Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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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 Special Relativity Theory says that the moving clock is slower. It results from the the transformation equation for time that shows time dilatation:
$$\Delta t' = \Delta t \gamma$$
where $\Delta t'$ is time measured in a reference frame considered stationary, and $\Delta t$ is measured in a reference frame consider... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/118968",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "15",
"answer_count": 7,
"answer_id": 4
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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?
| A window air conditioner is a small piece of equipment with relatively small heat capacity. But with heaters it depends, if it is electric it barely has much capacity and the room will feel quickly very cold once it is turned off. If your heater is steam radiator or forced water then it will take a long time for those ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/119115",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 4,
"answer_id": 1
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A pretty dumb question on observation Very often I have seen, that a bicyclist can balance himself better, while in motion, than he can while at rest(with his legs on the paddles of the bicycle).
Now, I know that objects, say, a disc with uniform mass-distribution, when thrown in space horizontally, rotating about an ... | This is not a dumb question: millions if not billions of people have been taught, incorrectly, that a bicycle's stability originates in the gyroscopic angular momentum of the spinning wheels. This is false, and among other things, would make it near-impossible to turn a bike if it were true.
In fact, a bike's stabili... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/119292",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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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 ... | We don't know if ∞ is the actual age of the Universe or its size. If we presume it is, we have to assume too that Time dilation itself was ∞ (and we wouldn't be here). But we can assume →∞ for each, e.g. a hyperbolic "history" & "size" of the Universe, which make age & size, for all intents & purposes, ∞-1.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/119441",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 4,
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How does separation of tracks affect the acceleration of a rolling ball on the tracks? If I have two metal rods arranged like a ramp with coefficient of friction $\mu$, at an angle $\theta$ to the ground, and a solid metal ball or radius $r$ and mass $m$ rolling down between the two tracks in such a way that it touches... | The separation of the rods does affect the acceleration even for constant separation, because (assuming a rolling motion) the relative amount of energy that goes into linear and angular motion is affected by the spacing.
If the rolling is assumed to be without slipping, we can solve the problem by conservation of energ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/119576",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Can you calculate unix timestamps (universal clock) from any planet? Given the definition of unix timestamp as the number of seconds elapsed since January 1st, 1970 as GMT+0, without leap seconds, is it possible to create a universal clock that will generate the correct timestamp?
Is the current definition of a second ... | Yes it is certainly possible to construct a universal clock.
If you are at rest with respect to the average matter in the universe (basically this means being at rest with respect to the cosmic microwave background), and not in a gravitational field, then you are a comoving observer. Every comoving observer will agree ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/119708",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Curl of an electromagnetic wave I can't understand the concept of the curl of an electromagnetic wave.
$$
\nabla \times E = -\frac{\partial \textbf{B}}{\partial t}
$$
All of the examples I find show a current through a conductor, or that paddle wheel in water which I fail to see the distinction of that with an E-M wav... | Generally, the curl of a vector field $\vec{v}$ in $\mathbb{R}^3$ is given by,
$$\nabla \times \vec{v}= \left(
\begin{matrix}
\partial_y v_z -\partial_z v_y \\
\partial_z v_x - \partial_x v_z \\
\partial_x v_y -\partial_y v_x
\end{matrix}
\right)$$
which may be viewed mathematically as simply the cross product of the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/119776",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
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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 ... | Let's assume $P_2$ is in $(0,0)$ at $t=0$. $P_1$ is in $(x_0,0)$ at t=0. (So A-P1 represents the x-axis)
The evolution of $P_2$'s position is given by $\vec{r}_{p2}(t) = u_2\cdot t\cdot(\cos(\theta),\sin(\theta))$ which you can easily get from decomposing.
The evolution of $P_1$'s position is given by $\vec{r}_{p1}(t)... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/119932",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Proving one field equation leads to the other Assume that the universe is homogenous and isotropic, and the following equation holds:
\begin{equation}R_{00}-\frac{1}{2}g_{00}R=8\pi GT_{00}; \space \space \nabla_{\mu}T^{\mu 0}=0.\end{equation}
How do I prove that the following equations are identically satisfied provid... | First what we know: $G_{\mu \nu} = R_{\mu \nu} - \frac{1}{2}g_{\mu \nu} R$ and $T_{\mu \nu}$ are tensors in that they transform properly under coordinate transformations ($G_{\mu \nu}$ by construction and $T_{\mu \nu}$ because of the EFEs), so it doesn't matter which frame we do our measurements in, this tensor equatio... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/120055",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 2,
"answer_id": 1
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Is the Earth round? Imagine you are a common man and want to prove that the Earth is Round, how would you prove it without any mathematical derivation or without the theory of the ships.
| To prove that the Earth is round, look at sunset on clear days. The sky is bright after the Sun has gone below the horizon. If there are some clouds these are still lit by the sun and cast crisp shadows. If the Earth were flat, the sky and clouds would get dark at the same time and any shadows would grow more and more ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/120123",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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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... | In a battery or a cell the concentration of electron in negative terminal is high and when wires a connected electrons flow from negative to positive. As you asked that why free electrons do not get attracted towards positive terminal, this is because if electrons gets attracted towards positive terminal the conductor... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/121195",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 4,
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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... | The d is not separation between points in reciprocal lattice. Actually, they do not even have the same units. d is the separation between lattice planes, as you said. What is related to reciprocal lattice vectors is the change (before and after scattering) in the wave vector of light: change in k = reciprocal lattice v... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/121261",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 4,
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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... | In both cases the potential energy for two interacting unit charges is
$$
U = -\alpha\frac{\hbar c}{r}
$$
The strong force is between color charges and has $\alpha \approx 1$, while the electric interaction is between electric charges and has $\alpha \approx 1/137$.
However the gluons, which carry the color force, are... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/121387",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
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What happens if the earth stops rotating? I was wondering what would happen to all the components on the surface of the Earth if the Earth suddenly stops rotating but does not stop revolving.
| Another effect depends on what you consider the Earth. If you only mean the core, mantle, and crust, the atmosphere and organic objects (and things made by said organic objects) would still have angular momentum. If the Earth suddenly stops, most of us would be at least flung to the ground, and would probably slide a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/121476",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Is it possible to have a perfectly black material? After reading this NASA article about the "blackest material", the following stuck out to me.
The tiny gaps between the tubes absorb 99.5 percent of the light that hits them
Is it possible to create a material that absorbs, not just all visible light, but all electro... | I believe user43495's answer to be quite accurate, and right, but I will add something here just as food for thought.
It has been hypothesised that the LHC could create miniature black holes. Even if it can't, there are many in space[citation needed]. These would be able to "absorb" all kinds of electromagnetic radiati... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/121536",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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What is the exact relation between a real oscillating body's time period with time? I took an empty bottle and placed it on the floor, then tilted the bottle to one side such that the the displacement caused a disturbance in its balance but not enough to completely tilt it over. The bottle started oscillating back and ... | No, you're not missing the obvious: this is a good question. The simple harmonic oscillator shoved down your throat in freshman physics and engineering courses is a linear system: any solution scaled by a scale factor is also a solution. So the period cannot depend on amplitude. The basic equation defining this beast i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/121616",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
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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?
| The neodymium magnet (Nd$_2$Fe$_{14}$B) has a tetragonal crystal structure with the $c$ axis much longer than the $a$ and $b$ axes. I did google for an image of the unit cell but couldn't find a nice one - you may have more luck. Anyhow, the crystal can be magnetised in any direction, but it is much more easily magneti... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/121744",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
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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... | After reading this article, which states that Olympic beach volleyball sand is specially engineered to not stick to people, I have to assume it is a property of the sand itself and not the shoes or the person (for the most part).
Generally speaking, wet sand will stick to dry objects and dry sand will stick to wet obj... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/121974",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "21",
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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 how to measure stellar aberration:
*
*Take a telescope and point it straight up. Attach it to something massive and steady, like a chimney stack. Let the scope act like a pendulum. It's fixed at the top, and moves at the bottom. The plane in which it swings is the local meridian. That is, it only swings north... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/122339",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
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Entropy as a state property The usual "proof" entropy is a state property is like that:
"Consider a system which undergoes a reversible process from state 1 to state 2 along path A, and let cycle be completed along path B, which is also reversible. Since the cycle is reversible we can write:
$$\int_1^2 \delta Q / T + ... | The usual argument is a proof of the existence of a function whose differential is $\delta Q/T$. The argument usually proceeds as follows:
Fact. (Physics) $\int_\gamma \frac{\delta Q}{T} = 0$ for any closed path $\gamma$ in thermodynamic state space.
Once you have this fact, you can prove that
Claim 1. $\delta Q/T$... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/122412",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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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... | Small-value inductors and capacitors are possible, but you also need extremely small size else the lumped system approximation your equation relies on becomes invalid. Let's say the wavelength of the light to produce is 700 nm. A distance of half that (350 nm) will cause an inversion (180° phase change). Generally, ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/122474",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "16",
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Figuring out the time period of an Atwood system
SO I was working on Atwoods, when I came up with the following problem, It is more complicated but i should understand this simpler scenario first.
As shown in the diagram above, (Atwood machine), mass $m_{2}$, is held up by a a small angle $a$,and released so I figured... | I'm quite confused about your calculation. E.g. I think $a=\theta$. However, to solve this problem, the proper Langrangian is:
$L=T-V=\frac12 m_1 \dot{r}^2+\frac12m_2(\dot{r}^2+r^2\dot{\theta}^2)-gr(m_1-m_2\cos(\theta))) $
You can find the e.o.m. by solving the Euler-Lagrange eqns.:
$0=\frac{\partial}{\partial t}\frac... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/122667",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Explosive energy in a container What happens when the explosive energy of a grenade or a bomb is contained in a container, if you will, and no energy can be released through the container in the form of heat or sound etc...? Just theoretically asking?
I just want to know what happens when we take a huge explosion or an... | The final state would be hot, high pressure gases inside, if it is a sealed container.
Examples of gases would be nitrogen and carbon dioxide, but depend upon the explosive material.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/122727",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Is any one compact dimension for one particle the same as for another particle? In the 3+1 dimensions of everyday life and GR particles can share the same extended dimensions. Probably all particles share the same 3+1 dimensions.
In string theory compact dimensions seem to be limited to each individual particle. Is the... | Let me try to rephrase what you're asking. Suppose we have the usual spatial dimensions $x$, $y$ and $z$, and a compact spatial dimension $w$. Then can we have two particles simultaneously at positions:
$$ P_1 = (x, y, z, w) $$
and
$$ P_2 = (x, y, z, w + \delta w) $$
In other words the particles are at exactly the same... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/122784",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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If magnets exert greater force on heavier objects, why is it possible to separate magnets from very heavy objects? I was thinking of the question "Do magnets exert more force on heavier (more massive) objects?"
I would think the answer is "yes", because for example if you have a magnet and 2 paperclips, they will both ... | I think the proximity of the molecules to the magnet create the force. So if you have a plate 1 sq. ft by 1/4" thick or 1 sq. ft by 2" think the additiona;l mass of the 2" piece doe add force but because the additional mass is further away from the magnet the additional magnetic force may be less that the force of g... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/122888",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
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Why does a wall act as a low-pass filter? Learning about the fourier transform and its connection to filtering/convolution got me curious about naturally occurring filters.
Why/how is it that brick walls naturally act as a low-pass filter (which requires something as seemingly complicated as convolution with the sinc ... | Any type of force waveform f(t) applied to the wall surface can be represented by the sum (integral if f(t) is not a periodic function) of sinusoidal vibration forces with different frequencies. Sound waves also cause physical forces on this air-wall boundary. This force creates the transmitted sound waves inside the w... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/123184",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
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If a window in a plane cabin breaks will a bunch of water vapor form? If a plane has some windows broken mid-flight (ie open) will the plane suddenly be full of water vapor because of the difference of pressure?
| Water vapor is invisible. I think you mean fog - fine water droplets condensed from water vapor.
Pressurized planes fly with an 8000 foot equivalent altitude and humidity in the cabin is low. But, at 35,000 feet (called Flight Level 35) it is likely one would get a brief fog. If loss of pressure is fast, you would onl... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/123270",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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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... | What makes you think an electron reflects photons as you have drawn?
*
*Electrons scatter photons in any direction, although not uniformly. (Examples: Thomson scattering, Rayleigh scattering, X-ray crystallography)
*The electron may absorb the photon for an arbitrary period of time, changing momentum and thus pos... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/123783",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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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 interference between all the rays emitted from the aperture to a fixed point on the screen can be constructive or destructive, depending on the various path lengths involved (measured in wavelengths). If you change wavelengths, the path lengths (measured in wavelengths) change. What is constructive interference bet... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/125903",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "51",
"answer_count": 9,
"answer_id": 6
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Geodesics in $\text{AdS}_3$ I'm having some trouble doing an easy computation with the $\text{AdS}$ space. I'm considering $\text{AdS}_3$ space with the Poincaré coordinates, so the metric reads
$$ds^2 = \frac{R^2}{z^2}(dz^2 - dt^2 + dx^2).$$
I want to compute the geodesics for a $t=\text{const.}$ slice, in order to ob... | The affine geodesic equation (GE)
$$ {d^2 x^{\mu} \over d\lambda^2} + \Gamma^{\mu}_{\alpha\beta} {dx^{\alpha} \over d\lambda} {dx^{\beta} \over d\lambda} ~=~ 0\tag{1}$$
depends on the parametrization: The affine GE (1) holds when the parameter $\lambda$ is affinely related to the arc length $s=a\lambda+b$ of the geodes... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/126031",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
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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... | You can assume either electric or magnetic field for simplicity, they both are present in light as it's electromagnetic wave.
Now, mode is a sustainable pattern in the fiber optic cable. Imagine waves on a string, only the integral multiples of half wavelengths effectively form a mode.
Let there be a complex output ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/126102",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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If empty space has energy, and space is expanding, is this energy equally distributed as space expands? The cosmological constant (dark energy) is often described in terms of empty space having a non 0 energy value and this energy being the source of the accelerated expansion of the universe. If space is expanding, wha... | Dark energy due to a cosmological constant does not get diluted by metric expansion of space. However, this does not violate energy conservation as the increase in energy will be cancelled by gravitational potential energy. The problem with general relativity is (some would say arguably) not energy conservation, but en... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/126151",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 3,
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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... | A South Easterly wind comes from the South East your diagram seems to show a North Easterly wind. As the ship is steaming into the wind the apparent velocity should be greater than the true velocity.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/126268",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
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Interpretation of dispersion relation In my research, I found that my system has the following dispersion relation:
$$\omega^2=k^2+k_0^2\ , $$
where $k_0^{-1}$ is an intrinsic lengthscale of the system and the units are chosen so that the wave speed is unity. This is what it's looks like (blue curve):
So for short wav... | I start my answer with the the second question (similar situations).
This is eerily similar to the free-particle dispersion relation (or the relativistic energy-momentum relation) in natural units ($c = 1$ and $\hbar = 1$),
$$\omega^2 = k^2 + m_0^2$$
This system of units is commonly adopted in particle physics and quan... | {
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Thermal expansion coefficient times temperature: under which condition is it unity? In Landau's Fluid Mechanics p. 8 (2nd edition) he writes for the thermal expansion coefficient $\beta = (1/V) (\partial V/\partial T)_P$:
For a column of gas in equilibrium which can be taken as a thermodynamically
perfect gas, $\bet... | Start with an ideal gas,
$$
V=\frac{nRT}p
$$
Then take the natural logarithm of this:
$$
\ln V=\ln T+\ln\frac{nR}{p}
$$
The derivative of both sides with respect to $T$ gives
$$
\frac{d\ln V}{dT}=\frac{d\ln T}{dT}+\frac{d\ln\frac{nR}{p}}{dT}=\frac{d\ln T}{dT}=\frac{1}{T}
$$
where we assume an isobaric situation so that... | {
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Is Coulomb's law accurate for moving charges? Can we use Coulomb's law to calculate the force between two charges which are not at rest? If not, what formula should be used to calculate the force? I searched it, but I couldn't find a clear answer.
| Lorentz's force is acting on the charge $$F = q(E+v\times B)$$
If the charge is moving in an uniform electric field $E$, there will be no $B$ and the force is $F = qE$. In the case of a non-uniform electric field (e.g. a point charge), the electric field at the charge will change in time and thus, by the Ampere's law, ... | {
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"source": "stackexchange",
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Superposition principle If $S=(v_{1},v_{2}......v_{n})$ is a basis for vector Space V, then every vector v in V can be expressed in the form of $v=c_{1}v_{1}+.......c_{n}v_{n}$ in an unique way.
Explain the significance of this result in Quantum Mechanics.
The answer to the first one is easy as its proof is based on Li... | So the result is that for any given vector v in V and for any given set $S = (v_1,v_2...)$ of basis states, there is a unique way of writing v in terms of the set S. The vector v is commonly used to represent a quantum state. The square amplitudes of the $v_i$ in v represent the probability of seeing $v_i$ when you do ... | {
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When is this integral zero? I have a particle with total energy $E$ confined in a potential
$$U(x) = -\frac{\cos^4x}{2} - m \cos x - f \sin x. $$
The constants $f$ and $m$ are both in the range (-2,2). The energy is such that the particle is in a bound state, with turning points $x_1$ and $x_2$ on either side of the or... | Differentiating the whole integral with respect to $f$ shows that it is strictly monotone decreasing in $f$ for $x_1<x_2$. Therefore $f=0$ is the only solution.
$$\frac{d}{df}\int_{x_1}^{x_2} \frac{\sin x dx}{\sqrt{E - U(x)}}=-\frac{1}{2}\int_{x_1}^{x_2} \frac{\sin^2 x dx}{\sqrt{E - U(x)}^3}<0$$
| {
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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... | I'll offer a simple explanation that relies only on the slope.
Suppose we have a line with slope 5, so for every 5 units up there corresponds one unit to the right. Now let us dilate the y axis by 3, that is, the spaces between each increment of 1 is now 3 times larger. In order for our slope to be invariant (equal 5),... | {
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Why is low resistance beneficial to ion exchange membranes? http://scitation.aip.org/content/aip/journal/jcp/139/11/10.1063/1.4821161
The article states that the graphene filter has a much lower electrical resistance than existing ion exchange membranes, giving the graphene an advantage. Why is having a low electrical ... | Ion-exchange membranes used in electrodialysis are used to separate a saline solution into a low concentration diluate and high concentration concentrate. The voltage that this salinity gradient generates needs to be overcome by an external power source, and the continual flow of inflowing water means that you consiste... | {
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Mathematica package for supergravity and string theory I am looking for a Mathematica package that can manipulate tensors for supergravity, string theory or M-theory. I am particularly looking for a package that can do spinor and Clifford algebra computations. Also, I would like this package to be able to do wedge and ... | As part of the sympy computer algebra system there are geometric (clifford) algebra modules. The latest can be found in my fork of sympy at
https://github.com/brombo/sympy
Their is a latex doc in the repository at sympy/doc/src/modules/galgebra/pdf/GA.pdf
Various examples are in sympy/examples/galgebra (especially look... | {
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what is this force that is able to surpass an entire planet's force on it? I have a wet teabag in an empty cup. If I will hold the teabag and touch the wall of cup with it, it will stick to the cup, like there would be glue or some magnetic field, but there's just water.
So, why does it happens? Why can just a little ... | Besides the adhesive force of water it might be good old friction, caused by the air pressure. As you mention the bag is wet. A vacuum could be created between the wall of the cup and the bag, causing the air to push the bag tight to the wall. This in turn causes a friction force between the wall and the bag.
| {
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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... | Actually the force which you are applying is not constant.
Let the force be $f$ and displacement be $d$, then when you draw a graph according to Hooke law (I.e. force is directly proportional to deflection, where $k$ (stiffness) is constant, it will look like a square, in that at any point you can find the amount of fo... | {
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Basis in quantum mechanics My quantum mechanics textbook (Primer of Quantum Mechanics, by Marvin Chester) says that both the momentum space and the position space are basis spaces. It also says that the momentum space is quantized while the position space is a continuum. I have two questions:
*
*Is the fact that the... | Answer to question one : The Principle of Quantum Mechanics by R. Shankar page 149 reads "Barring a few exceptions, the schrodinger equation is always solved in a particular basis. Although all basis are equal mathematically, some are more equal that others. First of all, since H = H(X,P) the X and P basis recommend ... | {
"language": "en",
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Does Mohs scale of mineral hardness always hold? According to Wikipedia's article on the Mohs scale of mineral hardness, materials / minerals with a higher rating cannot be "visibly" scratched by materials with a lower rating.
It goes on to admit that microscopic dislocations on the harder material do emerge though by ... | To add to the replies above, you must remember that hardness tests (like Vickers or Rockwell) measure the ability of a material to resist permanent (plastic) deformation. So in practice, you take a very hard material, like diamond, and use it to indent a range of other materials. You usually don't want the indenter and... | {
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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... | Boiling point is defined as the temperature at which the vapor pressure directly above the liquid is the same as the pressure of the environment. So, when boiling water in a room at 1 atm, it will begin to boil when the vapor pressure on the surface of the water reaches 1 atm (which is at 100 degrees Celsius). That is ... | {
"language": "en",
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Does a permanent magnet loose its magnetism? The question is slightly deceiving however still simple for those academics therefore, here I present my question:
If I take a para-magnetic material and put it very close to a homogeneous magnetic field, the para magnetic material will start to accelerate towards the magnet... | In a homogeneous field, the paramagnetic material does not move - why should it?
An acceleration towards permanent magnets just happens as their field is not homogeneous. You (partially) align the magnets in the paramagnetic material with the magnetic field and bring them closer together, this releases energy.
If you w... | {
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Strength of strong nuclear force vs distance? Is there at least an approximation of the decrease in strong nuclear attraction vs distance from the center of the nucleus?
| You should read the article in wikipedia on nuclear force.
Various models exist that describe the behavior of nuclear forces, which are the result of a spill over of the strong force, the force that exists within the proton and the neutron.
From the link
Force (in units of 10,000 N) between two nucleons that experie... | {
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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 ... | According to my limited understanding of density functional theory. Coulomb interaction is one of the correlation effects. Besides Coulomb interaction, there are interaction due to Pauli exclusion principle and change of kinetic energy compared with that of non-interacting electron gas.
| {
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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 ... | The surface formed by the bubble is such that its energy is minimized. Since increasing the interface between a liquid and air increases its energy due to surface tension, the bubble tends to reduce its radius, which implies that the pressure inside it must be higher than the pressure outside, and following this reason... | {
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Given eigenvalues of $\vec l^2$ and $\vec s^2$, calculate the eigenvalue for $\vec j^2$ There was an exam question that read approximatly:
Let $\vec j = \vec l + \vec s$. Given eigenvalues of $\vec l^2$ and $\vec s^2$, calculate the eigenvalue for $\vec j^2$.
We came up with
$$\vec j^2 = (\vec l + \vec s)^2 = \vec l... | In the special case where $\ell^2$ or $s^2$ has eigenvalue zero, then $j^2$ is fixed. Otherwise you must know the projections $m_\ell,m_s$ to find $j$.
| {
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what is the static pressure in a yield stress fluid? Suppose I have a tank filled and there is no slip at the walls. If the tank is filled with a Newtonian fluid and is in static equilibrium, we know that the pressure is defined as $p = \rho g z$.
But what if the tank is filled with a yield stress fluid. For example, t... | Below the yield stress your fluid is behaving like an elastic solid. Imagine putting your tank in zero g, so there are no forces, and then removing the base. The result would look like the left hand figure in the diagram below:
Now turn on gravity, or apply an external force and the result will be the middle diagram. ... | {
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Why do I hear the telephone ring through grandpa’s hearing aid before the actual phone rings? I was sitting next to my grandpa (Tato), who wears a hearing aid, on the couch. I’ve noticed that when the landline telephone rings I actually hear the phone ring through his hearing aid (less than one second) before I actuall... | Caller ID is sent after the first ring. Ironically, even though phone companies sequenced things that way to avoid delaying the first ring, some phones want to avoid bothering people until after the caller ID information is received or would be expected (if the caller hangs up or someone answers the phone before the c... | {
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How was Newton able to guess that gravitational force is inversely proportional to distance squared? This question is puzzling me since I learnt about the gravitation law in school. Why did Newton guess/assume that gravitational force is inversely proportional to the square of distance?
Did he verify that experimentall... | An inverse square law for gravity was already being considered in several places prior to Newton taking it up, and Newton was probably at least partly inspired to consider it by Hooke and Halley (exactly to what extent would be the subject of one of Newton's several priority disputes).
The basic reason for choosing an ... | {
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Finding particles in the classically forbidden regions Have particles ever been found in the classically forbidden regions of potentials?
For example, in a square well: has an experiment been able to find an electron outside the rectangular well (i.e. in the exponential fall-off regions) ?
And more importantly, has any... | There are numerous applications of quantum tunnelling. A few that pop in my mind right now are:
Radioactive decay:
Particles tunnel out of the nucleus of which they are bounded by a potential. Classically this is forbidden as the nucleus is very strongly being held together by strong nuclear forces.
Scanning tunneling ... | {
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Is there a substance that doesn't reflect OR absorb light from the visible light spectrum? Is there a substance that doesn't reflect or absorb visible light but may reflect light from another spectrum? Is there a theoretical substance that would have these properties?
EDIT:
Sorry I wasn't quite clear with my original q... | Yes, to the approximate extent allowed in the real world.
The condition that the material doesn't reflect visible light means that the material looks black. So consider various black coatings, for example, and ask what they do with electromagnetic waves at different frequencies than visible light.
Of course that you fi... | {
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How was the definition and the formula of work derived? Is it the best possible? Work done is defined as the dot product of force and displacement.
However, intuitively, should it not be the product of force and the time for which the body is acted upon by the force (force * time) because while time is independent of ... | If you spend ages pushing against a brick wall, it won't budge, and you haven't actually done any mechanical work; the wall has the same energy at the end. But do the same to a car (take the handbrake off first!), and you'll get it moving: the force you are applying is giving the car motion, and hence kinetic energy. I... | {
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Fringe Pattern Brightness for Young's Double-slit experiment Perhaps I have missed something in my notes, but I have noticed when looking at different sources that some textbooks/sites state that the fringe brightness for the young's experiment is the same for all the bright fringes. Others, say that the brightness "fa... | I'm sorry for the (extremely) delayed response, but the other answer fails to answer the question.
The reason for the intensity falling off with distance is mainly because of the slit width itself. Because of this width, the individual Fraunhoffer diffraction pattern is superimposed in the final observed pattern.
If th... | {
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Does Free Will Theorem imply that quantum mechanics plays crucial role in our brain’s functioning (consciousness)?
*
*Does Free Will Theorem imply that quantum mechanics plays crucial role in our brain’s functioning (consciousness)?
*Is opposite statement of Free Will Theorem right: If elementary particles have a ce... | The Free will theorem of Conway and Kochen is simply an unfortunately titled theorem that, just like Bell's theorem, rules out a certain kind of hidden variable theory, i.e. shows that measurement results cannot be ultimately determined (if it is not somehow determined what measurement will be made, that's the "free wi... | {
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What is the relation between photoelectric current and frequency of incident light? I googled it a bit and found that photoelectric current is independent of frequency(of incident light). Some further look revealed that actually "saturation current" is independent of frequency.I could not find about the instantaneous c... | Since we know that photoelectric current depends on the number of electrons emitted per second i.e. Intensity of incident light. But the intensity of light does not depends on frequency of incident light. Hence, we can conclude that :
The photoelectric current does not depends on frequency.
OR
increase in ... | {
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Can Minkowski spacetime be redefined as a non-flat riemannian manifold? Minkowski space time is defined in terms of a flat pseudo-Riemannian manifold. I have wondered if it can be redefined as Riamannian manifold and in the case what type of curvature would there appear.
Formally:
Let M be a semi-Riemannian manifold of... | We interpret OP's question (v3) as essentially asking
Can a Lorentzian manifold (with Minkowski signature) by coordinate transformations be redefined as a Riemannian manifold (with Euclidean signature)?
The answer is No since the metric signature of a pseudo-Riemannian manifold is invariant under general coordinate ... | {
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Normal modes of the 2D double pendulum I'm performing an experiment with a 2D double pendulum, and in part of it I want to investigate the normal modes of the double pendulum, where the pendula are not of equal length or of equal mass. My question is - how will I actually know when I've successfully excited a normal mo... | For a double pendulum there should be two normal modes. It sounds like you have done the analysis to determine the frequencies and mode shapes. If so, every motion will be of the form $x(t) =A \cos (\omega_1 t+\phi_1)+B \cos (\omega_2 t+\phi_2)$. If you fit the data to this form, you are in a normal mode if $A$ or $... | {
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Neil deGrasse Tyson says that electrons "teleport" between energy levels? This page:
https://blog.afach.de/?p=62
Discusses the error Neil deGrasse Tyson made when talking about electronic transitions (video included there). Tyson clearly said in his Cosmos series that electrons disappear from one level and appear in th... | Your questions reminds me of the movie "a serious men" by the Coen brothers (you should watch it regardless of the main character being a college physics professor). As some of the comments said, it is an oversimplification or a much more complex phenomenon. The only way to get some idea of what is happening is to unde... | {
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How does the movement of electrons produce radio waves? I'm mostly wondering about radio frequencies. I understand that voltage is the movement of electrons, and that the antenna acts as a light bulb, emitting at radio frequencies, following the reverse square law, some materials are opaque, some are transparent. Yet,... | Noorism philosophy of universe interprets this phenomena as one example to conversion of '' vacuum energy in to EM energy '' that is vacuum energy and EM are inter-convertible.An accelerating or decelerating electrons causes the fluctuation in the vacuum where C N F space time field is present. Charge and spin of elec... | {
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Is there inductance to a DC circuit? When a DC circuit is carrying current, large amounts or small, is there induced-emf due to the inductance? Or is it only applied to AC circuits?
| Yes, inductance exist in a DC circuit. The problem here is the similarity between the words inductance and induction. Inductance is not about change. In fact, inductance is measured in Henrys, which is a Weber per Ampere. Hence, there is no change. In contrast, induction is about change and does not exist is a DC ... | {
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What is $c + (-c)$? If object A is moving at velocity $v$ (normalized so that $c=1$) relative to a ground observer emits object B at velocity $w$ relative to A, the velocity of B relative to the ground observer is
$$ v \oplus w = \frac{v+w}{1+vw} $$
As expected, $v \oplus 1 = 1$, as "nothing can go faster than light"... | Physically, SR can't accomodate observers moving at $c$.
Mathematically, the limit is undefined. You have a function $f(v,w)$ defined in the $v-w$ plane, which has a square boundary. You're talking about approaching a corner of the square, but the value of the limit would depend on what path you chose to approach the c... | {
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How does exciting an electron's surrounding electromagnetic field cause 'electron excitation'? In more meaningful words than the ones above, how does adding energy to the EM field cause the electron to to change orbitals or oscillate in a different pattern.
| In the semi-classical approach you treat the electromagnetic field of the incoming light as a (sinusoidal, with angular frequency $\omega$) perturbation $H^{\prime}$ in the Hamiltonian of the atom. The wavefunction of the atom can be expressed in terms of a linear combination of its eigenstates, each with a multiplying... | {
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Potential Energy Concept Imagine a book that we lift it with a force that is exactly equal to the force of gravity so the forces cancel out and the book moves with a constant velocity.
Consider the situation after the book has been lifted, and it has come to rest once again. According to the work and kinetic energy la... | Let's say the book starts and stops from rest, as I believe you are assuming. The motion within this interval is unimportant, as you'll see.
The increase in gravitational potential energy of the Earth-book system came from your body. You did positive work on the system since your hand force and displacement are in the ... | {
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The Dirac-delta function as an initial state for the quantum free particle I want to ask if it is reasonable that I use the Dirac-Delta function as an initial state ($\Psi (x,0) $) for the free particle wavefunction and interpret it such that I say that the particle is exactly at x=0 during time t=0? If I use this init... |
I want to ask if it is reasonable that I use the Dirac-Delta function as an intial state ($\psi(x,0)$) for the free particle wavefunction and interpret it such that I say that the particle is exactly at $x=0$ during time $t=0$?
No, because the delta function is not compliant with the Born interpretation of the functi... | {
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Does a 4-current J determine a unique maxwell-faraday F tensor up to isometry? Maxwell's equations on a pseudo-Riemannian manifold $(M,g_{ab})$ say,
$$d_a F_{bc} = \nabla_{[a}F_{bc]} = 0,$$
$$\nabla_a F^{ab} = J^b,$$
where $d_a$ is the exterior derivative, $\nabla_a$ is the covariant derivative compatible with $g_{ab}$... | No, you also need an initial condition for the field, and a boundary condition for the field. A plane wave solution to the Maxwell equations has the same 4-current as vacuum, after all.
| {
"language": "en",
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Can "vacuum be brought" from outer space? Instead of creating vacuum in chambers on earth, why can't vacuum be brought from outer space in chambers? Outer space pressure ranges from $10^{-6}$torr to $10^{-17}$torr very very low. Is it possible at all?
| Never mind cost in dollars, it costs more in energy. Assume you had perfectly efficient pumps. To create a vacuum you have to push the air out of your chamber, if we assume we want $1 \text{ L}$ of vacuum, this takes
$$ W = PV = (1 \text{ atm}) (1 \text{ L}) = 10^9 \text{ erg} $$
of work.
But if you want to get your... | {
"language": "en",
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Crystal Momentum in a Periodic Potential I'm working through some basic theory on periodic potentials, and I would appreciate help in understanding the crystal momentum. Suppose we have a Bravais lattice with lattice vectors $\textbf{R}$. There is an associated reciprocal lattice with lattice vectors $\textbf{K}$ such ... | (1) Since $u(\textbf{r}) = u(\textbf{r}+\textbf{R})$, we can expand this part in terms of reciprocal lattice vectors, $u_k(\textbf{r}) = \sum_\textbf{G}{e^{i\textbf{G}\cdot \textbf{r}}u_\textbf{k-G}}$. We can therefore write:
\begin{equation}
\psi_{\textbf k+\textbf K} = e^{i(\textbf k + \textbf K)\cdot \textbf r}\sum_... | {
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Spectral series' formula of a given atom (other than hydrogen-like)? The hydrogen spectral series is given by the Rydberg formula:
The energy differences between levels in the Bohr model, and hence the
wavelengths of emitted/absorbed photons, is given by the Rydberg
formula:
$${1 \over \lambda} = R \left( {1 \ove... | There are, in general, no closed form solutions (aka formulas) for the spectra of multi-electron atoms. There are reasonably precise formulas for special cases, like approximate values of x-ray transitions from inner shell electrons, though. Unlike in case of hydrogen and Rydberg atoms, which can be treated as a non-re... | {
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How to differentiate between rotating frame and linearly accelerating frame? Two friends, $A$ and $B$ are part of an experiment. $A$ is placed in a closed box and made to accelerate in free space at an acceleration $g$. $B$ is also placed in a closed box, but is made to rotate in a circle at uniform speed, such that th... | The friend rotating and experiencing the centrifugal force may observe several effects that his linearly accelerating friend doesn't:
*
*the acceleration at different points of the box is slightly different i.e. the apparent gravitational field is non-uniform
*there is the extra Coriolis force acting on objects tha... | {
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Distance along projectile motion I was doing kinematics these days, projectile motion. And I did the basic concepts: range, max height, time of flight, projectile on inclined plane. I am curious to know how we would solve a question if it asks us to find the distance not range traveled by the particle undergoing projec... | For any curve in two dimensions described by a position $(x(t), y(t))$ as a function of time, the speed of such a curve at a time $t$ is
\begin{align}
|\mathbf v(t)| = \sqrt{\dot x(t)^2 + \dot y(t)^2}
\end{align}
where overdots here mean derivatives with respect to time $t$. To find the total distance traveled along... | {
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How can gravity affect light? I understand that a black hole bends the fabric of space time to a point that no object can escape.
I understand that light travels in a straight line along spacetime unless distorted by gravity. If spacetime is being curved by gravity then light should follow that bend in spacetime.
In N... | I think what the OP was missing is the principle of the equivalence between mass and energy, as well as the fact that light rays do bend even in a vacuum, and even if that bending shows a curvature so subtle that it remains far beyond our perception without magnification equipment.
As pointed out by Viktor Toth at ht... | {
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How to calculate explicit form of stress energy tensor in any situation? I know that the components of stress energy tensor are: energy density, energy flux, momentum density and momentum flux.
But can I explicitly calculate the form of stress energy tensor in any complicated situation?
Or explicit form is known only ... | Because the Hamiltonian – the total energy – determines the evolution of all dynamical degrees of freedom, via the Hamilton equations, and because all the other components of the stress-energy tensor are related to the energy density by Lorentz transformations, it follows that knowing the precise formula for the stress... | {
"language": "en",
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Thermal superconductivity I have heard several times of the concept of "thermal superconductivity" (As opposed to "electrical superconductivity"), but I am unclear on exactly what that could mean. It turns out to be really hard to google, since everything comes up with thermal effects on electrical superconductivity (c... | This is a very interesting question. In fact liquid helium-4 exhibits this property of "thermal superconductivity". What happens is that when one tries to establish a thermal gradient a "temperature wave", also referred to as second sound, propagates. This gives it effectively an infinite thermal conductivity or as you... | {
"language": "en",
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"source": "stackexchange",
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What exactly are crystal planes and how do they reflect x-rays?
*
*What exactly are crystal planes and how do they reflect x-rays?
*Are crystal planes real physical planes or just an abstract concept?
*What are these planes made of?
*If they are an abstraction, what do the x-rays hit and get reflected by? Indivi... |
*
*In the image above, you can see a series of Bragg planes drawn in the crystal. This is called one "set of planes". Another "set of planes" would be if one would just draw a series of horizontal lines through the atoms. (Of course by lines I mean planes, but they are projected here onto a 2D image).
*The planes ... | {
"language": "en",
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Will the Universe eventually stop expanding Sorry if this is a naive question, not being even a part qualified physicist in any way shape or form.
I've read that the universe is expanding and the rate of expansion is increasing. The assumption being that it will continue expanding indefinitely.
However isn't there anot... | The ball, in fact, is always accelerating downward, even though it is moving up for the first part of its trip. A ball that kept accelerating upward would just fly up out of the atmosphere.
| {
"language": "en",
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"source": "stackexchange",
"question_score": "5",
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Hooke's Law: why is only one force considered? I have a question about Hooke's Law springs.
What I learned is that a Hooke's Law spring gives a force F pushing left and right and each force equals $k \cdot |l-l_o|$
Let's say there is a mass block resting on a spring on a table. The amount of force on the mass block by... | Consider just the spring, without worrying what the ends of the spring are connected to:
If I'm stretching the spring then I'll be applying a force $F$ to one end. But assuming the spring isn't moving, the net force on the spring must be zero. That means there must be a balancing force of $-F$ on the other end so that... | {
"language": "en",
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How does dark matter collapse?: Entropy considerations Inspired by this question.
I believe that the usual explanation that preserves the second law of thermodynamics as an astrophysical gas cloud collapses under gravity is that the gas must heat and radiate, and while the entropy of the collapsed gas may be lower than... | Dark matter does not radiate photons by definition, but as I said in the comment to CuriousOne, dark matter may not have electromagnetic radiations to first order, but it does have gravitational radiation. The current Big Bang model accepts an effective gravitational interaction and thus the existence of gravitons, i.e... | {
"language": "en",
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"source": "stackexchange",
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How is the integrand concluded to be identically zero? In expanding the classical Klein-Gordon field in Fourier space to write it in terms of $\phi(\mathbf{p})$ instead of $\phi(\mathbf{x})$, I reached the following result.
$$\int \mathrm{d}^3p\exp({i\mathbf{p}\cdot\mathbf{x}})\left[\frac{\partial^2}{\partial \mathrm{... | Your first equation can be compared to (in one dimension)
$$
g(x)=\int dp\exp(ipx)f(p)=0 \,\,\, (*)
$$
Note that this is a statement applies to all x-values. The inverse fourier transform of $g(x)$ should give $f(p)$,
$$
f(p)=\frac{1}{2\pi}\int dx\exp(-ipx)g(x)
$$
As $g(x)=0$ according to to $(*)$ then $f(p)=0$.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is there a difference in handwritten nabla $\vec{\nabla}$ with an overset arrow and typeset nabla $\nabla$? According to some physicist at KIT it is usual to write the following when using pen and paper:
whereas in typeset texts you write $\nabla$.
Is that true? Are there sources for this convention?
| *
*Yes, there are sometime different conventions for indicating vectors in hand-writing and printing.
*Yes, overset arrows in handwriting and boldface in printing is one of those conventions.
*No, it is not the only convention.
*Yes, you should familiarize yourself with the most common conventions in your sub-dis... | {
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Amplification of magnetic field can we by any means amplify magnetic signal as we can with electric signal. As both electric and magnetic field can be represented in the form of a wave the analogy seems to be natural.
I want the input and output as magnetic signal.
| There are several ways to amplify the magnetic field, though the mechanism is not same as for electrical signal amplification, but still they are fruitful.
compression:- since a magnetic flux through a surface remains conserved, if we compress the field lines or stretch (or fold) the field line then we can increase th... | {
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What makes us move in time? Time is considered to be a dimension, and we are moving at certain rate in one direction in time. What force makes us move in time? I mean it must be ether time moving or us moving in time so there has to be some force that 'pushes'/'pulls'? Was this 'time inertia' acquired during big bang, ... | What makes heat move from hot to cold? Entropy. How can you calculate entropy microscopically? Start counting states!
What makes the universe change irreversibly from yesterday to tomorrow? Start counting states!
| {
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"source": "stackexchange",
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Using bra-ket notation? Am I using Bra-ket notation correctly? I want to define a superposition of the states, $|0\rangle$ and $|1\rangle$. Is it simply?
$|0\rangle + |1\rangle$
I can't find any non-technical information on it. I'm just a hobbyist.
| Close, but not quite. Since quantum mechanics deals in probabilities, it is necessary to "normalize" the state in order to use it in later calculations. The most general state for the two-state quantum system you're considering would be
\begin{equation}
|\psi\rangle = \alpha\,|0\rangle+\beta\,|1\rangle
\end{equation}... | {
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why are the square of the components of velocity equal? In Principles of Physics by Resnick,Halliday,Walker, when evaluating the $v_{rms}$ ,they first found $p = \frac{nM(v_x)^2}{V}$ & then substiuted $(v_{avg})^2 = \frac{1}{3} .v^2$ where $v^2 = (v_x)^2 + (v_y)^2 + (v_z)^2 $ saying that there are many molecules and al... | In essence, there is no reason why the gas should have more speed in one direction than in the other. So, we can say that the speed in each component is the same.
So, $v(x)=v(y)=v(z).$ Using the Pythagorean Theorem,
$v^2(xy)=v^2(x)+v^2(y),$ where $v(xy)$ is the speed in the $xy$ plane.
Using the Pythagorean theorem aga... | {
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How can I calculate the force that is applied on a tube by another tube? Let's say there is two tubes(cylinders with no tops or bottoms) with charges $q_1$ and $q_2$, radii $b_1$ and $b_2$, lengths $l_1$ and $l_2$. These tubes are located along the axis of each other's surfaces like in this figure:
If the electric fie... | This can be done in five steps (four integrals).
*
*Start with the force of two point charges: you know this equation
$$F=\frac{Q_1Q_2}{4\pi\epsilon_0 r^2}$$
*Integrate this force over an infinitesimally thin ring of charge: now you have the force of a ring on an off-axis point (hint: you only need the axial compo... | {
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Why isn't jumping against a wall an elastic collision? According to this calculator http://www.abecedarical.com/javascript/script_collision1d.html when low mass object hits high mass object it is reflected gaining opposite velocity almost the same as initial velocity.
If I jump onto the wall why my body is not reflect... | An elastic collision is defined as one which conserves energy. When you jump against a wall, most of your kinetic energy is dissipated as heat into your tissue as your legs and muscles absorb the impact. Therefore, energy is not conserved so by definition this is an inelastic collision.
| {
"language": "en",
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Conservation of momentum and energy in an explosion One simple problem is physics is to determine the mechanical energy difference after an explosion. To do this, you must assume that momentum is conserved because in a explosion you have internal forces, so, using Newton's third law, you get that the total momentum is ... | Before explosion the bomb is at rest. Its total momentum is zero. As it explodes, it breaks into many parts of masses $m_1,m_2,m_3$ etc which fly of in different directions with velocities $v_1,v_2, v_3$ etc. these diff parts have different momenta $m_1v_1,m_2v_2, m_3v_3$,etc. For eg,-
If the bomb explodes in two part... | {
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Does car tire pressure change with weight of car load? Does tire pressure measured by a meter on tire gauge change with load? (I am not interested in pressure produced by car tires onto the road).
Car spec usually says "inflate to 220kPa normal load, 300kPa full load". Does this mean the measured pressure should be 300... | layman, It takes more PSI to suspend a heavier load with equal square inches. Or the same PSI with more square inches. Rubber tires will mostly just flex to give more square inches. Foot print of tires x psi = weight of car
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/132892",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "42",
"answer_count": 12,
"answer_id": 11
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Who does work while walking? While walking, the work done by friction is zero.
But who does the work, actually? How someone is getting displaced?
This situation also arises when someone climbs without slipping or is climbing a ladder.
| You push the earth back and the earth pushes you forward by static frictional force.
Net work done by static friction is always 0 on the system consisting of your feet and the ground.
The kinetic energy that you gain while walking or running comes from the internal energy of your muscles.
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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"answer_id": 6
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Ice and liquid water interacting across a boundary Imagine we have two thermodynamic systems, one a mass of ice and the other an equal mass of liquid water, with both at 273.16K. Each system is isolated, except that they can interact with each other across a boundary that permits the exchange of heat but not matter or ... | Erik, nothing will happen (as you already know!).
Water and ice are in equilibrium at the triple point. No heat can flow at constant temperature. The water and ice have the same free energy per mole, so no spontaneous change can occur, and the total entropy cannot rise as a consequence of heat transfer.
It is much ... | {
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"source": "stackexchange",
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What is the difference between induced current and eddy current? I was reading today about electromagnetic induction and eddy currents. But while reading I was unable to differentiate between induced current and eddy current.
What is the difference?
| Eddy currents are induced circular currents in conductors exposed to an AC magnetic field. The term is often used for induced currents that cause unwanted heating and losses in conductors, e.g. in transformers and electrical machines. On the other hand, they are also being put to good use in eddy current brakes and ind... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Potential difference between point on surface and point on axis of uniformly charged cylinder Question:
Charge is uniformly distributed with charge density $ρ$ inside a very long cylinder of radius $R$.
Find the potential difference between the surface and the axis of the cylinder.
Express your answer in terms of the v... | All the above answers are correct, although none gives you an answer as to WHY you should NOT use a sphere and none addresses your "infinite gaussian surface" problem and you seem to be a bit confused on how things actually work (you have to understand how things work before you delve into the mathematics part).
So, ... | {
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"source": "stackexchange",
"question_score": "3",
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How are heat transfer rate and heat capacity constant of a material related? How are heat transfer rate and heat capacity of a given material is related?
When I was a kid I imagined it like "Capacity is like a container or bucket of some sort, if it gets filled easily it can give away heat easily. Metaphorically overfl... | Heat transfer rate is $dQ/dt$ where Q is heat and t is time.
Specific heat has to do with "how much heat do I need to raise the temperature of this object" (dependent on mass too). Water has a high specific heat since it requires a lot to raise the temperature of a given mass of water. Iron has a low specific heat sinc... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Why photon has a wave nature? Wave theory does not account for the photon model, which was developed only to explain quantum effects like photoelectric effect.
Then why do we talk about a photon's reflection and rarefaction, as that would require it to have wave properties? This has been mentioned here: (http://en.m.w... | You have really figured out the answer yourself. On one hand, you have a natural phenomenon (light) and on the other you have our models (wave description, photon description).
When speaking of the reflection of rarefaction of photons, the author implicitly assumes the reader to know about the wave-particle duality (se... | {
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Graph Theory and Feynman Integrals In Vladimir A. Smirnov's book Analytic Tools for Feynman Integrals, Section 2.3, the alpha representation of general Feynman integral takes the form
$$
F_{\Gamma}(q_1,\ldots,q_n;d) = \frac{i^{-a-h}\pi^{2h}}{\prod_l\Gamma(a_l)}
\int_0^{\infty}\mathrm{d}\alpha_1 \ldots \int_0^{\infty}... | What you need is Kirchhoff's Matrix-Tree Theorem which expresses ${\rm det}\ A$ as a sum of trees. You can find an easy "Fermionic" proof of this theorem and a list of original references in my article "The Grassmann-Berezin calculus and theorems of the matrix-tree type"
(arXiv version here if you do not have access t... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 1,
"answer_id": 0
} |
How can there be a voltage when there is no current? I'm told at school that the Electromotive Force (e.m.f) of a battery equals the potential difference between the terminals of the battery when there is no current.
How is that possible? How can there be a potential difference with no charge flowing?
| The analogy of electricity to flowing water may come in handy here. In this analogy, a potential difference is like a difference in height. One lake on top of a mountain and another in a valley, for example, might represent the two terminals of the battery, which are at different potentials. If you think about that si... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/133862",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 4,
"answer_id": 0
} |
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