Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Is the classification of particles into matter and anti-matter arbitrary? It is well known that every fundamental particle has a corresponding antiparticle, and that – except for particles which are their own antiparticle – for practically every pair of particles and antiparticles, one type of particle predominates. W... | The definitions have a pure historic reasoning which has to do with the order of verification of the existence of particles. The names stuck in the scientific community because a radical redefinition of names to suit language would be impractical and confusing.
As for the grouping of particles, it has strong mathemati... | {
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"timestamp": "2023-03-29T00:00:00",
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Why does mechanical equilibrium depend only on potential energy? As far as I understand, for a system to be considered in equilibrium, the sum of the forces that is applied to it must be $0$:
$\vec F = 0$
which is
$\partial \frac{E_p}{\partial x}\bigg\rvert _{x=x_0} = 0 $
But it only depends on the potential energy, w... | Equilibrium here just means that if a particle is placed at the location $x_0 = 0$ with $0$ kinetic energy, it will stay at that location. Imagine another location, say $x_1$, such that $\nabla V(x_1)\not = 0$, if a particle is placed there, it will start moving, if the kinetic energy is zero initially.
A simple exampl... | {
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"timestamp": "2023-03-29T00:00:00",
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Schwarzschild geometry, what is physical meaning of coordinates? A past exam has a question:
For the Schwarzschild metric external to a non-spinning spherical mass, what is the physical significance to the coordinates $t,r,\theta,\phi$?
Not sure how to answer this question, I am thinking there is some obvious canonic... | Well, since the metric is assymptotically flat, in $\infty$, $t$ and $\tau$ do indeed coincide, so you can view the time coordinate $t$ as the time measured by an inertial observer at infinity.
The radial coordinate $r$ is actually more of an "areal" coordinate. Consider 2-surfaces of constanat $t=T_0$ and $r=R_0$. The... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/338280",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Where is a classical computer better than a quantum one? Where is a classical computer better than a quantum computer? Is there any known domain where classical algorithms always beat quantum ones, say, both in terms of time and space complexity?
If yes, could you please give me examples?
If no, could you please pro... | As fs137 answered, a quantum computer can simulate a classical computer, and so from a purely complexity theory perspective, the classical computer is never superior to the quantum in an asymptotic sense (assuming $P\subset BQP$, currently an open question).
However, quantum computers currently operate with very low nu... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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"question_score": "2",
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Probability depends on volume dependence of the multiplicity function? The formula for the multiplicity of a monoatomic ideal gas is
$$\qquad \Omega(U,V,N)=f(N)V^NU^{3N/2}$$
where $V$ is the volume of position space, $U$ is the molecule's kinetic energy, $N$ is the number of indistinguishable gas molecules and $f(... | Not really.
You want to calculate the probability to find all the molecules in the left half of the volume.
Since the probability density is
$$\rho(\{q,p\}) = c_N \frac{e^{-\beta H(\{q,p\})}}{\Omega(U,V,N)}\ ,$$
where, $c_N$ is a constant and, to ensure the normalization, $$\Omega(U,V,N ) = c_N\int e^{-\beta H(\{q,p\}... | {
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Why are we able to break a vector along it's components or in other words why is it that a vector exists along $x$, $y$ and $z$ axis? Does a 3 d vector exist in three dimensions at once? It seems to me that a vector always changes axis along which it is to fit into the scenario. For example: Electric field in $x-y$ pla... |
Does a 3 d vector exist in three dimensions at once?
Absolutely, a general vector is $$\vec r=x \hat i+y\hat j+z\hat k$$ in Cartesian coordinates. This vector has a component in each of the three dimensions and all components are mutually orthogonal. Since the vector $\vec r$ is equal to the sum of these 3 components... | {
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A question related to time and motion I have a theory, I think that we cannot travel at speeds faster than light because, as we know,when you travel at speeds near light time passes slowly and that if we go further than light time may pause perhaps and that if time pauses its impossible to have motion because in 0 seco... | It is a common misconception to believe that if you move close to the speed of light you cannot move because time is slow. You do not experience anything different, other than how the rest of the universe looks to you. Everything will looks shorter and running very slow in time. But you will see the objects past you at... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/338741",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why can we tear a newspaper neatly one way but not the other way? When I try to tear the newspaper from top to bottom (or bottom to top), it's torn pretty neatly and like a line, but when I try to tear it from side to side, it goes all over the place and tries to lead the tear towards the top or bottom.
Why does this h... | Newspaper is made out of cellulose fibres (linear unbranched ones) bonded entangled together.
The fibre structure is anisotropic. The orientation of most of the fibres is along the direction of the movement of the machine.
In the direction of this orientation, it is relatively easier to tear a newspaper because it's... | {
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It's easy to 3d model a room via binocular vision, can it be done with 2 microphones and a beeper? Many algorithms exist to construct a 3d model from two cameras, is it possible to 3d model of a room via a speaker that produces a beep, and two microphones with arbitrarily good hearing skill (ie can sample continuously ... | http://www.pnas.org/content/110/30/12186.abstract
That's a link to a paper that claims to be able to do that with a "few" microphones. Of course, if the room is not convex, it has the potential to fall prey to the illumination problem.
With 2 microphones, you should be able to get an arbitrarily good map, but there w... | {
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What is Gray, from a physics POV? Quora explains how white and black colors fit into the spectrum of visible light. It explains that white is all colors together while black is the lack of color.
So, where is Gray? Gray is the mix of all-colors and no-color!! What does that mean? Can somebody explain Gray, the mysterio... | All colors are combinations of three wavelengths of visible light, red, green and blue.
*
*White = All Red + All Green + All Blue
*Black = No Red + No Green + No Blue
*Grey = unsurprisingly Half Red + Half Green + Half Blue!
Read this Wikipedia Page: https://en.wikipedia.org/wiki/RGB_color_model
| {
"language": "en",
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"source": "stackexchange",
"question_score": "14",
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Tipping point on fence panels? I deal in temporary fence panels - and my concern is the tipping point of our product out in the field.
Panels are 6' tall x 12' long (63#)
Stands are 23" long x 6" wide
We use sand bags (30#-40#) on the bases, but for whatever reason, they don't always stay on (or people take them).
Is a... | What you are dealing with is countering the torque induced by a wind load on the fence section by the torque that your sand bags apply to your base when the section tips. It is hard to estimate the wind load, but it should be proportional to the area of the section. If your 6' fence is stable with a 23" base and 40# ba... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/339335",
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"source": "stackexchange",
"question_score": "2",
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Meanings of the word "phase" I have been confused at points due to multiple uses of the word "phase".
*
*Mainly, when I think of a phase diagram, I think of a graph relating temperature to pressure, and segments the possible combinations of these values into regions in which a particular substance is "solid", "liqui... | The world phase comes from the greek phasys (ϕάσις), meaning "appearence", from the verb ϕαίνομαι, "to appear", "to show one self".
Therefore, you are correct when you say that the meaning of the word "phase" is different in the three cases you cited, but they all have in common the concept of appearence, state: the ... | {
"language": "en",
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What is the ratio of gluons to baryons? Gluons bond quarks into baryons (i.e., protons and neutrons). For example, two up quarks and one down quark form a proton while one up quark and two down quarks form a neutron. Is there one gluon per one baryon or two gluons per one baryon or what is the ratio of gluons to baryon... |
Is there one gluon per one baryon or two gluons per one baryon or what is the ratio of gluons to baryons?
Gluons are elementary particles in the current standard model of particle physics.
The first three columns from the left are fermions. Fermions obey Fermi-Dirac statistics, and carry charge. the lower two rows ... | {
"language": "en",
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In summer, should I close curtains during the day? In summer, that is when it's warmer outside the house than inside, one want to prevent the air in the house to warm up too much. Let's consider that all the windows are kept closed, that they are double panes and made of "Low-E" glass. During the day, does closing the ... | The heat from direct sunlight is about 1000 watts per meter squared in hot countries. If sunlight passes the glass, the percentage not reflected will heat the room .
During the day, does closing the curtains on the windows reduce the heating of the house?
Yes , depending on the color of the curtain , its reflectance/... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/340227",
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"question_score": "3",
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Difference between de Broglie wavelength and electromagnetic wavelength What is the difference between de Broglie wavelength and wavelength of electromagnetic radiation? Is there any relation between $\lambda=\dfrac{hc}{E}$ and $\lambda= \dfrac{h}{mv}$? (E stands for energy of electromagnetic radiation.)
| Yes, there is a relationship. The base relationship is between an object's momentum and its de Broglie wavelength:
$$
\lambda = \frac{h}{p}.
$$
For a particle that is not moving at relativistic velocities ($v \ll c$), we have $p = mv$ and so the relationship becomes $\lambda = h/mv$. However, for a photon, its moment... | {
"language": "en",
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Why are the absolute magnitudes in M5 galaxy so puny? Wikipedia gives the following as the HR diagram for M5:
The stars at the base of the red giant branch have absolute visual magnitudes of 15? That seems way, way too dim. The sun's absolute magnitude according to wikipedia is 4.83, although it doesn't state in wha... | It is a simple mistake. According to Layden et al. (2005), the distance to M5 is 7.76 kpc and has a V-band extinction of 0.11 mag. You need to subtract 14.56 mag from the y-axis to get the absolute magnitude.
As an aside, I did eventually find the incorrectly labelled diagram here. The "author", Lithopsian, gives no re... | {
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"url": "https://physics.stackexchange.com/questions/340538",
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Why a propagating pulse has no DC spectral component? I found in a text that : "Because the laser pulse represents a propagating electromagnetic wave packet,
the dc component of its spectrum vanishes. Hence the time integral over the
electric field is zero."
Why is it so? I mostly don't understand why should a pulse no... | The pulse having a DC component would imply that there is a constant electric field forever after and before the pulse arrives. Because light obeys a dispersion relation $\omega = c k$, a field with $\omega=0$ does not propagate. Hence, the DC component is spatially and temporally uniform. In that case, it is meaning... | {
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Why is the Schwarzschild radius associated with the tiniest micro black hole formed by a Planck mass twice the Plank length? If one calculates the Schwarzschild radius, $r_s$, of a Plank mass $m_p=2,18*10^{-8} (m)$ one gets:
$$r_s=2{\frac{G{m_p}}{c^2}}=1,48*10^{-27}*2,18*10^{-8}=3,22*10^{-35}(m)$$
Now the Planck length... | Planck mass black hole has to store 1 bit of black hole entropy. This requires 4 Planck areas. The 4Pi for the physical surface area of the sphere is "built-in" to the definition of BHE so you only need r^2.
| {
"language": "en",
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The definition of the Lorenz gauge condition The inner product of two vectors in space-time is:
$$(x_1, y_1, z_1, t_1) \cdot (x_2, y_2, z_2, t_2) = x_1 x_2 + y_1 y_2 + z_1 z_2 - t_1 t_2$$
So
$$(\frac{\partial }{\partial x}, \frac{\partial }{\partial y}, \frac{\partial }{\partial z}, \frac 1c \frac{\partial }{\partial ... | The Lorenz gauge condition is written as, $\partial_\mu A^\mu = 0$ which can be expanded as,
$$\partial_\mu A^\mu = \frac{\partial A^0}{\partial t} + \nabla \cdot \vec A = 0$$
in natural units, where we are simply doing what the Einstein summation convention instructed us to do, take a sum through the index, $\mu = 0, ... | {
"language": "en",
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What is the purpose of baking a ultra high vacuum chamber? I don't understand the purpose for baking a UHV. I know it's to remove contaminants, but I don't know how baking would do that. Sure, heat may dislodge trapped dirt particles or may even break some down, but the particles would still be in a UHV. Therefore, I'm... | You don't just bake it, you bake it while pumping on it with a vacuum pump.
A solid contaminant such as a grain of sand may actually not be a problem at all. The reason a contaminant is a problem is if it contains substances that are at least somewhat volatile, and that will gradually evaporate when the system is in n... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/341421",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Frames of reference of Maxwell's Equations The Maxwell's Equations are one of the most famous sets of equations physics have ever known. But just as different sets of equations are applicable to different frames of reference, where are Maxwell's Equations applicable? To be more specific:
*
*Are Maxwell's Equations ... | As they are conventionally written Maxwell's equations are valid only in inertial frames of reference in flat spacetime. This is because the derivatives in the equation are not covariant derivatives and therefore don't apply when the coordinate system is curved.
It is possible to write Maxwell's equations in arbitrary ... | {
"language": "en",
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Differences between optical laser and amplifier I am preparing for an applied optoelectronics exam and I am having some trouble with telling the differences between optical fiber laser and optical amplifier. For now I only came up with following differences:
*
*No Bragg reflectors and optical resonators in amplifi... | The main difference between a fiber laser and a fiber amplifier is the cavity.
A laser (fiber laser or solid state laser) is an gain media, a pump and a cavity whereas a amplifier has no cavity. The cavity allow selecting the oscillating mode so there is no need to seed with a signal to generate a single frequency. Bec... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/341974",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Riemann tensor definition for non vanishing torsion From the definition of Riemann tensor we have:
$$
\mathbf{R}\left( \mathbf{z},\mathbf{v},\mathbf{w}\right)=\nabla_{\mathbf{[v}}\nabla_{\mathbf{w}]}\mathbf{z}-\nabla_{[\mathbf{v},\mathbf{w}]}\mathbf{z}
\label{riemannnew}
$$
and computing the coordinates of $\mathbf{R}... | In the invariant notation $\nabla_X\nabla_Y$ corresponds to $X^a\nabla_a(Y^b\nabla_b)$, not $X^a Y^b\nabla_a\nabla_b$, eg. the vector field $Y$ also gets differentiated.
We can define $\nabla^2_{X,Y}Z=i_Xi_Y\nabla\nabla Z$, where here $i$ means "insert into the last empty argument", then we have $$ X^a\nabla_a(Y^b\nabl... | {
"language": "en",
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Are time loops real? I'm new to physics and I was wondering if time loops (like those seen in the movies Groundhog Day or Edge of Tomorrow) possible?
| The closest thing in mainstream theoretical physics is "closed timelike curves", paths along which you can travel and thereby return to the same place and time as you started, provided your velocity varies as the path requires. (Shortcuts through spacetime called Einstein-Rosen bridges or "wormholes" can be a part of t... | {
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"source": "stackexchange",
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Why does a surface always exert force normal to it? In whichever angle an object is thrown at a surface, the surface always exert force normal to it. But why? According to Newton's third law, if an object hits a surface at an angle, the reaction force provided by the surface must be equal and opposite to the applied fo... | A reaction force can surely be angled.
And it can then be split into a tangential part and a perpendicular part. The tangential part is called friction, and the perpendicular part normal force.
So, the reaction force is not at all always perpendicular - but there always is a perpendicular component (the one called nor... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/342562",
"timestamp": "2023-03-29T00:00:00",
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Why would an infinity corrected objective lens produce an image without a tube lens? I'm having a hard time wrapping my head around this situation I've come across. I'm essentially recreating a homemade microscope that my understanding would suggest shouldn't work. This setup uses a 10X Olympus PLAN N objective attac... | Are you sure it's an infinity objective and not an RMS standard 160mm one ;-)
It's also possible that you don't have it focussed at exactly it's working distance. Remember the objective is just a (complex) lens. It only produces an image at infinity when the object is at a particular distance. If you put the object fur... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/342610",
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How electrostatic charge is distributed in a tube? If a tube has an electrostatic charge, is the charge uniformly distributed across its body or do the charge distributions vary from inside walls and the head edges? If so, how is the charge distributed?
I appreciate if you can name some references elaborating the charg... | As pointed out in sammy gerbil's answer, the charge density is quite large near the corners of a conducting surface. If we look near the edges of the cylinder, at length scales much less than the cylinder's radius, the corner will "look like" two planes meeting with an "interior angle" of $3 \pi/2$. It is a general r... | {
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Is there any qualitative difference between the WZW $SO(2)_1$ and the WZW $SU(2)_1$ CFT? Consider the anisotropic spin-$\frac{1}{2}$ Heisenberg chain $$H = \sum_{n=1}^N S^x_n S^x_{n+1}+S^y_n S^y_{n+1} + \Delta S^z_n S^z_{n+1}$$
which for $\Delta = 0$ realizes the Wess-Zumino-Witten (WZW) $SO(2)_1$ conformal field theor... | Well, the names say it all... the symmetries are different. At the $SU(2)$ point, with the additional symmetry (for the Heisenberg chain it is an explicit symmetry, in the bosonized theory it is emergent) there are additional current operators. It is at a self-dual point of the T-duality.
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Electric field at surface of a surface charge distribution I've heard this statement in class:
"Electric field is discontinuous across the surface of a surface charge distribution."
Could someone please explain why this is so? I understand why electric field is not defined at the location of a discrete charge, but I d... | Suppose there is an interface between two media, $A$ and $B$, and that there is a surface charge density $\sigma$ on this interface. Consider Gauss' law applied to a pill box across this interface:
$$\iint_S \vec E \cdot d\vec S = \frac{1}{\epsilon_0}\iiint_V \rho \, dV.$$
In the limit as the pill box's horizontal leng... | {
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How is it that in a car crash, four 8mm bolts can anchor the seat to the car? In a car crash at for example twenty metres per second. I used suvat equations and newtons second law to work out the force as as body accelerates(negatively). I estimated that the distance travelled in the crash by the body would be roughly ... | You suggest $0.4\ \mathrm m$ stopping distance from $20\ \mathrm{m/s}$ velocity, which with $s=u^2/(2a)$ is a deceleration of $500\ \mathrm{m/s^2}$, or more than $50g$.
My guess is that is really the maximum deceleration your body might survive.
For $80\ \mathrm{kg}$ mass that is $40\ \mathrm{kN}$ of force.
The ultimat... | {
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Estimate of the effect of quantum disturbances on a macroscopic object I am self-studying P. Davies, D. Betts, Quantum Mechanics. Exercise 4 of Chapter 1 says:
"A snooker ball of mass $0.1$kg rests on top of an identical ball and is stabilized by a dent $10^{-4}$m wide on the surface of the lower ball. Use the uncertai... | The arrangement of two hard smooth spheres balanced one on top of the other is doubly unstable. I agree with Bob Knighton : probably the lower ball should be assumed to be fixed in place while the upper ball is balanced on it.
The question asks for a time, so you should use the Uncertainty Relation between energy and t... | {
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How is the equation of Mach number derived? Wikipedia states that for a pitot-static tachometer, the mach number for subsonic flow equates to
$$M = \sqrt{5\left[\left(\frac{p_t}{p_s}\right)^\frac{2}{7}-1\right]}.$$
How did they get to that result? Is there a derivation, or is it just from a polynomial fit of a tabulate... | $M$ is not the speed of sound. It is the Mach number -- the ratio of speed of the aircraft to the speed of sound. The equation is derived from Bernoulli's equation together with a suitable choice of $\gamma=C_P/C_V$ for air.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/343439",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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At what temperature do the laws of physics break down? I heard that as approaching the temperature of a kugelblitz the laws of physics break down, I saw this in the video The Kugelblitz: A Black Hole Made From Light, by SciSchow Space.
| Adding to @Emilio's answer, what happens during Planck's temperature is unknown. Our laws of physics does not seem to work at that temperature(@EvilSnack) for e.g. gravitational force. At that temperature, gravitational force seems to become as strong as other fundamental forces like electromagnetic forces, strong and ... | {
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Why is Higgs particle detected much later than top quark when it's lighter? The Higgs boson is lighter than the top quark. But the top quark was discovered in the mid-1990s where the Higgs boson escaped detection for two more decades. So if the energy has already been achieved to produce Higgs boson, why did it escape ... | With both particles you cannot detect them within their own lifetimes, only look at what they decay into. The top decays to a b jet and W (which can then become fermion anti-fermion or leptons) and is fairly distinctive. The dominant Higgs decay, however, is to two b jets. B jets are very common within the LHC and we c... | {
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Will overlapping two different beams of coherent light with different wavelength cause interference? If I use two different wavelength lasers to transmit light into a single mode optic fiber will they interfere with each other? If so, how much will be that interference.
| Yes, they will of-course overlap but it won't be the same pattern for when waves with same wavelength overlap. The resulting wave can be found from graphing simple addition of sine waves indicating the superposition at each point.
To explore this visually you can try the graphing calculator Desmos. Try changing the sl... | {
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Is there a case when it is better to use the integral form of the Maxwell equations rather than the differential form? I was wondering if there is a case where the integral form of the Maxwell equations is preferred over the differential form?
If you could provide with an example for each one of the equations I would ... | The integral forms are useful in (typically static) situations where the charge/current distribution is symmetric enough that you can use a symmetry argument to replace the surface/line integrals with a simple product of a uniform field strength times an area/length of an imaginary closed "Gaussian surface" or "Amperia... | {
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Conjugate variables in thermodynamics vs. Hamiltonian mechanics According to Wikipedia, the canonical coordinates $p, q$ of analytical mechanics form a conjugate variables' pair - not just a canonically conjugate one.
However, the "conjugate variables" I directly think of are the quantities of thermodynamics - e.g. Tem... | In thermodynamics, conjugate pairs are related by the Legendre transform (like $T$ and $S$, or $P$ and $V$). In classical mechanics, you use the Hamiltonian to get the conjugate variable in a slightly different way, although the Lagrangian and Hamiltonian are related by the Legendre transform as well.
In general, conj... | {
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What is the difference between the valence shell and the valence band? What is the difference between the valence shell and the valence band?
The valence band is usually defined as the highest filled band whereas Wikipedia defines the valence shell as the outermost shell of an atom in its uncombined state, which contai... | The valence shell is the outermost electron shell. An isolated atom's valence shell contain electrons with certain energy levels.
When atoms are brought into close proximity, repulsion of their electrons causes the energy levels corresponding to the shells to split into discrete energy bands. Thus the electrons will be... | {
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Pumping up bicycle tires with helium instead of air If I pumped up my bicycle tires with helium instead of plain air, what would happen if the applied force on my pedals was constant?
Would I go faster because of the reduced ground friction? Would I go slower because I would have less contact with the surface I'm ridi... | Others mentioned that the weight difference will be small, on the order of 10g (one should take into account the pressure in the tires). You should have in mind though that lighter tires also have smaller moment of inertia (rotational inertia), which should facilitate acceleration. Some people also mentioned helium's h... | {
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About light in the universe As a light source in the universe (e.g. sun) emits light in different directions, some of the light emitted reaches places like Earth, and some doesn't. So does the light that reaches the Earth disappear or it is reflected in other directions? And for the light that doesn't reach any place, ... | As you probably know, the light that you mention is an electromagnetic radiation, so it is part of a large spectrum in which $\textit{visible light}$ makes only a small part. Even the sun emits tons of radiation, but not all of it is visible light. When you say about the brightness of the Universe (referring only to th... | {
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Why surface normal is used while defining flux through an open surface? What is the significance behind defining normal to any surface? Why we do it?
| Geometrically, it's only the component normal to the surface that "pushes the stuff through" the surface.
As illustrated below, the "stuff" that "moves" parallel to the surface does not pass through this surface and so does not contribute to the flux through that surface. In the figure on the far right, the "stuff" ... | {
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How can we show Power = $\mathbf{F}\cdot \mathbf{v}$? How can we say that $$\text{Power} = \mathbf{F}\cdot \mathbf{v}$$
We know that small work done by a force $\mathbf{F}$ to displace an object by '$\mathbf{x}$' is
$$W = \mathbf{F}\cdot \mathbf{x}$$
So derivating wrt time, we get
$$\begin{align}
P=\dfrac{dW}{dt}&=\fr... | See that work is done only when there is a displacement. So if there is no displacement then even having a variable force will not account to any Power. Hence the first term is excluded.
$$ W = \int \mathbf F \cdot {\mathbf v} dt $$
$$P=\dot{W} $$
When applied to the integral along with fundamental theorem of calc... | {
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Total and static pressure: which one is measured? Which pressure is measure using measuring device in a pipe flow. My first intuition that it is the static pressure. This is confirmed by this Wikipedia article (link)
The concepts of total pressure and dynamic pressure arise from Bernoulli's equation and are significa... | The dynamic pressure represents the volumic kinetic energy of the fluid, so $P_{dyn}=\frac{1}{2}\rho v^2$, and the total pressure is $P_{tot} = P_{stat} + P_{dyn}$. Thus, a device that take the speed of the fluid into account measures $P_{tot}$, and one which does not will only measure $P_{stat}$. For the first case, y... | {
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How much "earth" does it take to create an "earth ground" for measuring voltage? I was contemplating the idea of a multi-meter that had a "built in" Earth ground to it, and if it did have this ability how much earth/dirt would it take to register as a true Earth ground to register voltage of 120v when touching a standa... | The ground/earth works because all the electricity suppliers agree to use the electrical potential of the earth as a reference point of zero voltage. Since the Earth is a conductor, if not a terribly good one, all electrical installations are in principle connected together to establish a uniform zero potential.
If you... | {
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Why does the Sun appear larger during the sunrise and sunset? Why does the Sun appear larger during sunrise and sunset compared to its size during midday even though its distance from the Earth remains fixed all the day? It is only during the Winter when the Sun is away from the Earth and that too is due to the motion ... | Yesterday we had a super moon full moon. At moonrise I held a transparent ruler at arm's length and measured the size of the moon against the ruler. It was 7.5 mm. At 11 pm I held the same ruler at arm's length against the moon which was now high in the sky. It was only 4 mm. This is not imaginary. It is real and obser... | {
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Why can a regular infrared camera not show temperature (thermography)? There are a lot of questions here dealing with infrared cameras and thermographic cameras. I think I understand the reason why a thermographic camera is able to retrieve the temperature values from any object and convert them to a falsecolor represe... | This is a common confusion, because both thermographic cameras and "normal" cameras with some IR capability are called IR cameras often.
The typical video camera with IR capability has a solid state semiconducting camera sensor normally used for capturing visible light, which relies on the photons interacting with elec... | {
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How can I use Newton's laws of motion to determine the force acting on the rope? Imagine there is a painter, weighing $180~\rm lb$, that is working from a bosun's chair hung down the side of a tall building.
Suppose that he pulls down on a fall rope with such a force that he presses against the chair with a force of ... | There are a variety of ways to solve this problem, but I solved it pretty easily by analyzing the painter, and the whole system (painter + chair), giving 2 equations and 2 unknowns.
The painter's force on the chair (100 lbs) $= M_p(g+a)-T$, where $M_p$ is the painter's mass (100 lbs / g), $a$ is the upward acceleration... | {
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Can a cycloidal pendulum be extended to make a full swing? A cycloidal pendulum is isochrone, meaning it's period is independent of it's amplitude. But a cycloidal pendulum - as usually depicted - doesn't do a full 360 degrees swing. Why is that? Is there a limit on how high a pendulum can swing, so that it is still is... | This sketch became too long to be a comment so I will post it as an answer anyway.
Let us say we have a wire forming a cycloid in the vertical plane as in the figure bellow
A friction-less bead into this wire will oscillate with known period $T$ independently of its releasing point. Assume we can symmetrically contin... | {
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Renormalization and canonical commutation relations My question is whether canonical commutation relations hold for renormalized quantum fields. Below I show reasoning which caused by doubts.
Consider a relativistic scalar QFT. We have spectral decomposition of two-point function
$$ \langle \Omega | \phi(x_1) \phi(x_2)... | The relevant axiom.
Any (canonical) field, renormalised or not, satisfies, by postulate,
$$
[\phi,\pi]=\delta
$$
where $\pi$ is the field conjugate to $\phi$. In Lagrangian field theory,
$$
\pi\overset{\mathrm{def}}=\frac{\partial \mathcal L}{\partial\dot\phi}
$$
Case 1.
If $\phi$ is an unrenormalised field,
$$
\mathca... | {
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Why does Newton's Third Law actually work? My father explained to me how rockets work and he told me that Newton's Third Law of motion worked here. I asked him why it works and he didn't answer. I have wasted over a week thinking about this problem and now I am giving up.
Can anyone explain why Newton's Third Law works... | I know i am too late for this answer but I couldn't stop myself from answering :). Also I am going to use the contradiction method which we generally use in mathematics.
Let us assume that it doesn't work .
So , nothing around you follows Newton's third law.
Now , you take a spring and try to compress it by applying a... | {
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Do commuting Hermitian operators correspond to compatible observables? As far as I know, two compatible observables have a complete set of common eigenvectors, and using this fact, one can prove that their corresponding operators are commutative. Well now is the converse true? Do any two commutative hermitian operators... | This question concerns more Mathematics than Physics, so it should be handled rigorously in order to avoid to generate even more confusion (I personally find quite confused this page Complete Set of Commuting Observables since it deals with the finite-dimensional case in the proofs and supposes that the statements are ... | {
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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... | There is a connection. According to
R.L.Jaffe (2005). "The Casimir Effect and the Quantum Vacuum". Physical Review D. 72 (2): 021301. arXiv:hep-th/0503158.
the Casimir force is simply the (relativistic, retarded) van der Waals force between the metal plates.
Another interpretation of Casimir force is that it is due t... | {
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Lorentz transformation of the four velocity Can we derive the velocity addition rule by directly transforming the four velocity?
| Theory-wise, the easiest way to use this is to use $w=ct$ and then your Lorentz matrix in 1+1 dimensions can be written as $$\begin{bmatrix}w'\\x'\end{bmatrix} = \begin{bmatrix}\cosh\alpha & -\sinh\alpha\\-\sinh\alpha&\cosh\alpha\end{bmatrix}\begin{bmatrix}w\\x\end{bmatrix}.$$
This is because the hyperbolic cosine and ... | {
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Prove there is an equipotential sphere between two point charges Given two point charges of opposite sign I need to prove that inside the electric field they create there is an equipotential sphere.
I'm very positive that this is more geometry than anything else and I really question why I've been given this exercise.... | The electric field around the charges will have rotational symmetry about the line joining them, so the problem can be reduced to 2D and the task of proving that the locus is a circle.
The only physics here is getting $r_1=ar_2$. The rest is geometry. One proof relates to the Apollonian Circles Theorem.
Using co-ordin... | {
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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... | Although your question isn't clear, I'll try answering what I've understood from your question. In your question, you have assumed force is constant. In case of constant force, yes acceleration will vary inversely with mass, i.e., as you say, kicking a bowling ball will produce lesser acceleration than a soccer ball.
H... | {
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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?
| The voltage drop across the parallel combination is equal to-
$ V - current*(R_1)$
where $V$ is the voltage across the terminals of the battery.
This is so as the sum of the voltage drops across $R_1$ and the parallel combination is equal to $V$.
Hence if current decreases, voltage acr... | {
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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;
$$a_1 b_1 = (a_1 b_1 + b_1 a_1)/2= a_1 b_1 + 1/2$$
where $a$ is the creation operator and $b$ is the annihilation operator, also
$$a_1 b_1 a_2 b_2 = \frac{1}{2} (a_1 b_1 + b_1 a_1) \frac{1}{2}(a_2 b_2+b_2 a_2) = (a_1 b_1+ \frac{1}{2})(a_2 b_2+... | {
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Moment of a force about a given axis (Torque) - Scalar or vectorial? I am studying Statics and saw that:
The moment of a force about a given axis (or Torque) is defined by the equation:
$M_X = (\vec r \times \vec F) \cdot \vec x \ \ \ $ (or $\ \tau_x = (\vec r \times \vec F) \cdot \vec x \ $)
But in my Physics class I ... | It is obviously a vector, as you can see in the 2nd formula.
What you are doing in the first one is getting the $x$-component of that vector. Rememebr that the scalar product is the projection of one vector over the other one's direction. Actually you should write $\hat{x}$ or $\vec{i}$ or $\hat{i}$ to denote that it i... | {
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Special Relativity: Does non inertial frame of reference work in SR? I started on my own learning about GR and SR two months ago, and I still do not have clear if it is possible or not. The following example was explained to me by someone who affirmed: "SR applies only on inertial reference frames":
Let's imagine we ha... | It is possible to use accelerated reference frames in special relativity. It is more advanced than many undergraduate texts cover. But, see for example chapter 7 of "Special Relativity", A.P. French, CRC Press, 1968. There it is shown that the direction of the acceleration is not necessarily equal to the direction of t... | {
"language": "en",
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Does this Nelson formula for Feynman integral have mistakes? In this paper (Maroun's PhD dissertation, 2013) at page 46 the following formula is given (apparently without a reference):
$$\int_0^{\infty } e^{i a x^s+i b x^p} \, dx=\sum _{n=0}^{\infty } \frac{\left(i b a^{\frac{1}{s}}\right)^n \exp \left(\frac{(i \pi ) (... | It is correct that there is a typo in the right hand side series expression. The term in the numerator of the series inside of parenthesis raised to the n power should be
$$
\left(iba^{-\frac{p}{s}}\right)^n.
$$
| {
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Why does my lampshade cast shadows right near the bulb? I've got an upside-down lampshade in my house on a post, and I noticed today that shadows were coming off the edge of it even at 6 inches from the bulb. Could someone explain the phenomena to me?
(I'm not at all Physics-oriented [lol I didn't do as I'd hoped on my... | Looks like your lampshade is made of either glass or plastic, probably with frosted surface. If that is the case, just think about the geometry: light from the bulb reaches the edge at shallow angles, and more of its path would be in that frosted surface; it effectively becomes "thicker" and therefore allows less ligh... | {
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Perpetual Motion Machines If you go on YouTube, you will find a large number of machines that work for almost forever. But why do all of them stop working after some time?
Which Law (Other than Conservation of Energy) prevents a machine from running till eternity?
| Most don't work due to the laws of thermodynamics, usually the first law which states that energy can neither be created or destroyed as you mentioned in your question . This stops the opportunity for many perpetual motion machines as most lose heat (and therefore energy) in the process. Without putting more energy in ... | {
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Why the excited states of an atom have an energy width? All my experience with textbook problems of quantum mechanics shows that the energy levels associated with the bound states of a confined quantum system are discrete and sharp. For example, the energy levels of the hydrogen atom. Why is it then said that excited s... | Leaving aside Doppler broadening and the other main practical reasons for line broadening, the fundamental reason is that the excited atom is coupled to all modes of the EM field equally, or at least there is an extremely wide frequency band of modes that are coupled.
So the atom "tries" to couple its excess energy int... | {
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If centripetal acceleration varies with time then which velocity do I get on integrating the acceleration As the particle is in circular motion there is no radial component of velocity but which velocity is being given by integrating the time varying acceleration then?
| From the definition of acceleration, we know that
$$\vec a = \frac{d\vec v}{dt}$$
So, $$ \int_{t_1}^{t_2} \vec a\ dt = \int_{t_1}^{t_2} d\vec v$$
$$\Rightarrow \int_{t_1}^{t_2} \vec a\ dt = \vec v_{t_2} - \vec v_{t_1}$$
$$\Rightarrow \int_{t_1}^{t_2} \vec a\ dt = \Delta \vec v$$
which is the change in the velocity ve... | {
"language": "en",
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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... | Using google for help, the peak around 625 nm is from Europium which is added to the phosphor to produce red light. Several of the smaller peaks greater than 625nm are also attributable to Europium as well. The large peak at about 550 nm is due to mercury as are the smaller peaks at around 415 nm and 440 nm. the phosph... | {
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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... |
How fast can you spin a proton or electron without breaking it?
Even in the link you give, spin is a quantum number which can increase if the energy input to the nucleus is increased, the individual nuclei going to higher energy bound states ( or quantum mechanically defined bands) in higher angular momentum quantum ... | {
"language": "en",
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Does the earth has any electric field as the earth's magnetic field is changing over time?
Earth's magnetic field changes over time because it is generated by a geodynamo
-Wikipedia
A time-varying magnetic field can produce electric field. So does the earth has electric field due to changing magnetic field?
| There are various ways to relate the electric and magnetic fields. Semoi gives one example, but in this context perhaps it is simpler to use an alternative relation:
$$ \mathbf E = -\nabla\phi - \frac{\partial\mathbf A}{\partial t} $$
This expresses the electric field $\mathbf E$ as the sum of two contributions. The fi... | {
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How many dimensions are there in the electric field? I am not a physicist. I am buying some polariser for my camera. Circular polariser intrigues me. Basically you pass light through a linear polariser, then through a waveplate, you get circular polarisation.
Wikipedia says the following:
By adjusting the thickness o... | In an electromagnetic wave (light), the electric and magnetic fields are perpendicular to the direction of travel. If the wave is traveling in the $z$-direction, then $E_z = B_z = 0$. So, yes, the fields are two-dimensional.
| {
"language": "en",
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Quantum Mechanic Interpretations Context I was watching this video "Do we have to accept Quantum weirdness?" and it said how currently there are several interpretations of quantum mechanics that are consistent with the facts.
Question For quantum mechanics, how does one decide on which is the "correct" interpretation? ... | That is precisely the problem. David Mermin said somewhere that every year a new interpretation of quantum mechanics is introduce and none are ever ruled out. This clearly points to the fact that interpretations of quantum mechanics are not Popper falsifiable. Thus, according to strict definition, interpretations of qu... | {
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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... | Take RI in two of the three optic axis directions in Biaxial gemstones. ie. Alexandrites and tanzanite positive signs.
| {
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Heat produced by a conductor I recently got to know about how the heat produced in a conductor. It's due to collision of electrons when drifting due to electric voltage But my question is Why doesn't a non current carrying conductor doesn't heat up due to collision of electrons in it as they are in random motion?
| In the end the energy that is converted to heat has to come from somewhere. In the sketched situation the electron has to be in an excited electron state so that it can relax into an energetically lower lying state due to the scattering event. If there is no net current in the conductor the electronic system is in ther... | {
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If the bicep connects closely to the elbow joint, would the bicep need to exert more or less force to lift an object? I would like to know whether a less or large amount of force is exerted by the bicep to lift and hold an object if the bicep is connected close to the elbow joint (fulcrum) than if the bicep is connecte... | To figure this out you can use the pivot formula. If the applied force $F_A$ is distance $r_A$ from the fulcrum and the exerted force, $F_E$, is distance $r_E$ from the fulcrum, then
$$
F_E=F_A\times r_A/r_E.
$$
If the bicep is connected close too the elbow joint it will have a smaller $r_E$ than if it is connected cl... | {
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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... | If your velocity is zero then due to work energy theorem the work done would be zero. But if you are accelerating then pseudo force would do the work
| {
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Can we derive Einstein-Hilbert action through action principle and Levi-Civita connection? Suppose that we take principle of least action as given. Also assume that any manifold allowed by the action would carry Levi-Civita connection (torsion-free characteristic). Also assume that the local symmetry imposed on the tan... | No, any action that is a scalar would satisfy your requirements. For example, you could have various terms that are functions of the various scalar curvatures $R$, $R_{ab}R^{ab}$, or $R_{abcd}R^{abcd}$, to give a few examples; you could probably invent more. You need some further requirement to fix the Lagrangian to be... | {
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Photoelectric effect, low frequency light Let's say we have a emitter, emitting light that has frequency f, less than the threshold frequency of a metal.
If you leave light shining onto that metal, for long enough, does the energy of the individual photons accumulate, on the electrons, so eventually they will ionize, o... | For simplicity let's consider the photoelectric effect in a thin metal foil:
The first step in the photoelectric effect is when a photon strikes an electron in the metal and transfers all its energy to it. The electron energy is now equal to the photon energy $h\nu$. If this energy is greater then the work function $\... | {
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Why is the direction of magnetic field from South to North Pole inside a magnet? Since magnetic field lines are the path taken by a hypothetical North Pole when it is in range of a magnetic field of a magnet, it is clear that the direction of hypothetical North Pole would be from North Pole to South Pole of a magnet no... | In nature, there is no magnetic monopole discovered yet. All of the magnets we have are created by certain kind of current (like the spin of an electron). Thus, the prototype of a magnet is a solenoid.
Now, there are a bunch of ways to argue the direction of the magnetic field in the solenoid. If you took introductory ... | {
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How is pion decay compatible with conservation of angular momentum? A pion is a spin-zero composite particle, so $S = S^z = 0$. A $\pi^-$ pion can decay into an antineutrino $\bar{\nu}$ and a negatively charged lepton $l$, each with spin-$1/2$. Let the direction of antineutrino motion be the positive $z$-axis. Since al... | Only the component of the spin wavefunction that has a nonzero projection onto $S=0$ will be present in the decay. That factor of $\frac{1}{\sqrt 2}$ gets factored in and reduces the decay probability by half (which is already taken into account).
| {
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Can anyone explain this condensation pattern? What is the hair-like "polymer" that condenses on the caps of the plastic cell vial? Inside vial are cells in a mixture of FBS and DMSO. The vials were frozen slowly in a special isopropanol-filled container (isopropanol does not touch the vials) to -80 degrees celsius, the... | The polystyrene container and your comments about the hairs moving suggest that they might be caused by static electricity.
This video shows ice crystals which formed on a plastic tube rack in a bucket of dry ice. They are attracted to a finger by static electricity, just as you described.
Water is made of polar molecu... | {
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Varying magnetic field, and a larger area? Considering this classical example:
The magnetic flux($\phi$) is increasing over some time(increase in $B$), and it's simple to indicate the direction of the induced current using Lenz law.
However, the magnetic field is only in a specific region, what if the magnetic field w... | A conducting metal coil in a varying magnetic field opposes the change in magnetic flux through it. This opposition induces a current in the loop, the direction of which can be found out by Lenz's Law.
Now we know that magnetic flux is given by $$\phi_B = \int B.dA$$ which is the summation of the scalar products of t... | {
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Continuum mechanical analogous of Maxwell stress tensor Maxwell stress tensor $\bar{\bar{\mathbf{T}}}$ in the static case can be used to determine the total force $\mathbf{f}$ acting on a system of charges contanined in the volume bounded by $S$
$$ \int_{S} \bar{\bar{\mathbf{T}}} \cdot \mathbf n \,\,d S=\mathbf{f}= \f... | Let's consider a point $\renewcommand{\vec}[1]{\mathbf{#1}}\vec{x}$ of the undeformed material, which moves to $\vec{x}'$ after deformation. We define the displacement vector
$$\vec{u} = \vec{x}'-\vec{x}.$$
The variation of $dl^2=d\vec{x}^2$ is then given by (implicit summation on repeated indices everywhere)
$$dl'^2 =... | {
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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? ... | If the particle is on an equipotential surface, then that means there is no force from the electrostatic field on your charge, while moving along that surface. If there are no external forces, that means that locally momentum in that direction is conserved, just consider Newton's laws:
$$ \frac{\text{d}\boldsymbol{p}}... | {
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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... | Probably yes.
The warmer air inside your room is less dense than the colder air from outside, so the latter can easily flow over the windowsill into the room, dislodging the warmer air, which escapes like smoke through the window.
If there are two openings allowing a strong draft to form, there shouldn't be much differ... | {
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Does Snell's window (the optical man-hole) work both ways? My physics book states: Just because you can see a fish under water (you are above; the fish is below) doesn't mean the fish can see you due to Snell's window.
Is this true? I would have assumed that someone standing in a boat surrounded by water would also hav... | Yes, light travels the reverse way. You cannot realize an optical diode with linear optical elements in absence of fields other the light itself. (Faraday effect with static magnetic field is needed for an optical diode for instance).
Most likely the textbook refers to the case where one practically cannot see the fish... | {
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Does entropy really not increase here?
Two vessels separated by a partition have equal volume $V_0$ and equal temperature $T_0$. They both contain the same ideal gas, and the particles are indistinguishable. The left vessel has pressure $P_0$ and the right vessel has pressure $2P_0$. After the partition is removed and... | The change in entropy is certainly not zero. It is greater than zero for this spontaneous process. Just because the Q in an irreversible process is zero does not mean that the entropy change is zero. The entropy change is the integral of dQ/T only for a reversible path.
I get $\frac{3}{2}P_0$ for the final pressure... | {
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How much time will it take to move an object whose length is equal to one light year? Suppose there's a stick whose length is one light year and I push it from one side by one centimeter. How much time would it take for its other side to move by one centimeter and why?
| It depends on the material. When you push one end of the stick, you move the atoms at the very end of the stick. Those atoms push the atoms next to them, those atoms push the next atoms, and so on down the stick. This is a sound wave that travels down the stick, so the time you have to wait for the other end to move is... | {
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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 ... | If you are willing to make gravitational time dilation count and if about a mile of elevation counts as human scale, then this is the coolest of my bookmarks I can share: http://www.leapsecond.com/great2005/
The author is an expert on atomic clocks and he set up an experiment to show they ran differently 1340 meters hi... | {
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Question when comparing two experimental results In my textbook it says that if two experimental results vary less than 3$\sigma$ then they can be considered to have arrived at the same result. My question is how do you determine this "x$\sigma$".
For example if i did an experiment to calculate $g$ and my result was ... | Given that both measurement have a 1 std. dev. random error estimate (all bets are off when systemantics and model dependencies rear their ugly heads!), then you are effectively comparing the difference of the measurements with zero.
So the error you use is the error of the difference.
Which means propagating the error... | {
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How can energy of oscillators be quantised but they can still vibrate at all frequencies? In Black Body radiation, Planck's law has a postulate saying
The wall of black body contains oscillators of all possible frequencies,ν.
There is one more postulate which says
The energy of these oscillators is not continuous ... | Your first statement can be understood if you take into account that a blackbody, is -by definition- an object or system which absorbs all radiation incident upon it and emits energy which is characteristic of this radiating system only, not dependent upon the frequencies which are incident upon it. So, it has to conta... | {
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Does quantum mechanics allows absolute energies? When we solve Schrödinger equation:
$$H\Psi=E\Psi$$
for a system, is $E$ an absolute energy? I mean, an energy that is not a difference between states.
Does this equation implies something about absolute or non-absolute entropy?
| The problem is that the Hamiltonian operator contains a potential energy $V$:
$$ \hat{H} = \frac{-\hbar^2}{2m}\nabla^2 + V $$
and the potential energy isn't an absolute energy because we are free to set the zero of the potential energy wherever we want. So the energy in your equation is not an absolute energy but depen... | {
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Confusion regarding gravity not being a force In high school, it was taught that formula for describing circular orbital velocity around a central body is derived by equating Newton's law of gravity with the centripetal force formula (under the logic that the inwards centeipetal force required is provided by the gravit... | TL:DR
Newton's law of gravity (used to describe velocity, and not force) is not wrong, it is just imprecise and has a limited scope for which it is accurate (I would not equate less widely applicable with less valid).
No, the fact that gravity is not a force, as Newton described it, does not mean that his calculations... | {
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What is the $\{q_i\}$-$t$ space called? In classical mechanics, the configuration space of a system of $f$ degrees of freedom is the $f$-dimensional space of the set of generalized coordinates $\{q_i\}=(q_1,q_2...q_f)$ of a system. While talking about the principle of extremum action, one draws a path in the $\{q_i\}$-... | The name could vary from author to author. In a non-technical setting I think you would find it under the name "extended configuration space". In more specialized contexts (e.g. Hamiltonian mechanics on symplectic spaces, field theory on fiber bundles, etc.) they are called contact manifolds or even just configuration ... | {
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Quantum Mechanics and Schur's lemma Today i was studying on a textbook and i crossed a paragraph that confused me a little.
Suppose you have an algebra generated by $\hat{X}$ and $\hat{P}$ and a function $f(\hat{X},\hat{P})$ that commutes with $\hat{X}$ and $\hat{P}$. Then you can prove that this function is proportion... | If $[x,f]=0$ then $f$ belongs to the commutant of $x$. Of course $x$ is in such a commutant, but $p$ isn't, therefore $f$ is a function of $x$ alone. Now, for any vector $\psi$ in the Hilbert space of the Schroedinger representation,
$$(f\psi)'(x) - (f\psi') = 0,\qquad\forall x$$
which implies that $(f'\psi)(x)=0$ for ... | {
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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 ... |
What if you could mechanically increase this speed? Say you had a charged capacitor, and one of the plates was given a parallel velocity. E.g. two concentric cylinders with a charge imbalance, with one of them attached to a motor. Wouldn't that create a very strong apparent magnetic field?
Well how large is relativis... | {
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Tensor in different coordinate system I have the tensors $F_{\mu\nu}$, $F^{\mu\nu}$ in coordinate system $(t,x,y,z)$ and want to transform these to coordinate system $(t',x',y',z')$ just by multiplicating matrices.
My idea was to calculate the Jacobians $J=(\frac{\partial x^i}{\partial x'^j})_{ij}$ and $J'=(\frac{\pa... | The idea is more or less correct but you need to be careful with the mixing of matrix and tensor notation. Let's say that $F_{\mu\nu}$ are the components of a matrix $F$, and $F^{\mu\nu}$ those of $F_U$ (for "upper"). Then $F_{\mu\nu}F^{\mu\nu}$ becomes $\operatorname{tr}(F F_U^T)$. Also you need to notice that $J'$ is... | {
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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... | If a hot metal object placed openly then heat can be transferred
*
*by means of conducting (the molecules in contact to the metal block)
*by convection (the flow of hot air in contact to the block)
*and by radiation.
| {
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Physical difference of waves produced by a deep and a treble I tried to find what the difference is on the pressure wave caused by a bass speaker and a wave produced by a treble speaker.
Off course the frequency is lower on the bass wave, but is that all? Why does the waves from the bass speaker appear to have a much ... | Because the bass frequency is lower, its wavelength is longer, because the speed of sound is roughly constant, so the sound wave travels further in one full cycle.
But the efficiency of the speaker depends on the ratio of its diameter to the wavelength. So a bass speaker must be bigger than a treble speaker.
| {
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Why are there two definitions for the functional derivative? I have seen two definitions for the functional derivative. Why are there two definitions?
*
*In Goldstein's Classical mechanics 3rd edition page 574 eq. (13.63), and also in a Student's Guide to Lagrangians and Hamiltonans by Patrick Hamill on page 55 eq. ... | For a functional
$$S~=~\int d^nx ~{\cal L}(x) , \qquad {\cal L}(x)~\equiv~ {\cal L}(\phi(x), \partial \phi(x), \ldots, x),\tag{0}$$
the second definition with notation
$$\frac{\delta S}{\delta\phi^{\alpha} (x)}\tag{2}$$
is the traditional definition of functional/variational derivative (FD), while the first definitio... | {
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Is there a "square root" version of the Einstein field equation? It is well known that the Klein-Gordon equation have a kind of "square root" version : the Dirac equation.
The Maxwell equations can also be formulated in a Dirac way.
It is also well known that the metric of general relativity have a kind of "square roo... | By taking the "Dirac square root" of the Hamiltonian constraint for GR, you naturally end up with Supergravity...so in some appropriate sense, SUGRA "is" a "square root" of GR. For more on this, see:
*
*Romualdo Tabensky, Claudio Teitelboim, "The square root of general relativity". Physics Letters B 69 no.4 (1977) p... | {
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} |
Construct operator such that division of expectation values is equal to expectation value of the operator Is is possible to construct an operator $\hat{C}$ out of $\hat{A}$ and $\hat{B}$ such that:
$$\frac{\langle \psi|\hat{A}|\psi\rangle}{\langle\psi|\hat{B}|\psi\rangle} = \langle \psi|\hat{C}|\psi\rangle,$$
for any s... | No. The r.h.s. is a quadratic form, while the l.h.s. is not. For example, under $\psi\to\lambda\psi$ the r.h.s. scales as $\lambda^2$ while the l.h.s. stays the same.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/359046",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 2,
"answer_id": 1
} |
The boundary conditions in a waveguide Suppose a cubic waveguide, made of perfect conductor, has only two open parallel sides. And the boundary conditions in this case are that the electric field at the surface must satisfy:
$$\vec{B} \cdot \vec{n}=0,$$
and magnetic field:
$$\vec{E} \times \vec{n}=0,$$
where the $\vec{... | This simply follows from the Gauss' law:
$$\nabla\cdot\vec E=\frac\rho{\varepsilon_0}.\tag1$$
Since we know that $\vec E\parallel\vec n$ at the boundary inside the waveguide, the divergence of $\vec E$ reduces$^\dagger$ to $$\nabla\cdot\vec E=\frac{\partial E_n}{\partial n}.\tag2$$
Since the waveguide doesn't have any ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/359176",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
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