Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Why do lasers cut? Is this a case of light acting as matter? All I found in Google was very broad. From a physics models perspective, why can photons emitted from a laser cut? Does this cut mean that the photons are acting like matter?
| Lasers "cut" as an interaction between matter and radiation (themselves different forms of natural substance)
A LASER (Light Amplification by Stimulated Emission of (Coherent) Radiation ) beam being coherent and high-energy (quantum-mechanically a-la Einstein-Planck relation, energy is directly analogous to laser frequ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/113431",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "48",
"answer_count": 6,
"answer_id": 5
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Galaxy rotation curve and dark matter I am reading "The Essential Cosmic Perspective" by Jeffrey O. Bennett, Megan O. Donahue, Nicholas Schneider, Mark Voit.
In Chapter 14, it is stated that an evidence of the presence of dark matter in our galaxy is that the rotational curve does not match that obtained from calculati... | There are two points here. First, the mass is more spherically distributed than one would expect from images. There is something like 5 times as much dark matter as baryonic matter, so even if all the baryonic matter is in a disk, the dark matter halo will be spherical and this will dominate the potential.
Second, in p... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/113497",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Why change in internal energy is zero in isothermal process In isothermal process $\Delta U =0$. But I am having trouble understanding it.
Say we have an ideal gas, and say my temperature is constant but I move the pressure, volume from $(P, V) \to (P-dP, V+dV) $. So the volume has expanded and system has done some wor... | See consider a cylinder with piston fixed, (i.e. it doesn't move) and the system is provided with a source with temperature $T$. Now as the piston does not move the volume is constant, so no work is done and internal energy is also constant and no heat is added since system and source are at the same temperature.
Now l... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/113586",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "15",
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Why does Minkowski space provide an accurate description of flat spacetime? What is the chain of reasoning (beginning, of course, from observations about the universe) that leads one to predict that Minkowski space provides an accurate description of space-time in the framework of special relativity?
That is, why shoul... | Minkowski space provides an accurate description of flat space-time simply because it was derived from the equation for light traveling in Euclidean space. There is nothing unusual about the metric - Minkowski metric is just a way of presenting the good old Euclidean space. And as in Special Relativity there is no grav... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/113656",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
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Apparent dimensional mismatch after taking derivative Suppose I have a variable $x$ and a constant $a$, each having the dimension of length. That is $[x]=[a]=[L]$ where square brackets denote the dimension of the physical quantity contained within them.
Now, we wish to take the derivative of $u = log (\frac{x^2}{a^2})... |
Where am I going wrong?
Recall
$$\frac{d}{dx}f(g(x))=f'(g(x))g'(x)$$
with
$$f(\cdot) = \ln(\cdot) \rightarrow f'(\cdot) = \frac{1}{\cdot}$$
and
$$g(x) = \frac{a^2}{x^2} \rightarrow g'(x) = \frac{-2a^2}{x^3}$$
Thus
$$\frac{d}{dx}\ln\frac{a^2}{x^2} = \frac{1}{\frac{a^2}{x^2}}\frac{-2a^2}{x^3} = -\frac{2}{x}$$
An alter... | {
"language": "en",
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In the case of riding a bicycle, why can the system of the bicycle and rider be accelerated if no external net force? According to Newton, if no external net force acting on a system then the system will keep its initial condition whether at rest or moving uniformly in a straight line.
Let's consider a boy riding a bic... | There are forces and torques in this system. Boy pushes on pedal and pedal pushes on boy. But for pedal to push on boy, bike frame pushes on pedal (at the axle of the pedals) and vice versa. Now there is a torque on the pedal which is transferred (through the chain) to the rear wheel. Rear wheel pushes on road, and roa... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/113799",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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How to calculate the velocity of this body?
Graph of a train (the body) is provided which starts from rest. What is the velocity after the train has 10 metres displacement?
Thats the only things provided for the question, please help me out here, I find that more variables will be required but the book states that n... | According to the graph, accelration is linearly dependent on displacement. Now, assuming the motion is rectillinear(along a straight line, and quite justified for 30 m displacement of a train).
It is not very difficult to find the equation of this straight line (intercept form).
And then, you'll need some calculus to f... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/113894",
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Is evaporative cooling more efficient with dry or moist air? I live in India, and in the summer season, the temperature can reach up to $45 \sideset{^\circ}{}{\mathrm{C}} .$ We use Split 1.5 Ton AC in our small office. The idea is to put an evaporative cooler on the inlet side of the heat exchanger of AC to give it mor... | If you’re recirculating the office-side air, evaporative cooling is unlikely to help. You’d be adding water vapor to the air which the AC would eventually just have to use cooling power to remove.
Depending on humidity, though, it may be very effective to use evaporative cooling to reduce the temperature of the air r... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/114156",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Why do turbine engines work? I know roughly how a turbine engine (let's say a gas turbine producing no jet thrust) is supposed to work:
The compressor forces fresh air into a combustion chamber, where it reacts with fuel to become hot exhaust gas. On its way out of the engine, the exhaust gas drives a turbine, and the... | I have the same question myself but I'll raise two points:
Firstly, the compressor is not just a turbine, but also, in many cases, kind of a centrifugal pump. In such a case, I don't think the pressure in the combustion chamber can push the pump backwards.
Secondly, in a high speed air-flow situation, the dynamics is q... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/114280",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Feynman's $i \epsilon$ prescription in loop expansion I have some questions about the $i\epsilon$ factor in Feynman diagrams. First, what is the physical meaning of $i\epsilon$ in loop amplitudes. Second, how does it ensures unitarity?
And third, Dyson series assume that incoming and outgoing particles are free, this c... | $\rm{i}\varepsilon$ is not a factor, but an addendum. It allows to integrate straight along the axis. It removes poles from axes in a "physical way" - by obtaining the right propagator. The right propagator does not need any adiabatic tricks.
Incoming and outgoing particles are not always free. In particular, the meani... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/114351",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why Does Change of Magnetic Flux Induce an emf? Why does change in magnetic flux with time through a coil induce an emf across it? Please explain what happens to the charges in the coil when magnetic flux changes?
Also, why does a constant magnetic flux not induce an emf?
| It is an experimental fact that a changing magnetic field induces an electric field and a changing electric field induces a magnetic field. This has been mathematically described in the all inclusive Maxwell equations.
Conductivity appears with the motion of charge in a conductor.The difference between insulators and ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is Newton's third law always correct? Newton's third law states that every force has an equal and opposite reaction. But this doesn't seem like the case in the following scenario:
For example, a person punches a wall and the wall breaks. The wall wasn't able to withstand the force, nor provide equal force in opposite ... | You can't apply to a wall the force bigger than it can withstand. If the wall breaks at some certain amount of newtons of the force applied then it follows that you applied this certain force. And of course the reaction of the wall equals the force applied.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/114669",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "16",
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"answer_id": 6
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Chemical effect on gravitation? We know, that gravitation field of charged black hole is different than one of uncharged.
I this true only for objects with singularity or is true for all objects?
If true, then may we say, that gravitation field of chemical molecule has footprints of it's chemical composition and state ... | Gravitational fields are not sensitive to chemical composition or state per se, except through the stress-energy tensor. The reason that a charged black hole has a different gravitational field is basically that the electric field has energy, and that energy is equivalent to some amount of mass, which is distributed ov... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/114729",
"timestamp": "2023-03-29T00:00:00",
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Starting a nuclear reaction In Chemistry, an amount of energy has to be supplied for a reaction to occur. This energy, known as the "activation energy", breaks up the bonds between molecues in the substance. It is equivalent to the total bond energy of the reactants.
However, in high school I learnt that the energy req... |
In Chemistry, an amount of energy has to be supplied for a reaction to occur. This energy, known as the "activation energy", breaks up the bonds between molecules in the substance. It is equivalent to the total bond energy of the reactants.
In chemistry activation energy is not the energy required to break a bond. I... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Why is the ratio of velocity to the speed of light squared in the Lorentz factor? Why is the ratio of velocity to the speed of light squared in the Lorentz factor?
$${\left( {{v \over c}} \right)^2}$$
My only guess is the value must be positive.
| Consider a particle of light moving along a sick of length $c\Delta t$ from the frame of reference of a stationary observer. i.e. The stick itself has velocity zero relative to the stationary observer.
Then consider another observer moving with a velocity perpendicular to the sick with speed $v$. The stationary obse... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/114913",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
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Temperature on the surface of the sun calculated with the Stefan-Boltzmann-rule In a German Wikipedia page, the following calculation for the temperature on the surface of the Sun is made:
$\sigma=5.67*10^{-8}\frac{W}{m^2K^4}$ (Stefan-Boltzmann constant)
$S = 1367\frac{W}{m^2}$ (solar constant)
$D = 1.496*10^{11} m$ (E... | The relationship of temperature between a planet and a star based on a radiative energy balance is given by the following equation (from Wikipedia):
$T_p = temperature\ of\ the\ planet$
$T_s = temperature\ of\ the\ star$
$R_s = radius\ of\ the\ star$
$\alpha = albedo\ of\ the\ planet$
$\epsilon = average\ emissivi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/114972",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Power fit to some experimental data I have to fit some data to a power law
$$ F=\alpha q^{\beta}$$
being $q$ and $F$ the experimental data points. What I usually do is taking logs so that
$$ \ln(F) = \beta \ln(q)+\ln(\alpha)$$
and apply least squares with uncertainties in both variables. How may I approach this in the ... | Taking the logarithms of negative numbers isn't a viable solution.
When you postulate $ F=\alpha q^{\beta}$ you are implicitly supposing that is F is a real number, q is positive.
Just make a least square fit using the absolute values of $F$, $\alpha$ and $q$:
If $ F=\alpha q^{\beta}$ then $ |F|=|\alpha| |q|^{\beta}$, ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/115088",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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Lagrangian point or dark matter? We know that spiral galaxies spin in a way such that we have to assume that dark matter is responsible for the extra mass required to do so.
My question is, can Lagrangian points (L1 and L2) be used to describe a galaxy's rotation instead?
Can we explain that objects far away from the c... | The objections posted by the answerers to the original question really just point to the need for a solution to an unrestricted many-body problem to actually answer the question fairly. Since the asker is a computer engineer I would suggest he code a numerical simulation. My intuition is that, although the bodies invol... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/115161",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Is it more efficient to stack two Peltier modules or to set them side by side? Is it more efficient to stack two Peltier modules or to set them side by side?
And why?
I have a small box that I want to cool down about 20 K below ambient -- cold, but not below freezing.
(I want to keep my camera cool, so I'm putting in t... | If efficiency is the issue, then definitely parallel TECs (or use a single unit rated for twice the power, same thing). The only reason for stacking TECs is to get a lower temperature. However that comes at great expense to efficiency and overall power consumption.
Another point is that paralleling TECs is actually m... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/116271",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "20",
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Electron indistintinguishability and handedness I just learned that right ad left handed electrons behave in a remarkably different way under the weak interaction.
Up till now I have been told that all the electrons are exact copies of one another and all this fermi-dirac statistics story.
Nonetheless, since right ha... | A massive electron in its rest frame is a mixture of left- and right-handed components. All electrons mix the same way, and so they remain indistinguishable.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/116337",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Light penetration in the ocean Is there an equation that describes the percentage of solar energy per wavelength that penetrates the ocean surface?
For example, this website states that only 44.5% of the surface light reaches a depth of 1 meter.
So, is there an equation that can be used to determine the percentage of... | The light intensity at a depth $d$ is given by the Beer-Lambert law:
$$ I = I_0 \exp\left(-\frac{d}{\ell}\right) $$
where $I_0$ is the intensity at the surface and $\ell$ is the depth at which the light intensity has fallen by 73%.
The depth $\ell$ is dependant on wavelength as seawater absorbs red light more strongly ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/116420",
"timestamp": "2023-03-29T00:00:00",
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What does QM say about the past rather than the future? In QM, the wave function (in the Copenhagen interpretation) is not an actual physical wave but a device to derive probabilities about the outcomes of experiments. The wave function encodes all the information about the system we want to derive predictions for. Pr... | On the fundamental level, QM is time-symmetric, hence it says the same about the past as about the future. The dynamics of the state is deterministic and given by the quantum Liouville equation (or, if you consider an isolated system in a pure state, by the Schroedinger equation). This state determines the probability ... | {
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What are the units for rate of movement through time? Thinking of time as the dimension orthogonal to depth, it seems logical that the rate at which a body moves through time could vary. Do units exist for rate of movement through time? The numerator seems clear (e.g. seconds), but what could the denominator be?
| When you are taking of RATE you already mean the flow of time.
So rate at which a body moves through time is not a physically correct statement.
According to the velocities of bodies the perception of time may be different but the rate of flow of events is TIME itself.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/116567",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Why Microchannel Plates can be operated only in vacuum? Why it is said that the Microchannel Plates can be operated in vacuum? What is the maximum pressure in which it can be operated? Also, while it is not operating, should it be kept in vacuum?
Is this because the semiconducting property of the channels can be affect... | The electrons need to get from the top to the bottom without any interference from any gas molecules that might be in the channels. If nothing else, collisions with gas molecules will degrade performance. At atmospheric pressure, I don't think the device would work at all. You can blow a hole through an MCP with ove... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/116622",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Is there any operator behind probability, in quantum mechanics? In Quantum mechanics, the probability of finding a particle at position $x$ is given by $|\psi(x)|^2$, where $\psi$ is the wave function. Wonder what is the operator which gives this probability? Is probability the result of any operator acting on $\psi$?
| The theory of quantum mechanics has been developed to explain observations, i.e. measurements. Without observations it is a floating mathematical construct.
One of the postulates to connect the mathematics with reality is:
To every observable there corresponds an operator which operating on the state function will give... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/116762",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Why are the 'color-neutral' gluons confined? What makes the two 'color-neutral' gluons
$(r\bar r−b\bar b)/\sqrt2$ and
$(r\bar r+b\bar b −2g\bar g )/\sqrt6$ different from the pure $r\bar r +b\bar b +g\bar g $ ?
Why don't they result in long range (photon-like) interactions?
| One could state your problem as " why are there only eight gluons accepted as physically existing from the SU3 symmetry . This link gives the answer simply, and it says that if the ninth all color neutral gluon existed, then as you guess, it would act similarly to the photon with interactions between hadrons that have... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/116851",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why does a ball bounce lower? If a ball hits the floor after an acceleration then why does it bounces lower? I mean the Energy is passed to the floor then why does the floor give back less Energy?
| At impact, most of the kinetic energy is transferred to elastic energy in the ball (by its deformation) and not to the floor. Some energy is also converted to other forms like heat and sound. These other forms of energy, are mostly losses and they are not recovered thus making the ball bounce back to a lower height.
Su... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/117091",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "24",
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Peaks in binding energy per nucleon Looking at the the binding energy per nucleon chart:
I observe peaks for N=4,8,12,16,20,24
while I expected to observe peaks for 2, 8, 20, 28, 50, 82, and 126 because I have heard that in correspondence of these numbers there is the completion of a nuclear orbital, so I expect a loc... | Your peaks at $A=4n$ are the so-called "alpha-particle nuclei," which have even proton number, even neutron number, and $N=Z$. In a very hand-wavy way you can say that alpha-particle nuclei are especially tightly bound because the alpha particle is especially tightly bound.
Inside of a nucleus you have separate orbital... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/117150",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Physical Interpretation of four velocity in GR I'm confused about the physical interpretation of the four-velocity $U^\mu=\frac{dx^\mu}{d\tau}$ in General Relativity. I know that it is a tangent vector to a particle's "worldline", but what does this mean more physically?
For example, I am comfortable with what $U^\mu$ ... | Accelerated particles do not have a "fixed" inertial reference frame. However, we can define infinitely many momentarily comoving reference frames (MCRFs) at each event. These are all related to each other through simple rotations. The four velocity at each event therefore is the time component of that event's MCRF's b... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/117408",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Moon's pull causes tides on far side of Earth: why? I have always wondered and once I even got it, but then completely forgot. I understand that gravity causes high and low tides in oceans, but why does it occur on the other side of Earth?
| Imagine that we have a very massive object in space. At some distance away (call it ten units) we release three tennis balls in a row:
The tennis balls all fall towards the massive object. But because gravity goes like distance squared, the nearer balls feel a stronger attraction than the farther balls, and they mov... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/118460",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "80",
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Placing two similarly charged particles in space Now, I will make a hypothetical situation. Assume that we place two similarly charged particles (lets take electrons) in space. Imagine that there is no other force acting on the particles except the repulsive force and the gravitational force of the particles. In other ... | Ok, so we all agree that $W = \vec F · \vec x$. If the force varies, then the total work on each electron is calculated using an integral:
$W = \int_{x_0}^\infty\vec F · d \vec x$
Here, $W$ is work, $\vec F$ is the electrical force, $\vec x$ is the distance of the charge from the center of your universe, and $x_0$ is... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/118531",
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Self-adjoint extensions with 'teletransporting' boundary conditions When choosing a self-adjoint extension of a Hamiltonian, in general one can obtain domains in which
(i) the probabilities teleport* between points on the boundary
and
(ii) boundary conditions locally conserve probabilities.
The ones which locally co... | Once you admit the tunnelling the "topology" of the problem changes to "particle in a circle with an infinite barrier". In fact, to avoid arguments with energy when crossing the barrier, it can be described as "particle in a circle with an infinite barrier in one point". So physically it can be argued to be a different... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/118668",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Why does a large train cause the ground to shake? I work in a 4 story building that is approx. 150 feet away from a set of train tracks. When a large (40+ car) freight train goes by, the shaking in the building is perceptible. As I've watched the train go by, there does not appear to be any side to side movement and ... | Since "enough" information is not available, one can only guess. My guess is that "most likely" resonance is what's causing the perception. The length, height, width, and composition of the building and its distance from the tracks, determines its "natural" oscillating frequency and the train's length and speed must c... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/118734",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "30",
"answer_count": 4,
"answer_id": 3
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Finding the components of the tensor for potential and kinetic energy I have a rather poor understanding of what a tensor is, but enough to apply it to the biggest part of the classical mechanics I'm studying.
However, I've run into a small problem while studying "Free vibrations of a linear triatomic molecule". (We're... | Your squared general coordinates correspond with the tensors diagonal axis. The others are the cross terms. Since we are dealing with commuting terms, it will always be of the form $2\eta_{i}\eta_{j}$ although it is truly $\eta_{i}\eta_{j}+\eta_{j}\eta_{i}$. Obviously, the $\frac{1}{2}$ is absorbed by the energy equati... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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How can $J_1^2, J_2^2, J_{1z}, J_{2z}$ commute mutually? I'm reading through J. J. Sakurai's Modern Quantum Mechanics book and currently looking at the "Angular-momentum addition" part.
Here, it says you have two options and that one option is to construct simultaneous eigenket $\vert j_1j_2;m_1m_2\rangle$ of $J_1^2, ... | From your statement "measure both at once", it seems you've misunderstood what's meant by "simultaneous measurement". It does not mean that you can run a single experiment to measure both "independent" values together. Rather, it means that in principle, you can measure one quantity without "ruining" the results of m... | {
"language": "en",
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Clocks in special relativity One book on special relativity says:
Any observer at rest relative to his own timepiece will see that other clocks moving with respect to him run fast - the greater their speed, the faster they are.
Other book says:
Observers measure any clock to run slow if it moves relative to them.
D... | The statement is
"Any observer at rest relative to his own timepiece will see that other clocks moving with respect to him run fast - the greater their speed, the faster they are".
According to one source, Don Koks (a physicist text book author)this statement is true..... on the condition A orbits B.
http://math.ucr.e... | {
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Intuition behind mass corrections to massless fermions I'm trying to understand the intuition behind the mass correction to massless fermions. To be concrete lets consider a theory with a massless Weyl fermion ($\psi $), as well as two massive particles, a complex scalar ($\phi $) and another Weyl fermion ($ \psi ' $),... | I guess that the confusion here is that you mix Weyl notation and Feynman diagrams with Dirac propagators. As you notice yourself, the theory has a global (anomalous) U(1) symmetry that prohibits a mass term $m\,\psi\psi$ (in Weyl notation). If I try to draw your diagram (ab)using the usual Dirac propagator lines for W... | {
"language": "en",
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"source": "stackexchange",
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Why does my house seem to warm faster in summer than it cools in winter? In summers when we switch off the air conditioner, the room seems to instantly get hot again.
But in winter, when we switch off the heater the room seems to remain hot for some time. Why this difference?
| When your house heats up, it is receiving the contribution from the hot air outside, plus the sun's radiated heat. When cooling in the Winter, the factors are the cooler air and the radiation loss, which is not comparable to the sun's.
| {
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Why $SU(3)$ and not $U(3)$? Is there a good reason not to pick $U(3)$ as the colour group? Is there any experiment or intrinsic reason that would ruled out $U(3)$ as colour group instead?
| Suppose that $\text{U}(3)$ was the gauge group. We can decompose this as
$$\text{U}(3)=\text{U}(1)\times\text{SU}(3),$$
which implies that in addition to the $\text{SU}(3)$ that has eight generators corresponding to eight gluons, there would be an additional generator for $\text{U}(1)$. The latter in principle corresp... | {
"language": "en",
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How does the choice of a particular vacuum in a field theory problem decide the number of Goldstone bosons? How does the field expansion method (by this I mean expanding your fields about a chosen VEV and plugging into a given potential so that the masses of the fields are given by the coefficients in front) corrolate ... | Where you have gone wrong is in accounting for the dimensionality of your
surviving subalgebra. In the first case, as you correctly see, the surviving SU(2) is, indeed, manifestly spanned by $\lambda_{1,2,3}$, so the remaining 5 generators are broken.
In the 2nd case, however, you should have noticed the less manifest... | {
"language": "en",
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Why can the entropy of an isolated system increase? From the second law of thermodynamics:
The second law of thermodynamics states that the entropy of an
isolated system never decreases, because isolated systems always
evolve toward thermodynamic equilibrium, a state with maximum entropy.
Now I understand why t... | While Bubble gave a nice example, let me try to explain this with "Clausius inequality". (You can read this on several sources, I like the explanation from Atkins' Physical Chemistry)
Let's start with the statement:
$$
|\delta w_{rev}| \geq |\delta w| \\
$$
Furthermore, for energy leaving the system as work, we can wri... | {
"language": "en",
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Time dilation at the Big Bang At the time the Big Bang happened the matter had enormous density. According the GR (I may be wrong here) such density dilates time.
If so, could it be that the time periods just after Big Bang which are usually considered happening in small part of a second (such as the Planck epoch), in ... | Is the universe finite or infinite?
If the big bang had infinite mass at the start then time dilation due to gravity would be infinite and time would stand still. That's the problem with trying to conceive of the start of time because it took infinitely long to start.
An infinitesimal length of time under infinite gra... | {
"language": "en",
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Finding the electric field around an electric eel I'm having problems solving for the electric field and the current that an electric eel generates. Would I use Gauss's law and treat it as a long charged wire? How would I find the charge of the electric eel? I'm really confused about what I can do and where to start.
... | Let's first make a 'textbook' calculation to get a feeling of the magnitude of the field. See below and sources for a more accurate description.
Suppose that the you can treat the eel as infinitely small. And take is length to be about 1 m long and can generate a voltage difference of 500 volts between its head and tai... | {
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Why is the constant velocity model used in a projectile motion derivation? I was re-studying university physics last week, I'm now in the chapter about kinematics in 2 dimensions and specifically the one treating projectile motion. In page 86 of his book (Serway - Physics for scientists and engineers) he derives the eq... | The force of gravity is in the y direction only.
There is no force on the particle in the x direction.
Therefore, the x-component of velocity is constant.
| {
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Find minimum distance between particles given initial position and velocity My friend gave me a question today:
We have a point $A$. At a distance of $x_0$ from the point. There is a particle $P_1$. There is another particle, $P_2$, at $A$. $P_1$ moves with velocity $u_1$ towards $A$. At the same instant, $P_2$ moves ... | You don't have enough information to properly answer the question.
If $u_1 \le u_2\ and\ \theta \ge \pi/2$, then the shortest distance occurs at the initial conditions.
When $u_1 > u_2$, then the shortest distance occurs when $\angle P_{1-initial}P_1P_2$ is $\pi/2$.
| {
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Conservation of energy and the 'crazy ball' product Well I'm not sure how many people remember the crazy ball - a small ball made of rubber which bounced like crazy. What I noticed is that the ball seemed to bounce higher than the point from which it was actually dropped. How is this possible? Doesn't this violate the ... | No, it doesn't violate energy conservation, and it doesn't bounce higher than the usual height, if you ''drop'' it (i.e. $v_{\rm initial} = 0$). If you add any force from your side, ''throwing'' it, then it will obviously bounce higher, but still won't violate energy conservation if you include the extra $\frac{1}{2} m... | {
"language": "en",
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Why is the Earth shaped like a sphere and not any other shape: cube, prism? Why is the earth shaped like a sphere and not any other shape: cube, prism?
| Feynman wants to say you something, listen to him!
What else can we understand when we understand gravity? Everyone knows the earth is round. Why is the earth round? That is easy; it is due to gravitation. The earth can be understood to be round merely because everything attracts everything else and so it has attract... | {
"language": "en",
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Why doesn't current flow when the wire is open? I realize this may be a hard to answer question but we are currently studying current in our school. One thing that struck me was why the heck doesn't it flow when the wire's closed?
When you connect the positive terminal of the battery (But do not connect the negative te... | At first, try to understand the working principle of a battery. Here is a video explaining what positive terminal and negative terminal are. If you don't have the load connected there, you will not have infinite amount of depletion of electrons in the positive terminal as after some time no $H^+$ will be able to reach ... | {
"language": "en",
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"source": "stackexchange",
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Bragg diffraction and lattice planes Crystalline substances show, for certain sharply defined wavelength and incident directions, very sharp peaks of scattered X-ray radiation.
From the illustration below we see that we get constructive interference when the path-length difference is a multiple of the wavelength $\lamb... | I think that the most appropriate way to think about the Bragg formula is in terms of a diffraction grating. In a diffraction grating one obtains sharp peaks because there are many slits with distance $d$ between them. The derivation of the intensity maximum for the diffraction grating case is similar to the Bragg case... | {
"language": "en",
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Difference in decay for muon and anti muon In a couple weeks, I will conduct a lab experiment where I measure the lifetime of the muons from the secondary cosmic radiation. For that, we have two detectors above each other, one will give a start signal, the other will give a stop signal, assuming the muon came to rest i... | If you consider a muon decay in vacuum then there is no difference between the lifetimes of muons and antimuons.
However a muon can interact with a proton via the weak force to form a neutron, while an antimuon cannot. Since the air is full of protons this means the muon lifetime in air is slightly shorter than the ant... | {
"language": "en",
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What makes nuclear binding energy so much stronger than chemical energy The strong force acting between quarks and responsible for holding protons together is 100 times stronger than the electromagnetic force. How come the nuclear binding energy derived from the strong force is millions time stronger than chemical ener... | Chemical forces are the result of the higher order moments, mainly of the electric field, of the neutral atoms. Look at these orbitals:
The five d orbitals in ψ(x, y, z)2 form, with a combination diagram showing how they fit together to fill space around an atomic nucleus.
These anisotropic shapes in space allow for... | {
"language": "en",
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Normal ordering in curved spacetime In the flat spacetime, one can perform normal-ordering to set the energy of the vacuum state to zero. I read in some places that this procedure cannot be consistently performed in the curved spacetimes. I have not found any explanation of this fact in the literature.
Why is this a ca... | The normal ordering procedure is nothing but the a recurrent machinery to remove vacuum expectation values by means of the so-called Wick's theorem procedure. There, the vacuum state is the unique Poincaré invariant one, the Minkowski vacuum. In curved spacetime there is no such an invariant state. Therefore the normal... | {
"language": "en",
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How is sweating a pipe an example of capillary action? I learned how to sweat a pipe today from my father. If you're not familiar with the process, this might help.
One thing that jumps out at me is this line (from the above link, as well as my father's explanation)
Solder, which melts at low temperatures, wicks into... | The basis for capillary action is attraction between the liquid and the solid, based upon intermolecular or interatomic forces.
When the liquid needs to rise against gravity to increase wetted surface area, an equilibrium is reached. However, capillary action does not need to be opposed to gravity. Capillary action s... | {
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Why isn't invariant notation common? In principle, one can write quantities in a manifestly invariant - rather than covariant - fashion in e.g. special relativity. For example, rather than writing just $x^\mu$, we could write the basis explicitly, and ask that the basis transforms oppositely to the components,
$$
x = x... | A physicist would write your first equation $x^a = x^\mu e_\mu^a$. The notation $x^a$ is invariant in your terminology. The $a$ is an abstract index. It is ostensibly not supposed to be thought of as ranging over a set of numerical values, but is just a marker that indicates that $x$ is a vector (i.e., rank 1,0 tensor.... | {
"language": "en",
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Second fundamental form How do I calculate the integral of the trace of the second fundamental form on a surface?
The formula used in the Gibbons, Hawking, York paper Action integrals and partition functions in quantum gravity, how do I derive it? Is it a universal or does it have any assumptions about the kind of spa... | The boundary term of the Einstein-Hilbert action is given by,
$$S= \frac{1}{8\pi G}\int_{\partial M} \! \!\mathrm{d}^3x \, \sqrt{-h} \, K$$
where $h$ is the metric on the boundary of the manifold, i.e. $\partial M$, and $K$ is the trace of the extrinsic curvature. Specifically, we have,
$$K=\nabla_a n^a$$
where $n^a$ i... | {
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Is the magnetization direction of a permanent magnet fixed? I am now playing with a permanent magnet made of Neodymium.
It is impressively strong.
A question is, is the magnetization direction of the magnet fixed relative to its crystal structure?
| Practically yes, but the true answer is a little bit complexer.
Below the level of the crytals, there are the magnetic domains. In a domain have the atoms the same orientation (and thus, the same magnetic dipole moment).
In the case of a magnetized ferromagnetic material, these magnetic pole of these domains are direc... | {
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"source": "stackexchange",
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Why $e$ in the formula for air density? I am reading a book that says that the density of air is approximately $D = 1.25 e^{(-0.0001h)}$, where h is the height in meters. Why is Euler's number $e$ used here? Was a differential equation used in deriving this formula?
| You can rearrange the terms to have any constant as the base of the exponent:
$D = 1.25 e^{(-0.0001h)}$
$= 1.25 (e^{0.0001})^{-h}$
$= 1.25 (2^{\frac{0.0001}{ln 2}})^{-h}$
$\approx 1.25 (2^{0.00014})^{-h}$
$= 1.25 \times 2^{(-0.00014h)}$
| {
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Why does angular momentum shorten the Schwarzschild Radius of a black hole? Angular momentum causes the event horizon of a black hole to recede. At maximum angular momentum, $J=GM^2/c$, the Schwarzschild radius is half of what it would be if the black hole wasn't spinning.
Can someone explain why angular momentum redu... | I will approach this question theoretically, although I feel the intuition follows nicely. If we talk about Kerr black holes - rotating black holes described by their mass and angular momentum, with no additional parameters such as charge etc. - then you can show that the radius of the event horizon is given by
$\boxed... | {
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Integrating the generator of the infinitesimal special conformal transformation (c.f Di Francesco, Conformal Field Theory chapters 2 and 4).
The expression for the full generator, $G_a$, of a transformation is $$iG_a \Phi = \frac{\delta x^{\mu}}{\delta \omega_{a}} \partial_{\mu} \Phi - \frac{\delta F}{\delta \omega_a}$... | The two questions posed above are exactly the same and one may prove both simply by substituting $x'_\mu$ and calculating. If
of not showing how the finite transformation of the SCT comes from but just states it. $$x'^{\mu} = \frac{x^{\mu} - b^{\mu}x^2}{1-2x\cdot b + b^2 x^2}$$
then
$$(x')^2 = \frac{(x_\mu-x^2 b_\mu)... | {
"language": "en",
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Why does sand stick to my shoes? Well, that's easy: the sand is wet, and my shoes are wet, and hydrogen bonding adheres the wet sand to my wet feet and to my shoes.
But then I walk home, and my shoes dry, and the sand on them dries, and some of the sand falls off. But some does not. It's really stuck: even several da... | I think this is because your shoes have tracks over the non-uniform surface to provide frictional force for movement,these holes allow the wet sands take longer time to evaporate, the outermost layer should get evaporate first, and fall off once the water is evaporated.If your shoe surface is facing directly downward, ... | {
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How much time passed for the passenger traveling with at speed-of-light spaceship? Let's suppose we have a spaceship with the exact speed of light. If a traveller takes this spaceship to go to proxima centauri (approximately 4 years light away from Earth) and come back, we (as observers on Earth) will see the ship com... | The quantity that tells you what time an observer travelling along a path $\gamma : [t_0,t_1] \rightarrow \mathbb{R}^4$ experiences is the proper time
$$ \tau = \int_\gamma \sqrt{\mathrm{d}x_\mu\mathrm{d}x^\mu}$$
Assuming flat spacetime, i.e Minkowski metric/special relativity, this reduces to
$$ \tau = \int_\gamma\sq... | {
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How stellar aberration is measured? A simple calculation shows that stellar aberration due orbital motion of earth is roughly 20 arcseconds. My questions are:
*
*Practically how this small value is measured?
*Does this value is in the range of accuracy of a 11 inch reflective telescope with a camera?
*And how t... | Here's a second, easier way. It has less precision, but it's more practical, at least if you want to simply see the basic effect.
Take a long-exposure telescopic photo of the celestial pole. Use the highest possible magnification. The star trails in the photo are centered on the pole, so you can infer the pole's positi... | {
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Help explain how direction change relates to acceleration I was doing some simple harmonic motion problems and I came across this picture describing the position, velocity and acceleration of a linear oscillator. At the moment in time when v is 0 the linear oscillator should not be moving, only changing directions. ... |
Is it because acceleration is only the difference in velocity at two different points in time and not one?
I think you've basically hit on the answer to your question here. Acceleration is the derivative of velocity with respect to time, which means it is the instantaneous rate that the velocity is changing with ti... | {
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Can an LC oscillator be used to generate visible light? The LC oscillator is most commonly used to generate radio waves for practical use and the frequency $\omega$ of the LC oscillator equals that of the electromagnetic wave so produced. So, can they in principle be used to emit visible light?
The frequency of visible... | If, by LC oscillator, you mean a circuit composed of an 'ordinary' inductor and capacitor etc. then the answer is no.
The equations for the LC oscillator are derived within the context of ideal circuit theory which is the limit of a number of assumptions.
To apply the results from ideal circuit theory to physical syste... | {
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Invariance of a tensor under coordinate transformation I know, that a tensor is a mathematically entity that is represented using a basis and tensor products, in the form of a matrix, and changing a representation doesn't change a tensor, is kind of obvious.
So does the invariance of a tensor under coordinate transform... | Regarding what you quoted: a vector is represented by the sum of a set of basis vectors times the vector components. If the components transform according to $L$, then the bases will transform according to $L^{-1}$, which means that when you multiply the bases with the components (to make the vector), you will get the ... | {
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How much does the sound definition vary during an LP (Vinyl)? This question came to me when I realized how the linear speed varies while listening to a Vinyl LP.
The linear speed variation has to be compensated with a variation in the resolution of the grooves, that is, since the linear speed decreases, the groove reso... | It should be obvious that the linear speed is inversely proportional to the distance from the center to that point on that groove.
Yes, speed varies over a record, so the wavelength of the wiggles in the groove gets shorter for the same frequency as you get further into the record. However, the master record was creat... | {
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How can such a wave exist at the surface of the sun? Recently, I came across the following picture from NASA's SOHO observatory:
It seems evident that this is a transverse wave (mind the
ring which is bright and dark). But how can this be the case if the
sun consists of gaseous matter?
| I agree it looks like a transverse wave - like the ripples on a pond. But I believe you are fooled by a simple thing: the waves you are looking at look like "illuminated ripples" but are in reality just changes in temperature (changes in brightness of the sun's surface).
If you have a shock wave traveling out across th... | {
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The Einstein-Hilbert Action On-Shell If one consider the Maxwell action as
$$S=-\int \mathrm{d^{4}}x\! \ \frac{1}{4}F_{ab}F^{ab} \,$$
one find the usual Maxwell equation
$$\partial_{a}F^{ab}=0$$
Then one can simply arrive the following the Maxwell on-shell action
$$-\int \mathrm{d^{4}}x\! \ \frac{1}{2}\partial_{a}(A_{... | The action you're considering yields Einstein's equations in vacuum, so $R=0$ (this follows immediately from contracting Einstein's equations). Therefore the action vanishes on shell.
| {
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Could Legolas actually see that far? The video “How Far Can Legolas See?” by MinutePhysics recently went viral. The video states that although Legolas would in principle be able to count $105$ horsemen $24\text{ km}$ away, he shouldn't have been able to tell that their leader was very tall.
I understand that the main ... | One thing that you failed to take into account. The curve of the planet (Middle Earth is similar in size and curvature to Earth). You can only see 3 miles to the horizon of the ocean at 6 feet tall. To see 24 km, you would need to be almost 100m above the objects being viewed. So unless Legolas was atop a very (very) t... | {
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Role of physics in the zeta function $\zeta$ and the Riemann hypothesis Hilbert and Polya suggested a physical way to verify the Riemann hypotesis about $\zeta(x)$. If the Riemann hypotesis is true, we can state all eigenvalues of physical problems are real. What is the connection between the eigenvalues and the $\zeta... | In http://arxiv.org/abs/1608.03679 , the authors consider a Hamiltonian
$\hat{H}=\frac{1}{I-\exp(-i\hat{p})}(\hat{x}\hat{p}+\hat{p}\hat{x})(I-\exp(-i\hat{p}))$,
where $I$ is the identity matrix (I suppose - I cannot type the symbol they use), and claim that "a formal calculation of the eigenstates $\{\psi_n\}$ and
eige... | {
"language": "en",
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"source": "stackexchange",
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The fundamental equations of electromagnetism I'd like to know what are the basic equations of electromagnetism, that can be used to formulate all the other laws and equations.
Those basic equations I can think of are Maxwell equations, Lorentz force equation and Coulomb's law. What are the other fundamental laws and e... | The basics about the direction of force and field comes from the "Fleming's Left Hand Rule" and the "Maxwell's Corkscrew Rule". In addition to these the Lorentz force law, i.e. F=q[E+(vxB)] gives the force on a charge moving through a magnetic and electric field [Neglect E if electric field is absent.] The Biot- Savart... | {
"language": "en",
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If the energy of an ant is smaller than an elephant, does that mean the ant is more stable than the elephant? I know that when a system is in its lowest level of energy, it is most stable. However, what if system 1 has lower energy than system 2, does it keep meaning so? Or do we need to examine their binding energies ... | I guess that you should not compare them with each other.
in fact stability is not a real thing.
we know that when a system has potential energy it has ability to do work and turn them to kinetic energy so that its velocity will be increased and as we know velocity(not important velocity of particles or bigger masses)m... | {
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Weighing head by angular momentum A popular Phys.S.E question asks how can I measure the weight of my head. One of the answers suggests measuring the moment of inertia.
My suggestion was to construct an apparatus that places the subject on a translatable carrier located on top of a rotating table. Sensors would allow ... | Regarding the second question:
The parallel axis theorem states, that if you have rotation around another axis than a body's center of mass, you only have to add the inertia tensor of a point mass at the location of the body's center of mass. And because of your setup, you will probably not be able to measure more than... | {
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Why ONLY Maxwell's equations are the basic equations of electromagnetism? In electromagnetism we say that all the electromagnetic interactions are governed by the 4 golden rules of Maxwell. But I want to know: is this(to assume that there is no requirement of any other rule)only an assumption, a practical observation, ... | The Maxwell equations only approximately describe electromagnetism, even in a pure vacuum. This is a consequence of quantum electrodynamics. One can derive corrections to the Maxwell equations; this was first done by Heisenberg an Euler in the regime where the fields only change appreciably over distances much larger t... | {
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Physical Role of Batter in Baseball Physically, what is the role of a batter in baseball?
My question is inspired by How does the speed of an incoming pitch affect the speed of a baseball after it's hit?
The answer to that question, that a faster pitch results in a farther hit, surprised me. I had thought that a batter... | It helps to think of the extreme cases here. If the bat was not moving (like a bunt), the resulting bounce does depend on incoming speed. Now, make the incoming ball really slow and the batter hitting fast. The result does not depend on incoming speed. The true answer is the superposition of these two cases.
| {
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Classic home experiments for an 8-year-old child My 8-year-old daughter's school report says that she's good at understanding the basic science she's doing, but she's having trouble seeing how experimental results lead to conclusions. Specifically, it says she struggles to appreciate how changing parameters in an exper... | How big is an atom?
Fill a sink with water. Find a chemical which, when dropped into water, forms a contiguous floating disk. Drop one drop of this chemical into water. Measure volume of drop and area of floating disk. This provides an upper bound on the size of an atom.
Falling speed versus mass/shape
Drop a book and ... | {
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How does the Alcubierre drive warp space in the vicinity of it's destination?
I don't understand how this could work. So lets say the drive is set to go 30,000,000 meters in a straight line to get to a distant planet. Now lets say the ship size is 20 meters. Now let's make the assumption that the warp field in the ... | The idea is that the object generating the "pit" in the front is in the center of the flat region in the middle. What happens is that the object in the middle begins to "fall" into the "pit" in front of it, due to gravitational attraction. The "pit", however, moves forward because it is a fixed distance away from the... | {
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Why do we deal only with large scale magnetic fields in astrophysics, and not electric fields? In astrophysics there is a lot going on about strong, large scale magnetic fields: in stars (prominences), magnetic dynamos, compact accretors collimating jets, etc. There's even a special computational formalism called magne... | The lack of the electric field in modeling plasmas stems from the Lorentz force,
$$
\mathbf F=q\mathbf E+q\boldsymbol\beta\times\mathbf B
$$
where $\boldsymbol\beta=\mathbf v/c$. For most astrophysical plasmas, the force is zero, so we have that
$$
\mathbf E=-\boldsymbol\beta\times\mathbf B
$$
So any time we see an ele... | {
"language": "en",
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Uncertainty principle with two photons Imagine an experimental setup in which you have to measure the momentum and location of a particle. To measure it we know we will have to affect it, and the uncertainty principle would come into the picture, but I have a different setup. The classical setup is that you fire a phot... | Your classic experiment 1) is quantum mechanical. Electrons and photons are elementary particles and interact individually as quantum mechanical entities.
The plot shows the elastic scattering of photon on electron, a computable process quantum mechanically thus the angular distribution is known. As we are talking qua... | {
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Why does wavelength affect diffraction? I have seen many questions of this type but I could nowhere find the answer to "why". I know this is a phenomenon which has been seen and discovered and we know it happens and how it happens. But my question is why would wavelength affect the amount of diffraction? I am looking f... | The greater the wavelength the heavier the wave. If you think of it visually, the heavier the wave the more energy needed to move the wave in a different direction. As a result, the greater the wavelength, less diffraction.
| {
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Natural entanglement system I'm a beginner and amateur interested in quantum physics.
I would like to know if entangled systems of natural states exist or whether such systems require human intervention?
Is it possible? Either no or yes, Why?
| The answer is definitely yes. The ground states (and low-lying eigenstates) of many-body systems are generically entangled. Examples include the ground states of local quantum field theories (which describe the fundamental particles and forces of nature) and ground states of fermionic lattice models (which describe muc... | {
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Difference between single mode and multi mode optical fibres? What is the difference between single mode and multi mode optical fibres? First off, I guess that by modes we mean the spatial modes of the electric (or magnetic?) field right?
Now: what makes a fibre able to support more than a single mode? I mean, what asp... | The V-number defines the mode of any fiber. It depends on wavelength, diameter of fiber and refractive index.
The v number is
\begin{align}
\ V^2 &= \frac{2}{} (_1^2−_2^2)\\\\
\end{align}
Each mode has an effective index that can be defined by:
\begin{align}
\ _ = _ \frac{2}{}\\\\
\end{align}
The effective index tel... | {
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Relative wind velocity explanation I am having trouble understanding the reasoning behind the solution in this Irodov General Physics problem:
problem 1.6.) A ship moves along the equator to the east with velocity
$v_0=30\;km/h$. The southeastern wind blows at an angle $\theta=60°$ to the equator with velocity $v=15... | I think you are referring to the I.E.IRODOV (Problems in General Physics) question number 1.6 (KINEMATICS)
South-Eastern winds don't go towards South-East, in fact it's the complete opposite, they originate from South-East and go towards North-West.
So, if you were to reverse the direction of the wind vector, the solut... | {
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Calculate electricity generation A friend of mine stays near a water stream and wanted help to use its water. The height up to which the water could be raised using the water flow is 12ft. How much electricity can it produce?
Is it at least enough to power half the house?
| The efficiency of large hydroelectric generators can be very high - up to 95% in ideal cases - however the efficiency of small installations is a lot lower and in particular it's hard to get efficient electricity generation if the flow rate is low, which is likely to be the case for your friend.
But lets see what the p... | {
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Thermal expansion coefficient times temperature: under which condition is it unity? In Landau's Fluid Mechanics p. 8 (2nd edition) he writes for the thermal expansion coefficient $\beta = (1/V) (\partial V/\partial T)_P$:
For a column of gas in equilibrium which can be taken as a thermodynamically
perfect gas, $\bet... | What he writes down is the relative change in volume with temperature, so it is true by definition. What may be confusing is that sometimes β denotes the thermal expansion coefficient in two dimensions, whereas the three-dimensional coefficient is meant here.
| {
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Why does the Walecka model not include pions? The Walecka or $\sigma$/$\omega$-model is an effective theory describing nucleon-nucleon interaction by an exchange of $\sigma$/$\omega$-mesons. Why does it not include interactions by pions?
| I want to cite the original paper of Walecka where he awnsers your question:
From Annals of Physics 83/2 (1974) p. 491 "A theory of highly condensed matter
"The reader might object to the fact that there is no one-pion exchange tail in this interaction; however, the strong spin and isospin dependence of the potential ... | {
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Magnetic field and Newton's third law If a magnet exerts force on a iron block (opposite and EQUAL), does a iron block also exerts force on magnet (via Newton's third law)? If yes then what magnetic property does it has to produce equal and opposite force on magnet considering that its not a ideal environment? If no th... | It's not a violation of the Newtons law. (As AcuriousMind answers on the comments)
It's the very same magnetic force which prevents one solid the penetrate another solid. The only difference is that this force is weaker and works only over very small distance. If you have a iron block and a rubber pushed to gether ie. ... | {
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Singularity in Newton's gravitational law If $r=0$ in the well know equation $F= G\dfrac{m_1\cdot m_2}{r^2}$, it will not follow that the force will be infinite?
May someone please clarify it to me?
| Assuming that $m_1$ and $m_2$ take up a finite amount of space (e.g., two spheres of mass with radius $r_0$), that equation isn't even valid for $r < r_0$, so there's no inconsistency.
The derivation follows from Gauss' law; it is analogous to the application of Gauss' law in electrostatics; the $m_1$ and $m_2$ are the... | {
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Gradient is covariant or contravariant? I read somewhere people write gradient in covariant form because of their proposes.
I think gradient expanded in covariant basis $i$, $j$, $k$, so by invariance nature of vectors, component of gradient must be in contravariant form. However we know by transformation properties an... | Most of the answers posted here are incorrect. The Wikipedia page for the gradient says
The gradient of $f$ is defined as the unique vector field whose dot product with any vector $v$ at each point $x$ is the directional derivative of $f$ along $v$.
A look at Theodore Frankel's The Geometry of Physics confirms this. ... | {
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Is there a difference between "average acceleration" and centripetal acceleration? Question adapted from Examkrackers MCAT prep book:
A particle moves along a half circle (diameter=$10\text{ m}$) at a constant speed of $1\text{ m/s}$. What is the average acceleration of the particle as it moves from one side of the ha... |
Is there a difference between "average acceleration" and centripetal acceleration?
Yes, in fact they're almost completely unrelated.
The average acceleration is defined as
$$\vec a_\text{avg} = \frac{\Delta\vec v}{\Delta t}$$
It is one quantity that partially describes the motion of a particle over an extended time. ... | {
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Wrong calculation of work done on a spring, how is it wrong? So I would have thought that this would be how you derive the work on a spring: basically the same way you do with gravity and other contexts, use $$W=\vec{F}\cdot \vec{x}.$$ If you displace a spring by $x$, then it exerts a force $-k x$, so $F=-kx$, since th... | The factor $\frac{1}{2}$ is due to the integral.
The wrong sign of yours is due to the fact that you have to counter the force of the spring.
So the Force if the Spring is $-kx$, but you have to pull in the direction it is extended, so apply the force $kx$, therefore the energy is positive $W=\frac 1 2 k^2 x$
| {
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In what sense is a quantum field an infinite set of harmonic oscillators? In what sense is a quantum field an infinite set of harmonic oscillators, one at each space-time point?
When is it useful to think of a quantum field this way?
The book I'm reading now, QFT by Klauber, claims its not true, which is it?
I would li... | For a free theory, say for one scalar field for simplicity, which gives a a linear differential equation for the field $\phi$, one can cast the Hamiltonian
$$
H=\frac{1}{2}\int d^3x \dot\phi^2+(\partial_i \phi)^2+ m^2\phi^2
$$
in this form (basically by taking a Fourier Transform):
$$
H=\mathrm{const}+\int \frac{d^3 ... | {
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Why does blowing on hot coffee cool it down? And will it cool off faster if you blow across the top of the cup or directly into the coffee?
Does it have to do with the fact that when you blow across the top of the cup the velocity of the air increases which causes an area of low pressure above the cup, resulting in st... | When we blow air it's temp is about 98.5°F the cup of coffee also heat when more heat a given to coffee its evaporation rate increases and gets cool down quickly
| {
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Distance from redshift I am looking for a exact derivation of a relation between redshift $z$ and distance $d$.
What I know is the definition
$$z=\frac{\lambda_{\text{observed}}}{\lambda_{\text{unshifted}}}-1=\sqrt{\frac{1+\frac{v}{c}}{1-\frac{v}{c}}}-1$$
and that the Hubble constant $H$ as a function of $z$ is:
$$H^2=... | Depending on the shape of the universe the luminosity distance is given by :
\begin{equation}
d_L(z) = \left\{ \begin{array}{rl}
\frac{(1 + z) c}{H_0 \sqrt{|\Omega_k|}} \sin \left[ \sqrt{|\Omega_k|} \int _0 ^z \frac{dz'}{H(z')/H_0} \right] & \mbox{for $k = 1$} \\
\frac{(1 + z) c}{H_0} \int _0 ^z \frac{dz'}{H(z'... | {
"language": "en",
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What will be the effect of placing a light source very close to a photodiode? What will be the effect of placing a photodiode really close to a laser source and what should be the appropriate distance between a light source and photodiode to get maximum output current?
| I assume that the laser is emitting a wavelength that the photodiode is sensitive to. If the laser has too much power, you would burn out the semiconductor. Since a laser is a collimate light source, the power lose is minimal for any distance unless there is fog.
What type of photodiode do you have? Some are like trans... | {
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Correlation in electron gas In the textbooks that I read (namely Ashcroft/Mermin , Marder, etc.) it seems that a distinction is made between the correlations in electron gas and a Couloumb interaction between the electrons. What is exactly meant by the concept of correlations? How is that connected to the interactions ... | It would be useful to have the exact reference in the text where "correlation" is mentioned, but I would argue that correlation is a word which characterizes the collective behavior of electrons in certain circumstances. Such circumstances are varied, but imply that their behavior (and that may be spatial dynamics, but... | {
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Why do bubbles make a sound? I have an understanding of how bubbles work. They encapsulate air (or other fluids) in a membrane caused by surface tension.
When they pop, there is often a sound. Sound is a type of energy, kinetic to be precise, that usually occurs from collisions. When a bubble pops I would assume that ... | Cavitation is the formation of bubbles in a liquid when a sufficiently strong negative pressure is applied. A point in the liquid experiences a “negative pressure” if the local pressure goes below the average pressure in the liquid. This can happen when water in a pipe has a very abrupt turn, near the propellers of shi... | {
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Is a falling, perfect sheet of fluid possible to create? This is a bit of an abstract question so I'll try explain this as best I can from the bottom up.
I would like to know if it is possible to observe a sheet of fluid, much like a sheet of glass, falling completely flat and level.
Imagine a volume of water that is a... | EDIT: replaced "fluid" with "liquid", thanks to Kyle.
I am not aware of any material with a liquid phase in near-vacuum. Probably, the liquid would evaporate and maybe a part of it freezes solid due to evaporation cooling.
EDIT: NeuroFuzzy pointed to a youtube video containing an ionic liquid, which is able to retain l... | {
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Pool in a submarine A common theme in aquatic science fiction is the submarine pool/access to the ocean. That terrible TV show Seaquest had it, The Deep & Deep Blue Sea (Samuel L Jackson is standing in front of it when the shark chomps him). My question is how this could possibly work? From what little knowledge I have... |
The implications are that you'd have to pass through an airlock to get to the room, and that it would only work to a certain depth.
Correct x 2.
You have 2 choices with an underwater habitat - build it really strong to take the pressure, or just pressurize it and you can make the whole thing out of plastic.
Submarine... | {
"language": "en",
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} |
Which ball touches the ground first? This is a very well known problem, but I can't find an answer in the specific case I'm looking for.
Let's consider two balls :
*
*Ball 1 weighs 10 kg
*Ball 2 weighs 1 kg
*Balls have identical volumes (so Ball 1 is much more dense)
*Balls have identical shapes (perfect spheres)... | I am not satisfied with the way @Bernhard answered, since it just shows the maximum velocity, thus only answering partially the question.
The air resistance can be written as :
$$
R = \frac{1}{2}\,C_x\, \rho\, S\, v^2
$$
Note : The mass of the object is not in this equation. This is very important.
Applying Newton's la... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/127791",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "40",
"answer_count": 6,
"answer_id": 2
} |
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