own, i.e. without interactions with a wire/current, or how such fields arise?
Permanent magnets have a nonzero magnetization $\textbf{M}$ which gives rise to bound volume and surface currents $\textbf{J}_b=\nabla\times... | {
"language": "en",
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Possible Error in Assumption - Griffiths Quantum Mechanics In "Introduction to Quantum Mechanics" by Griffiths, right at the beginning of section 9.1.1 (Time-Dependent Perturbation Theory, The Perturbed System), Griffiths states:
Now suppose we turn on a time-dependent perturbation, $H'(t)$. Since $\psi_a$ and $\psi_b... | That's why it's called perturbation. You use the Hamiltonian $H_0$ and you get a set of eigenfunctions. Then you add a perturbative Hamiltonian $H'$. Though you tweaked the Hamiltonian, the original eigenfunctions remains the same. You can always calculate the perturbative eigenfunctions using iteration method, but you... | {
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Why is it that the change in internal energy always uses the formula with Cv in regards to pressure/volume/temperature changes on a gas? Normally I would associate the use of $C_v$ with finding the energy taken into or leaving a system when the volume is kept constant. However, the formula to find $\triangle E_i$ (chan... | We call $C_v$ the heat capacity at constant volume because that is how it can be measured experimentally, by measuring the amount of heat Q added in a constant volume test and dividing by the temperature change. But, this physical property that we call $C_v$ has a more general meaning and applicability than that. In ... | {
"language": "en",
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One straw drinking from many containers of liquid One of my friends brought up a photo:
Which sparked a debate about whether the containers closest to the end of the straw would empty first. I was just wondering if someone could explain if the closest two containers would be empty before the furthest.
| The containers would empty at a different rate with a restrictive orifice separating the containers. These straws may very well qualify. Without knowing the plastic viscosity and yield point of the fluid and an exact measurement of the ID, length and exact suction on the straw it can not be answered accurately. BUT..... | {
"language": "en",
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Explain difference between internal energy and enthalpy I read that $U=q+w$ and $H=u+PV$ so aren't $PV$ and $w$ same?
If they are, can't we write $H=q+2w$?
Also,
$dU=$ change in internal energy wrt change in temperature keeping $V$ constant times $dT+$change in internal energy wrt change in volume keeping $T$ constant ... | According to the sign convention you are using, $$\Delta U=q+w$$where, for a reversible expansion or compression, $$w=-\int{PdV}$$So, $$\Delta U=q-\int{PdV}$$and$$\Delta H=\Delta U+\Delta (PV)=q-\int{PdV}+\Delta (PV)$$Integrating by parts, we get$$\Delta H=q+\int{VdP}$$
The quantity $$\int{\left(\frac{\partial U}{\part... | {
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If mass density curves space-time, then why isn't density (at each $x$, $y$, $z$) considered a dimension in space-time? From http://science.howstuffworks.com
"Theodor Kaluza theorized that a fourth spatial dimension might link general relativity and electromagnetic theory. But where would it go? Theoretical physicist ... | Because it doesn't add another term to the length element?
One way to understand the dimensionality of space is to examine the nature of the length element. In three dimensional space (and with a Cartesian basis) it is
$$ (\Delta s)^2 = (\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2 \;, $$
which you will note has three ter... | {
"language": "en",
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Theoretically, could there be different types of protons and electrons? Me and my friend were arguing. I think there could theoretically be different types of protons, but he says not. He says that if you have a different type of proton, it isn't a proton, it's something else. That doesn't make sense to me! There are d... | There are in fact 2 types of Protons - Protons and anti-Protons.
They interact and behave exactly the same way and are completely indistinguishable from one another. However they will mutually annihilate on contact.
Other than that refer to the other answers here. If a particle looks like a Proton, acts like a Proton, ... | {
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Mass of the asymptotic fields: physical or bare? If I understand it correct, then the physical mass $m$ of a particle, is the mass in presence of the interaction (i.e., the mass of the dressed particle) where as the bare mass $m_0$ is the mass in absence of interaction. However, in the derivation of LSZ reduction formu... | The physical mass can be defined as the pole of the propagator
$$\int d^4x e^{-iq\cdot x} \cdot\langle \Omega|T\{\Psi_l(x)\Psi^\dagger_{l^\prime}(0)\}|\Omega\rangle$$
where $\Psi_l$ are renormalized fields.
The LSZ reduction formula says that if a one-particle state with momentum squared $m^2$ has non-vanishing matrix ... | {
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What is the name of a quantity expressed in Tm? Consider the quantity defined as a magnetic field times a length is expressed in tesla*meter:
$Bl\ [\mathrm{Tm}]$
that arises for instance in the expression $F=BlI$.
What is the appropriate terminology for this quantity $Bl$?
| A common quantity is the magnetic flux, $\int \mathrm dA \, B$. That is measured in $\mathrm{T \, m^2}$.
Your quantity seems to be a linear flux density, so the flux density integrated along a single dimension. That would be a little strange though.
It could also be a line integral, like $\oint \mathrm d\vec l \cdot \v... | {
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Muon Decay Lagrangian I am working on figuring out the following problem
The muon decays to an electron and two neutrinos through an
intermediate massive particle called the W$^-$ boson. The muon,
electron and W$^-$ all have charge -l.
(a)Write down a Lagrangian that would allow for $\mu^-\rightarrow
e^-\bar{\nu... | Note that the Feynman diagram includes two different types of interaction vertex, so each one will need a term in the Lagrangian:$$-\mathcal{L}_{int}=g \bar{\nu}_\mu W^+ \mu + g \bar{\nu}_e W^+ e + \mathrm{h.c.}$$
Both terms have the same coupling $g$ because of the universality of weak interactions.
Usually, the energ... | {
"language": "en",
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What is the shape of the detector pattern in a Stern-Gerlach experiment with a beam source (instead of a fan)? I've been delving into Bell test experiments and woefully most sources fall into either dense physics papers, or very low level simplifications with lots of handwavium.
One thing in particular I'd like to und... | From a practical point of view the reason for using of a broad flat beam may be as simple as getting easy alignment and decent rate while not blurring the signal with a significant z-direction dispersion.
No need to over-complicate things.
| {
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What does it mean for a system to be integrable? I am reading this paper: http://aleph.physik.uni-kl.de/~korsch/papers/JPA_24_45.pdf and in section 3 they talk about the integrability of the system. What does that mean?
| The paper refers to the notion of complete integrability, aka. Liouville integrability, i.e. the property that there exist $n$ independent globally defined Poisson-commuting constants of motion. Here $2n$ is the dimension of phase space. In the paper $n=2$. See also this related Phys.SE post.
| {
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Motion of one body with reference to another I studied that Galileo was punished by the church for teaching that the sun is stationary and the earth moves around it. His opponents held the view that earth is stationary and sun moves around it.
The question i want to ask is if the absolute motion has no meaning,are the ... | *
*Here the important thing is the frame of reference. When we look from the earth frame, the sun is rotating around the earth.
*When we look from sun frame, the earth is rotating around the sun.
*When we look at them from outside of both frames, like when we are looking from the galaxy of sun system, then we come t... | {
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Measuring very small temperature differences Can one use a thermometer with $\pm$5 mK accuracy to measure a temperature difference of 2 mK (the measurement is near 100 mK temperature on a sample on an ADR)? Using the same thermometer, I am thinking to measure temperature of the sample, heat the sample slightly, measure... | Assuming the accuracy reported does not include any nonlinear factors, it refers to the inaccuracy in a single measurement, and will not vary much over the time of your experiment, then you can increase precision by integrating multiple measurements. Signal (the temperature) will add proportional to the number of measu... | {
"language": "en",
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Partition function - q-number or c-number, classical definition, etc Why is the partition function
$$Z[J]=\int\ \mathcal{D}\phi\ e^{iS[\phi]+i\int\ d^{4}x\ \phi(x)J(x)}$$
also called the generating function?
Is the partition function a q-number or a c-number?
Does it make sense to talk of a partition function in classi... | It is called a generating function, because one can use it to generate $n$-point functions with the aid of functional derivatives with respect to the source $J$. For instance, one can compute the two point function as follows:
$$ \langle\phi(x_1)\phi(x_2)\rangle = \frac{\delta}{\delta J(x_1)} \frac{\delta}{\delta J(x_2... | {
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Moment of Inertia of Annular Quadrant I am measuring the moments of inertia for various numbers of annular quadrants placed on a torsional oscillator. I know $\displaystyle{I=\frac{1}{2}M(R^2+r^2)}$ for a whole annulus. If I want the moment of inertia of only an annular quadrant, would I divide the formula above by fou... | *
*The MMOI about the geometric center is still $$I_{center} = \frac{m}{2} (r_1^2+r_2^2) $$
This is a result of the relationship ${\rm d}m = \rho z r \,{\rm d}r {\rm d}\theta$ and ${\rm I} = r^2 {\rm d}m$
$$ \begin{aligned} m & = \rho z \int \limits_{r_1}^{r_2} \int \limits_{0}^\Theta r\, {\rm d}\theta {\rm d}r & ... | {
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What is difference between operating wave function with operator of an observable and measuring for an observable? People say operator of an observable helps in measuring for an observable. We also know that measuring leads to collapse of wave function. But operator on wave function gives a number times same wave funct... | There are a few different points/distinctions that need to be made here.
1. The expectancy value when measuring an observable to which the operator $A$ can be assigned is $\langle A \rangle = \langle \Phi | A | \Phi \rangle$ for a system described by a wavefunction $|\Phi\rangle$.
2. If the value $a$ is measured, the c... | {
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Is Del (or Nabla) an operator or a vector? Is Del (or Nabla, $\nabla$) an operator or a vector ?
\begin{equation*}
\nabla\equiv\frac{\partial}{\partial x}\vec{i}+\frac{\partial}{\partial y}\vec{j}+\frac{\partial}{\partial z}\vec{k}
\end{equation*}
In some references of vector analysis and electromagnetism, it is consid... | Both. It's an operator that transforms as a covector under rotations. What this means is that if you rotate the coordinate system the gradient in the new coordinate system, $\nabla'$, can be written as:$$\nabla'_i = \sum_{j} R^{-1}_{ij} \nabla_j,$$ where $R^{-1}$ is the inverse of the rotation matrix, $\nabla$ is the g... | {
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Is there a notion of causality in physical laws? I was reading "A Few Useful Things to Know about Machine Learning" by Pedro Domingos and towards the end of the paper he makes this statement:
"Many researchers believe that causality is only a convenient fiction. For example, there is no notion of causality in physical ... | Saying that there is "no notion of causality in the physical laws" is likely a gross misinterpretation of the lack of time-asymmetry in the majority of physics. This is to say that many physical laws hold equally well given a flow of time in either the forward or reverse directions with respect to the flow of time we ... | {
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Why doesn't a permanent magnetic field not make a florescent light illuminate like an electromagnet field? Similar to this question: What is the difference between the magnetic field of a permanent magnet, and that of an electromagnet? mine is different because I want to know why a permanent magnet with the same field ... | A permanent magnetic field does not transfer kinetic energy to charge carriers like an applied electric field in a gas discharge tube. Thus electrons are not able to impact ionize or excite atoms so that they can emit light that would bring the fluorescent material in a discharge tube to fluorescence.
| {
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Does the warped space around the Earth push objects towards the Earth? In the following video, the theoretical physicist Michio Kaku states that space is pushing objects towards the earth. https://youtu.be/fEZupmpTcOU?t=1m59s
Is the warped space around the earth providing a force that is accelerating objects to the ear... | No, warped space is not "providing a force". Gravitation warps the space. In other words, the causality is gravitation->warped space, so you/Kaku have it backwards. Notice that, as with other causal effects, the warping of space travels at the speed of light.
| {
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Finding an approximate expectation value $\langle E_0|\hat{O}|E_0\rangle$ when i dont know the ground state? I'm assuming that i know the hamiltonian although i don't know it's ground state $|E_0\rangle$ and that i have a way to find $|\psi(s)\rangle\equiv e^{-\hat{H}s}|{\psi}\rangle$, $\forall s\in\mathbb{R}$ with uni... | Can we assume that all eigenvalues of $\hat H$ are bounded from below and/or positive and there is a gap $\Delta$ between the lowest and second lowest eigenvalue and every $| \psi \rangle$ can be expanded into sum of eigenvectors? If yes then we could explore the limit
$$
\lim_{s \rightarrow \infty} \frac{\langle \psi(... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Why the clock at rest runs faster, while another clock slows when moving? I have observed from my first question that it is hard for me to study the special relativity from every frame of reference. But, there is one most important question in my head right now that time runs slower for moving body if observe from rest... |
Please answer in brief and simple language.
If Alice and Bob are moving relative to each other with constant speed $v$, both of the following statements are true:
(1) Alice observes Bob's clock to run slow by a factor of $\frac{1}{\gamma_v}$
(2) Bob observes Alice's clock to run slow by a factor of $\frac{1}{\gamma_v... | {
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Gravity between two Photons (I searched for an answer online already but I couldn't quite find what I was looking for...)
I thought about this for a long time now. If two Photons fly in the same direction, one behind the other one, for my understanding the one behind the other one should be pulled towards the photon in... | From my understanding:.
Photons have a rest mass of zero, but the electromagnetic waves do carry energy which causes gravitational pull. Since light isn't affected by gravity because its rest mass is zero, but the space light is moving on gets curved. This is what causes light beams to curve around massive objects. Th... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Inclined Plane and Center of Mass Say there is a block sliding down an inclined plane that rests on a frictionless table. There is kinetic friction between the block and inclined plane. If the block slides downhill, then the kinetic friction acting on it points uphill. By Newton’s third law, the inclined plane will exp... | You are forgetting the normal force between the block and the wedge (inclined plane). This force has a horizontal component, pushing the wedge to the left as the block slides down to the right.
The 2 forces acting on the wedge due to the block are the normal reaction $N$ and the friction force $F=\mu |N|$ (see diagra... | {
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Why is water evaporated from the ocean not salty? I am wondering about this. When salty water in the ocean evaporates we are getting the clean distilled water. Why is that?
I was trying to think on this and maybe the comparative size/mass of water molecules to the size of different salts molecules plays a role here, bu... | Alcohol will boil off first
The boiling point is 78.37 °C
There will be some water but the ratio of alcohol in the vapor phase will be higher than the liquid. Water and alcohol are azeotropes so things flop at about 70% alcohol.
The size is not that much of a factor - hexane is volatile.
wiki
Table salt (NA CL) is no... | {
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"source": "stackexchange",
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Problem with Bogoliubov transformations of an operator I have a set of Bogoliubov transformation as follows:
\begin{equation}
a(\beta) = a \cos \theta (\beta) - \tilde{a}^\dagger \sin \theta (\beta)\\
\tilde{a}(\beta) = \tilde{a} \cos \theta (\beta) + a^\dagger \sin \theta (\beta)
\end{equation}
And their corresponding... | Based on some of the expressions that are provided, it seems the issue is one of notation. So, I'm going to be ratherpedantic. Let's define
$$ \{a, \tilde{a}\} \equiv \left\{N^{(1)}_{ij}, N^{(2)}_{ij}\right\}$$
so that
$$ A \equiv N^p_{ij} $$
where $p$ is an index that selects either $a$ or $\tilde{a}$ and $ij$ are ind... | {
"language": "en",
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What parts of a physics undergraduate curriculum have been discovered since 1966? What parts of an undergraduate curriculum in fundamental physics have been discovered since, say, 1966? (I'm choosing this because it's 50 years ago.)
Physics textbooks have moved on since 1966 (though even quantum mechanics was already ... | Maybe high-temperature superconductivity?
| {
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"source": "stackexchange",
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Should zero be followed by units? Today at a teachers' seminar, one of the teachers asked for fun whether zero should be followed by units (e.g. 0 metres/second or 0 metre or 0 moles). This question became a hot topic, and some teachers were saying that, yes, it should be while others were saying that it shouldn't be u... | The question cannot be answered generally because it depends on the situation - on what exactly you mean. If you mean "zero mass" then writing $0 \textrm{g}$ or $0 \textrm{kg}$ or something like that is very reasonable. If you mean an abstract, unitless zero from $\mathbb{R}$ - well, that one is unitless and should be ... | {
"language": "en",
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Where does the extra kinetic energy of the rocket come from? Consider a rocket in deep space with no external forces. Using the formula for linear kinetic energy
$$\text{KE} = mv^2/2$$
we find that adding $100\ \text{m/s}$ while initially travelling at $1000\ \text{m/s}$ will add a great deal more energy to the ship th... | Another much clearer way to see the effect of the Oberth effect is when you add the Potential energy to the equation.
When you perform a rocket burn inside the gravity well of a massive body, the propellant ends up in a lower orbit than if you perform the rocket burn outside of the gravitational well.
The difference in... | {
"language": "en",
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"source": "stackexchange",
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Field of a Polarized Object In Griffith's Electrodynamics, in the section 4.2, just after the equation 4.9, he writes "sleight-of-hand casts this integral into a much more illuminating form"...
I have a doubt in that. If the Gradient (or differentiation if carried out) is with respect to primed coordinates, how can var... | The point is that the 'scripty r' (i dont know how to write it here) depends only on the difference between the coordinates; note that
($\frac{\partial}{\partial x}$) $f(x- x')$ = -($\frac{\partial}{\partial x'}$)$f(x- x')$. What i am trying to say is that the 'scripty r' is a vector joining the primed co-ordinates to... | {
"language": "en",
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Solving a problem using Newtonian mechanics and D'Alembert principle yI have to solve that problem with two methods (applying Newtonian mechanics and the D'Alembert principle.
The problem consists in two balls inside a spherical cylinder, it consists in determine the minimum value of $M$ making the tube not to knock do... | If there is no friction between any contact surfaces, then the centres of the spheres, the points of contact and the axis of the cylinder will all lie in the same plane. So this is a 2D problem.
The 2 spheres exert horizontal forces on the cylinder at their points of contact with it. These forces are not aligned, so th... | {
"language": "en",
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Why are planets not crushed by gravity? Stars can be crushed by gravity and create black holes or neutron stars. Why doesn't the same happen with any planet if it is in the same space time?
Please explain it in simple way. Note: I am not a physicist but have some interest in physics.
| Planets are crushed by gravity! That's why, for example, Earth is a densely packed spherical rock rather than a loose cloud of dust.
There's just not enough crushing 'force' to do more than that.
| {
"language": "en",
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The central field approximation and the quantum number $n$ Under the central field approximation the Hamiltonian of a multi-electron atom is approximated as:
$$ \hat H= \sum_i \left( -\frac{\hbar^2}{2m} \nabla_i^2 +V(r_i) \right)$$
for some central potential $V(r_i)$. This can be solved separately for each electron, th... | The inter-electron repulsion contains a large spherically symmetric component. So, it is possible to construct a potential energy function $V(r_i)$ which is spherically symmetric. The Hamiltonian for such a potential is written as follows using perturbation theory.
$H$ = $H^*$ + $H'$
where $H^*$ = $\hat H= \sum_i \left... | {
"language": "en",
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Since quantum mechanics give you that photons have (relativistic) mass $m=\frac{hf}{c^2}$, why gravity does not accelerate it? Since quantum mechanics give you that photons have (relativistic) mass $m=\frac{hf}{c^2}$ why gravity does not accelerate it?? I know it changes its energy hence its frequency hence its wave le... | For a photon travelling toward a gravitational source, MC Physics would suggest that gravity would increase the kinetic energy of the rotation of a photon (ie., increase its frequency) and not its linear KE and velocity, which is limited by relativity.
For a photon travelling away from a gravitational source, MC Physic... | {
"language": "en",
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Why is nuclear force spin dependent? Why nucleons with parallel spins have greater nuclear force than the ones with anti-parallel spins?
I just want a clear and easy explanation. Thank you!
| Because of nature. Together with their positions, their isospins etc., the spins of the nucleons are degrees of freedom you might want to consider.
Since the aim is to reproduce experimental results, as @AMS said, using a potential which has the right spin dependence you are able to get some reasonable values for the v... | {
"language": "en",
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Are White Holes the inside of Black Holes? I read about a theory that says that The Big Bang could be actually considered a White Hole.
Than I started thinking. White Hole: an unreachable region from which stuff can come out. Black Hole: a reachable region from which no stuff can come out.
Well one seems to be the boun... | A black hole is very reachable from the outside. Once inside you can't get back. You quick fall to the center and are crushed at a singularity.
A white hole is a black hole running backwards in time. If you are inside, you can't avoid being expelled away from the singularity to the outside. Once outside, you can't get... | {
"language": "en",
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A question about the definition of proper length As I understand it, the proper length of an object is defined as the length of the object in its rest frame. In terms of the metric it is defined as the length of the spacetime interval between two space-like separated events, i.e. $$dl^{2}=\sqrt{ds^{2}}$$ (with the "mos... | When two guys are in the same reference frame then events for both of you occur at the same time coordinate - ie they are simultaneous. What I mean by this is that both guys will ascribe the same time coordinate to when an event A occurred. Of course depending on how far they are from A means they have to use different... | {
"language": "en",
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Is Moseley's law related to the Bohr model? Moseley's rule states
$$\frac{hc}{\lambda} = (Z-\sigma)^2 R (\frac{1}{n^2}-\frac{1}{m^2})$$
In what way is this linked to/derived from the shell model (which I assume means the Bohr model)? My textbook says they are related.
| First, consider an atom consisting of one electron orbiting a nucleus with atomic number $Z$. Since this is a hydrogenic atom, the energy levels of this electron are equal to
$$
E = \frac{Z^2 R}{n^2}
$$
for $n = 1, 2, 3, ...$, where $R$ is the Rydberg energy. If the electron goes from level $n$ to level $m$, it will... | {
"language": "en",
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What is the potential in a circuit? I have learnt that the potential in a point in an electric field is defined as being numerically equal to the work done in bringing a unit positive charge from infinity to the point. However, this is in the case of an electric field. What is the potential in a circuit say, consisting... | Usually one doesn't discuss potentials at a plate of the capacitor. One discusses the "potential difference" between the two plates of the capacitor. "Voltage" is always a difference between one point and another.
The voltage on the electricity supply in your house is the difference in potential between the line on th... | {
"language": "en",
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Resources for astrostatistics Being an astrophysic grad student with mathematical background, I have recently become interested in the field of astrostatistics. I know that this is a quite new field that combines astrophysics, statistics and data mining due to the huge amount of data that our telescopes are able to gen... | Profs. Eric Feigelson and Jogesh Babu at Penn State are widely seen as "Godfathers" of astrostatistics. Every year, they run the Summer School in Statistics for Astronomers which I attended in 2014.
The summer school's web page is publically accessible, and lecture slides and materials for exercise sessions in R with ... | {
"language": "en",
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Difference between "Periodic motion" and "Oscillating Motion" So far I know one of them is a special case of the other: The Oscillating motion being the special case of Periodic motion. But I don't know the precise "Kinematical definition" of each one. I mean when you have an "Equation of motion" for a particle, how wi... | From a physical stand point they are very similar. When we consider the orbit of a planet around a star, we consider its period. Hence, orbits are periodic in nature. We don't refer to the oscillations of the planet.
In contrast, say we have a spring with a mass attached, and set it out of equilibrium. We don't typical... | {
"language": "en",
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Breaking down sawdust pellets causing heat We just discovered that pellets (sawdust, animal feed, organic constituents) when re-hydrated give off heat. We understand this at molecular levels but are having a hard time sussing this out at a macro level. Do these pellets (pellet stove sawdust type in particular) absorb... | Nono. What you're assuming is wrong.
Hydration enthalpy is what is behind the scene, and its macro because it's Thermodynamics. Whenever you hydrate the sawdust particles, hydration enthalpy is given off which is what you've observed.
| {
"language": "en",
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Given that ice is less dense than water, why doesn't it sit completely atop water (rather than slightly submerged)? E.g.
*
*If we had a jar of marbles or something else of different densities and shook it, the most dense ones would go to the bottom and the less dense ones to the top.
(Image Source)
*If I put a cube... | People have been answering based on force balance, but there's an equivalent (and, in my opinion, more satisfying) answer based on energy conservation.
Suppose the ice cube is initially just on top of the surface of the water. If you lower it a tiny bit into the water, a tiny bit of water will be forced to move up, inc... | {
"language": "en",
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"source": "stackexchange",
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Magnetic focusing of microfocus X-Ray tube I've got this Russian X-Ray tube - BS-5. It has specified focus spot size of $\approx 6~\mathrm{\mu m}$.
It works, but I've seen brief mentions that in order to reach specified $6~\mathrm{\mu m}$ spot size one should use magnetic focusing. Does anyone have any guideline/link... | Looking around on the internet a bit, I found several resources that may be of interest.
*
*A patent, online here, that is for the magnetic focusing of x-ray tubes. It includes a nice description, as well as references and diagrams. According to the description,
A primary object of the invention resides in the pr... | {
"language": "en",
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"source": "stackexchange",
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Variation of electromagnetic action to obtain Maxwell's equations The electromagnetic action is given in the language of differential forms by
$$S[A]=-\frac{1}{4}\int F\wedge \star F$$
The variation of the electromagnetic action $S$ gives us Maxwell's equations
$$d\star F=0.$$
How do you take the variation $\delta S =... | Here we only consider the abelian case. Let $A\to A+\delta A$, and $F\to d(A+\delta A)=dA+d\delta A$.The action becomes
$$S[A+\delta A]=-\frac{1}{4}\int (dA+d\delta A)\wedge\star(dA+d\delta A).$$
So up to terms linear in $\delta A$,
$$S[A+\delta A]-S[A]=\frac{1}{2}\int \delta A\wedge d(\star F)+\mathcal{O}(\delta A^2... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Problem with physical application of Dirac Delta Consider the problem of projectile motion in 2 dimensions. Launch angle is constant. Range of projectile, $x$, then depends only on launch speed, $v$, and is given by
\begin{equation}
x=v^2, \quad v\in [0,1] \tag{1}
\end{equation}
Above equation has been non-dimensionali... | Answer offered by @Qmechanic, that Dirac delta function depends also on the functional form of its argument, is correct in regard to $\textit{dimensionless}$ equations. Answer offered by @ACuriousMind, that dimensions of Dirac delta correctly dictates the functional form of its argument, seems to work when dealing with... | {
"language": "en",
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What's a "colour triplet fermion"? I'm not a big fan of Science Alert, but this recent piece about the so-called SMASH model, whose gory details are apparently presented in arXiv:1608.05414 seems reasonable. I'm curious about this "Standard Model Axion Seesaw Higgs portal inflation" model, which they summarize it as fo... | A colour triplet fermion is simply a fermion that behaves like a quark with respect to the strong force, i.e. it transforms in the triplet (or fundamental) representation of the $\mathrm{SU}(3)$ gauge group of the strong force, often denoted $\mathbf{3}$. That this is indeed the meaning here can be seen on the bottom o... | {
"language": "en",
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Where does gravitational energy come from? We've all heard mass tells space how to curve and curved space tells matter how to move. But where does the energy to curve space come from? Likewise where does the energy that curved space uses to push planets around come from? I mean if I tell my son to clean his room, an... | The theory of General Relativity works with the energy momentum tensor and one has to work with the mathematics of it in order to really understand what is happening, not handwaving. It is a fact that all cosmological and astrological data follow the general relativity equations, as one can see in this link
The cosmol... | {
"language": "en",
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Is time absolute? If I take a spaceship and park it near the event horizon of a black hole and then measure the age of the universe by observing SNe Ia, then travel back out to normal space (no gravitational forces, at rest with respect to CMB), will the dates agree? That is, if the measured age of the universe is 13.8... | Well, no. We can construct a much simpler example to see this: fix a point in Minkowski spacetime, and consider two observers following worldlines from that point with a relative velocity. They can even both be inertial. At fixed Minkowski time the two observers measure different proper time.
The FLRW universe, however... | {
"language": "en",
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Jordan-Wigner transformation v.s. Bosonization Jordan-Wigner transformation is a powerful tool, mapping between models with spin-1/2 degrees of freedom and spinless fermions. The key idea is that there is a simple mapping between the Hilbert space of a system with a spin-1/2 degree of freedom per site and that of spinl... | I take a different stance than Qmechanic: bosonization is `simply' the continuum version of the Jordan-Wigner transformation. Of course Qmechanic is right in that field theories are much more subtle than lattices theories. Nevertheless, the fact that JW is so simple does not mean it is not relevant when thinking of bos... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Physics of variable settings on microwave ovens I've been learning how microwave ovens work and haven't been able to find any information on the practical way manufacturers create variable power settings.
If I understand magnetrons correctly they are only designed to emit one wavelength/frequency, so is there somethin... | Most microwave ovens simulate variable power by cycling full power on and off. However, some microwave ovens have truly variable power that is applied uniformly during the entire cooking time. These ovens are sold as having "inverter" technology. What they do is first change the 120 V / 60 Hz input power to something ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/291102",
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How much information can you obtain from a pulsar-black hole system? Imagine that we have detected an interesting source in the sky that we believe is generated by a pulsar orbiting a black hole.
The challenge here is the following:
What physically relevant information could you extract from the observation of this sy... | Well, you could try measuring the gravitational waves emitted from the system. If we assume an order-of-magnitude approximation for the strain $h$ as
$$h\sim\frac{1}{R}\frac{GM}{c^2}\left(\frac{v}{c}\right)^2$$
where $R$ is the distance to the source, $M$ is the sum of their masses, and $v$ is the orbital speed. For a ... | {
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Nuclear Shell Model - Spin of Nucleus I want to define the spin of the following nuclei: $^{15}_{\phantom{1}7} \textrm{N}$, $^{27}_{12} \textrm{Mg}$ and $^{47}_{20} \textrm{Ca}$. I have a scheme for the niveaus of the energies, see below:
Where left is for protons and right column for neutrons. I am not really sure ho... | The scheme is:
For a nucleus at the ground state, when the shells are full for one kind of nucleons, and
*
*The other has the last shell with only one nucleon, the nucleon
total angular momentum (in $1p_{1/2}$, this is 1/2) is the nucleus spin.
The reasoning is that all the others give angular momentum $0$, so $| \v... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/291345",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Why are angular frequencies $\omega=2\pi f$ used over normal frequencies $f$? When we first studying vibrations in crystals we begin by studying the monoatomic chain, and then go onto the diatomic chain with a series of alternating masses. In studying these we look to calculate the dispersion relation, which is the ang... | You are right in noting that $f$ is the more "physically intuitive" quantity, and at the end of the day measurements typically done in $f$, not $\omega$. However, the relationship between $f$ and $\omega$ is always $2\pi f = \omega$, so it is a very simple conversion to the point where people operationally don't really... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/291481",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 2,
"answer_id": 0
} |
Degeneracy of $\left|\pm k\right\rangle $: because of reflection symmetry or time reversal symmetry? Consider a free particle in one dimension. The Hamiltonian is
$$ H = p^2/2m . $$
It is well known that the momentum states $\left|\pm k \right\rangle $ are degenerate.
The problem is, are they degenerate because of ... | In general (i.e. ignoring coincidental degeneracy), eigenvalues of Hamiltonian are degenerate if there exist two operators which commute with Hamiltonian (so their corresponding observable is conserved), but which don't commute with each other.
A free particle has two non-commuting conserved quantities: parity and mome... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/291565",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
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