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I already understand that light cannot escape a black hole after passing the event horizon, so please do not explain that to me. What I would like to know is this:
a well known fact about light (a photon specifically) is that it travels at the speed of light, and at no other speed, which means that it has no rest mass,... |
I have read that usually if the speed of a fluid is much lower than the speed of sound (in that medium) then it can be treated as an incompressible fluid.
Where does this condition come from?
Is it possible to show it from the Navier-Stokes equation?
|
According to Bohr, electron revolves around the nucleus because of force of attraction between electron and proton. This force of attraction gives energy to the electron. So my question is this that- In which form does this electron get the energy?
|
Is the following differentiation correct:
$$ \frac{\delta}{\delta\eta\left(z\right)}\int d^{4}yS_{F}\left(z-y\right)\eta\left(y\right) = S_F\left(z-z\right)$$
where $\eta$ is a Grassmann-valued field and $S_F$ is the Fermion propagator, or is the result actually with a minus sign?
|
I couldn't understand something about the situation of a pearl that moves in a smooth vertical hoop in circular motion.
When the normal force equals 0 , the pearl didn't disconnect from the smooth vertical hoop, even though the pearl had velocity at that point.
Why the pearl didn't disconnect?
|
Einstein originally thought that special relativity was about light and how it always travelled at the same speed. Nowadays, we think that special relativity is about the idea that there is some universal speed limit on the transfer of information (and experiments tell us that photons, the quanta of light, move with th... |
Simple Model w/o Doppler
I have a speaker driven by an electrical signal. The pressure at the sampling point is some linear operator acting on the input signal: $L[ s(t)]$. Where $L$ combines the linear model representing the electrical components (LRC circuit) the mechanical components (mass-spring-dashpot) and the ... |
Which elementary particle has the greatest rest mass? (For the sake of this question I'll call a photon's rest mass 0, whether it is or isn't [actually, tell me if this is the right thing to do]).
|
Could anyone explain or refer to references on why the CDMT f(R) gravity model suffers from Instabilities any why the sign of ${\mu}^{4}$ matters.
|
OK so I am having a conceptual crisis about Hydrodynamics.
1) Since mass should be conserved, is $\frac{dm}{dt}=0$ ?
2) But I know that the formula $\rho_1u_1A_1 = \rho_2u_2A_2$ exists... and doesn't that mean the mass flux is conserved? Where does this formula come from?
3) How can we derive an expression for $\frac{d... |
This is the common problem of a charged particle moving in a static electric and magnetic field.
Say $\textbf{E}=(E_x,0,0)$ and $\textbf{B}=(0,0,B_z)$.
In the inertial frame of reference, the equation of motion is (1): \begin{equation} \frac{d \textbf{v} }{dt} = -\frac{q \textbf{B} }{m}\times \textbf{v} + \frac{q}{m}\... |
My lab studies the physiology of impact injury on biological tissues. I use a pneumatic cylinder to impart injury into a biological sample and then assess the molecular and physiological changes in that tissue. It is the first step in trying to understand the pathophysiology of traumatic brain injury. So, I have the ma... |
I don't know the math to do this, so I am asking here if someone can work this out with all of the details I'm providing.
Total mass EST.: 2,400 lbs.
Length from front to back: 14 feet 6 inches.
Ground clearance (space between floor and bottom of car base): 4.7 inches.
Height (from ground to top of roof): 4 feet and 5... |
Automated Visual Field test measures the patient light sensitivity in decibels.
Questions:
If one point has sensitivity of 30 decibels and another point has sensitivity of 27 decibels does it mean that point 1 is 2 times more sensitive than point 2?
If point 3 has sensitivity of 31dB and point 4 has 21dB does it mean ... |
I am referring to this,
http://home.web.cern.ch/about/updates/2014/04/lhcb-confirms-existence-exotic-hadron
So how does this work if we stick to keeping quarks in the 3 dimensional fundamental representation of $SU(3)$?
This bound-state seems to have 2 anti-quarks and 2 quarks. So with just 3 colours how do we make t... |
The Verdet constant of a magneto-optical material shows up in the calculation of the rotation of polarized light in a medium submerged in a magnetic field. The amount of rotation is given by
$$
\theta=VBd,
$$
where $\theta$ is the angle of rotation of linear polarized light, $V$ is the Verdet constant, $B$ is the magn... |
I have been following MH370 on the news just as everyone and latest reports seem to indicate that the black-box could be found. A recent info-graphic http://t.co/lyBBE9C2hF shows the insurmountable depth of the oceans and how the black-box could have sunk 15,000 ft! I wonder how long it would have taken for it to sunk ... |
I'm am sure that I must be missing something very simple, so apologies in advance.
Considering the Lorentz transformation $\Lambda$ of a spinor fields, for the plane-wave solution $u(p)$,
I cannot for the life of me agree why
(1)
$$ u^s(\Lambda^{-1} {p'}) = \Lambda_{\frac{1}{2}} u^s(p') $$
where
$$ p' = \Lambda p $$
Th... |
Why are the position and potential energy of a particle able to be measured precisely in Quantum Mechanics? I mean why do they commute with each other?
|
Referencing Stephen Hawking's recent paper Information Preservation and Weather Forecasting for Black Holes and this question. I understand concept of holding the information on the apparent horizon of a black hole for later release in the form of garbled radiation, but how is it that this differs ( if at all ) from th... |
We know that in the quantum harmonic oscillator $H=a^\dagger a$, $a^\dagger$, $a$, $1$ will span a Lie algebra, where $a, a^\dagger$ are the annihilation and creation operators, and $H$ is the Hamiltonian operator.
$$[H,a^\dagger\ ]= a^\dagger$$
$$[H,a]=-a$$
$$[a,a^\dagger]=1$$
So these four operators, $H=a^\dagger a$... |
When we deal with Special Relativity and we start considering spacetime instead of space and time each at once, we usually see books saying that we consider a space with four coordinate $x^\alpha$ with $x^0 = ct$. We also consider this manifold to be $\mathbb{R}^4$ and give to it the metric tensor $g = \operatorname{di... |
If Mr. E is aboard a spaceship traveling near the speed of light the usual reason for the spaceship not going faster than $c$ is the (relativistic) mass of the ship increases without bound, I think. Yet Mr. E says out loud what about the mass of the fuel? When the fuel's (relativistic) mass increases would its potentia... |
If a photon hits a 'perfect' mirror (with no environment interference) would the mirror move a bit?
|
I'm wondering why in this problem I can't apply newton second law? The mass $m$ of the moving part will be the mass solved in the problem.
|
I copy and paste all the proof here, but I'm confused about the last step, which is that the summation of the internal force and be written as two other summations.
|
For example, let's consider the electromagnetic interaction between a massless fermion and a electromagnetic externel sourse $A^\mu$, then the lagrangian is
$$\mathcal{L}=\bar{\psi}\gamma^\mu\partial_\mu\psi+ieA_\mu\bar{\psi}\gamma^\mu\psi$$
and how can we calculate the Feynman diagram and $\mathcal{M}$ of it?
But acco... |
I often hear about planes stalling when they lose lift due to low airspeed/too high angle of attack. Why don't birds stall? Does it have to do with the structure of their wings and their flexibility, or their higher power/weight ratios relative to aircraft?
|
A particle is projected vertically upwards from point $A$ on the ground. It takes $T_1$ time to reach point $B$ but it still continues to move up. If it takes further $T_2$ time to reach ground from point $B$ then height of point $B$ would be?
|
Please try to answer in layman terms, i am only starting to study thermodynamics (And physics)
In my book one of the curiosity parts gives that fans don't actually cool the room but by hitting the air particles they increase their kinetic energy, these high speed particles hit us and hence evaporate our sweat, making u... |
Is there a difference in the electronic configuration for singlet and triplet states?
For example, He atom has 1s2 configuration in its ground state (singlet state)
But what about when the He atom is excited. It can come in both states (Signlet and Triplet)
Can I tell from the excited electronic configuration whether t... |
How is the Plane of the Solar System oriented to the Sun's motion through space: parallel, perpendicular, or some other angle?
|
Problem
Current is the amount of charge that is flowing through a component per unit of time.
For a given voltage, Ohm's law tells us that if we increase the resistance, then the current must decrease.
But what's actually happening to decrease the current?
My reasoning so far - is it correct?
More resistance (if we'r... |
How to prove that
$$[\hat{L}^2,\hat{\textbf{p}}] = i\hbar(\hat{\textbf{p}}\times\hat{\textbf{L}} - \hat{\textbf{L}} \times \hat{\textbf{p}})$$
I tried to expand $\hat{L}^2$:
$$[\hat{L}^2,\hat{\textbf{p}}] = [\hat{L}^2_x+\hat{L}^2_y+\hat{L}^2_z,\hat{\textbf{p}}]$$
And
\begin{align*}
[\hat{L}^2_x,\hat{\textbf{p}}] ... |
I wanted to ask about the situation of a pearl that moves in a smooth vertical hoop in circular motion as described in the following sketch.
According to a simulation found in the internet , a moment after this situation , when the pearl reached the point C , the pearl keeps moving in circular motion.
What causes the ... |
Ok, this is definitely a silly question and is partly inspired by the last 20 minutes or so of the film The Avengers, so look to that if you can't picture the situation.
In the film a portal is opened up above new york, to somewhere in deep space. I.e. from an area where the gravitational field is effectively uniform a... |
$V=IR$
Right?
$100 (\rm{V}) = 0 (\rm{A}) \times 100 (\rm{\Omega})$
Lets say something has $100 \rm V$ potential But since this object is surrounded by air and current is not flowing therefore there has to be $100 \rm{\Omega}$. Right? But then the equation does not work as 100 does not equal 0?
You get infinite resista... |
In quantum mechanics can the mass and the linear momentum of a particle be measured precisely or do they commute ?
|
I recently started grade 11, and this concept confuses me, since if we place a charge $q$ on a potential $V$, I do not completely comprehend what values would need to be substituted which would give me the formula.
The closest I have gotten is $F = kq_1/r^2$ thus
$PE = kq_1/r$, $k = 9 \times 10^9N$
Now i do not underst... |
Does the gravitation of Earth have a limit? when a body projected vertically with $v=11km/s$ (escape velocity) from Earth's surface does this means that it does not return back to Earth?
|
Heisenberg's uncertainty principle is one of the most fundamental principles on which quantum mechanics is based on. But it is also one of the most confusing laws we encounter. My doubt is whether the uncertainty is due to observation error or due to dual nature of matter ?
Dual nature of matter states that a particle ... |
What are the experimental (indirect) evidence for the cosmic neutrino background? Where can I read more about this?
The discussion on the wikipedia page about the C$\nu$B seems to me to be more about the evidence of the number of generation of neutrinos, than about the cosmic neutrino background...
|
I've been watching Susskind's lectures on Quantum Entanglement, and something he said regarding (non-)commuting projection operators confused me.
Consider two subspaces {$|a\rangle$} and {$|b\rangle$} of Hilbert space, with operators $K$ and $L$ for which:
$K |a\rangle = \lambda |a\rangle (1)$
$L |b\rangle = \mu |b\ra... |
A ball is thrown upward in a train moving with a constant velocity. Where will it land?
My intuition tells me that the ball will fall at my back. But my book says that it will return back to the thrower.
|
I am interested in computing the integral of this function:
\begin{align}
\int_0^\infty\frac{2du(u^2+1)}{(1-e^{2\pi u})},
\end{align}
which of course at first sight, does not converge. But in QFT it's usually possible to regulate such a function. Thus, the question is, does anyone know how to regulate this function?
|
Let's consider a 0-dimensional $N \times N$ Hermitean one matrix model.
It is defined by a potential V(M). Its partition function
is
$$Z = \int_{H_{N}} dM e^{-\frac{1}{g}V(M)}$$
where $H_{N}$ is the space of $N \times N$ Hermitean matrices
and g is the coupling constant. I usually think at such a matrix model as
a 0... |
Hamiltonian is defined by $H_I = \hbar \omega (\hat{a}^+ \hat{a} + 1/2)$
What is the expectation value of the energy on the number state
$$\vert \psi \rangle = \frac{1}{\sqrt{2}} ( \vert 1 \rangle + \vert 2 \rangle )$$
So I think that its
$$\langle E \rangle = \langle \psi \vert H_I \vert \psi \rangle$$
$$ = \hbar \om... |
From basic principals, how does one prove that energy is conserved? Or a little more specifically - Why does this hold:
$$\Delta \mbox{ PotentialEnergy} + \Delta \mbox{ KineticEnergy} = 0 $$
Or, for extra credit, why does this hold:
$$\Delta \mbox{ PotentialEnergy } + \Delta \mbox{ KineticEnergy} + \Delta \mbox{ Therma... |
I know that superfluidity is caused by the fluid having zero viscosity. This only happens at very low temperature, so the fluid (e.g. Helium-4) is a Bose-Einstein condensate.
I also know that in a Bose-Einstein condensate all the particles are in the ground state.
Now, that said:
How can this explain superfluidity? Ma... |
Meaning by "atmospheric geostationary satellite" a vehicle capable of hovering 30 km above Earth surface, hence insde atmosphere, for unlimited time, making use of air propellers, solar panels and batteries.
How much energy is needed to keep an object steady in air at 30 km above surface?
There are two possibilities: a... |
I'm looking at the radiosity equations for heat transfer
http://en.wikipedia.org/wiki/Radiosity_(heat_transfer)#Radiosity_method
Specifically, I'm hesitant to accept the equation:
$$ \dot Q_i = \frac{ A_i \epsilon_i }{ 1 - \epsilon_i } ( \sigma T_i^4 - J_i )$$
My analysis is as follows: power goes out via Stefan-Boltzm... |
As an electric motor spins, the energy from the electricity is 'conducted' to the rotor by the magnetic fields. However, when the motor is stopped, the energy becomes heat and burns up to motor. What causes this heat to be formed? Is it purely generated by the current flowing through the wire or is the magnetic fiel... |
Momentum is defined as
$$p = \gamma m_0 v$$
And here is another law
$$E^2=(m_0c^2)^2+(pc)^2$$
And this website says the energy of a red photon is $1.9074 eV$. Also, light has a rest mass of $0$. The problem is that by the first equation implies momentum is $0$, and then the second equation would imply energy is $0$, an... |
To my knowledge there are three types of acceleration when a body (e.g. a rod) is moving in a circle about an axis. These are:
Angular acceleration : this is the rate of change of angular velocity.
Tangential acceleration : this is the linear acceleration of the system in a tangential direction to the circle and equal... |
My question is why the electroweak vacuum of the Standard Model have to electroweak charge and QCD color neutral? What goes wrong if electroweak vacuum has either non-zero charge or color quantum number?
|
The molecular weight of water is 18.015 gram. The number of moles of water in one liter (1000 gram) will be:
$3.34\times 10^{25}$ molecules (in 1kg).
We know that latent heat of vaporization of water is $L_v= 2.26\times 10^6$
then the amount of heat required to rise one molecule of water will be
$1.47\times 10^{-19}$ j... |
In quantum field theory, scalar can take non-zero vacuum expectation value (vev). And this way they break symmetry of the Lagrangian. Now my question is what will happen if the fermions in the theory take non-zero vacuum expectation value? What forbids fermions to take vevs?
|
We've all heard of the diffraction of radio waves over a mountain and the diffraction of water waves through a gap, but why does this effect depend on wavelength?
I'm looking for as simple answer as possible - if it's a bit hand-wavey that might be OK.
Another thing that troubles me is when I read the effect of diffra... |
Is it true that the following identity holds for the Feynman prescription Dirac propagator:
$$ S_F(x) \stackrel{?}{=} \gamma^0[S_F(-x)]^\dagger\gamma^0 $$
where $S_F$ is defined as the Green's function:
$$ (i\gamma^\mu\partial_\mu-m)S_F(x-y)=i\delta(x-y) $$
This is somewhat related to a previous question of mine: Gree... |
A few days ago I started to use the Mathematica package FeynCalc and one thing confuses me: Assume we have a four-vector $p_\mu$ and we contract it with the epsilon tensor. FeynCalc produces $\varepsilon^{\mu\nu\rho\sigma} p_\sigma = \varepsilon^{\mu\nu\rho p}$...what does the momentum as an index mean?
Furthermore, th... |
What is the difference between angular frequency and angular velocity? I think one is used for SHM and the other for circular motion? Also can both be used for centreptal accelartion? I think angular freq$=2\pi f$ and angular velocity$=d\theta /dt$? Please confirm or expalin. Are they the same thing for circular motion... |
In his book "QFT" (vol. 1) Weinberg writes the expression for an arbitrary spin massive field:
$$
\hat {\Psi}_{a}(x) = \sum_{\sigma = -s}^{s} \int \frac{d^{3}\mathbf p}{\sqrt{(2 \pi)^{3}2 \epsilon_{\mathbf p}}}\left( k_{1}F_{a}(\mathbf p) \hat {a}^{\sigma}(\mathbf p )e^{-ipx} + k_{2}G_{a}(\mathbf p) {\hat {b}^{\sigma}... |
I keep reading the same phrase about the very short life time of the top quark:
Because the t-quark decays on a shorter than the characteristic QCD interaction-time it cannot hadronize. Therefore it give to possibility to be seen as a bare quark.
I cannot find any more information beyond this simple phrase. There a... |
So, objects are certain colors because they are absorbing every color except for that one. So why is it that if I take a projector and project a blue image on a red wall, the red wall still reflects the blue image rather than absorbing the blue light? I don't know if this is considered a dumb question, but I was thinki... |
If I have these theoretical predictions:
\begin{align}
\omega_{p_1} = 4.5132 \pm 0.0003~\text{rad/s} && \omega_{p_2} = 4.5145 \pm 0.0002~\text{rad/s}\\
\omega_{b_1} = 0.0707 \pm 0.0003~\text{rad/s} && \omega_{b_2} = 0.0700 \pm 0.0002~\text{rad/s}
\end{align}
And I got these experimental results:
\begin{align}
\omega_{p... |
I got some naive questions on the ground states of honeycomb Kitaev model (with open boundary conditions):
(1) Consider a simple case that $J_x=J_y=0$, then the model reduces to $$H=J_z\sum_{z\text{ }\text{links}}S_i^zS_j^z.$$ It's obvious that $H$ has highly degenerate GSs (degeneracy$=2^N$, where $N$ is the number o... |
What is meant by normalized projection operator? What is its physical meaning in quantum mechanics? I am pretty confused regarding the physical interpretation of both projection operator and normalized projection operator.
|
Is the atmospheric pressure in a closed container the same as that of the surroundings (1 bar at sea level)?
Consider a tube with both ends open with one end dipped into water (like a pipette in chem lab). Now if we close the other end with a thumb and draw it out of the water, the water level in the tube will be hig... |
"The diagram below represents a simple circuit composed of 5 identical light bulbs and 2 flashlight batteries. Which bulb (or bulbs) would you expect to be the brightest?
a) V only
b) V and W only
c) V and Z only
d) V, W, and Z only
e) all five bulbs are the same brightness"
The solutions say the answer is d, but ... |
I am having some trouble understanding three-phase alternating current. I realize that most houses are not three-phase but single phase. Would that not mean that at some point when the flow of electricity switches direction it will stop and the electrical motor would stop under single phase?
Also, I also realize that ... |
In Minkowski spacetime, two observers, $A$ and $B$, are moving at uniform speeds $u$ and $v$, respectively, along different trajectories, each parallel to the y-axis of some inertial frame $S$. Observer $A$ emits a photon with frequency $\nu_{A}$ that travels in the x-direction in $S$ and is received by observer $B$ wi... |
Typically, one way of understanding the physics of an interacting quantum system is by diagonalizing the Hamiltonian. In principle, can we always diagonalize a Hamiltonian, such that it is expressed in terms of non-interacting particle states? If so, is the diagonalization unique?
|
I'd like to ask some questions about flipping two coins related to statistical mechanics, e.g. microcanonical distribution, phase space distribution function etc... after I rephrase the coin flipping problem into the language of statistical mechanics.
In probability theory, given the following problem
Random experimen... |
I have a working knowledge of wave-particle duality, I think. I know the de Broglie wavelength is a sort of probability of finding a particle in a specific position, and is calculated by $\lambda=\frac{h}{\vec{p}}$. I have a couple questions I'm hoping to have cleared up, though.
First, since $\vec{p}$ is momentum, a v... |
The background: I'm doing some simulation work involving the diffusion equation in 1D. Specifically I have some temperature profile, constant thermal conductivity and fixed temperature at each end of the system.
I know that we can write:
$$
\tau = \frac{L^2}{\kappa}
$$
where $\tau$ is the characteristic time scale, $L... |
Since a polarization of the wave is described by complex numbers, we can try to give that mathematical formalism geometrical meaning. With having two different axes, one imaginary and other real, it is possible to represent the motion of the wave in three dimensions as the motion of 2 waves in two planes. These two pla... |
The three Mandelstam-variables are defined as:
$$s=(p_A+p_B)^2=(p_C+p_D)^2,$$$$t=(p_A-p_C)^2=(p_B-p_D)^2$$$$u=(p_A-p_D)^2=(p_B-p_C)^2.$$ Where A and B are the incoming particles and C and D are the outgoing particles, and the second equation follows from the conservation of 4-momentum.
The Mandelstam-variable $s$ gives... |
In the following question, what is meant by linear probability density function? Is it a uniformly distributed variable or triangularly distributed? Thanks in advance.
The kinetic energy of any object in motion is given by the $E(v)=\frac{1}{2}mv^2$, where $v$ is the velocity in m/s. Someone measures the speed of stud... |
In a system where multiple liquids and solids are mixed together with different specific heats at different initial temperatures, reaching an equilibrium temperature, how do all of these things relate to the masses? How could I use all the information given of the other objects to find the mass of one object in the sys... |
Consider two entangled photons with two mutally conjugate circular polarization. What happens when one photon which is, say, left hand polarized gets destroyed. Will the other photon retains its right hand polarization or will it assume some random state? There is another possibility that it looses its circular polariz... |
A $\pi^0$ consists of an up and anti-up quark. However, I also learned that when a particle and its anti-particle meet, energy is produced.
So, my question is that how can $\pi^0$ exist? Won't it turn to energy instantly if it is formed?
|
In a helicopter if you want to give it a forward pitch, you change the angle of the blades when it is in this position ----
So the two blades experience unequal lift and because o gyroscopic precession the helicopter pitches forward (instead of pitching sideways, which is intuitively expected)
Up till this it's clear ... |
I recently read in a book that combination of two simple harmonic motions of equal amplitude in perpendicular directions differing in phase by pi/2 is circular motion.
I don't seem to understand this because I am not able to figure which two forces in circular motion are acting to cause two different simple harmonic mo... |
I'm looking at sample calculations of moment of inertia of a sphere here.
In the first example (disc method), it has the integral as $dI = \frac{1}{2}r^2 \,dm$, while in the second example (shell method), $dI = r^2 \,dm$. Why is this so? Where does the 1/2 come from?
|
Imagine I put a floating probe inside the subglacial ocean of Encelado or Europa: how much power should my radio have to be able to communicate from external surface with the probe?
Or, in different words, how much attenuation do 100 km of solid ice cause to a radio signal at, say, UHF frequency?
|
I've been searching for this for a while. There is a principle of equivalence in general relativity: http://en.wikipedia.org/wiki/Equivalence_principle
But I need the principle of equivalence in thermodynamics. Is it the same as the second law of thermodynamics? http://en.wikipedia.org/wiki/Second_law_of_thermodynamics... |
I want to determine how many minutes a satellite is in a circular orbit around the Earth at about $1000 km$ altitude. I assumed that the Sun-Earth vector lies exactly in the orbital plane of the satellite. Also, in this case, the Sun can be seen as a point light source and the distance to Earth is infinite. Is it possi... |
I had an interesting dream, where advanced civilization compress their body with technology, that turn off space betweens atoms/particles. They travel in small spaceship with billions citizens very effectively.
Crazy idea, but my question is how much smaller will the human body be, when we hypothetically get of every s... |
If we consider the Frank elastic free energy in the equal constants limit (for more details, see here Chapter 4.1.) with an external magnetic field, we have
$$
F = \frac{1}{2}\int \text{d}^3 r\left ( K|\nabla \cdot n|^2 + K|\nabla\times n|^2 -\Delta\chi |n\cdot H|^2 \right),
$$
where $K$ is the elastic constant, $n$ i... |
I found this expression in my SR notes:
$$ (\Lambda^{-1})^{\lambda}_{\ \ \ \sigma} = g^{\lambda\mu}~\Lambda^{\rho}_{\ \ \ \mu} ~g_{\rho\sigma} = \Lambda_\sigma^{\ \ \ \lambda}$$
I know where it comes from, so I don't need a proof, but:
First off, I thought that when doing matrix multiplication the dummy indices had to... |
Recall that $\mathrm{d}LIPS_2$ (one particle decaying into two particles of the same mass) is given by
$$\mathrm{d}LIPS_2 = \frac{\vert{\bf k_1'}\vert}{16\pi^2\sqrt{s}}\mathrm{d}\Omega_{cm}.$$
In a given decay, is all the angle dependence included in dLIPS? If I recall correctly, this does not need be the case, or els... |
I'm learning Maxwell's electromagnetic equations and i can't wrap my head around this problem:
Given the volume $x\in [0,1], y\in [0,1], z\in [0,1]$, electric field $\vec E(x,y,z,t)$ and material constants $\epsilon, \sigma, \mu$ how can i find the magnetic field $\vec B(x,y,z,t)$ knowing that $\vec B(x,y,x,0)= \vec 0... |
In a confocal cavity, a beam traverses the length of the resonator 4 times between two transmissions along the same ray.
.
For example, in the above figure, path difference between two beams that get transmitted along beam 1 is an integral multiple of 4 times the cavity length. The same holds for transmission along r... |
Why do lighter objects float and denser sink? I understand this from the perspective that if the object can displace the equal mass of water it will float, but I wonder from the perspective of gravity! How does gravity cause Archimedes' principle? It must be gravity, right, because in space Archimedes' principle doesn'... |
I'm a beginner of QFT. Ref. 1 states that
[...] The Lorentz group $SO(1,3)$ is then essentially $SU(2)\times SU(2)$.
But how is it possible, because $SU(2)\times SU(2)$ is a compact Lie group while $SO(1,3)$ is non-compact?
And after some operation, he says that the Lorentz transformation on spinor is complex $2\t... |
I understand what three-phase power is. But when I look at some pictures of a double-circuit-three-phase-power-line I see two or three lines close together? What is the purpose of these lines close together?
(the wires are attached by smaller wires or connectors)
Is there a separate alternator for the second group o... |
As a mathematics graduate student whose research area lies in low-dimensional topology (more precisely, invariants of 3-dimensional topological manifolds), I heard that there exist multiple applications of this theory to theoretical physics, and moreover, that many mathematical problems in the field actually arise from... |
I woke up this morning thinking about spinning discs. Could someone verify whether my reasoning below is correct?
Problem 1
Suppose have two identical uniform discs constrained to move in a plane. Set disc $A$ spinning about its centre of mass, clockwise viewed from above. Now collide it with disc $B$.
Assume that fric... |
When an index of the Kronecker-delta tensor $\delta_a^b$ is lowered or raised with the metric tensor $g_{ab}$, i.e. $g_{ab}\delta^b_c$ or $g^{ab}\delta_b^c$, is the result another Kronecker-delta tensor?
|
Is it possible, and has it been attempted, to use quantum mechanics to deduce Newtonian, macroscopic level mechanics laws as was the case of statistical mechanics deriving thermodynamic relations?
|
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