Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Does gravity have anything to do with Van Der Waals forces? Does gravity have anything to do with Van Der Waals forces? Just throwing this out there, I was wondering if they do because gravity is such a weak force and the VdW forces at the molecular level could seem to be a good intermediary force between gravity and t... | An author called Zhang has indeed suggested they are related: https://arxiv.org/abs/1303.3579. As Zhang alludes to, "dark energy" is basically the new cosmological constant.
And I have seen other work by an author called Dmitriev - https://arxiv.org/abs/physics/0611173 - that suggests gravity is experimentally dependen... | {
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Varying pressure in container with aperture The following diagram pictures a simple container filled with water. At the bottom of the container is a chamber with bottom B. Also directly above the chamber is an aperture that can completely open and close, sealing off the lower chamber or allowing unrestricted water flow... | What one could think is that what makes the pressure increase underwater is the weigh of the water column above it.
That is half true. In fact, it is the whole water above that pushes. So the water above the aperture also pushes.
So the pressure doesn't depend on the size of the aperture (at least when the equilibrium ... | {
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What is the universal definition of the order parameter that is valid irrespective of the nature of the phase transition? Plausible definition Consider a phase transition from phase 1 to phase 2. The order parameter is zero in one of the phases 1 or 2 and nonzero in the other.
For example, in normal (phase 1) to super... | The order parameter is discontinuous for first order phase transition at the transition point. However, it need not be zero in any of the phases between which the first order transition takes place. For example, the liquid-to-gas transition or vice-versa below $T_c$, the order parameter is $\rho_{liq}-\rho_{gas}$, is n... | {
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Why does acceleration due resulting force depends on mass while acceleration due gravity doesn't? Objects intrinsically resist to be accelerated due to their masses. A clear example would be kicking a soccer ball vs kicking a bowling ball. The latter ball will resist much more to be accelerated than the first one due t... | Because measure of inertia (mass $m$) and the gravitational charge (mass $m_g$) happen to be the same.
That's a good question, actually, even if not that clearly formulated.
From Newton's 2nd law, $F=dp/dt$, with constant net force and mass, one gets
$$a=F/m$$
And Newton' gravitation law says that $F_g= GMm_g/R^2$, so ... | {
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Does increasing the resistance in a branch of a parallel circuit decrease the overall current?
In the above question, why does R3 increase? If R2 increases, wouldn't the parallel combination's resistance increase? If so, wouldn't the circuit have less current? Then why would the voltage across R3 increase?
| When "the circuit has less current", then there will be a smaller voltage drop across R1. It's (a little bit) harder to calculate the currents in the individual branches R2-4, but you don't have to. If the sum of the voltage across R1 + R2-4 is constant (that is not explicitly stated, but I will assume you have a const... | {
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If someone were to put really small objects 10x spaced on a background, would they see the objects or the background? If someone were to put a sheet full of 1 micron x 1 micron black squares as a grid on a white piece of paper, and spaced them 10 microns apart (up-down, left-right, obviously diagonal doesn't count), wo... | American pop artist Roy Lichtenstein made some relevant art:
^Above, if you are close enough to the image, you can clearly see black dots on white background
^Same image, just resized... the face appears gray instead
So in general, the answer to "How do black dots on white paper look?" will depend on viewing distance... | {
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Definition of symmetrically ordered operator for multi-mode case? As I know, Wigner function is useful for evaluating the expectation value of an operator. But first you have to write it in a symmetrically ordered form. For example:
$$a^\dagger a = \frac{a^\dagger a + a a^\dagger -1}{2}$$
For single mode case where the... | Symmetrically order expansion of the ladder operator is written as follows;
a1b1=1/2(a1b1 +b1a1)= a1b1+1/2
a=creation operator b= anihilatinoperator, also
a1b1a2b2=1/2(a1b1 +b1a1)1/2(a2b2+b2a2)= (a1b1+1/2)(a2b2+1/2)=a1b1a2b2+1/2(a1b1)+1/2(a2b2)+1/4
| {
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Could a computer unblur the image from an out of focus microscope? Basically I'm wondering what is the nature of an out of focus image. Is it randomized information? Could the blur be undone by some algorithm?
| In this article the limits of the details that can be recovered using deconvolution are derived. It's explained that noise leads to limits on how effective deconvolution can be to recover details. In the ideal case there will only be Poisson noise due to the finite number of detected photons. The smallest recovarable d... | {
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Moment of a force about a given axis (Torque) - Scalar or vectorial? I am studying Statics and saw that:
The moment of a force about a given axis (or Torque) is defined by the equation:
$M_X = (\vec r \times \vec F) \cdot \vec x \ \ \ $ (or $\ \tau_x = (\vec r \times \vec F) \cdot \vec x \ $)
But in my Physics class I ... | Torque (Force Moment) is a vector that describes the location of the Force line of action.
*
*Lemma: If you give me a force vector ${\vec F}$ and a moment vector about the origin ${\vec M}$ then I can define a line whose points obey the relationship $\vec{M} = {\vec r} \times {\vec F}$. This line has direction parall... | {
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Why does an yellow object absorb blue instead of all colors other than yellow? I've always thought that an object appears to be of certain color X because it absorbs all other colors and reflects only X. But my current textbook(and some quick googling) tells me this is not the case.
As far as our eye is concerned, the... | @Mike already explained the color bit, but no one yet did quite answer "what's happening to all other frequencies".
Typically, for pigments, those photons get absorbed by the material of the object and converted to heat, as detailed in a very accessible manner in The Physics Classroom and here.
Another way photons can ... | {
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Special Relativity: Does non inertial frame of reference work in SR? I started on my own learning about GR and SR two months ago, and I still do not have clear if it is possible or not. The following example was explained to me by someone who affirmed: "SR applies only on inertial reference frames":
Let's imagine we ha... | The claim that a certain physical theory "applies only in inertial reference frames" is not even logically possible. "Physical theories" describe physical quantities, which by definition are independent of one's reference frame or choice of coordinates. At most, one could claim that "many of the equations found in stan... | {
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How does a man inside bubble ball accelerate without an external force? As Newton's Laws states an object should be in rest or in constant velocity if no external force is applied. A man inside a stopped car cannot push the car as he is not giving any external force.But a man inside a bubble ball can make it move. What... | By moving his weight around inside the bubble ball, and utilizing friction between his body and the ball, coupled with friction between the ball and the ground, the man can cause gravitational force to topple the ball and move it over the ground.
If the center of mass of the ball moves to one side of the ball, gravity ... | {
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Time dilation from different frames of reference I am trying to understand time dilation as a total newbie. This question is all about my trying to understand enough such that in a work of fiction an offhand comment (about FTL being a bit silly) makes sense.
If a ship were to travel for a period of say 25 years at a ve... |
Obviously "ship B" would experience 25 years of waiting plus 1 day of travel before they meet. Would "ship A" experience 25 years plus 1 day, or much more time?
Well that is quite simple:
A travels 25 years then waits N * 1 days,
where N is how many times faster A's clock runs, according to A. (How many days A's clo... | {
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How could I measure the colour spectrum of a light bulb and investigate how closely it matches a black body radiation curve? Here is my research question:
What is the colour/spectrum produced by each globe type? What is the temperature equivalence? How closely does a globe match a black body radiation curve?
I will b... | If you need to do the experiment yourself, and you dso not have a spectrometer available, you can make a crude spectrometer using a diffeaction grating and a cylindrical lens. Make a thin slit in a piece of black paper, and let some of the light from your bulb pass through the slit. Put the diffraction grating again... | {
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Speed of electrons in a wire What is the speed of electrons in a copper wire, used to charge a device? If there is a fixed speed, how is it determined?
| There is no point in speaking about the "speed of an electron in a copper wire". You may ask the drift velocity of the electron under an applied potential. The electrons are randomly scattered by phonons (lattice vibrations) as well as the metal ions. Under an applied field, in addition to the thermal random motion, th... | {
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Observing Two-Beam Interference at Home I want to know how difficult it would be for me to observe two-beam interference at home.
I have:
*
*A laser pointer.
*A non-polarizing beam-splitter.
*A mirror.
*Two concave lenses.
*An uneven shaky floor, some chairs, and tape.
*Patience that spans an entire day.
Thi... | I think you need less than that, though my setup may result in a very narrow viewing region.
A concave lens form a virtual image behind it, reflect the image with a mirror and you get two point sources.
| {
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Pure geometry proof of parabolic mirror property Is there a proof of the property that parallel rays of light incident upon a parabolic mirror converge to its focus that does not resort to Cartesian coordinates?
| Yes, there's plenty such proofs, but the choice between them depends on which of the multiple equivalent definitions of a parabola you take, and exactly what restrictions you place on the allowed proofs.
Physicists normally think of parabolas as the locus of equations of the form $y=x^2$, but you're explicitly looking... | {
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What does the spikes and curves in the spectral graph for compact fluorescent lights represent?
I have read from sources that the curves are generated by the phosphors in the bulb, and the spikes are caused by the mercury vapor.
However, if the mercury vapor's release of uv particles combine with the phosphors to prod... | A fluorescent lamp is filled with mercury (Hg) gas. When you switch on the lamp the gas starts emitting light. However in contrast to the sodium lamps which are widely used in street lighting (the orange lamps), mercury emits UV light (mainly 254 nm) which is not only invisible for us, but could also harm us in the sam... | {
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How fast can you spin a proton or electron without breaking it? If you spin a single nucleus containing multiple nucleons fast enough it will fly apart.
Is there a speed limit to a spinning proton or electron assuming it's held at a fixed location with a strong magnetic field?
What speed would either have to attain bef... | You can't spin up an electron. The only way that is possible is if as a string you can put angular momentum on it that way. The energy required to do that would be near Planck scale energy. So I will say this is not possible with the electron FAPP.
For the proton you can spin it up. This is the Regge trajectory that ha... | {
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Can transverse sound waves be polarized? I know that polarization only occurs in transverse waves and polarization of light occurs as EM wave is a transverse wave. But sound waves are both transverse and longitudinal in solids. So can polarization occur for the transverse part? But we cannot stop the sound wave from pr... | "Sound" is a pressure phenomenon, and has no polarization.
It is possible to send acoustic shear waves through an elastic solid (and that transverse component can have a direction) - but not through a gas.
Just to confuse you more - in an anisotropic medium, different directions of shear may propagate at different velo... | {
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Traveling Wave Equation $\sin(kx-wt)$ vs $\sin (wt-kx)$ In my textbook most if the times it uses $A\sin(wt-kx)$, but occasionally there is a problem using $A\sin(kx-wt)$
So i just changed it from $A\sin(kx-wt) \to -A\sin(wt-kx)$
but does the amplitude change to $-A$?
Is the wave going downwards first?(as negative ampli... | Yes that is correct.
If we look at the addition formulae for sine functions we see that $$\sin (A - B) \equiv \sin A\cos B - \cos A\sin B$$ and that $$\sin(B-A) \equiv \sin B\cos A - \cos B\sin A$$We can easily see that the second equation is just $-1$ times the first equation. By adding amplitude all we are doing to t... | {
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What is an order parameter? Thermal average or spatial integral of a thermal average? Sometimes the the order parameter is defined as the thermal average of a spatially varying field $\textbf{m}(\textbf{x})$ i.e., $\langle\textbf{m}(\textbf{x})\rangle$.
Sometimes the order parameter (density) is defined as the spatial ... | In the magnetic system, most of the time, people just calculate the thermal average of the magnetization at an arbitrary spatial point, say, $\langle m(\mathbf{x}) \rangle$. If you want to get the $M$ (the total magnetization), you just need to do a spatial integration over that.
In your problem, I think the authors ar... | {
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What does the refractive index for e.g. alpha mean? When I look for some materials like https://en.wikipedia.org/wiki/Barium_sulfate and want to extract the refractive index then there is written: (nD)=1.636 (alpha). And sometimes also for beta and gamma.
What does this mean? The refractive index is mostly dependent on... | The Greek letters are not related to wavelength but to the directions in crystals. In anisotropic crystals the speed of light (and so the index of refraction) depends on the polarization of light and the direction of propagation relative to the crystalline axes. As your link shows, Barium sulfate has an orthorombic str... | {
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Does a glass of water at room temperature emit (infrared?) radiation While reading the introduction to Feynman's lectures, it's mentioned how a glass of water cools down through evaporation, when some molecules get a bit extra energy and break free. If it's not a closed system, energy will be gradually taken away from ... | As @lemon explained, every body emits electromagnetic radiation if its temperature is above absolute zero
The peak wavelength of the radiation emitted by a blackbody is given by Wien's law: $$\lambda=2900/T$$ where T is the temperature in K, and the wavelength ($\lambda$) is in $\mu m$.
For a temperature of 300K (27C)... | {
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Two-dimensional collision conservation of energy According to wikipedia (https://en.wikipedia.org/wiki/Elastic_collision), and the sources cited in the article, the new velocity after a two-dimensional, elastic collision, can be calculated by rotating the reference frame so that components perpendicular to the line of ... | We can write the kinetic energy of a particle moving in 2 dimensions as $$E=\frac{1}{2}mv^2=\frac{1}{2}mv_x^2 + \frac{1}{2}mv_y^2$$
Where $v_x$ and $v_y$ are the perpendicular components of velocity. If we take $v_x$ to be the velocity perpendicular to normal, the conservation of energy for $2$ colliding particles $1$... | {
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How to tell if spherical waves reach infinity? Say you consider spherical waves (momentum eigenstates) propagating outwards from some starting point $r = r_{0} $ (not defined for $r < r_{0}$) with $k \in \mathbb{R} $:
\begin{equation}
\psi\left(r, t\right) = \left( A {e^{ikr} \over r} + B {e^{-ikr } \over r } \rig... | As stated, your question does not have a well-defined answer. If you had a definition for what you meant by "reaches infinity," then we would have something to work with.
Certainly the wave $\psi$ is not eventually $0$ as the term $e^{ikr}$ keeps it alive for infinitely many $r$. On the other hand, as you note, the lim... | {
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What are practical uses of over-damping? We have been given this task of preparing some small research on critical damping and comparing its behaviour and uses with over-damping. I am done with everything else but have been unable to find practical uses of over damping. It'd be great if someone could explain where it's... | 'Critical Damping' is a descriptive term given to 2nd order linear dynamic systems where the damping factor is ~ 1.0. And for the 2nd order system critical damping provides a settling towards your equilibrium point as quickly as possible without overshoot or bouncing about the equilibrium state: a smooth however rapid ... | {
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Why are there more trapped protons during solar minima? Reading about trapped protons and eletrons in van Allen belts, I get the understanding that the number of trapped electrons increase during a solar maximum (which I find logical because we have more solar flares etc.), but that the number of trapped protons increa... | Without the influence of an external force, the protons will happily gyrate around the magnetic field while bouncing from pole-to-pole as they drift around the Earth in the radiation belts. During a geomagnetic storm, the Earth's field changes rapidly causing protons in the radiation belts to either precipitate into t... | {
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Does work done depend on the frame of reference? Suppose I am sitting on a bench and looking at a moving car. Force is applied on the car by its engine, and it makes it displace, hence some work is done on the car. But what if I am sitting in the car and looking at the bench? The bench covers some displacement, but who... | Wikipedia says
In physics, work is the product of force and displacement.
Or to put it mathematically $$\overrightarrow W =\int_{\overrightarrow x_{i}} ^{\overrightarrow x_{f}}\overrightarrow F\cdot \overrightarrow {ds}$$ here ${\overrightarrow x_{i}}$ and ${\overrightarrow x_{f}}$ are initial and final position vect... | {
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How much power in a lightning strike? The Biblical story of 1 Kings 18:20-40 relates how a lightning strike ignited a bulls carcass, as well as a wood pyre, both of which had been thoroughly wetted with abundant water. Is there enough power in a lightning strike to do this? Does the power of a mountain top lightning st... | A lightning strike can blow a tree or power pole into splinters. You can see it on Youtube. A "bolt from the blue" can strike from a cloud 10 miles away. Thunderheads reach up to 90,000 feet, so the height of a mountain makes little difference. Some of the deadliest strikes have been in the Tetons. Can what you read in... | {
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What are the k-vectors in Ewald summation? Ewald summation is a common technique for computation of forces on charged particles in "infinitely periodic" (crystalline) systems.
I'm trying to understand Ewald force calculation from this website. The below image summarizes the two contributions to the force on a given ato... | The $k$-space contribution is intended to be the reciprocal space. The mighty power of Ewald summation is to split a slow converging summation into two rapidly converging series: this trick is made employing the Fourier transform and evaluating the summation on the phase space.
The definition of the vectors $k$ are the... | {
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How can I calculate the sensitivity of a seismometer? I would like to know how to find the minimum ground motion a seismometer can measure, specifically if a certain seismometer can measure 1 micron/sec velocity. I have a few specs from the datasheet but I'm not a seismologist and am trying to figure out how to relate ... | The dynamic range in system design describes the relationship between full scale output to the noise floor. Signal levels below the noise floor cannot be measured directly. If the signal path is digitized the digital resolution would normally be taken into account for the noise floor assessment.
The full scale range ... | {
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What happens to photons over distance? According to this diagram:
And a few articles I have read, the number of photons emitted from a point source is exactly the same, and the reason why we detect fewer photons as we move away from the source is because the photons spread over distance. If that's true, then why is th... | As you suggest the fall in intensity with distance in water, ice, etc is because the photons are absorbed. If you did your proposed experiment in space you would indeed detect all 10,000 photons.
There is a minor complication that we need to be aware of. If you shine a beam of light through some material then the light... | {
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Closed container buoyant force A closed container of water contains a Styrofoam block attached to the bottom of the container by a massless string. When the system is accelerated upwards, what happens to the tension in the string?
Background: I am an MCAT Physics teacher and this question was on an MCAT. Assuming the... | First, how is it that Styrofoam can float?
Because when partially immersed in water the weight of the displaced water (upthrust) is equal to the weight of the Styrofoam.
If the Styrofoam is fully immersed why must it be tethered by a string?
Because the upthrust (weight of displaced water = mass of displaced water $\... | {
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Is the fact that 100 kPa equals about 1 atmosphere accidental? Typical atmosphere near sea level, in ambient conditions is around 100,000 pascals.
But the pascal, as the unit, is not defined through Earth atmospheric pressure. It's defined as one newton per square meter. The newton is $\rm{kg \: m}\over s^2$. So, $\rm[... | This is a coincidence. There's nothing about the atmosphere that would make it have a nice relationship with the Earth's rotation or diameter, or the fact that water is plentiful on the surface.
On the other hand, it's important to note that the coincidence isn't quite as remarkable as you note, because of a version of... | {
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What is the meaning of the Hermann-Mauguin symbol $R$? In the International Tables for Crystallography A, table 4.3.2.1, the trigonal lattices are identified as having space group IT numbers 143 through 167. However, only space groups 148, 155, 160, 161, 166, and 167 have $R$ in their Hermann-Mauguin symbols, the other... | All those spacegroups labelled with $R$ have two settings, one with a hexagonal unit cell and one with a rhombohedral unit cell. The complete notation would be e.g. $R3 :\!\!R$ for the latter and $R3 :\!\!H$ for the former. The standard setting is the hexagonal one.
Let's take the example of $R32$. In rhombohedral axes... | {
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Why is unit of pressure (psi) used to determine things like bite force of an animal? Whether in tv documentaries or journals, whenever they talk about an animal's bite force, it's measured in PSI anytime imperial units are used (ex: National Geographic, NIH Journal). Many even seem to highlight the fact that it's pound... | I absolutely agree with Jon Hilden. Bite strength is a torque. The limit of an animals bite must be a function of jaw muscle strength and jaw geometry, unless you're about to crush your teeth, which involves a whole different set of numbers than those given for bite strength (e.g., 30,000 psi vs. 150 psi). A couple of ... | {
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Klebanov-Witten and Conifold equation I'm a bit confused by some that is understood in the following papers: 1 and 2. I understood that there is a GLSM with fields $A_i,B_i$ with $i=1,2$ whose moduli space is the conifold described with the constraint $z_1z_2=z_3z_4$ (page 5 of 1). But when I define the "mesons" $z_1=A... | *
*The snippet you're looking for here is at the top of page 10. The conifold coordinates are of course never matrix-valued. When the $A_i$,$B_i$ are matrix-valued, the conifold coordinates are $z_i = Tr A_i B_i$.
*I'm not sure exactly where you're referring to, but I would suppose that it's because $W$ is not reno... | {
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How to show a sum of positive definite operators is still positive definite? Consider a Hamiltonian $H$ of the form
$$\begin{split}H&=\sum_{i,j}A_{ij}^\dagger A_{ij},\\
A_{ij}&=(1-\sigma_i^z\sigma_j^z)e^{-g (\sigma_i^x+\sigma_j^x)},\end{split}$$
where $g\in\mathbb{R}$ is a real parameter and $\sigma_i^x$ and $\sigma_i... | Three remarks. One, a sum of positive (semi)definite matrices is again positive (semi)definite. The proof is really easy. Let's work over the reals for simplicity. A matrix $H_I$ is positive definite iff for any vector $v$, we have
$$v^T \cdot H_I \cdot v > 0\,.$$
Now let $H = \sum_I H_I$ be a sum of a finite number of... | {
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What do they mean when they say that it does not require any work to move a charge from one point to another in an equipotential surface? In the textbook it says that no work is required to move a charge from one point to another on an equipotential surface. Do they mean work by the electric field or work by anything? ... | It takes work to transfer kinetic energy into the charged object and get it moving, sure. But if the object was already moving, it wouldn't lose any energy by moving along the equipotential. Furthermore, you could decrease the work needed to stop and start by just moving slower, with no work needed in the limit of infi... | {
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Do gases mix faster when of unequal temperature? Or,
Is my room aired quicker during winter?
I always feel that in winter, after opening the window, my study room becomes breathable quicker than in summer. Now, this is of course highly subjective, but even though I see no rational explanation supporting such a pheno... | There are a few things that would be going on here.
1. Convection
There's a common expression "heat rises". That is because things are heated, their density often lowers. In fluids (such as air and water), if there is a density difference in an open space, you will create a flow from high to low density (going from h... | {
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Does Earth's precession rate change with the seasons? As Earth's precession is caused by the differential solar, etc., attraction to its 'spare tire', then does the rate go to ~zero at the equinoxes and ~twice the average at the solstices? (preferred answer: yes :-)
Or is there some 'carry-over' 'precessional momentum'... | The contribution to the precession from the sun does depend on the time of year (basically because tidal forces have a azimuthal symmetry around the line connecting the bodies but no polar symmetry), but there is also a contribution of similar magnitude from the moon, so the overall effect has a more complicated time d... | {
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Has the curvature of spacetime been measured at the human scale? The curvature of spacetime has been observed many times from the deflection of light around massive astronomical objects. But has it been observed around small objects in a lab?
In the Cavendish experiment, the gravitational attraction between two masses ... | Yes it has, on 11th Feb last year - it did make many mainstream news reports. In one of the largest "labs" ever built, each arm is 2.5km long. I guess that fits the criteria "human scale" within certain limits.
http://en.wikipedia.org/wiki/LIGO
You may also read about various other methods here
https://en.wikipedia.org... | {
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Can quarks tunnel out of a proton? Can a virtual electron tunnel away from its antiparticle? I know that particles can tunnel through an impassable barrier. But what happens if a quark tunnels out of a proton?
Has that ever been observed?
And what about virtual particles?Can they tunnel away from each other?
| As you may know, it is only possible to tunnel if the barrier reaches a maximum and then starts decreasing again, so as to reach an area of potential < than the energy of the particle, where this can exist.
The quarks are bound by the strong force, which is quite weakly binding at very short distances ("asymptotic free... | {
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Bernoulli's theorem In Bernoulli's theoram as stream lines cannot intersect each other and even water is nearly incomprehensible then how is it possible to all the water which got in come out, eg 100 stream lines goes in from one side then 100 stream lines should come out the other end whereas the area is decreased and... | Stream lines have no radial dimension (width).
You can keep squishing them infinitely close together, because they just describe the motion of the fluid.
What you describe does have implications for continuity though. Since mass flow has to stay the same (no mass being created/destroyed), if the area decreases, the fl... | {
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Why is translation energy a continuum and not quantized? When starting the study of quantum theory, usually the teacher separates the functions in electronic, vibrational, rotational and translational parts.
As far as I know, we should solve Schrodinger equation for each movement; and as far as I know, rotational and ... | If you are in a finite system, translational energy is quantized as well.
The simple example is the infinite square well potential, which is just a finite one-dimensional free particle (also often called a particle in a box). The fact that the wave function must goes to zero on the boundary means that the energy level... | {
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Derivation of Newtons second law of motion from the principle of conservation of energy Is newton's second law a consequence of the principle of conservation of energy? How can we arrive at
net force = rate of change of momentum
using only the law of conservation of energy?
| Conservation of energy isn't strong enough to reproduce Newton's second law. As a counterexample, consider a situation with no potential energy, $U(\mathbf{x}) = 0$. There is no force, so according to Newton's laws, the particle should move with constant velocity, $\mathbf{x}(t) = \mathbf{v}t$. But conservation of ener... | {
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Why is energy usually concentrated on low frequency modes in dynamics? In all structural dynamics applications I have seen, the motion is mostly governed by low frequency modes. For example, a pretty accurate approximation of buildings dynamics can be obtained with the two or three lower frequency modes, provided the m... | I believe there are two factors in play:
*
*Ease of excitation. If you have wind driving a tall building, there is a force along the entire length of the building. This is most likely to excite the lowest frequency mode - in order to drive a higher mode, the driving force must be out of phase between different parts... | {
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Why do the clouds near the horizon appear two dimensional? Look at the photo. The clouds right above us seem real, but those near the horizon appear as if they are from a painting.
They lack depth and are visually flat. Why is that?
| I believe it's because of two reasons: relative distance and angular size. If we see cumulus clouds near overhead (stratus clouds would be a separate argument due to height and shape), they're relatively near and apparently 3D. But on the horizon in any direction, much further away and generally speaking smaller angula... | {
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Would mechanically moving electrons create a super-strong magnetic field? According to this Veritasium video, the magnetic field in a wire with a non-zero current is an artifact of special relativity. A moving charge sees a speed difference between the wire and the electrons in it (since the electrons are moving). Due ... | The magnetic field is created by a current as in the number of electrons per second. The speed of the electrons is thus irrelevant, only the current value in Amperes is important. Therefore the problem you are describing does not exist. However, if you rotate charged objects, such as by attaching them to a fan, they wo... | {
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When is the heat transfer between a solid and fluid conduction or convection? I know that the heat transfer between solids and liquids occur via both conduction and convection.
However, I am not sure about the fine line that separates them. For example, what is the mode of heat transfer when a hot piece of steel is pu... | I will use the term fluid, that refers to both liquid and gas phase.
It is conduction if single fluid particles transport heat via Brownian motion. It is convection if a macro scale movement of fluid particles is involved. Usually both are playing a role, but for smaller differences of fluid and solid temperatures cond... | {
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Why is the S-Matrix element essentially the residue of the Green function (LSZ formula)? On Wikipedia, quite similar to the script I am following the LSZ formula is given as
$$
_{out}\left<p_1,...,p_n| q_1,...,q_m \right>_{in} =\\
\int \prod_i^m \left(\textrm{d}x^4\, i e^{-q_ix_i}(\square_{x_i}-m^2)\right)\prod_j^n \le... | The argument is completely general. The right hand side of your equation should really have a limit, where the squares of the four momenta are taken to $m^2$; i.e., they are put on shell. Now, the correlation function is multiplied by $p^2-m^2$, so the only way the limit is gonna be nonzero is if the correlation functi... | {
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Is there a "square root" version of the Einstein field equation? It is well known that the Klein-Gordon equation have a kind of "square root" version : the Dirac equation.
The Maxwell equations can also be formulated in a Dirac way.
It is also well known that the metric of general relativity have a kind of "square roo... | *
*Since Nature has fermionic matter we are anyway ultimately forced to rewrite the metric in GR in terms of a vielbein (and introduce a spin connection). See e.g. my Phys answer here. The fermionic matter obeys a Dirac equation in curved spacetime. This however would not amount to a square root of EFE.
*There exist... | {
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Construct operator such that division of expectation values is equal to expectation value of the operator Is is possible to construct an operator $\hat{C}$ out of $\hat{A}$ and $\hat{B}$ such that:
$$\frac{\langle \psi|\hat{A}|\psi\rangle}{\langle\psi|\hat{B}|\psi\rangle} = \langle \psi|\hat{C}|\psi\rangle,$$
for any s... | Let's say that this equation holds for particular $|\psi \rangle$. Putting $N |\psi \rangle$ would result in:
$$
\frac{\langle \psi| \hat{A} |\psi \rangle}{\langle \psi| \hat{B} |\psi \rangle} = |N|^2 \langle \psi| \hat{C} |\psi \rangle
$$
Which of course can hold only for $|N|^2 = 1$.
| {
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What happens to the period of a pendulum if a spherical bob were to spin around the axis of the string? Consider a normal pendulum with a spherical bob oscillating back and forth. Would the period of the pendulum be longer, shorter or unchanged if the bob were to spin around the axis of the string that holds it?
| Rotation will create a gyroscopic tilting force perpendicular to the plane of oscillation, as the gyroscope "tries" to remain oriented the same way. This causes precession, giving the gyroscope oscillations of it's own.
Simplistically, It may be modelled as a compound pendulum, one pendulum on the end of another. Ther... | {
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Finite dimensional representations of Lorentz group I am trying to understand the topic in the title but I found some difficulties.
For example, I understand that $\left(\frac{1}{2},0\right)\otimes\left(\frac{1}{2},0\right)=\left(1,0\right)\oplus(0,0)$ which is a consequence of Clebsch-Gordan decomposition and the sca... |
[...]However, if i consider the following: $(\frac{1}{2},\frac{1}{2})=(\frac{1}{2},0)\otimes(0,\frac{1}{2})$, i don't understand how to decompose it. I know that represents a four vector field, with a temporal scalar component (spin 0) and vector component (spin 1) but i don't really understand why.
There is nothing ... | {
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Do fields describing different particles always commute? Is it true that field operators describing different particles (for example a scalar field operator $\phi (x) $ and a spinor field operator $\psi (x) $) always commute (i.e. $ [\phi (x), \psi (y) ]=0, \forall x,y $) in interacting theory?
Or is it true only at eq... | The Schrödinger-picture annihilators for different sorts of particle commute; so e.g. if you've got creation and annihilation operators for neutrinos as well as electrons in some sort of box, those operators commute across species but within one species do not commute with their adjoints.
Note that if you add time-depe... | {
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Variational Baeriswyl wavefunction for 2 dimensions I am reading this article.
The model hamiltonain of 2D square lattice for spinless fermions is written as:
$$H=H_{kin}+H_{int}=-\frac{J}{2}\sum_{<n,m>}c_n^\dagger c_m+\frac{V}{2}\sum_{<n,m>}n_nm_m$$
with J=hopping, V=interaction potential, $<n,m>$ nearest neighbor pai... | $H_{kin}$ can be written as:
$$\begin{bmatrix}c_k^\dagger & c_{k-\pi}^\dagger\end{bmatrix}\begin{bmatrix}\epsilon(k) & 0 \\0 & \epsilon(k-
\pi)\end{bmatrix}\begin{bmatrix}c_k \\ c_{k-\pi}\end{bmatrix}$$
and $\epsilon(k-\pi)=-2*t*\cos(k-\pi)=2*t*\cos k=-\epsilon(k)$ and at half-filling $Q=\pi$. As $c_k^\dagger$ and $c_{... | {
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Why are work and energy considered different in physics when the units are the same? There is a question that explains work and energy on stack exchange but I did not see this aspect of my problem. Please just point me to my error and to the correct answer that I missed.
What I am asking is this: Why in physics when ... | If your velocity changes from 5 m/s to 8 m/s, you say your velocity has changed by 3 m/s (assuming same vector direction) and your new velocity is 8 m/s. This seems like a very obvious statement; 3m/s represents change and 8 m/s the measure. In essence, a change in a vector or scalar quantity will have the same units a... | {
"language": "en",
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Location of lens having effective focal length We know a/c to Gullstrand's equation that the effective focal length of two lenses separated by a distance $d$ is given as $$\frac{1}{f_{eq}}=\frac{1}{f_1}+\frac{1}{f_2}-\frac{d}{f_1f_2},$$ but the equation doesn't clarify on the position of the lens having this effective ... | Well, the distance will simply be the EFL - i.e. given the position of the final spot/image the lens will be at the EFL distance.
| {
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If I say time is the fourth dimension am I wrong? As far as I know the prevailing view is that time is the fourth dimension, but I've read there is also a spatial fourth dimension and even higher spatial dimensions after that so I hesitate to say that time is the fourth dimension. So, if I say time is the fourth dimens... | Whatever you say you are almost certainly wrong (this is nothing personal). If history teaches us anything, it is that (despite our tendancy to be enamoured with our more recent achievements) any given theory is sooner or later proven to some extent "wrong".
Probably including that one, (but neglect that for now :-) )... | {
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Relationship between displacement field and dislocation density tensor Let $u$ denote the displacement field in a solid body $\Omega \subset \mathbb{R}^3$ in the realm of continuum mechanics. Suppose we know that the restriction of $u$ to the boundary $\partial \Omega$ is discontinuous i.e. $u|_{\partial \Omega}$ is no... | Consider a dislocation loop inside the body. There is no discontinuity of the displacement field on the boundary.
Consider now that a dislocation went through your body. The displacement has a jump even there is no dislocation in the body.
You may want to restrict $u$ to $u$ modulo $b$, where $b$ is the size of the Bur... | {
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Is energy $E$ in Schrödinger equation an observable/ Can $E$ be measured? Take this quantum approach to estimate mean energy of a molecule:
$$\langle\psi|H|\psi\rangle=\overline E$$
Question:
Is $E$ an observable? How we can compare it to an experimental value? i.e how to experimentally measure it and what are the stat... | That is the expectation value of the energy. $\hat{H}$ is the Hamiltonian operator which corresponds to the energy of the system. So by evaluating $\langle\psi|\hat{H}|\psi\rangle$, you get the expectation value of the energy. The expectation value is the average of measurements performed on particles that are all in t... | {
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Turbulence Model on Unsteady Navier Stokes I am asking you if the Unsteady (Time-Dependant) Navier-Stokes Equation is able to predict accurately the Flow Turbulence? I know that the RANS (with different Turbulence Models like Spalart–Allmaras, k–ε and k–ω models...) is the most used method for simulating the Turbulence... | Turbulence, being a random, chaotic, unsteady and 3D phenomena, is not straightforward to be computed. However, there are some approximations in the form of turbulence models that have made it possible to predict the flow.
The models you mentioned Spalart–Allmaras (one-equation model), k–ε and k–ω models (two-equati... | {
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Interpretation of Hubble Diagram
According to my professor's notes, this is the Hubble Diagram. Unfortunately, I do not know what the y-axis is referring to. Is it the absolute luminosity?
| The quantity $m-M$ is the difference between the apparent magnitude and absolute magnitude, and is referred to as the distance modulus, $\mu$. The relationship between $\mu$ and distance, $d$, is logarithmic, i.e.
$$\mu=5\log d+5+\text{corrections}$$
where the correcting terms account for observational effects. In cosm... | {
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Electric field charged disc and L'Hôpital's rule I have been looking at the electric field of a charged disk and have a question about the use of l'Hopital's rule for the limiting case of electric field at points along the axis $z\gg$ disc radius $R$.
$$E = \frac {q}{2\pi\epsilon R^2} \left(1 - \frac {z}{\sqrt{z^2+R^... | To use L'Hôpital you either have to solve a $\frac{0}{0}$ or $\frac{\infty}{\infty}$ kind of limit. I'll rewrite your expression to better show if this is the case:
$$E = \frac{q}{2 \pi \epsilon}\frac{\sqrt{z^2+R^2}-z}{R^2 \sqrt{z^2+R^2}}$$
(I just calculated the common denominator and separated the constants from the ... | {
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What is the total energy of the Universe? The Law of Conservation of Energy states that:
Energy can't be created nor can be destroyed. It only changes from one form to another.
According to this the total energy in a closed system never changes. I was wondering what this constant energy is when the closed system is t... | In fact, for our Universe, the total mass-energy and angular momentum are undefined and undefinable. In addition, note that the total mass-energy of a system in general relativity cannot be generally defined. There are, however, a few tools one can employ to measure the total mass-energy of a system in the case of asym... | {
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Distribution of loss in a transmission line to minimize power dissipation This post will ask how to distribute loss in a transmission line so that the line has a known total loss, while dissipating the least amount of power.
We'll refer to "gain" of a transmission line, but we're thinking of the case where the line is ... | Define
$$\Phi(x) \equiv \int_0^x dx\, \ln g(x) \, .$$
Note that $\Phi(0)=0$ and $\Phi(L)=\ln G$.
Then
\begin{align}
-\frac{P}{A_\text{in}^2}
&= \int_0^L dx \, \Phi(x)' \exp ( \Phi(x) ) \\
&= \int_0^L dx \, \frac{d \exp \Phi }{dx} \\
&= \exp (\Phi(L)) - \exp (\Phi(0)) \\
&= G - 1 \, .
\end{align}
Therefore, $P$ doesn't ... | {
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Does the temperature coefficient of a material depend on temperature? In my textbook, a relationship is plotted between the resistance of the material and the temperature, and the temperature coefficient is defined as the slope of that graph divided by an arbitrary resistance $R_1$ on the graph. Does that mean that the... | Yes,temperature coefficient of resistance depends on temperature to some extent. At small temperature changes resistance versus temperature graph is linear which implies temperature coefficient is independent of temperature. At higher temperature the graph is nonlinear which implies temperature coefficient is now not i... | {
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Use of negative frequency for the sake of simplifying mathematics? How can we use the idea of negative frequency for the sake of simplifying mathematics if negative frequency does not exist (to my knowledge) in nature ? For example, when plotting the spectra of a Fourier series.
| As other answers, if it makes the mathematics smoother or more tractable than equivalent mathematics without the use of negative frequency, why wouldn't you embrace the technique?
However, this is a physics site, so a more satisfying answer is going to give a meaning for negative frequency. Already you have the beginni... | {
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Physical explanation of Joule heating The heat $Q$ generated in a wire, for a current $I$ flowing through a wire of a given resistance $R$, for a time $t$ is given by $Q=\mathscr{k}I^2Rt$ where $\mathscr{k}$ is the proportionality constant. For a given wire the resistance R is fixed. Is it possible to explain physicall... | The pd, V, across the wire tells you how much energy is transferred to thermal in the wire per coulomb flowing. But the current, I tells you the rate of flow of coulombs. So VI tells you the energy transfer per second. Now here's the key thing: in a metal wire at constant temperature, I is proportional to V, that is $V... | {
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In physics sometimes we find energy that is negative. What does the negative sign indicate? Sometimes we see energy that is negative, for example, the energy of an electron in orbit. We know energy is something that can do something. In this view does negative energy mean something opposite someway?
| Take the simplest atom, the H atom. A hydrogen atom consists in a proton and an electron. When a proton and an electron bind to form a hydrogen atom, there is a release of energy. So in order to break the atom into its constituent parts, one has to provide an amount of energy. The amount of energy required to break the... | {
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Does providing more heat to a pan of boiling water actually make it hotter? Sometimes my wife has a pan of water 'boiling furiously'. Is the extra heat (wasted in my opinion) actually making any difference, apart from reducing the amount of water in the pan - which could be done by pouring some away?
|
Is the extra heat (wasted in my opinion) actually making any difference,
It is if you put a lid on the pot to retain the heat.
apart from reducing the amount of water in the pan
"all" the vigorous boiling"
*
*agitates the water (which can be important for cooking)
*indicate a hot burner, which will quickly brin... | {
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Directions of static & kinetic friction? Static friction :
Static friction opposes relative motion between two surfaces. The car is moving at some tangential velocity relative to the road. Thus, static friction should act in the opposite direction. Yet it acts down the incline rather than parallel to the motion of the ... | Why shouldn't kinetic friction increase the kinetic energy of the block?
It shouldn't increase the relative kinetic energy between the block and the plank; but because the friction isn't between the block and the static surroundings, there is no reason that it can't increase the kinetic energy of the block relative to ... | {
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Why steel can be blunted by ice? As an ice skater I cannot understand why I need to sharpen my blade very often since the hardness of steel is higher than that of ice for sure. Since steel is much harder than ice, how can ice change the shape of steel?
| Friction affects both surfaces. The material which is 'harder' is not immune to wear while the 'softer' material wears down. Both materials are worn down, to a different extent. Some of the ice breaks off the floor, some of the steel breaks off the skate.
The relative amount of wear depends (inversely) on the relative... | {
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Validation of Work-Energy Theorem Is the work-energy theorem valid when there's an impulsive force during motion of considered body?
For eg: Consider a man jumping from some height into a swimming pool of certain depth, if we apply work energy theorem from his initial position to final position (Change in Kinetic Energ... | Work requires both force and displacement. You could say that the displacement is a result of the force, which depends on the duration that the force is applied.
So work done might be small, even though a huge force has acted. If that huge force just applied at an instant, as an impulse, then the work is not as big as ... | {
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How to show barometer height is independent of area I have seen this question asked before (https://forums.studentdoctor.net/threads/please-help-explain-this-concept.724066/) however, I don’t fully understand the explanation given. I am trying to understand why a mercury barometer will always rise to the same height i... | Pascal's theorem states pressure is the same in all directions. This means that the pressure at the surface of the barometer dish is the same in all directions.
Bernoulli's theorem states that the sum of the inertial, potential and pressure components in a steadily flowing incompressible fluid is constant. Well, the ... | {
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Correction factor for my formula obtained by Rutherford scattering results I did an experiment on Rutherford scattering , finding the number of counts at an angle $\theta$. The problem is that I had a single sensor i.e. I measured the counts at a single position , and the scattering occurs over a cone. I was thinking o... | The angle $d\phi$ that your detector subtends (out of a possible $2\pi$) changes with $r$; if the circumference of the "hoop" is $2\pi r \sin\theta$, and the dimension of the detector perpendicular to the $\theta$ direction is $d$, then
$$d\phi = \frac{d}{2\pi R \sin\theta}$$
where $R$ is the distance to the detector.
... | {
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Why is electromagnetic wave (light) a sine wave? If I remember correctly solutions to the wave equation are any periodic function. My question is related to light.
Is there a reason why light waves are sine waves?
Theoretically where do sine waves come from as representation of a photon?
| In your comment to eranreches answer you ask
If we are able to measure the E and B fields in time of light would we measure sine wave?
Yes, if you accept a indirect measurement. Generating radio waves one accelerate a lot of electrons in the antenna rod and by this a huge number of photons in phase get emitted. Altho... | {
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Co and contravariant: tensors or components? I am learning Special Relativity and have a question: given a four vector $\vec{x}$ whose contravariant components are $x^\mu$, do the covariant components $x_\mu = g_{\mu\nu}x^\nu$ make reference to a different physical/geometrical object other than $\vec{x}$?
I mean, for ... | For orthogonal coordinate systems, the covariant and contravariant components are the same. The difference shows up when you have oblique coordinate systems. Here's a pretty good explanation of the difference with some illustrations:
http://www.farmingdale.edu/faculty/peter-nolan/pdf/relativity/Ch04Rel.pdf
| {
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Why is it "bad taste" to have a dimensional quantity in the argument of a logarithm or exponential function? I've been told it is never seen in physics, and "bad taste" to have it in cases of being the argument of a logarithmic function or the function raised to $e$. I can't seem to understand why, although I suppose i... | The reason your instructor called it 'bad taste' rather than just outright wrong is because people will do this all the time with the logarithm. The logarithm is unique because it lets you split out multiplicative factors into additive terms, so people will write something like
$$\log(r/r_0) = \log(r) - \log(r_0) = \lo... | {
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Commutator of intrinsic derivatives in NP formalism when timelike and null congruence are both given Suppose we have a congruence of affinely parametrized null geodesics (light rays), with tangent vector $\ell^a$, and a congruence of timelike curves (observers), with tangent vector $u^a$, such that the observers measur... | As usual when it comes to apparent contradictions like this, the error lies in an assumption. Specifically, when I say that $r$ is the null parameter of a congruence of null curves $c_1$ and thus $D = \partial_r$, what I am actually doing is taking a chart such that $c_1^{-1}$ is one of the coordinate maps. So far so g... | {
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Rationale behind the linearised Navier-Stokes equation Some applications of fluid dynamics consider the linearised Navier-stokes equation where the advection term $(\vec{u}\cdot\vec{\nabla})\vec{u}$ is dropped.
I am trying to build a convincing argument for this based on scale analysis. I tried to find something about... | This is exactly what we do to for the Stokes flow.
Instead of $P_0$, we use the dimensionless quantity, Reynolds number (Re), for linearising the Navier-Stokes in the limit $Re \rightarrow 0$.
Refer to the wiki page on Stokes flow and Reynolds number for more details.
| {
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Why does entropy explain why a colder object won't spontaneously give off energy to a hotter one? I'm very new to my studies of entropy, but in my view entropy is the amount of disorder in a system, which I know is unimaginatively true and not really demonstrative of any true understanding I might have on the subject. ... | I guess the focus needs to be put on the cold object. If we place a cold object in a hot environment, intuitively, we would say the cold object will not give heat out to its hot environment. Using the concept of entropy and $ds = \frac{\delta Q}T$, we find, if $\delta Q$ is negative, entropy will decrease, which violat... | {
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Tensorpart of NN potential The potential of the nucleon nucleon interaction includes a tensor part which is given by:
$S_{12}(\hat{\pmb{r}}) = \hat{\pmb{r}} \cdot \pmb{\sigma_1} \hat{\pmb{r}} \cdot \pmb{\sigma_2} - \frac{1}{3} \pmb{\sigma_1}\cdot\pmb{\sigma_2}$
Where $\hat{\pmb{r}}$ ist a unit coordinate space oper... | Consider the general symmetric rank 2 tensor:
$S_{ij} = \frac{1}{2}(T_{ij}+T_{ji})$
It has 6 independent terms. However, one of them is a scalar times the unit tensor:
$\frac{1}{3}{\rm Tr}({T})\delta_{ij}$.
so it doesn't really count as a rank 2 tensor part. The so-called natural form for a rank 2 tensor is:
$ T^{(2)}_... | {
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Can ferromagnetism be described by classical physics? It may sound as a trivial question, but I am very confused about the origin of ferromagnetism. According to Bohr–van Leeuwen theorem, ferromagnetism cannot be predicted by classical physics. Therefore quantum physics is required. Actually, people say that the quantu... | I have found the following interesting answer to the question, from "Introduction to the Theory of Ferromagnetism, Amikam Aharoni".
| {
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The electric field derivation from Liénard-Wiechert versus Griffiths are subtly incompatible I have a follow-up question from my answer to a previous question.
The electric field of a point charge moving at a constant velocity, as derived from the Liénard-Wiechert equation, reads
$$ E = \frac{q}{4\pi\epsilon_0} \frac{(... | I bought Griffifths's book and looked at his derivation.
I thought he had something wrong because I didn't read it carefully enough. His angle theta is not the angle I thought it was. We have the direction from the source at retarded time to the target, $n$. And we have the velocity vector, $v$. I thought theta was the... | {
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Is torque in an electric motor generated from repelling magnetic dipoles and the Lorentz force on a solenoid? So in an electric motor the torque is generated from the Lorentz force on the current carrying wire by the interaction with the outer magnetic field. There is also another interaction between the magnetic dipol... | The torque which you get via the Lorentz force comes out to be $BIA$ where $A$ is the area of the coil ie length $L$ times the width of the coil.
The magnetic dipole moment of the coil is $IA$ and the torque is the cross product of the dipole moment and the magnetic field which works out to be $IA\,B$ with the orient... | {
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Where does the energy for electron degeneracy pressure come from? I just watched a web video about white dwarf stars. It mentions that the star’s electrons flow among the degenerate matter. Since most of the electrons can’t be in the lowest state, due to Pauli’s exclusion principle, they get bumped to higher states and... | The answer is that you have to do work on the gas to compress it enough for it to become degenerate. The work done is $\int P\ dV$ and this work is used to increase the internal (kinetic) energy of the electrons.
In a white dwarf star, the work is done by the gravitational force. As the core of a proto-white dwarf shri... | {
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Light bulb longevity I have a summer home in North Carolina where there are more people in the summer than in the winter. Light bulbs seem to last longer in the winter when there is less demand on the system. I suspect the line voltage drops with the higher use. Would this affect the life of the bulb?
| The bulb life highly depends on the voltage. The lifetime is limited due to tungsten evaporating from the filament. This process is more intense at a higher voltage, especially because the heat power is proportional to the square of the voltage.
Having said this, the voltage usually drops with higher use, which is in s... | {
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How to find the direction of velocity of a reference frame where two events are simultaneous in case of a space-like interval Suppose in a inertial reference frame $S$, an event $A$ occurs at $(ct_A, x_A, y_A, z_A)$ and event $B$ occurs at $(ct_B, x_B, y_B, z_B)$.
Now the invariant interval of these two events is,
$$I... | This problem would have given me fits when I first learned relativity, but since I've started using the geometric point of view as the tool I reach for first it is almost trivial.
The direction is easy: boost in the direction from the earlier to the later event as measured in your current frame. Why? Because you want t... | {
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Geocentric frame of reference and superluminal speeds I have a couple of questions on frames of reference.
From my understanding, we can do math in an accelerating frame of reference as long as "fictitious" force terms are correctly added. From this point of view, is there anything wrong with viewing the Earth as stati... | You're right - but so too are the photons. They're moving "faster than light", too, in this frame!
You see, talking of "light speed limits" is really just pseudo-Newtonian mechanical heuristics on top of the actual gist of relativity theory, which is that information can transmit between some places in space-time and n... | {
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Information contained in a quantum simulation
The system in the picture has a box filled with $N$ classical particles which can either be on the left or the right side. Let this system have a Hamiltonian $$H= \frac{\mathbf p^2}{\sum 2m_i} + V(x, t) $$ where V becomes infinite at $\pm \frac{L}{2} $. Let it be represen... | In general, the entropy of a system is written
$$
S_\text{tot}=S_{EE}+S_\text{thermal}
$$
where EE denotes the entanglement entropy. In a thermal classical system, you have no ignorance associated with the possibility of states being entangled. However, a quantum computer simulates the classical system using some quant... | {
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When must an alien civilization send off a signal that can reach us today? Given the rate of expansion of the universe and the speed with which galaxies separate: Can a rough estimate be given, at which time T (in its proper time) a civilization that lives on a planet which is X light years away from Earth today would ... | What you are looking for is the size of the past lightcone of our present moment, trying to find the time $T$ when it is $X$ lightyears in radius. Measured in co-moving coordinates the distance is $$\chi(T)=c\int_T^{t_{now}} \frac{dt}{a(t)}$$ where $a(t)$ is the scale factor of the universe. Note that by now the expans... | {
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Eigenvalues of the exchange operator determined by the particle type (boson or fermion) in a two particle system While dealing with a two particle system in QM (the particles are identical),
the net wave function of the system would be simply the product of the wavefunctions of the individual particles in the given po... | The spin-statistics theorem relates the bosonic/fermionic nature of a particle to the type of exchange symmetry of indistinguishable many-particle wavefunctions. Possibly it is easiest to consider the consequences of this exchange symmetry in 2-particle systems.
For fermions, states must be antisymmetric so that
$$
\v... | {
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What is the Bandgap energy of Rubidium? Could anyone please tell me the bandgap energy for alkali metals like rubidium and cesium?
| An early paper is "Energy Bands of the BCC Metals rubidium and cesium", A. M. Radwan, Cryst. Res. Technol. 23(6) 785-791 (1988). The results shown are focused on the bands near the Fermi Energy. It shows the parts of the next higher band(s) that are overlapping with the conduction bands.
There is also "Method for Perfo... | {
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What is the equation of relative motion for two objects moving in straight lines? If two objects, A and B, are moving in the same direction along straight lines in a plane, they might be diverging, converging or moving in parallel.
If we wish to describe B's motion with respect to A, what is the equation of motion?
For... | As pointed out by other writers, the relative distance of B to A is given by $\vec{r'}=\vec{r_B} - \vec{r_A}$. So it is necessary to calculate the positions of both objects for a given time. The unit vector for the direction of the first object is $\vec{e_1} = \frac{3}{\sqrt{13}}\hat{i} + \frac{2}{\sqrt{13}}\hat{j}$ . ... | {
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} |
Why is work done equal to $-pdV$ only applicable for a reversible process? In thermodynamics, when we're interested at gases, I know that the work done can be written to be $-pdV$ for a reversible process ($p$ is the pressure of the system, and $V$ is the volume of the system).
This is because $$dW=Fdx=-pAdx=-pd(Ax)=-p... | Please note that work is always $-pdV$ irrespective of any method. It is valid for reversible as well as irreversible. But then how to obtain full expression for work? The expression $-pdV$ represents the infinitesimal quantity of work. So we need to get finite quantity of work. So, we need to look one step forward... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/369188",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 4,
"answer_id": 3
} |
What is the universal definition of 'inertia' in fields? In my physics class we recently did the Gravitational Field unit, and the idea of gravitational field strength was introduced:
$$g=\frac{F}{m}=\frac{GMm}{r^2}\frac{1}{m}=\frac{GM}{r^2}$$
After doing that unit, now we're on to Electric Fields, and the idea of elec... | This is an odd use of the term inertia. I would usually define the field strength as the force per unit charge, where the word charge refers to the property generating the field. Note that electrical charge is one form of the general term charge - the terminology can be a bit confusing. The term charge has a precise de... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/369335",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Mass and Newton's Second Law While trying to understand the second law of Newton from "An Introduction to Mechanics" by Kleppner and Kolenkow, I came across the following lines that I don't understand:
"It is natural to assume that for three-dimensional motion, force, like acceleration, behaves like a vector. Althoug... | Consider a solid sphere with mass $m_1$. Now lets say there is a hole through the center that runs horizontally from end to end. Inside this hole is another mass $m_2$ that slides without friction.
If you were to push the sphere horizontally you will have $F_x = m_1 a_x$. But if you push vertically you would get $F_y =... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/369817",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "23",
"answer_count": 8,
"answer_id": 7
} |
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