Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Why does rotation occur? So it sounds like a dumb question, as it is very intuitive why rotation occurs. However, can you give me a scientific explanation as to why whenever I exert a force on a body it tends to move, but when it is tied to something or I am pushing it through the edge of an object, it rotates? What is... | It's implicit in Newton's second and third laws together with one crucial assumption.
Consider the simplest system - two point masses linked by a massless infinitely stiff tether. Now impart a force on one and write down the equations of motion for the point masses given the tether. You will find that the system's rot... | {
"language": "en",
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Finding atmospheric pressure using temperature of boiling water I was checking the temperature inside my oven using a multimeter with a temperature probe. I had set the oven's thermostat to 190o C, and it had reached equilibrium, but the measured temperature was well below what I had set the thermostat for. Having no... | Steam Table says that the saturation temperature for Water @1040 hPa is 100.7°C. Conversely, the saturation pressure at 98°C is 943.9 hPa.
Saturated Steam Table
Check the accuracy of your temperature probe as well as that of your barometer.
For the connection of Temperature, Pressure and Elevation, see Barometric formu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/301525",
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Heisenberg equation of motion In the Heisenberg picture (using natural dimensions):
$$
O_H = e^{iHt}O_se^{-iHt}. \tag{1}
$$
If the Hamiltonian is independent of time then we can take a partial derivative of both sides with respect to time:
$$
\partial_t{O_H} = iHe^{iHt}O_se^{-iHt}+e^{iHt}\partial_tO_se^{-iHt}-e^{iHt}O_... | With some definitions to make time dependences explicit, your equation (4) can be made sense of. Let's take the following:
Let $O_s$ be an operator depending on time and other parameters $O_s:\mathbb{R}\times S\rightarrow \mathrm{Op}$, where $S$ is the space of the other parameters and $\mathrm{Op}$ is the space of ope... | {
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Evolution of neutrinos flavor states What do we mean by saying that neutrino flavor states do not satisfy the schrodinger equation? How does the time evolution of states look like?
| Because of the way neutrinos are (I'm going to try to keep this simple) the flavor eigenstates are related to the mass eigenstates via:
$$
\vec{\nu}_f = \bf{U} \vec{\nu}_m,
$$
where the vector $\vec{\nu_f}$ has flavor eigenstate components ($\nu_{\mu}$, $\nu_{e}$, $\nu_{\tau}$), the vector $\vec{\nu}_m$ has mass eigens... | {
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Why do we assume weight acts through the center of mass? The weight of a body acts through the center of mass of the body. If every particle of the body is attracted by earth, then why do we assume that the weight acts through the center of mass? I know that this is true but I can't understand it. Does it mean that the... | Force that acts on the center of mass does not exert any torque on an
extended body. So, gravity 'acting on the center of mass' means a force
that accelerates, but does not rotate, its target.
There is tidal torque on
the Earth by the Moon, but this is because the Earth is not a rigid body, and
changes shape (and ... | {
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"url": "https://physics.stackexchange.com/questions/301854",
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How do Faddeev-Popov (FP) ghosts help path integrals? How does the inclusion of Faddeev-Popov ghosts in a path integral help to fix the problem of over counting due to gauge symmetries?
So, after exponentiating the determinant for the inclusion of either anti-commuting or bosonic variables and the corresponding extens... | In a nutshell, the Faddeev-Popov (FP) determinant (and its integral formulation via FP ghost variables) can be viewed as a compensating factor in the path integral $Z$ to ensure that the path integral $Z$ does not depend on the choice of gauge-fixing condition. See also this Phys.SE post.
For a simple gauge theory (li... | {
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Independence of coordinates in the Hamiltonian formulation I was told the following statement
It is often true that the Lagrangian method leads more readily to the EoMs than does the Hamiltonian method. But because we have greater freedom in choosing the variable in the Hamiltonian formulation of a problem (the $q$ an... | Coordinates $q$ and momenta $p$ are independent variables in Hamiltonian formalism. Dependence of $p$ on $\dot{q}$ appears after solving the Hamiltonian equations of motion
\begin{equation} \dot{q}^i=\frac{\partial H}{\partial p_i}.
\end{equation}
Doubling of independent variables in comparison with Lagrangian formulat... | {
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How matter waves travel faster than light? I read this in my physics textbook. It says that matter waves travel faster than light. Why is it so?
Also are matter waves G-Waves?
| In the original non-relativistic formulation of wave mechanics by Schrödinger, his waves did indeed travel faster than light, and in fact their velocity was infinite. The propagator which showed the influence of one space time point on another clearly allowed superliminal influences.
His theory had other problems as we... | {
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Can gravitons travel faster than the speed of light? It is common knowledge that not even light can escape black holes, but since the black hole is emitting gravitons, and the gravitons travel in the direction away from the black hole, and it is escaping successfully, are they faster than light?
| "Nothing can propagate faster than light" is a condition in GR.
Gravitons are not postulated by GR.
Hence the two (speed limit, and gravitons) are defined by two different theories and it would not be possible to compare things from two different theories unless we are able to combine the two theories, which has not ha... | {
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How does a Galilean telescope form an enlarged image even though it has a diverging lens? I have been reading about Galilean telescope and the picture in the book is something like this:
After rays pass through the converging lens, there is a real image formed which is intercepted by the diverging lens but as I learn... | There is your answer, the Galilean telescope - the assembled telescope as a whole with EVERY component part of it in its correct place - magnifies.
But you did raise a concern in your question that a diverging (or concave) lens cannot form an enlarged image. That is also correct. Such a lens, standing alone, a single ... | {
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Why doesn't hydrogen gas exist in Earth's atmosphere? The root mean square velocity of hydrogen gas at room temperature is:
Gas constant: $R=8.31\ \mathrm{J\ K^{-1}\ mol^{-1}}$
Molar mass of hydrogen gas: $M=2.02\times10^{-3}\ \mathrm{kg/mol}$
$$\begin{align}
v &= \left(\frac{3\times8.31\ \mathrm{J\ K^{-1}\ mol^{-1}}\t... | Brief explanation in human words:
Hydrogen is a small atom so its mean velocity (3.4 km/s) would be much higher than air molecules (0.5km/s); some hydrogen atoms would be travelling faster than the escape velocity.
The escape velocity on the Earth is 11.2 km/s so you might expect the Earth to have hydrogen gas. However... | {
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Why does stacking polarizers of the same angle still block more and more light? I have some sheets of polarization film. They came in a big box, all stacked at the same angle. I noticed that the entire stack of them lets almost no light through, even though they're all at the same angle.
I pulled out two, and those two... | An ideal (theoretical) polarizer will only let in light along a certain axis.
This is impossible in real life. Any polarizer that you can purchase will let in light in a range of possible polarization angles. Additionally, manufacturing processes cannot guarantee perfect alignment with the apparatus holding the polariz... | {
"language": "en",
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Why is it so much easier to fall when walking down a slope? When I walk uphill on an icey road, I almost never slip/fall. But if I walk downhill or even on a relatively flat road, I slip/fall frequently.
What is the physics reason behind this, and are there any tips to reduce the chance of falling (other than shoe modi... | I think it is better to say that concept of torque is working here.
When you walk on floor, there is no force which can provide a torque to your body. But when you walk on a slope, a component of gravitational force provide you a torque which results in falling.
| {
"language": "en",
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How does the sun really produce light in terms of waves? Electromagnetic waves are caused by changing electric and magnetic fields, and these are caused by a charge possible oscillating like an antenna or a varying current etc.
My question is, with the sun, where is this source that causes the electric and magnetic fi... | The Sun is made of plasma, which is a gas of bare ions and electrons. The energy released from nuclear fusion heats this plasma, and the moving charges emit electromagnetic waves.
Note that in other, colder radiating bodies (like a tungsten filament or a human body), the radiation is emitted by other means; in this cas... | {
"language": "en",
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The position of an element on a periodic sound wave So I am looking at the equation used to locate of a small element relative to its equilibrium position on a periodic sound wave. The equation is defined as below:
$s(x, t) = A\cos(kx - wt)$
Now I understand why the use of a sinusoidal function, but the equation is exp... | The general equation for the displacement could be
$$s(x, t) = A\cos(kx - wt)+B\sin(kx-wt)$$
It appears that the author has made a choice that $s(0,0) =A$ and $B=0$ which results in $s(x, t) = A\cos(kx - wt)$.
Others might have chosen $s(0,0) =0$ and $A=0$ which results in $s(x, t) = B\sin(kx - wt)$.
Another possib... | {
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Example of compact operators in quantum mechanics Can anyone give an non-trivial example of compact operators in quantum mechanics? Of course, any operator on a finite-dimensional Hilbert space is compact.
| All the normal quantum states of a given W* algebra of quantum observables are represented as compact (actually trace class) operators on a given Hilbert space (where the algebra of observables is represented).
In other words all the usual states of quantum mechanics in the Schroedinger representation, i.e. density mat... | {
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Newton's Law of Cooling as boundary condition to Heat Equation I am reading a book on Partial Differential Equations, and they derived the 1 spatial dimension heat equation from scratch (using a rod as an exmaple with end points at $x=0$ and $x=L$) and then gave a couple possible boundary conditions with appropriate ph... | In the situation where the temperature of the left end of the rod is less than the surrounding temperature then you got that the graph of the temperature should slant upwards in the right direction kind of like the in this graph
Remember that heat is always transferred from points with higher temperature to points wi... | {
"language": "en",
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Grashof number as a ratio of buoyant and viscous forces The Grashof number is supposed to be a ratio of buoyant forces to viscous forces.
I find this hard to believe, since if
$$F_b=\beta g \rho \Delta T$$
is the buoyancy force, the definition of the Grashof number,
$$\text{Gr}=\frac{\beta g\Delta T L^3}{\nu^2},$$
imp... | you both are right. I think the closure point is that the velocity $U$ which is normally the velocity outside the boundary layer (BL) in the forced convection problem, here is defined in terms of the buoyancy force. This comes in when going from the dimensional form of the BL equations for natural convection to the non... | {
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Optimal laser wavelength for heating air Lets say I want to heat air with laser,what wavelenght should I chose,ultraviolet,infrared or something in visible spectrum? To clarify,I want the laser beam to lose power and get converted to heat in shortest amount of distance possible. I am looking for maximum absorbtion, to ... | As you need to heat air to high temperature anyway, maybe you should consider a very high-power (pulse) laser that induces breakdown in air (https://www.rp-photonics.com/laser_induced_breakdown.html ); after the breakdown, air will be ionized and will absorb more power. Ideally, you should choose shorter-wavelength las... | {
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Deriving relativistic momentum (wikibooks) I asked a question about a derivation of relativistic momentum here, but I didn't really get an answer that helped me. So I looked up a different but similar derivation on Wikibooks (see here), and I have a different question now about this other proof.
Somewhere near the end ... | First a little clarification: this derivation is, although effective, a bit old-fashioned since it uses a concept like the relativistic increase of mass, which is now considered an outdated and confusing interpretation of processes in special relativity.
Nevertheless, the answer to your question comes from a few lines ... | {
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Why does torque produce a force on the axis of rotation? If a door is rotated about its fixed axis in (outer) space, a force parallel to the door on the hinges will arise due to centripetal force on the centre of mass and conservation of momentum (Newton's third law).
But any torque on the door will create a force on ... | If you view the torque as Force * Radius * Sin(angle between force and door) then you can see that t/r is the component of force perpendicular to the door if that force were applied at radius r from the hinge. Now imagine the forces on the hinge if you wanted to generate the same torque at various radii. The closer I ... | {
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Rolling in smooth inclined plane Can a body posses pure rolling in smooth inclined plane.In smooth
inclined plane the centre of mass of body is accelerating.So to maintain the pure rolling there should be angular acceleration.But no one provides the torque because the only forces Gravity and Normal reaction passes thr... | Whenever a simple roll starts rolling on earth, it is the earth itself that provides the angular momentum.
In your case, the roll on the say, for example, 30 degrees inclined plane always exerts its force perpendicular to the plane, i.e.pointing at (90-30)= 60 degrees into the earth. That means your roll kicks the ear... | {
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Why are all my separable solutions orthogonal polynomials in $L^2$? I spent a few hours today solving the Laplace and Schrodinger equation on a variety of domains, and kept finding solutions to the separated equations that were orthogonal (polynomials) in $L^2$, e.g. the quantum harmonic oscillator
$$-i u_t = u_{xx}-x^... | You have discovered the spectral theorem - (generalized) eigenvectors of self-adjoint operators like the Hamiltonian are orthogonal to each other and if the spectrum is discrete, they form an orthonormal basis.
| {
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Can the Mikheyev-Smirnov-Wolfenstein (MSW) effect be modified by non-standard neutrino-neutrino interactions? The MSW effect describes how propagation of neutrinos through matter can resonantly enhance the neutrino mixing. The reason for this enhancement is that the presence of electrons in matter changes the energy le... | Indeed non-stardard interactions can modify neutrino mixing. Here's one paper that discusses a few types of NSI and their effect on the solar survival probability.
*
*R. Bonventre, A. LaTorre, J.R. Klein, G.D. Orebi Gann, S. Seibert, and O. Wasalski, "Nonstandard models, solar neutrinos, and large $θ_{13}$", Phys. Re... | {
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Momentum of an electron acting as a wave Was working on a problem with electrons acting as waves in diffraction. Part of the question asked me to calculate the momentum of the electron. Since I was dealing with waves I used the following equation:
$h=pλ \implies p = h/λ$
Since $λ = v/f$ we can substitute that in, resul... |
Since I was dealing with waves I used the following equation:
$$h=pλ \implies p = h/λ$$
This is fine.
Since $λ = v/f$ ...
True for all waves, yes.
... we can substitute that in, resulting in $p = hf/v$.
This is okay, but we don't usually find people talking about the "frequency" of an electron matter wave.
Sub... | {
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Why don't humans burn up while parachuting, whereas rockets do on reentry? I guess it has something to do with their being both a high horizontal and a vertical velocity components during re-entry. But again, wouldn that mean there is a better reentry maneuver that the one in use?
| As others explained, the maximum speed of a parachutist is much smaller than that of orbital vehicles. But this is because parachutists jump from a relatively small height: the record jumps by Eustace (https://en.wikipedia.org/wiki/Alan_Eustace) and Baumgartner (https://en.wikipedia.org/wiki/Felix_Baumgartner) were per... | {
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Where does all the heat go during winter? I do not understand where actually the heat in our surroundings go during the winter season. Is it radiated out into space? I know it cannot coz global warming would not be a issue then. It might get absorbed but where? I tried figuring it myself but couldn't please help.
| Energy does get dissipated to space in Summer and in Winter. Think of CO2 like the difference between covering yourself in a very thin sheet or no sheet. In Winter, you'd still feel very cold if you had just a thin sheet covering you, and in Summer just a bit warmer. As CO2 increases, the sheet gets a little thicker e... | {
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How force exerted by spring is always opposite to the direction of displacement in Hooke's law Suppose a spring lying on a horizontal table, displaced from its equilibrium length by an external agent. The external agent is removed, the spring will head back to its equilibrium length. Here, the direction of spring force... | Occasioned by your comment @Fracher's answer :'But when moving from extreme to mean this does not seems true', i think that you mixed up the vectors 'displacement' and 'velocity' which can have opposite directions.
So i will try to explain the situation as simple as i can (and it is):
Hooke's law for a spring is oft... | {
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Can a (micro) black hole be used to make a microscope? We have seen that black-holes can be used as a telescope. Is there a chance that light bending from a micro black-hole can be used to create a microscope?
| the difference between a microscope and a telescope:
microscopes are used to magnify small objects that are at a short
distance from the viewer whereas telescopes are used to magnify large
objects that are at a large distance from the viewer.
In gravitational lensing a black hole is used as a lens to see objects fath... | {
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Why is a nonzero VEV for a spinor field said to break Lorentz invariance? Consider a spinor field $\psi(x)$. Its vacuum expectation value is given by $$v=\langle 0|\psi(x)|0\rangle.$$ Using the fact that the vaccum is invariant under Lorentz transformation, we get, $$v=\langle 0|\psi(0)|0\rangle.$$ Why is it that, if $... | The $v$ you write is itself a spinor, not a scalar. A non-zero spinor is obviously not invariant under Lorentz transformations, so a non-zero spinorial VEV breaks Lorentz invariance of the 1-point function.
| {
"language": "en",
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Did inflation stop because of energy density drop or some other reason? If I am understanding big bang correctly... During big bang
Approximately $10^{−37}$ seconds into the expansion, a phase transition caused a cosmic inflation,
Which was 'free lunch' of energy and it continued for some time but then suddenly 'fr... | There is no single answer, since there are many models for inflation and no one knows if any of them are correct.
Broadly speaking, what all the models contain is a scalar field at early times with a non-zero value, which is often termed a false-vacuum. The energy density of this field completely dominates the dynamics... | {
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Can an accelerating frame of reference be inertial? In physics problems, the earth is usually considered to be an inertial frame. The earth has a gravitational field and the second postulate of the general theory of relativity says:
In the vicinity of any point, a gravitational field is equivalent to
an accelerated ... | I think I understand what you mean. In an inertial frame, an object on which no net forces act, moves with a constant speed along a straight line. On earth this doesn't even approximately hold.
If you still want to consider this as approximately inertial, the conclusion must be that the earth itself is present (as mas... | {
"language": "en",
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Is the magnetic field of a moving electron caused by length contraction in the direction of motion? Consider an electron moving relative to us. Because the space in the electron's rest frame is contracted relative to us in the direction of the electron's velocity, the electric field lines are squeezed in the same direc... | There is the effect called magnetism, and then there is the effect that you described.
Some basic things about magnetism: There's no magnetism between a moving charge and a still standing charge. There's no magnetism between charges that move along a line.
And now some basic things about the effect you described: There... | {
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What is the correct way to estimate the work done by a climber? My teacher gave us a worksheet with word problems and their solutions. It is in German, so I have tried my best to translate it to English:
A 26 year old man climbs Mount Everest (8848 m) in only 8 hours 10 mins from the base camp at 5300 m. Estimate the ... | "Estimate the 'lifting work'" is the key part. Well, what is the lifting work? What are you lifting against? Gravity. What's the force gravity exerts? $F_{gravity} = mg$ (neglecting variations in $g$ as you go up the mountain). Therefore, the force in your formula $W=F\cdot \Delta S$ is the force of gravity.
| {
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How do scientists know Iron-60 is created during supernovae? I know that the meteoroids contain Ni-60, which is formed after decaying Fe-60, and as per my study, I got to know that Fe-60 is formed during the time of a supernova. But I wonder how scientists know/find that these elements were created during that event?
| As always, it depends on what you mean by know/find. As aptly illustrated by Kyle Kanos, theoretical arguments show that $^{60}\mathrm{Fe}$ is naturally produced through stellar nucleosynthesis in the last stages of the life of massive stars, and then injected into the InterStellar Medium (ISM) by SN explosions. This h... | {
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Why does each plate receive a charge exactly the same magnitude in parallel plate capacitor? When a parallel plate capacitor is connected through a cell, each plate of the capacitor receives a charge with the same magnitude, but with the opposite sign. Is it because of the battery or the area of the plates?
| Suppose you have a simple circuit with a capacitor and a power supply:
You want to create a charge on the capacitor, so you turn on the PSU to add some extra electrons to the upper plate:
But the number of electrons in your circuit is constant. The power supply can't create or destroy electrons. All it can do is act ... | {
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Interpretation of geodesic constant of motion The Schwartzschild metric in standard coordinates with signature $(1,-1,-1,-1)$ is given by
$$ds^2=(1-\frac{r_s}{r})\ dt^2 - (1-\frac{r_s}{r})^{-1}\ dr^2 - r^2(d\theta^2+\sin^2\theta\ d\phi^2).$$
As the Schwartzschild metric is independent of time then it has a time-displac... | The Killing vector is
$$
\xi_t~=~\sqrt{1~-~r_s/r}\partial_t
$$
and reduces to you case in the asymptotic region, or on the rest frame of any observer. For $\xi_\mu U^\mu~=~\epsilon$ what this tell us is the metric may be expressed as
$$
1~=~\epsilon^2~-~\frac{1}{{1~-~r_s/r}}(U^r)^2~-~r^2\left((U^\theta)^2~+~sin\theta(U... | {
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Double-slit experiment with two different mediums How the interference pattern will look like in a double-slit experiment done with two different mediums? Air before the slit and glass after the slit.
| There would be no difference qualitatively. The pattern is due to path difference after the slit, which would change by a factor of refractive index $n$ and therefore would change the fringe width compared the case of air..
However, if the upper half is filled with water and bottom half is air, the pattern will change.... | {
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Direction of normal force on stick on box
What is the direction of the normal force on the stick in this case, assuming gravity? Is it right angled with the stick? Or is it upwards? Or is it impossible to determine?
| Normal is a synonym for perpendicular.
The normal force is as you show it, perpendicular to the slanted object. Gravity is a separate force having a different agent (the earth) and plays no role in determining the direction of the normal force. Friction is parallel to the surface, and is not a normal force.
| {
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Wave packet expression Speaking in general about plane waves propagating along $z$ (electro-magnetic waves, for example; not necessarily particles represented as waves), a wave packet can be defined as
$$A(z,t) = \int_{\omega_1}^{\omega_2} A ( \omega ) e^{j (\omega t - kz) } d\omega$$
In particular, this expression is ... | The complex form
$$A(z,t) = \int_{\omega_1}^{\omega_2} A ( \omega ) e^{j (\omega t - kz) } d\omega$$
is the most common because it is compact (easy to write and read). As usual in physics, one writes complex expressions and when one wants the "real" thing, one takes the real part of the expression.
However, if you rea... | {
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Charged plasma and ion grid in interaction in ion thrusters I was just wondering .....
In this Image of an ion thruster, when the positively charged particles pass through the grids, wouldn't they just bombard the negatively charged grid(a fraction of them). This means that there must be a constant adjustment to maint... | You say "constant adjustment" as if you expect a motor with a PID controller to be spinning cat's fur on the grid to keep its charge ;P
The grid keeps it charge with 1.) a battery and 2.) by connecting both electron guns' filament to the positive grid. An electron gun is a special filament that when heated (by passing ... | {
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What is an induced electric field? I have read in many books about induced current in a coil (Faraday's law), and also the motional emf across a moving conductor in a magnetic field. But somewhere I read about induced electric field due to a time varying magnetic field.
And I think that Induction of electric field is... |
Current I through the solenoid sets up a magnetic field B along its axis and a magnetic flux Φ passes through the surface bounded by the loop.
Since charges are at rest (v=0) so magnetic forces Fm=q(v X B) cannot set the charges to motion.Hence induced current in the loop appears because of the presence of an electric... | {
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Why the electrons below the Fermi level do not conduct electricity? Physically, why is it that the electrons need to excited above the Fermi level to conduct electricity? In other words, why is the current zero when the electrons lie below the Fermi level? Does Pauli exclusion principle play any role here?
| Here is my way of thinking of it intuitively:
Each electron in an atom resides at a specific energy level (or state). Pauli's exclusion principle prevents any of them to occupy the same exact energy state.
When putting two equal atoms close together, they have identical electrons at identical energy states. Again Pau... | {
"language": "en",
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Does alpha radiation penetration depth decrease exponentionaly with distance? imagine there is 1mm² square area with thin film of Americium 241,kind of like the button in smoke alarms,lets theoreticaly imagine it gives 1000 becquerel of 5 MeV alpha radiation,that is 1000 particles per second.Now I know Americium gives ... | Alpha particles interact with matter via multiple small interactions.
The word "small" is used to indicate that the energy lost by an alpha during each interaction is small compared with the kinetic energy of the alpha.
So the alpha progresses through matter slowly losing kinetic energy.
So the graph of count rate wh... | {
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Will a contiguous, low-Re, low-Ca, liquid body always become a sphere at zero gravity? Let's assume zero gravity, zero initial speed everywhere, $Re \ll 1$ and $Ca \ll 1$
Will such a liquid body always become a sphere or will it sometimes split?
Formally speaking, I'm talking about
$$
\lim_{viscosity -> \infty} \lim_{t... | If the initial fluid blob had symmetric dumb-bell shape, then fluid pressure will be higher at its waist, and there will be flow from waist region to the two bulging regions, resulting in breakup into (at least) two smaller droplets (read up Rayleigh-Plateau instability). In other words, even if velocity is zero everyw... | {
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Why doesn't Young's modulus change with length and diameter? In this question:
The Young modulus of steel is determined using a length of steel wire and is found to have the value $E$.
Another experiment is carried out using a wire of the same steel, but of half the length and half the diameter.
What value is obtained... | From the given information how did you "calculate the Young's modulus for the 2nd experiment"?
You cannot assume that in the second experiment the force and extension are the same as in the first experiment because they are not.
For a given force the extension would be twice in the second experiment as that in the firs... | {
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How does $I = \mathrm{d}q/\mathrm{d}t$ work for a capacitor? When the capacitor is charging in a circuit consisting of a resistor, a capacitor and an alternating sinusoidal generator at $t=0$, the charge across the capacitor is 0 and the current is $I =\mathrm{d}q/\mathrm{d}t$. Does this make the current zero too? Whil... | If you apply a sinusoid generator to an RC series circuit, at t=0
the sine(2pi * f * t) is indeed zero. But the voltage on the capacitor
is NOT zero, rather the sum of I*R and the capacitor voltage is zero.
That's because 'a sine wave' means a sine wave that started
long ago, and at time t=0 it just came off a half-cy... | {
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What happens to temperature as volume increases (charles law) Let us take Boyles law to start.
Assumptions:
*
*Gas is perfect.
*In a massless piston that can be expanded with no friction
*Adiabatic
If we were to decrease the volume of the piston, the pressure inside would go up because the gas molecules would be... | Compressing a gas that is not at absolute zero will increase its temperature because a finite volume of gas at a finite temperature has a set amount of heat energy. when that set amount of heat energy occupies a smaller space its temperature rises. Conversely when it occupies a larger space its temperature goes down. s... | {
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Doppler effect and apparent frequency What is meant by "apparent frequency"?
I mean the answer we get by applying the formula; what does it signify?
If it is the frequency received by the observer, does it mean that the observer receives the same frequency no matter what the distance of the source?
Shouldn't distance o... | Doppler effect is the change in frequency (pitch) of a source when there is a relative motion between the source of the observer. It occurs in both sound and light waves.
| {
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Proton spin/flavor wavefunction I am currently working through Griffiths' Introductory to Elementary Particle Physics and I'm a little confused about a particle's spin/flavor wavefunctions. As a specific example, I've attached Griffths solution to the proton's wavefunction, and the formula he used to get it.
I unders... | Note that Griffiths is very careful to match each of these terms,
$$udu ~~\Leftrightarrow~ \uparrow \downarrow \uparrow,$$and if you match both terms at once you get two sign flips: $$(\downarrow \uparrow \uparrow - \uparrow \downarrow \uparrow)\otimes (duu - udu) = (-1)^2 (\uparrow \downarrow \uparrow - \downarrow \up... | {
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Why does a system expand isothermally? Considering the first step of the Carnot process, heat is transferred from a bath to the system with both at the same temperature. But how does this process start? Why should the system spontaneously absorb heat and expand as a result. And even if I pull on the piston an infinites... | It is as you say. On the isothermes the system is at the same temperature as the bath. Therefore no energy is exchanged at first. Now reduce the pressure on the system ("pull the piston"). The system reacts by increasing its volume to go back to mechanical equilibrium. It does work on you! It does work because a pressu... | {
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A helpful proof in contracting the Christoffel symbol?
Out of all of my time learning General relativity, this is the one identity that I cannot get around.
$$ \Gamma_{\alpha \beta}^{\alpha} = \partial_{\beta}\ln\sqrt{-g} \tag{1}$$
where $g$ is the determinant of the metric tensor $g_{\alpha \beta}$.
With the Chr... | Recall the matrix identity
$$\tag{1}\log\det M=\operatorname{tr}\log M.$$
If $M=M(\lambda)$ is differentiable in $\lambda$, then
$$\tag{2}\frac{d}{d\lambda}\log\det M=\operatorname{tr}\left(M^{-1}\frac{d}{d\lambda} M\right).$$
The proof of $(1)$ for symmetric matrices follows from the usual formulae for the trace and... | {
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Why viscosity depends on the scale of things? Water feels like honey for bacteria and air is very viscous for small insects.
My question is why viscosity depends on the scale of things?
| As @Tropilio indicated, viscosity does not depend on the scale of things. But in bacteria and small insects, the flow passages are very small (i.e., the surface to volume ratio is very large), and the viscous drag on the flowing fluid occurs at the flow surfaces. So viscosity has a bigger relative effect when the flu... | {
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Why doesn't increasing resistance increase brightness if $P=I^2\cdot R$ Light bulb brightness increases with power, $P$.
So why doesn't increasing $R$ increase $P$ and hence increase brightness as $P=I^2\cdot R$ due to $P=I\cdot V$ and $V=I\cdot R$?
I read increasing $R$ decreases brightness.
| You can use any of these formulas to calculate $P$:
$$P = I^2 \cdot R$$
$$P = \frac{V^2}{R}$$
They are both correct and will give same result. You can not tell which one is "dominant".
But to use these formulas you need to know not only $R$ but also $I$ or $V$. And to analyze these formulas you need to know how $I$ or ... | {
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Speed of block sliding on frictionless ramps Here's the question:
My book says the answer is C. How is it not A?
I know that all the potential energy is transferred to kinetic energy. With algebra, knowing Kinetic energy is (1/2) * m * v^2 and gravitational potential is mgh, I solve for h which results in (v^2)/2g
Ok ... | I have another solution:
Ok basically we can think of 2 phases. One where it goes from the first ramp down. The other phase is from down to another ramp, however this time at some height where velocity is equal to half the velocity at the bottom.
Considering the first phase, we know that all potential get's transformed... | {
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What is the significance of the phase constant in the Simple Harmonic Motion equation? The displacement of a particle performing simple harmonic motion is given by $x = A \sin(\omega t + \phi)$ , where $A$ is the amplitude, $\omega$ is the frequency, $t$ is the time, and $\phi$ is the phase constant. What is the signif... |
What is the significance of $\phi$?
The phase angle $\phi$ represents the relation between the displacement and velocity of the simple harmonic oscillator at the point in time arbitrarily designated as $t=0$. In particular,$$\tan\phi = \omega \frac{x(0)}{v(0)}$$
The point in time at which $t$ is zero is completely ar... | {
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Acceleration of car. One dimensional motion easy problem A car starts from rest and accelerates uniformly over a time of 5.21 seconds for a distance of 110 m. Determine the acceleration of the car.
My attempt at solving the problem:
$$a(x) = \frac{v - u}{t}$$
where
$v =$ final velocity
$u =$ initial velocity
$$$$
I get... | The displacement is equal to the area under a velocity $v$ against time $t$ graph as shown below.
If the body starts from rest and its final velocity is $v_{\rm f}$ then the average velocity is $\dfrac{v_{\rm f}}{2}$ and that is were your missing "$2$" comes from.
| {
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What causes change in planet's angular velocity? A satellite moving in an elliptical orbit will increase in angular velocity as it nears a planet. I understand that this is consistent with angular momentum. But what causes the increase in angular velocity if there is no torque acting on the satellite?
| The gravitational force is a central force so there is no change in the angular momentum of the planet about the Sun but that does not mean that the angular velocity cannot change.
You can think of it as the moment of inertia of the planet about the Sun getting smaller as the planet gets closer to the Sun thus increasi... | {
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An appropriate way to store neodymium magnets Okay so I've bought a few small neodymium magnets to play around with, they're very powerful and I really like them, but I was wondering what's the actual best way of storing those magnets in a way that doesn't affect their magnetic fields or degrades them in any way.
I'm c... | Before modern rare earth permanent magnets, magnets required a 'keeper', metal bar that would shunt the flux between poles. This would prevent a loss in magnetization that could occur over time for materials like AlNiCo.
But with rare earth magnets like NdFeB keepers are not required. They will hold their strength, eve... | {
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The equilibrium concentration of vacancies In the derivation of the equilibrium concentration of vacancies by statistical mechanics method, I was stumped by this procedure (marked by "?").
$\textbf{Physical Model}:$
1.Solid viewed as a collection of $N$ atomic sites;
2.Each site may or may not be occupied, and assume n... |
Why we don't consider the internal energy of the whole system rather than the vacancies?
Every atom being exactly at a crystalline site represents the minimum energy configuration. (Aside: This configuration only happens at absolute zero temperature.) What this energy is is irrelevant; it's some constant. You might a... | {
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What is a "Standard value"? Temperature:a measure of the warmth or coldness of an object or substance with reference to some standard value.
I really tried searching lots AND lots for what is "Standard value" is... But I still don't understand what does it mean in that sentence.
Can someone please tell me what do the... | At present the standard value is defined as follows:
The kelvin, unit of thermodynamic temperature, is the fraction $\dfrac{1}{273.16}$ of the thermodynamic temperature of the triple point of water.
It follows that the thermodynamic temperature of the triple point of water is exactly $273.16 $kelvins, $T_{\rm tpw} = ... | {
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Is it correct to say that matter and antimatter are opposite in all quantum properties that are conserved? Matter and Antimatter are always created in pairs, with the exception of CP Symmetry Violation. Thus, in order for some quantum properties to be conserved, these properties must be opposite in the particle and ant... |
Therefore, is it right to conclude and define an antiparticle as a particle with opposite conserved quantum properties?
You have the right idea.
Note that antiparticles are required to ensure that a theory is causal. In other words, a measurement at $x$ should not affect a measurement at $y$ if the separation betwee... | {
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Accretion neutron star; mass gain 0.8m? My textbook on Astrophysics says the following about accretion (translation):
Assume we have a particle with mass $m$ that falls on a neutron star; $R\approx 10$ km, $M\approx 1.4M_{\text{sun}}$, so $v_{ff}=2GM/R\approx 0.64c$, and $E_{kin}=1/2mv^2\approx0.2mc^2$. The particle f... | As you wrote yourself "this energy is converted to heat and radiation".
Especially the radiation will not be captured by the neutron star, I will simply radiate away as the particle falls towards the neutron star.
As for the heat, it will also radiate way, but over longer time-scales.
So if you subtract the radiation a... | {
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Do physicists use particle "energy" to refer to kinetic energy? In 1963, this paper was written about the effects of radiation on solar panels. The paper states that:
When electrons at energies greater than 145 KeV and protons at energies
greater than 98eV bombard a silicon crystal, they can displace an atom from t... | Yes. Bombardment implies kinetics. The (rest) mass of electrons and protons is fixed, it would make no sense to discuss it as a variable. More generally, a particle's energy can be considered to be composed of its rest mass, its kinetic energy, and it's potential energy. There's no single meaning to the term, in fact, ... | {
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Translation of Vectors I am a bit confused about translation of vectors. In the first class in physics itself we are told that we can translate vectors as we like to the desired position to do whatever that we are trying to do. For example, if someone draws two random vectors then to get the sum, we translate them, ma... | What you are describing is a property of vectors. Vectors are not defined by their location in space. They are only defined by their magnitude and direction.
Intuitively speaking, a vector describes displacement from its start point to its end point. The displacement between these two points is only defined by how much... | {
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is spontaneous magnetization and magnetic susceptibility a thermodynamic properties? Are spontaneous magnetization and magnetic susceptibility a thermodynamic property? How do you determine whether a property is thermodynamic or not?
| A macroscopic magnetic system is a thermodynamic system like that of a hydrostatic system. The former is described by the thermodynamic variables $(\textbf{H},\textbf{M},T)$ and the latter by $(P,V,T)$. Therefore, magnetization $\textbf{M}$ (not necessarily spontaneous) is a thermodynamic property and it's the analog o... | {
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"url": "https://physics.stackexchange.com/questions/311999",
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Can you build a compass that is attracted to the South Pole? Was just curious, since all compasses point to the North Pole.
South is just the opposite polarity of of North, so it seems very likely, but I've never seen an example of this. Is there any videos demonstrating this?
Could a South attractor be added to a stan... | If possible do as @AccidentalFourierTransform explained in a comment, namely:
Get a standard compass. Clean off the paint in one end of the needle, and pain the other one. Congrats, now you have a compass that is attracted to the South Pole!
Be aware, that some compasses are embedded in an oil capsule, so disassembli... | {
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Is the Moon in a "Freefall" Around the Earth?
The force of gravity keeps our Moon in orbit around Earth. Is it correct to say that the Moon is in “free fall” around Earth? Why or why not?
I think the answer is yes. The moon is falling towards the Earth due to gravity; but, it's also orbiting the Earth as fast as it's... | The moon is falling towards but "missing" Earth. Had it no sideways motion, it would certainly just fall straight down and crash. So yes, you can say that.
| {
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Can relative velocity be found? Can you find the relative velocity between two cars with constant velocity of U1 and U2=-U1. In other words is there any kind of experiment you can do to understand that you are moving also and not just seeing the other car with 2U1?
|
"...to understand that you are moving also and not just seeing the other car with 2U1"
That you are moving with respect to the ground? Yes. You can look at the ground and see that it is moving relative to you, so you must be moving relative to it.
| {
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Brewster's Angle In the explanation of Brewster window, wherever in the literature I have looked up, it considers the unpolarized light with only two polarization components: the s and p components.
But, in case of unpolarized light, the electric field oscillates in all directions, so at Brewster angle the p polarized... | Every linear polarization can be decomposed along two directions, one perpendicular to the other.
You correctly know that one of them will be partially reflected and partially transmitted, while the other completely transmitted. For a linear polarization along one of these two directions, you have a correct understandi... | {
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Experimentally measure velocity/momentum of a particle in quantum mechanics In the context of quantum mechanics one cannot measure the velocity of a particle by measuring its position at two quick instants of time and dividing by the time interval. That is,
$$ v = \frac{x_2 - x_1}{t_2 - t_1} $$ does not hold as just af... | Your method for measuring observables is perfectly good but there are many other ways to measure observable quantities.
Firstly, there is no perfect way to measure these observables, but the most commonly used one is to measure its deflection when it is passing through a magnetic field. In cloud chambers, charged parti... | {
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Transforming a sum to an integral: why does it work? The problem at hand has been discussed in loads of previous questions (1, 2, 3)), and my version can be stated as follows.
Consider the sum $$\sum_{\mathbf k} \ln(1+e^{-(\alpha+\beta \varepsilon_k)}) \ .$$ We are summing over, say, two dimensional k-space lattice $\m... | Why does it work? By assuming the separation distance between the points in the discrete space is negligibly small compared to the total volume, we can make use of the definition of the Riemann integral.
Say we are summing over discrete points $\mathbf k$ in k-space $$\sum_\mathbf{k}\ f(\mathbf k)\ .$$
If we want to ... | {
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Bounce of a ping pong ball vs bounce of other things (How does the material affect ?) Yesterday I saw that a ping pong ball bounced nicely on a hard surface but poorly on a mattress.On the contrary ,I saw that other things (a pen for example) bounced poorly on a hard surface but nicely on a mattress
Please I want to kn... | See here the shape of the object matters.
As the ping pong ball has following two reasons -
*
*The spherical shape provides it a perfect impact while returning through the hard surface. While the mattress has the resistance towards the motion of the ball and lets it loose its impact very quickly.
*The pen has the... | {
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What will be the velocity component in $x$-direction?
In the figure, the particle is hitting the surface at an angle $\theta$ and velocity $V_2$ along the $y$ direction.
Is there a name for this velocity? Can it be called orthogonal velocity?
I have worked out the velocity to be as following:
$V_x = \frac{V_2}{\cot(\t... | I think you would describe the direction of $V_2$ as oblique, in contrast to normal (perpendicular to the surface) or glancing/grazing (almost parallel to the surface). The same terminology is used for light rays.
Well that is your conceptual question answered, so no more guidance is needed - ok?
| {
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Relation between source slit aperture and it's distance from the plane of the secondary slits in Young's Double Slit Experiment In Young's Double Slit Experiment (YDSE), the relation between the source aperture (my book says source size... I'm assuming they mean aperture) s and distance from the plane of the two slits ... | As one could see s/S < λ/d is an inequality and not an exact equation. It's a recommendation and advice based on experience.
To draw the full picture let me tell you some historical facts. At the beginning the scientists (Grimaldi in the sunny Italy describes this) used a pinhole in a darkend window (and a mirror in f... | {
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Why does a simple pendulum or a spring-mass system show simple harmonic motion only for small amplitudes? I've been taught that in a simple pendulum, for small $x$, $\sin x \approx x$. We then derive the formula for the time period of the pendulum. But I still don't understand the Physics behind it. Also, there's no an... | It just means that the pendulum will only execute SHM with small angles for which the pendulum subtends as it oscillates.
For larger angles the motion of the pendulum deviates from being simple harmonic; that's why the small angle approximation is required in the derivation.
EDIT:
Even for a horizontal mass-spring sys... | {
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Current as the time derivative of the charge I have been told that the current $i$ can be defined as
$ i = \displaystyle\frac{dq}{dt} $,
where $q$ is the charge and $t$ is the time.
I do not understand this definition because, if the charges are moving so that the net charge remains constant in an infinitesimally thin... | Realise that, in case of electric current, it is the free electron that moves while the nucleus stays fixed. Hence, when we say charge, in this case, we actually refer to the free electrons that are moving inside the wire.
We do not consider the positive nuclear charges. Obviously the net charge is $0$ across any cross... | {
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Condensation of Water. Classroom Controversy In our test there was a question that went like so:
Question 4 You have a glass of iced water on an unshaded picnic table and went for a walk for 30 minutes. When you return you noticed
the glass has water on the outside of it.
a. In terms of heat transfer explain what ha... | I noticed that one commenter said that the question is inherently ambiguous concerning whether you count condensation that has rolled off the side of the glass.
Question: Would there have been more or less water on the outside of the glass if the picnic table was in the shade?
Indeed, if I were to interpret it in a p... | {
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Is it possible to make a destructive interference generator? Is it possible to make a light source that shifts waves of light to cause destructive interference to cancel the other light source out to make it fully dark?
| in theory yes you can do it. But real word is harsh, the light you see every day is mix of almost all wave lenght so to interfire whit that you would need emiter that send all waves but moved by pi/2 (to make it simple i asume every wave is sinusoidal). It might work at still viev but at dinamic you wolud have to know... | {
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Can an object falling in vacuum generate electricity by itself? When an object falls through vacuum, gravitational potential energy is converted to kinetic energy. Is there some way to get electrical energy out of the equation by itself (i.e. somehow convert the gravitational potential energy to electrical energy)? I... | Floris posted an answer that assumes the object is large enough for different parts of it to experience noticeably different gravitational forces. This is one way to accomplish it and written rather well, so I won't discuss that case further.
If you require that the object is small enough that all parts of it would be ... | {
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Can Zener Breakdown be converted to Avalanche breakdown? Wikipedia says:
The Zener effect is distinct from avalanche breakdown. Avalanche breakdown involves minority carrier electrons in the transition region being accelerated, by the electric field, to energies sufficient for freeing electron-hole pairs via collision... | Once you have any kind of breakdown, it dramatically reduces the differential resistance contributed by the depletion region, so if you double the external voltage, you're not doubling the voltage across the depletion region, but increasing it just a little bit, while an increasing fraction of the voltage drop occurs i... | {
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Looking for a good casual book on quantum physics I'm looking for something that is going to blow my mind without any scientistic ideas (e.g. something that sounds like science, but doesn't have anything in common with science), written by a professional physicist who spent a lot of time considering "what it all means... | I very much enjoyed "The Quantum Universe: Everything That Can Happen Does Happen", by Brian Cox and Jeff Forshaw. I believe that it was written for a slightly-above-lay audience, so your knowledge of maths and stats should be more than sufficient to get through it. The book has a witty and conversational style, but is... | {
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What does one second after big bang mean? Consider the following statement:
Hadron Epoch, from $10^{-6}$ seconds to $1$ second: The temperature of the
universe cools to about a trillion degrees, cool enough to allow
quarks to combine to form hadrons (like protons and neutrons).
What does it mean to say "from $10^... | While not at all obvious, it turns out that our best models of cosmology suggest that there exists a special frame of reference in which the distribution of the entire universe's matter and energy appears extremely uniform on very large (i.e. cosmological) scales. When we talk about the age of the universe, we always ... | {
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Method of image charges for a point charge and a non-grounded conducting plane I know how to solve Laplace's equation for a point charge in front of a grounded conducting infinite plane. But I want to know what happens (both physics and math) when the infinite conducting plane isn't grounded, or is connected to a poten... | If you would like to define V at infinity as zero and the conducting plane as not grounded, you can also think of the solution as a superposition of two different elctrostatic cases: Take the fields expression of a single charge and a grounded plane, and sum this with the fields given off by a plane of fixed potential.... | {
"language": "en",
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Density of states of Bogoliubov quasiparticles For a simple fermionic system the formula for calculating the density of states (DOS) is $N(E) = \sum_{n}\delta(E-E_{n})$ where $\{E_{n}\}$ is the set of eigenvalues obtained after diagonalizing the hamiltonian. Now to diagonaloize a hamiltonian with pair correlation terms... | Some information is missing, but I think that maybe if you expand the terms ($\sum_{k}c_{k\uparrow}^{\dagger}c_{-k\downarrow}^{\dagger}$) with the Bogoliubov transformation, some ortogonal operators may cancell and so you can separate the hamiltionian in terms of each $\gamma$ operator and $|u_k|^2$ and $|v_k|^2$. Afte... | {
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Would a gas "weigh" less than a liquid if they have the same mass? Thought experiment: I acquired two boxes of the same dimensions and same weight. One box contains $1\ \mathrm{kg}$ of water at room temperature while the other box has $1\ \mathrm{kg}$ of water, but in steam form, because the temperature of the box is a... | If both boxes are the same size and weight, contain the same mass of water, and the same mass of air, the weight of both boxes will be the same, and the buoyant force on the boxes from the air that they displace will be the same. With "all things being equal", the two boxes will weigh the same when put on the electron... | {
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Schrödinger equation and non-Hermitian Hamiltonians Is the Schrödinger equation still valid if we use a non-Hermitian Hamiltonian with it? By this I mean does:
$$\hat{H}\psi(t) = i\hbar\frac{\partial}{\partial t}\psi(t)$$
if $\hat{H}$ is not Hermitian?
| There is nothing stopping you from writing $\hat H\Psi(x,t)=i\hbar \partial_t\Psi(x,t)$ for arbitrary $\hat H$. The physics is in $\hat H$, not in the differential equation.
Now, if you want to get there, why not write even more generally
$$
\hat{\cal O}\Psi(x,t)=\partial_t\Psi(x,t)
$$
and get rid of the $i\hbar$ fac... | {
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Doppler effect differs when the entity moving is different
Why is the doppler shift different when whether the source is moving or the observer? Although they are traveling at the same speed. Noticing that the difference can't be neglected when the speed is a big fraction of the speed of sound.
| You would think that it wouldn't matter whether it's the source or the observer that's moving in the doppler effect. An argument might be that when the observer is moving, you can just choose a difference reference frame in which the observer is instead stationary and the source is moving, or vice versa.
The problem wi... | {
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What kind of wave motion is described by grass moving in the wind? You know that sort of 'rolling' illusion when wind blows across long grass, like in the "amber waves of grain" line from America the Beautiful
It's not the same motion as dropping a rock in water, which causes an up and down motion.
And if wind blows a... | There are three basic kinds of mechanical waves: Transverse waves, longitudinal waves, and surface waves. Surface waves propagate along an interface between differing media.
One way to describe wind blowing across tall grass is as a surface wave. The grass is held in place by its roots. The tops and sides of the gras... | {
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Liquid vs. gas cooling I have an aluminum can that needs cooled. I put it in the refrigerator, where it is cooled by the cold air surrounding the can.
If I were to place the same can in water that had been cooled to the same temperature as the refrigerated air, would the can cool down faster?
I'm inclined to assume th... | Heat transfer can occur by radiation, convection (natural or forced), conduction, or through a phase change. For the case of an Al can whose temperature is changing by a few degrees, it may be the case that conduction dominates (and conduction also plays a part in convection).
The most important material property in ... | {
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Ball inside an accelerating frame Why does a ball inside a moving bus at rest start moving backwards when the bus suddenly accelerates? Also does the moving ball have some acceleration?
This is my theory:
Initially the bus and the ball are at rest. When the bus starts accelerating, due to inertia of rest, the ball resi... | Analyse it this way .
If the bus is infinitely long such that there is no force from the walls and there is no friction also. Then in the road frame the ball stays where it is ( because no force acts on it ) while the bus moves forward.
In the bus frame the bus is at rest while to the bus the ball accelerates back whic... | {
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How do I find the time evolution of a ket? I have a question which reads:
Let \begin{bmatrix}
{E_0} & 0 & A \\
0 & E_1 & 0 \\
A & 0 & E_0
\end{bmatrix}
be the matrix representation of the Hamiltonian for a three-state system with basis states $|1>, |2> \mbox{and } |3>$.
a. If the state ... | Your reasoning is perfectly correct. Here it is in a complete form.
Let us write the Hamiltonian in the following way to make things clearer
$$ \hat{H} = E_0(|1 \rangle \langle 1|+|3 \rangle \langle 3|) + E_1|2 \rangle \langle 2| + A(|1 \rangle \langle 3| + |3 \rangle \langle 1|) $$
It is then straightforward to see t... | {
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What is the difference between mean free path and intermolecular distance? Why is the mean free path not be equal to the intermolecular distance?
A particle moving in a particular direction should strike the object in that direction after the traveling the same distance as the distance between them initially.
| The difference lies in the cross section of the particles.
Consider two equally large volumes containing an equal amount of particles, but the particles in volume A are twice the radius of the particles in volume B. In this case, the inter-particle distance is the same in both volumes, but the mean free path in volume ... | {
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Minkowski spacetime with a twist? Minkowski spacetime the has a flat metric of Lorentzian signature (-1,1,1,1).
It is well known (c.f. Geroch 1967 & citation there) that whether a manifold admits a metric of Lorentzian signature is equivalent to the question of whether it admits a nowhere vanishing timelike vector fiel... | Let me try answering this (assuming I understood the question).
In 4 dimensions you do not have a unique axis of rotation. Instead, there are two of them (so-called stationary plane which is fixed under a rotation). So in Minkowski space, when you rotate something around a time axis, you also rotate it around one of s... | {
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When can one omit a total time derivative in the Lagrangian formulation? I am studying Lagrangian and Hamiltonian mechanics and i am using Landau & Lifshitz and Goldstein books. Both of them state that a modified lagrangian $$L'=L+\frac{df}{dt}$$ gives the same solutions than $L$ wich i kind of understand but its not t... | Remember that the physics you get from a Lagrangian is due to a variational problem where you seek to extremize the action
$$S = \int_{t_1}^{t_2} L \, dt$$
So, the reason you can remove a total time derivative from your Lagrangian is because its contribution to the action is fixed:
$$\int_{t_1}^{t_2} \frac{df}{dt} \, d... | {
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Why does space have the topology of a three sphere? Suppose that $U(x)$ is an element of the gauge group say $SU(2)$ and suppose $U(x)=1$ as $|\vec{x}|\to\infty$. Then, why does space have the topology of $S^3$?
This is done in Srednicki page 571. Note that I'm not asking how to prove that $SU(2)\cong S^3$. What I'm a... | I think i got it,correct me if i am wrong.
We consider stereographic projection from the North pole $p$. Since Stereographic
projection is a one-to-one correspondence between {$S^n−p$} and $R^n$ and since,
$U(x)=1$ as $|\vec{x}|\to\infty$ we can regard $U(\infty)$ as the image of the
point $p$ then, instead of havin... | {
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Conservation of momentum in refraction Light, when passing through a boundary refracts. How is momentum conserved here? There can't be an impulse, the energy doesn't change.
| Momentum is conserved because the refracting medium/media at the boundary experience an equal and opposite change in momentum when the light changes speed and direction.
Light can push things - usually imperceptibly.
I'd stop there - but you did use the "how" word.
It's an electromagnetic interaction. The photon change... | {
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Is there a $n$-dimensional system such that the minimal action from a path from $x$ to $y$ is the scalar product? Suppose we work (with a particle) in $\mathbb{R}^n$.
Is there a Euler-Lagrange equation associated to the particle in question such that the minimal action of all path going from a position $x\in \mathbb{R... | The non-relativistic free point particle with Lagrangian
$$L~=~\frac{m}{2}\dot{\bf q}^2 \tag{1}$$
and with Dirichlet boundary conditions
$$\tag{2} {\bf q}(t_i)~=~{\bf q}_i\quad\text{and}\quad {\bf q}(t_f)~=~{\bf q}_i,$$
has Dirichlet on-shell action
$$S({\bf q}_f,t_f;{\bf q}_i,t_i)~=~ \frac{m}{2} \frac{({\bf q}_f-{\bf... | {
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If free quarks can't exist, how did the universe form? As I understand, the Big Bang started with a photon gas that then created the other particles. Thus obviously there would be some free quarks in the early Universe unless quarks are always created in pairs for some reason. How does physics resolve this?
| In the first stages of the Universe Quarks and Gluons were asymptotically free. This state of matter is called Quark-Gluon Plasma. Then, as the temperature of the Universe kept decreasing, the so-called hadronization (quarks combine to form hadrons) took place.
The coupling constant of the QCD (which, to make it simple... | {
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"url": "https://physics.stackexchange.com/questions/317672",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "12",
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Gaussian integral formula for matrix product I am looking for a way to prove that
$$ \det (M \cdot N) = \det(M)\det(N) \tag{0}$$
Where $M$ and $N$ are matrices with continuous indices, so that $\det$ is a functional determinant. A way to show that $(0)$ is wrong would also be welcomed.
This question is about the follo... | The statement seems to be wrong even for an infinite number of discrete indices.
Consider for example the vector space of square integrable functions on the positive integers, i.e. sequences $\{f_1,f_2,\cdots\}$ s.t. $\sum_{i>0} |f_i|^2 < \infty$, and consider the shift operator $S:f \mapsto Sf$, where
$Sf = \{ f_2,f_3... | {
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"url": "https://physics.stackexchange.com/questions/317771",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
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