Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
How to compute $L_{\rm eq}$ from temporal pressure data I have pressure vs time data. how can I compute sound equivalence Level $L_{\rm eq}$ in decibels? can this be done from a frequency spectrum assuming that it is constant?
| Based on this website, sound equivalence level is defined as
$$L_{eq} = 10 \log{\left( \frac{1}{p_{ref}^2} \frac{\int_0 ^T p_A(t)^2 dt}{T} \right)}$$
where $p_{ref}$ is a reference pressure (usually $20 \times 10^{-6} \text{ Pa}$), $p_A(t)$ is sound pressure, and $T$ is the time period of integration.
Given a frequency... | {
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If we say the universe is expanding, shouldn't it be expanding relative to something? I don't understand, if everything in this world is relative to something else, then cannot we essentially say that nothing exists independently? We say that the universe is considered to be the ultimate 'background'. However, if we sa... | The universe is expanding, in the sense that things in it are getting farther apart. It is not expanding into anything because it already is everything. There simply is nowhere else to expand into.
Lets knock it down one dimension. Your universe is the surface of a balloon. The balloon is slowly being inflated. Your un... | {
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"url": "https://physics.stackexchange.com/questions/119312",
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Redshift 1+z - CMB Temperature lower? I know that $\frac{\lambda_2}{\lambda_1} = 1 + z$
Suppose a galaxy had redshfit $z=3$. Does this mean that the wavelength becomes $4\lambda$?
Then by wien's law where $\lambda \propto \frac{1}{T}$, does this mean that the temperature now observed is $\frac{1}{4} \times 2.73 K$?
| No, it does not. The redshift $z$ is defined, as you already know, by $$z+1=\frac{\lambda_{\text{now}}}{\lambda_{\text{then}}}$$
If we consider a photon that was emitted at redshift $z=3$ the formula yields $$\frac{\lambda_{\text{now}}}{\lambda_{\text{then}}}=4$$ this tells us that the wavelength we observe now is four... | {
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Basic of Capacitor I've 2 capacitors; plate area, difference between plates and dielectric is same. Only thing is that the metal used in plates is different. Since the formula $\displaystyle C=\frac{\varepsilon A}{d}$ states, it won't affect but why?
| The only property of metals used in deriving $C=\varepsilon A/d$ is that they are perfect conductors. Ideally, all metals have this property. So even if you change the metal, it should not matter.
But if you use something other than metal, then it will of course change the capacitance.
| {
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Why doesn't De Broglie's wave equation work for photons? Well, as I am learning about quantum physics, one of the first topics I came across was De Broglie's wave equation. $$\frac{h}{mc} = \lambda$$
As is obvious, it relates the wavelength to the mass of an object. However, what came to my mind is the photon. Doesn't ... | What you have there isn't actually de Broglie's equation for wavelength. The equation you should be using is
$$\lambda = \frac{h}{p}$$
And although photons have zero mass, they do have nonzero momentum $p = E/c$. So the wavelength relation works for photons too, you just have to use their momentum. As a side effect you... | {
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Why is the constant velocity model used in a projectile motion derivation? I was re-studying university physics last week, I'm now in the chapter about kinematics in 2 dimensions and specifically the one treating projectile motion. In page 86 of his book (Serway - Physics for scientists and engineers) he derives the eq... | If we assume there is no wind and air, the only force acting on a projectile in the air is the force of gravity. The force of gravity acts in vertical direction, thereby affecting the vertical component or Y component of velocity only.
Newton's 1st law says that a particle will continue to be in its state of rest or mo... | {
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Help needed to interpret question - Spin States of electron pair in Helium?
For the last part, I'm not sure what they mean by "explain how to form eigenstates of the total spin $\hat S^2$ and $S^z = S_1^z + S_2^z$. Are they simply referring to the spin singlet and tripplet states?
I know for tripplet states total spin... | You know that the total spin operator is given by
$$ {\bf S}^2 = ({\bf S_1} + {\bf S_2})^2 = {\bf S_1}^2 + {\bf S_2}^2 + 2 {\bf S_1}\cdot {\bf S_2}$$
and the most general state is given by
$$\left|s,m\right> = a\left|\uparrow\uparrow\right> + b\left|\downarrow\downarrow\right> + c\left|\uparrow\downarrow\right> + d\... | {
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Constraint and Applied forces In D'Alembert principle forces are classified into constraint and applied forces? Is this classification different from internal-external forces?
| Yes, they are different.
One must define what the system under study is. Usually, it consists of a number of sub-systems. A marble, for example, has as sub-systems many many atoms. Two point masses connected by a massless spring has two sub-systems. Internal forces are forces between sub-systems: the interatomic... | {
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Why is the speed of light arbitrarily the limit? I know Einstein was great and all. Why is it that exactly at the speed of light is where infinite energy is required to accelerate any object with mass? Is it simply because the math of relativity checks out and explains most of everything? Are there any physicists who d... | It's not actually. It's not like light has some special status in the Universe. It's just that there is a maximum speed, and light, among other things, tends to get very close to that limit. In practice light is slowed down by its environment, and there was even speculation at one point, that light mad a bit of mass an... | {
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Why would we need to ground an AC source I'm new to this field hence this weird question. Why would we need to ground an AC source? Why wouldn't it be enough to have just one pole to get an AC current going? I understand why it wouldn't work in DC case where current is flowing in one direction. However, in case of AC s... | If you have only one wire, leaving its end open, you still have current flowing in the conductor, but the efficiency will not be optimal due to impedance mismatch. Since the aim is to transport power, we need the other wire to optimize the efficiency.
| {
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Concrete example of a two-dimensional harmonic oscillator I am a student of mathematics and some time ago I showed in general that for a two-dimensional harmonic oscillator one can apply the recurrence theorem. So far so good.. now I would like to have a concrete example of a two-dimensional harmonic oscillator. Can yo... | The harmonic oscillator is so incredibly important in physics as a whole because of the following consideration. For a more or less smooth potential $V(x)$ with a local minimum at position $x_0$, one can taylor-expand around that minimum:
$$V(x)\approx V(x_0)+\frac{V''(x_0)}{2}(x-x_0)^2+\mathcal{O}((x-x_0)^3).$$
The li... | {
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Is there a reaction force on the ball in a vertical circular motion? You have a light string. At one end of the string there is a ball modelled as a particle. The string has negligible mass. The other end of the string is fixed at a point and the ball is undergoing circular motion.
At the bottom, the centripetal force ... | A ball in a circular path is constantly accelerating(just a change in motion) so using $$F=ma$$
We can tell that if the ball has mass, and is moving in a circle, it will have some force exerted on it.
Since the ball is tied to the string, the string pulls on the ball with the same amount of pull, as the ball is pulling... | {
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Symmetry factor of $n$-point one-loop diagram If we have a one-loop diagram in $\phi ^ 3$ scalar field theory with $n$ external lines, then what is its symmetry factor?
I have drawn the diagram I am looking for, but instead of $6$ external lines, I want the diagram to have $n$ external lines. Please ignore the arrows ... | Cheng and Li's appendix gives the generic symmetry factor $S^{-1}$ with
$$S=g\prod_{n\geq 2}2^{\beta}(n!)^{\alpha_n},$$
where $\alpha_n$ are the number of pairs of vertices connected by $n$ identical self-conjugate lines, $\beta$ is the number of lines connecting a vertex with itself, and $g$ is the number of permutati... | {
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What interaction is responsible for the 21 cm Hydrogen line transition? The 21 cm Hydrogen line is from the transition between the hyperfine levels of the ground state of the hydrogen atom.
So, what interaction is coupling the hyperfine levels?
I suspect that it is not the usual EM interaction, which causes the 1s-2p ... | The 1s energy level is split into two levels, one where the electron spin and nuclear spin are parallel, and the other where the electron spin and nuclear spin are antiparallel.
The 21 cm line is the transition between these two 1s levels.
The transition is a magnetic dipole transition.
| {
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How is sweating a pipe an example of capillary action? I learned how to sweat a pipe today from my father. If you're not familiar with the process, this might help.
One thing that jumps out at me is this line (from the above link, as well as my father's explanation)
Solder, which melts at low temperatures, wicks into... | Since you need to use flux on the pipe first the flux "primes" the connection so that when you heat the fitting and the flux burns off the solder is pulled into the joint to replace it.
| {
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Why don't we consider electrostatic energy of the pair in the case of pair production? I have seen this Wikipedia article and many others, but in none of them I find any mention of the electro-static energy of the generated pair. Why?
I mean, the energy conservation should be written as
$h\nu = E_+ + E_- + Electrostat... | It depends what you mean by "electrostatic energy".
When we are talking of pair production we are talking of physics at the quantum mechanics framework.
FEYNMAN DIAGRAMS for pair production by a gamma ray (left) or an electron (right). These represent the processes in the preceding sketch.
Lets take the simplest ... | {
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Why doesn't a wall move when you push it if there's space behind it?
In the first screen you can see that if a person were to push a wall within a typical household the wall would not move while keeping themselves tractioned to the floor. If you push hard and do not traction yourself, you move back.
In screen two if ... | The force of friction is greater in heavier objects. Moreover the object is attached to the ground. The force applied by us is not strong enough to pull it out. That's why the wall didn't move
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/121688",
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Do radio waves travel around the Earth or through it? Whenever you hear someone illustrating/describing the transmission of radio waves they always make it seem like they'd travel perfectly around the Earth to another distant location. For example, a radio wave sent by alternating current to be received from an interce... | Amateur "ham" radio operators who communicate with HF (3.0 to 30 MHz) frequencies can hear their own signal as it has circumnavigated the globe. This almost only happens with operators using Morse Code (CW) where the distinct signal can be heard and detected with sub-second intervals.
Also, ham operators make a distin... | {
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Why is the outside run of high presure line on a ductless mini-split airconditioner insulated? On every ductless mini-split air conditioner I've ever seen, both the high and low pressure lines are insulated between the compressor and the building.
It seems like the liquid refrigerant coming out of the condensing coil ... | I can see the outside of an airconditioner, bought more than ten years ago. It is not an inverter, but it does heat in the winter. There is one well insulated tube entering the wall ( and a water tube coming out).
For heat pumps it makes senseto insulate well both lines, since the use is reversed in winter, and I do no... | {
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Fermion as a mixture of particle and antiparticle The solution to the Dirac equation (in the Dirac basis) are 4 coupled fields. The first 2 of them represent a particle (spin up/down), the other 2 fields are the antiparticle (spin up/down). When the particle is observed from its rest reference frame, the antiparticle s... | Strictly speaking, a "particle" is only a quantum notion which must be understood in the context of quantum field theory, as a asymptotic state "in" or "out", in some interaction.
So, classicaly, stictly speaking, there is no "particle"
You are speaking of the classical Dirac equation, which is a classical field equati... | {
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"url": "https://physics.stackexchange.com/questions/121922",
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Black hole thermodynamics in a time dependent metric For a time dependent space time metric, to get the thermodynamics, does the standard procedure of Wick rotating the time, and then calculating the free energy, work ?
| In principle it should not. The problem with the Wick rotation is that what you are doing is embedding the Lorentzian manifold in a complex manifold of which it is a slice, and then looking for a different slice with Riemannian signature. In general there is no such Riemmanian slice, and even if it does exist it need n... | {
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Can a fundamental particle black hole with conserved charge emit Hawking radiation? Let's says there is a fundamental particle:
*
*That is so massive that it is a black hole by itself (Compton wavelength < Schwarzschild radius)
*That carries a conserved quantum number (e.g. charge of an exotic interaction) which n... | This is really a comment, but it got too long for the comment box.
The problem is that the Hawking calculation is semi-classical. That is, it assumes the spacetime curvature is given by the (classical) Einstein equation. Once the radius of the event horizon decreases into the quantum regime the approximations Hawking u... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/122055",
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Will two perpendicular orbits settle into a disc? Scenario:
*
*one "fixed" object (like the sun...) of mass X
*two "planets" (P1 and P2) of mass Y
*P1's orbit is perpendicular to P2's orbit, and the sun is the center of both orbits
*P1 and P2 will never collide
My question is: Will this setting (P1 and P2 orbit... | Note that circular orbits never exist in nature, and that the scenario that you described would be very rare. The reason why most solar systems have planets with coplanar orbits is because these planets were formed from an accretion disk, which as the name implies, is a very thin (but dense) cloud of dust and debris o... | {
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Concept of separation of charges in lightning clouds I have read in an article that when lightning strikes in the clouds the cloud disintegrates into two parts of which the negatively charged part is bigger than the positively charged one. Why does this happen?
Here is the screenshot of that article which is a textbook... | I think you just missunderstood the textbook article. It says,
There are ice particles in the clouds, which grow, collide, fracture
and break apart. The smaller particles acquire positive charge and the
larger ones negative charge.
Not the clouds grow, collide, fracture and break apart, but the ice particles. In ... | {
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Melting and Boiling Points of Odd Materials In Chemistry, I was taught that there are three main states of matter: solid, liquid, and gas, and that heat and pressure determine that state. For some substances, the line is blurry between them.
Some materials don't seem intuitively to do this--nor have I been able to fin... | I'm not sure I would focus on the the liquid to gas phase change. Sublimation, seems better behaved. I've heard that some alloys do not have well defined melting points. I don't know if something like that occurs in sublimation. But imagine a crystal lattice consisting of two fairly different substances. In this case i... | {
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Why can't the work done by a non-conservative force be zero? Why can't the work done by a non-conservative force be zero? The displacement along a closed path is always zero. So, whatever be the type of force, variable or constant, the work has to be zero. Why do we need to calculate the work done for individual paths?... | For forces that change along the way, displacement is not the thing to calculate work with. Let $\gamma : [0,1] \rightarrow \mathbb{R}^3$ be the (closed or open) path that the particle the force is exerted on follows. Then, the work done along that path is
$$ W[\gamma,F] = \oint_\gamma \vec{F}(\vec{x})\cdot \mathrm{d}\... | {
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How quickly should a fluid come to hydrostatic equilibrium? Let's say I'm holding a one-liter water bottle, full of water, which I then drop.
Before dropping the water bottle, the equilibrium is for there to be a pressure gradient in the water canceling the gravitational force on the water. While the bottle is in free... | You could start with a pack of cards and ask how long does it takes for the whole pack to free fall after
*
*the bottom card supporting the rest of the pack is released
*all cards are individually held from the sides, and then released at
the same time.
From this, I think the answer to your original questio... | {
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Uniformity in a solenoid I know the magnetic field strength increases as the number of turns in the solenoid increases.
However, I've learnt the field inside the solenoid is usually nearly uniform.
So, does the number of turns in the solenoid effect the uniformity of the field inside the solenoid? Does the field gets c... | It is all relative depending on one's measurement scale. A small homogeneous area may be found in a relatively short (length) to diameter (width) solenoid but the homogeneous area will be minute and perhaps not useful or measurable as homogeneous with a 'standard' Tesla/gaussmeter probe due to the probe's relatively la... | {
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Could Legolas actually see that far? The video “How Far Can Legolas See?” by MinutePhysics recently went viral. The video states that although Legolas would in principle be able to count $105$ horsemen $24\text{ km}$ away, he shouldn't have been able to tell that their leader was very tall.
I understand that the main ... | In the spirit of your question, having two eyes and assuming you can use them as an array (which requires measuring the phase of the light-something eyes don't do) allows you to use the distance between them for $D$ in the resolution equation. I don't know the spacing of an elf's eyes, so will use $6 cm$ for convenie... | {
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Why does a mirror reverse polarization of circularly polarised light? A glass mirror (with metal backing layer) will reverse the polarisation of circularly polarised light upon reflection.
A polished piece of metal will also reverse the polarisation of circularly polarised light upon reflection. (I have tested and conf... | While rob is correct about the quantum mechanical picture I think that this case is at least as easy to understand as in the classical description.
Classically circular polarization can be described in terms of a time-varying linear polarization, so let's just look at two points on a wave.
I'm going to chose a beam in ... | {
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Black and white matters. But why and how? I know black conducts heat while white reflects it.
But they are colors after all.
If a metal is painted black, it conducts more heat or at a rapid speed than it would do before it was coated.
But, as far as I know, colors don't have any special "substance" in them, which might... | I believe that there are some incomplete/incorrect assumptions in this question: the bulk thermal conductivity of a metal will not be affected by a surface coating; it's response to radiative heating will be affected though.
This part of the difference in thermal response to radiative heating is based on the equality ... | {
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Work done in pulling a rope from a boat
A boy sitting on a boat pulls on a rope with a constant force $F$ over a duration of time $t$. The other end of the rope is either tied to a bridge or to another freely floating boat of equal mass. Does the boy do more work in the case of the bridge, or in the case of the other ... | You are mostly correct. Since you are only asked for a qualitative result, you can simplify what you said:
If the boy pulls on rope with force $F$ for time $t$, it will move a certain distance $d$. If the other end of the rope is fixed, the work done is $F\cdot d$. If the end of the rope is moving towards him, the tota... | {
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What's the conserved quantities correspond to the generator of conformal transformation What's the conserved quantity corresponding to the generator of conformal transformations?
| The conformal charge in CFTs is a special case of any other standard treatment of classical field theory (e.g. chapter 1 of Peskin & Schroeder).
In flat space with $(1, n)$ signature and spacetime $(t,x_1, ..x_n)$ coordinates, we consider a conformal killing vector field with components $\epsilon^\mu$. We assume our f... | {
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Black holes and Time Dilation at the horizon What is the difference between proper time and the observer time?
Whilst thinking about Black holes, when we see the Schwarzschild metric
$$c^2\tau ^2 = \left ( 1 - \frac{r_{s}}{r} \right )c^2t^2 - \frac{r^2}{1-\frac{r_{s}}{r}} - r^2d\Omega ^2,$$
and compare it with Einstei... | This is essentially the same effect that you get in special relativity as the velocity approaches the speed of light.
If you take a clock and accelerate it towards the speed of light then it will run slowly. If you could get the clock to the speed of light (which you can't of course) then it would stop completely. To u... | {
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Fork and Sheet Lightning I've noticed that during British lightning storms, I have only ever seen sheet lightning
However, on holiday in other countries, I frequently see Forked Lightning
Q) Is this just caused by cloud, or is it two distinct forms of lightning?
Q) Is there a reason Britain only seems to get the she... | As a long time resident of the UK, I can confirm that forked lightning is not uncommon in the UK, so I think that the OP has just been unlucky. Of course this is just anecdote.
| {
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Why ONLY Maxwell's equations are the basic equations of electromagnetism? In electromagnetism we say that all the electromagnetic interactions are governed by the 4 golden rules of Maxwell. But I want to know: is this(to assume that there is no requirement of any other rule)only an assumption, a practical observation, ... | I appreciate @ACuriousMind's comments on my question and thank him/her for pointing out the link that he/she has pointed out. I also apologize for being somewhat reluctant about mathematics in my comments when I posted the question.
The question was whether Maxwell's equations are the only equations that govern the ele... | {
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Analytical problems with Green's function I have a question about the right definition of the Green's function in physics. Why do we introduce (or not) an infinitesimal, positive number $\eta$ to the following definition:
$$\left[ i\hbar\frac{\partial}{\partial t} - \hat{H}(\mathbf{r}) \pm i\eta\right]G(\mathbf{r},t;\m... | I know complex analysis and the residuum theorem. This kind of thinks are introduce to evaluate some integrals of the form $\int\limits_{-\infty}^{+\infty}$ with some function which have a pole in $0$ and then You add an infinitesimal to evaluate an integral using residuum theorem. My question is why can't You just go ... | {
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How to calculate required energy to displace a pendulum? How can one calculate the amount of energy needed to displace pendulum with given mass m and string length L to $\alpha$ degrees from resting position when acceleration due to gravity is known?
| By considering the variation in the potential energy $V=mg\Delta y$ due to the vertical displacement $\Delta y$.
A displacement of an angle $\alpha$ would move the mass of the pendulum horizontally by $\Delta x=L \sin\alpha$ and vertically by $\Delta y=L(1- \cos\alpha)$.
Therefore the energy required for a displacement... | {
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How is heat transferred to a thermometer? Quick question. I can't seem to find a satisfactory answer online. How does a thermometer measure the average kinetic energy of atmospheric air? I assume that the energy is transferred by molecular collisions, and this somehow raises the temperature of the alcohol by doing work... | Taking out your last analogy about the speedometer (which I don't find useful but it might work for you), I would add that in a sealed thermometer, thermal equilibrium between the external media and the alcohol is mostly reached by exchange of electromagnetic radiation (photons). But heating or cooling or the glass mol... | {
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Derivation of (2.45) in Peskin and Schroeder I'm having trouble understanding the step
$$\left[\pi (\vec{x},t),\int d^{3}y ~(\frac{1}{2} \pi (\vec{y},t)^{2}+\frac{1}{2}\phi (\vec{y},t)(-\nabla^{2} +m^{2})\phi (\vec{y},t)) \right]$$ $$ =\int d^{3}y ~(-i\delta^{(3)}(\vec{x}-\vec{y})(-\nabla^{2} +m^{2})\phi (\vec{y},t)) ... | This is really straight forward, once you get used to the notation. (Don't you hate it when people say that?)
$$[\pi (\vec{x},t), (-\nabla^{2} +m^{2})\phi (\vec{y},t)] ,$$
Here you need to remember that $\nabla^2$ acts on the $\phi(\vec{y},t)$ only, so $\pi$ can pass right through this wave operator. Now when you evalu... | {
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Can matter be created from energy?
The small, hot, dense early universe the size of an atom was made up entirely of energy, it wasn't until after the expansion began and the universe cooled down some of that energy began converting into the first atomic nuclei.
This quote seems a little dubious but I think this is wo... | They are actually trying to do so in the lab. They need a very potent laser (I believe they didn't reach the critical power yet).
The idea is simple, inside the lase cavity you generate a very powerful electromagnetic field, powerful enough such that the photos have enough energy to transform a virtual electron-positro... | {
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Can two single particles interfere with each other? Groups of particles can interfere with one another; In the double slit experiment when measuring single photons at the screen each one arrives at the screen in a random manner and they only show the interference pattern once several particles are detected.
Obviously ... | Classical particles such as electron, proton and neutron of course interfere with each over. No doubt. Photons interfere too. See https://en.wikipedia.org/wiki/Photon_bunching.
If you ask about the double slit experiment with single photons the common answer is yes. A single photon interfere at the position of the slit... | {
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Would computers accelerated to high speeds compute "faster" from our point of view? I woke up to this thought yesterday:
Lets say Computers A and B have exactly the same specifications and at time T both are set to process an algorith that would normally take exactly 1 year and exactly at T the A computer is accelerate... | 1) No, because it's actually going slower from your perspective. In special relativity, "the fastest wristwatch is always your own".
2) Yes, but remember that it's farther away from us now, so it will take some time to get to us (if it was travelling at 0.5c it will take 50% longer to get to us).
3) Mostly in that as a... | {
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Trying to combine red, green and blue to produce white I tried to mimic the mechanism of typical screens to produce white color out of red, green and blue.
What I did is displayed the attached image on the screen, and moved far away as to let the diffraction effects take place, so that the three colors appear as if the... | While David Hamman's answer is correct, I wanted to expand a little bit on his answer:
When you use a CRT, you are looking at emitted light. In the case of emission, there is no "absolute" white - something will only look gray in comparison to something else with the same color ratio but brighter. When you turn up the ... | {
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Ground state Phase Diagram of Bose-Hubbard Model The Hamiltonian of Bose-Hubbard model reads as
$$H=-J\sum\limits_{<i,j>}b_i^{\dagger}b_j+h.c.+\frac{U}{2}\sum\limits_{i}n_i(n_i-1)-\mu\sum\limits_in_i~~~~~~~~~(1)$$
For this we plot phase diagram in ( $J/U$, $\mu/U$ ) space.
Same way if I want to plot phase diagram of... | In principle, it is very simple and straightforward.
The problem is to map out the region where the integer filling state is the ground state. Suppose you have $L$ sites. Take $N=L$ particles, find its ground state energy, which is denoted as $E_g(L)$. Note that here the Hamiltonian does not contain the $\mu $ term. D... | {
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Why does a wine glass with less water resonate at a higher frequency? In this video https://www.youtube.com/watch?v=hWwM7F-zaHs, Professor Lewin showed that for the tube, the less water there is, the longer the effective length of the tube and therefore, the lower the frequency.
He then demonstrates an opposite effect ... | For the pipe, it is the air that is vibrating. When the column of air is shorter the frequency is higher.
In the case of the wine glass, the glass (not the air) is vibrating. Add water and you increase the inertia of the glass, which lowers the frequency of the resonance. The air may also resonate - but for something t... | {
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Is there a difference between "average acceleration" and centripetal acceleration? Question adapted from Examkrackers MCAT prep book:
A particle moves along a half circle (diameter=$10\text{ m}$) at a constant speed of $1\text{ m/s}$. What is the average acceleration of the particle as it moves from one side of the ha... | Centripetal acceleration is a type of acceleration but Average acceleration is the calculation of acceleration. They are different.
| {
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Is there a metatime required for space-time to change? Space-time is thought to curve and ripple. Is a kind of metatime required in or during
which such events take place?
|
Space-time is thought to curve and ripple.
Space-time, i.e. the set of all events under consideration (specificly: coincidence events), together with all relations between these events (primarily: by listing who, among all principal identifiable participants, took part any one coincident event), is thought to be not... | {
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Sum of Green's functions in condensed matter I am working on the Ginzburg-Landau model for Charge density waves, and I am carrying out the sum of Green's functions to calculate the terms in the GL model.
Is the sum's order over $ \vec{k} $ (or eventually $ \vec{r} $) and $\omega_n$ important? Mathematically the questio... | If the whole summation converges, then the two summations commute.
For example, the following summation diverges, so the two summations do not commute,
$$\sum_{i\omega}\sum_k\frac{1}{(i\omega-k)^2}.$$
However if we consider the following convergent summations, you can change the summation order freely.
$$\sum_{i\omega}... | {
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Ampere's law and Biot-Savart law gives different terms for magnetic field in middle of a current running in a loop
I would like if someone could clarify this issue for me:
When dealing with a current $I$ running in a loop with radius $R$ and looking for the magnetic field in the middle of the loop.
By using Ampere's l... | Your calculation of $B$ using Ampere's Law is not correct. The integration surface should have its area perpendicular to the current and should have one of the sides go parallel to $\vec{B}$. The choice of surface, when using that form of Ampere's Law, is usually a square or rectangle. That's why using it for a single ... | {
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Why are most accurate reflective surfaces not white? Since white is our perception of reflection of light, why are mirrors and other metallic objects that are more grey or silvery capable more reflective than a white object?
This is somewhat related: What is the difference between a white object and a mirror? but I'm w... | This is similar to why a glass of water and a glass of milk look different. We can use geometric optics (used in 3D animation ray tracing) to explain this.
When a light ray (of any color) hits a mirror, it reflects as another light ray. But for a white nonreflective surface, it is scattered in all directions.
From the ... | {
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How would an X-ray scanner identify a mirror? A mirror is under normal circumstance used to reflect Electromagnetic radiation also known as photons (light) and in airport security or medical facilities, they use X-rays to detect anomalies inside objects or bodies to detect narcotics or injuries. However, I always wonde... | dmckee points out that an ordinary mirror doesn't reflect X-rays, but if you could find an X-ray mirror and put it in your case it would just appear black.
When you look at yourself in the mirror you're seeing light from your skin/clothes that hits the mirror and is reflected back towards your eyes. But airport X-ray m... | {
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My basis set isn't orthonormal? I'm implementing a little QM calculation just for fun and to make sure I understand how it works (calculating the helium ground state energy). My problem is that my basis set doesn't seem to be orthonormal. I'm using the spherical harmonics for the angular part and the Slater type radi... | Indeed, the Slater-type orbitals (radial wave functions) are not orthonormal – they are not even orthogonal to each other. The $\delta_{n,n'}$ Kronecker delta symbol doesn't appear in the inner product and it can't because the $r$-dependent integrand is positively definite and there is no room for cancellation.
Their n... | {
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"Lack of inversion symmetry" in crystal? Apparently (first paragraph of this article) the lack of inversion symmetry is some crystals allows all sort of nonlinear optic phenomena.
Now. Does anyone know of an intuitive or just physical explanation as to why this is the case?
What does inversion symmetry mean and what i... | In nonlinear optics, the typical approach seems to be: take the relation between the polarization and electric field $P=\epsilon_0 \chi E$ and start adding correctional terms based on the Taylor series.
$$P=P_0+\epsilon_0 \chi^{(1)} E+\epsilon_0 \chi^{(2)} E^2 +\epsilon_0 \chi^{(3)} E^3 +...$$
This particular phenomena... | {
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Proof of Liouville's theorem: Relation between phase space volume and probability distribution function I understand the proof of Liouville's theorem to the point where we conclude that Hamiltonian flow in phase-space is volume preserving as we flow in the phase space. Meaning the total derivative of any initial volume... | I do not think probability distributions are preserved by the Hamiltonian flow...consider a probability distribution that is a $\delta$-function on the phase space at initial time (you have just one point with probability one), so it is a particle with fixed coordinate and momentum. If you evolve in time by the Hamilto... | {
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Why is the pressure inside a soap bubble higher than outside? Apparently, the air inside a soap bubble is under higher pressure than the surrounding air. This is for instance apparent in the sound bubbles make when they burst. Why is the pressure inside the bubble higher in the first place?
| The increased pressure is caused by the surface tension between the soap and the surrounding air. This can be seen by a simple equilibrium energy argument. The total energy of the system reads
$$
E = E_i + E_o + E_s \;,
$$
where $E_i$ is the energy associated with the air inside the bubble, $E_s$ is the interfacial e... | {
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Is speed of light and sound rational or irrational in nature? Just as circumference of circle will remain $\pi$ for unit diameter, no matter what standard unit we take, are the speeds of light and sound irrational or rational in nature ?
I'm talking about theoretical speeds and not empirical, which of course are ratio... | It depends on the unit you want to express it.
If you choose c/100 as the speed unit, c will be expressed with a rational number. If you choose c/π, you'll have an irrational one.
That depends on measure, not on nature.
| {
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Which ball touches the ground first? This is a very well known problem, but I can't find an answer in the specific case I'm looking for.
Let's consider two balls :
*
*Ball 1 weighs 10 kg
*Ball 2 weighs 1 kg
*Balls have identical volumes (so Ball 1 is much more dense)
*Balls have identical shapes (perfect spheres)... | This problem can be easily solved by the formula “F=ma”.
You must be familiar with the reason why it would fall at the same rate in vacuum.
But if we talk about the free fall in atmosphere, as you said there will be friction off course, and as the objects have the same shape, it’ll be same.
As the force of friction is... | {
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Is it possible to produce images of pair production in home-made cloud chamber? There are some nice pictures on the web showing the counter-spiralling paths of an electron positron pair produced in a bubble chamber with a uniform magnetic field, for example:-
(source: bigganblog.com)
Would it be practical to produce a... | These electron-positron pairs are created by gamma rays. I don't know anything about how to make a cloud chamber, but detecting cosmic gamma rays at the surface of the Earth is very very rare. The atmosphere is very opaque to gamma rays (Source). Cosmic gamma rays burst are commonly detected on satellites orbiting the ... | {
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Calculate water flow rate through orifice I'm not very good with fluid physics, and need some help. Imagine the following setup with water contained in-front of a wall with an opening on the bottom:
How do I calculate the water flow $Q$?. I have made some re-search and found I need to (partially) calculate the pressur... | The NCEES: FE Reference Handbook has some good material on fluid flow through a submerged orifice in its fluid mechanics section. You can search for it online. NCEES will provide you with one free of charge.
| {
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About the definition of expectation value in quantum mechanics In quantum mechanics, the expectation value of a observable $A$ is defined as
$$\int\Psi^*\hat A\Psi$$
But in probability theory the expectation is a property of a random variable, with respect to a probability distribution:$$E(X):=\int X\;d\mu$$
I can't se... | Since you want a bit of mathematical rigor:
A quantum state is a self-adjoint positive trace class operator on a Hilbert space with trace 1. This is called density matrix $\rho$. In its simplest form, given $\psi\in \mathscr{H}$, $\rho$ is the orthogonal projector on the subspace spanned by $\psi$. Let $E_\rho(\cdot):D... | {
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Recent missed opportunities à la Freeman Dyson There is an excellent paper by Freeman Dyson from 1972 (here) and therein the author cites old talks by Hilbert (here) and Minkowski (chapter 2 here) speaking about similar topics, namely how opportunities for discoveries could be better if mathematicians and physicist wor... | There was an FQXi essay competition on this subject in Spring 2015:
"Trick or Truth: the Mysterious Connection Between Physics and Mathematics"
Here is the home page with links to winners and other entries:
http://fqxi.org/community/essay/winners/2015.1
The competition is meant to encourage an informal style, readable ... | {
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Why does light travel at the same speed when measured by a moving observer? I know the hypothesis that the light speed is constant is retained by experiments. But is there any theory explaining why the light speed is constant no matter how an observer moves relative to light?
My question is, specifically: Suppose an ob... | A personal point of view is that you may consider that Lorentz transformations apply primarily on momenta, and not primarily on (infinitesimal or not) space-time coordinates.
This is, of course, a "strong" postulate.
If you assume (some additional postulates are needed there) that transformations are linear, and that ... | {
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How would an X-ray mirror work? I was wondering if light can be reflected how can someone reflect X-ray of what material does it need to be made of and is its design completely different to that of our original mirrors? Does this mean during long-space voyages in which radiation is an problem why can scientists not dev... | There are a lot of X-ray mirrors in space and around the world. Applications are X-ray astronomy, synchrotron sources, some medical and litographical application. So it is not something theoretical.
All these mirrors have in common is to reflect light at grazing incidence, they are shaped in way to focus the light in a... | {
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Who proposed the bulk-edge correspondence principle? Who proposed the bulk-edge correspondence principle?
The principle is often quoted in counting the number of zero energy states localized on the interface between two insulators with distinct band topology. However, I could not retrieve who was the first to say that.... | Maybe it is R. Jackiw and C. Rebbi (Phys. Rev. D 13, 3398)
When explaining the quantum Hall effect, Hasan and Kane (Rev. Mod.Phys. 2010, 82: 3045–3067) said "This interplay between topology and gapless modes is ubiquitous in physics and has appeared in many contexts. It was originally found by Jackiw and Rebbi (1976) i... | {
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Has anyone experimentally shown the quantized thermal hall conductivity in Quantum Hall systems? For background:
In a $D=2+1$ state with edge modes described by a chiral $( c_L \neq c_R )$ CFT there is a predicted thermal Hall conductance associated with the gravitational anomaly at the edge. This is the case for integ... | The experiment on kxy has not been done yet, to my knowledge, but there are several (recent) experiments which are closely related and probe the heat flow through the edge channels of a Hall bar in the fractional regime: http://www.nature.com/nature/journal/v466/n7306/abs/nature09277.html or http://www.nature.com/nphys... | {
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Why does Pluto's orbit cross Neptune's orbit? Why does Pluto's orbit cross Neptune's orbit? Is this a fault in Newton's law of gravitation?
| Pluto's average distance from the Sun is larger than Neptune's but Pluto's orbit has a higher eccentricity – the elliptic orbit is more squeezed, less uniformly circular, and such ellipses simply do intersect each other.
The elliptical orbits with properties first identified by Kepler's laws do follow from Newton's la... | {
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In a Big Crunch, would there be more mass than at the Big Bang? I found multiple questions where it is stated that dark energy increases as the universe expands. Assuming a big crunch scenario, will this dark energy "go away" again as the size of the universe decreases again, or will there be more energy (=mass) at the... | Point A) The same mechanism that causes the amount of dark energy to increase as the universe expands will cause the amount of dark energy to decrease if the universe contracts.
Point B) A universe that includes an increasing amount of dark energy due to the same mechanism that exists in our universe (in theory) makes ... | {
"language": "en",
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Double rainbows In my garden, when I'm watering the plants I sometimes see a rainbow or two. How did two rainbows appear? Why can't I see three rainbows then, or how can I see three rainbows?
| The two rainbows that are formed are the primary and secondary rainbows respectively, in order of their intensity or brightness, as you may call it. A primary rainbow is formed as a result of a three- step process: Refraction with dispersion, followed by total internal reflection and then refraction.
The secondary rain... | {
"language": "en",
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How to calculate the drag coefficient using terminal velocity? I was wondering if it were possible to calculate the drag coefficient by allowing an object to reach terminal velocity. Can you rearrange the terminal velocity formula to give the drag coefficient?
| Following on Spaderdabomb answer,
the drag force $F_D$ acts on the body and, as such, it balances with the other forces and the inertia of the body ($\sum\vec{F} = m\tfrac{d\vec{u}}{dt}$).
When you consider a situation where the body is at terminal velocity, this means its velocity is constant (at least in that directi... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Why is baryon or lepton violation in standard model is a non-perturbative effect? The baryon number B or lepton number L violation in the standard model arise from triangle anomaly. Right? Triangle diagrams are perturbative diagrams. Then why the B or L violation in Standard model is said to be a non-perturbative effec... | It is a non-perturbative effect because it is 1-loop exact.
The triangle diagram is actually the least insightful method to think about this, in my opinion. The core of the matter is the anomaly of the chiral symmetry, which you can also, for example, calculate by the Fujikawa method examining the change of the path i... | {
"language": "en",
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"source": "stackexchange",
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Energon: is it possible? I'm always quite curious about the "Energy cube" in Transformers, or namely Energon.
Is it really possible to store energy, such as electricity, into such a compact form? safe to distribution, and seems nothing left after being consumed?
ps. Wikipedia has a page for Spark, which is more for tr... | It is possible to capture positrons (antiparticle of electron) in a magnetically confined plasma - the repulsive forces get very large unless you do something to equalize the charge. The energy density that could be achieved is stunning.
This was the principal plot line behind Dan Brown's "Angels and Demons" - this pla... | {
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Kinetic Energy of a Particle Consider a particle of mass $m$ in $6$ dimension. Its coordinate w.r.t. origin $\left(0,0,0,0,0,0\right)$ is given as $\left(x,y,z,\dot{x},\dot{y},\dot{z}\right)$. If we denote $r = \sqrt{x^2+y^2+z^2}$, then which of the following two is the kinetic energy of this particle:
*
*$T = \frac... | The kinetic energy is $T = \frac{1}{2} m (\frac{d \vec{r}}{d t})^2$
$$\vec{r} = x \vec{i} + y \vec{j} + z \vec{k}$$
The first exprssion is right.
| {
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How much of the sky is visible from a particular location? From a particular point how much of the sky can be observed. For simplicity sake let us assume the particular point is the head of a 6 foot tall man floating in the middle of the ocean with no visible barriers between him and the horizon. If he stays in exactly... | Visible objects in low-Earth orbit (such as the International Space Station) take about 90 minutes—5,400 seconds—to complete a single orbit. Unequivocally far beyond the mesosphere at 240-250 miles above Earth, such objects might provide a rough proxy for measuring the portion of blue "sky" that is visible.
Now when v... | {
"language": "en",
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Is it possible to 3D print a mirror to create a high quality telescope? Is it possible to 3D print a mirror with todays available materials?
If so, would there be a reduction in image quality?
| The highest resolution 3d printers I know of are around 1600dpi, which is a resolution of about 15$\mu m$. Telescope mirrors have to be smooth to fractions of a wavelength of light, so the resolution of current printers is nowhere near good enough.
Whether 3D printers could one day be good enough is a different questio... | {
"language": "en",
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Differences between probability density and expectation value of position The expression $\int | \Psi\left(x\right)|^2dx$ gives the probability of finding a particle at a given position.
If wave function gives the probabilities of positions, why do we calculate "expectation value of position"?
I don't understand the c... | Let $\Omega\subseteq \mathbb{R}^n$; then $\int_\Omega \lvert\psi(x)\rvert^2dx$, for a normalized function $\psi\in L^2(\mathbb{R}^n)$ gives the probability that the particle is in the region of space $\Omega$, but does not give any further information on its position. If you want to obtain a quantitative information on... | {
"language": "en",
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What is $c + (-c)$? If object A is moving at velocity $v$ (normalized so that $c=1$) relative to a ground observer emits object B at velocity $w$ relative to A, the velocity of B relative to the ground observer is
$$ v \oplus w = \frac{v+w}{1+vw} $$
As expected, $v \oplus 1 = 1$, as "nothing can go faster than light"... | As pointed out by zakk, any proper time of objects moving at light speed would be zero.
That means physically that there does not exist any point of time where you could perform the addition c + (-c). Example: A photon is emitted at A and absorbed at B. There is no point of time A < t < B where the photon is actually ... | {
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How to approximate acceleration from a trajectory's coordinates? If I only know $x$- and $y$- coordinates of every point on a trajectory without knowledge of time information, is there any way to approximate Cartesian acceleration angle at each point? Time interval between every two points is very small, ~0.03 second. ... | From the path you need to find the radius of curvature $\rho$ at each point. This would be kind of noisy unless you have really precise data. Your best bet into input all the x and y points into cubic spline in order to get what the derivatives $x'$ and $y'$ are (in units of length per frame). In addition, you need to ... | {
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How to determine the sign of the s-wave scattering length? I guess it is relatively easy to determine the magnitude of the scattering length $a$.
We just need to measure the scattering cross section. In this way, we can determine the value of $a^2$.
But how to determine its sign?
| One way to measure the magnitude is by looking for a density-dependent energy shift. If you transfer atoms between, say, two hyperfine states with a microwave transition, the resonant frequency of this transition will change due to the mean-field shift from the interactions. If you start with an interacting mix of stat... | {
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Is interstellar flight possible in near future in a way that would keep our civilization alive? Is interstellar flight possible in the near future in a way that would keep our civilization alive?
I mean is it practically possible to obtain technology that would enable us to travel to nearby habitable earth-like planets... | It's easy after we rebuild ourselves first. We need to replace biological brains by digital brains. The problem we now have is that if we travel, we carry a biological machine that is much more advanced than the most powerful supercomputer we can build today, physically to the point of destination. This biological mach... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/130450",
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Angular Momentum Conservation Definition Did I missed something in angular momentum definition?
Two identical bodies rotate around mass center.
Now I invented anti-gravity and turning gravitational switch off.
Those two bodies will move now in straight line with constant velocity and angular momentum conservation is co... | One does not need to switch "gravity off" to make a system like that. Replace gravity with a simple string, and cut the string. Physically that's completely equivalent to your problem, as far as I can see.
And while this may seem counterintuitive, the angular momentum in a system of a mass rotating at the end of a str... | {
"language": "en",
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What's the relationship between uncertainty principle and symplectic groups? What's the relationship between uncertainty principle and symplectic groups? Does the symplectic groups mathematically capture anything fundamental about uncertainty principle?
| Yes, of course, symplectic groups describe generalized situations that reveal the uncertainty principle.
The reason for the relationship is that the symplectic groups are defined by preserving an antisymmetric bilinear invariant,
$$ M A M^T = A $$
where $M$ is a matrix included into the symplectic group is the equation... | {
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Is our universe an emulation? I was watching one of Neil Degrasse Tyson talks and there was a scientist (can't recall his name sorry) who was talking about a recent discovery:
"Doubly-even self-dual linear binary error-correcting block code" has been discovered embedded within the equations of superstring theory.
Is... | If you were a simulated person inside an emulation, would you ever be able to tell the universe was emulated? the answer is no, not if it is set up correcty.
| {
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If MOND theory doesn't explain gravitational lensing, couldn't well placed black holes explain it? When I first heard about star velocity as a function of its distance from the center of the galaxy and the difference between prediction and observation I immediately thought "there must be a threshold where gravity react... | You should not take claims about the failure of MOND to reproduce strong gravitational lensing too seriously. In this review article the authors, Benoît Famaey and Stacy S. McGaugh, state:
Due to the fact that all the above models were using the Bekenstein μ-function (α = 0 in Eq. 46), and that this function has a te... | {
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Given a slanted pipe Question: I have a pipeline that is tilted. I know the length of the pipeline, and the pressure (90psi) that is felt at the very bottom. I'm trying to find out how much liquid has leaked out if the pressure at the bottom decreases to 80psi.
Is the pressure felt at the very bottom directly proportio... | The pressure at the bottom of a pipe, or any other column of liquid, for that matter, is directly proportional to the height of the liquid.
The pressure of the liquid is equal to:
$\rho h$, where $\rho$ represents the density of the liquid, and h represents the height.
So, assuming that the cross-sectional area of the ... | {
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Finding the density of gold crown using archimedes principle Question: As shown in diagram below the crown has a mass of 14.7kg when measured above water and 13.4kg when measured in water. Is the crown made of gold?
I have this following solution provided:
The apparent weight of the submerged crown, $w'$,equals the a... | Consider $w$; it's the volume of the object times its density times $g$.
Consider the buoyant force; it's the volume of the object times the density of the fluid times $g$
So, what's the ratio of the weight to the buoyant fore, when you cancel out the constant factors?
| {
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What is entropy really? On this site, change in entropy is defined as the amount of energy dispersed divided by the absolute temperature. But I want to know: What is the definition of entropy? Here, entropy is defined as average heat capacity averaged over the specific temperature. But I couldn't understand that defini... | In terms of the temperature, the entropy can be defined as
$$
\Delta S=\int \frac{\mathrm dQ}{T}\tag{1}
$$
which, as you note, is really a change of entropy and not the entropy itself. Thus, we can write (1) as
$$
S(x,T)-S(x,T_0)=\int\frac{\mathrm dQ(x,T)}{T}\tag{2}
$$
But, we are free to set the zero-point of the entr... | {
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Physical applications of matrices and determinants Other than notation devices, I don't see any direct application of matrices/determinants in physics. For example, they are just a different way to write a partial derivative and determinants find if they can be explicitly solved if written down as simultaneous equatio... | Lie groups are fundamental for talking about anything related to symmetries in physics on a level of some rigor, and every finite-dimensional Lie group is a matrix group. Consequently, the trace as a basic matrix operation shows up anywhere where invariance on the adjoint action of the group is needed, and the matrices... | {
"language": "en",
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Hugh Everett's MWI According to Hugh Everett's many worlds interpretation, all the possibilities of one action can happen at the same time in other parallel universes, so how come we can't see these worlds? now I bumped into something called the quantum decoherence but I can't seem to get how this decoherence work?
| To "see another World" would require doing a measurement that involves (partially) reversing the effect that led to the split. In practice this is impossible to realize because the observer is a macroscopic object itself and it will decohere very fast. Decoherence means that the system becomes correlated with the envi... | {
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Is there an alternativee method of transmitting wireless electricity? I have currently been researching a lot lately about wireless transmission of power.
Currently the only methods I have seen that is viable is magnetic induction, and high voltage discharge (Tesla coil and Van de Graff generators).
The 2 methods above... | You can build microwave antennas of any desired size and directivity. The thermodynamic efficiency of a properly designed microwave link should be around 50%, even though the cost would be horrendous. And if you really need lots of remote power, you can simply get yourself a nuclear power plant at that location. Not th... | {
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Question about infinite sum in quantum field I read from some books of number theory that $$\sum_{n=1}^{\infty}\frac{1}{n^s} = -\frac{1}{12}\text{,when } s=-1.$$
Now is there such a result $$\sum_{n=1}^{\infty}\frac{1}{n^s} = \pi \text{,when } s=1,$$or $$\sum_{n=1}^{\infty}\frac{1}{n^s} = c \pi \text{,when } s=1 \text... | Valter's answer is completely correct, but I'll just briefly expand on it to address the specific values you ask about. The place to go, really, is the Wikipedia page Particular values of Riemann zeta function, which lists mosts of the values of $\zeta(s)$ (which, as Valter explained, equals
$$\zeta(s) := \sum_{n=1}^{... | {
"language": "en",
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Bekenstein bound for electron? Using the Wikipedia version of the Bekenstein bound, and substituting the Wikipedia values for electron mass and radius, one obtains 0.0662 bits. Does this really mean that a system, any system, placed inside a sphere the size of an electron, and weighing no more than an electron does, is... | One can't take results like that too seriously at the scale at which an electron would apply. In particular, the classical general relativistic model, applied naively to a point mass electron would tell you that the electron has too large a charge and angular momentum to have a black hole horizon, and would instead be... | {
"language": "en",
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The Effect of Tortoise Coordinates Referring particularly to
http://arxiv.org/abs/hep-th/9909056
in regard to the wave equation for Schwarzschild-AdS black holes (p.4), I'm trying to understand tortoise coordinates.
So starting with the 4-dimensionalSchwarzschild-AdS metric in the general form
$$ds^2=-f(r )dt^2+\frac... | The form of $V$ does not change. What you mean by $V(r_*)$ is $V(r(r_*))$ so you would've to explicitly find $r$ in terms of $r_*$ (which is impossible) to fully express your potential in terms of $r_*$.
| {
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Do charges flow from strong insulator to weak insulator? Do static charge in a strong insulator flow to a weaker insulator when both stay in contact with each other? For example, when an insulator weaker than air placed in a medium of air, would the static charges on the insulator be absorbed to the air slowly and fina... | The Triboelectric effect is the process through which materials can become electrically charged through friction when they come in contact with other different materials.
These materials do not have to be insulators for this effect to take place however if they are good conductors the charge will usually flow away.
The... | {
"language": "en",
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Unequally charged hanging pith balls I have done a problem which asks us to find the charge on two equally 'massed and charged' pith balls which are left hanging on a string with a certain length that repels each other and attains an equilibrium point making an angle (the string) with the vertical.
The problem was qui... | As long as your product $|q_{1}||q_{2}|$ remains the same as in the case where you had the equally charged spheres, then yes, you will get the same value for the angle (provided the masses are equal). This is because the electrostatic force acts equally on both charged spheres.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/132982",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Scientists observe the laws of the physics but, Where do they come from? Has anyone ever considered how the laws of physics that we study came into being.
| Based on what we know, both from science and philosophy, these are both ill-phrased questions. You can get as many answers to them as you like, and they will all be equally meaningless, because none will bare any logical relationship to known facts about the universe we live in.
Now, there are much better question alo... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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A step in zeta function regularization I'm just wondering about the mathematical step
$$\sum_{n=1}^\infty n\exp[-\epsilon n\sqrt x]=\frac1{\epsilon^2 x}-\frac1{12}+\mathcal O(\epsilon).$$
Why is this equality so? I see that
$$\sum_{n=1}^\infty n\exp[-\epsilon n\sqrt x]=-\frac1{\sqrt x}\frac{\partial}{\partial\epsilon}\... | The geometric series formula tells us
$$
\sum_{n=1}^{\infty} e^{-\epsilon n\sqrt{x}} = \frac{e^{-\epsilon \sqrt{x}}}{1-e^{-\epsilon\sqrt{x}}}.
$$
The derivative with respect to $\epsilon$ of the left hand side gives $-\sqrt{x}$ times your sum. Therefore your sum is equal to
$$
-\frac{1}{\sqrt{x}}\frac{\partial}{\partia... | {
"language": "en",
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Could we tell the difference between population I and II (or even III) neutron stars? This question is related to thoughts I was having about the mass-radius relationship for neutron stars. Is it unique? Is there a single relationship between $P$ and $\rho$ or is there any chance that the NS "remembers" the composition... | The distinction between populations is one of
*
*what fraction of nucleons are neutrons and
*how the nucleons are grouped (i.e. atomic species)
In the bulk of a neutron star nucleons are no longer grouped in atoms and find their equilibrium by transforming from proton to neutron and back again, so the naive an... | {
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What does a supernova look like at its peak luminosity? I know that in some types of supernovae, the cause of the increased luminosity is the radioactive decay of certain elements ejected during the explosion, so a question came to my mind.
If the ejected material carrying the isotopes that decay to give the electromag... | Your math does check out:
\begin{align}
r&=vt \\
&=0.05\cdot2.9979\times10^{10}\frac{cm}s\cdot4\cdot604800\,s\\
&=3.63\times10^{15}\,cm\\
&=36.3\times10^9\,km\\
&=0.012\,pc
\end{align}
When a supernova explodes, it enters the free expansion phase, it's position is linear in time ($r=vt$, as used above). It stays in t... | {
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Why should an area vector point normal to the surface? Why is it that the direction of an area vector should be always along the normal drawn to the surface? Can't it also be some other angles with the plane?
| This convention is extremely convenient when doing things that physicist often like or need to do, such as computing a flux through a surface. When the area vector is chosen normal to the surface, one can simply take use an dot product to get what you're looking for.
In the context of differential forms, this also turn... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/133466",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 3,
"answer_id": 0
} |
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