Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Do photons experience every moment in time and position in space simultaneously? Would it be more correct to say that a photon, traveling at the speed of light, would experience all points in time simultaneously, and therefore be everywhere at once? It might be just our perception that seems to portray them as moving?... | A photon traveling at speed of light has a lightlike worldline. It has one place of emission and one place of absorption. The spacetime interval between both points is empty (=0), that means that no spacetime is between them. That means, if a photon would experience something, it would experience both points as simulta... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/200918",
"timestamp": "2023-03-29T00:00:00",
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What type of matrices do we mean by $I_{D2}$ and what is Chandrasekhar decomposition? Suppose that $A_{2\times 2}$ is a hermitian matrix, so it has real eigenvalues $\lambda_1$ and $\lambda_2$ and corresponding orthonormal eigenvectors $\underline u_1$ and $\underline u_2$ and we know it can be written as the sum of tw... | From the general properties of 2x2 matrices, if ${\underline u}_1$, ${\underline u}_2$ are the eigenvectors of $A_{2x2}$, then
$$
{\underline u}_1 {\underline u}^{*T}_1 + {\underline u}_2 {\underline u}^{*T}_2 = I_{2x2}
$$
As for the Chandrasekhar decomposition, perhaps the explanation on pgs.269-271 in "Direct and In... | {
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What is the time period of an oscillator with varying spring constant? It is well known that the time period of a harmonic oscillator when mass $m$ and spring constant $k$ are constant is $T=2\pi\sqrt{m/k}$.
However, I would be interested to know what the time period is if $k$ is not constant. I have searched hours af... | To obtain some kind of practical answer, you have to determine how k varies. For example, if k varies with temperature, I would determine its value at -50, 0, and 50 degrees, then use those values and calculate T (which varies inversely as the square root of k). I would Use more points if a higher accuracy is require... | {
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A heavy rope is attached to one end of a lightweight rope
If one end of a heavy rope is attached to one end of a lightweight rope, a wave can move from the heavy rope into the lighter one.
(a) What happens to the speed of the wave?
(b) What happens to the frequency?
(c) What happens to the wavelength?
My instructor... |
here is an animated version of image
for more in formation refer to http://www.physicsclassroom.com/class/waves/Lesson-3/Boundary-Behavior
and a good tool for playing with
https://phet.colorado.edu/sims/html/wave-on-a-string/latest/wave-on-a-string_en.html
| {
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"timestamp": "2023-03-29T00:00:00",
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Why does a moving fan seem transparent? We all know when fan starts moving faster, we cannot see its blades. Why is this?
First I assumed persistence of vision may be the reason. But that can happen with blade also right? Image of blade can remain in our memory and moving fan can appears as a circular plane with blade... | The eyes are measuring the number of photons of each color that are hitting a given point of the retina – that are coming from some direction.
This is a function of time, $f(t)$, for each point. However, when this function is changing too quickly, the eye can't see the changes. Effectively, the eye may also see the ave... | {
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"url": "https://physics.stackexchange.com/questions/201504",
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The Thomson scattering optical depth for a photon ar radius r I am looking to understand some more about the physics of gamma ray bursts. In particular I am looking at the origin of the "prompt emission". Some of the energy associated with this prompt emission is thought to come from the photosphere of the expanding fi... | The origin of this equation is reasonably well explained in Abramowicz (1991).
If you take a relativistically expanding enevelope and only consider Thomson scattering, then as the electron scattering cross-section in the co-moving frame $\sigma_T$ is independent of frequency, then the mean free path of a photon in the ... | {
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The pressure in a container of water is based on depth. So what happens if I remove the bottom of the container? So I understand that if we have a system that involves a container of water the pressure will equal atmospheric pressure at the top and as we go further down the container the pressure will increase with dep... | Take a 1-cm square tube and place it vertically in the container from top to bottom, touching the bottom so that the bottom of the container is the bottom of the tube.
The pressure at the bottom of the tube is nothing but the weight of water it is supporting - the water in the tube.
Supporting means to keep from fallin... | {
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Peskin eqn 7.2 contradiction They state $$\langle\Omega|\phi(x)|\lambda_{\bf p}\rangle=\langle\Omega|e^{iP\cdot x}\phi(0)e^{-iP\cdot x}|\lambda_{\bf p}\rangle \tag{7.4}$$
where $|\lambda_{\bf p}\rangle$ is a state of momentum ${\bf p}$. They then rewrite this as
$$\langle\Omega|\phi(0)|\lambda_{\bf p}\rangle e^{-ip\cdo... | Perhaps I am overlooking the real problem here, but isn't it clear that by doing
$$
H\rightarrow H+E_0
$$
both the vacuum and the one particle state energies get shifted by the same amount
$$
H|\Omega\rangle = E_0\,,\qquad H|p\rangle =E_0+E_p
$$
so that $E_0$ Actually cancels out
$$
\langle\Omega|\phi(x)|p\rangle=e^{i... | {
"language": "en",
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Does sound show wave-particle duality? We know that light and electrons both show wave-particle duality. Or in other words we can say that they can be both seen as a wave and a particle. Can a similar theory be applicable for sound? Can sound also be explained as a particle as well as a wave?
| The notion you should look up and learn about is the phonon. It is a quasiparticle that arises in the quantum description of acoustics in condensed matter. The description is simplest and clearest in regular lattices of atoms / quantum particles, so it doesn't work so well for sound in a gas. But phonons can be thought... | {
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Directional subwoofer? I was thinking. The subwoofers that I've seen are a circular parabolic surface section (or perhaps a circular circlic(?) surface section?) and are considered omni directional.
I would guess that this is because the longitudinal waves would have to move through the focus of the parabola/circula... | Audio speakers are, in general, not particularly directional. That is to say, the sound emitted from the speaker spreads out in all directions. With the exception of ultrasound frequencies, it is impossible to 'beam' sound energy along a narrow path with a speaker of practical dimensions.
This is due to the relative si... | {
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Can we reconstruct 1D potentials in QM from the spectrum? Knowing the potential, we can find the spectrum of the Schrödinger operator. The converse question is: Knowing the spectrum, can we reconstruct the potential? As an example, a harmonic potential has an equally spaced spectrum. But is the converse true?
This is,... | The answer is no, I am afraid. As you may well know, the self-adjoint Laplace operator $-\Delta$ on $L^2(\mathbb{R})$ has purely absolutely continuous spectrum $\mathbb{R}^+$.
Now let $V\in L^{\infty}(\mathbb{R},\mathbb{R}^+)$ be an arbitrary bounded positive function. Then $-\Delta_x +V(x)$, where $V$ acts as a multip... | {
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Why array of telescope is used? To increase the resolution of an instrument, smaller wavelength and larger aperture is desirable. It is mentioned in some textbooks that the "effective" diameter of a telescope can be increased by using arrays of smaller telescopes. I just wonder why it is possible because every telescop... | Picture yourself looking into a large mirror on the wall. Now picture the mirror is made up of smaller, tiled mirrors. You will still see your reflection. If you begin to remove the tiles, so that there are only a few left, you can still use them to reconstruct the image of your face that was given by the original m... | {
"language": "en",
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Creating nanosecond pulses from a CW laser source Experimental setup question.
If anyone aware of a technique to create pulses of several nanoseconds at a around 10Hz repetition rate from a CW laser source?
| You could use an electro-optic modulator. These don't need kV supplies, can have very fast rise/fall times, and can be fully programmable by using a digital delay generator (these can also be triggered optically for extremely good accuracy, preventing timing drift between the delay generator and whatever source you're ... | {
"language": "en",
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Nucleon-meson interaction Suppose interaction lagrangian between neutron-proton doublet and $\pi$-mesons:
$$
\tag 1 L_{\pi pn} = \bar{\Psi}\pi_{a}\tau_{a}(A\gamma_{5} + B)\Psi , \quad \Psi = \begin{pmatrix} p \\ n\end{pmatrix}
$$
Is it possible to derive it from the first principles? I realize that proton and neutron a... | This interaction cannot be derived from QCD. It is also not quite correct.
1) QCD conserves parity (for $\theta=0$), and the pion field is a pseudoscalar, so $B$ must be zero.
2) The pion is an (approximate) Goldstone boson, so it is derivatively coupled
$$
{\cal L}=\frac{g}{f_\pi}\bar\psi\tau^a\gamma_5\gamma_\mu\parti... | {
"language": "en",
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Is the electrostatic field really static? Does thermal vibrations not affect it? We know that if a conductor has any net charge, the charges reside on the surface. The electric field immediately outside the surface is perpendicular to the surface. But the charged particles, say the conductor has net electrons, will be ... | Yes, these thermally generated currents (Johnson noise) generate magnetic fields. This means that even non-magnetic materials generate a very-small magnetic noise if they are conductive. This actually places a limit on very-sensitive magnetic field measurements in shielded environments because the shields are usually c... | {
"language": "en",
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Fringe width and spacing and number of slits in diffraction experiments In a single slit experiment, the fringes are not equally spaced and aren’t of equal widths—the central maximum is the widest, the secondary maxima grow narrower and narrower outward, and the minima grow wider and wider outward.
In a double slit in... | When you pay attention to the left or right area of your double slit experiment you will see at the end the typical intensity distribution of a single slit. So a multi-slit arrangement is nothing all as the sum of two single slits. Of course the intensity distribution depends from the distance between the two slits. Ar... | {
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What's the difference between semiconductor and insulator (besides band gap)? The typical classification of electronic materials is metal-semiconductor-insulator. Is there any actual difference between a semiconductor and an insulator, besides the size of the bandgap?
| Basically they are the same from a physics point of view, if you only look at crystalline materials. A semiconductor is defined to be insulating at $ 0 K $, while conducting at room temperature, although I don't recall, what level of conductivity is required to count as semiconductor.
Technically, insulators are a more... | {
"language": "en",
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Is potential energy frame dependent in special relativity? In newtonian mechanics, As far as I'm aware, only kinetic energy is dependent on frames of reference, since kinetic energy is a function of velocity(squared) and velocity is dependent on frames of reference, therefore kinetic energy is frame dependent.
In newto... | Yes potentials are frame dependent. Let us take the electric and magnetic fields as an example. The electric field can be written as:
$$\vec E=-\frac{1}{c} \frac{\partial \vec A}{\partial t}- \nabla \phi $$
Where $\vec A$ is a vector potential and $\phi$ a scalar potential. Like wise, the magnetic field can be writte... | {
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Find constant acceleration with only initial speed and distance Given the problem:
"A car moving initially at 50 mi/h begins decelerating at a constant rate 60 ft short of a stoplight. If the car comes to a stop right at the light, what is the magnitude of its acceleration?"
While this problem seems simple, I can't see... | The total distance traveled during the constant acceleration is 60 feet. Over the course of 60 feet the velocity has to go from 50mph to 0mph. That means the average velocity is 25mph. So, what amount of time going 25mph is equal to 60 feet? Then take that time and divide the change in velocity by it to arrive at the a... | {
"language": "en",
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Rockets and distance I am trying to create an equation which allows for me to change the aspects of the rocket so i can calculate the distance traveled vertically. My idea is for a rocket that only moves vertically; with this i can calculate the amount of time it would take to make it past the first Lagrange point. ... | You've almost got it!
The constant thrust comes from a mass rate $\mu$ of fuel being expelled at a velocity $v_f$ as opposed to the speed of the rocket itself $v$. Therefore the equation is instead:
$$ (m_0 - \mu t) \frac{dv}{dt} = \mu v_f - \alpha \frac {(m_0 - \mu t)}{r^2},$$
where $\alpha = G M.$ Hence the gravitati... | {
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What's the difference between the work function and ionisation energy? In a particular textbook, the work function of a metal (in the context of the photoelectric effect) is defined as:
the minimum amount of energy necessary to remove a free electron from the surface of the metal
This sounds similar to ionisation ene... | On first reading they do sound similiar, but they are entirely independent energies and concepts.
The work function of a metal refers to the minimum energy required to release an electron from the surface of a metal by a photon of light. The work function will vary from metal to metal. You might have a read of these... | {
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When does the concept of electric field in classical electrodynamics fail, and QED is needed? It is really hard to find reference to when the traditional concept of electric wave, especially TEM wave, fails, and needs to be replaced by quantum electrodynamics.
So when does the concept fail? At high frequencies of elec... | It fails when the photon number is small. Since the electromagnetic field can never be zero because of the third law of thermodynamics this automatically couples the temperature, the effective volume and the photon number to each other. As a result it is experimentally impossible to do experiments with single photons a... | {
"language": "en",
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Problem imagining how does a black hole merger look like from far away Suppose we have two black holes moving on a path of direct frontal collision. Is it correct that from far away, due to time dilation, we can never "detect" that the two black holes merging or colliding? Would we perceive the relative motion of the t... | Luckily black holes emit Hawking radiation, so in some sense we can see them.
So first there are two glowing balls approaching each other, after some time there will be one glowing ball that is twice as large as one of the initial glowing balls. (I'm considering black holes of same size)
And during the collision the ba... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/205606",
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"source": "stackexchange",
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Searching for a textbook on Imaging I'm hoping someone can recommend a book that will cover the physics involved in optical range image capture. I have a degree in physics, so I am looking for something on the technical end. To expand, I would like the book to cover the chemistry of how images are recorded on film and... | I think a good recommendation for a book that covers the physics involved in imaging is (regarding my Astrophysics background) 'Observational Astrophysics' by Pierre Lena, Daniel Rouan, Francois Lerund, Francois Mignard and Didier Pelat. Another recommendation, more basic, is 'Optics' by Eugen Hecht. Furhtermore, there... | {
"language": "en",
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Help me understand Gauss law Suppose I have the following, the gaussian surface is the drawing in the middle. So charge enclosed is zero, and then eletric field must be zero since the area of the gaussian surface is not zero. But, clearly the eletric field is not zero in the middle, because if you put a charge there it... | Gauss law says that the total flux going through a closed surface is equal to the charge inside the surface. You can think of flux as the number of field lines going in (or out) through the surface.
In your example there is no charge inside the sphere so the total flux through the surface of the sphere is zero. On one ... | {
"language": "en",
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Question Regarding torricelli's theorem/Law I recently studied about bernoulli's equation/principle.
After the derivation of the said equation , my book gave some applications of the principle, which include torricelli's theorem/law.
In deriving torricelli's law from bernoulli's principle, the pressure at the opening ... | I agree with don_Gunner94's answer.
If the fluid come out from the constricted passage to atmosphere,it will experience atmospheric pressure,which is same as the pressure acting at top of the container.
Even according to Bernoulli's principle,
Static pressure + Dynamic Pressure = Constant
Therefore, the pressure acting... | {
"language": "en",
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What is the difference between flow and expansion? Fluids (both liquids and gases) will move from one point in space to another due to a potential gradient. Some examples may be:
1) horizontal pipe flow, a fluid will move from a region of high pressure to a region of low pressure.
2) inclined open channel flow, a flui... | *
*A gas can expand by filling more volume than before. Like a balloon in a pressure chamber where the pressure is suddenly lowered. No net motion (no flow) happens here.
*A water stream can flow continously without simultaneous expansion. Consider a circular stream that ends where it starts. As a bathtub where ther... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/205947",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why is the K shell electron preferred in the photo electric effect? I have read in many books and on Internet as well that photoelectric effect is only possible when an electron is emitted from the K shell of the metal. Why not other bonded electrons?
| The premise of your question is false. The photoelectric effect will occur whenever radiation interacts with the bounds electrons of an atom.
There is a sharp increase in absorption when the energy of the radiation exceeds the binding energy of a particular "shell". For Rb, for example, the NIST XCOM database shows cle... | {
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What happened here in this Taylor-Couette Flow experiment? I came across this video of Taylor-Couette Flow on YouTube. Originally I was looking for a visualization of the wavy Taylor vortices induced by the angular motion of the inner cylinder.
However, I found something strange (as you can see at the end of the video)... | This is what's happening in the video. I've drawn just a single drop, and for convenience I've ignored the curvature of the plates (it's harder to draw curves!):
It looks as if the (red in this example) ink drop is being mixed with the fluid, but actually it's just being stretched out into a thin sheet. When you turn ... | {
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Infinitesimally change a operator in QM Reading Balian, "From Microphysics to Macrophysics", I've found the following identity:
If we change the operator $\hat{{\mathbf{X}}}$ infinitesimally by $\hat{{\delta\mathbf{X}}}$, the trace of an operator function $f(\hat{{\mathbf{X}}})$ can be differentiated as if $\hat{{\math... | $f(\hat{X})$ usually "means" $\sum a_n \hat{X}^n$. So, big hint: Let $y$ be your infinitesimal and let $\hat{Y}$ be some operator.
\begin{align*}
&\mathrm{Tr}f(\hat{X}+y\hat{Y})-\mathrm{Tr}f(\hat{X})=\\
&\int \langle q| \sum a_n (\hat{X}+y \hat{Y})^n|q\rangle \mathrm{d}q-\int \langle q| \sum a_n \hat{X}|q\rangle \math... | {
"language": "en",
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Fluid speed and fluid density How does fluid density affect fluid speed?
Basically I am trying to figure out if, with all other quantities remaining constant, would an increase in fluid density cause the fluid speed to increase/decrease?
For example, would water and honey have different fluid speeds in a pipe, because ... | You could look at viscosity and its effects for yes, and at some never happened story of a guy dropping something from a tower and concluding something for no.
We're not allowed to give straight answers, so I hope this is vague enough.
| {
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Coffee Straw Physics When I put my little, cylindrical coffee straw into my coffee, the liquid immediately rises about half a centimeter up the straw without provocation. This is also the amount of coffee that the surface tension of the coffee will allow to stay in the straw when removed from the liquid in the cup.
Kee... | Just to extend my comment about Capillary action which is the reason for the liquid rising through the capillary (straw in your case), I show this animation of how the diameter of the capillary (d) effects the height of the liquid (h) that rises above the contact surface.
The relation of $h$ and $d$ used to simulate th... | {
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Invariance of law of conservation of angular momentum under a Galilean transformation Given a reference frame O' moving at a constant speed $\vec{V}$ in relation to another reference frame O, I want to prove that
$\vec{r_{1B}} \times m_1\vec{v_{1B}} + \vec{r_{2B}} \times m_2\vec{v_{2B}} = \vec{r_{1F}} \times m_1\vec{v... | It is true that angular momentum is conserved in all frames, but the actual value of the angular momentum will, in general be different.
If you look at the extra terms you will find that they correspond to the change in the angular momentum of the centre of mass about your chosen origin.
\begin{align}
\mathbf{r}_{CM}\... | {
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"url": "https://physics.stackexchange.com/questions/207185",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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How to determine the acceleration and position as a function of time
An object is losing mass at a rate k in kg/s. The object is acted on by a force F. Determine the acceleration and position as a function of time.
I know the answer for the position function is
$$
x(t) =\left (\dfrac{Fm_0}{k^2}\right)\left[\left(\df... | Recall Newton's 2nd law in the form $F=\frac{dp}{dt}$, where $p$ is momentum, namely $p(t)=m(t) v(t)$. Reformulating the equation gives you $F=\frac{dm}{dt}v+\frac{dv}{dt}m$. Using $m(t)={m}_{0}-kt$ yields the differential equation $$F=-kv+\stackrel{.}{v}\left({m}_{0}-kt\right)$$
Solve the equation to get $v(t)$, integ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/207410",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why can scalars have a sign? I wondered to myself why some scalars have a sign, if they do not have a direction. After all, the plus and minus indicate the direction of the scalar on a one-dimensional axis.
So, for example, why can temperature have a sign? Why can't mass?
| There is case where the definition is not crystal clear:
Chemical reaction rates.
The rate of a chemical reaction, $n R \rightarrow m P$ (where $n$ is number of reactants $R$ changing into $m$ Product $P$ molecules on every event), is given by:
$v = - \frac{1}{n} \frac{d R}{d t}$
Now in theory this should be a scalar, ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Velocity of an Electron as it Passes through a Uniformly Charged Ring I've been presented with a problem in which an electron is placed a certain distance x from the center of a positively charged ring and allowed to move freely. The ring has a known charge density λ. I am tasked with finding the velocity of the electr... | The total energy at the initial point should equal the final energy.
i.e. $$V(x)=V(0)+KE$$ ($x,0$ are along the axis of the ring.)
The potential at a point on the axis of the ring is given by: $$V(x)=\frac{kQ}{\sqrt{R^2+x^2}}$$
From this, we get: $$-\frac{keQ}{\sqrt{R^2+x^2}}=-\frac{keQ}{R}+\frac{1}{2}mv^2$$ From this ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/207727",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Do photons decay as they travel in free space From maxwell's equations, it occurred to me that photons are stable. Decrease in electric field creates magnetic field and vice versa and somehow there is a harmony that allows photon to exist as long as it travels with c. Therefore I wouldn't think photons would decay as t... | No - assuming they don't hit anything they don't decay.
The distance dependant "decay" is the drop in the number of photons per volume as the volume gets bigger - it's not a decay of individual photons. It's the same as a crowd dispersing as it leaves a subway exit - nobody is disappearing.
Photons can lose energy as t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/207919",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How is $ \frac{dv}{ dt} = a $? I know how , in the physical sense -
$$\frac {dv}{dt} = a$$
But, even after thinking a lot, I am not able to see the fault in this -
$$\frac {dv}{dt} = \frac {d(st^{-1})}{dt}
= \frac {sd(t^{-1})}{dt}
= s*(-1)*t^{-2}
= \frac {-s}{t^2}
= \frac {-v}{t}
= -a$$
I know something is ... |
I know how , in the physical sense - $$\frac {dv}{dt} = a$$
But, even after thinking a lot, I am not able to see the fault in this
- $$\frac {dv}{dt} = \frac {d(st^{-1})}{dt} = \frac {sd(t^{-1})}{dt} = s*(-1)*t^{-2} = \frac {-s}{t^2} = \frac
> {-v}{t} = -a$$
I know something is terribly wrong here but I'... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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What is the relation between energy levels of hydrogen atom in Bohr's solution to that of Dirac solution In Dirac solution for hydrogen atom, the energy levels are calculated as positive
\begin{equation}
E=\frac{mc^{2}}{R(t)\sqrt{1+\frac{z^{2}\alpha^{2}}{\left(n+\sqrt{\left(j+\frac{1}{2}\right)^{2}-z^{2}\alpha^{2}}\ri... | The $E$ in your expression is the quantity calculated using the operator $i\hbar\frac{\partial}{\partial t}$, so it is the total energy. As $n \rightarrow \infty$ this energy $E$ goes to the rest energy of the electron $m_ec^2$ as we'd expect. For finite $n$ the energy is lower than $m_ec^2$ with the difference being t... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why does everything written on a page appear in concentric circles when we rotate that page? When i put a pencil in the middle of a paper and rotate it very fast, whatsoever is written on it, will appear in concentric circles. What is the reason behind this phenomenon and what is it called?
| Fast things appear blurry to your eyes, and the distance from a point on the paper to your pencil is fixed. The distance from an ink dot on the paper, to the tip of your pencil where you press down, cannot change. Call this distance $d$. The only positions the point is allowed to be at when you spin the page around, ar... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/208311",
"timestamp": "2023-03-29T00:00:00",
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How can the unstable particles of the standard model be considered particles in their own right if they immediately decay into stable particles? How can the unstable particles of the standard model be considered particles in their own right if they immediately decay into stable particles?
It would appear to a layman su... |
How can the unstable particles of the standard model be considered particles in their own right if they immediately decay into stable particles?
Nobody has an issue calling the electron a particle. Ditto for a neutron. It's stable in a nucleus, and the fact that a free neutron decays in circa 15 minutes doesn't much ... | {
"language": "en",
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"source": "stackexchange",
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Are white noises always Markovian? Are white noises always Markovian? I am a bit confused about it. As white noise always has a constant power spectrum， its auto correlation function must contain a delta function of time. Thus the correlation time of the noise vanishes. But I don't know whether they can be called Marko... | Whether a noise process is truly memoryless is very hard to test. Strictly speaking it's impossible to say that it is memoryless because the memory could be longer than the longest time series we can analyze. In practice a lot of low-entropy pseudo-random generators can make synthetic signals that are physically indist... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/208522",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Temperature of a falling meteor I am reading "What if?" article https://what-if.xkcd.com/20/ and I'm interested in it's scientific background. Mr. Munroe writes:
As it [the meteor] falls, it compresses the air in front of it. When the air is compressed, it heats it up. (This is the same thing that heats up spacecraft ... | The most significant contribution to the heat generation is the the exothermic reaction of iron in the meteorite with atmospheric oxygen and nitrogen. The oxides and nitrates that form at the leading entry surface are not uniform. They will distribute themselves so that there is the greatest possible entropy among them... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/208722",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Clarification about Wave-particle duality Okay,so I am learning about the double slit experiment done with electrons. I saw this picture, which shows the interference pattern being built up slowly with increasing number of electrons:
I just wanted to confirm whether I have the correct understanding. The fact that the... | From the theory of light waves we know that for similiar experiment an interference pattern occurs when light quanta interacts with the system. Now with electrons there is an unique "wave" for that particular experiment that guides those electrons that hit the screen. Initially electrons must have equal speed and direc... | {
"language": "en",
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Why does wavelength determine the energy of a photon? The professor for my first-year university chemistry class remarked that the wavelength of a photon determines its energy. Why is it that the case?
I've only completed high-school physics so far, so please bear that in mind in answering this question.
Thank you.
| Why does the wavelength determine a photon's energy?
In the 19th century, it was thought that the energy of light was determined only by its intensity. Then, experiments, particularly the photoelectric effect, showed that this was not so: a low-intensity short-wavelength light can cause reactions that intense light of... | {
"language": "en",
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Trying to understand lowest configurations of carbon My study group is debating about which are the three lowest configurations of carbon. I've been arguing that the electron has to jump to the 3s level for the configuration to be different. Others have suggested that the two valence electrons just have to change their... | By 'electron configuration' can be understood the way an atom's electrons are arranged in atomic orbitals, in accordance with Pauli's Exclusion Principle, the Aufbau Principle and Hund's Rule, of the lowest possible total energy (known as the Ground State).
For carbon (Z=6), six electron have to be placed in the correc... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Gamma matrices and trace operator I'm trying to show that the trace of the product of the following three Gamma (Dirac) matrices is zero, i.e. $$\text{tr}(\gamma_{\mu} \gamma_{\nu} \gamma_{5})=0 \text{.}$$ I attempted to use the fact that the trace operator is invariant under cyclic permutations and linear, and that $$... | Substitute two values for $\mu$ and $\nu$.
If $\mu=\nu$, then using $(\gamma^\mu)^2 =\pm1$ and $tr(\gamma ^5) =0$ you have finished.
If $\mu \neq\nu$, then use $tr(\gamma ^\mu\gamma ^\nu) =0$ with the two remaining $\gamma$ .
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Definition of a line charge with Dirac delta function Is the following statement correct for a line charge distribution $λ(x)$?
$$ρ(\mathbf r)=λ(x)δ(y)δ(z)$$
If yes - what does it say?
|
$$\rho(\mathbf{r})=\lambda(x)\delta(y)\delta(z)$$
describes a charge density in the form of a (possibly infinite, depends on what your allowed x values are in the system) line in 3D space, where $\lambda(x)$ is the linear charge density as a function of x. The delta functions indicates the charge density is concentrat... | {
"language": "en",
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Why is it easier to drop on to a downslope? On a bicycle, why is it easier to land from a drop or jump on a slope going downwards than landing on a flat surface or on an upslope?
I've already heard answers such as "because that's how a bike can best keep going with all the momentum it's carrying from the drop" but I'm ... | Maybe this will satisfy more:
When you imagine a body (or a bike) think of the velocity vector in space, that vector upon impact will cause a reaction in the direction of the normal vector of the surface you are falling uppon:
As you can see, the upwards reaction from the surface on the velocity vector will be multip... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What has the potential energy: the spring or the body on the spring? Particles have gravitational potential energy due to its position in the gravitational field. We say the particle has potential energy and not the Earth (the body doing the work). Why is it not the same with a spring doing work on a body?
It is my und... | Potential energy like Force occur in pair. If one has some potential energy due to 2nd, 2nd will have the same potential energy as the first. In the Gravitational potential energy equation :
$U = \frac{GMm}{r}$
The potential energy is dependent on both the masses. This value is same regardless whether it is for 1st or ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/210221",
"timestamp": "2023-03-29T00:00:00",
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Why isn't the acceleration at the top point of a ball’s journey zero? When I shoot a ball vertically upward, its velocity is decreasing since there is a downward acceleration of about $9.8\,\mathrm{ms}^{-2}$.
I have read that at the top most point, when $v = 0$, the acceleration is still $9.8\,\mathrm{ms}^{-2}$ in th... | When you shoot the ball upwardly, gravity acts on it with a force $mg$ where $m$ is the mass of the ball and $g=9.81 ms^{-2}$ the Earth's gravitational acceleration.
If the initial upward velocity was $v_0$ then the instantaneous velocity $v$ is given by:
$v=v_0-gt$, so after some time $t=\frac{v_0}{g}$ the balls's vel... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Can tidal forces significantly alter the orbits of satellites? I would assume that there are other larger, more significant, forces acting on artificial satellites, but can tidal forces drastically alter the orbit of a satellite over time?
I was thinking this could especially be an issue for a satellite in geostationa... | No, the movement of water bodies on earth does not significantly influence the orbit of man made satellites. Due to the movement of the water, and the shape of the earth, the center of gravity of the earth shifts slightly. Sometimes this pulls the satellite a bit more to the front, and sometimes a bit more to the back ... | {
"language": "en",
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Contradiction in a simple torque/rotation problem - two ways of calculating external force don't agree Suppose we have a rigid system of two point objects (both of unit mass) connected with a massless rod, with the objects horizontal on the x axis, at a distance $r_1$ and $r_2$ from the origin, respectively. A vertical... | The 2nd solution you wrote down appears to be the correct solution. Offhand, I see two problems in the first solution. First, I think that a problem with the first attempted solution is that you made a subtle mistake in assuming that F=ma means that $F=mr_1α$. That seems like a plausible step at first but if you examin... | {
"language": "en",
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Physical intuition about the inertia tensor I'm studying Mechanics on Goldstein's book (Classical Mechanics) and Spivak's book (Physics for Mathematicians) and I'm in doubt about the physical intuition about the inertia tensor. On both books, the inertia tensor appears naturally when computing the angular momentum $L$ ... | I have also encountered the same problem until recently I understood the meaning behind the indices.
Although there are a lot of definitions of a tensor, we are left to decide which one is palatable for the kind of context we are in.
$I_{xy}$ means how much the 3D object would be accelerated in the $y$ axis when I appl... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/210690",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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Why are there only two linearly independet quartic Higgs terms for the adjoint $24$ in $SU(5)$ GUTs? I've read the statement in countless papers, for example, here Eq. 4.2 or here Eq. 2.1 without any further explanation or reference, that the "most general renormalizable Higgs potential" for an adjoint (=24 dimensiona... | The easiest answer to your question can be gleaned from a nice book by F. Iachello, Lie Algebras and Applications, Lect. Notes Phys. 708 (Springer, Berlin Heidelberg 2006), DOI 10.1007/b11785361 , ISBN-10 3-540-36236-3
SU(5) (~ A4) has rank 4, and thus 4 independent Casimir invariants (your φ transforms like the ad... | {
"language": "en",
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Is there a special name for thermodynamic process during which no work is performed? Let $W$ denote the work done on a system during a thermodynamic process. Is there a commonly-accepted, dedicated term for a process during which $W=0$?
| Not in general, no. In the special case of no volumetric work being done, we call the process isochoric. Volumetric work occurs when there is a change in the volume of the system, whether due to an external agent or due to the system itself. There are plenty of ways, however, that work could be done on a system without... | {
"language": "en",
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Primitive unit cell of fcc When I consider the primitive unit cell of a fcc lattice (red in the image below) the lattice points are only partially part of the primitive unit cell. All in all the primitive unit cell contains only one single lattice point.
My question is how much each point at the corners of the red prim... | The counting of 1/8 (corner) or 1/2 (face) is only relevant to the shared cubic cells. For the primitive cell, all atoms are shared by 8 primitive cells, thus, 8 x 1/8 = 1, which can be seen by the drawing of physicopath.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/210963",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Central force law An object has an orbit in polar coordinates as $r(\theta) = a\theta^2$ (where $a$ is constant).
Assuming the central force is directed towards the origin $r=0$, how can I know which central force law lead to such an orbit? And how to find $r$ and $\theta$ as function of time?
| I don't want to give away the answer directly. So I will provide some hints.
A central force in polar coordinates has to be of the form: $$\vec{F} = m\vec{a} = m(\ddot r - r \dot \theta^2)\hat r$$
Now try to mess around with your $r(\theta) = a\theta^2 $
I believe you need to specify $\dot \theta$ in order to solve the... | {
"language": "en",
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How does color (or reflection in general) work? I'm confused, does the absorption and emission determine the color of something? Or does that only happen when something is emitting energy?
When light hits an object, the photons get absorbed, then emitted with a different wavelength right?
| Not really as in your assumption, if that happens, you can have (for example) either fluorescence or raman. The color you see is determined by the light which is reflected from the object, i.e. by the light which is missing compared to the white light. Each material only reflects certain wavelengths, and absorbs others... | {
"language": "en",
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Why does light bend? I read about the dispersion of light by a prism and a block (slab), but I don't understand why light bends at all.
I know that red light has the longest wavelength and that energy is inversely proportional to wavelength, hence red light contains the least energy. I also know that it bends the least... | To answer this question first you need to understand what prisms are made of, usually glass, that is silica (SiO2).
Now the atomic size of for example an atom inside the prism is 60 pm, that is 0.06 nm.
Now this size is very small compared to visible light photons' wavelength which is about 400-700 nm.
When the photon'... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/211473",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Stability of a system of Brownian particles with non-physical collision A few months ago I wrote this simulation of a system of circles bouncing off each other. It's a two-dimensional box with elastic balls in it that bounce off each other. I came back to it and noticed that I didn't sanitize the input for the "elastic... | Since you programmed the simulation, you should know or otherwise have access to the underlying equations simulating the dynamics of your particle collisions. If this dynamic equation is a linear difference equation, you can transform the equations into the z domain and express the equations as a transfer function. As ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/211974",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What happens to mass during beta decay? Sorry for being ignorant, but I'm in high school and our chemistry teacher barely went over beta decay. I decided to do some research and learned that in β+ decay, positrons are emitted from protons in order to turn it into a neutron. But positrons have mass, so where does that m... | In beta decay, the mass difference between the parent and daughter particles is converted to the kinetic energy of the daughter particles. For instance, in the decay of the free neutron,
$$
\rm n \to p + e^- + \bar\nu_e, \tag{$\beta^-$ decay}
$$
the difference between the mass on the left and the mass on the right is ... | {
"language": "en",
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How proof the Lorentz algebra using the Poincaré algebra?
Show that
$$[J_{i},J_{j}]=i\varepsilon_{ijk}J_{k},\quad [K_{i},K_{j}]=-i\varepsilon_{ijk}J_{k}, \quad [J_{i},K_{j}]=i\varepsilon_{ijk}K_{j},$$
using $$[M_{\mu\nu},M_{\rho\sigma}]=ig_{\nu\rho}M_{\mu\sigma}+ig_{\mu\sigma}M_{\nu\rho}-ig_{\mu\rho}M_{\nu\sigma}... | Just to take one term: letting $\mu = \rho = 0$ and $\nu = i \in \{1,2,3\},\;\sigma = j \in \{1,2,3\}$ we can immediately write$$[M_{0i},M_{0j}] = [K_i, K_j] = i g_{i0} M_{0j} + i g_{0j} M_{i0} - i g_{00} M_{ij} - i g_{ij} M_{00}.$$
Antisymmetry means $M_{00} = 0$ and the fact that $g$ is diagonal [more specifically, $... | {
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For a diatomic molecule, what is the specific heat per mole at constant pressure/volume? At high temperatures, the specific heat at constant volume $\text{C}_{v}$ has three degrees of freedom from rotation, two from translation, and two from vibration.
That means $\text{C}_{v}=\frac{7}{2}\text{R}$ by the Equipartition... | "At high temperatures, the specific heat at constant volume $C_v$ has three degrees of freedom from rotation, two from translation, and two from vibration." I can't understand this line. $C_v$ is a physical quantity not a dynamical system. So how can it have a degrees of freedom?? You can say the degrees of freedom of ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/212986",
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Where does the energy go in a rocket when no work is done? While playing Kerbal Space Program, I wondered where my chemical energy would go when fired at 90° to the motion. It would do no work on the rocket, but all that energy has to go somewhere, right? Anyway, my question is, where does the energy go?
| If a train is moving along the tracks at 60 mph and there's a crosswind at 30 mph the crosswind, in fact, does not do any work on the train. That's because the train's motion is constrained by the rails so that it cannot move in the direction that the wind is pushing it. If you remove the constraint its motion will cha... | {
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Time derivative of Noether charge I understand that the Noether charge can be written as
$$ Q= \int~\mathrm d^3 x ~J^0$$ and the time derivative of the Noether charge is zero $$ \dot Q=0 $$
but how would you explicitly calculate it?
| While Sebastian nailed it in his comment, I'll post the same as a proper answer.
The four-vector current $J^{\mu} = (J^0, J^i) \equiv (J^0, {\vec J})$ obeys the continuity equation
$$\partial_{\mu} J^{\mu} = 0,$$
or in other words:
$$\frac{\partial J^0}{\partial t} + {\vec \nabla}\cdot{\vec J} = 0$$
This represents t... | {
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Gradient, divergence and curl with covariant derivatives I am trying to do exercise 3.2 of Sean Carroll's Spacetime and geometry. I have to calculate the formulas for the gradient, the divergence and the curl of a vector field using covariant derivatives.
The covariant derivative is the ordinary derivative for a scalar... | I made two YouTube videos explaining how to due precisely these problems.
The first one explains how to use standard covariant derivatives (what you are using) to compute the divergence and gradient in spherical coordinates:
https://www.youtube.com/watch?v=jEvPY6-ISUI
And the other explains how to compute the curl in ... | {
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Maintaining symmetry? Minkowski metric is found to be
$$ds^2=-dt^2+dr^2+r^2d\Omega^2$$
where $d\Omega^2$ is the metric on a unit two-sphere.
Why should we keep track of the $d\Omega^2$ so that spherical symmetry holds well?
| See your own question here: Why do people put exponentials there
You can multiply by functions of $r$ on each of the terms. What you cannot generally do is "muck" with the $r^2 d\Omega$ part itself. That's what gives you the part of the distance that corresponds to the angular directions on the sphere. If you change... | {
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Modes inside a cavity and black body radiation Consider a perfect conductor that encloses a spatial volume such as a parallelepiped or cylinder. If we solve Maxwell's equations inside that volume, seeking solutions that depends on time with a dependency of the form $e^{-i\omega t}$, we find that only TE and TM modes ca... | It's true that a hollow conductor has a minimum cutoff frequency.
However, a hollow conductor is not a black body.
A black body has perfect absorption of radiation at all frequencies, while a perfect conductor perfectly reflects all radiation.
A black body emits radiation according to the Planck law.
Since the black bo... | {
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Thermal state vs equibilibrium state Could someone explain what's the difference between a thermal state and an equilibrium state? Or is it even the same?
| Basically there are two types of equilibrium in thermodynamic context :
*
*Thermal equilibrium. It's when in system there are no heat flow :
$$ {\frac {d Q}{d t}}= 0 $$
*Thermodynamic equilibrium. No net flow of matter or energy in a system.
So for example take a look at this diffusion process of dye in a water. In... | {
"language": "en",
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Will this rope break due to the tidal forces or not? While I was thinking about how tidal forces can make objects float at the surface of a planet orbiting a massive object like a black hole, the fact that any material on the Earth isn't held together by gravity only, but also by chemical bonds which give it its tensil... | Between points A and C. The effect of having the Earth there is that it is providing a link between the center of mass of the Earth (C) and the test sphere (A). Effectively, there is an infinitely strong, rigid rod going from B to C, which is then connected to the rope. The tensions in that rod (the Earth) must matc... | {
"language": "en",
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The Speed of Sound Just a question about Physics I'm doing at school.
If the speed of sound is inversely proportional to the density of a material, why does sound travel faster in solids (it is the most dense).
I have read that it takes more energy for sound to travel in dense materials so it takes longer but then neig... | short answer: wave speed (indeed, its square) is the ratio of rigidity and mass. For (most) solids and liquids, as compare to gaz, the point is not that they are denser, but that they are near-incompressible: numerator wins.
| {
"language": "en",
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"source": "stackexchange",
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Killing Vectors in Schwarzschild Metric Given the Schwarzschild metric with $(-,+,+,+)$ signature,
$$\text ds^2=-\left(1-\frac{2M}{r}\right)dt^2+\left(1-\frac{2M}{r}\right)^{-1}dr^2+r^2(d\theta^2+\sin^2\theta\,d\phi^2)$$
the lack of dependence of the metric on $t$ and $\phi$ allow us to read off the Killing vectors $K_... | If all components of the metric are independent of some particular $x^\nu$, then you have the killing vector $\vec{K}$ with components $K^\mu = \delta^\mu_\nu$. That is, the contravariant form just has a constant in the appropriate slot and zeros elsewhere. In Schwarzschild, you have $K^\mu = (1, 0, 0, 0)$ and $R^\mu =... | {
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Why are HCP materials brittle while FCC materials are ductile? Why are hexagonal close packed materials brittle, While face centered cubic is ductile. Is it related to crystal planes?
| please learn a few definitions
Slip plane – is the plane of greatest atomic density.
Slip direction – is the close-packed direction WITHIN the slip plane
Slip system = slip plane and slip direction TOGETHER
THEN;
5 independent slip systems are necessary to make a polycrystalline
material ductile.
HCP - Has three sli... | {
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How to find the direction of an eddy current? Suppose there is a magnetic field going from left to right. Suppose a thin sheet of metal conductor (e.g. a 1m*1m square) is dropped through the magnetic field such that the plane of the conductor is PERPENDICULAR to the magnetic field.
Now I know that by Faraday's Law, the... | An eddy current is generated due to Lenz's law, so the current will produce a magnetic field in order to oppose the change that created it right.
So for example, You move a metal sheet into a magnetic field, a current will be created so as to OPPOSE this force moving it into the field. So the force that the eddy curren... | {
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Single Slit Diffraction I am trying to derive the intensity variation function for a single slit diffraction.
Sorry for the poor diagram...
So I decided to take the amplitudes of the waves originating from the slit on the left (wherein the variable that denotes distance within the slit is $l$) and integrate the amplit... | It is not possible to write a closed form equation for the Fresnel diffraction pattern. Usually one will use the Cornu spiral to evaluate problems like this.
The Cornu spiral is a graphical tool that maps the phase / amplitude contribution of a infinitesimal element of the aperture.
(image by R. Nave, from http://hyp... | {
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Are chemical bonds matter? So it recently blew my mind that chemical bonds have mass. And that a spring that's wound up similarly weights a little more.
But there is a distinction between mass and matter.
I believe that a chemical bond, even though it has mass, is not considered matter and is instead a form of energy... | I have to say you have this backwards. Energy is released when atoms form bonds and therefore a decrease in mass takes place.
$E_{unbondedsystem}$ < $E_{bondedsystem}$ $therefore$ $M_{unbondedsystem}C^2$ < $M_{bondedsystem}C^2$
| {
"language": "en",
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"source": "stackexchange",
"question_score": "8",
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Streamlines and line of flow of fluid particles
*
*Can the streamlines of a fluid particle show the position of the particle at a time(using the streamlines)?
*I know that streamlines cannot intersect because at a specific instant the particle reaching the intersection will have two different directions of motion (i... | *
*On a steady flow, streamlines correspond to the trajectory of "fluids particles" or parcels. (Not to be confused with the one of the real "particles" that are the molecules.)
*But if it's not a steady flow, it's wrong. You might even see appearant source and sink in the lines that do not exist as a flow.
*Steady ... | {
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What it sounds like when I'm travelling at the speed of sound totally hypothetical here:
lets say a man is playing a song on a guitar and I begin travelling quickly away from the guitar, if I were to reach the speed of sound, what will I hear? (my assumption is that I will hear a single note humming in a constant stat... | You would hear Whoosh... and Boom! The sound of air rushing past your ears traveling at the speed of sound and the shock waves would entirely drown out the sound of any guitar even with the most powerful amps! ;)
And if you say well then remove the air and do the experiment in space - you will not hear any sound since... | {
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Significance of Time constants in LR and RC circuits What is the significance of a time constant in a circuit? Is there any use of knowing the time at which the charge in a capacitor is 1-1/e times its total charge?
What is special about the capacitor having 63% of total charge?
(I know how to find time constant)
| As you may know, it takes infinite time to charge a capacitor. So, the time when the capacitor is 100% charged never comes. Thus, we require a Time Constant to help us understand the time when the capacitor has got a decent amount of charge and after which the rate of charging becomes really slow and thus charging furt... | {
"language": "en",
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Raw data acquirable from amateur astrophotography What raw data can I possibly acquire from an 8" Classical Dobsonian Telescope, and a DSLR? Could anything eye-opening to amateur astronomers be computed or calculated first-hand with such equipment? I'm sure scientists must've considered this equipment "advanced technol... | I just stumbled upon your question. If you go to astrobin.com and put Dobsonian in the search field. You'll see a huge number of excellent images taken with Dobsonian telescopes. Most are of the moon and planets but a few are of the brighter deep sky objects such as the Great Orion Nebula. There are better instrume... | {
"language": "en",
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"source": "stackexchange",
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integrability and area-preservation property of dynamical systems Suppose we have a map defined on a plane, $x_{1}=f(x_{0})$, where $x \in \mathbb{R}^{2}$. Assume it is integable: there exists a function $I$ of the phase space variable $x$ such that $I(x)=I(f(x))$. I do not assume global integrability in the sense of L... | No.
How about, e.g., the Hénon map with $a=1.25$ and $b=0.3$? It has an attractor, so it's not area-preserving, and this attractor is periodic, so the system is integrable.
Unless our definitions don't match, any integral map in $\mathbb{R}^n$ that has an attractor is a counter-example to integrability and area-preserv... | {
"language": "en",
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Is Earth really a magnet? I am a student of class 9. When I was going through magnetism and read that an earth is a magnet I got some doubts. My question is: is earth really a magnet? Doesn anyone have any proof that earth is a magnet? Is there a magnetic core at the center of the earth? Has anyone reached the core of ... | The difference between a magnetic substance and non-magnetic substance is their difference in spin alignment or we may call it spin polarity. That is why we have ferromagnets, diamagnets and antiferromagnets. You can google for more information on source of magnetism.
The Earth behaves as a magnet because it affects t... | {
"language": "en",
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How to start an artificial gravity? I understand how artificial gravity in space stations works. It is by normal force the wall exerts on the foot.
But I wonder how to start it in the first place. I just learned about centrifugation in a centrifuge. To start, the side-wall of the tube produce a tangential acceleration... | You are quite correct that if you have items floating freely inside your space station they won't experience any artifical gravity as the station starts spinning. The artificial gravitational acceleration of an object is a consequence of its tangential velocity $v$ and is given by:
$$ g = \frac{v^2}{r} $$
where $r$ is ... | {
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Conformal compactification and the use of spinors (Twistor theory) I was reading the book from Huggett and Tod "An introduction to twistor theory" and as the book evolves they reach to the necessity to "found" a Lie derivative of a spinor respect to a conformal vector field. Then, they explain the problem that one has ... | Twistor equations are invariant under conformal rescaling of metric and all geometric notions used in twistors are essentially conformally invariant. Twistors are reduced spinors of the pseudo-orthogonal group O(2,4) which happens to be locally isomorphic with conformal group of Minkowski space. So the description of s... | {
"language": "en",
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What is Pressure Energy? While deriving Bernoulli's Theorem, our teacher said that the sum of KE, PE and Pressure Energy per unit volume remains constant at any two points.
$$P + \rho g h + \frac{\rho v^2}{2} = \text{Constant}$$
In this, he stated that the first term is Pressure Energy per unit Volume. What exactly is ... | Consider a gas that apparently moves in the $x$-direction with speed U. The molecules are also in random motion with velocities (u',v',w'), and they also have internal energy $i$ per unit mass, coming from rotation or vibration.
The energy of an individual molecule is $$(m/2 )((U+u')^2+v'^2+w'^2+i)=(m/2)(U^2+u'^2+2Uu'+... | {
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Splitting molecule The photon reacts with the binding electrons orbiting the two atoms.
The photons have the 'correct' wavelength for Bond Dissociation Energy (BDE).
'Splitting' the molecule involves applying the photon wavelength to separate the electron from the molecule.
With the photons being applied between the bi... | When a molecule absorbs a photon it reaches to an excited state and there are various mechanisms in which the molecule can relax. Dissociation of the molecule is just one of the possibilities.
It is not necessary to ionize (to separate the electron from) the molecule for dissociation to occur. What is necessary is to e... | {
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What is the definition of linear momentum? Every where and book I search I get that the definition of linear momentum is the amount of speed (quantity of motion) contained in it or simply it is mass $\times$velocity? So, what is an appropriate definition of linear momentum? What did Newton think when he discovered it... | I suppose Newton may have devised the momentum equation to numerically express how objects of exact speeds (but different densities) would create different effects upon impact and perhaps how much energy would be needed to move such objects to a given speed. Consider the following:
*
*a wood ball (25g, 33.5 cc) hur... | {
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Why light moves sideways? Greatings!
I'm trying to understand special relativity and have one question bugging me.
In almost every book or video about the subject there is a thought experiment with moving light clock. I hope I need not elaborate on the sutup and the outcome of the experiment.
So the question is this: ... | There are many ways to convince yourself that light will travel sideways w r t the ground observer. One simple way to see this is to check how transverse velocities add in relativity. The vertical component of emitted photon ( you can check this!) In the ground frame is $c/\gamma=\sqrt{c^2-v^2}$ where $v$ is the speed ... | {
"language": "en",
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How does inhalation work? In school, we learn that during inhalation, the diaphragm expands, causing air to get sucked into our lungs. You can feel this suction by putting your hand over your mouth while inhaling.
Why is that? Does the expanded capacity of the lungs cause the air outside my body to rush into my body to... | From what I've gathered, I think my initial guess is correct. Air tries to maintain a constant pressure. According to the ideal gas law, there are two ways to maintain the same amount of pressure with an increasing volume: 1) increase the amount of gas, and 2) increase the temperature of the gas.
| {
"language": "en",
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Why does a ruler continue to slide after toppling? I was playing with a small ruler by repeatedly toppling it, see diagram below:
The ruler, standing $h$ tall and approximately a regular bar, is prevented from free-rotating by a fixed ridge (a book, usually) in point $O$ and then allowed to topple until it hits the $x... | As noted by John Rennie in the comments, there will be a point as the ruler falls where it loses contact with the ridge and begins to slide to the right. The idea here is that if the ruler were to keep its pivot point fixed, then at some point, the force applied by the pivot point would have to switch from having a co... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/217025",
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Sterile neutrino constraints (summary of results) Constraints on sterile neutrinos come from an amazingly wide range of different sources. From astrophysical observations (review1, review2) to particle physics experiments (MiniBooNE, Daya Bay, LSND, MINOS)
I have been reading about the astrophysical observations (e.g. ... | First of all, one should distinguish the mass scale of the sterile neutrino. This review talks a lot about the keV sterile neutrino and even heavier cases, that however are not very interesting from the point of view of neutrino oscillations, because their mixing is typically very small. The keV sterile neutrino has po... | {
"language": "en",
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What would be the implications for current theories if gravitational waves are not detected? Let's assume that scientists trying to detect gravitational waves get a huge raise in funding, design even better experiments, and run them for decades, but just can't find any gravitational waves whatsoever. How would theories... | In many ways it is almost inconceivable that they don't exist in some form or other as it would be difficult to reconcile the absence of gravitational waves with special relativity. It's only when you have an infinite speed of propagation, such as in Newtonian gravity, that you would not expect to see gravitational wav... | {
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How many photons does my remote control garage opener emit? Every time I drive up to my house I imagine all the photons spitting out of the remote control garage opener when I press the button. And I imagine the door opener in the garage receiving them. There must be a ton of these particles going in all directions if ... | Most likely, your garage door opener operates at a frequency of 315 MHz. Multiplying by Planck's constant, that means each photon has energy of about $2\times 10^{-25}$ joules.
Most likely, your garage door opener operates at about $1/10$ of a watt (or less, per comments below). So each second, it emits 1/10 of a j... | {
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Does turning a spoon in water raise the temperature? I read about Joule's experiment proving the transformation of mechanical work into heat. But say I have a bowl with some water, and I start turning a spoon in it very fast, thus doing work — the water won't get hotter! What am I missing?
I think maybe the work I put ... | Well first you have the energy in the form of kinetic energy of the spinning water. Once you let that water settle, it DOES get hotter.
The only problem is that water has a high specific heat (it takes a LOT of energy to heat up water), so you don't notice the water getting hotter since the amount it's heating up is n... | {
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What is the distance between two objects in space as a function of time, considering only the force of gravity? What is the distance between two objects in space as a function of time, considering only the force of gravity? To be specific, there are no other objects to be considered and the objects in question are not ... | This is the elliptic case of the radial Kepler problem, the equation for time as a function of position is
$$ t(r) = \sqrt{ \frac{d^3}{2 g} } \left( \arccos\left( \sqrt{ \frac{r}{d} } \right) + \sqrt{ \frac{r}{d} \left(1 - \frac{r}{d} \right) } \right) $$
where t is the time, r is the position, d is the initial (maxim... | {
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Difference between convexo-concave and concavo-convex lenses? What is the difference between concavo-convex and convexo-concave lenses? We dont say convexo-plane for plano-convex. Does that mean concavo-convex and convexo-concave are essentially the same?
| The most important thing to remember is that a CONVEX lens (meniscus if you like) is thicker in the middle than at the edges, no quibbles, no exceptions. It accordingly causes a beam of light passing through to converge, and is said to have positive optical power.
Conversely for CONCAVE.
A plano-CONVEX lens still is a ... | {
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"answer_id": 1
} |
Direction of $\textbf{H}$ and $\textbf{B}$ inside and outside a bar magnet I seem to have encountered a contradiction when thinking about the directions of $\textbf{H}$ and $\textbf{B}$ inside and outside a bar magnet.
Suppose that a bar magnet has a roughly constant magnetisation M pointing along the positive z direct... | $B$ actually behaves as you explain, however there's a problem
with $H$.
You say:
"However, the field lines must also curl around and meet the top surface of the magnet, where $H$ will therefore need to point in the negative z direction."
Why the field lines need to meet the top surface of the magnet?
Outside the magn... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/217848",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 2,
"answer_id": 1
} |
Tension in string question
Problem: A 12.0-kg box resting on a horizontal, frictionless surface is attached to a 5.00-kg weight by a thin, light wire that passes without slippage over a frictionless pulley (the figure (Figure 1). The pulley has the shape of a uniform solid disk of mass 2.10 kg and diameter 0.520 m.
W... | *
*some of the tension goes into accelerating the pulley rotationally. Specifically $\Delta T \;R = I \frac{ \dot{v}}{R}$
*Again you have to account for the mass moment of inertia of the disk. You could write $F_{net} = (m_1+m_2+\frac{I}{R^2}) a$
*The masses do not rotate so their mass moment of inertia is of no use... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/217984",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Veterans Day Memorial in the U.S For the ones who know about it:
How many more times will the Veterans Day Memorial stones' holes "align" perfectly?
Some info from this site:
At precisely 11:11 a.m. each Veterans Day (Nov. 11), the sun's rays pass through the ellipses of the five Armed Services pillars to form a perf... | The answer to your question can be found in the description of the engineering of the monument
You can read the whole story at that link; I will just quote the most pertinent statement:
Using the statistical mean of the 100-year data, the altitude and azimuth angles for the structure were adjusted to provide time/erro... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/218066",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
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