Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Why are ropeway pillars tilted? While skiing I have noticed that ropeways pillars are usually tilted to be perpendicular to the slope (fig.1). If the gravity is pulling straight down, why aren't they vertical as they are supposed to support ropeway's weight? Is there something more they "do"?
Also there are pillars whi... | The cable is pulling up the slope and the masses are pulling down vertically, the net force is slightly angled forward and that's what the poles support.
| {
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Why do we care only about canonical transformations? In Hamiltonian mechanics we search change of coordinates that leaves the Hamilton equation invariant: these are the canonical transformations.
My question is: why we want to leave the equations invariant? I mean: we want to solve a differential equation (the Hamilton... | It's for the same reason that Einstein sought a covariant form for the equations of gravity. The equations should not be dependent on our coordinatisation of space. This he called general covariance.
In classical mechanics, canonical transformations leave invariant the Hamiltonian and this means it leaves invariant th... | {
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Potential Difference of a battery - What does it mean? I have studied current electricity for a while now. When I look back at basic concepts, I am quite clear about what current, electron, resistance is. But I cannot imagine about the potential difference or voltage of a battery. Or in a circuit, it is said that poten... | In short, this arose from a hydrodynamic analogy: the electrostatic potential is similar to pressure, the electrical resistance is similar to the hydraulic resistance of the pipe, the electric current is similar to the flow rate of a liquid. Battery voltage similar to hydraulic head. More details on this concept can be... | {
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Is it easier to balance a free-standing ladder when standing on the bottom step or the top step? This video shows someone climbing a ladder not resting against a wall: https://youtu.be/bWOSbEtDAas . I was wondering if it's harder to balance the ladder when you're standing near the bottom, or standing near the top.
Intu... | At the bottom. You will begin to fall as soon as the center of mass of the system passes through the vertical plane of the legs of the ladder. As you point out, this happens more easily up high by simple geometry.
You also mention a higher moment of inertia associated with being up higher. This is true, but really only... | {
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How to build an antisymmetric selfdual tensor out of two 4-vectors? In problem C of section 1.4 of Ramon's Field Theory: A Modern Primer, we are asked to build a field bilinear in $\chi_L$ and $\psi_L$, two left-handed weyl spinors, which transforms as the (1,0) representation of $\text{SL}(2,\mathbb{C})$. This represe... | Since both fields transform as $(\tfrac{1}{2},0)$ we can treat them as $SU(2)$ spinors and ignore everything else. So the question is how do you multiply two $j=\tfrac{1}{2}$ spinors to get a $j=1$ vector? Easy enough, just use regular Pauli matrices:
$$ b_L^{\pm,0} = \psi_{L\alpha} \sigma^{\pm,3}_{\alpha\beta} \chi_{L... | {
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Spaghettification on quarks? Imagine a nucleon falls into a black hole, I would expect the gravitational force acting on each quark to be drastically different but due colour confinement wouldn't there more pairs of quarks being spawned. Would this adds even more mass to the black hole and where do this energy comes fr... | A similar issue arises outside the context of quantum gravity. This question is similar to asking where the energy comes from to elastically distort a solid object under gravitational tidal force as an object falls.
For example, consider Newton’s famous (but possibly apocryphal) apple falling from the tree. The Earth’s... | {
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What happens to the quantum information of a particle and an antiparticle when they annihilate? I understand that the quantum no-deleting theorem dictates that it's impossible to delete quantum information, so what happens to the quantum information of a particle and an antiparticle when they annihilate each other?
| First of all, the particles don't disappear: they turn into other particles. But it's not as simple as just "electron + positron -> two photons". A state containing an electron and a positron is really only well defined as $t \to -\infty$, when we can think of the two particles as being infinitely far apart and hence h... | {
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The reasoning behind doing series expansions and approximating functions in physics It is usual in physics, that when we have a variable that is very small or very large we do a power series expansion of the function of that variable, and eliminate the high order terms, but my question is, why do we usually make the ex... | The idea behind any expansion is to express a "complicated" function in terms of simpler ones. In the case of a series expansion, the simpler ones are polynomials. Thus for instance the function
$$
\frac{1}{a+x}-\frac{1}{a-x} \tag{1}
$$
is a difference of two approximately equal quantities when $x/a\to 0$ and so app... | {
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$Q$-factor for damped oscillator (not driven)? How would this be defined?
Some of the Q-factor definitions I have encountered include:
$$Q=2\pi\frac{\text{Energy stored}}{\text{Mean power per cycle}}\\Q=2\pi\frac{\text{Energy stored}}{\text{Energy lost per period of
oscillation}}\\Q=2\pi\frac{1}{\text{Fractional powe... | The Q factor is $ 2\pi$ divided by the fraction of energy lost per cycle. If you drive the oscillator externally and keep the stored energy constant then you have to supply this fraction at every cycle.
Note: this definition does not require Q to be constant.
See https://en.m.wikipedia.org/wiki/Q_factor
| {
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Hamiltonian description of a system I know that phase space is the Hamiltonian description of a system, where we deal with position and momentum in equal footing. My question is in this phase space are those position and momentum are basis for that system?
As far as I know they are independent, in Hamiltonian dynamics,... | If the question is if the Hamiltonian phase space has the structure of a vector space equipped with a scalar product, the answer is negative, in general.
It is true that generalized coordinates and momenta of a system with $n$ spatial degrees of freedom are locally represented by $2 n$ real numbers and $\mathbb R^{2... | {
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Running coupling constants within a highly compressed object I wonder is it possible. in highly compressed objects, such as neutron stars and black holes, (I'm not sure that this applies to singularities), that the physical conditions within these objects partially mimic the conditions assumed to exist shortly after th... | The short answer is no. Compressed objects form from gravitational interactions, and the unification of coupling constants at some unification scale would only alter the type of matter being compressed, and not the nature of the compression itself. In order to resolve a singularity, one would need a modification of Gen... | {
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If the universe is flat, does that imply that the Big Bang produced an infinite amount of energy? Too much density and the universe is closed, analogous to a sphere in four dimensions: you travel in a straight line and you end up where you started. Too little and you have a saddle: not sure about the destination if yo... | If it was completely flat, you wouldn't talk about volume. The universe isn't completely flat, it does have a volume (like a pancake, it's called 'flat', but it definitely has a volume). For a truly flat object, your formula would need a surface density and surface area, and you would get a finite answer.
| {
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Where does it getting wrong , when using $v^2 - u^2 = 2as $ down the incline, for different object having different moment of inertia? Well, Consider a situation there is a sphere and a ring, of same mass $M$ and radius $R$. They both starts rolling down the inclined plane. We know moments of them as well, $$I_\text{sp... | Your kinematic equation of $v^2-u^2=2as$ is correct, but just like your question here you are neglecting the effects of friction, which gives rise to different accelerations for each object.
Considering the net force acting on each object, we actually have two forces with components acting down the ramp: gravity ($mg\s... | {
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Photons exerting force Since gravity affects photons, and forces always work in pairs.
Does this mean that photons have a resultant force.?
And would we be able to harness this resultant force to move objects using light?
|
Does this mean that photons have a resultant force?
Yes it does. If we send a light ray past a massive object and the path of the light ray is changed that means the momentum of the light is changed, and to conserve momentum the momentum of the massive object would also change. It would look like this:
This shows a... | {
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Are there any open questions in theoretical quantum physics? I am wondering if there are any open questions about the structure of quantum mechanics. If so, how do you know that this is an open question? Topics that come to mind are electron spin, probability amplitudes, and decoherence. I am interested in the foundati... |
Are there any open questions in theoretical quantum physics?
There is at least this million dollar open question:
The successful use of Yang-Mills theory to describe the strong interactions of elementary particles depends on a subtle quantum mechanical property called the "mass gap": the quantum particles have positi... | {
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Could you use ferrofluid to electromegnetically propel a rocket using it as a fuel? Could you accelerate ferrofluid through a solenoid to provide lift
| A ferrofluid is basically tiny iron particles suspended in oil; so your proposal is effectively to use iron particles for reaction mass in a rocket. Yes, that can be done, but specific impulse is proportional to exhaust velocity. It is easier to accelerate very low-mass particles like ions to high velocities in a sho... | {
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To what extent is the heat in the focal point due to visible light? When focusing sunlight on a piece of paper, e.g. with magnifying glass, the paper will be charred and might eventually even burn (assuming low cloudiness). To what extent is the heat a result of the focus of the visible light, rather than to other part... | It's mostly just the visible light, with some infrared.
Typically, glass doesn't transmit so well outside the visible spectrum, as shown in the graph in this answer. Near infrared gets through ok, but ultraviolet transmittance drops off fairly quickly. And then you have to take dispersion into account: different wavele... | {
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What gives mass to black hole? I like to know when a dying star collapsed into a black hole, is there anything inside or on the event horizon that is interacting with higgs field?
| To answer the question in the title of this post: the mass of a black hole, and the gravitational field propagated by that mass, come from the mass of the object which originally collapsed and formed the black hole, plus any mass which fell into it after that.
Since the gravitational field of a black hole was in exist... | {
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Is there anything special about ebonite and fur? I'm from Czech Republic, born 1980. From elementary school, we all remember this mantra:
When ebonite rod is rubbed with fox fur, electrostatic charge is created.
Electrostatic charge is created by rubbing ebonite rod with fox fur.
Rubbing ebonite fur with fox fur ... | You're looking for the triboelectric effect.
The triboelectric series is an empirical table of materials in order, such that materials high on the list tend to give electrons to materials lower on the list. Fur is high, ebonite is low. Materials of similar index don't build up much charge separation from rubbing, while... | {
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Why do mirrors not follow brewster's angle? Normally a material will have an angle where the reflected light is completely polarized. Now say we have a mirror (implemented by a conductive silver coating) that reflects most of it's incident light. https://physics.stackexchange.com/a/10925 says that this imperfect mirror... | I think you may have misunderstood the answer to the question you cited. It says that light reflected from a silvered mirror will be mostly unpolarized. This is true whether the silver is on the front or back surface. There is a very slight polarization due to the less than ideal properties of the silver.
The front ... | {
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Still Confused about Linear Momentum in a Circle
A point mass with mass $m$, distance $r$ from circle and constant tangential velocity and constant angular velocity is swung around a circle. ($p$ is linear momentum)
Angular momentum is radius x linear momentum. It is conserved.
If $r$ is increased, linear momentum... | Linear momentum is conserved when there is no force acting on the system. If you increase the radius, you will have to exert a force on the system. If this could be done without a force then you could accelerate the particle to high speed and then increase the radius to infinity. This would violate conservation of ener... | {
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Mass hanging from spring in free fall
Q: A mass $m$ hangs from a massless spring connected to the roof of a box of mass $M$. When the box is held stationary, the mass-spring system oscillates vertically with angular frequency $\omega$. If the box is dropped falls freely under gravity, why does the angular frequency in... | A mass hangs by a spring from the roof of a box under gravity, and the mass-spring system oscillates vertically with angular frequency w.
Then the box is dropped and falls freely while the mass is moving downward.
The string is stretched until the box and the mass are traveling at the same velocity. Then the spring pul... | {
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Is it possible understand Berry curvature as Gaussian curvature in some limit? I would like to understand the Berry curvature and the Chern number from mathematical geometry-topology.
I understand that in electronic QHE, there is a map from $k^2$ to a vector space where the eigenvectors "live". These eigenvectors are ... | The Berry connection and Berry curvature only appear due to the wave nature of physical systems. That is why it also plays a role in photonics, acoustics and other classical wave equations.
The Berry connection and Berry curvature are a connection and a curvature in the mathematical sense on a vector bundle, commonly ... | {
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Quantum tunneling in a capacitor Ampere's law of Maxwell's equation includes displacement current as the Maxwell's correction.
Suppose consider a capacitor with a thin distance of separation. For an applied voltage do they posses some tunneling current?. If so, Do we have to include these tunneling current in the Maxwe... | Quantum tunneling is defined when there are wavefucntions describing the particles in potential wells. The potential wells are defined in the solid plates of the capacitors and any effect of tunneling can only happen over distances where a potential well can be modeled accross the capacitor gap.
Quantum mechanical effe... | {
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Will any charge oscillating in space create an EM wave? Would it be correct to say that any charge oscillating in space (regardless of the spacial amplitude) at a given frequency will emit an EM wave of the same frequency?
related: What change in an EM field is required to create an EM wave?
| It depends on the available space. In a free space - yes. In a perfect cavity the proper cavity modes are discrete and start from some minimal frequency. So a "slow" charge oscillations may not excite even the lowest cavity mode. The corresponding EMF is then purely reactive and may not propagate.
| {
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Relationship between CO2 concentration and thermal conductivity of the air in a volume? How much would the percentage of CO2 in a room need to change in order to make a measurable change (using transient hot wire method) to the thermal conductivity of the air inside room? Are there other changes to the air composition ... | I don’t think you can get enough CO2 into room air to have a signal and still breathe it.
Humidity might be a much stronger signal. Particularly at just above room temperature, the thermal conductivity varies significantly with humidity:
(From here, which has more info)
| {
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Are problems with self-energy of point charge in classical electrodynamics solved by field quantization? Classical electrodynamics gives strange results when considering a moving charge in its self generated field (Abraham-Lorentz equation).
Some 50 years ago there were many efforts and publications about how to interp... | No, in QED the main term of the self-action diverges and it is discarded, just like in CED.
P.S. In CED one can see that the main self-action term is a self-induction. It is not a desirable radiation reaction ("small") term, but an additional inertial ("big") term.
In QED it is less visible, but there it is still a sel... | {
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Is it possible to entangle particles for their path? In the figure below, you have a source of entangled particles that then sends these particles in opposite directions.
Each stream of particles heads towards a double slit with a detector screen beyond the slits. Is it possible to entangle these particles with respe... | For the configuration you've drawn, no, that won't be possible.
If you modify the source so that it has the capability to point independently at slit A (resp. B, C, D) without illuminating the slit B (resp. A, D, C) in the process, though, then the answer is yes, that's a perfectly possible state. In this form (and unl... | {
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Why we neglect the $\hbar ω/2$ in the Hamiltonian of the the Electromagnetic Field? After the quantization of the electric and the magnetic field, we get the Hamiltonian of the electromagnetic field:
$$H= \hbar ω(a^{\dagger}a +1/2) .$$
with $\hbar$ the planck constant and $a^{\dagger}$ the creation operator.
Why can w... | The "quantization" procedure is ambiguous: it may contain terms proportional to $\hbar$ disappearing in the classical limit. So, we can consider Rabi Hamiltonian as a result of quantization too. The rest has been already explained in the previous posts.
| {
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Stability in Nuclear Shell Model As far as I understand , a particular sub-shell is filled with either protons or neutrons, $2*(2l+1)$ number of them, and never both together since protons and neutrons fill up levels separately in the shell model.So, are the magic numbers (2,8,20...) achieved by filling either of the e... | Yes, a magic number is achieved when there is a magic number of either protons or neutrons. In your example of p=2 protons and n=6 protons ($^8$He), we might then expect expect it to have "magic" properties such as a preference for a spherical shape and large gap in energy between the ground state and the first excite... | {
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If electric fields add, and intensity is proportional to $E^2$, doesn't superposing light violate energy conservation? We know that the energy in a wave goes as electric field amplitude squared($E_0^2$) as given by poynting vector but the amplitude of electric fields are added linearly. To see why this creates a parado... | Is is the key point of interference in optics (Young double slits or Michelson interferometer...).
On a bright fringe, the intensity is $4I0$ but this is compensated by the dark fringes, with zero intensity. Energy is conserved but with a different spatial repartition.
Sorry, I understand the question a little better. ... | {
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How does the heat capacity of an object come into play in thermal radiation? So say there's a cube in space acting as a blackbody.
Each side is 2 metres. Initial cube temperature is 400 Kelvin. Mass is 15 kg.
Say the heat capacity is 500 J/kgK. How would that affect thermal radiation? Or is it not a factor? How does i... | The temperature determines the rate at which energy is radiated away (other factors, such as the emissivity, the temperature of the surroundings, and the geometry are also relevant).
The heat capacity determines how quickly the temperature changes as internal energy is changed. All other things being equal, a hot obje... | {
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Probability of obtaining an eigenvalue for a degenerate spectrum of continuous eigenstates I'm trying to find the probability of obtaining an eigenvalue $\lambda$ which has a degenerate set of eigenstates $\phi_1(x)$, $\phi_2(x)$, and $\phi_3(x)$. Now, I want to know if this approach is correct for doing this:
$$p=\lef... | Your expression is correct. The probability is indeed given by
$$p=\left|\int\phi_1^*(x)\psi(x)dx\right|^2+\left|\int\phi_2^*(x)\psi(x)dx\right|^2+\left|\int\phi_3^*(x)\psi(x)dx\right|^2$$
The expression $\langle\phi\vert\psi\rangle$ is an inner product. For the case where you have a finite dimensional space, you have... | {
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Why does sound behave differently in water than in air? I noticed in some experiments at home that sound does not behave the same in water than in air. Is there a good scientific explanation to this?
I noticed that the sound sounded distorted in water but not in air.
I also used a software that I could use to hear the... | Human ears are evolved to furnish a good impedance match between sound waves traveling in air, and the nerve array inside your ear that turns vibrations into electrical impulses. This means that the greatest possible amount of sound wave energy will be conveyed to those nerves, across the greatest possible range of dif... | {
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If I leave a glass of water out, why do only the surface molecules vaporize? If I leave a glass of water out on the counter, some of the water turns into vapor. I've read that this is because the water molecules crash into each other like billiard balls and eventually some of the molecules at the surface acquire enough... | From a thermodynamic point of view, at fixed pressure, the vaporization takes place when the temperature exceeds the temperature of change of state $ Tc (P ) $
Within the liquid, the pressure that is to be taken into account is the hydrostatic pressure. This pressure is a little greater than 1 bar and the associated va... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Conceptual understanding of operators in QM Do operators in QM represent in some fashion the action of the measurement apparatus on a state being measured? Usually operators in QM are introduced as abstract transformations whose eigenvectors/eigenvalues are axiomatically the possible results of measurement, with an exp... | I think that in the same sense as previous members have answered the hamiltonian has a certain role to play in the time evolution of the system.If viewed from the schrodinger picture it is the state of the system which evolves but in heisenberg picture it is the operator or rather the expectation value which evolves in... | {
"language": "en",
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"source": "stackexchange",
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Dot product in E&M
I'm learning graduate level E&M. Textbook is a famous Jackson book. What I would talk now is about pp.295-298 in 3rd ed. I attached the photo of p.298.
It says (paragraph above eq.(7.15) and footnote in the photo) that $\vec{n}\cdot \vec{n}=1$ doesn't mean n is unit vector if n is complex vector. An... | The reason is quite simple: the use of the “standard” (i.e. real) dot product is the more familiar notation to physicists. Of course, you could absolutely rewrite everything in terms of some Hermitian inner product $\langle\cdot,\cdot\rangle$ and the equations might become a bit cleaner, but this would come at the expe... | {
"language": "en",
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What's the difference in a $P$-$V$ diagram that is curved versus one that is straight?
So what would the difference be between the graph above versus one that has the same initial and final points but the path is curved. I'm sure it has something to do with temperature, so does it mean temperature is constant? Or is t... | In an isotherm, which is a path through the $PV$ diagram where temperature $T$ is held constant, curved lines are formed. $P$ as a function of $V$ is given by the ideal gas law.
$$PV = NkT \Rightarrow \boxed{P = \frac{NkT}{V}}$$
So, the isothermal curves are similar to the shape of $y = 1/x$ in the first quadrant.
Howe... | {
"language": "en",
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Are powers of the harmonic oscillator semiclassically exact? The Duistermaat-Heckman theorem, although too complex for me to completely grasp, states that under some conditions, the partition function for a special class of Hamiltonians is semiclassically exact. The harmonic oscillator is exact and should be an element... | There are at least 2 types of partition functions:
*
*A finite-dimensional integral $$Z~=~\int \!dq~dp ~\exp\left\{-\frac{i}{\hbar}H(q,p)\right\}$$ with some $U(1)$ circle action, which OP didn't specify. Here a (Wick-rotated/oscillatory) Duistermaat-Heckman theorem applies.
*A loop-space functional integral $$Z~... | {
"language": "en",
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Friction acting as an internal force I was solving this problem in my assignment:
Assuming a frictional force F acts on the block of mass m, a force -F will act on plank of mass M. Hence, the net work done by frictional force should be zero, as friction is an internal force , but option D is given incorrect. What's t... | For the free body system we can write this equations:
$$m\,\ddot{x}_m+F_\mu=0$$
$$\dot{x}_m=-\frac{F_\mu}{m}\,t+v_0\tag 1$$
$$M\,\ddot{x}_M-F_\mu=0$$
$$\dot{x}_M=\frac{F_\mu}{M}\,t$$
Where $F_\mu$ the friction force between the block and the plank.
the friction force work is:
$W=\int \,F_\mu\, dx=\int_0^{t_s}\,\,F_\m... | {
"language": "en",
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Different expressions for distance & displacement : $\int$$d$$|\vec r|$, $\int$$|$$d$$\vec r$|, and $|$$\int$$d$$\vec r|$ I came across these expressions in my book. And the book says that all these are different from each other.
The expressions are : $\int$$d$$|\vec r|$, $\int$$|$$d$$\vec r$|, and $|$$\int$$d$$\vec r... | Notation matters. You have probably seen $\int d|\vec{r}|$ written as $\int dr$, without vectors.
*
*In 1D, this is the same as $\int dx$. The letter for the disttance is not relevant.
*In more than 1 dimension, it's the integral along the radius. For example, in a circle, you'd integrate for all angles and also ... | {
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What is the relation between chemical potential and the number of particles? Chemical potential is defined as the change in energy due to change in the number of particles in a system. Let we have a system which is defined by the following Hamiltonian:
$$H = -t \sum_i^L c_i^\dagger c_{i+1} + V\sum_i^L n_i n_{i+1} -\mu ... | At zero temperature, to find the relation between $\mu$ and the particle number you have to know the ground-state energy $E_N$ of the system with $N$ particles, and then $\mu= E_{N+1}-E_N$ Consequently you have to solve your Hubbard model exactly before anything else.
Once you have done this, you can approximate t... | {
"language": "en",
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Creation operator acting on a coherent state. Occupation number operator For a coherent state
$$|\alpha\rangle=e^{-\frac{|\alpha|^{2}}{2}}\sum_{n=0}^{\infty}\frac{\alpha^{n}(a^{\dagger})^n}{n!}|0\rangle$$
I want to find a simplified expression for $a^{\dagger}|\alpha\rangle.$ I can only get this $$\begin{align}
a^{\dag... | There's no easy expression for $a^\dagger\vert\alpha\rangle$ but you are interested in $\hat N\vert \alpha\rangle$ the easy way is
\begin{align}
\hat N\vert\alpha\rangle &= \hat N e^{-\vert\alpha\vert^2/2}
\sum_n \frac{\alpha^n}{\sqrt{n!}}\hat N\vert n\rangle\, ,\\
&= \hat N e^{-\vert\alpha\vert^2/2}
\sum_n \frac{\alph... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How big would a black hole have to be to absorb the Sun? How big would a slow moving black hole have to be to absorb or otherwise destroy the Sun?
| The odds of a roaming stellar blackhole entering the solar system is less than 1 in a trillion. There are two predominant types of a black hole in the universe. The first are supermassive black holes found churning at the center of galaxies. These don’t pose any threat to us at least until our galaxy collides with the... | {
"language": "en",
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Does the existence of electrons validate the integral form of electric fields? For an arbitrary charged object, it seems to be the case that we express it as a continuous sum (sum on the reals/integral) of point charges $dq$ that have a canonical Coulomb's law force.
That is to say, for an arbitrary charged object, we ... | It was experimentally verified that assuming a continuous charge distribution was a good approximation for most, if not all, of the macroscopic electric phenomenon. A continuous charge distribution is no equivalent to a distribution of charged point particles. Assuming a continuous charge distribution can actually be t... | {
"language": "en",
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How do I derive the angular frequency of a simple pendulum through conservation of energy? Is it possible? I'm not exactly sure what I'm doing wrong.
So far I've gotten:
$mgl(1-$cos$\theta) = \frac12\omega^2l^2$
Which then gives $\omega = \sqrt\frac{2g(1-cos\theta)}{l}$ which is incorrect. Where am I going wrong??
| The problem is $v=wr$ only works for constant acceleration case, for rotational motion. So we cannot just say $d\theta /dt=\omega$.
The total energy of the system
$$E=1/2m\dot{\theta}^2 l^2+mglcos(\theta)$$
Since theres no external force acting on the system.
$dE/dt=0$
Hence
$$m\dot{\theta} l^2\ddot{ \theta}+mglsin(\t... | {
"language": "en",
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How to start moving in at $Re\ll1$ I find it difficult to see how something can accelerate (and therefore increase its velocity, e.g. start to move) in a $Re\ll 1$ situation.
It is customary, at low Reynolds numbers, to ignore inertial effects. This means that the nonlinear terms in the Navier-Stokes equations vanish. ... | You are right. Swimming is impossible if Re<1. The forward motion is neutralized by the backward motion.
The only way to create propulsion is the screw. That's why the small swimmers has a long tail, they are rotating it, instead of flapping it back and forth.
This all is explained well in this old National Committee ... | {
"language": "en",
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Why some forces follow superposition principle? Let there be a system of $n$ source charges and a test charge $Q$. When we say superposition applies to electrostatic force, we conclude that the interaction between a given source charge and the test charge is independent of interaction between other source charges and t... | Superposition holds only because experiments show it to be true.
"Superposition is not a logical necessity, but an experimental fact"
Source of quotation:- Introduction to Electrodynamics, David J Griffiths
| {
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Faster ways of computing feynman diagrams Obviously the machinery of QFT allows us to calculate processes, such as QED diagrams, to great precision, and whilst it is effective, it seems there are many processes that make calculations (say by hand) significantly slow.
Are there any recent developments in our machinery t... | There are a number of computer algebra systems for evaluating Feynman diagrams and doing other particle physics calculations, such as FeynCalc, FORM, GiNAC, Package-X, etc.
| {
"language": "en",
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"source": "stackexchange",
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Classical angular momentum components are numbers. Can they be generators of some symmetry group? In Quantum Mechanics (QM), angular momentum turn out to be the generator of rotational symmetry. This is trivial to see because in QM, angular momenta are defined by the commutation relations $$[J_j,J_k]=i\hbar\epsilon_{jk... | As you mention, they're not "just numbers" - they are functions of the coordinates and momenta. And, as such, they can indeed be used as generators of some symmetry group via the usual tool for the job in hamiltonian mechanics: the Poisson bracket.
Here, you won't be much surprised to learn that the mutual relationship... | {
"language": "en",
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Pressure due the atmosphere Usually when we consider the pressure exerted by gas, there is nothing to do with the weight of the gas. On the contrary the atmospheric pressure is defined as the weight of the gasses. What is the difference here?
| This is actually a pretty interesting question.
For starters, it depends on the system you are analyzing. Atmospheric gasses are basically an open system that stays together due to the force of gravity. All the gas further down is supporting the weight of the above gasses. The force of this weight on top pressurizes... | {
"language": "en",
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Computation of $e^{i \hbar \omega a^{\dagger} a} a e^{-i \hbar \omega a^{\dagger} a}$ I need to compute terms like :
$$e^{i \omega t a^{\dagger} a} a e^{-i \omega t a^{\dagger} a}$$
Where $[a,a^{\dagger}]=1$ (they are the bosonic annihilation/creation operators).
I wonder if there is a simple formula for this. Indeed,... | Hint: there is a general identity
$$ \exp(\hat{X})\hat{Y}\exp(-\hat{X}) = \hat{Y} + \left[\hat{X},\hat{Y}\right] + \frac{1}{2!}\left[\hat{X},\left[\hat{X},\hat{Y}\right]\right] + \frac{1}{3!}\left[\hat{X},\left[\hat{X},\left[\hat{X},\hat{Y}\right]\right]\right] + ...\ ,$$
which I believe would be useful for your purpo... | {
"language": "en",
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Why is iron the peak of the binding energy curve? If Nickel-62 and Iron-58 have more binding energy per nucleon than Iron-56 does, then why is iron-56 shown as the peak of the binding energy curve? Also, does adding neutrons always make the atom more stable because it will increase the strong nuclear force but not add ... | *
*The "folk wisdom" that iron-56 has the highest binding energy per nucleon is in fact incorrect; both iron-58 and nickel-62 have a higher binding energy per nucleon, with nickel-62 being the highest. I can't do much better than citing an article on the subject:
M. P. Fewell, "The atomic nuclide with the highest m... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How can I determine a planet's mass based only off of information about its orbit and its parent star? I'm coding a video game with procedurally generated planetary systems and I want some and I want to make sure I'm at least somewhat scientifically correct. I've reached the part in my code where I know where a planet ... | The simple two-body problem won't give you bounds or constraints on planetary masses. However, one has to take into account the effects of planet-planet interactions which change the scenario. In particular, one has to take into account the effect of orbital resonances ( see the wikipedia page on this topic ) which may... | {
"language": "en",
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Why aren't particles constantly "measured" by the whole universe? Let's say we are doing the double slit experiment with electrons. We get an interference pattern, and if we put detectors at slits, then we get two piles pattern because we measure electrons' positions when going through slits. But an electron interacts ... | Distinguishing which slit is which is the factor that causes the wavelike interference pattern to disappear. Experiments show that the more the path can be determined the more they look like single photons.
Here's some notes on a course where this is worked out explicitly for a Mach-Zender quantum interference experim... | {
"language": "en",
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Diffusion equation Lagrangian: what is the conjugate field? Morse and Feshbach state on p. 313 without elaboration that the diffusion equation for temperature or concentration $\psi$ and its "conjugate" $\psi^*$ (quotation marks theirs) has the Lagrangian density:
$$L=-\nabla\psi\cdot\nabla\psi^*
-\frac{1}{2}a^2(\psi^... | The conjugate field ψ∗ is but the complex conjugate of ψ, so an extra degree of freedom to expedite derivation of the diffusion equation,
$$
\nabla^2 \psi = a^2 \partial_t \psi ,
$$
analogous to the Lagrangian of the free Schroedinger equation, real in that case--only.
*
*But, since this equation does not mix rea... | {
"language": "en",
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Why did recombination make the universe transparent? It is commonly said that after the universe cooled enough for ionized Hydrogen to settle down into neutral Hydrogen, i.e. recombination, the universe became transparent. A reason I have heard for this is that most photons don’t have the right energy to be absorbed by... | When a photon with insufficient energy to move an electron from one energy level to a higher energy level (including to complete ionization) the photon may change direction, but not energy. During a period of time, say e.g. one second, about the same same number of photons move towards the observer, just as if there we... | {
"language": "en",
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Why do electromagnetic waves have the magnetic and electric field intensities in the same phase? My question is: in electromagnetic waves, if we consider the electric field as a sine function, the magnetic field will be also a sine function, but I am confused why that is this way.
If I look at Maxwell's equation, the c... | This is one of those 'why' questions that physics can or cannot answer, depending on what you want from answer to 'why'.
If equations are a satisfactory explanation, then the Maxwells Equation in Emilios answer are a complete answer.
Unfortunately, not far beneath the surface of that answer is 'why do Maxwells Equation... | {
"language": "en",
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How can be $\frac{1}{4\pi R^2}\int_{S}V_{ext}(R)da= V_{ext}(0)$ physically explained? I was working out problem 3.1 (4th edition) of Introduction to Electrodynamics by Griffiths, which asks you for the average potential over a spherical surface due to a charge located inside the sphere (as well as verifying an equation... |
How can be the average potential due to an external (out of the sphere) charge $q$
be equal to the average potential due to a charge $q$ located at the center?
It's not. The average potential over a spherical surface of radius $R$ due to a point charge a distance $z > R$ from the center of the sphere is $$V_\text{... | {
"language": "en",
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Unification of gravity and electromagnetism Have there been any attempts at unifying gravity and electromagnetism at least at classical level since Hermann Weyl's idea of gauge principle (1918)? We now have Standard Model which is very successful and many other theories. But gravity and electromagnetism are long range ... | Most physicists are not interested in unifying just gravity and electromagnetism, because electromagnetism is already fully unified with the weak nuclear force. They’re now sometimes just called the electroweak force.
Furthermore, the strong nuclear force has closer similarities to the electroweak force than gravity do... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why does the $\phi$-cubed theory have no ground state? In the book of Sredinicki's, he claimed that the $\phi^3$ theory has no ground state, hence this is not a physical theory.
My question is that I can't see why this system has no ground state. And I don't understand either the explaination he gave. For example, what... | Work on a spatial lattice of finite extent so that the field operators and the Hamiltonian are well-defined as (unbounded) operators on a Hilbert space. Consider any Hamiltonian of the form
$$
H = \epsilon^D \sum_x \Big(\Pi^2(x)+V\big(\phi(x)\big)\Big)
\tag{1}
$$
where $\epsilon$ is the lattice spacing, the sum is over... | {
"language": "en",
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Can muons exist in space? Since muons produce when cosmic rays crash and collide into air molecules in the atmosphere, one would think that there would not be any muons in space. Is it true?
| They can exist in space, but only briefly. Muons are unstable, with a short lifetime of only 2.2 microseconds in their rest frame. They decay usually into an electron and two different kinds of neutrinos. Interplanetary and intergalactic space is not completely empty, and muons could be produced in space by occasional ... | {
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Lagrange equations in a conservative system, understanding $\nabla_i$ For a system of multiple particles with conservative forces: $\mathbf{F}_i = - \nabla_i V$, with $V \equiv V(\mathbf{r}_1,\dots,\mathbf{r}_N)$ the potential in function of the position of the $N$ particles.
When considering constraints, we can trans... | FWIW, in this context of Lagrangian mechanics, one often writes the derivative of the $i$th particle position ${\bf r}_i$ as
$$ \nabla_i ~=~\frac{\partial}{\partial {\bf r}_i}. $$
| {
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Confusion over units in force equation? While discussing Newton's laws, our book says
Force is proportional to rate of change of momentum
so they say
F is proportional to mass * acceleration if mass is constant
So $F=kma$ where $k$ is a constant.
They then say we choose a unit of force such that it produces accele... | The unit of force in the International System is Newton (N), which is equal to kg m/s$^2$. Newton is a derived unit, all units can be expressed as a product of the seven base units of the SI. Therefore, the $k$ in the formula is dimensionless.
The book explains that you can choose $k=1$ so that Force can be defined as ... | {
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Bernoulli's equation basics While deriving the Bernoulli's equation, we write the change gravitational potential energy as $mg(h' - h)$ , say where $m$ is the mass and $h'$ and $h$ are the two heights. Why we don't consider the centre of mass in this case? I mean why we don't have this term written as
$\frac{mg(h' - h... | In the derivation of Bernoulli's equation we consider a small element of a fluid so that we can assume that all fluid particles in the element has same pressure, velocity etc.
The potential of this small element is the one to be considered in Bernoulli's equation, the height of the element itself is neglected.
You aske... | {
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Does a colored filter reflect their color of light? At the moment I'm somewhat confused by the concept of colored filters; common sense states that they allow only their color of light to pass through(i.e. red filter lets red light through), but, if they appear to be a specific color, wouldn't that indicate that they r... | I would expect that the highest quality filters do not reflect any of their colour (red for example) and only appear red because everything behind them appears red. As it blocks out all the other wavelength's of visible light. A red filter like that would appear black in a completely blue room, however it is not actual... | {
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"answer_id": 1
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How do you measure the chemical potential? It is clear how to measure thermodynamics quantities such as temperature, pressure, energy, particle number and volume. But I have no idea how to measure chemical potential.
Could someone please provide some examples of how one could measure the chemical potential?
| You can measure it indirectly by using other extensive quantities and applying thermodynamic relations (see https://en.wikipedia.org/wiki/Table_of_thermodynamic_equations). For instance, you could use $$\mu = (\frac{\partial G}{\partial N})_{p,T}$$
As for measuring it directly, it is not possible to measure it directly... | {
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Why the entropy change is not zero in the irreversible adiabatic process? Why the entropy change is not zero in the irreversible adiabatic process?
...while it is defined as the integral of the heat added to the system over its temperature.
| Although entropy change is defined in terms of a reversible differential transfer of heat divided by the temperature at which the heat is transferred, you can have entropy change without heat transfer. Since entropy is a state function independent of the path between states, you can calculate it by assuming any reversi... | {
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When the voltage is increased does the speed of electrons increase or does the electron density increase? I am just a high school student trying to self study, please excuse me if this question sounds silly to you.
I know that current is a product of the speed of electrons and the electron density.When current is incre... | Current is the amount of charge (electrons) passing a point in a wire per unit time. Voltage is the amount of energy in joule in every charge of 1 coulomb moving through the wire. Increase in current translates to increase in speed of electrons moving past our reference point. Electron density in a wire remain relative... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How much time does it take for a broken magnet to recover its poles? I understand that when you cut a magnet you end up with 2 magnets but I wonder how much time does it take to the magnetic domains to rearange and form the new pole. I know the answer may vary depending on the size of the magnet, the material, and some... | It takes zero time because no domains need to rearrange when a permanent magnet breaks in two. The spins in each half are still aligned and still produce a magnetic field.
The idea that magnets have “poles” is a misconception. There are no magnetic poles in nature, or at least none that we have found. (And physicists h... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Why is air pressure higher in winter than in summer? At the top of a mountain, say Mt Everest, atmospheric pressure is low.
So shouldn't the same thing be true for winter season.
I.e air pressure in winters should be lesser than that in summers.
But it's the opposite.
Can someone please explain why ?
| The pressure profile of earth from the surface all the way to the last layer of atmosphere is a decreasing/negative gradient, why is that? It's gravity. The strength of gravity on a mass is inversely proportional to the square of distance away from the gravity source. Air layers closer to the planet weighs more than la... | {
"language": "en",
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Fourier transform property in Feynman 1986 Dirac Memorial Lecture In his famous 1986 Dirac Memorial Lecture, Feynman refers to a Fourier transforms theorem holding in case F(w) satisfies "certain properties", while being restricted to positive frequencies only:
as I am interested in better understanding said "certai... | His point is that if the integral defining $f(t)$ converges for all real $t$ then $f(t)$ on the real axis is the boundary value of a function that is analytic in the lower half plane. (Observe that taking $t\to t-i\tau$, $\tau>0$ improves the convergence of the integral) Now analytic functions that have a limit poi... | {
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"source": "stackexchange",
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Cavity optomechanics Hamiltonian In cavity optomechanics the radiation pressure exerted by light moves a mirror in a cavity. Because of that the resonance frequency of the cavity changes due to change in length of the cavity (cavity frequency, $\omega_{cav} = n\pi c/L$, $L$ is the length of the cavity). The Hamiltonian... | *
*As it was correctly pointed in the other answer, only one mode is considered coupled to the oscillator, which is why one need not use additional creation/annihilation operators.
*The frequency of this mode does change as the mirror moves! The wavelength of the cavity mode is however huge compared to the displaceme... | {
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Demonstration of the completness of an orthonormal set of functions I find this concept of completness a little bit dense when it comes to prove this property of some set of orthonormal functions. In one of my classes, my professor proved this for the orthonormal set of functions $\left\{ \sqrt{2/L} \sin( n \pi x/L) \r... | Do you accept that known complete sets of functions, I.e. delta functions, exist?
If so, proving that you alternate set can reproduce the delta functions is enough. Since combining functions is linear, you can thereby always use your functions to make the deltas you need to make anything else.
| {
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If sound is a longitudinal wave, why can we hear it if our ears aren't aligned with the propagation direction? If a sound wave travels to the right, then the air molecules inside only vibrate left and right, because sound is a longitudinal wave. This is only a one-dimensional motion. If our ears are oriented perpendic... | Sound travels outwards from a source in all directions. The waves that are set in motion are spherical.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/465203",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "17",
"answer_count": 9,
"answer_id": 0
} |
Why does a car's steering wheel get lighter with increasing speed I've noticed it is difficult to turn the wheels of a car when the car is stationary, especially cars without power steering, which is why the power steering was invented. However, I've noticed it becomes feather light when traveling at speed (some model... | As others have posted, the forward rotation of the wheel reduces the 'scrubbing', however, there is an opposing force which should be mentioned, the gyroscopic effect which would cause the steering to become more difficult to turn the faster the wheels rotate.
| {
"language": "en",
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"source": "stackexchange",
"question_score": "19",
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"answer_id": 3
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Can solar mirrors be used for amateur telescopes? Recently I have been fascinated by astronomy and telescopes. I have a small refactor telescope, but it cannot see very far, so I was interested in buying a larger telescope. Unfortunately, I cannot afford to purchase a good quality telescope, so I was trying to think of... | No, it isn't. Just by looking at the reflection pattern in the photo, you can see that the consistency of focus across the surface of the mirror is lousy- certainly good enough for lighting ants on fire, but nowhere near good enough to produce good images.
If you live in or near a big city, you probably have an amateur... | {
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Virtual images - Work of a brain or work of a lens? I am just a high school student trying to self study, so please excuse me if this question sounds silly to you.
Many people tell me that virtual images are formed when two rays that are diverging appear to come from a point, therefore our brain thinks that it is comin... | Both of you are correct.
The diverging rays converge at the retina and we see an image.
The brain's role is to locate the source(point from which the rays appear). Since there is no real source, our brain just extrapolate the diverging rays an make them meet at point.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/465680",
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"source": "stackexchange",
"question_score": "2",
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Work when there is more than 1 force I know that for an object with an applied force, the work done is
$$W = Fd \cos \theta.$$
I was wondering what would happen when there is another force (e.g. friction)? Is it better to say that the work done for a general case is
$$W = F_{net} d \cos\theta.$$
| I think @garyp has answered the question in his comment. That is, we can either discuss about work done on the object by a specific force $F$ or total net force $F_{net}$. Therefore, how the work is calculated depends on what force you want to discuss with.
| {
"language": "en",
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Do Maxwell relations hold during a phase transition? Maxwell relations are found by taking mixed derivatives of a thermodynamic potential. Does this mean that they do not hold at a first-order phase transition, where the thermodynamic potential is discontinuous?
| You are right, if, at a phase transition, second derivatives of a thermodynamic potential do not exist at that point Maxwell's relations are not valid anymore.
However, the sets of points of non-analyticity are confined on hyper-surfaces, in the thermodynamic state space, which partition it into regions of analyticity... | {
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Why do prism split light at angle instead of curving it? I assume that when light goes through matter, it doesnt really slow down, but the waveform is pushed back due to some resonance with the atoms.
EDIT: Interference is probably a better word than resonance here
I also assume that the above effect is responsible for... | At first all light components from different wavelengths move in air at same straight line.After they fall on the surface of the prism,they get splitted according to their wavelengths . Because prism has a constant cofficient of refraction, all the light from different wavelength move in the prism at different st... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Are Electrons in a Circuit Subject to Newton's Third Law? Consider a simple electrical circuit made up of a battery, an incandescent bulb, and wire. The battery and bulb are equal in mass and are on opposite sides of a circle made up by the wire. Lastly, the circuit is operating and floating freely in microgravity.
Si... | Newton's laws do apply. The overall system will not rotate. While the electrons are rotating in one direction, the rest of the gear will indeed be rotating imperceptibly slowly in the other. But the rotation is constant, as the propulsive EMF is being exactly opposed by collision forces between electrons and metal atom... | {
"language": "en",
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"source": "stackexchange",
"question_score": "4",
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EW theory vertices I'm trying to undertand the following vertex:
Initial state of up and anti-down quarks with finalk state made of $W^+$ boson. Does it go with left or right projector? I think that from Lagrangian it should go with left projector but the vertex with $e^+$ and $W^-$ in initial state and $\bar{\nu}_e$ i... | It would be helpful if you just wrote the Lagrangian terms you are looking at.
Destroying a Left-handed u and R antidown to create a W+ corresponds to the vertices
$$
W_\mu^- \overline {d} P_R\gamma^\mu P_L u + W_\mu^+ \overline {u} P_R\gamma^\mu P_L d ,
$$
while destroying a R-positron and a W- to yield a R-antineutr... | {
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Why is a delta resonance decay not a radioactive decay A delta resonance decays as given in http://hyperphysics.phy-astr.gsu.edu/hbase/Particles/delta.html . I wonder, why is it not a radioactive decay? In principle, most/all decays should be radioactive as it is a quite broad description:
Radioactive decay (also know... | The key point is that the technical definition is limited to atomic nuclei, the delta particle is definitely not a nucleus because it's lifetime is too short for playing any kind of role in an atom.
Said otherwise, it's impossible to form an atom out of a delta particle, and as such you don't consider the decay of a d... | {
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Why is there so much iron? We all know where iron comes from. However, as I am reading up on supernovas, I started to wonder why there is as much iron as there is in the universe.
*
*Neither brown dwarfs nor white dwarfs deposit iron.
*Type I supernovas leave no remnant so I can see where there would be iron relea... | The solar abundance of iron is a little bit more than a thousandth by mass. If we assume that all the baryonic mass in the disc of the Galaxy (a few $10^{10}$ solar masses) is polluted in the same way, then more than 10 million solar masses of iron must have been produced and distributed by stars.
A type Ia supernova r... | {
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Maxwell Tensor Identity In Schawrtz, Page 116, formula 8.23, he seems to suggest that the square of the Maxwell tensor can be expanded out as follows:
$$-\frac{1}{4}F_{\mu \nu}^{2}=\frac{1}{2}A_{\mu}\square A_{\mu}-\frac{1}{2}A_{\mu}\partial_{\mu}\partial_{\nu}A_{\nu}$$
where:
$$F_{\mu\nu}=\partial_{\mu} A_{\nu} - \par... | The relation as you state it does not hold. Only the space time integral of both hands of the equation is equal under suitable boundary conditions. So this would be an error.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/467007",
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Hawking radiation and mass annihilation Now, i just heard that the particle anti particle pairs that zip in and out of existence every planck second both have positive mass. if that is so, how does hawking radiation work? black holes lose mass when the particle with negative mass falls into the black hole and cancels o... | The quantum fluctuations you are referring to are 'virtual pairs'. One could object that their creation is a violation of the conservation of energy principle, but this is allowed in quantum mechanics due to the brevity of their existence. Their creation and annihilation leaves no net gain or loss to the total energy o... | {
"language": "en",
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How does the green function for the wave equation in three dimensions preserve the ordering of noises between a speaker and a listener I was provided with the following equation in class for the Green's function of a three dimensional wave equation:
However, I am confused as to how this form of the Greens function pre... | Implicit in this solution is the fact that the origin of the coordinate system is located at the speaker, at the moment in time in which they emit a pulse of sound.
In other words, the speaker is located at the origin, so $ \mathbf{r}_{speaker} = \langle 0, 0, 0 \rangle $, and they emit a pulse of sound at $ t = 0 $. ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Why do we ignore magnetic field vector during polarization? Most light sources in nature emit unpolarized light. Natural light sources consist of very large number of randomly oriented atomic emitter, which emit polarized light randomly. A linear polarizer is a device whose input is light of any polarization state and ... | Well , when we linearly polarise (just for the sake of convenience ) an electromagnetic wave , both the electric and magnetic fields oscillate in a fixed direction , so we can say that both the electric as well as the magnetic fields are polarised.Obviously, a light ray cannot have its electric field oscillating in o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/467827",
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"source": "stackexchange",
"question_score": "3",
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Strong empirical falsification of quantum mechanics based on vacuum energy density It is well known that the observed energy density of the vacuum is many orders of magnitude less than the value calculated by quantum field theory. Published values range between 60 and 120 orders of magnitude, depending on which assumpt... | Our back of the envelope prediction for the order of magnitude of the vacuum energy is indeed very wrong! However, keep in mind that
*
*It is possible to precisely fine-tune free-parameters of the theory to match the measurement. This is achieved through a delicate cancellation between so-called tree-level parameter... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/467939",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why a softer phonon is easier to get excited In Kittel's book, "Some other structure B may have a softer or lower frequency phonon spectrum than A. As the temperature is increased the phonons in B will be
more highly excited (higher thermal average occupancies) than the phonons in
A."
Can you let me know why softer pho... | Phonons with low energy are called "soft" for this reason. It means the same.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/468265",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Flux received by a negative charge Consider two charges $+q$ and $-Q$ placed at a distance, note charge $q$ and $Q$ are different in terms of magnitude.
My question: is number of flux lines received by $-Q$ proportional to its own charge, or does $+q$ charge have anything to say at all?
As according to gauss law
Sour... | The answer would be "yes, but...".
In an universe with global neutral electrical charge, the flux through a closed surface is proportional to the charge inside the surface, but it means that it is also proportional to the charge outside the surface, because both are opposite but equal in absolute value.
Your drawing sh... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/468360",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Can quantum deletion error-correcting codes be constructed? I'm wondering whether or not we can construct quantum deletion error-correcting codes. The quantum deletion error is defined by the partial trace. If we can, could anyone give an example?
| Such a code has not been discovered until a few months ago.
Ayumu Nakayama and Manabu Hagiwara discovered the first example.
It encodes one qubit to eight qubits.
The details are written in the following paper.
The First Quantum Error-Correcting Code for Single Deletion Errors,
Ayumu Nakayama, Manabu Hagiwara,
IEICE Co... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/468518",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Effect of earth's rotation in ballistics For this purpose, let's consider earth's rotations constant. Do earth rotation momentum get transfered to any object (a missile for example) that get's lauched? If so, why do we have to consider earth rotation when lauching the missiles? Wouldn't just follow earth rotation? (Btw... |
Do earth rotation momentum get transfered to any object (a missile for example) that get's lauched?
Yes
That is why they build rocket launch sites as close to the equator as possible, so that they can use that velocity to help reach orbital velocity. At the equator the Earth is moving roughly 1000 miles per hour, and... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/468682",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 5,
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Difference between voltage, electrical potential and potential difference I am having hard time to visualize these two concepts in my mind seriously.
First of this confusion came from two parallel plates that was connected to a power supply, charged then disconnected from power supply and then separated from each othe... | For parallel plates where the separation $d$ is much smaller than the dimensions of the plates (diameter for circular plates), and the potential difference between the plates is $V$, the electric field $E$ is given by
$$E=\frac{V}{d}$$
Where the electric field $E$ is directed from the + plate to the – plate.
Capacitanc... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/468938",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 5,
"answer_id": 4
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Intuitive "story" explaining how orientation of spin axis affects up/down observation? Is there a "convenient fiction" that explains why the angle of an electron's spin axis affects the probability of it being observed in a spin up or spin down state?
By "convenient fiction", I mean a story or image that provides usefu... | I am afraid there is no way to get an intuition. The Stern-Gerlach experiment implies a description of the reality in terms of a superposition of states. In case of the electron spin you have Up and Down states related to the direction in which you measure. A surrogate of intuition could be the coefficients of the base... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/469562",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 0
} |
What are equations of state in thermodynamics? So I am having real trouble understanding what equations of state are and how we form them. My issue stems from reading multiple sources. So I understand that an equation of state is used to build a relationship between variables to describe a state of a system.
For exampl... | An equation of state is a relation between intrinsic quantities of a system in equilibrium.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/469746",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 4,
"answer_id": 3
} |
What is $Z$ useful for in a CFT? As an example, the partition function of a free boson on a torus with modular parameter $\tau$ is,
$$Z(\tau,\bar{\tau}) = \frac{1}{|\eta(\tau)|^2}.$$
In quantum field theory, the partition function allows us to compute correlators and in statistical physics one can also compute quantiti... | In two-dimensional CFT, the torus partition function is useful because it sometimes encodes the space of states, and because modular invariance of the partition function constrains that space of states. The partition function encodes the space of states provided the CFT is rational (i.e. we have finitely many represent... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/470341",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 1,
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How does $r$ depend on $\varphi$ in the Schwarzschild metric? I am confused about the Wikipedia derivation of the equation
for geodesic motion in the Schwarzschild spacetime. The derivation of this equation involves variation with respect to the longitude $\varphi$ only then the variation with respect to the time $t$ ... | Before varying a Lagrangian or an action, all variables are considered independent. The classical equations of motion then correspond to the subset of possible trajectories that leave the action stationary. That is, before varying the action, $r$ and $\varphi$ are indeed independent coordinates. They only depend on one... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/470585",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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If atmospheric pressure is 76 cm of $\text{Hg}$ , why won't 76 cm of mercury stay in an open tube when suspended in air? If we keep an hold a tube in air with the closed end up and open end downwards, containing mercury upto a length of 76 cm, why does the mercury not stay in place? Shouldn't atmospheric pressure exert... | I never experimented with mercury but I did with water. Here a summary of results.
Take a small bottle, fill it with water and invert it keeping mouth closed, e.g. with a cardboard piece. Now remove the cardboard sliding it horizontally: you'll see that water stays put if bottle's mouth diameter is under a certain thre... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/470858",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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"answer_id": 3
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