Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
How to treat differentials and infinitesimals? In my Calculus class, my math teacher said that differentials such as $dx$ are not numbers, and should not be treated as such.
In my physics class, it seems like we treat differentials exactly like numbers, and my physics teacher even said that they are in essence very sma... | As you see from the variety of answers there are many possibilities to interpret differentials mathematically exact.
One nice simple interpretation is as coordinates of tangential vectors.
Consider an equation
$$
z = f(x,y)
$$
describing a curved surface in three-dimensional space ($z$ is the height).
Then the equation... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/92925",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How much up will an object of mass $m$ will be vertically lifted if a constant acceleration $a$ is given so that resulting force is more than weight? Yesterday My friend asked me a question which put me into a confused state.
If a body of mass m is given a vertical thrust of $F$ such that $F > mg$, and the $F$ is allow... | Although this is old, I can't leave this wrong information here without comment. Newtonian physics only works at low velocities. According to Einstein's theory of relativity, the mass will continue to accelerate until it nears the speed of light. It will not exceed the speed of light. It will, however, keep moving aw... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Why in some cases $0\alpha$ component of stress-energy tensor don't form 4-vector? In electrodynamics there is Poynting vector and energy density, which refer to $0\alpha $ components of stress-energy tensor, don't create 4-vector. Analogous situation with mass density and mass current density in general relativity. So... | Maybe I did not understand your question. However, referring to the stress-energy tensor, the four-vector you want is:
$$S_\nu = \int_{\Sigma_t} T_{0\nu} d^3x$$
where $\Sigma$ is the rest 3-space $x^0=t$ of Minkowski reference frame with coordinates $x^0,x^1,x^2,x^3$. In view of the relation $\partial_\mu T^{\mu \nu}=0... | {
"language": "en",
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The physical interpretation of Newton's constant $G$ It is well known that the speed of light $c$ can be interpreted as the speed limit for information propagation. Similarly, the Planck's constant $h$ is interpreted as the minimum quantum package of action/entropy. Is there a similar interpretation for the Newton's co... | Any interpretation in some sense underlines the property that you find interesting.
Maybe Schwarzschild radius or Planck's mass could be used to give a satisfactory interpretation of G. Otherwise it's just a coupling const. like the fine structure const.
| {
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"url": "https://physics.stackexchange.com/questions/93373",
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Dielectric constant or permittivity of metals I'm wondering what the dielectric constant or permittivity of metals is --particularly copper. Do metals have an infinite permittivity?
|
In electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium.
Yes, metals have infinite permittivity as they completely ne... | {
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Predicting the direction of sound incorrectly? When i was sitting outside my house yesterday, I heard a strange sharp sound. I could not point out it's exact direction but apparently looked like coming from left but later my friend told me that an accident had occurred (due to which the strange sound came) and it total... | Your brain uses lots of tricks to try to localize the sound including comparing the timing between when your ears hear the sound as well as the various distortions your head and ear shapes reflect, refract, and attenuate the sound. For example, if a sound is perfectly behind you, you can hear that it's behind you, not... | {
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Why doesn't Newton's Second Law include higher-order mass? I suspect this has been asked here before, but I didn't find anything using Search.
Why is Newton's second law only second-order in position? For instance, could there exist higher-order masses $m_i$ with
$$F(x) = m\ddot{x} + \sum_{i=3}^{\infty} m_i x^{(i)}?$$
... | One avenue of approach is to consider what this would imply for the simple harmonic oscillator -- that is, if Newton's Second Law was $F = m x^{\left(n\right)}$ :
$$
m x^{\left(n\right)} = - k x \ \ \ \Rightarrow \ \ \ x^{\left(n\right)} + \omega^2 x = 0,
$$
where $\omega = \sqrt{k / m}$. Assuming a solution
$$
x = A ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Satellites and gravitation A satellite with mass $m$ orbits a planet of mass $M$ in a circular path with radius $r$ and velocity $v$. Due to some internal technical failure, the satellite breaks into two, similar parts with mass $m/2$ each. In the satellite's frame of reference, it appears the two parts move radially, ... | There is something strange with the problem. In particular, when the satellite divides, the consevation of lineal momentum implies both parts moving each with the same tangential velocity (same direction) in the orbital direction but half mass, so $(mv/2+mv/2=mv)$ (orbital velocity). The angular momentum cannot be zero... | {
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Does a photon instantaneously gain $c$ speed when emitted from an electron? An excited electron loses energy in the form of radiation. The radiation constitutes photons which move at a speed $c$. But is the process of conversion of the energy of the electron into the kinetic energy of the photon instantaneous? Is there... | Taking an atom as an example, the initial state must already be a state of the combined atom-field system. It cannot be an eigenstate, then the atom would not decay. This with the exception where the initial state involves the atomic ground state and the field vacuum state.
But how is such a state created? One possibil... | {
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"source": "stackexchange",
"question_score": "13",
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Proper time along path in Minkowski Space Consider the path $x^\mu(u)$ in Minkowski space; such that:
$$t = \frac{a}{c} \sinh(u) , \quad x = a \cosh(u) ,\quad y = 0 ,\quad z = 0 $$
where $a$ is a positive constant and $u$ is a parameter
Use equation:
$$ c \nabla \tau = ds = \sqrt{\eta_{\mu\nu} \dot{x}^\mu \dot{x}^\nu}... | Let us assume that you use the metric:
$$\left\{ \eta_{\mu \nu} \right\} = \begin{pmatrix} 1 & 0 & 0 & 0 \\
0 & -1 & 0 & 0 \\
0 & 0 & -1 & 0 \\
0 & 0 & 0 & -1 \end{pmatrix}
$$
(Note that you could also use:
$$\left\{ \eta_{\mu \nu} \right\} = \begin{pmatrix} -1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Low rank entangled states In some recent works, I got the information that low rank mixed states need not be bound entangled. In particular, for the system $3\otimes 3$ there is no bound entangled states. Can anyone tell me how to prove it or give a proper reference?
| There do exist bound entangled states in 3x3 dimensions, see P. Horodecki, Phys. Lett. A 232, 333 (1997), or the review http://arxiv.org/abs/quant-ph/0702225 (Eq. 64). On the other hand, there are no bound entangled states in 2x2 and 2x3 dimensions (but again in 2x4).
| {
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Dielectric constant of water I need the dielectric constant of water from $10^{-2}$ Hz to $10^4$ Hz. As stupid as it may seem, I cannot find much info. I've googled for days. All I can find is close to GHz. And the only info close to Hz, ($100$ Hz) shows a great variation. A relative dielectric constant at $100$ Hz of ... | Sometimes "absence of evidence" leads to "safe to extrapolate" . My bet is that the dielectric value is, to more precision than you could use, constant from 0 to 1 MHz. I notice the wikipedia entry under permittivity suggests at least 0 to 1kHz.
However, your search-fu may be wanting, grasshopper. I found this calc... | {
"language": "en",
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Velocity distribution in Plummer's models and others mass distributions The Plummer's sphere is an model for the mass density in a globular cluster of stars. For an $N$-body simulation I have initialized the position of $N$ masses with a Monte-Carlo technique but cannot find a way of initializing the velocity initial c... | The Plummer model has a potential of the form
$$
\Phi(r)=-\frac{1}{\sqrt{r^2+1}}
$$
(obviously ignoring all constants). Equating the above with the kinetic energy, you get
$$
\frac12v_e^2+\Phi(r)=0\to v_e(r)=\sqrt{2}\left(r+1\right)^{-1/4}
$$
This velocity is the maximum velocity you can have at a radius $r$, so we mus... | {
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Difference between $SU(2)$ and $SU(2)$ gauge transformations? I hear this jargon all the time, so what is the difference?
(Of course this is nothing special to $SU(2)$, but rather I just took it as an example)
| SU(2) is a type of group, that is a collection of objects that have certain properties.
An SU(2) gauge transformation refers to the observation that certain objects in certain equations remain invariant if you multiply them by the elements of the SU(2) group.
How this works is easiest to see with rotations on vector do... | {
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Law of attraction Could you please explain that since we know Newton's law of Universal Gravitation says all masses attract each other. Thus, we humans should be attracted as well or any other daily life objects. Why is it that we don't feel that attraction to be prominent?
| The gravitational force is proportional to the mass of each object. The proportionality constant is incredibly small compared to other forces. Thus, we only feel (and observe) gravity when the masses are very large (such as the earth, planets, the moon, and the sun).
| {
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Energy spectrum, mass spectrum, and mass gap In Arnold Neumaier's nice answer to this question:
The energy spectrum in quantum field theory
it is remarked that
'If there is a mass gap (i.e., if no representation of tiny positive mass exists), the states can be restricted to their rest frame, where the spatial momentum ... | A massless particle doesn't have a rest frame. Recall that in the rest frame, the momentum vector is given by
$$ p^\mu = (E,0,0,0)$$
and it must satisfy $p^2 = m^2$ where $m$ is the particle's mass. Now examine what happens for a state with $m^2 = 0$...
| {
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"source": "stackexchange",
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How can the commutator operation not be transitive? I noticed the following:
$$[L_{+},L^2]=0,\qquad [L_{+},L_3]\neq 0,\qquad [L^2,L_3]=0.$$
This would suggest, that $L^2,L_+$ have a common system of eigenfunctions, and so do $L^2,L_3$, but $L_+,L_3$ don't. How is that possible?
| Commutativity is not a transitive relation: If operator $A$ commutes with $B$ and $C$,
$$AB=BA \quad\text{and}\quad AC=CA,$$
then there is no reason that $B$ and $C$ should commute.
Example: Take $A=y$, $B=x$, and $C=p_x$.
In particular, if commuting selfadjoint operators $A$ and $B$ have a common basis of orthonorm... | {
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Time dilation and relativity We've just started with relativity and I got a question regarding an exercise we got.
A spaceship passes by earth on its way to planet X, at the moment it passes by Anna is born on the spaceship. Can the spaceship travel fast enough so that it reaches planet X before Anna's first birthday(s... | In the earth's frame of reference nothing can go 100 ly in less than 100 years. No surprise there.
In Anna's perspective nothing can go 100 ly in less than 100 years.
So what's the problem? How can Anna go 100ly in 1 year? The answer is that 100 Anna years is considerably different compared to 100 Earth years due to t... | {
"language": "en",
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Can a mass matrix be asymmetric? I am developing a mathematical model of a mechanical device consisting basically of coupled harmonic oscillators. It turns out that the system mass matrix is asymmetric. I seem to read somewhere that a mass matrix has to be symmetric, but I am not sure. So I would like to know whether i... | I agree with the answer of Lubos (and ja72 is right that there is also a positivity criterion). However, since you repeated the question again to ja72, let me explain the answer of Lubos more explicitly and with more details.
Suppose that in your system of harmonic oscillators the kinetic term is defined with a mass ma... | {
"language": "en",
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Why does ice form on bridges even if the temperature is above freezing? So with this "arctic blast" continuing, I've noticed that for my area, the temperature drops below freezing just long enough to cause freezing rain, but then the sun comes out and the temperature rises immediately. However, on bridges, ice continue... | I've pondered that as well. And here is my thoughts.
Roadways have the benefit of being "insulated" by the earth under them. So in freezing conditions, the ground underneath is still liberating heat and the roadway may not be at 0C/32F quite yet.
Bridges, however, do not benefit from being insulated by the earth- the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/95705",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "20",
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"answer_id": 5
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light beams of the sun
We receive sunlight on earth surface. What type of light beams are these?
Random/Parallel/Converging/Diverging
I think it should be Diverging as Sun is radiating these beams away. But in one book, answer is given as Random, in another it's Parallel.
| "Beams of light" refer usually to an idea from geometrical optics, that light is composed of rectilinear beams. This is not entirely exact, as we know light is better described as a wave.
One can still use beams or rays if they are redefined as, say, lines of shortest path from the source of elementary (spherical) wave... | {
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Tension in string due to surface tension Suppose you take a loop of string and place it on the surface of a liquid, the string should become taut due to surface tension. How would you be able to calculate the tension in the loop of string?
My main difficulty in solving this problem is the direction in which surface ten... | Because it is string, virtually one dimensional, all the force it can support is parallel its length - the tension T.
If you put a drop of oil on the water, inside the loop, it spreads because the energy of the oil-water interface is less than that oil-air interface.
The loop stops expanding (equilibrium) when an incre... | {
"language": "en",
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is there any relation between resistance and magnetism? i was holding a resistance wire(insulated) coiled up and both of its ends were connected to a Ohm-meter it was showing 18 ohms while the circuit was on i pulled the coil from both ends and made that a straight wire with barely a knot in between and observed that t... | Since the Ohmmeter is measuring at DC, there are no inductance effects present. The change in resistance is likely due to a change in stresses in the wire. This wikipedia article on the piezoresistivity describes the effect.
| {
"language": "en",
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Higgs field - the vacuum expectation value I have already asked questions about the Higgs mechanism. But what still interests me is the following: The vacuum expectation value of the Higgs field is responsible for the emergence of the elementary particle masses, together with the Yukawa coupling constant.
What causes ... | Spontaneous symmetry breaking happens, if the vacuum of the theory lies not at $\phi = 0$, but at $\phi = v$, (i. e. $V'(0) \neq 0$, but $V'(v) = 0$).
In order to make sense of your QFT expansion, you want to expand fields around the vacuum. This justifies the plane-wave approach and the expansion of gauge transformati... | {
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Is tripleaxis planet possible? Imagine. Our solar system. Our sun. Then earth and moon orbiting it. And you have "powers" to create any planet you want, any size, any density, any weight and any velocity. Would it be possible for you (using all knowledge of earth), to create a natural satellite to moon? Whose trajector... | This is possible. For example, this post provides a good explanation of the math involved.
The key point is whether an object lies in the planet's Hill sphere or the moon's Hill sphere:
Can the Moon have a moon?
Yes, the Moon could have a sub-satellite. If we look at a system of the Earth, Moon, and a sub-satellite, t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/96602",
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Transformation of Electromagnetic Four-Tensor I apologize if I am missing something obvious, but I am in my first class with tensors and I am still learning the notation. I am running into a problem with the transformation of the transformation of the four-tensor for electromagnetism that is given by
$$
F^{\mu \nu} =
... | The notation means
\begin{align}
\sum^3_{\alpha, \beta = 0}{\Lambda^\mu_\alpha \Lambda^\nu_\beta F^{\alpha \beta}}
&= \sum_{\alpha=0}^3\sum_{\beta = 0}^3\Lambda^\mu_\alpha \Lambda^\nu_\beta F^{\alpha \beta} \\
&= \Lambda^\mu_0 \Lambda^\nu_0 F^{00}+\Lambda^\mu_0 \Lambda^\nu_1 F^{0 1}+\Lambda^\mu_0 \Lambda^\nu_2 F^{0 2... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/96693",
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Does optical fiber preserve the angles of incoming light? I am reading up on optical fibers and there's one thing I haven't understood yet:
*
*Does an optical fiber preserve the angles of incoming light?
For example, if we light two LEDs in front of an optical fiber (within its acceptance cone) and hold the other... | Two extreme cases:
For a very thick multi-mode fiber, the angles are somewhat preserved I think.
The opposite extreme is a thin single-mode fiber, in which the angles are most definitely not preserved. The light enters the fiber or it doesn't, there is no other spatial or angular information.
So the answer to your ques... | {
"language": "en",
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How does a canvas water bag cool water? I was reading about this water bottle by Botl that behaves like a canvas water bags to keep water cool. I found out that this idea is an old idea and cars would drive with water bags in front as shown below.
Here is what I found out about them: it seeps water through the bag an... | heres the whole way these water bags work you soak them in water first then fill them and hang them up the water inside keeps the bag wet and the outside surface moisture evaporates cooling the water inside the water is not ice cold only cool but much better than what it would be with no cooling effect at all
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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Why does the windshield of my car freeze even if the outside temperature is above freezing? Under what conditions does the windshield of a car freeze even if the outside temperature is above freezing?
It is not clear whether this is related to the question why bridges freeze with non-freezing outside temperatures (see ... | The outside temperature may be above the freezing point but with a clear sky radiation from the car can escape outside the atmosphere. There the temperature is very low, so energy is transferred away from the car. What happens depends upon the material. The windshield is a bad conductor of heat, so radiative energy los... | {
"language": "en",
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Commutators involving functions I am looking for the commutator:
$$[\mathrm e^{aq},p]$$
My approach is to Taylor expand the function:
$$\left[\sum_n \frac{1}{n!}(aq)^n,p\right]$$
I know that $[q^n,p]=ni\hbar q^{n-1}$
So how do I account for $n$ commutators?
| It seems to me that the approach formulated by the OP is perfectly sound! The OP demonstrates that he is familiar with the commutator between q^n and p. In order to use this formula, he proposes to apply Taylor series expansion to the target function. That is okay.
The only problem is that the OP got cold feet and stop... | {
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The workings of the Hall effect? I want to ask about the workings of the Hall effect. Why do the electrons come to rest on the edge of the wire? The magnetic field pushes them up, and the electric field pushes them forward. Shouldn't they reach the top of of the conductor and then stop moving up but continue moving for... | I think you are confused about what the Hall effect does. You ask: "Why does the magnetic field stop them from continuing to flow?" The answer is: it doesn't. Take this setup:
Here, the magnetic field is pointing up, in the +z direction. The conventional current in the purple conductor is flowing towards us (electrons... | {
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Why does a bottle shrink when you pour hot water in it? I think the title says pretty much. Last night I poured hot water in a half full bottle of water and closed the cap. The bottle immediately shrunk. Why? My girlfriend suggested that the hot water has less oxygen in it and thus consumes some of the oxygen in the bo... | if it was a plastic cola bottle it is because the plastic is a cross linked polymer, and is designed to be heated and then pressurized into a mold, and cooled under pressure to maintain its shape. this particular plastic was chosen because of its low failure rate in this process ( holes and deformities ) it is very muc... | {
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Would sea water moderate a nuclear submarine meltdown? My son asked me:
If nuclear submarines get sunk or blown up, what is to stop them going into nuclear meltdown?
I thought about it and came to the conclusion that because they're in the sea the water itself would act as a coolant, stopping nuclear meltdown.
Is th... | In fact, the water would act as a neutron moderator, speeding up the reaction. However, reactor pressure vessels are quite sturdy, and it would be very unlikely for the salt water to enter the pressure vessel.
| {
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The speed of light as it approaches a massive body No matter how fast you go, you will aways perceive the speed of light as constant. Taking that as a fact, the special relativity theory was formulated. Now, for what I understand about general relativity, just by standing here on the surface of the planet under the eff... | Both observers would perceive the light at the same speed. Any observer in any frame of reference anywhere in the universe will see light travel at the same constant speed. In terms of an light under gravity - if the light is approaching the massive object it will have a Doppler blueshift, while if the light is going a... | {
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Generator of Velocity Transformations - Galilean Transformations Under a Galilean transformation, the coordinates and momenta of any system transform as:
$$ t \rightarrow t',\\ \vec r\:' = \vec r + \vec vt,\\ \vec p\:' = \vec p + m\vec v $$
where $\vec v$ is velocity of frame moving w.r.t it. Now, what will be unitar... | Time translations are generated by $H$, as expected. The generator for Gallilean boosts $\vec{K}$ is related to the CM operator $\vec{R}=1/M\sum_i m_i\vec{x}_i$,
$\vec{K}=M\vec{R}$. See http://en.wikipedia.org/wiki/Schr%C3%B6dinger_group for some references.
| {
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Why is there water coming out of a car’s tail pipe? I notice yesterday that my neighbor’s car had water coming out of the exhaust pipe in the morning. My first response was since the hot exhaust is hotter than the cold tail pipe, heat is transferred from the hot exhaust through the pipe, and with enough moisture in the... | I too was observing this problem for quite some time with my new car equipped with gasoline injection system instead of the earlier carburetor type. The water dripping from the tail pipe is observed when the car is taken for a short run and stopped.
Obviously, the hydrocarbon fuel (petrol) is oxidized more or less full... | {
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Does physics have some division schema which divide physical amounts into these two classes? Does physics have some division schema which divide amounts into these two classes? :
*
*A) amounts which can be counted by natural numbers (for example many units can be counted by number of electrons, photons per second et... | Generally speaking, particles are quantized: you have $0,1,2,3,4\dots $ of them. Even in quantum mechanics, you may not know how many you have, but if you measure it you will get a natural number. Most other quantities are real numbers and can take any real value. It is very hard to say why-some would say that is t... | {
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Definition of Ohm in SI basic units in words One way Wikipedia defines Ohm is (this is also teached in school):
$$1\Omega =1{\dfrac {{\mbox{V}}}{{\mbox{A}}}}$$
They describe this definition in words, too:
The ohm is defined as a resistance between two points of a conductor when a constant potential difference of 1.0 ... | I'm not sure there's much of a point to what you're asking. The intuitive way to understand an Ohm is to use $\Omega = V/A$. If you want to use SI units, you can, and the math indeed tells you that your other definition is correct, but you're not gonna get much out of it. Indeed, the most you could do is to separate it... | {
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Apparent depth and the viewing angle Does the viewing angle of a person observing a coin placed in a bucket of water affect the apparent depth in any way?
| Apparent depth of the object is given by the following equation,
$$AD=\frac{RD}{n_{ab}}$$
Where $AD$ is apparent depth, $RD$ is real depth, and $n_{ab}$ is the refractive index of medium b (denser medium) w.r.t medium a (rarer medium).
As real depth and refractive index is going to be constant always (for the given p... | {
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Why superconductors aren't used in space? As we all know temperature of space is near to absolute zero.Then why super conductors aren't used there?
| The intensity of the light from the Sun at the orbit of the Earth is around 1.4 kilowatts per square metre. For comparison, a domestic heater is usually around 3 kW, so a satellite with a 2m surface area (admittedly this is bigger than most satellites) facing the Sun needs to dissipate as much energy as used to heat yo... | {
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Is the $N$ factorial in the Partition function for $N$ indistinguishable particle an approximation? I suspect that the $N$ factorial in the partition function for N indistinguishable particles
$$ Z = \frac{ Z_0^N } {N!} $$
is an approximation. Please someone correct me if I am wrong and why or why not. Thanks.
A simp... | It is indeed an approximation. As suresh says, the approximation holds only when each particle is in a different single-particle state, or more precisely, when the number of states in which each particle is in a different single-particle state vastly outweighs the number of states in which more than one particle is in ... | {
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Why aren't solar panels efficient? Why can't solar panels produce 1 Kw per 1 square meter? This is the energy of the Sun's radiation per square meter on Earth but solar panels don't come close. Why can't we trap all that energy? Where is the rest of the energy going?
| No energy conversion process completes at 100% efficiency. Using the sun, gasoline or nuclear, none of these will generate power at 100% of total potential power available.
That figure of 1KW/m^2 is for total available light energy correct? Due to how solar panels work (I don't think I have enough knowledge to speak on... | {
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Temperature and resistance? Why does resistivity increase with temperature?
The explanations I have heard so far are that increasing temperature increases vibrations in the lattice structure resulting in the number of collisions increasing.
But the vibrations from thermal energy are random, so around half of the vibrat... | I think you have some of the right intuition, but the orders of magnitude of the problem need to be considered. Look at Electricity and Magnetism by Purcell. http://www.amazon.com/Electricity-Magnetism-Vol-II-Berkeley/dp/0070049084 They have a chapter on these concepts.
The idea is that conductivity in a metal is pri... | {
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Can a car skid while moving in a circle? How can a car skid if it is moving around a circular road? It is understandable that it can topple but I feel it impossible that a moving car can skid. It is hard to imagine that a car would skid while traversing a circular path. The wheels of the car are rotating so it seems ... | If you're asking whether it is impossible to skid while turnning at all, I have a tree in my front yard (well, my parents' front yard) that says that it is. Just imagine the case where friction goes to zero (for example, there might be a layer of ice on the road.)
If you're asking whether the path will be circular, ju... | {
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Sign in the photon propagator The Klein Gordon propagator is given (I use Peskin and Schroeder's conventions, if it matters...),
\begin{equation}
\frac{ i }{ p ^2 - m ^2 + i \epsilon }
\end{equation}
The photon propagator (using Feynman gauge) is
\begin{equation}
\frac{ - i \eta^{\mu\nu}}{ k ^2 + i \epsilon }
\end... | Yes, there is a physical significance. The longitudinal mode $A^0$ is pure gauge, it does not propagate (in other words, the equation of motion for $A^0$ is a constraint [Gauss Law], not an equation of motion and it's canonical momenta is identically 0 , meaning we cannot impose canonical commutation relations on it). ... | {
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How to get conductivity from Green function $\mathcal{G}(x_1,x_2,\tau)$ of inhomogeneous system? I'd like to study an inhomogeneous system, i.e., momentum is not a good quantum number therein. Therefore, I tried to calculate temperature Green functions like $\mathcal{G}(x_1,x_2;\tau)$, or its twofold Fourier transforma... | Losing translation invariance is one of the big problem when studying disordered system (for example). In that case, one usually averages over the disorder to render the system translation invariant (on average), with its own technical difficulties. The applications for transport properties are explained in the Mahan o... | {
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Renormalizing QED with on-shell fermions When renormalizing QED, we calculate the 1 loop correction to the fermion-fermion-photon vertex using the diagram,
$\hskip2in$
When doing the calculation we typically let the photon go off-shell but demand that the fermions be on-shell. In other words,
\begin{equation}
q ^2 >... | Putting the fermions on-shell or off-shell doesn't change the divergent part of counterterms. In the renormalization schemes, the counter terms are determined to cancel the divergencies. You can put $p^2=m^2$ or $p^2=-\mu^2$ or etc in the diagrams to determine the counter terms, but notice that the derived renormalizat... | {
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Rms value of rectified output from a half wave rectifier The rms value of an alternating quantity which is the input to a half wave rectifier is $\frac{I_{max}}{\sqrt2}$.
Then the rms value of output should be $\frac{I_{max}}{2} \sqrt 2$. But it is given every where that it is $\frac{I_{max}}{2}$. Please tell me wher... | You can simply use the definition of rms value of a periodic signal. If the signal at the input of your half-wave rectfier is $v_{in}(t)=V_{max}sin(\omega t)$ for $t\in [0,+\infty[$ the output will be $v_{out}=V_{max}sin(\omega t)$ for $t\in [kT,(k+1/2)T]$ and $v_{out}=0$ for $t\in [(k+1/2)T,(k+1)T]$. Then the definiti... | {
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Divergent thin lens producing real images The question is as in the title, can a divergent lens produce a real image, when backed by a convergent lens?
Which are the conditions to be respected?
This was a homework and I have received the solution but I think is wrong.
Basing this on research already done online, the o... | Any discussion of the type of image a lens can form (real or virtual) must include information about the type of object that is being used.
A divergent lens, by itself, can form only a virtual image of a real object.
if we pre-condition the light from the object by passing it through a converging lens, then the resulti... | {
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Power of Shockwaves My question is about shockwaves and their power when they are created/how do they lose their power?
Let's say that we have ground 0 with 10 grams of TATP on it. The detonation velocity of TATP is 5,300m/s. How can we calculate the pressure it will make and the shockwave's power when it is detonate... | I know this is unrelated, but I'd recommend avoiding doing anything with TATP if possible. I manufactured it once and didn't get hurt, but there have been a fair number of people who have been maimed or killed while working with it.
The pressure of the front should decrease as $1/r$, as explained on the Wiki page on sp... | {
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Intrinsic parity of particle and antiparticle with spin zero I need to prove that the intrinsic parities of a particle and antiparticle with spin zero are the same. Can I prove that by an argument that operator of $P$-inversion commutes with charge conjugation operator for the spin-zero particle?
$$
\hat {P}\Psi = \pm ... | I slightly deviate from your notation and use $\phi $ to denote the scalar field as its more standard. Also I should point out that quantum fields are operators and thus under a transformation they get acted on from both the left and the right.
The complex scalar field is given by,
\begin{equation}
\phi (x) = \int \... | {
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free energy and entropy my understanding of free energy and entropy is that as entropy of a system increases its free energy decreases. As sun has free energy and this energy is being converted to useful work, and its entropy is increasing. Its entropy will continue to increase till its material is exhausted to cease f... | So a large increase in entropy would decrease the activation energy. Together with the change in enthalpy, they decide the spontaneity of the reaction. If the expression for the Gibbs free energy is negative at a given temperature, the reaction is spontaneous, meaning that it occurs.
| {
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What does it take to recreate double slit experiment with detectors? Is there any way to recreate this experiment with detectors at home?
I need detectors If I want to recreate the interference pattern.
I have a little know-how in electronics so If I need to buy a detector there wouldn't be a problem using it. The thin... | The question is what exactly it is you would like to observe. If all you are after is an interference pattern, then you could build a double slit experiment with shallow water waves or (classical) laser light. While these are classical waves, the underlying mechanism (maxima and minima due to interference of waves) is ... | {
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Bulk flow of air in a long tube between Antarctica and Australia? I have a 5km diameter clear plastic tube which is open at each end and runs from the center of Antarctica to Lake Eyre in Australia. The tube is on the ground where it can be and at sea level on the ocean.
Will there be bulk flow of the air in the tube? ... | Assuming the tube is insulated along its whole length (which I think is the intent of the question although it's not stated), I think a flow in either direction is stable and sustaining, but there is no particular reason it will form in either direction if the initial conditions are that the air in the tube is still. ... | {
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Is there any way to annihilate matter without the use of anti-matter? Is there any way to annihilate matter without the use of anti-matter? And vice versa? I mean, for example is it possible to totally convert the mass of a proton into "pure energy" without use an anti-proton?
| Note that this is possible even if we restrict ourselves to stay within the rigorous realms of the Standard Model. E.g. the deuteron is known to be unstable, it will decay via instanton tunneling to a positron and an anti-muon neutrino (or an anti-muon and anti-electron neutrino). The deuteron lifetime would be about 1... | {
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How to calculate fluid's temperature change in a pump? To calculate the pressure at the outlet of a pump we use pump performance characteristics i.e. charts giving pump head as a function of volumetric flow. When the fluid flows through a pump, it's temperature slightly rises.
Is there a formula or other method to cal... | First Law of Thermodynamics :
Q - W = Δ E system
Assuming the Q = 0 and W of the pump negative and Cp of water = 1 Btu/lb-F:
W = 500 x GPM x v x (P2 – P1) = 500 x GPM x (T2 – T1)
W = 500 x GPM x v x (P2 – P1) = 500 x GPM x (T2 – T1)
W = v x (P2 – P1) = (T2 – T1)
T2 = v x (P2 – P1) + T1
(Where v is the average speci... | {
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Solar panel maximum efficiency at specific frequency and temperature? I talked to a professor about solar panels and their efficiency. It seemed that the main reason solar panels aren't that efficient is because it can only accept a single energy input size. Anything below is ignored and anything above only gives the e... | In theory, you could get almost $100\%$ efficiency from a solar cell exposed to light with the photon energy just above the band gap. Each absorbed photon generates an electron of almost the same energy. The problem is that there are only so many band gaps available, so you have to find a light source at the correct ... | {
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What are the differences between supperlattices and Multiple Quantum Wells Semiconductor Structures? Semiconductor Optoelectronics:
What are the differences between multiple Quantum Wells and supperlattices.
| Normally, you call a system either MQW or superlattice based on a width of the band formed by interaction of the levels in adjoint QWs. If the bandwidth is small enough (in comparison with temperature, characteristic times, etc., whatever is important for your problem) and you may consider carriers as localized within ... | {
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Does a mirror help a near-sighted persion see at a distance clearer? A near-sighted person without eye-glasses can not clearly see things at distance.
If he takes a photo of the things at distance, he can see the things from the photo much clearer, because he can place the photo much closer to his eyes.
If he turns his... | Assuming the mirror has no curvature then things would not look clearer.
You have to think about the image as it is being projected, our eyes doesn't perceive reflected image as being at the point of reflection but rather perceives the image as being a set distance from our eyes.
To clarify if you imagine your eyes co... | {
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How to obtain the distance traversed by a free falling body equation? I know that the distance that a free falling body has traverse through time is given by $d=0.5*g*t^2$. I would like to know how to get to this equation to study a bit more how it was obtained. I have been searching around with any luck. Could anybody... | The equation comes from Newton's second law:
$$ F = ma $$
Galileo didn't know calculus (because Newton and Leibniz hadn't discovered it yet) so he couldn't derive the equation mathematically. Since we do know calculus we know that acceleration is the variation of velocity with time:
$$ a = \frac{dv}{dt} $$
And also the... | {
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What do I get when measuring on top of metal/insulator/metal by kelvin probe? I am using a macroscopic Kelvin Probe for work function measurement. There's one confusing condition. If I measure a trilayer thin film stack with a structure of ITO(bottom)/PMMA(100-200nm)/Al(top), what can I get?
Am I obtaining work functi... | Even if the floating Al film is (nearly) disconnected in DC, it is still capacitively coupled to the substrate. Since Kelvin probe techniques use capacitance modulation, the behaviour of the experiment will be more or less identical to the case of a connected film, since tip-film capacitance is so tiny compared to the ... | {
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Why does a remote car key work when held to your head/body? I was trying to unlock my car with a keyfob, but I was out of range. A friend of mine said that I have to hold the transmitter next to my head. It worked, so I tried the following later that day:
*
*Walked away from the car until I was out of range
*Put ke... | The folks at Remcom set out to debunk this myth.
https://www.remcom.com/examples/keyless-entry.html
They ended up showing why it works.
Great software, I've designed a bunch of 2.4 GHz antennas with it that worked quite well in significantly impaired environments.
| {
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Definition of Ampere On Wikipedia it says:
This force is used in the formal definition of the ampere, which states that it is "the constant current that will produce an attractive force of $2 × 10^{-7}$ newton per metre of length between two straight, parallel conductors of infinite length and negligible circular cro... | The ampere is used, among other things, to derive the volt, which is the electric potential difference that a current of one ampere has to flow across in order to deliver a power of one watt. (The watt itself is defined mechanically, from second, meter and kilogram).
One volt is around the same order of magnitude as th... | {
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Why does my kettle only make a noise when it is turned on Almost as soon as I turn my kettle on it starts to make the familiar kettle noise, yet very shortly after turning off the power the boiling noise stops and the kettle is totally silent. The temperature of the water is (almost) the same as when I turned it off. S... | The noise is either from the AC electricity, which would be a 60Hz buzzing, or from small bubbles forming on the heating element itself. When the electricity stops, both the buzzing and the bubble formation will stop as well.
Bubbles create sound due to quickly expanding from a small nucleus.
Here's a book I found wit... | {
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Inductance of a solenoid? My textbook is using Faraday's law to explain the self inductance that happens in a solenoid with changing current.
According to Wikipedia, Faraday's Law is:
The induced electromotive force in any closed circuit is equal to the negative of the time rate of change of the magnetic flux through ... | Inside the solenoid there's no (component of the) magnetic field that isn't perpendicular to the loops, so treating a solenoid as if it has closed loops is valid approximation.
Perhaps you can understand it better if you approach the solenoid as a single wire and see what the emf does from that point of view.
| {
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How does a half-life work? Carbon-14 has a half-life of 5,730 years. That means that after 5,730 years, half of that sample decays. After another 5,730 years, a quarter of the original sample decays (and the cycle goes on and on, and one could use virtually any radioactive isotope). Why is this so? Logically, shoul... |
Logically, shouldn't it take 2,865 years for the quarter to decay,
rather than 5,730?
Imagine that the quantity $q(n)$ of something decays as
$$q(n) = Q\cdot 2^{-n}$$
where $n$ is the number of half-lifes.
Initially, there is quantity $q(0) = Q\cdot 2^0 = Q$ of something.
After 1 half-life, there is $q(1) = Q \cdot... | {
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Position of two bodies as a function of time, special case I'm looking for a closed equation like $x=f(t)$ (if there is) for a simplified case of the two bodies problem:
Suppose that we have two point-like objects with the same mass, nothing more than their own gravity is effected on them.
The initial distance between ... | There is no explicit solution for the position as a function of time. Here are a three related questions: 1, 2 and 3.
This path is basically a Kepler orbit with zero angular momentum. This means that the eccentricity is equal to one and the semi-major axis is your case equal to $\frac{D}{2}$.
From such an orbit you can... | {
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Convert $\text{mm}^2$ to $\text{m}^2$ Stuck on a very very basic concept.
I have $1750\text{ mm}^2$ and need to get into $\text{m}^2$.
I figured $1750\text{ mm}^2 = (1750\text{ mm}) \cdot (1750\text{ mm})$, but I know this isnt right.
| The superscript $^2$ in $1750\text{ mm}^2$ refers to a squaring of the units, not the number $1750$.
A more transparent way to write this is $1750\text{ mm}\cdot\text{mm}$. The idea is now to multiply by $1$, but $1$ written in a clever way:
$$1=\frac{1\text{ m}}{1000\text{ mm}}$$.
Can you see how that number is concep... | {
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Where is the Higgs Field? Where is the Higgs Field? I get the idea of how it works but I couldn't find anything explaining where it is.
| This question is similar to "where is the electromagnetic field?" And the answer is: the electromagnetic field is everywhere; it exists at every point in space-time, but it simply happens that its average value is zero (or close to zero) at points far away from charges, currents, and waves.
The Higgs field, like the el... | {
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Mass density of dark matter in solar system near us What is the approximate mass density of dark matter in our solar system at the radius of the Earth's orbit?
I would like some idea of the mass of dark matter going through each cubic meter of material on earth.
| Density of dark matter in the Sun's orbit (Sun rotates with speed υ ≈ 220 km/s at a
distance r = $2.57\times 10^{20}$ m from center of Milky Way ):
ρ☼=$8.737\times 10^{−22}$ $kg/m^3$ = $78.5\ \mu J /m^3$ or 522000 protons/m$^3$.
To learn more, you can find in mini-novel "Flippon" at the Flippin Theory website: http://... | {
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What may be effect of air friction to the velocity of satellite? What is the effect of air friction to the velocity of satellite? I have heard satellite's speed increases with air friction. But I'm in confusion how is it possible?
| I would expect the speed of the satellite to slow down upon reentry; not speed up. Most terrestrial satellites, even ones in low Earth orbit, do not encounter sufficient atmosphere or air resistance to significantly degrade their orbits so that they reenter the atmosphere. It is true that the Iridium satellites in LE... | {
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Regarding derivation of Probability Current The question for the full derivation of Probability Conservation -> Probability Current was already asked here:
Probability current. I apologize for not retyping it out, but it's already beautifully done in latex which I have yet to become proficient at.
I can follow most o... | If you look at ChrisR's answer in Probability current, you can see that the complex conjugation is applied to both sides of the equation.
Since the terms on both sides are complex numbers, this is easy to do. It is not necessary to think deeply about what complex conjugation of some operator should be. Just write all t... | {
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How to Determine the voltage polarity of inductor in a circuit? The Voltage polarity across the inductor is same as that across the capacitor since both are in parallel and the voltage across them must be same.
But when Inductor, capacitor and resistor are connected as shown in the second figure what would be the volt... | You don't need to worry about the convention you choose because the solution of the corresponding differential equation will automatically adjust the polarity. For the sake of simplicity, I usually use the passive convention as follows.
| {
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Is a capacitor in an open circuit charged? Say I have a circuit consisting of a battery, a wire, an open switch, and a capacitor. The circuit is open since the switch is open.
My book says that the capacitor will only be charged when the switch is closed, but I don't see why this is true. I would expect the capacitor t... | Your argument is: If the circuit is open, the current must be zero. Consequently the field must be zero. For the field to be zero, the capacitor's field must cancel out the battery's field. Therefore the capacitor must be charged.
Replace the capacitor with a resistance. Following your argument in the same way, there m... | {
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Prove EM Waves Are Transverse In Nature Why we say that EM waves are transverse in nature? I have seen some proofs regarding my question but they all calculate flux through imaginary cube. Here is My REAL problem that I can't here imagine infinitesimal area for calculating flux because em line of force will intersect (... | You say the
em line of force will intersect (if perpendicular) surface at only one point.
This is not the case for a plane wave, which is the simplest case one usually considers. I think I know what's going on to make you think this. This may or may not be the issue that helps you.
Take this typical picture of an E... | {
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Can someone please explain the "infrared catastrophe"? In my readings I've run into this idea of an "infrared catastrophe" associated with 1/f noise. As far as I can tell it is because when you graph the periodogram of the 1/f signal you see the PSD goes to infinity as frequency goes to 0. Not sure what that means pr... | The infrared catastrophy seems to be named after a mimic of the ultraviolet catastrophy of the black body radiation .
In physics, an infrared divergence or infrared catastrophe is a situation in which an integral, for example a Feynman diagram, diverges because of contributions of objects with very small energy approa... | {
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What is relation between electrons and photon? What is the relation between electrons and photons? Why do atoms get excited when their electrons come in contact with photons? Why do electrons go from a higher to lower energy level when emitting a photon?
| Photons are a quanta, or particles of light. The bare minimum piece of light. Consider them like "packets" of light.
Einstein theorized and proved the Wave-Particle Duality which described the nature of light as both a wave and a particle, and this is how photons were originally speculated upon.
What came from this h... | {
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What are the means to consider that a specific function is phase of an oscillator? I hope the experts of the field forgive me for this n00b questions, but I am just trying to understand physics. Assume the following function:
$$\phi(t)=\omega t+\cos(\omega t)$$
The above function has the property that:
$$\phi(t+T)-\phi... | For the future readers (if any), I highly suggest the Synchronization book. In page 31 of the book there is a thorough discussion of the phase. I am not quite sure writing the books material would be a copyright infringement but I highly recommend it to the ones who are curious to learn more.
| {
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What is the commutator of an operator and its derivative? Is it possible to calculate in a general way the commutator of an operator $O$ which depends on some variable $x$ and the derivative of this $O$ with respect to $x$?
$${O}={O}(x)\\
\left[\partial_x{O}(x), O(x^{\prime})\right]=?
$$
To be honest I don't quite unde... | Notice that in $[\partial_xO(x),O(x')]$, the partial derivative only acts on $x$, not on $x'$. So we can pull the partial derivative operator out of the bracket and get $\partial_x[O(x),O(x')]$.
| {
"language": "en",
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Special relativity: how to prove that $g = L^t g L$? We have
$$X^\textrm{t}gX = 0 \iff X^\textrm{t}L^\textrm{t}gLX = 0,$$
where $X$ is a column vector of length four, $L$ is a non-singular $4 \times 4$ matrix, 't' denotes matrix transpose, and
$$g = \left(\begin{matrix}
1 & 0 & 0 & 0 \\
0 & -1 & 0 & 0 \\
0 & 0 & -1 ... | You ask
doesn't it immediately follow that $g=L^tgL$ ?
Nope.
Consider, for example, $L = aI$ where a is a nonzero real number, and $I$ is the $4\times 4$ identity matrix. This matrix $L$ is nonsingular, and it has the property that
\begin{align}
X^tgX = 0\,\quad\text{if and only if}\quad X^tL^tgLX = 0
\end{align}... | {
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Why don't the leaves of an electrometer repel each other in water? A normal electrometer filled with air will repel like it should do for electrostatic demonstration, but what if it is filled with water instead or even oil, what will happen?
My guess is that the water is charged too, making the net repelling force equ... | Here, we shall discuss about relative permittivity $\epsilon_r$. Permittivity $\epsilon_s$ of a substance is the measure of the resistance offered by a substance against the flow of electric field lines. Greater the value of $\epsilon_s$, fewer will be the number of electric field lines flowing through the substance. $... | {
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Rate of probability loss from absorbing boundary The following is the solution to the 1D diffusion equation with diffusion coefficient D, initial particle position $x_0$, and a perfectly absorbing boundary at $x=0$ (s.t. $P(x=0)=0$).
$$
P(x;t)=\frac{1}{\sqrt{4 \pi D t}}e^{-\frac{(x-x_0)^2}{4 D t}} - \frac{1}{\sqrt{4 \p... | PART 1 (an unrelated alternate derivation of $P(x,t)$:
You can give a purely combinatorial derivation of the form of $P(x,t)$ based on the partitioning of random walks.
Let $x>0$, let the absorbing boundary be located at $x=0$, and let the initial source be located at $x_0>0$.
In the absence of an absorbing boundary,... | {
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Current through two inductors after a long time I'm having trouble with visualizing the following problem, which is asking me for the final, steady current in both inductors $L_{1}$ and $L_{2}$. I was thinking that after a long time, essentially the current will be stable and thus there will be no induced current in th... | I was thinking that after a long time, essentially the current will be stable and
thus there will be no induced current in the inductors
When we use inductors, we deal with induced EMF and not induced current. The induced EMF works to reduce the net potential across the inductor altering the amount of current that fl... | {
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Using an electric winch to compress a spring and launch an object I'm having trouble grokking the relationship between a winch's pull/torque and a spring's potential energy.
I would like to compress a spring using an electric winch and figure out how far it will be able to launch an object.
*
*If the spring's maximu... | *
*I am assuming that by 'winch's force' you mean the maximum force that can be generated by the torque produced in the winch. If this force is not higher than the load, then no it cannot pull it. The maximum potential energy the winch can hold depends on how much turns it is given, the properties of the spring are to... | {
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Limits of integration for the radial wave function of the Hydrogen atom in the WKB approximation I am working a problem where we have to find the energy eigenvalues for the radial wave function of the hydrogen atom for $\ell=0$ using the WKB approximation. I am sure that I set up the integral properly, I am just a litt... | The limits of integration are the turning points
| {
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Derivation of Euler's equations for rigid body rotation
Sorry for using this image, but I thought this was the most convenient way of asking this question. Please zoom in.
I do not understand from the line, "Now, in the body frame $T = (T_{x'}, T_{y'}, T_{z'})\ldots$"
How is that in the body frame? That should be in t... | It clearly states that "...the body frame co-rotates with the body...". So what you are calling $L'$ is in fact $L$ itself. The torque will be the same in both reference frames.
| {
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When combining three spin $\frac{1}{2}$ particles what are the corresponding states? I want to combine three spin half particles and this is what I have so far.
I used the lowering operator $J_{-}$ on the top states and found the following states fine:
$$|\frac{3}{2},\frac{3}{2}\rangle , |\frac{3}{2},\frac{1}{2}\rangle... | We know 2 x 2 = 3 + 1. (A symmetric vector and an antisymmetric scalar state). Add one more:
2 x 2 x 2 = 3 x 2 + 1 x 2 = 4 + 2 + 2.
"4" is symmetric, with
uuu = 3/2,
uud + udu + duu = 1/2,
ddu + dud + udd = -1/2,
ddd = -3/2 .
The scalar times a spinor is a mixed symmetry j=1/2:
+1/2 = (ud-du)u
-1/2 (ud-du)d
The r... | {
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Help understanding proof in simultaneous diagonalization The proof is from Principles of Quantum Mechanics by Shankar. The theorem is:
If $\Omega$ and $\Lambda$ are two commuting Hermitian operators, there exists (at least) a basis of common eigenvectors that diagonalizes them both.
The proof is:
Consider first the ca... | Note that he explains above: "Consider first the case where at least one of the operators is nondegenerate, i.e. to a given eigenvalue, there is just one eigenvector, up to a scale." So he uses the assumption that the operator is nondegenerate and the definition of nondegeneracy (or a statement equivalent to the defini... | {
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What gives Maglev trains forward horizontal motion? Maglev trains have superconductors which are immune to magnetic field lines with low enough temperature. Due to this property, they levitate on magnetic rails as magnetic field lines are bended below them to create magnetic river.
But, isn't the lift force vertical he... | There are many systems for maglev trains. For the system of my question, I found that forward horizontal motion can be given by Linear Induction Motor.
| {
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Can effect of gravity be broken (counteracted) by electric force? Can we make a jacket using an electronic circuit that uses electric force to cancel the effect of gravity so that we get lifted in air.
| Yes you can levitate yourself with an electric force, however there are a few caveats:
*
*The ground beneath you needs to be charged
*You need to be in a very dry area (i.e., very low humidity)
*You are okay with levitation heights being on the order of a few $\rm mm$
We're likely not going to have an electrosta... | {
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Why does the dimension of the electric charge depend on the number of spacetime dimensions? We can find via dimensional analysis that the dimension of the electric charge varies with the dimension of space-time $(D+1)$:
$$[\text{charge}] = (\text{eV})^{(3-D)/2}.$$
It is dimensionless if there are three spatial dimensio... | Comment to the question (v6): It seems that OP is basically seeing the effect that Gauss's law forces Coulomb's law to be
$$\tag{1} F~=~ k_e \frac{Q_1Q_2}{r^{D-1}} $$
in $D$ spatial dimensions. If we choose Lorentz–Heaviside/CGS/Gaussian units with $c=1=\hbar$, then Coulomb's constant $k_e$ becomes dimensionless. It th... | {
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Is radioactive decay spontaneous or random? When it comes to radioactive decay, what is the difference between random and spontaneous?
For example, when the count rate of a radioactive isotope is measured, the readings fluctuate. Is this a demonstration of the randomness of the process, or of its spontaneous nature?
| The best way to differentiate is to look at the count-rate vs time graph. Random nature of radioactivity is indicated by the fluctuation of the count-rate.
Whereas, spontaneous means that the process of radioactivity is not dependent upon any external environmental conditions like temperature, pressure, magnetic/electr... | {
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Symmetry Breaking And Phase transition
*
*Is every phase transition associated with a symmetry breaking? If yes, what is the symmetry that a gaseous phase have but the liquid phase does not?
*What is the extra symmetry that normal $\bf He$ has but superfluid $\bf He$ does not? Is the symmetry breaking, in this case,... | Let me answer your first question: Phase transitions do not necessarily imply a symmetry breaking. This is clear in the example your are mentioning : The liquid-gas transition is characterized by a first order phase transition but there is no symmetry breaking. Indeed, liquid and gas share the same symmetry (translatio... | {
"language": "en",
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Scattering geometry question While reading up on light scattering I came across this slide:
My vector maths is a bit rusty and I am having trouble understanding the last term (scattering geometry).
What is the significance of $\hat{r} \times \hat{E_{i}} \times \hat{r}$
| First of all the hats on $\hat r$ and $\hat E_i$ indicate that these are unit vectors.
$$(\vec A \times \vec B) \times \vec C \neq \vec A \times (\vec B \times \vec C)$$
See Vector Triple product
Which means that $\vec A \times \vec B \times \vec C $ without parenthesis has no meaning. So I shall assume parenthesis ar... | {
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What happens when we bring an electron and a proton together? I have a couple of conceptual questions that I have always been asking myself.
Suppose we have an electron and a proton at very large distance apart, with nothing in their way. They would feel each the other particle's field - however weak - and start accele... | To provide a graphic version of Punk_Physicist's answer, we have the Feynman diagram for that particular interaction:
This diagram evolves in time from bottom to top, ie take a piece of paper, and run it upwards along the diagram to see how the system evolves. We have an electron and a proton coming towards each other... | {
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Uncertainty principle in Quantum mechanics The Uncertainty principle says that "△x△p>h/2"; we cannot precisely obtain both position $x$ and momentum $p$ simultaneously.
Is this because the uncertainty is the natural characteristic or it is because we do not know additional values? (ex. like additional 11 dimensions in ... | It is an intrinsic property of our universe. There were some alternative interpretations, like the "hidden variables" (there are a swarm of deterministic random things going on that we don't know or cannot know about that cause the quantum randomness) but they have been experimentally disproven (Bell's theorem).
You ha... | {
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Total Electrical potential energy of two particle system I recently have been studying Electro-statics and I couldn't understand properly how the potential energy of two particle system is found.
Suppose you have two particles with charges $Q_1$ and $Q_2$ respectively. The distance between them is $r$. What is the to... | As far as I remember, that $\frac{1}{2}$ comes because $Q_1$ isn't just in a potential $\varphi_2(\mathbf{r})$ that just happens to be there, but is being created by another charge, $Q_2$. Taking potential with respect to the other means: let $\varphi_1(\mathbf{r}) = \frac{1}{4\pi\varepsilon_0} \frac{Q_1}{|\mathbf{r} -... | {
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Could one measure a stick to an arbitrary precision by having its length estimated by enough people? I remember reading somewhere that the problem of exact time-keeping on ships could have been solved a lot earlier than it was if somebody would have had the idea of keeping time with a whole array of imprecise clocks - ... |
I remember reading somewhere that the problem of exact time-keeping on ships could have been solved a lot earlier than it was if somebody would have had the idea of keeping time with a whole array of imprecise clocks - taking the average of clock-times would have given a precise time.
Define precise . Precise for tim... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/105782",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
"answer_count": 10,
"answer_id": 9
} |
Does field line concept explain electric field due to dipole? Consider an electric dipole consisting of charges $-q$ and $+q$, separated by a distance $2a$ and placed in free space. Let $P$ be point on the line joining the two charges (axial line) at a distance $r$ from the centre of $O$ of the dipole.
You can obse... | If you take a permanent magnet, and place a sheet of paper over it. Now sprinkle iron filings on it, and you pretty much get this diagram. This has been the mainstay of field theory since Faraday's time.
A test charge at rest will begin to move in the direction of the field line. Since there is nowhere that it can r... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/105915",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 0
} |
Why does the topological entropy scale with $\log(L)$ in 1D? Why, in one dimension, does the topological entropy scale with the size of system as $S \sim \ln L$, while in a 2D system it scales with $S \sim L$? Why does dimensionality play such an important role here? I mean, is there any simple but straightforward ide... | As pointed out by Prof. Wen, the question is not "correct" in itself. Below are some facts:
(1) For both gapped and gapless 1D systems, there is no topological entanglement entropy.
For 1D gapped system, the entanglement entropy is $S\sim L^0$.
For 1D critical system (CFT), the entanglement entorpy is $S\sim\log L$.
(2... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/105967",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 2,
"answer_id": 0
} |
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