Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Why do strings split in string theory? In string theory, we are told strings can split and merge if the string coupling is nonzero, even while the worldsheet action remains Nambu-Goto or Polyakov plus a topological term. However, a classical solution, in say the light cone gauge, shows that provided the worldsheet time... | Some cases to ponder over.
A closed string splits into two closed strings, which then merge again into a single closed string. The overall string worldsheet has the topology of a torus. There is an SL(2,Z) group of large diffeomorphisms acting upon this worldsheet. The contribution to the partition function comes from... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/32821",
"timestamp": "2023-03-29T00:00:00",
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Rotation, cats landing on their feet, and conservation of angular momentum Let θ be the orientation (angle) of a body (such as a cat), and let ω be its angular velocity.
It is well-known that θ can change even when the body is not rotating, using the conservation of angular momentum; that is, even when ω = dθ/dt = 0.... | Good answer from bobuhito. Here's another explanation. Satellites have reaction wheels (which are not gyroscopes) to help them change orientation.
If you sit still on a rotating stool, and you want to change direction, and you are holding a long heavy rod, simply hold the rod over your head and rotate it horizontally a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/32882",
"timestamp": "2023-03-29T00:00:00",
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Explanation for $E~$ not falling off at $1/r^2$ for infinite line and sheet charges? For an infinite line charge, $E$ falls off with $1/r$; for an infinite sheet of charge it's independent of r! The infinitesimal contributions to $E$ fall off with $1/r^2$, so why doesn't the total $E$ fall off the same way for the infi... | The true explanation is, of course, the math. But I'm guessing you're familiar with the calculation. For an intuitive understanding, I'd put it like this: when you're very close to an infinite sheet of charge, the contributions to $\vec{E}$ of the pieces of charge far away from you mostly cancel out, because e.g. the e... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/32948",
"timestamp": "2023-03-29T00:00:00",
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Why are there photographs of nuclear tests? I was looking at old photographs of the nuclear tests on the bikini atoll. It dawned on me that you don't want to run film through airport x-rays, as it exposes the film. I've been told that a nuclear explosion emits all energy on the spectrum (IR to Gamma). If this includ... | One possibility to consider: Many of these photographs were taken long enough AFTER the explosion that much of the energy of the explosion has gone into stirring up debris rather than the initial flash. If only the initial flash was photographed, there would be a bright spot at the location of the bomb, and almost no... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/33044",
"timestamp": "2023-03-29T00:00:00",
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What is the spectrum of the Earth's albedo? I was recently discussing climate change with a friend and was surprised (and embarrassed) to learn that the heat capacity of CO${}_2$ is not higher than that of nitrogen contrary to my assertions. After further research, I found that the relevant capture cross sections acco... | There CERES satellite has been measuring light reflected from Earth. In principle the raw data is available from NASA though I imagine some work will be necessary to process it.
| {
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What is a good introductory book on quantum mechanics? I'm really interested in quantum theory and would like to learn all that I can about it. I've followed a few tutorials and read a few books but none satisfied me completely. I'm looking for introductions for beginners which do not depend heavily on linear algebra o... | *
*Mark Beck, Quantum Mechanics: Theory and Experiment, might be the best QM book there is. The math needed is modest, but knowledge of optics and electromagnetic waves is almost necessary.
You can also try two simpler, very short books by Valerio Scarani (aimed at, mainly, high school students),
*
*Quantum Phy... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Why is there this asymmetry between the two foci of an orbital ellipse? Why does the Earth revolve with the Sun at one of its foci? Does the other focus do nothing? Why is there this asymmetry in our solar system?
| I'm almost certain there used to be an answer to this question, but it seems to be gone, I'll write another one. The Earth and Sun both orbit their mutual barycenter (disregarding any other objects of course). That one point is a focal point of both ellipses, and all three focal points are collinear.
It may appear asym... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Equations of fluid dynamics and differential geometry Where can I look for equations of fluid motion written in terms of nifty things from differential geometry like exterior derivative, Hodge dual, musical isomorphism?
Preferably both with and without assumption of Newton viscosity model.
Since one can get momentum an... | I've made a small document featuring fluid dynamics equations in terms of vector-valued differential forms. The document with information on any further developments can be found on my page.
| {
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Understanding Tensors I don't seem to be able to visualize tensors. I am reading The Morgan Kauffman Game Physics Engine Development and he uses tensors to represent aerodynamics but he doesn't explain them so I am not really able to visualize them. Please explain in very simple ways. I just want to understand the basi... | Tensors are abstract algebraic or differential geometric objects (in the latter case we're actually talking about tensor-valued fields) which are made from 'products' of vectors and covectors.
There's no tangible explanation for what a tensor is because the concept is so general that tensors can fill very different rol... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/33470",
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How will you measure speed in km/hr in space? How is the speed of an object in space measured? Also more importantly how do you measure your own speed in space? On the road we use a speedometer which tells us the speed easily. How is it done in space?
| One possibility is to measure your speed relative to the ions around you. Aeroplanes in the early days had the same problem. They used ventura pipes where the drop in air pressure was a function of speed. This was air speed not ground speed. A tail wind meant their air speed was in accurate. They did spot checks on lan... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/33511",
"timestamp": "2023-03-29T00:00:00",
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Time-dependence in LCAO I would like to study time-dependence (TD) in linear combinations of atomic orbitals (LCAO).
The Hückel method enables quick and dirty determination of MOs for suitable systems (view link for assumptions). The basis function $\phi$ is the 2pz orbital.
Any molecular orbital (MO) is described as
$... | The ground state of benzene is an eigenstate of the hamiltonian and as such its time dependence is trivial - it only acquires a phase with time at a rate equal to the ground state energy (modulo $\hbar$), and if it's only the ground state you're interested in then you can ignore this phase.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Height of the atmosphere - conflicting answers Okay. I have two ways of working out the height of the atmosphere from pressure, and they give different answers. Could someone please explain which one is wrong and why? (assuming the density is constant throughout the atmosphere)
1) $P=h \rho g$, $\frac{P}{\rho g} = h = ... | Neither calculation is anything approaching physically realistic, but I guess you know that and you're just interested in why the two approaches give different answers.
Take your equation from your second method:
$$ 4\pi r^2 P = \rho V g $$
If the area is a flat sheet you have $V = Ah$ and $A = 4\pi r^2$, and substitut... | {
"language": "en",
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How is acceleration computed in the leap-frog algorithm in computer simulations of particles? I am reading the book Computer Simulation of Liquids by Allen and Tildesley (here is another link). On page 80, the authors describe the leap-frog algorithm, which is used extensively in molecular dynamics (MD) simulations. ... | The acceleration ${\bf a}(t)$ is simply computed from Newton law $F = m a $. It's a function of the forces on the particle, which is (assumedly) computable from the positions ${\bf r}(t)$ (of the entire system, i.e. all particles) at time $t$.
This can be seen also in the figures, in the three schemes the acceleration ... | {
"language": "en",
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Mechanism of pair production and annihilation of matter Pair production is where an energetic photon on its interaction with strong electric field surrounding a nucleus produces an electron-positron pair. Annihilation is its converse where an electron-positron pair produces two photons on interaction with nucleus.
But ... | Electron and positron can annihilate in free space, but a single photon cannot be turned into electron-positron pair because conservation of energy-momentum cannot be satisfied. The nucleus in pair production absorbs some of the momentum.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/33800",
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Is dimensional analysis used outside fluid mechanics and transport phenomena? Most dimensionless numbers (at least the ones easily found) used for dimensional analysis are about fluid dynamics, or transport phenomena, convection and heat transfer - arguably also sort of fluid mechanics.
My understanding of dimensional... | I use dimensional analysis regularly, but not often to derive equations. I find it most useful when I've been doing some algebra and ended up with some equation - I plug in the dimensions of the variables in the equation to check that the left and right sides agree. This is a quick crosscheck for my working. Agreement ... | {
"language": "en",
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What are the properties of the partially polarized light on refraction? When a ray of ordinary light is passed on the surface of the water the reflected light will be completely polarized( vibrations in one plane).
My question is what will be plane of vibration in the partially polarized light that undergoes refraction... | The reflected light is not completely polarised. It's certainly true that $s$ polarised light (i.e. light polarised in the plane of the surface) is more strongly reflected, but except at the Brewsters angle $p$ polarised light is reflected as well.
The plane of polarisation of $s$ and $p$ polarised light is not changed... | {
"language": "en",
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Special Relativity Second Postulate That the speed of light is constant for all inertial frames is the second postulate of special relativity but this does not means that nothing can travel faster than light.
*
*so is it possible the point that nothing can travel faster than light was wrong?
| There are various ways to formulate special relativity. The different approaches illustrate various different aspects of the theory so one of the tricks is to choose the formulation best suited to the question you're asking. My own favourite approach is based on the invarience of the proper time, and in fact this answe... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/34024",
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Meaning of the first and second laws of the photoelectric effect I was reading the introduction to quantum mechanics in my physics book and it begins with a discussion of the photoelectric effect and energy quantas.
The first law, the one that says that the intensity of the photoelectric saturation current is directly ... | In the photoelectric effect one photon displaces one electron, so the way to understand it is to consider the properties of the photons.
If you take light of a fixed frequency, $\nu$, then the energy of the photons is fixed at $h\nu$. That means the intensity of light is proportional to the number of photons, and becau... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/34082",
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Is there a non-perturbative remormalization? If so, how does it work? Is there a method to renormalize a theory without using perturbative expansions for the divergences? For example, is there a method to get masses and other renormalized quantities without using expansions and counterterms?
O have heard about Lattice ... | Non-perturbative RG methods exist and are useful. They have been used to understand several phenomena in (nonequilibrium) statistical mechanics.
*
*NPRG of the KPZ equation
*Reaction-Diffusion processes
*Critical dynamics
*Nonequilibrium steady-states
*Voter models
*Branching and annihilating random walks
*3D ... | {
"language": "en",
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$\lambda=\frac{2h}{p}$ instead of $\lambda=\frac{h}{p}$? I am studying quantum physics and there is something I don't understand:
*
*I know that for any particle $E=hf$ (Einstein relation) and
*$v=\lambda f$ ($v$ is the speed of the particle).
*I also know that the kinetic energy is $E_k=\frac{mv^2}{2}$.
Solving... | I) One must distinguish between the group velocity
$$v_g~=~\frac{\partial E}{\partial p}~=~v,$$
and the phase velocity
$$v_p~=~\frac{E}{p}~=~\left\{ \begin{array}{cl}
\frac{v}{2} & \text{in non-rel. QM (Schr. eq.) where}~ E~=~ \frac{p^2}{2m}, \cr
\frac{c^2}{v}& \text{in rel. QM, QFT (Dirac eq., KG. eq.) where}~ E~=~... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/34214",
"timestamp": "2023-03-29T00:00:00",
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What criteria distinguishes causality from retrocausality? The brilliant philosopher David Hume remarked that if two events are always found to be correlated to each other with one event happening prior to the other, we call the earlier event the cause and the latter event the effect. However, it has been pointed out t... | There is no difference between causality and retro-causality (i.e. all causality is retro-causality and all retro-causality is causality).
For example: Causality can be understood like a wave-function of light - because light is a mechanism of causality. All mechanisms of causality are interacting all the time at every... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/34303",
"timestamp": "2023-03-29T00:00:00",
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"question_score": "10",
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Is anti-gravity (i.e. repulsive gravity) possible in theoretical physics? Is anti-gravity (i.e. repulsive gravity) possible in string theory?
I have read some articles about scientists making assumptions about the existence of anti-gravity, but is it possible in string theory?
| As it happens we do observe anti-gravity (i.e. repulsive gravity) in the form of the dark energy. There are speculative ideas to describe this from string theory, though these are far from widely accepted.
In general relativity the curvature of space time is controlled by the stress-energy tensor. To get anti-gravity... | {
"language": "en",
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Why doesn't the percentage of oxygen in Earth's atmosphere diminish significantly with altitude? According to numerous sources online, the percentage of oxygen is approximately the same at sea level and 10,000 meters. Since oxygen is heavier than nitrogen, shouldn't the percentage of oxygen decrease with altitude?
| If you were to surround the atmosphere by an adiabatic envelope and allow it to come to equilibrium, it probably would settle into such a state. However, the atmosphere is not a static place. It is actively mixed due to heating of the ground by the sun, and by cooling of the upper atmosphere by radiation into space. Th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/34580",
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"source": "stackexchange",
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How can I estimate the elasto-optic coefficients ($p_{11}$ and $p_{12}$) of a material? I am attempting to estimate the elasto-optic coefficients ($p_{11}$ and $p_{12}$) of $\mathrm{TiO}_2$ and $\mathrm{ZrO}_2$, where $p_{11}$ and $p_{12}$ refer to the elements of a strain-optic tensor for a homogeneous material as giv... | Elasto-optic properties are complex tensorial properties, and I don't think there is any good way to estimate them short of:
*
*measuring them experimentally
*calculating them through quantum chemistry methods (CRYSTAL14 is one code with such features)
*finding them in the literature
Luckily for you, a simple s... | {
"language": "en",
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The observation of a non-SM resonance at 38 MeV Was reported here. Of course if this is real it is very exciting. It leads me to the question: given that it took so long to find this resonance at a meager 38 MeV, is it possible that all SUSY particles are hiding down in the MeV or KeV range (or lower)?
| You say that you are siding with COMPASS.
However, that is an ambivalent statement.
COMPASS first released the opinion that the signal at around 40 MeV is an artifact of their methods of analysis and their equipment. Since I have no access to their methods and equipment properties, I had to accept such statement. Altho... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/34698",
"timestamp": "2023-03-29T00:00:00",
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Why are breeder reactors not more prevalent? I recently learned about breeder reactors, which are able to create more fissile material than they consume. They seem to be superior to the types of nuclear reactors currently in use. What are the reasons why breeder reactors are not more prevalent.
| Uranium is also substantially cheaper than plutonium and the difference between costs saved and the adoption cost is not enough to warrant adoption on a large scale.
Another point is that, for many of Soviet-era breeder reactors, the coolant was liquid sodium, which, as we all know, doesn't react in a safe manner with ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/34811",
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Why is current not 0 in a regular resistor - battery circuit immediately after you closed a circuit? In regular open circuits with either a capacitor or inductor element, (when capacitor is uncharged) with a battery, when a switch is closed to complete the circuit the current is said to be 0 because current doesn't jum... | In real life, the current can't jump instantaneously because there is always some finite inductance in a circuit. However, this is just a typical idealized textbook problem where the inductance is assumed identically zero, so the current can jump instantaneously according to the assumptions of the problem. Note the c... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/35042",
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What happens when a bare 3d topological insulator is subject to a magnetic field? Effective field theory of 3d topological insulators (TI) predict some novel electromagnetic effects. Unfortunately it require a gapped surface which is hard to achieve experimentally. Then I have two questions.
1.
Is $\nabla P_3=0$ for a... | Thank you for you answer. But there might be different interpretations of the word "topology." In the TI case, "topological" means universal, independent of material properties while when it comes to the concept of "topological orders," "topology" implies robustness. After all, it is merely a name whose meaning varies... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/35100",
"timestamp": "2023-03-29T00:00:00",
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What are the differences between dark energy and a cosmological constant? My possibly mistaken understanding is that dark energy changes with time, whereas a cosmological constant is, well, constant. What about gravitational clumping? Detecting relative motion?
| My view is that dark energy is like hot air in a balloon. It's density does not stay constant, but decreases as the universe expands, like every other form of energy.
Like other forms of energy, it would also be subject to the second law of thermodynamics and would cool down, slow down, and get sucked into black holes,... | {
"language": "en",
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Does the 'mAh' rating of a battery have something to do with its power? I'm curious about the 'mAh' of a battery: how can this impact the power of the battery?
I've done some research on the internet, and most of the articles I found explain about the 'amount of charge stored' inside the battery, or in other words, th... | I support the answer given by Martin Beckett.
The energy of the battery(that you used) is, 700mAh*6V. The voltage applied across the impedance is constant 6V. Depending on the impedance, the current flows through it. If the current requirement is high(more than 700mA, it runs for 1 hour at that current), you need to ge... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/35265",
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Modulus of Elasticity Consider a cube of unit dimensions. Let $\alpha$ and $\beta$ be the lateral and longitudinal strains. The expressions for moduli of elasticity on applying unit tension -
1) At one edge: Young's modulus $E=\frac{1}{\alpha}$
2) Normally to all the sides: Bulk modulus $K=\frac{1}{3(\alpha-2\beta)}$
3... | For instance, let us derive 2). Let us consider a unit cube and apply unit tension along $x$, unit tension along $y$, and unit tension along $z$ (to derive bulk modulus). For example, tension along $x$ causes strain $\alpha$ along $x$ and strains $-\beta$ along $y$ and along $z$ (the sign of lateral strain is typically... | {
"language": "en",
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Kepler problem: flows generated by constants of motion This is part of an admission exam problem, found at
http://www.sissa.it/mp/admission/tests//2008_common.pdf
Consider the Hamiltonian of Kepler problem
$$H(\boldsymbol{r},\boldsymbol{p})= \frac{|\boldsymbol{p}^2|}{2\mu} +\frac{\alpha}{|\boldsymbol{r}|}, \qquad \mu>0... | The flow generated by a function $f$ on the phase space $T^*M$ (whose coordinate functions are $\mathbf{q}$ and $\mathbf{p}$) is a set of new coordinate functions $\mathbf{Q}(\mathbf{q}, \mathbf{p}, t)$ and $\mathbf{P}(\mathbf{q}, \mathbf{p}, t)$, (parameterized by a parameter $t$ (time)) satisfying the first order dif... | {
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Extract energy from magnets Is it possible to "extract" energy from a magnet, making it lose its magnetism? Or, to put in another way, is magnetism a form of energy? (I am not talking about potential energy in a magnetic field). Since matter is equivalent to energy, is the property of magnetism equivalent as well?
| You cannot extract energy from magnets. You can just disrupt the orientation of the molecules(dipoles) in the magnet(by heating or so..). The answer to the question is same as the answer to the question, "Can you remove charge of an electron??" or "Can i extract energy from the charge of an electron?". Its impossible. ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/35565",
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A problem of missing energy when charging a second capacitor A capacitor is charged. It is then connected to an identical uncharged capacitor using superconducting wires. Each capacitor has 1/2 the charge as the original, so 1/4 the energy - so we only have 1/2 the energy we started with. What happened?
my first though... | You're sloshing charge around!
You've set up an LC circuit (if there's a current there's an L - if for no other reason the electron's mass), so when the capacitors are equally charged, the current is at it's maximum. Currents have an energy associated with them! If you work it out with the current term included, you'l... | {
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How can quantum (Internet) network be possible? According to the knowledge I have, there are routers, switches etc. Therefore, packets would have to be "measured" before continuing on. (If not, how will anyone know the damn IP address?)
But this effectively ends any advantage of quantum channel..
So how is quantum netw... | There is nothing avoiding you to transmit routing information by classical channels, then the quantum packets would be routed according to the classical information and shared by the receiver and sender in those headers
| {
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Complete set of observables in classical mechanics I'm reading "Symplectic geometry and geometric quantization" by Matthias Blau and he introduces a complete set of observables for the classical case:
The functions $q^k$ and $p_l$ form a complete set of observables in the sense that any function which Poisson commute... | Blau called them a 'complete set' in analogy to the quantum mechanical picture, where a observable commuting (read Poission-commuting in the classical case) with a complete set of commuting observables is proportional to the unit, i.e. a 'constant'. This is called (first) Schur's lemma.
| {
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Was the Universe's entropy equal to zero at the Big Bang? Is zero-entropy state unique? It is postulated by many cosmologists that at the Big Bang time the universe was in an unusual low entropy state.
Does this claim specifically mean that the entropy of the initial universe was zero?
Is zero-entropy state unique for ... | I understand that there was zero entropy or at least low entropy that became self agitated to bring about the big bang. The closest example to zero or very low entropy is a solution of Dropleons with quasiparicles structures in a liquid state that are self propagating. This is based on the initial conditions of the so... | {
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Driving a solution of optical isomer molecules with the resonant frequency What happens when we drive a solution of optical isomer molecules (enantiomers) with a microwave radiation in resonance with the tunneling frequency of the molecules (the frequency of the transition between the eigenstates of the Hamiltonian)? ... | Usually, optical isomers are defined when tunneling can be neglected (that is, when the torsional barrier between the isomers is very large that the isomers can be isolated and are considered stable). Then the ground state of the Hamiltonian is degenerate. From Quantum Mechanics it is a question of taste weather you ch... | {
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Group Velocity and Phase Velocity of Matter Wave? In quantum mechanics, what is the difference between group velocity and phase velocity of matter wave? How can it also be that phase velocity of matter wave always exceeds the speed of light?
| I will not go into math (because many already did ) but will try to explain physics.
Wave function describes the wave of probability (this of course rough analogy) it means when it travels in space, information of probability (probability of finding the particle) travels with it, thus this is phase velocity (which can ... | {
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How to incorporate effects of gravity in a many-electron system? In the weak interaction limit, behaviors of electrons can still be described by a 1-partitcle equation with a modified mass, where the change in mass can be understood as effects of other neighboring electrons as a single electron drags along. Since the c... | A possible answer:
A single electron couples to gravity in the usual way. When a large number of electrons are put together, coupling to gravity shouldn't disappear. Gravity, gravitational force actually, can be thought of an additional "electric field" ${\bf E} = \frac{m}{q_e}{\bf g}$ or $q_e{\bf E}=m{\bf g}$.
Then, ... | {
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Why doesn't magnetic monopole found in spin ice modify the Maxwell's Equations? The magnetic monopole predicted by Dirac nearly a century ago(1) was found in spin ice as a quasi-particle(2). My question is: why doesn't the magnetic monopole found in spin ice modify Maxwell's Equations? (I know they are not elementary p... | According to this review paper, in the ground state, the 2in2out spin arrows are considered "pseudo magnetic fields" because of the zero divergences everywhere. As one spin arrow (or dumbbell) is flipped, that pseudo magnetic field has nonzero divergences at two sites. It's not a real magnetic field, however, the magne... | {
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Reason for the Gaussian wave packet spreading I have recently read how the Gaussian wave packet spreads while propagating.
see:
http://en.wikipedia.org/wiki/Wave_packet#Gaussian_wavepackets_in_quantum_mechanics
Though I understand the mathematics I don't understand the physical explanation behind it. Can you please ex... | Ron's answer is (as always :-) definitive, and if you're going to accept an answer you should accept his. However I thought it was worth attempting a more general explanation.
Remember that the gaussian packet describes the probability distribution of the particle. When the packet spreads it doesn't mean the particle i... | {
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Can water be magnetized? This may be a stupid question, so feel free to shoot it down.
Assuming all atoms have a magnetic moment, I would assume the water molecule too would have a resultant magnetic moment; ergo, it may be possible to magnetize a body of water.
Can water be magnetized?
| Pass a lot of electricity through a small amount of water(behaves as an electric conductor). There will be field around it. If you want to have magnetism for a non-electrocuted water, its impossible(to get higher B values). But, using some solutes you can increase the magnetic property of water.
| {
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Quantum Mechanics- Antenna emitting electromagnetic radiation Radio signals are being transmitted in a frequency of $ 8.4 \times 10^9 \text{s}^{-1} $ and being received by an antenna that is capable of receiving power of $ 4 \times 10^{-21} \text{Watt} $ ($ 1 \, \text{Watt} = 1 \, \text{J s}^{-1} $ ) .
Estimate that n... | How can you calculate the number of produced photons if the only known thing is the frequency?
To calculate the number of photons received (or emitted) per second, you have to divide the received (emitted) power by the energy of one photon $\hbar\omega=h\nu$.
| {
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Maxwell equation boundary conditions on a conducting sheet I'm having difficulties solving boundary conditions for an infinitely thin conducting layer in a presence of an alternating field.
I use the Maxwell equations:
$\nabla \cdot \mathbf B = 0$
$\nabla \cdot \mathbf D = \rho$
$\nabla \times \mathbf E = i \omega \mat... | Your problem is singular, so you need to use distribution. Vector field operators reads:
div(B)={div(B)}+n12.(B2-B1)*delta(S)
curl(E)={curl(E)}+n12x(E2-E1)*delta(S)
{div(B)} is the function derivative, and delta(S) is the 2D delta distribution located on S.
Then you equate the regular part with the regular part and the... | {
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What was the first discovery of the delta baryon $\Delta^{++}$? The delta baryons (also called delta resonances) are a family of subatomic hadron particles which have the symbols $\Delta^{++}$, $\Delta^{+}$, $\Delta^{0}$, and $\Delta^{−}$ and electric charges +2, +1, 0 and −1 elementary charge respectively.
*
*i wan... | You may find useful this paper from the particle data group listings:N AND Delta RESONANCES . It gives a concise explanation and references of what the resonances are. You may chase the original references there.
There are many Delta resonances as you can see in the table, with different masses. It is only within each... | {
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Decomposition of deformation into bend, stretch and twist? I'm wondering is there any way to decompose the deformation of an object into different components? For example, into stretching, bending and twisting part respectively? The decomposition could be applied to any description of deformation, either to deformation... | There is no such general decomposition, simply because bending and twist can only be defined for rods (where there is a longitudinal direction of reference). So it makes no sense to talk about "bending" of a sphere, for example.
If we focus our attention on bodies that can be assimilated to a rod or prismatic piece, th... | {
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If the earth would stop spinning, what would happen? What would happen if the earth would stop spinning? How much heavier would we be? I mean absolutely stop spinning. How much does the centrifugal force affect us?
If you give technical answers (please do), please explain them in laymen's terms, thanks.
Edit: I am aski... | At the equator, the centrifugal acceleration is
$$R\Omega^2 = 6,378,000\times (2\pi / 86,400)^2 = 0.034 \,{\rm m/s}^2 $$
which is 0.3% of the gravitational acceleration. So at the equator, you would immediately feel heavier by 0.3% or so. However, the difference would be smaller at other places of the globe. That woul... | {
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Matrix mechanics for those with wave mechanics background Just curious:
Is there any book or resource that teaches matrix mechanics (quantum mechanics) only without wave mechanics stuff - meaning that the book assumes wave mechanics background.
| If you want to learn Matrix Mechanics, there's no better book than "Quantum Mechanics in Simple Matrix Form" by Thomas Jordan. It's elementary mathwise; it's a thin book. You'd see matrices everywhere in the book; even the Heisenberg Uncertainty principle (alla non-commutative) is treated that way in the first chapte... | {
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Is Heisenberg's matrix mechanics or Schrödinger's wave mechanics more preferred? Which quantum mechanics formulation is popular: Schrödinger's wave mechanics or Heisenberg's matrix mechanics? I find this extremely confusing: Some post-quantum mechanics textbooks seem to prefer wave mechanics version, while quantum mech... | The true fathers of quantum mechanics – Heisenberg, Born, Jordan, and later Bohr – started with matrix mechanics; it was the picture in which the classical equations of motion were easier to be understood as a limit of the new theory. That was in 1925. That was how quantum mechanics was born for the first time.
Within ... | {
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Importance of phase in probability amplitude in QFT I have started teaching myself QFT from the textbook by A. Zee. From reading that book, my idea of a path integral in field theory is the probability amplitude to go from a given field configuration to a different field configuration. At a point, he adds a source func... | As Lubos Motl mentions in a comment, the physically observable object is not the partition function itself
$$ Z[J]~:=~ \int D\varphi~e^{\frac{i}{\hbar}(S+J\varphi)}, $$
but instead closer related to quantum averages$^1$, e.g. the one-point function
$$ \langle \varphi(x) \rangle_J ~:=~\frac{\int D\varphi~e^{\frac{i}{\hb... | {
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Proving $t=(1+\sqrt{1+2hg/v^2 } ) (v/g)$ for a thrown ball If we throw a ball from the hight point $h$ from the earth, with initial velocity $v’$, how to prove that the time it takes the ball to reach the earth is given by:
$$t=\frac{v}{g}(1+\sqrt{1+\frac{2hg}{v^2} } )$$
| For a free falling object without air resistance you have two equations
$$ y = h + v'\,t - \frac{1}{2} g t^2 $$
$$ v = v' - g\,t $$
with $h$ the initial height, $v'$ the initial velocity (upwards is positive), $y$ the height at time $t$, and $v$ the velocity.
Solve them when $y=0$ for $v$ and $t$.
Reference: projecti... | {
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Will cosmological gravitational waves be weaker or stronger than astrophysical ones? Will gravitational waves of cosmological origin be weaker or stronger (higher amplitude $h \simeq\Delta L/L$) than those created from astrophysical sources?
I'm having a real hard time finding the amplitude of cosmological gravitationa... | there is chance to detect the waves
Observable Spectra of Induced Gravitational Waves from inflation
https://arxiv.org/abs/1203.4663
...A recently discovered observational by-product of an enhanced power spectrum on small scales, induced gravitational waves, have been shown to be within the range of proposed space base... | {
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Determining the center of mass of a cone I'm having some trouble with a simple classical mechanics problem, where I need to calculate the center of mass of a cone whose base radius is $a$ and height $h$..!
I know the required equation. But, I think that I may be making a mistake either with my integral bounds or that $... | I am not sure about this formula. Lets start by taking the vertex of the solid cone to be $O(0, 0, 0)$ in cylindrical coordinates ($r$, $\theta$, $z$). Then take the height of the cone to be $h$ and the base of the cone to have radius $a$. In this case the we know that
$$r = \frac{a}{h} z.$$
The formula for the center... | {
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Why is NASA interested in Gamma ray bursts? Gamma-ray bursts(GRBs) are flashes of gamma rays associated with extremely energetic explosions
why nasa interested to Gamma ray burst?
| NASA is an agency involved in, among other things, astronomical research, and GRBs are a hot topic in astronomy/astrophysics. On its own website the agency states that according to one of its three main mission directives NASA "explores the Earth, solar system and universe beyond; charts the best route of discovery; an... | {
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What does the term liquid mean in condensed matter physics? In condensed matter physics, people always say quantum liquid or spin liquid. What does liquid mean?
| Historically, the terms gas, liquid and (crystalline) solid meant, respectively: weak/no interactions between particles, strong interactions but statistical translation/orientation invariance, and finally breaking of translation/orientation invariance. Applied to more spin systems, a liquid would have translational inv... | {
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New physics at high energies, cosmic rays, particle-detectors in space New physics is expected at high energies and cosmic rays have high energies, so have there been or are there any plans to put particle detectors in space to study cosmic rays for new physics ?
| There are particle detectors in space right now, and many more planned. They not are to used to study ultra-high energy cosmic rays because those puppies are very, very rare indeed.1 Instead they study electromagnetic bands that do not penetrate the atmosphere and cosmic rays a more ordinary energies.
1 Large scale gr... | {
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Weak isospin confinement? According to the Wikipedia article on color confinement:
The current theory is that confinement is due to the force-carrying gluons having color charge [...],
i.e. because the gauge group is non-abelian. But that is equally true for the weak force. Does that mean that above the electroweak... | Confinement is prevented because the Higgs mechanism occurs at a scale which is much larger than the SU(2) confinement scale. W's and Z's acquire large masses and the coupling never becomes strong. If we were to lower the electroweak symmetry breaking scale then the theory would eventually become confining. Note that t... | {
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How can such a high exponent arise in this physics equation? This site http://what-if.xkcd.com/14/ states that during a helium flash, "the reaction rate is proportional to the 40th power of the temperature".
Taking for granted that this is true, how can such a large exponent arise in a physic equation? It just mak... | Expanding the comments above:
The quantity in question probably doesn't obey a power law in the traditional sense. It is most likely an exponential law $y(x) = e^x$, since it involves thermodynamic Boltzmann factors and quantum tunneling probabilities, and both are exponential.
Having said that, it can still be locally... | {
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quantum entanglement at microwave frequencies Entanglement of optical photons using non-linear crystals has been around for a long time. Macroscopic entanglement using diamonds recently reported in the literature and receiving considerable attention. Quantum mechanics in biology has been the subject of fascinating re... | The first report on entangled microwaves seems to be http://arxiv.org/abs/1204.0732. A clear proof of spatially separated entanglement with degenerate frequencies is reported in http://arxiv.org/abs/1210.4413.
| {
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Linear algebra for quantum physics A week ago I asked people on this site what mathematical background was needed for understanding Quantum Physics, and most of you mentioned Linear Algebra, so I decided to conduct a self-study of Linear Algebra. Of course, I'm just 1 week in, but I have some questions.
*
*How is t... | There is a nice book aimed at gifted high school students, written by Thomas Jordan at the University of Minnesota, Duluth. Called Quantum Mechanics in Simple Matrix Form, it's a short introduction to complex numbers, linear operators, and QM. I believe the author used it to teach a summer school for high school studen... | {
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Do intergalactic magnetic fields imply an Open Universe? According to a paper on the arXiv (now published in Phys Rev D), they do. How credible is this result? The abstract says:
The detection of magnetic fields at high redshifts, and in empty
intergalactic space, support the idea that cosmic magnetism has a
prim... | I'd say no, though the paper seems credible in its methods I believe it is neglecting to account for the fact that we can only measure the Visible Universe.
This may require a little explanation as I don't mean there are some extra layers or dimensions, but that we can only see $\dfrac{4}{3}\pi(14.5\cdot 10^{9}\ \mathi... | {
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Is the number of rays projected by a source of light finite? Take a source of light which gives out infinite number of rays, each ray with finite number of photons and each photon with a finite amount of energy,
Then, Aren't the number of photons become infinite and hence the energy in the beam of light becomes infinit... | A good definition for Ray of light is provided by Wiki. It is a theoretical term ideally used to mention the propagation of light in Ray optics (simply, it's an assumption of a path that light may take along its direction). You could draw infinite number of rays from a point source of light. We require rays (at least w... | {
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How is the phase shift of light measured? This may seem like a simple question, but I cant seem to make any headway.
Consider the following; I have two beams of light, a reference beam $(A=\cos(wt))$ and phase shifted beam $(B=\cos(wt+\phi))$.
What is the normal way (say in a lab) that $\phi$ is detected & measured wi... | Briefly, one technique for observing phase shifts in light is Phase Contrast microscopy which garnered Fritz Zernike the 1953 Nobel prize in physics.
| {
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What are the applications of Gauss's law in technology? Freshmen physics textbooks use Gauss's law plus symmetry to calculate the electric field.
I was wondering if this method of finding the electric field using a symmetry is used in real applications in life, science, research, or technology. For example do researche... | do researchers use symmetry to find the electric field due to a charged virus that is spherically symmetric?
The answer is no. Why they need to reinvent the wheel? They just use the known formula that exists for such situations that can be proved using Gauss Laws (though they all can be proved without using Gauss laws)... | {
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What are some of the best books on complex systems and emergence? I'm rather interested in getting my feet wet at the interface of complex systems and emergence. Can anybody give me references to some good books on these topics? I'm looking for very introductory technical books.
| Maybe these three lectures about emergence could be interesting to get a first overview of the topic. Therein Prof. De Deo explains for example that emergence has a lot to to with what new phenomena can occurre when coarse graining (or renormalizing) microscopic degrees of freedom of a large system to obtain an effecti... | {
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Why is amplitude of a wavefunction to propagate from $q$ to $q'$ governed by $e^{-\frac{i}{\hbar}HT}$ unitary operator? In the textbook Quantum Field Theory by A. Zee, it says:
In quantum mechanics, the amplitude to propagate from a point $q_i$ to a point $q_f$ in time $T$ is governed by the unitary operator $e^{−\fra... | In Dirac notation, the propagation is given by $|q_i\rangle \to |q_f\rangle = e^{-iHT/\hbar}|q_i\rangle$. That this relation obeys the Schrodinger equation can be checked easily: Define $|q(t)\rangle = e^{-iHt/\hbar}|q_i\rangle$, where $0\le t\le T$. Then,
$$
\frac{\mathrm{d}}{\mathrm{d}t}|q(t)\rangle = -\frac{i}{\hbar... | {
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Physical meaning of some operators formed by $|Q\rangle \langle Q|$ In Dirac's formulation of quantum mechanics,
Suppose that $q$ represents position observable.
About $|q\rangle \langle q|$: what does this operator mean? I do get that it results in an operator, but unsure of what physical meaning it has. The same with... | $|q\rangle \langle q|$ is an operator that maps the state $\alpha$ to
$$|\alpha\rangle \mapsto |q\rangle \langle q|\alpha\rangle $$
You may easily calculate what the new state on the right hand side is. Because $\langle q|\alpha\rangle$ is a simple inner product – it is equal to $\alpha(q)$ if you express the state $\a... | {
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Why less temperature at high altitude Why there is always cold at high altitudes. e.g. at peak of mountains. Also as we go high from sea level, temperature starts decreasing. Why is it?
| Crazy Buddy is quite correct that it's because gas expands and cools as it rises, but there is more to it than that.
For something to be be heated it must either absorb EM radiation, or it must be heated by some hot object it's in contact with. Air doesn't absorb light so it can't be directly heated by sunlight. Instea... | {
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Distribution of charge on a hollow metal sphere
A hollow metal sphere is electrically neutral (no excess
charge). A small amount of negative charge is suddenly
placed at one point P on this metal sphere. If we check on
this excess negative charge a few seconds later we will find
one of the following possibilit... | Your homework question is from http://panda.unm.edu/Courses/Malloy/PHYS161//Physics_161_Home_files/Lecture22.pdf
Which one is correct
b)
and why?
*
*Metal conducts.
*Charges can travel freely in a conductor.
*Like charges repel
*The charge carriers move as far apart as they can be
*The furthest apart they c... | {
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Adiabatic expansion I'll start off by saying this is homework, but I ask because I don't understand how the math should work (I don't just want an answer, I'd like an explanation if possible). I understand if this is still against the rules, and I apologize if it is.
I have to calculate the work done by a sample of dry... | Have a look at the Wikipedia article on adiabatic processes. The key equation you need is:
$$ PV^\gamma = K $$
where $K$ is a constant and the value of $\gamma$ depends on what type of gas you have: for air $\gamma = 7/5$. As with any expansion the work done is the integral of PdV, so:
$$ W = \int_{V_1}^{V_2} PdV = K \... | {
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How do I integrate $\frac{1}{\Psi}\frac{\partial \Psi}{\partial x} = Cx$ How do I integrate the following?
$$\frac{1}{\Psi}\frac{\partial \Psi}{\partial x} = Cx$$
where $C$ is a constant.
I'm supposed to get a Gaussian function out of the above by integrating but don't know how to proceed.
| You can do the following. From
$$\frac{1}{\Psi}\frac{\partial \Psi}{\partial x} = Cx,$$
We can write the following interal equation
$$\int \frac{1}{\Psi} \mathrm{d}\Psi = C \int x \mathrm{d}x,$$
$$\ln \Psi + \kappa = \frac{1}{2} C x^{2}.$$
where $\kappa$ is our constant of integration. The above can then be simplifi... | {
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What is the physical meaning of the action in Lagrangian mechanics? The action is defined as $S = \int_{t_1}^{t_2}L \, dt$ where $L$ is Lagrangian.
I know that using Euler-Lagrange equation, all sorts of formula can be derived, but I remain unsure of the physical meaning of action.
| The action is a functional of not-yet-defined functions $q(t)$ and $\dot q(t)$ such that its minimum (or a stationary condition $\delta S =0$) determines a family of possible real motions of a physical system as differential equation general solutions. The final choice of one real motion out of this family is determine... | {
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Why has the trace of the energy-momentum tensor to vanish for conserved scaling currents to exist? In this paper, the authors say that the trace of the energy-momentum tensor has to vanish to allow for the existence of conserved dilatation or scaling currents, as defined on p 10, Eq(22)
$$ \Theta^{\mu} = x_{\nu} \Theta... | Without the internal part:
The divergence $$\nabla_\mu (x_\nu \Theta^{\mu\nu}) = x_\nu \nabla_\nu \Theta^{\mu\nu} + \frac12(\nabla_\mu x_\nu + \nabla_\nu x_\mu) \Theta^{\mu\nu} $$
where I used that $\Theta^{\mu\nu}$ is symmetric. Recalling that the energy-momentum tensor is divergence free, the first term drops out. As... | {
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Statistics of bound states of anyons with order pq Anyons with fractional statistics are possible in 2 spatial dimensions, as shown by Wilczek. Suppose we have two identical anyons of spin 1/pq, where p and q are integers more than 1. Then, interchanging both of them will pick up a phase factor of $e^{-2\pi i/pq}$, rig... | The OP is missing something very important. The case where p=q is the most interesting. Consider the specific example where p=q=2. We have two spin-1/4 anyons. Exchanging them counterclockwise (orientation matters!) picks up a phase factor of $i$ or $-i$ depending upon the specifics. If you're not careful, you'd say a ... | {
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Free falling objects My teacher and I are in the middle of an argument because she says that if you were to drop two objects at the same time and the same height, but with different initial velocities, both of them would hit the ground at the same time. She also said this was proven by Galileo's unregistered experimen... | The best way to prove something is wrong, is by performing a simple experiment, giving a counterexample. Take two identical objects (balls, pens, books). Throw one of the objects upwards and the other object downwards, so they have different initial velocities. The moment you let them go, they are in free fall. I am qu... | {
"language": "en",
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why sometimes touching old flickering tube lights starts them properly In my old house there are two old tube lights. Some times they don't start properly, (specially at evening time, may be it is because of low voltage), they starts flickering i.e. on and off continuously. And when my elder brother touches them, mostl... | I've found this to be the case, too. Generally, my shop lights will flicker when turning on, especially when it is colder outside .
There are two basic phases to this kind of light bulb: a start-up phase, and an operating phase. The start-up requires more voltage, because you are initiating the plasma stream between t... | {
"language": "en",
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Does the earth's magnetic field affect the sleeping position of a person? I remember reading somewhere:
when you sleep in a way subjecting your body to cut the geomagnetic
field at right angles, you become highly emotional whereas when it
is Parallel, it cools your mind.
Meaning, it's better to sleep with your bo... | I am S M Pandi from India.
I am doing research on this area from my childhood ( when i was 14 years ).The behavior of human brain is related to Earth magnetic field only. As per my research , The Human Brain is reacting over the influence of the Earth's magnetic poles. ( in practical life , it matters just directions... | {
"language": "en",
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Why do physicists believe that particles are pointlike? String theory gives physicists reason to believe that particles are 1-dimensional strings because the theory has a purpose - unifying gravity with the gauge theories.
So why is it that it's popular belief that particles are 0-dimensional points? Was there ever a ... | Elementary particles don't really have a shape or a size, these are emergent qualities that stem from interactions between particles. In quantum physics a particle is represented by its quantum state, and if you want to describe that in space you get a wave function which tells us how much of the particle is present at... | {
"language": "en",
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Theoretical treatment of Hydrogen bond? I would like to understand how the Hydrogen bond can be described through the Schroedinger equation. I don't need numerical methods that one uses them to simulate it, rather I need its treatment from theoretical point of view that can show also the probability of that electron wi... | The following references contain relatively complete treatments of hydrogen-bonding between two oxygens -O-H...O- using differential equations based on the quantum harmonic oscillator:
*
*Self-Consistent Einstein Model and Theory of Anharmonic Surface Vibration. I, Progress of Theoretical Physics, Vol. 58, No. 3, S... | {
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Parabolic motion and air drag Are this equations correct, in order to calculate the parabolic motion of an arrow with the computation of the drag with the air?
$$
\begin{cases}
x(t)=\left(v_0-\frac{1/2C_DA\rho v_0^2}{m}t\right)\cos(\theta)t\\
y(t)=\left(v_0-\frac{1/2C_DA\rho v_0^2}{m}t\right)\sin(\theta)t-\frac{1}{2}gt... | As ja72 points out, the formulas you have produced are, apart from a missing $\frac{1}{2}$ factor, what you would get if drag was proportional to the square of the initial velocity, not the instantaneous one.
For quadratic drag, you need to solve the following pair of equations:
$$m \dot{v_x} = -k\sqrt{v_x^2 + v_y^2} v... | {
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The notion called aether I am trying to learn relativity theory and going through an introductory text on special relativity. I stumbled on the Michelson-Morley experiment. The book claims (accounts) that the result of this experiments banished away the concept of Aether. In order to understand how exactly the results ... | Wikipedia is always a good place to start: Luminiferous aether.
Short answer: the aether was postulated as the medium through which light propagates. In the years prior to quantum mechanics and Relativity, Maxwell's equations very successfully characterized electromagnetic radiation as a wave, and solidified the wave n... | {
"language": "en",
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Dropping an anchor from a boat
A yacht on a lake drops its anchor overboard. What happens to the water level in the lake?
*
*It rises very slightly.
*It falls very slightly.
*It stays exactly the same.
*It's impossible to say.
My understanding is that due to Archimedes principle, when the anchor is in the boat,... | When Anchor is in boat,according to law of floatation:The liquid displaced will be equal to weight of Anchor.
But when Anchor is sinked,the liquid displaced will be equal to volume of Anchor.
So it depends on density maybe
| {
"language": "en",
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"source": "stackexchange",
"question_score": "7",
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Widom-Larsen Theory Does the Widom-Larsen theory pose a credible underpinning for Low Energy Nuclear Reactions, often incorrectly referred to as "Cold Fusion"?
http://arxiv.org/abs/cond-mat/0505026
| No, it doesn't.
"Heavy electrons", such as muons, can catalyze nuclear reactions by screening the charge. And electrons in solid-state crystals often have a high effective mass. So what can go wrong?
Nuclei have to get very close for fusion, far closer than the inter-atomic spacing. The electron needs to be become shar... | {
"language": "en",
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Chiral anomaly in odd spacetime dimensions In odd number of space-time dimensions, the Fermions are not reducible (i.e. do not have left-chiral and right-chiral counterparts).
Does this mean that there is no such thing as 'chiral' anomalies in odd number of space-time dimensions, when these fermions are coupled to gaug... | There is no chiral anomaly/gauge anomaly if the spacetime dimension $2\ell+1$ is odd, partly because $SO(2\ell+1)$ has real or pseudo-real representations, but no complex representations.
There may instead be parity anomalies in odd spacetime dimensions. In fact, there is a dimensional ladder of related anomalies
$$\t... | {
"language": "en",
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Why do diamonds shine? I have always wondered why diamonds shine. Can anyone tell me why?
| Diamond has a very high refractive index (about 2.42 compared to about 1.5 for glass). The amount of light reflected at an air/whatever interface is related to the refractive index change at the interface, and generally speaking the bigger the refractive index change the more light is reflected. So if you compare a dia... | {
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Why do non-stick frying pans work? Modern non-stick frying pans use a mixture of titanium and ceramic that is sandblasted onto the pan surface, and then fired to 2,000 °C (according to Wikipedia).
Can anyone explain (at the molecular level), Why cooking materials do not stick to these surfaces?, a hydrophobic effect wo... | I don't own any such pans, but I understand that they use a ceramic coating on top of a titanium base. The non-stick behaviour is down to the ceramic and not the titanium.
I'm not sure anyone knows exactly what causes food to stick to pans, and I suspect it's lots of different mechanisms. Anything that contains protein... | {
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Dirac equation as Hamiltonian system Let us consider Dirac equation
$$(i\gamma^\mu\partial_\mu -m)\psi ~=~0$$
as a classical field equation. Is it possible to introduce Poisson bracket on the space of spinors $\psi$ in such a way that Dirac equation becomes Hamiltonian equation
$$\dot{\psi}~=~\{ \psi,H\}_{PB}~?$$
Of c... | In my opinion, one cannot rigorously [*] define the bracket. Suppose that you use the Dirac field equation for arriving to the ordinary Lagrangian density
$$
\mathcal{L} = c \bar{\psi} \left( i\hbar \gamma^\mu \frac{\partial}{\partial x^\mu} \right) \psi
$$
This is a function of the spinor components $\psi_i$ and their... | {
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Origin of Higgs ghosts In M. Veltman's Diagrammatica, appendix E, one can find the full Standard Model lagrangian. Some sectors (e.g fermion-Higgs and weak sectors) contain so-called Higgs ghosts $\phi^+,\phi^-$ and $\phi^0$.
Are Higgs ghosts Faddeev-Popov ghosts?
If so,
why does the Higgs field, not being a gau... | The Higgs ghosts are not Faddeev-Popov ghosts. (For starters, the Faddeev-Popov ghosts in the standard model are Grassmann-odd, while the Higgs ghosts are Grassmann-even.)
The Higgs ghosts are Goldstone bosons for the spontaneously broken part of the electroweak symmetry $SU(2) \times U(1)$, which, popularly speaking,... | {
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More than one time dimension We know that space-time dimensions are 3+1 macroscopically, but what if 2+2?
Obviously it is tough to imagine two time dimensions, but mathematically we can always imagine as either having two parameters $t_1$ and $t_2$ or else in Lorentz matrix
$$\eta_{00} = \eta_{11} = -1$$ and, $$\eta_{... | As Cumrun Vafa explains in the video linked to below the picture of him in this article, F-theory works in a total of $10+2$ dimensions. The signature of the last two infinitesimal dimensions is ambiguous, so that they can indeed both be timelike. Since these are only infinitesimal dimensions, any causality issues etc ... | {
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Optics: Derivation of $\vec\nabla{n} = \frac{d(n\hat{u})}{ds}$ I have been given this formula from optics here, with no background:
$$\vec\nabla{n} = \frac{d(n\hat{u})}{ds}$$
Where $n$ is the refractive index and $\hat{u}$ is a unit vector tangent to the path $s$ that light takes inside a medium.
Does anyone know if t... | This equation is called the ray equation and it can indeed be derived from Fermat's principle. I guess you can find more about its derivation in, e.g., Born and Wolf's Principles of optics or in Fundamentals of Photonics by Saleh and Teich.
| {
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If wave packets spread, why don't objects disappear? If you have an electron moving in empty space, it will be represented by a wave packet. But packets can spread over time, that is, their width increases, with it's uncertainty in position increasing. Now, if I throw a basketball, why doesn't the basketball's packet s... | Short answer is it won't disappear because the integral of the probability density is still 1 even for a highly spread wavepacket, i.e. the object will still be found somewhere.
Slightly longer answer is that, if I start with a Gaussian wavepacket with width $a$, then after time $t$, the width will have spread to $$\sq... | {
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What determines which observables are QM? Spin, position, and velocity are observables which are QM for quantum particles. My question is, what determines whether an observable is QM or not?
For example, why is electric charge not QM? That is, why don't (or can't) particles exist in a superposition of being positive an... | What I think you're really asking is: why can an elementary particle (say an electron) be in a superposition of different momenta, or different spins, but not in a superposition of different charges? The reason is that all electrons have −1 charge. If an electron could have either a +1 or a −1 charge, then quantum mech... | {
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What does the velocity of a wave mean? I know that the velocity of a wave is given by $v=\lambda f$ but what does this velocity represent in the physical sense. For instance, if I am told a car moves at a velocity of 5 $m/s$ I know that the car itself will cover 5 meters in displacement every second. What part of the w... | The velocity of a wave can be though of as the rate of change of displacement of any single peak. In more generic terms, It's the speed of a surfer who is riding the wave with no relative displacement.
| {
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Is physics rigorous in the mathematical sense? I am a student studying Mathematics with no prior knowledge of Physics whatsoever except for very simple equations. I would like to ask, due to my experience with Mathematics:
Is there a set of axioms to which it adheres? In Mathematics, we have given sets of axioms, and ... | Physics is usually not rigorous. But there is a branch of physics, called mathematical physics, in which physics is treated with full mathematical rigor.
There everything begins with formally stated assumptions (axioms) from which everything else is rigorously deduced.
In particular, there are fully rigorous treatments... | {
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How to calculate gravity inside the star? Gravity must decrease due to less effective mass when going inside the object but also must increase with depth inside the star due to its higher density. Is there a model or formula approximating gravity calculations along the radius (from center to surface) of the stars?
| Here is an example for the Sun.
The figure below plots a (reliable) estimate for the interior density profile of the Sun, $\rho(r)$.
So for a given radius $a$, the mass interior to that radius is given by
$$ M(a) = \int^{a}_{0} 4\pi r^2 \rho(r)\ dr $$
And of course the gravitational field strength assuming spherical sy... | {
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Can you put a magnetic ball into a hollow magnetic sphere? if all magnets have to have two poles(one north one south), is it possible to construct a hollow sphere where the inside face of the sphere was one pole, and the outside face another pole?
is it also possible to make a magnetic sphere (not hollow) where the out... | Possibly by using a nonmagnetic sphere as your center and pressing a neodynium cobalt alloy around it sealing the outside sphere shut. I have thought about it for a bit but have no opportunity to attempt such thing.
| {
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Interacting representation of the Poincaré group In his QFT book, Weinberg claims what follows (Vol I, pag. 144-145): given a (free) representation of the Poincaré group with generators $\bf P$ (spatial translations), $H_0$ (time translations), $\bf J$ (rotations), and ${\bf K}_0$ (boosts), one obtains another (interac... | There is no rigorous proof for this, as there is no known way to make sense of the interaction part of a local Hamiltonian at fixed time in such a way that $H$ becomes self-adjoint. The reason is that
quantum fields are distributions only, and the product of distributions is ill-defined in general. There are nonrigorou... | {
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Does the exact string theory $S$-matrix describe all physics there is? Suppose someone manages to evaluate the string theory $S$-matrix to all orders for any and all vertex operator insertions including non-perturbative contributions from world-sheet instantons and re-sum the whole series to obtain the exact non-pertur... | No, first because string theory is based in a number of approximations/assumptions and second because not every physical question can be answered assuming that processes take an infinite time and involve objects separated infinitely as is assumed in the S-matrix approach.
The S-matrix approach is excellent for particle... | {
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Can small clouds reflect enough light to hurt your eyes/blind you? I looked out my window a minute ago and immediately noticed a very bright spot where a cloud and a jet/plane trail met. The spot was so bright that I thought the sun was behind it because it left that typical "burn-in shape" in my vision even when I clo... | Cloud albedo, the ability to reflect solar radiation, can reach as high as 90% due to reflection from water droplets according to Wikipedia. Additionally, jet trails (contrails) are made up of water or ice droplets and could also exhibit significant albedo.
It seems very possible that for optimum Sun-cloud-viewer geome... | {
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"answer_id": 0
} |
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