Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Why can we only "see" reflected light? This is a question thats been bothering me a while. I don't even know if it makes sense or not (like if it is a physics question or becoming a philosophical one). But here it goes. The crux of my question basically is that we all know that we can't see light (like in its photon or... | You can see the light which enters in your eye and is absorbed by your retina. So you cannot see the light passing by because it is not going towards your eye. If it meets an object, however, light will be reflected or scattered and part of it will go towards your eye. You will then see the light coming from the object... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/325535",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is spacetime (simple explanation)? Can someone please explain concept of spacetime in simple language? What is it and how it is important in the universe?
Wherever I have tried searching this concept, I have come across most complicated explanations.
A simple example will be appreciated.
| Whenever you draw a curve of a trajectory over time you are using spacetime as a concept. It is just a space with n+1 dimensions, where n is the number of space dimensions.
When we draw such diagrams on a piece of paper we usually omit one or two of the space dimensions (e.g. recording only the x position in space; y ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/325602",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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A free-fall electron I am reading Wheeler and Taylor's Spacetime Physics. In Ch2, Wheeler mentioned:
"for gravity, any free-fall frame is an inertial frame." (roughly)
I am left wondering if that is true for electrical force:
Consider one charge is under a statistic electrical field. The charge is in free-fall. Is t... | Perhaps I'm misunderstanding the quote, but I think there's a distinction between the false statement...
Anything falling in a gravitational field is in an inertial frame
... and what I believe the quote means...
In the frame of reference gravity itself, something falling [in a gravitational field] is inertial, be... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/325705",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Opposite of particle decay I have read about particle decay, a process in which one particle becomes several other particles. However, I have not been able to find much information about its opposite: several particles combining into one particle. Is such a process possible, and if so, under what conditions? For exampl... | Even if the reaction is not prohibited by energy/momentum or other conservation laws, it would have a tiny cross section: shooting one kind of particle at a target is easy, but shooting two at the same time, not so much (particularly if one is an antineutrino). However there is such a thing as electron capture by a pro... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/325790",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "21",
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How can length be a vector? Length and current both are not vectors. Then how can we assign the vector $l$ to the length of a wire carrying current while calculating for a current carrying conductor in a magnetic field. Also why in Biot—Savart law do we take small length element $dl$ as a vector?
Why is length sometime... | $d\vec \ell$ is not a length. It is a vector of infinitesimal length (of length $d\ell$) that is in the direction of the current flow.
Current, on the other hand, is a vector as it flows in specific directions. It is often not indicated by a vector sign (for historical reasons) because in circuits the current will ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/325895",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Can only two equal EM-wavelength interfere? If so why is that? When there are two waves of light with the same wavelength they can constructively or destructively interfere with each other. But can for example a wave of 532nm interfere with a wave of 533nm. How exactly must they be the same and why can't (if so?) diffe... | Waves of different wavelength/frequency interfere intermittently, which produces periodic modulation called beat frequency. The beat frequency corresponds to the difference between the frequencies. It is what musicians are listening for as they tune their instruments.
It's easiest to visualize this by thinking about... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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How do you calculate the resulting magnetic field for multiple sources? I've been looking at some fusion reactors and I keep wondering how putting some kind of extra magnet in some configuration would affect the field, but I don't know how to figure it out. Like for example if you took a solenoid and sat a permanent ma... | Since the Maxwell's equations are linear partial differential equations, you can compute the magnetic field due to multiple sources by superposition.
A really important application relies on the superposition principle for magnetic fields is the Biot–Savart law i.e. the fact that the magnetic field is a vector sum of... | {
"language": "en",
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How did Rutherford conclude that most of the mass (as well as the positive charge) was concentrated in the nucleus? Geiger and Marsden's experiment led Rutherford to believe that the positive charge and most of the mass of the atom was concentrated in a small region. I understand what led him to conclude the way the po... | This is a good example of how Science works.
Geiger and Marsden observed that some of the alpha particles were being backscattered. This is inconceivable if the alpha particle is scattered by a lighter particle.
If one considers a particle of mass $m$ and initial velocity $v_1$ striking a target of mass $m'$ at rest, ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/326320",
"timestamp": "2023-03-29T00:00:00",
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How would electromagnetic induction violate neither the conservation of energy or Newton's first law? The basic premise of electromagnetic induction is that supposedly when you have a magnetic field moving, it generates an electromotive field perpendicularly, yeah? But if you had a hypothetical space where Newton's fir... | When you move a magnet through a coil or even through space , a non conservative electric field is induced in space in a circular form. But, since energy is conserved in any case which can only be possible in this case if the motion of magnet is opposed so that the kinetic energy of moving magnet is converted into elec... | {
"language": "en",
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Diffeomorphism invariance and correlation functions Consider the following paragraph taken from page 15 of Thomas Hartman's lecture notes on Quantum Gravity:
In gravity, local diffeomorphisms are gauge symmetries. They are redundancies. This means that local correlation functions like $\langle O_{1}(x_{1})\dots O_{n}(... | In gravity theories gauge invariance is diffeomorphism invariance, so local operators are not gauge invariant because there are no preferred coordinates, you can always reparametrize them - choose another coordinates, and the operators will, in general, change.
As for 2, its just the way of saying that transformatio... | {
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What is the relation between image velocity, object velocity and mirror velocity? Suppositions used:
Velocity of image = VI
Velocity of object = Vo
Velocity of mirror = VM
I Know the fact that VI=-Vo supposing mirror at rest
and VI=2VM supposing object at rest
Now considering both mirror and object in motion, VI=2V... | I think that, since the velocities are in different directions, $2V_M -\left(-V_O\right) = 2V_M+V_O$.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/326992",
"timestamp": "2023-03-29T00:00:00",
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Have we directly observed the electric component to EM waves? For example, has anyone has directly observed charges oscillating due to standing EM waves? I am particularly interested because it'd demonstrate that radiation has a transverse electric component to it. Anything else (historical or modern) that shows that l... | It depends on what you mean by "directly observed charges oscillating" and whether the formation of a standing wave is essential.
Using microwaves to demonstrate that they can be polarised you can infer the direction of oscillation of the electric vector in an electromagnetic wave.
If there is a horn receiver as we... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/327076",
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"source": "stackexchange",
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Why is the South Pole Telescope located exactly at the South Pole? I read that there is less atmospheric interference for the telescope at the South Pole because the atmosphere is thin and there is less water vapor in the air. However this seems to be true for many locations on Antarctica? Are there any other reasons t... | Just guessing here, but ...
Compare the regions with really good skies with the places that have infrastructure and people present. Most of the installations are coastal, right? Are those good places to put a telescope? And while the whole inland plateau has good skies, it has few occupied site, and only one operated b... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/327190",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "22",
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Why do we equate an indefinite integral to a specific value? Suppose we want to obtain a displacement vector defined as $\mathbf s(t) = x(t)\mathbf i + y(t)\mathbf j + z(t)\mathbf k$ from the components of a velocity vector $\mathbf v(t) = \dot x(t)\mathbf i + \dot y(t)\mathbf j + \dot z(t)\mathbf k=\mathbf 0$. Accordi... | In physics we frequently leave off the limits of the integral when the limits can be figured out from the context. So, in the first case, the actual relation is:
$$x(t) = x(0) + \int_0^t \dot{x} \operatorname{d}t'.$$
Most often, though, when the limits are left off the implied limits are over all possible values of the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/327303",
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How does a electric quadrupole oscillate? I know that in static a electric quadrupole is made of two positive charges and two negative charges, distributed as in the following figure:
What I don't understand is when it oscillates and radiates, does it oscillate like two antiparallel electric dipoles, or it oscillates ... | If you want a truly quadrupolar oscillation, then it needs to oscillate as in the four-dipoles model, i.e. there is a current linking all adjacent pairs of localized charges, which is crucial to the formation of the correct quadrupolar symmetry for the radiation pattern.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Can we add attraction forces? From Newton's Law of gravitation we know that:
$$F=G\frac{m_1m_2}{d^2}$$
For simplicity, let's say that both $m$ are $1\;\mathrm{kg}$ and that the distance apart was $1\;\mathrm{m}$. Yielding $G$ as the attraction force in Newtons. Hence $F= 6.67\times 10^{-11}\;\mathrm{N}$.
Now what if y... | You need to multiply by four not by two. To see why let's draw the situation:
You are assuming the situation is as shown in the top diagram. So the two $M_1$s attract each other and the two $M_2$s attract each other. Those are the forces shown by the red lines.
But you also need to include the force between $M_1$ on ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/327551",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How is it possible to define work for friction in several dimension? I have been taught that, given a force field F, the work done by the force over a certain curve $\gamma$ is defined as the line integral of said field along $\gamma$.
But this makes sense only if force can be written as a function of position, as it i... | I have been taught that, given a force field F, the work done by the force over a certain curve $\gamma$ is defined as the line integral of said field along $\gamma$.
Friction is a force, but is not derived from a force field (in any useful sense). So your statement, while true, is inapplicable. (We were not "given a f... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/327656",
"timestamp": "2023-03-29T00:00:00",
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Defining the surface gravity of a black hole Consider the following two definitions of the surface gravity of a black hole (taken from page 23 of Thomas Hartman's lecture notes on Quantum Gravity):
*
*The surface gravity is the acceleration due to gravity near the horizon (which goes to infinity) times the redshift ... |
What does it mean for the acceleration due to gravity near the horizon to go to infinity?
It means that a person dangling near the horizon feels an almost infinite pull of gravity, and he observes that anything dropped almost immediately reaches almost the speed of light.
Why do we multiply by the redshift factor a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/327924",
"timestamp": "2023-03-29T00:00:00",
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Construction of first Brillouin zone For a square lattice with lattice translation vector, $T=a\hat{x}+a\hat{y}$, we find that the reciprocal lattice vectors are given by, $$A=\frac{2\pi}{a}\hat{x},$$ and, $$B=\frac{2\pi}{a}\hat{y},$$ such that the Brillouin zone ranges from $-\frac{\pi}{a}\to\frac{\pi}{a}$. That is it... | For the First case where you have a square lattice, the first Brillouin zone is a square that lies between $\frac{-|A|}{2} \rightarrow \frac{|A|}{2}$ in the $\hat{x}$ direction and $\frac{-|B|}{2} \rightarrow \frac{|B|}{2}$ in the $\hat{y}$ direction. Assuming that you chose a lattice point as your origin in the k-spac... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/328053",
"timestamp": "2023-03-29T00:00:00",
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Fluid Dynamics in a Syringe I am currently working on a project where we use syringes to extrude some viscous materials. I will explain what I am trying to do and I just want to know what size of tubing would be better for me. I have a 10 cc syringe connected to 3/32" tubing with luer lock and at the very end, it is at... | I believe you want a smaller tube. The pressure has to reach a point where it is great enough to push through the needle. I larger tube has more space to fill, so you have to push the plunger farther, to build enough pressure, to push the fluid through the small needle. Pressure will build faster in a small tube, which... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/328193",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Why are clockwise and anticlockwise moments not balanced in this equilibrium scenario?
If we take moments about the peg, which is directly below centre of mass of the cone (which is $r$ cm from its circular base) we get $3rTcos(90-ø) = Trcos(90-ø)$. $T$ = tension in string. Clearly this has no solution unless T is 0. ... | The force $T$ acts through the peg, therefore its moment about the peg is zero. Taking components of $T$ vertically (and horizontally) is not going to alter this situation.
You have actually already balanced moments when you assumed that the CG of the cone lies vertically below the peg. The only force acting on the con... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/328343",
"timestamp": "2023-03-29T00:00:00",
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What are quarks and leptons in Quantum Field Theory? Are the different quarks and leptons different kinds of oscillations of the same underlying quark field and lepton field, or same kinds of oscillations of different up, down and so on quark fields, and electron, electron neutrino and so on lepton fields? Or is there ... | Quantum field theory in general doesn't know about quarks and leptons. It knows about bosonic and fermionic fields (e.g., scalar fields, vector fields, spinor fields) and their interactions.
So think of quantum field theory as a framework. The Standard Model of particle physics fills this framework with specific conten... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Mass-luminosity relation for a fully convective star I'm trying to show that the mass-luminosity for a fully convective star is
$$L \propto M^{\frac{113}{66}}$$
I know that the energy generation is via pp-chain and the opacity is due to $H^{-}$ ions such that:
$\epsilon = \epsilon_0 \rho T^3$ and $\kappa = \kappa_0\rh... | The bit you are missing is that the radius of the star is determined by the opacity.
Hydrostatic equilibrium yields
$$P_R = \frac{GM}{R^2}\int \rho\ dr,$$
where $P_R$ is the pressure at the radius where light can escape. This in turn is related to the opacity $\kappa$ by
$$\int \kappa \rho\ dr = \bar{\kappa}\int \rho\ ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/328716",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why Faddeev-Popov ghost cannot exist in external line? I was studying the path integral quantization of non-abelian gauge field. After the path integral quantization, the action becomes
$$\mathcal{L}=-\frac{1}{4}F^a_{\mu\nu}F^{a\mu\nu}-\frac{1}{2\zeta}(\partial_{\mu}A^{\mu a})^2 +\partial^\mu\bar c^a(D_{\mu}c)^a$$
Fey... | On one hand, the S-matrix does not depend on the gauge-fixing condition. On the other hand, there exist a unitary gauge, where Faddeev-Popov ghosts decouple from the theory.
References:
*
*M.D. Schwartz, QFT and the Standard Model, 2014; Section 28.4.
*C. Itzykson & J.B. Zuber, QFT, 1985; Subsection 12-5-5.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Why are stars spherical whereas (some) galaxies are disks? I read here that galaxies become disks if there is a lot of gas in them, since their angular momentum is conserved while their energy decreases due to collisions of the gas particle. I have two questions about this:
*
*Why is the disk the configuration that ... | The post you're referred to explains reasonably well why spiral galaxies are discs. So why are stars not disc like. The simple answer is: a disc-like object cannot be a star.
But what is a star? A star is an object that at its core has the right conditions for thermo-nuclear reactions, in particular temperatures $T\sim... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/329120",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How does a helicoper auto-rotate? The force of the air pushing on all blades would equal out. Wouldn't it? So, I was learning about helicopter and how they auto rotate and I learned that when the engine fails the helicopter starts to fall and the air is thrown up at the blades which turns them like a windmill. I though... | It's exactly the same as when an aircraft glides, except the "wings" go in a circle.
As a student pilot in a fixed-wing aircraft you practice this many times.
The instructor pulls the power to idle and says "You just lost your engine..."
The first thing you do is push the nose down, so you're in a downward glide.
Since... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/329272",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is "velocity distance" in astrophysics? I was reading some papers on astrophysics, and in several of them, I've encountered velocity being used as distance. Or more precisely, distance being in dimensions of distance over time. For example, a paper referred to a group of galaxies at "roughly $2000\:\mathrm{km\:s^{... | It is used because of uncertainty in the Hubble constant. The relationship between recession velocity and distance is given by
$v=H_{0}d$
Where $H_{0}$ is the Hubble constant. Since that isn't known precisely, distances aren't known precisely, so talking about distances doesn't necessarily make sense.
Taking about th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/329391",
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Conformal symmetry with Goldston bosons I am looking for examples of the physical systems with both conformal symmetry and Goldston bosons. The systems can be in any physical context, like QCD phases, Condensed Matter (Graphene, etc), or SUSY gauge theories.
Naively, in 1+1D gapless system, we can more easily have conf... | You can't have unbroken conformal symmetry and Goldstone Bosons (GB)'s at the same time because the GB decay constant $f_\pi$ is dimensionfull in $d>2$. And in $d=2$ there are no (physical) GB's.
Even more physically, a theory of GB has a cutoff $\Lambda$ and its therefore not scale invariant.
The only way out to th... | {
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Why is my reasoning to derive the bistatic radar equation wrong? The ideal effective antenna aperture is calculated from $A_{eff}=G\lambda^2/4\pi$, G being the antenna gain.
Why is it that in a bistatic radar setup with a transmitter and receiver fixed on the Earth and a moving aircraft, the bistatic radar equation onl... | Your reasoning is logically right even for monostatic radar when detecting a moving target. As for your question, you need to note that the radar equation is merely used to calculate the power received from the target to the receiver antenna, in order to calculate the maximum detection range of the radar given its mini... | {
"language": "en",
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Degrees Of Freedom of Spring-mass system
Consider 2 masses $M_1$ and $M_2$ connected with a spring of stiffness $k$, resting on a smooth frictionless surface. Now, each mass has its own 1 DOF along the $x$-axis. And the system has 1 constraint , i.e. the spring.
So, in all there should be 2(1)-1= 1 DOF for the system... | Imagine a system of your two masses $m$ and one spring, spring constant $\kappa$ but with two other spring, spring constant $k$, attached to the masses as shown in the diagram below.
This system certainly has two degrees of freedom.
You have two masses and a displacement along a straight line for each of the masses w... | {
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"url": "https://physics.stackexchange.com/questions/329944",
"timestamp": "2023-03-29T00:00:00",
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Is gravity non-negligible compared to the electromagnetic force? Consider two electrons approaching each other at rather fast speeds, maybe even coming close to colliding. Does gravity play any role in this event? If so, how much influence does it have? Do we need gravity in charged particles?
| For electrons, the gravitational force is much smaller than the electric forces. To get an idea about how small, let's math.
$$F_g = \frac{Gm_1m_2}{r^2}\, , \, F_e = \frac{kq_1q_2}{r^2}\\
\frac{F_g}{F_e} = \frac{Gm_1m_2}{kq_1q_2}$$
Notice, the distance separating the electrons does not matter when comparing the forces... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Wiedemann-Franz law The Wiedemann-Franz law states that the ratio of thermal conductivity $\kappa$ and electrical conductivity $\sigma$ for metals fairly accurately obeys $\kappa/\sigma = LT$, where $T$ is the temperature and $L$ is the Lorenz number, whose value is in the order of $2 \cdot 10^{-8}$ in SI units.
Assumi... | That's a pretty neat question, I think. The restriction that it only should be applied for metals means that the dominant thermal carriers are going to be electrons, and since the thermal and charge carriers are the same particle, there is some simple ratio of the two. I suppose there is unease about the use of "Law" d... | {
"language": "en",
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Why is $R\cos{a} = mg$ in circular motion compared and not $R = mg\cos{a}$?
Normally, if an object of mass $m$ is inclined to the horizontal at an angle $b$, we set the reaction force of the object on the inclined plane as $R = mg\cos{b}$ (if we resolve the force of gravity so the line of action coming out of the plan... | Never, ever, just blindly memorize formulae.
What you need to do is draw a free-body diagram of your particle, which will have an angled normal force, and a downward gravitational force, and you know that the net acceleration is inward with magnitude $v^{2}/r$. You can either rotate your reference frame so that the ... | {
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Does an increase in entropy always result in an increase in heat, or can there be increased entropy without an increase in heat? Most situations I can think of where entropy increases also results in an increase in heat, but just wondering if that is a rule. Are there any cases where heat does not increase with entropy... | *
*If you have a room with oxygen in one half and nitrogen in the other half, and you now remove the wall between them, then they start mixing more and more. Entropy increases. Before, you knew exactly which atoms you pointed at, when you pointed somewhere, but the more time that passes, the less sure you are of which... | {
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At what rate do I need to accelerate for my car to become a fusion reactor? I was sitting on the bus on my way home, and this popped into my mind.
As a car accelerates, the air pressure at the back of the car increases as air is pushed back due to inertia. This pressure will be constant, assuming a constant rate of acc... | For fusion one needs order of MeV energies in the center of mass system of the fusing nuclei.
As all molecules are accelerated at the same time and direction, it is only fusion with the molecules accumulating on the glass back window that has meaning i.e. the question should be at what car acceleration the atoms of a... | {
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Tension direction for pulleys in connected mass systems I got caught up with a conceptual question dealing with a practice problem with connected mass mechanics.
Looking at the solution lecture notes is the following image for the Free Body diagrams for each mass, and the pulley, respectively:
Obviously, the Free Bo... | Intuitively speaking, the mass $m_1$ is decreasing the speed. So it must reduce the speed of the system by exerting a force on the pulley that opposes that direction of movement. So $T1$ must be leftwards.
| {
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Can a current be induced in this coil-magnet configuration? Coil is moving around ring magnet made of two arch shaped magnets with poles opposing each other like so:
Would a current flow in coil? or be canceled out?
| With the coil in open circuit, you will have a voltage difference at its terminals. Let's assume the coil moves cw or that the magnet moves ccw. Seen from front, let's call the bottom blue N pole and the top blue end S pole. The lines of flux are all concentrated in the iron except at the gaps where they extend in the ... | {
"language": "en",
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What is the energy of a single charge system? I will try to limit the question in the case of the electric fields, but is something that applies also to the magnetic ones.
There are two ways to express the energy in a capacitor:
*
*By Voltage : $U = 1/2 CV^2 $
*And by Field : $U = 1/2 \varepsilon E^2Ad$, With Ener... | Potential energy is always defined for multi particle systems but can be defined for a single particle(in this case it is charge and hence electrostatic potential energy) if we assume the other charge to be present at infinity(a point far away from the vicinity of the charge will do) then you can calculate the potentia... | {
"language": "en",
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Why can't electrostatic forces "pierce" through thin obstacles the way magnetic forces do? We know that two magnets attract or repel each other even when we keep a very thin obstacle between them such as paper. Why doesn't the same hold good for two charged objects?
| The implied assertion that magnetostatic fields can penetrate thin layers better than electrostatic ones does have some truth to it and the reason is that there is no free magnetic charge, whereas matter is electrically charged. If a material is conductive, electric charge migrates until there is no force on it, or unt... | {
"language": "en",
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Are there experiments that deal with the headlight effect? If I am not mistaken, the Ives-Stilwell experiment measures the frequency of emitted light to test the relativistic doppler formula.
Is there anything like this for light intensity? Have we measured the headlight effect?
Anything like precision tests that are... | In some respects this is unsurprising, as you have to use relativistic engineering to get a synchrotron to work right in the first place: but when you do get a synchrotron running, you will observe that there is a characteristic "synchrotron radiation" and indeed one of its properties is that it's 'strongly collimated'... | {
"language": "en",
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Questioning validity of SHM of vertical mass-spring system Horizontal mass spring system is good but vertical mass spring system confuses me.
Q1. Can there be two restoring forces in an SHM?
Q2. If no, then weight of mass seems to disturb SHM as down extreme position below the mean position would be much farther than... | Gravity is just a constant force, so all it does is just shift the spring force linearly. This means all that happens is that everything gets shifted downward and that's it.
With a horizontal spring, we have $F = -kx$ as usual.
With a vertical spring, there are now two forces: the spring restoring force $F_{1} = -kx$... | {
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Newton's rings - white light? I am familiar with the concept of optical path, constructive and destructive interference. The basic premise to discuss these concepts is coherence, which is why I am perplexed by the phenomenon of Newton's rings.
From what I understand, this experiment was first conducted by Robert Hooke... | Two salient reasons:
*
*The interference is between the reflexions from two neighboring surfaces;
*The distance between these two surfaces is small - only a few wavelengths of visible light.
Point 1 means that it is only the phase difference that is important in determining the throughgoing / reflected light for ... | {
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Does light travel through a waveguide faster than electricity through a wire So I have heard that using photons to compute is faster than electrons. I was wondering why exactly that is? Is it because light travels through a waveguide faster than electricity through a wire?
| Yes, a photon traveling inside a waveguide is a lot faster than an electron inside a wire. A photon propagates in the transverse direction to the dimension of the waveguide. Electrons face resistance inside of a wire. This resistance causes Joule heating effect to take place. This decreases the rate of transmission of ... | {
"language": "en",
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Does the deflection of a photon passing near a star/planet depend on its frequency/energy? Eddington already proved that starlight passing our Sun is deflected more according to GR compared to the outcome of Newton. But does this rate of deflection also depend on the frequency the photons has?
A photon doesn't have a r... | It does not depend on the frequency of the photon. Formally, the deflection angle is a function of the mass of the body deflecting the light (the Sun in your example):
$$
\theta = \frac{4GM}{rc^2}
$$
Intuitively, even in Newtonian gravity how much a particle is deflected does not depend on its mass, the reason being th... | {
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EM duality transformation I have read that by defining a dual transformation as
$$
\begin{pmatrix} F'^{\mu \nu} \\ ^*F'^{\mu \nu} \end{pmatrix}
=
\begin{pmatrix}
\cos (\alpha ) & \sin (\alpha ) \\ -\sin (\alpha ) & \cos (\alpha )
\end{pmatrix}
\begin{pmatrix} F^{\mu \nu} \\ ^*F^{\mu \nu} \end{pmatrix}
$$
where
$$
... | This follows immediately from the first equation that you wrote. Just fix a $\mu \nu$ and obtain that the corresponding component of the Electric/Magnetic field is given by what you wrote in the last equation.
| {
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What is the real life utility dot product and cross product of vectors? Today, my teacher asked us what is the real life utility of the dot product and cross product of vectors. Many of us said that one gives a scalar product, and one gives a vector product. But he said that, that was not the real life utility of the d... | A few roughly mentioned by our teacher:
1-The cross product could help you identify the path which would result in the most damage if a bird hits the aeroplane through it.
The dot product could give you the interference of sound waves produced by the revving of engine on the journey.
2-solar panels need to be install... | {
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One Particle State in Interacting QFT (Eqs. 4.88 4.89 in Peskin & Schroeder) How to derive equation 4.88 in section 4.6, page 108, of Peskin & Schroeder?
$$\left|k_{1}k_{2}\right\rangle\propto\lim_{T\rightarrow+\infty(1-i\epsilon)}e^{-iHT}\left|k_{1}k_{2}\right\rangle_{0}.\tag{4.88}$$
How to derive equation 4.89?
$$\li... | I would like to hazard a guess here. From equations (4.23) and (4.25) in the book, $$U(T,-T)=T\{\exp[-i\int_{-T}^{T}dtH_{I}(t)]\}=e^{iH_{0}(T-t_{0})}e^{-iH(2T)}e^{iH_{0}(T+t_{0})},$$ where $t_0$ is some reference time at which the Schroedinger and interaction pictures coincide. We then get $${}_{0}\langle k_1k_2\rvert ... | {
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Matrix representation of the Clifford group The Clifford group $C_n$ on $n$ qubits is defined as
$$C_n = \left\{ U \in U(2^n) \mid \sigma \in P_n \rightarrow U\sigma U^\dagger \in P_n \right\}/U(1),$$
where
$$P_n = \left\{ \sigma_1 \otimes \dots \otimes \sigma_n \mid \sigma_i \in \{I,X,Y,Z\} \right\},$$
and $X,Y,Z$ are... | There are algorithms to generate all elements of the Clifford group for a specified number of qubits. One implementation is available here: http://www.cgranade.com/python-quaec/ (see the qecc.clifford_group(nq, consider_phases=False) iterator). The code implementing this can be seen here. It basically generates all pos... | {
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Where does the force actual act?
Why are the two mass of $m_1$ and $m_2$ not multiplied by minus one?
I know that two minus multiplied gives you plus by but I mean the two masses are attracting so they should have a sign like so $$F_g=\frac{G(-m_1) \times (-m_2)}{r^2}$$
I ask these because equation would actual give t... |
Actually the picture you've attached is a little sketchy about which force is acting on what. If I denote the force on $2$ due to $1$ as $F_{21}$ then the force on two would be given as in the picture. What the negative sign means is that the force on $2$ due to $1$ acts towards the direction of -$\vec{r}$ (as the fo... | {
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Why are Grassmann fields never classical? I see this statement in many QFT books (e.g. Altland & Simons' Condensed Matter Field Theory) but the author never explains why.
Can you briefly explain why Grassmann fields never have a classical meaning (preferably physical arguments) and possibly point out some good referenc... | Let me put things in broader perspective. Bosonic fields are quantized in terms of commutators with a prefactor $\hbar$. Classical limit leads to commuting variables that may be represented by complex numbers. This is by the way the first step to devise numerical applications of path integrals. Fermionic fields require... | {
"language": "en",
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Calculating energy released in nuclear fission Consider the neutron induced fission $\text{U-235} + n \to \dots \to \text{La-139} + \text{Mo-95} + 2n$, where $\dots$ denotes intermediate decay steps.
I want to calculate the released energy from this fission. One way would be to calculate the difference of the binding... | The released energy is the difference in energy of intitial/end products. For a nucleus, the energy is given by its mass, which in turn can be calculated as the difference of "naive mass", i.e. all single constituents' masses summed up, and the binding energy. This is the calculation you'll have to do. Obviously, all t... | {
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How do we realise the wave for an electron orbiting a nucleus in its first orbit as per bohr model? How do we realise the wave for an electron orbiting a nucleus in its first orbit as per bohr model?
As per my textbook, we can account for as to why angular momentum is quantised. But I fail to understand what would the ... | The electron wave for the $1^{st}$ orbit would be like a circle (not exactly a circle) moving up and down the orbit.
$mvr=\frac{h}{2\pi}$
If the motion of the wave was broken in 3 stages, it would look something like this :
Stage 1 :
Stage 2 :
Stage 3 :
Why is this possible :
Bohr's model assumes that the electron ... | {
"language": "en",
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Is Fresnel diffraction really visible if slit width is similar to distance from screen or does diffraction disappear in that case? Diffraction phenomena occur when, named $a$ the amplitude of a slit and $\lambda$ the wavelenght, $a \sim \lambda$ or even $a<\lambda$ (full illuminated screen).
Therefore if $a\gg\lambda$ ... | You are taking
there are two types of diffraction: Frahunofer diffraction and Fresnel diffraction
too literally. There is only one kind of diffraction physics: waves interfering with each other. The Fresnel and Frahunofer prescriptions are two approximation regimes for making the problem of computing results in clos... | {
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How to prove the constant speed of light using Lorentz transform? I read the light-clock example in my book which proved the time dilation formula by assuming that the speed of light is constant for all observers. But I've trouble in understanding it the other way around. Lorentz transformation is just a correction to ... | From $ds^2=c^2dt^2-dx^2$, we see that light-speed travel is equivalent to $ds^2=0$. But $ds^2=\eta_{\mu\nu}x^\mu x^\nu$ is manifestly Lorentz-invariant, so if $ds^2=0$ holds in some reference frame it also does in others obtained by arbitrary Lorentz transformations.
| {
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Calculate kinetic energy of neutrons in nuclear fission How can I calculate the mean kinetic energy of an emitted neutron in a nuclear fission. Take for example the fission of U-235 to Ba-141 and Kr-92.
A calculation which just shows that the mean energy will be in the range of "fast" neutrons (> 1MeV) would be enough... | I still won't plug the numbers in for you but I'll explain the principle.
You start off with your $^{235}$U and all the energy that is wrapped up in there will be our total (we can see how much we have to play with from the mass excess). Then, through fission, you get your $^{141}$Ba and $^{92}$Kr and two neutrons
$^\d... | {
"language": "en",
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If atoms were held by gravitational (instead of electrical) forces
"If atoms were held together by gravitational (instead of electrical) forces, a single hydrogen atom would be much larger than the known universe."
- from Grifffith's Introduction to Electrodynamics
I don't understand this. If the atoms were held to... | To find the radius of the orbit, we first need to consider the centripetal force on the electron ($\frac{m_ev^2}{r}$) which is equal to the gravitational force between the proton and the electron in this case. ($F_g=\frac{Gm_em_p}{r^2}$)
Using this, and the fact that the angular momentum of an orbit is quantised, (i.e.... | {
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Why do different letters sound different? If one sings the letter "A" and "M" at the same volume and pitch, the two letters are still differentiable. If both pitch and volume are the same however, shouldn't the sound be the exact same?
| You don't sing a single pitch - you sing a frequency and its harmonics. Using a simple spectrum analyzer, this is me "singing" the letter A and M, alternately (AMAMA, actually):
The letter "A" is the one with more harmonics (brighter lines at higher frequencies), the letter "M" seems to have a bigger second harmonic.... | {
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How do we prove analyticity of Schwinger functions? Starting from Wightman axioms, we can define the Schwinger functions as the Wick-rotated Wightman functions (as for instance is explained in the book by R. Haag, Local Quantum Physics).
The Schwinger functions have a set of properties, which essentially come from the ... | If your starting point is a Wightman theory then you can find a proof in Section II.3 of the book "The $P(\Phi)_2$ Euclidean (Quantum) Field Theory" by Simon. If your starting point is a given set of Schwinger functions satisfying the Osterwalder-Schrader axioms then an alternative derivation is in the book "Quantum Ph... | {
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Find the speed of the block in this question
The figure shows a block (assumed to be a point) being pulled by an ideal string across an elevated pulley. At any time $t$, let the horizontal distance of the block be $x$ from the pulley. The length of the string is $l$ and the height of the pulley is $h$ from the ground.... | Because $u$ is only a component of the block's velocity ( along $\hat{r}$) it also has a component along $\hat{\theta}$. The sum of the two along the vertical is zero and along the horizonal gives the speed of the block.
(If it was the only component, then the block would fly, hence it obviously has a component along $... | {
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What is the induced electromagnetic field of a point charge? If I move a point charge on some trajectory, then it will produce an electric field as well as a magnetic field. As the charge is moving, and as a point charge can not produce a steady current, then due to a varying current, an electromagnetic field will be i... | When there are time varying fields we can write $E$ in terms of the vector potential $B=\nabla\times A.$ $$E=-\nabla V - \frac{\partial}{\partial t}A.$$
If we go to the Coulomb gauge, the term $E_{Coulomb}=-\nabla V$ is just due to the Coulomb potential of the charge as in ordinary electrostatics. And the second term $... | {
"language": "en",
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Meaning of perturbative and non-perturbative renormalizability What is meant by a theory to be (1) perturbatively renormalizable, (2) perturbatively non-renormalizable, (3) non-perturbatively renormalizable, and non-perturbatively non-renormalizable? In each case, what are at least one example of such theories?
| *
*Perturbatively renormalizable (or simply renormalizable) theories are those which can be consistently renormalized by tweaking values of a finite number of parameters to any order of perturbation theory. The key moment here is that the finite number of parameters is fixed prior to choosing the order of perturbation... | {
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Cylinder , charge on surface, why is B inside zero? Suppose we have a cylindrical wire of radius a carrying a current I. If the current is uniformly distributed over the surface of the wire, the magnetic field inside is zero.
We can prove that easily using Ampere's law. However, when I try to picture it in my head I c... | Just for picturing it...meaning this is not exact:
If you are not in the middle, where it is clear, but close to one side you may see it like this: the length over which you see a wire approximately straight is sort of given by the angle. Hence, the amount of wire with approximately opposite direction on the other side... | {
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Why are springs shaped the way they are? Why are springs coiled the way they are? Why not some other shape? Is the shape due to its elasticity or something?
| The shape is due to the underlying principle of what a coil-spring actually does.
A spring is originally a long (often metal) wire. When you coil it, you are changing the way the forces can be applied to the spring.
For coil springs, you are making two surfaces that are often flat or have connections, that can be coup... | {
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Simultaneity in Newtonian mechanics How would Newtonian mechanics answer the train and moving light question?
The setup is:
A train is moving in the positive x_axis with speed c/2. A person stands in the middle of the train. There are two light bulbs at both ends of the train. The light goes off at the same time (ab... | According to Newtonian Mechanics, the observer on the ground would see the light travelling to the right at a speed $V=\frac{3c}{2}$, and the light travelling to the left will have a speed $V=\frac{c}{2}$. This is because we assume the Galilean transformations are true. Hence the two light beams appear to reach both s... | {
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Dirac's quantization of electric charge I was following Nakahara's book Geometry, Topology and Physics, specifically subsection 10.5.2. I do understand how he obtains the equality,
$$ \Delta \varphi = \int \mathrm d\varphi = \int \limits^{2\pi}_{0} 2g \, \mathrm d\phi = 4\pi g$$
and that therefore this has to be a mult... | Please note that the transition function $t_{NS}$ defined on the equator $U_N \cap U_S \approx S^1$ of the bundle $P(S^2, U(1))$ is given by the formula:
$$ t_{NS}(\phi) = \exp[i\varphi(\phi)] \qquad (\varphi:S^1\to \mathbb R) \tag{10.90}$$
and it is periodic in the azimuthal angle $\phi\ $: $\ t_{NS}(\phi +2\pi) \equi... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Do charged particles always travel in a spring shape around magnetic fields or only when the magnetic field is from a solenoid? I have seen two contradictory descriptions of how electrons and other charged particles travel around magnetic fields; in one, they travel in circles around magnetic field lines, in the other... | The same path they would take around an electromagnet. They appear to spiral the wrong way, but if you imagine the pole being made up of a bundle of small poles, they are being pushed to the side where they are running parallel to the electrons around the atoms in the poles. If the magnetic field is above a critical le... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Why does "liquid glass" putty turn cloudy when deformed? What physical process is taking place to make it look cloudy? What's changing to make it turn back to clear over time?
While they seem pretty secretive about the exact composition, but I did find this MSDS. Section 3 mentions it contains "Silicone Polymer Contain... | I believe it is simply air entrained. Air will make putty look cloudy. Air very slowly bubbles out of the viscous fluid, returning (most) of its transparency. I suspect putty has some small yield strength, permanently trapping the tiniest bubbles and thus permanenty losing some of its like-new transparency.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/337723",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why is light bent but not accelerated? Light is bent near a mass (for example when passing close to the sun as demonstrated in the famous sun eclipse of 1919). I interpret this as an effect of gravity on the light.
However, it seems (to me, at least) that light is not accelerated when it travels directly toward the (ba... | You are missing special relativity and general relativity. In special relativity the speed of light in vacuum is always c, no matter the reference frame of measurement.
Also classical electromagnetism, light, emerges from a confluence of the quantum mechanical constituents which are photons and have zero mass. A photo... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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An identity of time-ordered operators that intertwines between the Schrödinger picture and the interaction picture Let $V(t)$ and $H_0$ be two operators where $V(t)$ has explicit time dependence while $H_0$ is time independent.
I am trying to prove the interesting identity,
$$T(e^{-i\int_{t_{0}}^{t} dt' (H_0+V(t'))})~=... | OP's identity follows from the operator identity
$$ \forall t\geq 0:~~ L_1(t)~=~L_2(t), \tag{0}$$
where we have introduced (for later convenience) the following shorthand notation
$$L_1(t)~:=~T\left[\exp\left\{\int_0^t \! ds ~(H_0+V(s))\right\}\right]\tag{1}$$
and
$$L_2(t)~:=~e^{tH_0} T\left[\exp\left\{\int_0^t \! ds ... | {
"language": "en",
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The direction of magnetic field in a coil This question is just to clarify a problem I am having regarding Lenz-Law.
In the following picture, the magnet comes in the coil and inducing the coil making the bottom of the coil north and is pushing the magnet out. But if you look at the way the magnetic field is coming out... | Magnetic fields of a coil and a magnet must have opposite orientations, because if the magnet comes in to to the coil it must be repelled from it.
Let us suppose that it is not the case. The magnet is attracted by the coil and thus accelerates towards it. It is moving faster and faster so the rate of change of the magn... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/338273",
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Is harvesting of electrons during neutron beta decay possible? Is it possible in the decay cycle to harvest the neutron when it decays to an electron. For example if the neutron saturated boron rod was submerged in an electrolytic solution with an anode and cathode set up with some kind of catalyst in the solution. I w... | It's not exactly like your idea, but something very like this is done in betavoltaic batteries. They don't harvest the beta electrons themselves. Instead the kinetic energy of the electron generates electron-hole pairs in a semiconductor and this generates an electric current.
| {
"language": "en",
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Sphere rolling up a step A sphere of radius R is rolling without slipping with a velocity v and collides inelastically with a step of height h < R. What is the minimum velocity for which the sphere will be over the step?
Relevant equations
Total kinetic energy (maybe):
$\frac{1}{2}I\omega^{2}+\frac{1}{2}mv^2$
Gravitat... | Angular momentum can be conserved but only under a certain condition.
The angular momentum just before collision about a point = angular momentum just after collision about the same point.
Hence,we shall conserve angular momentum about the tip of the elevation(as shown in second picture).
Anugular momentum about extern... | {
"language": "en",
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In the semiclassical approximation, should I expand the generating functional around saddles of the sourced or the unsourced action? Consider a Euclidean path integral say in a real scalar field theory.
$$
\int d[\phi]\exp(-I[\phi])
$$
In the semiclassical approximation, we consider stationary points of the action and... | Since we want to deal with path integral by using the stationary phase approximation, you will need to take the stationary points of the sourced action: these regions contribute coherently to the path integral (cause the phase changes very little over a small region surrounding each stationary point) giving the main co... | {
"language": "en",
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Obtaining a general equation for velocity (in 2D projectile motion) I'm trying to obtain a general equation for the instantaneous velocity of a projectile moving on a Cartesian plane.
I began with the equation for a projectile's trajectory (air resistance neglected):
$$y = x(\tanθ) - \frac {gx^2}{(u^2)(\cosθ)^2}$$
wher... | Is your goal simply to write down an equation that relates $v_x$ and $v_y$, without reference to $x$, $y$, or $t$?
If so: Such an equation can’t exist, for the simple reason that $v_x$ is a constant while $v_y$ varies over the trajectory. If you found some relationship $f(v_x, v_y)=0$, you could differentiate it with r... | {
"language": "en",
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Insulated box of air at temperature $T$, is dropped from height $H$, what is the temperature of the air inside box on the ground? In an effort to understand more about the first law I was wondering about the potential energy term and how it would influence the gas inside the box I made this question and tried to answer... | $Energy\space of\space the\space system\space (E) = Internal\space energy\space (U) + PE_{system} + KE_{system}$,
$\Delta E =\Delta U+\Delta{PE} + \Delta{KE}$,
The condition for $\Delta E =\Delta{U}$ is $\Delta{PE}=\Delta{KE}=0$.
The first law of thermodynamics gives us the relation between the change in energy of the ... | {
"language": "en",
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Energy contributions of Hamiltonian density In Lancaster and Blundell, Quantum Field Theory for the Gifted Amateur, p.99, the Hamiltonian density is
\begin{equation}
\mathcal{H}=\frac{1}{2}[\partial_0\phi(x)]^2+\frac{1}{2}[\nabla\phi(x)]^2+\frac{1}{2}m^2[\phi(x)]^2,\tag{11.5}
\end{equation}
and it tells us that the ene... | Each of those terms represent the price to pay, in terms if energy, to have some specific configuration of the field:
*
*configurations that change with time (price is estimated by time derivative)
*configurations that change with space (price is estimated by the gradient)
*magnitude of the field (mass plays a ro... | {
"language": "en",
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Does current run forever in water? (assuming the supply voltage is there forever) Suppose pH of water is $6$, I think this means there is one $\text{H}^{+}$ ion for every $10^6$ water molecules.
When we plug in the battery, I believe we see a current as the $\text{H}^{+}$ ions drift to the $-ve$ side of the battery a... | It is energetically unfavourable to split a water molecule into the two ions $\text{H}^+$ and $\text{OH}^-$ i.e. you need to put in energy to do it. However at room temperature water molecules have a range of energies and there are always a few molecules with enough energy to ionise. So any sample of pure water at ever... | {
"language": "en",
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$2+1$-dimensional Einstein gravity is topological and only non-trivial globally $2+1$-dimensional Einstein gravity has no local degrees of freedom. This can be proved in two different ways:
*
*In $D$-dimensional spacetime, a symmetric metric tensor appears to have $\frac{D(D+1)}{2}$ degrees of freedom satisfying $\f... | Bob Knighton's answer is very detailed. But I want to add a few remarks. You can try to prove this identity
$$ R_{\mu\nu\rho\sigma} = \frac{R}{D(D-1)} (g_{\mu\rho}g_{\nu\sigma}-g_{\mu\sigma}g_{\nu\rho}). $$
Then, it's straightforward to show that for 1+1 spacetime, the Einstein tensor $R_{\mu\nu} - \frac{1}{2}Rg_{\mu\n... | {
"language": "en",
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How to calculate tension? below is an experiment set up to test the effect tension has on the frequency of various guitar strings. It's hard to see the string in the picture, but it's attached to a weight and I was wondering how you could calculate the tension on the string? What equation/formula would you use? We know... | The tension on the string is equal to the weight of the hanging object, plus the weight of the string that is hanging from the pulley. To calculate this, measure the hanging length, $l$. Then, for a string of mass $M$ and length $L$, the mass of the hanging portion is $m=M\frac{l}{L}$.
| {
"language": "en",
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How do we know that nuclear decay is truly random and spontaneous? Nuclear decay is said to be random and spontaneous, but how do we know for certain, that it is not just a lack of understanding of some other unknown force?
Doesn't everything in the universe just depend on the starting conditions, so arguably nothing i... | I broadly agree with existing answers at the time of writing. I hope I can add something helpful. I would like to underline the role of model-making in science. The physical world does what it does, and in science we construct models. The models help us build insight into the nature of the physical world. But the model... | {
"language": "en",
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"source": "stackexchange",
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Charged sphere inside opposite charged sphere If we enclose a negatively charged sphere inside a positively charged sphere, do we get the electric field only due to the outer sphere?
If we do, how? Also, where did the negative charge went ?
| In terms of a picture with your 15 negative charges on the inner sphere and your 20 positive charges on the outer sphere, the charges rearrange themselves as follows.
You will have 15 negative charges on the outer surface of the inner sphere and 15 positive charges on the inner of the outer sphere.
The remaining five ... | {
"language": "en",
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Why does a massless, frictionless piston move from high pressure to low pressure? Consider an ideal gas kept in a rigid cylinder with a movable massless, frictionless piston at the top. Let the pressure inside the cylinder be $P$ at pressure exerted by the surrounding on the cylinder be $p$. Let $$ P>p $$
Now since the... | The bigger force wins.
Pressure is force per area. Let's calculate the forces:
$$F_{inside} =PA\qquad\text{and} \qquad F_{outside} =pA$$
The push from the inside is larger than from the outside, $F_{inside} >F_{outside}$. Easily seen since the areas are equal.
The bigger force wins. The piston moves outward.
Now si... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Kutta-Joukowski theorem applied on a Joukowski airfoil (derivation) I have a doubt about the derivation of the Kutta-Joukowski theorem for a Joukowski airfoil. I know the results, but my main objective is to know how get these ones.
Consider for the initial plane a cylinder centered on $\zeta_0$, with a circulation -$\... | you have transformed circle into ellipse by, $z = \zeta + \frac{b^2}{\zeta}$ ,
Now you have to do the inverse by tranforming ellipse into circle,
So the standard text books (Milne Thompson, etc) use,
$\zeta = \frac{1}{2}z + \frac{1}{2}{\sqrt{z^2-4b^2 }}$ .
Myself tried to transform ellipse into circle with the aove... | {
"language": "en",
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The derivation and formula to calculate Potential Energy seems quite confusing? Ok, so I am in the 10th grade, and Physics is my life, and so I always try to enquire things. We were studying the chapter of Work and Energy during our Physics lecture, and when our lecturer described the derivation of formula to calculate... | There have been a couple of questions similar to this recently, which you should look at. As for your specific question, you have to accelerate the object upward in order to increase its potential energy, so you are inherently giving it kinetic energy by increasing its gravitational potential energy. In other words, th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/341042",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Is the divergence of the propagator between same two spacetime points a pathology? This question is same as the question here which is not answered yet.
By Poincare invariance, the propagator of any field theory $G(x,y)$ must be a function of $|x-y|$ and by dimensional arguments $$G(x,y)=\langle 0|\phi(x)\phi(y)|0\ran... | This is indeed a pathology for the computation of some quantities, such as any quantities derived from the stress energy tensor
$$T_{\mu\nu} = \lim_{x\to y} D_{\mu\nu} G(x,y)$$
For some differential operator $D_{\mu\nu}$. This can be easily renormalized, though, as it can easily be shown that in the coincidence limit $... | {
"language": "en",
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Is atmospheric pressure exerts force from all directions of the object on the surface of the earth? This question came to me as I was solving problem asks the length of the fluid in a open tube when the tube makes particular angle with horizontal surface by giving the height of the fluid when tube was standing straight... | Pressure is exerted by a fluid in directions perpendicular to the surfaces of objects which contains the fluid.
To solve this problem you must understand that when the tube is tilted only a component of the mercury in the tube can exert a pressure along the length of the tube as it's a liquid. This is because the pres... | {
"language": "en",
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Why the four gauge bosons that correspond to the $SU(2)\times U(1)$ electroweak force before symmetry breaking are not listed in the Standard Model? If I correctly understand this, the four gauge bosons that correspond to the electroweak force before symmetry breaking are the W1, W2, W3, and B. How come the W1, W2, W3,... | They're listed under $W^+$, $W^-$, $Z$, and $\gamma$ (the photon). Those observed particles are constructed from linear combinations of $W^1$, $W^2$, $W^3$, and $B$ in the dynamical symmetry breaking of the Higgs mechanism, with $\gamma$ being the massless Nambu-Goldstone boson that results from the process (see commen... | {
"language": "en",
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"source": "stackexchange",
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Bounds of Integration (with respect to something that is not time) I have been reading Richard Feynman's lectures and came across an interesting proof regarding the Earth's gravitational force. At one point in the proof, Feynman uses the following the integral:
$\int_{R+a}^{R-a} dr$
(13.18 on http://www.feynmanlectures... |
In this integral, r is the distance between a point in space and the surface of the Earth, ...
Almost. Actually, based on the diagram in the derivation, $r$ is the distance from the point in space to the ring of mass that is part of the spherical shell. It $is$ a distance like you describe, but it is the distance to ... | {
"language": "en",
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Neutron stars - only neutrons? I was at a museum recently, and there was a display on neutron stars. It said that neutron stars are made only of neutrons, which honestly didn't make much sense to me - neutrons decay very quickly on their own, so how do neutron stars "last", so to speak?
So naturally, I checked wikiped... | The picture from Wikipedia is (qualitatively) correct and so is your intuition.
Neutrons are unstable and decay unless the decay is blocked by the presence of a degenerate electron gas with a Fermi energy that is as large as the maximum possible energy of the electron produced in a beta decay.
If all fermion species ar... | {
"language": "en",
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Is the presence of a magnetic field frame-dependent? I do not have a strong background in physics, so please refrain from using complex mathematics in any answers :)
I was on
this site, and I read:
When an electrical charge is moving or an electric current passes through a wire, a circular magnetic field is created.... | You have to make a distinction between the generation and the detection of a magnetic field. If you generate a magnetic field, but can't detect it, for all intents and purpose, it is the same as not generating it.
In the example you give, even though there is motion of both the charged particle and the compass, ther... | {
"language": "en",
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How do car sunshades work? By putting these sunshades in the windows of a car, one can considerably negate the interior heating effect. What is the physics behind this?
I searched for it online but couldn't find a thorough and comprehensive answer. One thing which I got to know that visible light enters through the w... | My guess is that the black shade is absorbing the heat rather than the air in the cabin. Also, if that shade is an adhesive type of sunshade that actually sticks to the glass then perhaps the heat is more readily conducted to the glass and back out of the car.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/341958",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Velocity of a Mechanical Wave on a String I recently read a derivation for an equation which governs how quickly a wave is transmitted along a string, $v = \sqrt{\frac{T}{\mu}} $, where T is the tension in the string, and $\mu$ is the mass per unit length along the string. The derivation makes sense but gives a more ma... | More mass means more inertia. Thus, it takes more force to move a differential mass on the string, and that differential mass responds more slowly than a "lighter weight" string because the acceleration of that differential mass must follow Newton's 2nd law (a=F/m). This means that the wave speed on a string of large... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/342037",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why is $\nabla \times B$ perpendicular to $B$? I'm considering a magnetic field inside a load capacitor where
$$\boldsymbol{\nabla}\times\textbf{B} =\mu_{0} \varepsilon_{0} \frac{\partial\textbf{E}}{\partial t}\\
\textbf{j}_{c}=0.$$
Why is $\boldsymbol{\nabla}\times\textbf{B}$ is perpendicular to $\textbf{B}$?
| The condition that the magnetic field and its curl be orthogonal is satisfied, generally, for plane-wave situations where the curl is given simply by $\nabla\times\mathbf B = i\mathbf k\times \mathbf B$, as well as a number of similarly 'nice' geometries, but it is not a general property of electromagnetic fields.
In t... | {
"language": "en",
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How to choose the best Gaussian surface? Are there some basic rules so that I could choose a Gaussian surface according to my physics problem? Are there any guidelines for how to choose an appropriate Gaussian surface for the system of charges you are analysing?
| Mathematically the Gaussian surface should be chosen so that
$\vert \vec E\vert$ is constant on the surface so that
$$
\oint\vec E\cdot d\vec S = \int \vert\vec E\vert dS\cos\theta
=\vert\vec E\vert\int dS\cos\theta
$$
so that evaluate the magnitude of $\vec E$ from the charged enclosed by
your surface.
In practice,... | {
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How to justify the maximal value of a star's magnetic field at surface? In many lectures, it is stated that the maximal value $B_{\text{max}}$ of the magnetic field at the surface of a star can be found in Newton's gravitation theory by equating the gravitational potential energy with the magnetic field energy. For a ... | The total energy of a star must be less than zero for it to be a gravitationally bound object.
The total energy is the sum of negative gravitational potential energy (your expression assumes a star of uniform density) and positive terms due to gas pressure, turbulence, rotation and of course magnetic fields.
The maximu... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What happen when a helium balloon is floating inside a moving train?
Let's assume a helium balloon is suspended into the floor of a moving train. We already know how it will react during acceleration, deceleration, and constant speed as illustrated in figure no 1, 2, and 3. However, what will happen to the balloon if ... | Ideally, there will be no external force acting on the balloon in the horizontal direction so it will move along with the train in accordance with Newton's First Law.
However in reality, there will be collisions with gas particles present in the coach which will give it some random velocities.
| {
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"answer_id": 1
} |
Why does an electron emit a photon towards the other electron during electromagnetic repulsion? In the Quantum Electrodynamics theory, the repulsion between electrons is caused by the exchange of photons. This exchange can be represented with the help of Feynman Diagrams, but why the electron has to necessarily emit a ... | Each charge is a source of a force field acting on the other charges, immediately or with retardation, whatever. It is an experimental fact.
The total field of a charge can be represented as a near field (virtual photons) and the radiated field (real photons).
The real photons are never absorbed, but scattered. The vi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/342881",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
} |
How to implement this single-qubit unitary? I was reading this paper on qubit state preperation, and encountered an interesting type of single-qubit gate:
\begin{align}
U_\theta = \left(\begin{matrix} \cos\theta & \sin\theta \\ \sin\theta & -\cos\theta \end{matrix}\right) = \cos\theta\, \sigma_z + \sin\theta\, \sigma_... | Consider the most general rotation as
$$
R_{\mathbf{n}}(\theta)=e^{i \theta (\mathbf{n}.\mathbf{\sigma})}
= \begin{pmatrix}
\cos \theta + i n_{z} \sin \theta & i n_{x} \sin \theta + n_{y} \sin \theta \\
in_{x} \sin \theta -n_{y} \sin \theta & \cos \theta - i n_{z} \sin \theta
\end{pmatrix},
$$
which we have obtained ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/343044",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 2,
"answer_id": 1
} |
Understanding the units of number density I understand that we can measure any general number density $n$ as,
$$ n = \frac{N}{V}$$
for total number $N$ and volume $V$. This puts the units of number density as $\text{length}^{-3}$ e.g. $\text{cm}^{-3}$
Now suppose the number density varies with radius as e.g.,
$$ n(r) =... | In several comments, it was mentioned "just make the units of $N_0$ whatever they need to be, without concern as to why. I thought I might add to that.
Units are a funny thing because in many cases, they serve no deeper purpose than to ensure you did the math correctly. Take Hooke's law as a classic example. Hooke's... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/343310",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 4,
"answer_id": 2
} |
Lagrangian and Hamiltonian formalism for damped pendulum Suppose I have a simplified pendulum (massless string of length $l$, ball of mass $m$ and some non-zero volume). I want to derive the equations of motion, but I want to take air resistance under account. I know how to do it by applying Newton's 2nd law, but is th... | In a sense yes; you'll need to write the force of air resistance as if it can be derived from a velocity dependent potential.
A common example of this is a particle in a magnetic field. The force of the magnetic field on the particle depends on its velocity, so the potential is written as $\vec{A} \cdot \vec{v}$.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/343553",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 2
} |
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