Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Why does humidity cause a feeling of hotness? Imagine there are two rooms kept at the same temperature but with different humidity levels. A person is asked to stay in each room for 5 minutes. At the end of experiment if we ask them which room was hotter, they will point to the room with the higher humidity. Correct ri... | When the ambient humidity is high, the effectiveness of evaporation over the skin is reduced, so the body's ability to get rid of excess heat decreases.
Human beings regulate their body temperature quite effectively by evaporation, even when we are not sweating, thanks to our naked skin. (This, supposedly, is also what... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "30",
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In general, why do smaller guns have more felt recoil? Why is recoil easier to control on a more massive gun compared to a smaller gun with the same bullet. Presumably the bullet leaves both guns with the same momentum, but the larger gun seems easier to control. Since the momentum you have to control is the same in bo... | Newtons 3rd Law:
When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.
Momentum is product of mass and velocity. The heavier gun has more mass, so, for the same momentum, it must have less "backwards" velocity, so l... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/196312",
"timestamp": "2023-03-29T00:00:00",
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How can the magnetic field surrounding a current-carrying wire ever be uniform? My book says that to find the force a current-carrying wire exerts on a moving charge, one uses $B = (\mu_0 / 2\pi)(I/r)$ to find the magnitude of magnetic field around the wire, and then uses that to find $F_B = q v B \sin\theta$, which is... | The field around the wire isn't uniform. When you calculate the force on a charge in a magnetic field, you use the value of the field at the point where the particle is. So, $$F_B = qvB\sin\theta$$ is not just for a constant field. If the field varies from position to position in space, then the force the particle feel... | {
"language": "en",
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Is there some no-go theorem for $D=9$ Kaluza Klein QCD+EM? While QCD is a typical product of AdS/CFT and some other research trends in extra dimensions, I have never found in the literature an example producing the non-chiral part of the standard model, colour plus electromagnetism, or even color alone, from D=9 Kaluza... | With an answer selected (and bounty awarded) it is time to open a community wiki for explicit references on work along the line of getting QCD + EM, or alternatively QCD alone or QCD + "4th colour" extracting the group from the extra dimensions.
*
*An early 1975 work of founding fathers of string theory claims to ha... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/196610",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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Conical train wheels I've been reading about how the conical shape of train wheels helps trains round turns without a differential. For those who are unfamiliar with the idea, the conical shape allows the wheels to shift and slide across the tracks, thus effectively varying their radii and allowing them to cover differ... | The contact with the rail creates a kinematic center of rotation where the reaction forces meet. The rail car will tend to rotate about this center as a result of side loads.
*
*If the center is above the center of mass, the rail car acts like a hanging pendulum. A small deflection will cause a restoring torque opp... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/196726",
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Why is the index of refraction different for different wavelengths? The index of refraction can be written as
$$n=\frac{\lambda_v}{\lambda_m}$$
where $\lambda_v$ is the wavelength in a vacuum and $\lambda_m$ is the wavelength in the medium. I’ve been told that since wavelength appears in the definition of an index of r... | I think you will have an easier time viewing the index of refraction from a speed-point of view.
Consider the following: The energy of a given photon is determined by its frequency (color):
$E = h \nu $
(h being the Planck constant)
Assuming the photon does not lose energy when entering the material, its frequency must... | {
"language": "en",
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Can a magnet damage a compass? I've heard the claim before that a magnet can ruin a compass, and was about to repeat it to my son when I realized it sounds like complete nonsense. Googling turned up such unsubstantiated and illogical answers as this one and unanswered questions as this one but nothing that sounded rea... | Yes a magnet can damage a compass.
The compass needle is a ferromagnetic material.
The degree to which a ferromagnetic material can "withstand an external magnetic field without becoming demagnetized" is referred to as its coercivity.
Another magnet near the compass needle imposes a magnetic field upon the compass... | {
"language": "en",
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Dirac delta function definition in scattering theory I'm studying scattering theory from Sakurai's book.
In the first pages he gets to the following expression:
$$\langle n|U_I(t, t_0)|i\rangle=\delta_{ni}-\frac{i}{\hbar}\langle n|V|i\rangle\int_{t_0}^t e^{i\omega_{ni}t'} dt',\tag{1.9}$$
where $U$ is the propagator in... | If you go to these limit right away and get delta functions you might later face problems such as need to evaluate meaningless expressions, e.g. $\delta(x)^2$ or $\delta(0)$. This can often be avoided by adding so called regulators (in this case this role is played by $\epsilon$). These should be removed after all mani... | {
"language": "en",
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Are Hubble Telescope Images in true color? Like many others, I have marveled at the images made available from the Hubble Space Telescope over the years. But, I have always had a curiosity about the color shown in these images. An example is shown below. Are the colors we see, such as the yellows, blues, and so on t... | Sort of.
As Space.com writes,
The raw Hubble images, as beamed down from the telescope itself, are black and white. But each image is captured using three different filters: red, green and blue. The Hubble imaging team combines those three images into one, in a Technicolor process pioneered in the 1930s. (The same pro... | {
"language": "en",
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How to predict bound states in a 1D triangular well? Assume we have a (single) particle in a potential well of the following shape:
For $x \leq 0$, $V = \infty$ (Region I)
For $x \geq L$, $V = 0$ (Region III)
For the interval $x > 0$ to $x < L$, $V = -V_0\frac{L-x}{L}$ (Region II).
The potential geometry is reminiscent... | The wavefunction $\psi(x)$ satisfies
$$
-\frac{\hbar^2}{2m}\psi'' + V_0\left(\frac{x}{L} - 1\right) \psi = E\psi, \quad 0 \leq x \leq L\\
-\frac{\hbar^2}{2m}\psi'' = E\psi, \quad x > L
$$
Since the bound states have $E < 0$ let's introduce
$$
k = \frac{\sqrt{-2mE}}{\hbar}\\
\varkappa = \frac{\sqrt{2mV_0}}{\hbar}
$$
The... | {
"language": "en",
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How do I know what variable to use for the chain rule? In my textbook the tangential acceleration is given like this:
$$a_t=\frac{dv}{dt}=r\frac{dw}{dt}$$
$$a_t=rα$$
I understand that the chain rule is applied here like this:
$$a_t=\frac{dv}{dt}=\frac{dv}{dw}\frac{dw}{dt}=rα$$
What I don't understand is why we have to ... |
What I don't understand is why we have to apply the rule in this specific way?
How do I know how the chain rule must be applied?
We don't have to. You don't know. Somebody just found out that by using that specific method, the result ended up neat and simple.
Nothing is wrong with another method. You get the same t... | {
"language": "en",
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Difference between $|d{\bf r}|$ and $d|{\bf r}|$ What is the difference between $|d{\bf r}|$ and $d|{\bf r}|$ and why are both of them not always equal to each other?
My question might seem stupid to some and will probably get downvoted but I have thought on the question but still can't comprehend any difference betwee... | If
$$
\overrightarrow{r}=r_{x}\widehat{i}+r_{y}\widehat{j}
$$
then
$$
\left | \overrightarrow{r} \right |=\sqrt{r_{x}^{2}+r_{y}^{2}}
$$
and
$$
d\left | \overrightarrow{r} \right |=\frac{r_{x}dr_{x}+r_{y}dr_{y}}{\sqrt{r_{x}^{2}+r_{y}^{2}}}
$$
on the other hand
$$
d\overrightarrow{r}=dr_{x}\widehat{i}+dr_{y}\widehat{j}
$... | {
"language": "en",
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Stability and Laplace's equation Consider four positive charges of magnitude $q$ at four corners of a square and another charge $Q$ placed at the origin. What can we say about the stability at this point?
My attempt goes like this. I considered 4 charged placed at $(1,0)$, $(0,1)$, $(-1,0)$, $(0,-1)$ and computed the p... | The Coulomb Potential is a solution to Laplace's equation in 3 dimensions. In 2 dimensions the equivalent solution is a logarithmic potential. You have written down the Coulomb potential for 4 charges but then treat the problem as 2 dimensional, which is causing your problems. To resolve this you need to add a load of ... | {
"language": "en",
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Why aren't calculation results in error propagation at the center of the range? We have two copper rods, with $L_1$ and $L_2$ as their lengths respectively, and we want to glue the two bars together, with glue that's infinitesimally thin.
$$\begin{align}
L_1 &= 20 ± 0.2\ \mathrm{cm} \\
L_2 &= 30 ± 0.5\ \mathrm{cm}
\end... | When proving addition of fractional uncertainties, one neglects the product of uncertainties. In your case the product of fractional uncertainties is (0.01)(0.02) = 0.0002 which is considerably less than the sum of them 0.01 + 0.02 = 0.03. This is the discrepancy you see in multiplication example. Nevertheless if you t... | {
"language": "en",
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"source": "stackexchange",
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Is heat conduction impeded at interfaces between dissimilar materials? Sound in air essentially echoes off concrete walls, rather than penetrating them, because of the difference in the material properties of air and concrete.
By analogy, are there pairs of solid materials where their interface would be very inefficien... | It turns out that there can be resistance to heat flow at an interface between two different materials, even if there are no gaps. It is discussed on Wikipedia, under the heading "Interfacial thermal resistance". It is associated with mismatches in the frequencies of the thermal vibrations (quantized as phonons) asso... | {
"language": "en",
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thin film interference of light
In a thin film interference (reflective system) I know that condition for maxima is
$$2\mu t\cos(r)=(2n\pm 1)\frac{\lambda}{2}$$ and for minima is $$2\mu t\cos(r)=n\lambda$$ and for transitive system it's just the opposite.
but what happens if then film is very small such that $$\lim_... | If the film is thinner than half a wavelength then there is no thin-film interference (until you get into complex surface plasmon effects).
Thin-film interference works with thick films so long as they are multiples of half a 1 or 1/2 a wavelength. The main practical difficulty is making thick films that are uniform re... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/199408",
"timestamp": "2023-03-29T00:00:00",
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Eddy Currents – Tubes with slits When a magnet falls down a tube, eddy currents form and flow around the tube, perpendicular to the direction in which the magnet falls.
However, when there is a vertical slit in the tube, are either no eddy currents formed (since they cannot complete a rotation), or alternatively do mu... | Yes, there should be smaller eddy currents formed when the tube has a slit in it. Those same eddy currents will also be formed in the tube without a slit, on top of the current that goes all the way around the circle. The important thing is that the primary current gets cut off by the slit, reducing the amount of energ... | {
"language": "en",
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Is a bomb's shockwave strong enough to kill? I'm watching a movie, The Hurt Locker, and the first scene shows an IED explosion which kills a soldier. Of course movies don't depict explosions with maximum realism, but I noticed the debris and smoke / flame didn't reach him, and it made me curious about whether invisible... | The other answers already mention pressure and heat.
A bomb sets nearby bodies in motion with a speed depending on the strength of the explosion, the distance to the body, and how much surface area of the body was facing the bomb. While - as explained in the other answers - being set in motion is rarely lethal, being ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/199730",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "27",
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Thermodynamics about turbines 1.A turbine is rated at 650 hp when the flow of water through it is 0.85 m3/sec. Assuming an efficiency of 84%, what is the head acting on the turbine.
| This is a nice question on $\color{blue}{\text{Hydraulic Turbine}}\ \color{red}{ \text{(FLUID MECHANICS)}}$
Given $$\text{rated power}, P_{\text{rated}}=650 \ H.P.=650\times 746=484900 \ W$$
$$\text{discharge}, Q=0.85\ m^3/sec$$
$$\text{efficiency }, \eta=84\ \text{%}$$
Let, $H$ be head under which the turbine is worki... | {
"language": "en",
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How does uncertainty/error propagate with differentiation? I have a noisy temperature (T) vs. time (t) measurement and I want to calculate dT/dt. If I approximate $dT/dt = \Delta T/\Delta t$ then the noise in the derivative gets too high and the derivative becomes useless. So I fit a smoothing spline (smoothing paramet... | Model two consecutive measurements as the real values plus some noise.
Call the first measured temperature $T_1$ and the second $T_2$.
Call the measured noises $\gamma_1$ and $\gamma_2$, and suppose that they are drawn from a distribution $\Gamma(\gamma)$ and are uncorrelated.
The (approximation to the) derivative is
$... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "14",
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Is there experimental verification of the s, p, d, f orbital shapes? Have there been any experiments performed (or proposed) to prove that the shapes of the s,p,d,f orbitals correspond to our spatial reality as opposed to just being a figment of the mathematics that give us something to visualize?
| A few years ago the XUV physics group at the AMOLF Institute in Amsterdam were (to my knowledge the first to be) able to directly image the orbitals of excited hydrogen atoms using photoionization microscopy. For more details see the paper,
Hydrogen Atoms under Magnification: Direct Observation of the Nodal Structure ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/200143",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "25",
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Which power equation to use: $P = I^2 * R$ or $P = V^2 / R$? Given are ideal max voltage $V = 200\;\mathrm{V}$ and max current $I = 5\;\mathrm{A}$.
Therefore:
*
*ideal resistance is $$R = \frac VI = \frac{200 \;\mathrm{V}}{5\;\mathrm{A}} = 40 \;\mathrm{\Omega}$$
*ideal max power is $$P=IV = 5 \;\mathrm{A}* ... | You have changed the resistance from $40\Omega$ to $20\Omega$ and $60\Omega$ but did not change anything else. You must always allow for
$$V=I*R$$
If the resistance halves but the voltage stays the same, then the current doubles, and hence your power quadruples.
With $20\Omega$ the current is:
$$I=V/R=200/20=10A$$
Powe... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Electric field a distance z above the midpoint of a straight line segment In Griffiths there's an example to evaluate the Electric field a distance z above the midpoint of a straight line segment of length 2L. Which carries a uniform charge $\lambda$.
In that calculation, the author used the fraction of charges dq w... | He is making use of a well-chosen coordinate system to create a symmetric system. That greatly simplifies the concept and makes the integral easy.
I bet that somewhere, he doubles the result of the integral. He has also made an argument that the $x$-components will add to zero (again, using symmetry).
Choosing a coordi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/200329",
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Is the change in orbital of an electron the only way a photon is created I would like to know if there are any other ways in which photon's are being emitted other than in the case an electron's orbital around a nucleus changes.
| Yes. There are loads of physical processes in which photons are created. It won't be possible to list them all out but well known examples are matter-antimatter annihilation (e.g. electron-positron annihilation, at lower energies.), the acceleration of charged particles, radioactive decay (notably, Gamma Decay), etc.
| {
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"source": "stackexchange",
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How relevant is the Heisenberg Uncertainty Principle? I was originally surprised to see that,
$$\Delta x \cdot \Delta p \gt {{\hbar} \over 2}$$
But, then I realized that $\hbar/2=5.27 \cdot 10^{-35}$. According to this other question, the smallest length ever measured was on the order of $10^{-18}$. Of course at that p... | In a hydrogen atom the kinetic energy is on the order of $8$ eV. From $T = \frac{p^2}{2m}$ we get that the typical momentum is about $3$ keV/c ($m = 511$ keV/$c^2$). On the other hand $\hbar/(2a_0)\approx 1.2$ keV/c where $a_0$ is the Bohr radius, which is about the size of a hydrogen atom. Since these quantities are o... | {
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Can you huddle next to a fridge in sub-zero temperatures and keep warm? There's a saying I've heard in so many places.. "It was so cold that we used to huddle next to our refrigerator to keep warm..." I had heard this phrase uttered some 30 or so years ago, and it's stuck with me ever since...
Which gets me thinking...... | Refrigerators are not designed to warm up air. If the outside temp is -40 C and you open the door of a fridge set to 4C, the air in the open fridge will quickly cool to -40C and the fridge compressor will turn off. Refrigerators are designed to maintain a maximum temperature setting, not a minimum temperature settin... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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One-point function and vacuum expectation value in $\phi^4$-theory The one-point function (and all other odd correlation functions) in the $\phi^4-$theory, for example, calculated from the generating functional, always gives zero value in absence of external source i.e., $J=0$. To prove this it requires the invariance ... | You should work out the minimum energy state of your system (classically) to find the vacuum expectation value. I assume you're working with the standard $\phi^4$-Lagrangian
$$\mathcal L=\frac{1}{2}(\partial \phi)^2-\frac{1}{2}m^2\phi^2-\frac{\lambda}{4}\phi^4 $$
which corresponds to the Hamiltonian
$$\mathcal H=\frac... | {
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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... | From Newton's second law we have (whether $k$ is constant or not) that:
\begin{equation}
m\ddot{x}+kx=0
\end{equation}
The only difference is whether or not $k$ is a function of $t$ or not. If it is a function of $t$, the only general way to solve this differential equation is by using Taylor expansions. Let us take:
\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/201078",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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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... | My intuition is that the frequency should stay the same because the waves in the light rope are caused by the waves in the heavy rope. The point where the ropes attach will oscillate with a common frequency. So, for $(b)$, the frequency would be the same. For $(c)$, use the equation $v= f\lambda$. You already correctl... | {
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Why don't both equivalent forms of this delta function give the correct answer? I am a bit confused on a basic problem involving a Dirac delta function being integrated over in a multiple integral.
The original problem is to find the probability distribution in position-momentum $(z,p)$ space of a ball bouncing up and ... | TL;DR: Substitution inside the delta function yields a Jacobian factor
$$ \tag{1} \delta(f(v))~=~ \sum_{v_{(0)},f(v_{(0)})=0 }\frac{1}{| f^{\prime}(v_{(0)})|} \delta(v-v_{(0)}). $$
Here the sum is over the zeroes $v_{(0)}$ of the function $f(v)$.
Let us for simplicity consider velocity $v$ rather than momentum $p=mv$.... | {
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Why do I not observe single/double escape peaks for K-40 A question on gamma spectrometry here. If I'm looking at a background gamma spectrum with a big peak at 1460KeV (approximately 180 counts) and I attribute this peak to the presence of K-40, should I expect to see the single and double escape peaks for K-40? If I ... | Very hard to tell without knowing how the spectrum was produced (type and size of the detector, resolution, anticompton, ...). Anyway 180 counts do not seem so many. The single escape peak is normally weaker and the double escape even more, especially if you are just above the pair production threshold. Sounds reasonab... | {
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Eigenspaces of angular momentum operator and its square (Casimir operator) The casimir operator $\textbf{L}^2$ commutates with the elements $L_i$ of the angular momentum operator $\textbf{L}$:
$$
[\textbf{L}^2, L_i] = 0.
$$
However, the $L_i$ do not commute among themselves:
$$
[L_i, L_j] = i\hbar\epsilon_{ijk}L_k.
$$
... | When I was asking this question, I didn't understand the relation between the commutativity of two operators and their eigenspaces:
If an operator $A$ commutates with another operator $B$, then $A$ leaves the eigenspaces of $B$ invariant:
$$
B\psi = \epsilon\psi \implies BA\psi = AB\psi = \epsilon A\psi
$$
But this doe... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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"answer_id": 4
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Light Absorption of a glass I've the $n$ (refractive index of the glass sheet ) and $t$ (the thickness of the glass sheet)
with this information, how can I find the amount light absorption of the glass sheet?
| To add to Rob Jeffries's answer: the absorption data for glass are separate from the refractive index and are measured by measuring the attenuation of light through a known thickness of glass, after taking account for the reflected amounts as described in Rob's answer.
Theoretically, the refractive index and the absopt... | {
"language": "en",
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"source": "stackexchange",
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Humans on earth seen from traveling space ship If I would stand on a space ship traveling with a speed of 0,99c I would be moving 7 times slower from Earth's perspective. But if I would look back on Earth I would see everything moving 7 times faster then from my perspective. Right?
| Absolutely not. Both you and the people on Earth would see each other moving $7$ times slower. To repeat myself: you would see them going $7$ times slower and they would see you going $7$ times slower.
This is because of the main principle of special relativity. As long as neither of you is accelerating there is nothi... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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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... | A typical subwoofer range might go all the way up to 200Hz. That would produce a wavelength of over 1.5m. Lower sounds will have even longer wavelengths. A lot of the energy from the sound is just going to step around objects that are much smaller in size.
If that cone is small, the shape doesn't matter much. The... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Dissolving photoconductor (TiOPc) from Laser Printer drum possible? When I was thinking of a Lab-On-a Chip Application which combines a lensless microscope and an optical tweezers I saw the ODEP-concept:(http://pubs.rsc.org/en/content/articlelanding/2013/lc/c3lc50351h#!divAbstract).
This works like a laser printer. Th... | I think the TiOPc on printer drums may be TiOPc nanoparticles embedded in some kind of organic binder, rather than solid TiOPc.
See this: http://patents.justia.com/patent/20140054510 for example for the challenges of dissolving TiOPc in anything.
The binder on the other hand should be easy to dissolve; try acetone ... | {
"language": "en",
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Is configuration space in any similar to vector spaces? The question may sound silly. If it is I'm sorry for it but I just couldn't find an answer anywhere else.
I have just learned about vector spaces and their properties and on the other hand have also started with Lagrangian mechanics. The author writes: "The config... | They are not related structurally: Configuration space is a manifold which in general has no vector space structure. For example $\mathbb{R}$, the configuration space of a free particle moving on a line can be viewed as a vector space (you can sensibly "add" two configurations to get a new one and so on), but if you co... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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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... | Now I know an answer, so I draw it here.
Direct derivation of nucleon-meson interaction is possible from chiral perturbation theory, which arises from the QCD spontaneous symmetry breaking. We look for finite classical field configurations which leaves chiral action finite. Since homotopic group $\pi_{3}(SU(3)) = Z$ is... | {
"language": "en",
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"source": "stackexchange",
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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 you are right. You end up having a varying electric field which generates a varying magnetic field which in turn generates an electric field etc... This causes a particular type of radiation called black body radiation.
| {
"language": "en",
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"source": "stackexchange",
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Why can we see through rain? I am gazing through my office window into a heavy rain. I am thinking that raindrops are like small lenses that bend the light. Thus I am surprised, that I can clearly see other buildings through the window.
So, why is it that we can see through the rain? Is the density of raindrops simply... | Two main reasons. First, the raindrop density is really low. Recall how it may sometimes seem it's pouring rain but you go out and barely get hit with some 10 droplets per second. It makes sense, when it's raining, it's still mostly air. If rainfall is $10\, {\rm mm/h}$ at $10\,{\rm m/s}$, the density of droplets must ... | {
"language": "en",
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"source": "stackexchange",
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Fleming's right hand and left hand rule Why are there two rules: Fleming's left hand and right hand rules? What is the difference between the two and why can't we use just one rule?
Suppose the magnetic field is from right to left and the motion of the wire is downwards then according to the right hand rule the induc... | Similarities: in both the rules the thumb gives the direction of force/motion, the index finger gives the direction magnetic field and the middle finger gives the direction of current.
Differences:
1) Left hand rule: This rule is used when magnetic field direction and current direction are given and you have to find th... | {
"language": "en",
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"source": "stackexchange",
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Galvanic Cells and Electric Potential In a battery or a galvanic cell, the electric potential of the battery is due to a difference of charges between the two cells like in a capacitor? So it is the electric field due to this separation that is driving the electrons? if yes, why we call it electromotive force of a batt... | The electric field is established only when we connect +ve and -ve of a battery with some resistance between them.
There will be no electric field when the battery is in ideal state. But we need a measure for expressing the power of battery so our physicists introduced EMF, because measuring it with electric field does... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why do people wear black in the Middle East? I have read various dubious explanations as to why people often wear black in the heat, from cultural to somehow encouraging the evaporation of sweat (unconvincing). So, does anyone know what, if any benefit there is to black clothing in hot dry conditions? It is certainly c... | As it was explained in one of Halliday's books, the reason is that the black dress heats the air inside it up, thus causing a continuous flow of air in between the skin and the dress. The cold air flows in from below, gets heaten up, and gets out from above, providing a continuous ventilation.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/204012",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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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... | Well let's pick the $(Ox)$ axis as a reference of frame and take the origin of time the instant the car starts deccelerating with a magnitude $a$:
Since we are talking about decceleration it is clear that:
$$
\frac{dv}{dt}=-a
$$
So:
$$
v(t)=v_0-at
$$
And:
$$
\frac{dx}{dt}=v_0-at\\
x(t)=v_0 t -\frac{a}{2}t^2
$$
Now we k... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What's the difference between the work function and ionisation energy? In a particular textbook, the work function of a metal (in the context of the photoelectric effect) is defined as:
the minimum amount of energy necessary to remove a free electron from the surface of the metal
This sounds similar to ionisation ene... |
There is definitely a relationship between the work function and ionisation energy of the elements. See the above figure in which I plotted the work functions (blue) and ionisation energies (yellow) of the elements named in the table of the former answer.
If you plot them against each other, it shows an definite, tho... | {
"language": "en",
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When does the concept of electric field in classical electrodynamics fail, and QED is needed? It is really hard to find reference to when the traditional concept of electric wave, especially TEM wave, fails, and needs to be replaced by quantum electrodynamics.
So when does the concept fail? At high frequencies of elec... | .Your title asks about the electric field. The content is about the electromagnetic waves, two different entities.
Electromagnetic waves emerge from an innumerable number of single photons. As one cannot have water waves with just a few molecules but need of the order of $10^{23}$ (avogadros number) one cannot measure ... | {
"language": "en",
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"source": "stackexchange",
"question_score": "6",
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Hermitian 2x2 matrix in terms of pauli matrices In my studies, I found the following question: Show that any 2x2 hermitian matrix can be written as
$$
M = \frac{1}{2}(a\mathbb{1}+\vec{p}\cdot \vec{\sigma})
$$
with $a=Tr(M)$, $p_i = Tr(M\sigma_i)$ and $\sigma = \sigma_x \hat{i}+\sigma_y \hat{j}+\sigma_z \hat{k}$.
I did... |
I did show that this equation works, but I want to know how to prove it just working with the fact that the Pauli matrices span a basis in 2x2 Hilbert space and that M is hermitian.
You can do this if you can specify exactly what you mean by "span a basis in 2x2 Hilbert space," which sounds really convoluted and math... | {
"language": "en",
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"source": "stackexchange",
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How do you determine the symmetry of spatial wave functions? I have been reading about the ways to determine the ground of state of an atom. There are three Hund's rules in determining which electronic state is a ground state. And the second rule says you need to maximize the orbital angular momentum while considering ... | Simply put, angular momentum eigenfunctions with total angular momentum quantum number $L$ will have well-defined parity $(-1)^L$.
| {
"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 ... | Here is a proof on wikipedia if any one else wants to follow along. The proof states that the pressure in the water is zero (I will take atmospheric pressure to be zero) after it has exited the hole. This is because there is no longer fluid on top of it after it goes out the hole. However, the proof does not say that ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Motion of center of mass I was reading about COM and forces and came upon this in my book.
If a projectle explodes in air in different paths,the path of the centre of mass remains unchanged.This is because during explosion no external force (except gravity ) acts on the COM.
My question is, even though the author rea... | The passage means that the center of mass follows the same parabolic trajectory it would have followed had there been no explosion. This includes the effect of gravity.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/206127",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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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 term "K-shell" stems from an older, now less used terminology for the 'electron shells' of multi-electronic atoms.
In this terminology, electrons with Principal Quantum Number $n$ equal to 1 where said to belong to the K-shell, those with $n=2$ the L-shell, those with $n=3$ the M-shell etc.
For an alkali metal like... | {
"language": "en",
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When I take a Gaussian surface inside an insulating solid sphere, why does the outer volume have no effect on the electric field? Say I try to find the magnitude of the electric field at any point within an insulating solid sphere. I know that in the case of a conductor, the electric field within it is 0. However, I ha... | This is somewhat similar to why the rest of the earth doesn't influence the gravitational field inside it. By the same logic, the net electric force of all of the charges on 1 half of the outer side cancel each other due to the presence of corresponding charges on the other half, resulting in no net field due to the ou... | {
"language": "en",
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Finding action-angle variables Given a 1 d.o.f Hamiltonian $H(q,p)$ what is the general procedure for finding action angle variables $(I, \theta)$?
I have read the Wikipedia page on action angle variables and canonical transforms but have difficulty applying the general methods to specific problems. Can someone explain... | In local coordinates the canonical transformation to action angle coordinates $(q,p)\rightarrow (Q,P)$ can be related by,
\begin{equation}
\boxed{P_i=\frac{1}{2\pi}\oint p_idq^i \ \ \ \ \ \text{and}\ \ \ \ \ Q^i=\frac{\partial }{\partial P_i}\int p_idq^i}
\end{equation}
For Example:
Consider the one dimensional harmon... | {
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"source": "stackexchange",
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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... | Consider a one-parameter family of operators $X + \epsilon Y$, and let $f$ be an analytic function. Then we formally use linearity of the trace to obtain
\begin{align}
\mathrm{tr}[f(X + \epsilon Y)] = \mathrm{tr}\left[\sum_{n=0}^\infty c_n(X+\epsilon Y)^n\right] = \sum_{n=0}^\infty c_n\mathrm{tr}[(X+\epsilon Y)^n]
\e... | {
"language": "en",
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"source": "stackexchange",
"question_score": "4",
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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 have to ask yourself -- what is driving the flow? Would the driver change or stay the same as your fluid changed? What are the variables conserved in a flow (ie. speed, energy, density, momentum, temperature, etc. -- I intentionally listed some that are conserved, some that are not).
In other words, think about ho... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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"answer_id": 0
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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... | You have 3 different materials in your experiment: a liquid (coffee, could be water), a solid (plastic straw) and a gas (air). You have interfaces between all three: liquid-air, liquid-solid and solid-air. In the case of the plastic of your straw, adhesion forces are stronger between plastic and water than plastic and ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
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Taking the classical limit $v\ll c$ in special relativity I'm trying to understand some of my class notes. My professor reached 2 equations:
$$m_0c^2 \frac{d\gamma}{dt}=\textbf{F} \cdot \textbf v\tag{1}$$
and
$$m_0\frac{d\gamma \textbf v}{dt}=\textbf F\tag{2}$$
where the bold letters are 4-vectors. He then wrote that ... | The small parameter in question ought to be $\beta=v/c$. If you expand $\gamma\approx 1+ 1/2 \beta^2 - 1/8 \beta^4$, you find
$$
\begin{align}
\gamma &\approx 1+ 1/2 \beta^2 +\mathcal{O}(\beta^4)\\
c^2\gamma &\approx c^2 + 1/2 v^2 -1/8 v^2\beta^2 + \mathcal{O}(\beta^4)
\end{align}
$$
Neglecting $\beta^2$ and higher po... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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How force is transferred from one body to another If there are 3 coins , namely 1 , 2 and 3 as in figure.
When coin $1$ strike coin $2$ ,the coin $2$ passes the force to coin $3$ and the coin $3$ moves away.
Case :1
How does this happen?
What exactly happens there and passes the force on coin $1$ to coin $3$?
How d... | A different example from your coins, but the same idea, is Newton's cradle.
Pull one ball away, it hits the first ball in the line and comes to nearly a complete halt. The ball on the opposite side, like your coins, gets most of the initial velocity and almost instantly swings in an arc nearly, but not quite as high... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/207175",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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When I boil a kettle, what stops all the water from turning (exploding!) in to steam in one go once it reaches 100°C? While making a cup of tea in the office kitchen, a colleague asked me this question and neither of us could answer with any certainty. We're guessing it has something to do with the pressure of the colu... | If you want to see all water in a container immediately turn to steam, you need a transparent container that you can seal. Fill the container 50% with water and tightly seal it. Place the container on an open flame and let it heat up. While it is heating, walk far away and watch the container through binoculars from... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/207295",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "72",
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Near energy In the null of a Hertzian dipole Since $\mathbf E = -∇Φ - ∂\mathbf A/∂t$ one expects an oscillating $\mathbf E$ field even in the null of a Hertzian Dipole unless the two right hand side terms cancel -- which they do in the far field of the null.
However, in the near field of the null, the terms do not comp... | I believe this apparent contradiction to stem from a misunderstanding that energy can be transferred only by the one mechanism to which the Poynting vector applies:
The Poynting vector is defined as ExH, and applies to a "launched" electromagnetic wave in propagation. In your example, the energy is being transferred b... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/207399",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Most general Ansatz for cylindrically symmetric metric in GR? How would the most general Ansatz for a cylindrically symmetric metric in GR look like?
To make this question more substantial, here is an example of what I have in mind. I ask this question in the spirit of how the Scharzschild solution can be derived from... | According to "Exact Solutions of the Einstein Field Equations", the most general cylindrically symmetric metric is
\begin{equation}
ds^2 = e^{-2U} (\gamma_{MN} dx^M dx^N + W^2 d\phi^2) + e^{2U} (dz + A d\phi)^2
\end{equation}
With Killing vectors $\eta = \partial_\phi$ and $\zeta = \partial_z$, and all functions indepe... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 1,
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Mass - Unification of inertial and gravitational definitions As a kinetic definition, mass of a body is a measure of the translational inertia of the body. There is also the gravitational definition of mass. Can these definitions (inertial and gravitational) empirically be proved to be equivalent? Also, are these defin... | A priori, they could have been different things. The Equivalence Principle - the hypothesis that they are actually the same - is a core input to the theory of General Relativity. To the extent that General Relativity is empirically validated, we have evidence that these really are the same.
There's no complete theory... | {
"language": "en",
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"source": "stackexchange",
"question_score": "3",
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Method of image charge for cylindrical conductor I am simply puzzled that only for spherical and planar conducting surfaces the method of images is applied. Is it (really) impossible to find image charge or charge distribution which can simulate the behaviour of potential in the volume of interest. Is there any method ... | This work is an investigation into the nature of the imgage of a point charge on the axis of the cylinder:
https://www.researchgate.net/publication/338881609_The_image_of_a_point_charge_in_an_infinite_conducting_cylinder?showFulltext=1&linkId=5e30d95f458515072d6aab92
It finds that the image is made up of a disk surface... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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How to find kinetic energy given relativistic linear momentum? The relativistic energy of a particle is given by the expression
\begin{equation}
E^2 = m^2c^4 + p^2c^2
\end{equation}
The rest energy is $E_{0}=mc^2$ and the momentum is $p=mc$. In the rest frame, the kinetic energy is $T=E-mc^2$.
Ok, now in another frame... | By definition, these equations are true in any frame.
Linear momentum is $p=\gamma mv$,
energy is $E=\gamma mc^2$,
rest energy is $E_{0}=mc^2$,
kinetic energy is $T=(\gamma-1)mc^2$.
We've been given that in this frame $p=mc$.
From this, we must conclude that $p=\gamma mv = mc$. Correct? $p=\gamma m v$ true in any ... | {
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"timestamp": "2023-03-29T00:00:00",
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minimum hyperbolic distance for Rutherford Scattering I saw in a textbook that gave the minimum distance for a hyperbolic trajectory in Rutherford scattering is given by
$$r_{min}= \frac{1}{4\pi\epsilon_0}\frac{Z_1Z_2e^2}{2E}\left(1+\frac{1}{sin\frac{\theta}{2} }\right) $$
But I'm not sure how to derive it? Could anyo... | You're right on track but don't have enough equations. The equations which give you the solution are:
\begin{align}
k&=\frac{Z_1 Z_2 e^2}{4 \pi \varepsilon_0} \tag{1}\\
E&=\frac{1}{2}m v_{min}^2+\frac{k}{r_{min}} \tag{2}\\
\frac{1}{2}m v_{min}^2&=E \frac{b^2}{r_{min}^2} \tag{3}\\
b&=\frac{k}{2 E} \cot\left(\frac{\theta... | {
"language": "en",
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"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... | Take for example an electron and a muon. The muon is unstable because it decays into an electron and two neutrinos in about 2$\mu$s. But a muon is not in some sense an excited electron. Both particles are excitations in a quantum field and they are both as fundamental as each other. The electron is stable only because ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Single Narrow Sunbeam I saw a single narrow sunbeam this cloudy, post-rain, morning as I was driving. The narrow beam, which seemed only a couple of inches wide, came directly from the sun, arched slightly and ended on the hood of my car. This beam turned with me as I entered a curve, then was gone. I've seen this a... | 'Arched Slightly' is a key comment here. Light does not bend unless going from one medium to another. Therefore, if the narrow beam of light seemed to bend in its path, it had to have been a phenomena of reflection or refraction. It could be that you were sampling only part of a larger beam that was somehow getting to ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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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 ... | It is true that the most contribution to heat comes from compressing the air. The temperature of a falling meteor was in fact in my aerodynamics II exam where I had to predict its temperature using shockwaves. According to my estimation it was about 10,000 K. You need a proper understanding of compressible air flows in... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/208722",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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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.
| Well, actually it doesn't. Knowing the wavelength allows you to calculate the energy, but it does not "determine" it in a causal way.
Energy (E), wavelength ($\lambda$) and frequency ($\nu$) are related by $$E = h\nu =\frac{hc}{\lambda}$$ so if you know the wavelength or the frequency you can determine the energy. I th... | {
"language": "en",
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What are skeleton diagrams and what is their use in qft and many-body physics? How does one construct skeleton diagrams from specific Feynman diagrams (e.g. for the electronic Green function in QED and in many-body gases, for the polarization function, for the vertex function, for the photon Green function, for the pho... | Skeleton diagrams are usually used to discuss general properties of the perturbation series in field theory. They help to prove renormalizability of a theory, or to prove properties of correlation functions.
However, they are not used in general for explicit calculation. (The main counter example is the Diagramatic Mo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/209032",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Would a tachyon be able to escape a black hole? Or at least escape from a portion of the hole inside the photon horizon?
| Yes, it would. Tachyons are a hypothetical object that can travel faster than light. They also require infinite energy to slow down as they grow faster the more energy they lose. A tachyon positioned right may as well get stuck in the center for a Planck or two I don’t know but that would speed it up A L O T. Tltr: the... | {
"language": "en",
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Superposition of two wave functions of different Hilbert spaces I am trying to think of this problem for quite some time. Let's say, we have two sets of wave functions $\lbrace|\psi\rangle\rbrace$ and $\lbrace|\phi \rangle\rbrace$ and they belong to two different Hilbert spaces. That is,
$$\hat{H_1}|\psi\rangle=E_1|\ps... | Two different Hibert spaces correspond to two different physical systems. Superposition of wave functions makes sence for one system (for one Hilbert space), since addition of vectors (quantum states) is defined in a particular vector space (Hilbert space). What you can do is to create a new Hilbert space by forming th... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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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 $$... | Start noticing that ${(\gamma^{\alpha})}^2 =1\cdot g^{\alpha \alpha}$ and that
$$
\textrm{tr} (\gamma^{\mu}\gamma^{\nu}\gamma^5)=
\textrm{tr}\left(\frac{1}{g^{\alpha \alpha}}{(\gamma^{\alpha})}^2\gamma^{\mu}\gamma^{\nu}\gamma^5\right)=\frac{1}{g^{\alpha \alpha}}\textrm{tr} (\gamma^{\alpha}\gamma^{\alpha}\gamma^{\mu}\g... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Amplitude of light across material boundaries Does the amplitude of the light ray decrease when it moves from a rarer to a denser medium?
I think that since amplitude depends upon the energy of the light ray, it should decrease. This is because of the kinetic energy of the light wave decreases (velocity decreases as li... | The amplitude of the electric field in the medium depends on the medium's permittivity, which is not directly related to its density.
Kinetic energy of the light wave decreases(velocity decreases as light travels from rarer to denser medium), hence the energy of the wave falls.
This is not true -- the energy in an e... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/209806",
"timestamp": "2023-03-29T00:00:00",
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What experiments have been done that confirm $E=mc^2$? What experiments have been done that confirm $E=mc^2$?
Are there experimental results that contradict $E=mc^2$?
Or are experimental results consistently showing this famous formula to be true?
| Another set of experiments which support $E=mc^2$ are Compton scattering experiments. The mass-energy of the electron is an important quantity in analyzing these events, and the results are consistent across a wide range of energies for the primary photon and scattering angles. The energy of the secondary photon is gi... | {
"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 ... | When you're landing from a jump, you're moving in a forward and downward direction. Landing on a downward slope simply eases the transition as this is already your direction of momentum. A flat or uphill slope will rapidly change your momentum to match the surface.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How to calculate force / torque on non-flat lever, i.e. dolly See attached image. The mass is being rotated on a lever where the pivot point (P) is a certain distance ($L_2$) from the right angle at the bottom. How do I calculate the force necessary to apply horizontally at point U to lift the mass in the worst case (i... | If the lift angle is $\theta$ (shown at zero in the diagram) then the payload lever arm is $$x_1 = \tfrac{L_1}{2} \cos \theta+L_2 \sin\theta$$
The force lever arm is $$x_3 = L_3 \cos\theta$$
Static balance exists when $$ \left. \vphantom{\int } (M g) x_1 = F x_3 \right\} \\F = \frac{x_1}{x_3} M g = \frac{\tfrac{L_1}{2}... | {
"language": "en",
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Why isn't the acceleration at the top point of a ball’s journey zero? When I shoot a ball vertically upward, its velocity is decreasing since there is a downward acceleration of about $9.8\,\mathrm{ms}^{-2}$.
I have read that at the top most point, when $v = 0$, the acceleration is still $9.8\,\mathrm{ms}^{-2}$ in th... | You throw the ball upwards with velocity $v$ and it returns to your hand with velocity $-v$. Let's draw a graph showing the velocity as a function of time:
Acceleration is defined as:
$$ a = \frac{dv}{dt} $$
so it is the gradient of the line in this graph. The velocity-time line is straight so the gradient is constant... | {
"language": "en",
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Can tidal forces significantly alter the orbits of satellites? I would assume that there are other larger, more significant, forces acting on artificial satellites, but can tidal forces drastically alter the orbit of a satellite over time?
I was thinking this could especially be an issue for a satellite in geostationa... | Satellites in geosync are not "precisely positioned". Instead, they drift around and require station-keeping thrusters. If, by "tidal forces" you mean gravitational forces associated with the sun and the moon, then the answer is yes, and the effects are quite important.
| {
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Why must the speed of the aether wind be so small compared to the speed of light? I was doing some reading on the Michelson-Morley Experiment. One of the principle equations for the equations is this one.
$$\frac { 2w }{ c } \times \frac { 1 }{ 1-\frac { { v }^{ 2 } }{ { c }^{ 2 } } }$$
Where v is the speed aether wi... | The speed of the earth in its orbit about the sun is about 30 km/s.
Michelson assumed that the speed of the earth through the rest frame of the ether was of this order.
| {
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What are the functions of these coefficients $c_1,c_2,c_3,c_4$ in $ \psi_{sp^3}= c_1\psi_{2s}+ c_2\psi_{2p_{x}} + c_3\psi_{2p_y}+ c_4\psi_{2p_{z}}$? Hybridised orbitals are linear combinations of atomic orbitals of same or nearly-same energies. Atomic orbitals interfere constructively or destructively to give rise to a... | This is quantum mechanics, my friend.
The statement simply says that one hybridized orbital consists of many "pure" orbitals. In your first equation, one hybrid orbital has four pure orbitals $2s, 2p_x, 2p_y, 2p_z$. The coefficients in front of each term can be thought of as how much of one particular kind of pure orb... | {
"language": "en",
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Primitive unit cell of fcc When I consider the primitive unit cell of a fcc lattice (red in the image below) the lattice points are only partially part of the primitive unit cell. All in all the primitive unit cell contains only one single lattice point.
My question is how much each point at the corners of the red prim... | Referring to your figure:
Each corner atom contribute, 1/18.
Top, bottom, left and right atoms on the faces each contribute, 1/9.
The closest and furthest atoms on the faces each contribute, 2/9.
To calculate these numbers one needs to find angles which are nothing but 60 or 120 degrees.
Here is the method explicitly:
... | {
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Conditions on expressing magnetic field in terms of curl of current density Given a current density distribution $\mathbf J(\mathbf x)$ inside a closed bounded region $\Omega$, the magnetic field at any point $\mathbf y$ outside of $\Omega$ can be expressed as
$$
\begin{aligned}\mathbf B(\mathbf y)&=\frac{\mu_0}{4\pi}\... | Interesting observation. As you have stated, the second equation only valid when the boundary contains all the current distribution inside. But is this what you are asking? You should open this question for objections as well.
| {
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Where does the force appear when considering object interactions in another reference frame? Imagine I am sitting on an asteroid with my buddy and drinking a beer. When the bottles are empty we throw them simultaneously in opposite directions perpendicular to the asteroid's movement. What will happen?
From the logical ... | The caveat here is that the second law is stated that net force is equal to the change in momentum.
Assuming you and your buddy are not too wasted and are able to synchronize throwing the bottles off with the exact same force, exactly in opposite directions and through the center of mass, the net force is zero, and the... | {
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Does a changing magnetic field impart a force on a stationary charged particle? Does a collapsing and re-establishing magnetic field impart a force on a stationary charged particle? Does the charge particle get repelled and or attracted? Does it move or spin?
| that curlE=dB/dt basically comes from faraday's flux law. this flux law doesn't work in all case unlike lorentz force. When a loop is moving, the flux law and lorentz force argument, both will lead to the same result. But in the case when a loop is static, it feels like lorentz force law doesn't work here but flux rule... | {
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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?
| Understanding the refractive index of a material assists to understand the colors to expect under given lighting. When light is traveling through a medium it's phase is shifted according to the material's optical properties and especially the distance which light will travel inside the material. This also applies to th... | {
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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... |
I came to know that red light has the longest wavelength and then I read a formula, Energy is inversely proportional to wavelength.
This is a quantum mechanics formula, $E=h\nu,$ where $\nu$ is the frequency.
That means that red light contains the least energy . And it bends the least. WHY? Why does it not bend as m... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/211473",
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New particles found using the LHC After finding the Higgs boson in 2012, CERN. What did the CERN found recently using the large Hadron Collider?
| Here is a (partial?) list of new hadrons discovered at LHC experiments
$\chi_b(3P)$: a $b\overline{b}$ bound state, discovered by ATLAS in 2011
$\Xi_b(5945)^0$: a $bsu$ bound state, discovered by CMS in 2012
$\Xi_b^\prime(5935)^-$ and $\Xi_b^\star(5955)^-$: $bsd$ bound states, discovered by LHCb in 2014
$P_c(4380)$ and... | {
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Interpretation of cosmological redshift I was trying to understand why we cannot explain the observed redshift of distant galaxies using special relativity and I came upon this article by Davis and Lineweaver.
Unfortunately when I arrive at section 4.2, where the authors explain why we cannot use special relativity to ... | This is just the approximation that $\beta \equiv v/c \ll 1$.
Because, $\frac{1}{1-x} \approx 1 + x$
$$\left[ \frac{1+\beta}{1-\beta} \right]^{1/2} \approx \left[ (1 + \beta)^2 \right]^{1/2} = 1 + \beta$$
Thus, $\frac{v}{c} \approx \frac{H}{c}d$, and $$v \approx H\cdot d$$
| {
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"url": "https://physics.stackexchange.com/questions/211797",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why is torque the cross product of the radius and force vectors? I understand the torque vector to be the cross product of the radius (moment arm) and force vectors, but that means the torque would be perpendicular to the radius and force vectors, which makes no sense to me, e.g. a force applied tangent to the surface ... | A force acts upon a line of action in 3D space. The force vector can be anywhere along this line and it won't change the situation.
Torque is the moment of force because it conveys the (perpendicular) distance where this force acts upon. Any component of location along the line of action needs to be ignored and this i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/212042",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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What is a Christoffel symbol?
*
*What is a Christoffel symbol?
*I often see that Christoffel symbols describe gravitational field and at other times that they describe gravitational accelerations. Then, on some blogs and forums, people say this is wrong because Christoffel symbol is NOT a tensor and thus has no phy... | The Christoffel symbols occur as soon as you have
curvilinear coordinates, even in a flat space
(i.e. without any gravity or curvature).
Consider a flat space with curvilinear coordinates ($x^1, x^2, ...$).
Because of the curvilinear coordinates the tangent vectors
($\vec{e}_1, \vec{e}_2, ...$) vary from place to plac... | {
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Lowering/raising metric indexes So, I was chatting with a friend and we noticed something that might be very, very, very stupid, but I found it at least intriguing.
Consider Minkowski spacetime. The trace of a matrix $A$ can be written in terms of the Minkowski metric as $\eta^{\mu \nu} A_{\mu \nu} = \eta_{\mu \nu} A^{... | The mistake you made is this: $\eta^{\mu}_{\nu} \neq \eta_{\mu\nu} $. When you raise index $\mu$ from downstairs to upstairs, the matrix elements change. $\eta^{0}_{0} = 1$, $\eta_{00} = -1$. That is why if you take the trace of $\eta_{\mu\nu}$, you get 2, but if you take the trace of $\eta^{\mu}_{\nu}$ you get 4.
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Pendulum's motion is simple harmonic motion For a pendulum's motion to be simple harmonic motion (S.H.M.) is it necessary for a pendulum to have small amplitude or S.H.M. can be produced at large amplitudes as well?
If it is really necessary for an S.H.M. to have small amplitudes then why is it? because even at large ... | It's just because at large angular displacements, it does not approximate the SHM of, say, a block on a spring with no friction. The restoring force is not in the direction of the displacement; therefore it does not act like SHM.
| {
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What is the 'area law' in the context of matrix product states? I am trying to get into the topic of matrix product states by reading this:
A practical introduction to tensor networks: Matrix product states and projected entangled pair states. R. Orús. Ann. Phys. 349, 117 (2014), arXiv:1306.2164.
There, often, the wo... | The area law says that the entanglement of any part of a system with the rest of of the system scales like the boundary (the "surface area") of the region. E.g., in a one-dimensional chain, the entanglement of a contiguous block with the rest should be bounded by a constant, and in 2D, the entanglement of e.g. a squar... | {
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Bernoulli principle and particle Bernoulli principle describes the flow of a fluid for steady, incompressible flow along a streamline. But it is said for a particle of a fluid along a streamline. My question is a particle of fluid refers to a molecule or a group of molecules?
| Bernoulli is a continuum rather than a microscopic description of fluid flow. Where you have used 'particle' it should really be 'parcel' of fluid which indicates it is a group of some statistical representative amount of particles (e.g. molecules) which collectively exhibit macroscopic behavior.
| {
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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?
| Very little of the energy from a rocket engine ever goes to the kinetic energy of the rocket. The only way you get perfect conversion to KE of the rocket is when the propellant is directed in the opposite direction of motion and when the ejection velocity is exactly equal to the speed of the rocket. In that case, the p... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/213279",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 3,
"answer_id": 1
} |
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... | The gradient is a vector, not a covector, hence :
\begin{equation}
\vec{\nabla} f = \nabla^\mu f = g^{\mu\nu} \nabla_\nu f = g^{\mu\nu} \partial_\nu f
\end{equation}
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/213466",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
"answer_count": 5,
"answer_id": 0
} |
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?
| What we mean by spherical symmetry is that if we take our geometry and consider the surface at constant $r$ it will have the same geometry as a spherical shell, that is the metric will be:
$$ ds^2 = R^2 \left( d\theta^2 + \sin^2\theta \, d\phi^2 \right) \tag{1} $$
where $R$ is some arbitrary constant. If we refer back ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/213641",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Seemingly a paradox on the eigenstate thermalization hypothesis (ETH) In the research field of Many-body Localization (MBL), people are always talking about the eigenstate thermalization hypothesis (ETH). ETH asserts that for a isolated quantum system, all many-body eigenstates of the Hamiltonian are thermal, which mea... | The initial state does not need to be one of eigenstates of the hamiltonian, it could be superposition. Therefore time evolution will change it. I don't think your first assumption is correct.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/213733",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 3,
"answer_id": 2
} |
Can two 2500 K light bulbs replace one 5000 K bulb for growing plants indoors? In an effort to assist an old Greek woman I find myself in need of greater minds.
A 5000 Kelvin light bulb is required for her indoor fig plant. Can I get away with substituting two bulbs each in separate fixtures emitting 2500 Kelvin each? ... | probably not - the 5000K is to do with the spectrum of light emitted - it will be bluer than the 2500K light. Both 2500K lights will have the a 'redder' spectrum.
To be honest it is not even that straightforward as the temperature is an indication of the average overall temperature that the light appears to emit from.... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/214057",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 1
} |
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