Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Physics-based derivation of the formula for entropy I am looking for a derivation of the formula
$$S~=~-\Sigma_ip_i \log (p_i).$$
for entropy, from first principles. I only wish to assume the laws of physics, and without involving concepts in information theory. (After all, the concept of entropy and Boltzmann's formu... | The expression
$$
I = \sum_i -p_i\log p_i
$$
is a function of probabilities $p_i$ and although it is often called entropy, it is not the thermodynamic entropy of Clausius (that $S$ from thermodynamics defined through $\int dQ/T$). This is not only because of absence of $k_B$, but also because in order to give $I$ value... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/44647",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Is Pauli-repulsion a "force" that is completely separate from the 4 fundamental forces? You can have two electrons that experience each other's force by the exchange of photons (i.e. the electromagnetic force). Yet if you compress them really strongly, the electromagnetic interaction will no longer be the main force pu... | The Pauli Exclusion Principle isn't a fundamental force because it doesn't have the same origin as the 4 fundamental forces. It's like the pressure you feel from a normal gas in that it definitely exists, but it comes from the fact that you have many particles in the system and are averaging over their behavior. We usu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/44712",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "70",
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How to determine whether a large container is air-tight? In constructing a kitchen-waste digester at home, I use a 50 Litre HDPE drum. The base of the drum is holed with a plug fitted to allow drainage when necessary.
The top has two openings - one for inlet, the other to act as outlet for the generated fluid CO2/CH4.... | A 300 liter container might not fit completely in a bathtub, but you might submerge different parts of it a different time and then check for bubbles, depending on its overall shape.
Or you can just fill it with water and see if it drenches.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/44784",
"timestamp": "2023-03-29T00:00:00",
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The requirements for superconductivity Which properties are sufficient evidence for a material to be not superconducting?
I am looking for a set of statements like
If the material is semiconducting, it is not superconducting
Edit:
I am not looking for a definition of superconductivity, or for introductional literatu... | This question has a semi-canonical answer; Matthias' rules for superconductivity. This was a real set of empirical criteria proposed well before the cuprates were discovered, but here is the tongue-in-cheek version (I'm not sure who to attribute this presentation to, however -- comments appreciated).
*
*Symmetric la... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Does matter with negative mass exist? Or does it exist mathematically?
Is it really inconsistent with a common-sense, mathematics or known physical laws?
As far as I understand, if it exists, it must be far away from the "positive" matter because of repelling force, so it explains why there is no observations of such... | So far as we know $m \geq 0$ --all observations are compatible with this--.
Mathematically you can imagine negative masses, imaginary masses or many other masses, but this does not mean they are real.
No, negative mass is not consistent with the idea that the total energy of the Universe is zero. This zero of energy is... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/44934",
"timestamp": "2023-03-29T00:00:00",
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Velocity vs Time Bounce Could someone please explain the trajectory of the ball that is bouncing in this picture...
The vertical component of the velocity of a bouncing ball is shown in the graph below. The positive Y direction is vertically up. The ball deforms slightly when it is in contact with the ground.
I'm not ... | Initially, the ball is at rest. Therefore, the initial velocity is zero as mentioned in the graph. The negative gradient states that the ball has a downward acceleration. The moment, it hits the ground, the velocity reaches to its maximum. Then, it starts accelerating in the upward direction. The graph indicates a larg... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/45007",
"timestamp": "2023-03-29T00:00:00",
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Hamiltonian in position basis Let $ H = \frac{-h^2}{2m}\frac{\partial^2 }{\partial x^2}$. I want to find the matrix elements of $H$ in position basis. It is written like this:
$\langle x \mid H \mid x' \rangle = \frac{-h^2}{2m}\frac{\partial^2}{\partial x^2} \delta(x -x')$.
How do we get this? are we allowed to do $\l... | Wave functions of position states are Dirac delta functions:
$$| x' \rangle \leftrightarrow \varphi_{x'}(\xi) = \delta(\xi - x')$$
If we apply the Hamiltonian to the wave function, we obtain
$$\hat{H} \varphi_{x'}(\xi) = -\frac{\hbar^2}{2 m} \frac{\partial^2}{\partial \xi^2} \varphi_{x'}(\xi) = -\frac{\hbar^2}{2 m} \fr... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What's the difference between two Hydrogen atoms? If we are given two Hydrogen atoms, would the only difference between them would be their quantum state (Energy level or eigen value, and the corresponding Orbital or eigen state) and their location (say you are the origin and each of the Hydrogen atoms are located an a... | One talks of a molecule only if the constituents are in a bound state, which implies that they are withnin a microscopic distance of each other.
The probability that the two hydrogen atoms in an $H_2$ molecule are at arm length distance is extremely small, far smaller than inaccuracies of the traditional hydrogen mode... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/45114",
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What is the expectation value of the number operator when the vacuum has a VEV? The number operator N applied to a field whose vacuum has zero VEV gives $N|0>=0$. What if we apply it to the Higgs field?
The background of this question is that in popular scientific accounts, the Higgs field is sometimes described as a '... | If a field $\phi(x)$ has a nonzero VEV $v$, the field whose Fourier components define the creation and annihilation operators is $\phi(x)-v$, which has a zero VEV, and again $N|0\rangle=0$.
An interpretation in terms of the original $\phi$ is highly ill-defined and cutoff-dependent, and cannot be given a sensible phys... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/45204",
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What size will the Sun become once it is a red giant? How big will the Sun be once it becomes a red giant? How much of the solar system will it engulf?
| This is answered in How fast will the sun become a red giant?. I'm just adding a note here because it's not answered directly in a form a non-expert might spot.
The maximum size of the sun is estimated to be 256 times it's current radius, the Earth's orbit is 215 times the sun's radius - so it will consume Mercury, Ven... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/45252",
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Special Relativity Could someone explain to me how special relativity works?
I know there are thousands of sources and databases of knowledge out there, but I find it difficult to understand, even after reading up on those sources.
(Note: if you're an admin to close my question down, would you please be so nice as to p... | I agree with Crazy Buddy that Lay explanation of the special theory of relativity? is a good approach to SR, but my own preference is to view it a bit differently. You probably heard it said that general relativity is a geometrical theory. Well special relativity is a geometrical theory as well.
If you take two points ... | {
"language": "en",
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Physical intuition for higher order derivatives Could somebody give me an intuitive physical interpretation of higher order derivatives (from 2 and so on), that is not related to position - velocity - acceleration - jerk - etc?
| I've always liked the discrete explanation.
In physics, you can almost always approximate a function $f: \mathbb{R} \to \mathbb{R}$ by saying what the value of $f$ is at a discrete set of points $\{x_i\} \subset \mathbb{R}$.
If you do this, you approximate the derivative by looking at how $f$ changes when you move from... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Given Newton's third law, why are things capable of moving? Given Newton's third law, why is there motion at all? Should not all forces even themselves out, so nothing moves at all?
When I push a table using my finger, the table applies the same force onto my finger like my finger does on the table just with an opposin... | This is a really valid doubt and most of us have this on our Mind while trying to understand Newton's third law.
Now yes, $\vec{F_1}=-\vec{F_2}$ is valid and the forces here are an action reaction pair acting in opposite direction with the same magnitude.
So why doesn't a body remain in equilibrium?
These forces(th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/45653",
"timestamp": "2023-03-29T00:00:00",
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Why is temperature constant during melting? This is an elementary question but I do not know the answer to it. During a phase transition such as melting a solid to a liquid the temperature remains constant. At any lower temperature the heat provided went to kinetic energy and intermolecular potential energy. Why is it ... | Roughly speaking, this additional energy will be at first step kinetic, it will increase molecule bouncing around there equilibrium points, until it will be enough to take them out of that equilibrium, and then this energy spent to make the phase transition.
More precisely your confusion is because of the fact that the... | {
"language": "en",
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Effect of gas or liquid within a compound lens system Hi my question is if a compound lens system if filled with gas or a liquid how does it affect the system when compared to the lens system being separated by air alone. Does this affect the focal power of the system or the effective power at all.
| The angle of refraction at the surface of a lens (or any other boundary) is given by Snell's law:
$$ \frac{sin\theta_1}{sin\theta_2} = \frac{n_2}{n_1} $$
where $n_1$ and $n_2$ are the refractive indices of the two media. Suppose $n_1$ is the air and $n_2$ the glass: the refractive index of air is pretty close to one, s... | {
"language": "en",
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Why don't we use the concept of force in quantum mechanics? I'm a quarter of the way towards finishing a basic quantum mechanics course, and I see no mention of force, after having done the 1-D Schrodinger equation for a free particle, particle in an infinitely deep potential well, and the linear harmonic oscillator.
... | Beside the reasons already provided, I will add that that because forces in there classical meaning are not fundamental, what is more fundamental? it's potentials, and what is even more fundamental are fields, and the usual classical forces, are nothing more than (roughly speaking) a sum of the effects/interaction of t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/45869",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Evaluating propagator without the epsilon trick Consider the Klein–Gordon equation and its propagator:
$$G(x,y) = \frac{1}{(2\pi)^4}\int d^4 p \frac{e^{-i p.(x-y)}}{p^2 - m^2} \; .$$
I'd like to see a method of evaluating explicit form of $G$ which does not involve avoiding singularities by the $\varepsilon$ trick. Ca... | Expanding on dmckee's comment:
The $+i\epsilon$-trick has the blessing of OCD mathematicians because it follows directly from a deep fact about the group of spacetime translations: the group $\{e^{-i\langle P,x\rangle/\hbar}| x \in \mathbb{R}^n\}$ of spacetime translations is the boundary of an analytic semigroup $\... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Canonical Commutation Relations Is it logically sound to accept the canonical commutation relation (CCR)
$$[x,p]~=~i\hbar$$
as a postulate of quantum mechanics? Or is it more correct to derive it given some form for $p$ in the position basis?
I understand QM formalism works, it's just that I sometimes end up thinking... | Your running into circles will stop once you commit yourself to a choice.
What to regard as postulate is always a matter of choice (by you or by whoever writes an exposition of the basics). One starts from a point where the development is in some sense simplest. And one may motivate the postulates by analogies or whate... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/46110",
"timestamp": "2023-03-29T00:00:00",
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Conservation of Energy in a Capacitor Consider a parallel-plate capacitor in free space. A negatively charged point particle with initial velocity $v$ passes through the space between the pair of parallel plates (with an initial path perpendicular to the normal vector of the plates).
The point particle accelerates tow... | This question is quite a common one for those first learning about capacitors.
First, let's remember that an electric field caused by stationary charges is conservative--this can easily be explained since a single charge creates a conservative field, and superposition of two conservative fields creates another conserva... | {
"language": "en",
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Terminology for opposite null lines Is there a name for two null lines that lie on the opposite sides of the null cone? Each line can be obtained from the other by reflection in the axis of the null cone (the time-axis). In terms of world-lines, this corresponds to two photons moving in the opposite directions. If ther... | There isn't an official standard name for opposite null lines. Note that opposite null lines are not a coordinate-independent geometric (invariant) notion, and hence it is not a very useful concept. If two null lines happen to lie on opposite sides of the light-cone in one reference frame, then they may not lie on oppo... | {
"language": "en",
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Photons arriving from the Sun Given that the Sun is a bit less than 10 light minutes away from Earth, is it correct to assume in principle (I understand actual processes in the core of the Sun make the situation at a photon's emission far more complicated) that the photons that hit a human eyes on a clear day actually ... | Solar photons arrive to the Earth about 500 seconds after leaving the photosphere. However, the very energetic photons created in the Sun's core take many millions of years to arrive on Earth as they traverse the radiation and convection zones before arriving at the photosphere.
| {
"language": "en",
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How do I start learning particle physics? I am 16 at the moment. I am really interested in physics. Especially particle physics. Can someone please tell me how to start learning the subject. like what to learn first. like which fundamental theories and concepts, the math needed in it, etc, etc.
| What you want to learn is called "Quantum Field Theory", but it is a subject that requires having learnt other things first. At least some differential calculus, Special Relativity and Quantum Mechanics (a subject that itself requires some other previous knowledge).
But you can try. The simplest serious text above popu... | {
"language": "en",
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Potential Energy tends to infinity on the N-Body Problem I need help to solve this problem related with the N-Body problem, i dont understand quite well what I need to define or to express in order to solve it.
We assume a particular solution to the N-Body Problem, for all $t>0$, and $h>0$, where $h$ is the total energ... | From virial theorem, stationary states are given by $2T=U$. The "particular solution" your teacher is assuming is a gravitational collapse where $U \gt 2T$ and therefore $U\rightarrow \infty$ as $t\rightarrow \infty$. Of course, the interparticle distance goes to zero in a collapse but this is not a collision: there is... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/46526",
"timestamp": "2023-03-29T00:00:00",
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Non-Degeneracy of Eigenvalues of Number Operator for Simple Harmonic Oscillator
Possible Duplicate:
Proof that the One-Dimensional Simple Harmonic Oscillator is Non-Degenerate?
I'm trying to convince myself that the eigenvalues $n$ of the number operator $N=a^{\dagger}a$ for the quantum simple harmonic oscillator ar... | Recall $ \hat{H} = \left( \hat{N} + \frac{1}{2} \right) $ and $ \left[ \hat{a}, \hat{a}^\dagger \right] = 1 $ (dropping $\hbar$ and $\omega$).
*
*Assume the ground state $\left|0\right>$ is non-degenerate. You can prove this by solving $\left<x\right|\hat{a}\left|0\right>=0$ in position representation, but I don't k... | {
"language": "en",
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Is there Pair production in between charged plates In classical electromagnetic theory, If parallel plates are charged oppositely and placed close to each other, there will be no charge will not flow from one plate to another.
How does this situation change if one considers Quantum electrodynamics? Can the electric fie... | Yes, the effect you're looking for is called Schwinger pair production. It requires immensely strong electric fields (of the order of $10^{18}$ V/m) for a constant field.
One of the methods for computing the rate is the worldline method, described briefly here. To follow it, some knowledge of effective action methods... | {
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Internal energy according to the van der Waals equation I am trying to derive the internal energy of a gas which obeys the van der Waals equation.
I have however encountered some problems. I calculate the integral of $dU$ from $V=0,T=0$ to $V=V, T=\infty$ to $V=V,T=T$.
I can calculate the work:
$$\left(p+\left(\frac{a... | You can't just subtract infinities and write $\infty-\infty=0$. In fact, $\infty-\infty$ is a major example of an indeterminate form. The result may be anything and needs a precise analysis to be obtained. Moreover, as you realized later, there was really no $\infty-\infty$ over there, it was $\infty-f$ where $f$ is fi... | {
"language": "en",
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The meaning of imaginary time What is imaginary (or complex) time? I was reading about Hawking's wave function of the universe and this topic came up. If imaginary mass and similar imaginary quantities do not make sense in physics, why should imaginary (or complex) time make sense?
By imaginary I mean a multiple of $i... | Let'me just sketch an idea to inroduce "imaginary time" .
A photon in a black hole or in a singularity, has to disappear, it is energy should be 0.
If that photon had a previous existence, the black hole has to distruct its energy:
$E, A$, or its energy $a+a-=\left(N+\frac12\right)h\nu$
The simplest way is to c... | {
"language": "en",
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Is it possible to reduce the sound, when two metal objects collide (perhaps with some coating) without reducing the rigidity of the surface? I have a system, where there are ball bearings on the pistons that clamp the metal plate with special dents for ball bearings. The system should be precise, because it is used for... | The sounds waves will emanate at the point of impact and then echo off of various boundaries. You will want to engineer those boundaries to minimize or more likely direct the reflections and lead the energy to where it can be absorbed and converted to heat. I think the simplest way to do that is to make what the ball b... | {
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Could an NEO strike the moon with sufficient velocity for the shrapnel to escape Lunar gravity, and be attracted by Earth's? Between the news item of an asteroid giving Earth a close shave, and another news item of the impending GRAIL impact ; I find myself wondering whether a NEO could be a hazard to Earth via the moo... | I guess you are referring to objects like 2012 DA14 which weighs about 130,000 metric tons.
Lunar meteorites have reached the Earth's surface before. So yes, it is possible.
There don't seem to be any large NEOs that have any significant chance of such an impact in the near future.
According to the UK Natural History... | {
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What is the Laughlin argument? The fundamental question is
Why is Hall conductance quantized?
Let's start with the Hall bar, a 2D metal bar subject to a strong perpendicular magnetic field $B_0$. Let current $I$ flow in the x-direction, then the y-direction develops a voltage $V_H$. The Hall conductance is $\sigma_H ... | Laughlin explains the whole derivation, including the point mentioned, nicely in his Nobel lecture:
http://www.nobelprize.org/nobel_prizes/physics/laureates/1998/laughlin-lecture.html
What helped me in addition to understand Laughlin's text was the appendix of Jean Dalibard's lecture "Artificial Gauge Fields for Quantu... | {
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Why does the nature always prefer low energy and maximum entropy? Why does the nature always prefer low energy and maximum entropy?
I've just learned electrostatics and I still have no idea why like charges repel each other.
http://in.answers.yahoo.com/question/index?qid=20061106060503AAkbIfa
I don't quite understand w... | Well, I'd mention that entropy is significantly more counter intuitive than some may think. In particular since all microstates have equal probability, or in other words are equivalent, if you were to cut your finger off, the state were the chunk comes back into place all by it self if a perfectly valid assumption. The... | {
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experimental technique for measuring temperature of an ant I am taking a course on thermodynamics. I have a question from my text(halliday & resnick,physics-1). They asked me to measure temperature of an ant or an insect or a small body,like a small robot. If I build a thin thermometer then it is probable that surface ... | Ants are cold blooded. Therefore the temperature of an ant is the ambient temperature in which it exists at the moment. If the ant is in an environment of variable temperature and is moving around, then it has no temperature in the thermodynamic sense. If it is in a region of uniform temperature, then that is its te... | {
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Can one heat up a vacuum? I've got a question about heating a vacuum. If there were, say, a container in space, at 2.7 degrees kelvin (the typical temperature of space, if I'm not mistaken) and as empty as space (as close to a vacuum as space allows), how would one go about pressurizing and heating that container? If... | "space" is at 2.7K because that's the temperature of the microwave background.
If you put an empty box in space the walls of it will eventually end up at 2.7K (in theory) and so anything inside it can only cool to that temperature. If anything was hotter it would radiate heat to the colder walls and if anything tried t... | {
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Is the Earth's atmosphere a Faraday cage? X-ray telescopes are required to be above the atmosphere as the atmosphere blocks EM waves with wavelengths < UV . Does this mean that the Earth's atmosphere can be thought of as a Faraday cage only allowing low energy light to pass through?
| No, there is no relation. Earth's atmosphere is not a Faraday cage.
A Faraday cage requires conductor with freely moving electron so that the potential energy inside the cage is always constant by the rearrangement of electrons.
On the other hand, Earth atmosphere is opaque (see figure) in the short wavelength limit be... | {
"language": "en",
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Why is the colour of sunlight yellow? I was going through the preliminary papers of other schools and found a question that I did not know. It was "Why sunlight appears yellow?". Can anyone answer it?
| The reason why the sun is yellow is because the color is determined by additive combination of its component spectrum.
In other words, the sun emits a range of light that we can see, from violet to red, at different intensities. To compute the net color, the color we see, you must add together the radiation. In the cas... | {
"language": "en",
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Why does motion help you balance on ice skates? It's almost impossible to balance on a single ice skate if you're standing still. But give yourself just a little forward motion—it doesn't take very much—and it suddenly becomes easy. You can stand there on one leg and glide effortlessly half way across the rink. Fric... | In motion, the skate easily tracks left and right to find balance. At rest, the skate resists side to side motion. The skater awkwardly pivots over the fixed skate waving arms. Fore and aft skate motion however, is all too easy, usually the beginning skater's downfall. Any forward motion of the skate while the body i... | {
"language": "en",
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"source": "stackexchange",
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Change in intensity of electric field with constant velocity Consider a +Q charged particle is travelling towards another test charge +Q. Now what would be the difference in electric field experienced by the test charge(avoid the gradual decrease in distance between them)? Would the field lines look compressed and eff... | If you are looking for an effect separate from the particle's position, at classical velocities there isn't one. The electric field is
\begin{equation}
\mathbf{E}=\mathbf{E}(\mathbf{r},t),
\end{equation}
that is, the electric field is only a function of the position $\mathbf{r}$ and the time $t$. At any given instant... | {
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Don't understand the integral over the square of the Dirac delta function In Griffiths' Intro to QM [1] he gives the eigenfunctions of the Hermitian operator $\hat{x}=x$ as being
$$g_{\lambda}\left(x\right)~=~B_{\lambda}\delta\left(x-\lambda\right)$$
(cf. last formula on p. 101). He then says that these eigenfunctions... | Well, the Dirac delta function $\delta(x)$ is a distribution, also known as a generalized function.
One can e.g. represent $\delta(x)$ as a limit of a rectangular peak with unit area, width $\epsilon$, and height $1/\epsilon$; i.e.
$$\tag{1} \delta(x) ~=~ \lim_{\epsilon\to 0^+}\delta_{\epsilon}(x), $$
$$\tag{2} \del... | {
"language": "en",
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"source": "stackexchange",
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First and Second Moment of Mass I recently came across the definition of the Center of Mass of a system as the point about which the first moment of mass is zero.
Further, it defined Moment of Inertia as the second moment of mass.
My question is, What is this 'moment of mass'?
|
I don't know whether this is right or wrong, coz its like bringing back the high school...
When physicists define a "moment of something", then it necessarily means Distance $\times$ the "something". Moment of mass simply implies Distance $\times$ Mass.
For a system of $n$ particles, in order to obtain the center of ... | {
"language": "en",
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Total Energy of the Universe? I've heard the total energy is zero, but I've also heard it cannot be said to be zero since there's so much unknown stuff in the universe. Is that true?
| Conservation of energy doesn't actually apply in any straightforward way to cosmology. The modern understanding of energy conservation is that it is a consequence of Noether's theorem and time translation invariance. In other words, the laws of physics are the same as they were yesterday and they will be tomorrow. This... | {
"language": "en",
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Banach Space representations of physical systems I think most physicists mostly model physical systems as some kind of Hilbert space.
Hilbert spaces are a strict subset of Banach spaces.
Questions:
*
*Can physical systems really have non-compact topologies, as a Banach
space has?
*Does anyone have an example of ph... | Hilbert spaces are occur everywhere where the Lagrangian\Hamiltonian is quadratic in derivatives. If the Lagrangian is non-quadratic then the Hilbert spaces are no longer so convenient. In particular in analysis of Navier–Stokes equations the Banach spaces(not Hilbert spaces) are active used.
| {
"language": "en",
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"source": "stackexchange",
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Why doesn't my pinhole camera work? We all know that light travels in straight a line, which can be proved by pinhole imaging as in the picture shown :
But when I'm doing this little experiment with an apple, no matter how I change the distance between the object and the pinhole, an image can never be observed on the ... | Take a look at this picture - and ask yourself why the operator of the camera has the cloth over his head (the cloth is black on the inside) as he is looking at the back of his camera - which has a piece of ground glass where the image from his pinhole camera is forming:
This used to be how photography was done:
Align... | {
"language": "en",
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Earth moves how much under my feet when I jump? If I'm standing at the equator, jump, and land 1 second later, the
Earth does NOT move 1000mph (or .28 miles per second) relative to me,
since my velocity while jumping is also 1000mph.
However, the Earth is moving in a circle (albeit a very large one),
while I, while... | Ugh, assuming constant radial gravity $g$ I need to solve the equations of motion in polar coordinates $r$, $\theta$ as
$$ \ddot{r} = r \dot{\theta}^2 - g \\ \ddot{\theta} =- \frac{2 \dot{r} \dot{\theta}}{r} $$
which I do not know how to do. When I find out I will add to this answer. This system varies the direction o... | {
"language": "en",
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Evaporation of water content from a solid material by applying low pressure I have a raw material which melts at $96\ ^\circ C$. My aim is to make water content evaporate at temperature below this temperature.
I can apply vaccume oven for this. I want to know at what pressure the water evaporates by keeping low tempera... | Water will evaporate as long as the relative humidity of the surrounding air is below 100%, although the process may be (very) slow. You seem to be confusing evaporation with boiling, but you don't need to boil the water in the material to dry it.
It depends a lot on your configuration, but you are probably better off ... | {
"language": "en",
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How to calculate the Darcy-Weissbach friction factor for shear thinning laminar flow in a pipe? The Darcy-Weissbach friction factor for laminar flow would be $\frac{64}{Re}$
Now, having a shear thinning (non-newtonian) fluid where the viscosity is not constant how do I arrive at $Re$?
To know an apparaent viscosity, I'... | In my view, the objective of knowing the friction factor, is for one to be able to calculate what is the pressure drop needed to push a given flow $Q$ through a given pipe diameter. This kind of relations exists for several models of non Newtonian fluid, take for example the power law model:
$\tau=K\gamma^n$
In this ca... | {
"language": "en",
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Showing that position times momentum and energy times time have the same dimensions I've been asked to show that both the position-momentum uncertainty principle and the energy-time uncertainty principle have the same units.
I've never see a question of this type, so am I allowed to substitute the units into the expres... | I think you are on the right track. There are a couple of bits of advice you may follow:
*
*You may simply note that if $A \geq B$, then it follows that $A = B$ is a valid solution, thus $A$ and $B$ must have the same units.
Therefore $\Delta{p}\Delta{x}$ has the same units as $h$ which has the same units as $\Delta... | {
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How come vibrations? We all know that sound sensation is produced only when sound waves reach upto us. We all know that sound waves are disturbances propagating in air, Vibration is necessary for the generation of sound, but it always forces me to ponder that how was it known or deduced that vibration is necessary for... |
how was it known or deduced that vibration is necessary for any form of sound wave?
It is likely that theories involving wave propagation have been around for thousands of years.
The speculation that sound is a wave phenomenon grew out of observations of water waves. The rudimentary notion of a wave is an oscillato... | {
"language": "en",
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What is the covariant expression for action of the Lorentz force density on charge-current density? In a continuous medium the Lorentz force density is known to be written in the form:
$f_\alpha = F_{\alpha \beta} J^\beta$,
where $F_{\alpha \beta}$ is an electromagnetic field tensor, and $J^\beta$ is a charge-current d... | For a cold (no pressure) charged gas the electromagnetic filed must contain a self-field contribution too in order to describe the density variations due to repulsion of charges. Plasma equations contain it all.
| {
"language": "en",
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"source": "stackexchange",
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Quantum superposition of states: experimental verification How can somebody demonstrate the quantum superposition of states directly by other means than the double slit experiment?
And why can't macroscopic objects like a pen be in superpostion of states? Will it ever be possible to have an object like a pen to be in s... | Others have covered the usual microscopic systems that are currently amenable to controlled quantum manipulations, but there are in fact "macroscopic" objects (to some definitions of the word) that can be placed in quantum superpositions. These fall broadly within a field known usually as cavity optomechanics, which ha... | {
"language": "en",
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Can an induction coil heat two layers of metal? Imagine we have an induction coil which is strong enough to heat a sheet of metal. We can put a sheet of ferromagnetic metal close to the coil at distance $h_1$, and it gets heated to temperature $t_1$, or at distance $h_2 > h_1$ so that the sheet gets heated to temperatu... | The answer is no. The penetration depth of the magnetic field in the first sheet is too small. Read this for example. The penetration depth $\delta$ is typically given by a formula looking something like this:
$$
\delta=\sqrt{\frac{\rho}{\pi\mu f}}\approx\sqrt{\frac{1\cdot10^{-7}}{\pi\cdot8.8\cdot10^{-4}\cdot20\cdot10^... | {
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Clarifications about Poisson brackets and Levi-Civita symbol I need some clarifications about Poisson brackets.
I know canonical brackets and the properties of Poisson Brackets and I also know something about Levi-Civita symbol (definition and basic properties), but I have some doubts.
I don't know how I could apply Po... | 1.) Always choose indices in such a way that the free indices on both sides of the equation match. Furthermore, make sure that you don't mix up summation indices of different summations.
2.) Linearity implies that if you enter a sum as the argument of a Poisson brackets, you get a sum of Poisson brackets, with each of ... | {
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Geometrical significance of gauge invariance of the QED Lagrangian The QED Lagrangian is invariant under
$\psi(x) \to e^{i\alpha(x)} \psi (x)$, $A_{\mu} \to A_{\mu}- \frac{1}{e}\partial_{\mu}\alpha(x)$. What is the geometric significance of this result? Also why is $D_{\mu}=\partial_{\mu}+ieA_{\mu}(x)$ called the cova... | You can interpret gauge invariance in terms of fiber bundles. One can think of a fiber as the space of configurations of the gauge field, connected by gauge transformations.
The covariant derivative is called "covariant" because it transforms covariantly, i.e.
$\begin{equation}D'_\mu=U^{-1}(x)D_\mu U(x)\end{equation}... | {
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What is the electrical conductivity (S/m) of a carbon nanotube? I have been searching around for a while for this but I am having trouble finding any actual figures, all I can seem to find is that it is "very high".
So I am wondering, does anyone have any figures of what the electrical conductivity of a carbon nanotube... | The numbers will greatly vary depending on the kind of nanotube. The following are some examples from cursory Google searches.
Electrical conductivity was increased by 50 percent to 1,230 siemens
per meter.
http://news.ncsu.edu/releases/wms-zhu-cnt-composites/
And that’s not all: colossal carbon tubes are ductile ... | {
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Crystal momentum and the vector potential I noticed that the Aharonov–Bohm effect describes a phase factor given by $e^{\frac{i}{\hbar}\int_{\partial\gamma}q A_\mu dx^\mu}$. I also recognize that electrons in a periodic potential gain a phase factor given by $e^{\frac{i}{\hbar}k_ix^i}=e^{\frac{i}{\hbar}\int k_idx^i}$. ... | While all the statements you made about crystal momentum only apply exactly for Bloch states in which the momentum operator is diagonal, the fact that the phase due to the vector potential is $e^{i \int A}$ is true for all states in the one-charged-particle Hilbert space.
This is of course a manifestation of the fact t... | {
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What is the nature of the correspondence between unitary operators and reversible change? Why does the formalism of QM represent reversible changes (eg the time evolution operator, quantum gates, etc) with unitary operators?
To put it another way, can it be shown that unitary transformations preserve entropy?
| Like all 20th century physics, the formalism is invariant with respect to time reversal. This was true in classical mechanics and it remains true in QM because canonical quantization does not alter the meaning of energy - it just becomes an evolution operator. Unitary operators satisfying $A A^{\dagger} = I$ are associ... | {
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Shape of a string/chain/cable/rope/wire? The height of a string in a gravitational field in 2-dimensions is bounded by $h(x_0)=h(x_l)=0$ (nails in the wall) and also $\int_0^l ds= l$. ($h(0)=h(l)=0$, if you take $h$ as a function of arc length)
.
What shape does it take?
My try so far: minimise potential energy of the... | Your approach so far is correct. Now, the first thing to do is to create a coordinate axes. In this case, I will say that the “poles” are at x=-a and x=a, and y=0 is the point where the rope is attached to the “poles”. Now, we can assume constant linear density μ. This is not strictly necessary, but it makes the calcul... | {
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Translation Invariance without Momentum Conservation? Instead of the actual gravitational force, in which the two masses enter symmetrically, consider something like $$\vec F_{ab} = G\frac{m_a m_b^2}{|\vec r_a - \vec r_b|^2}\hat r_{ab}$$ where $\vec F_{ab}$ is the force on particle $a$ due to particle $b$ and the units... | Your forces are always equal. It is the accelerations that are unequal in case of equal masses. The situation is similar to the Coulomb interaction. The total momentum is conserved. There is no problem here.
EDIT: As Michael Brown kindly pointed out, the forces are implied to be different. Then indeed the momentum cons... | {
"language": "en",
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What is the current through the lamp? We have the following circuit:
A neon lamp and a inductor are connected in parallel to a battery of 1.5 $V$. The inductor has a 1000 loops, a length of $5.0 cm$, an area of $12cm^2$ and a resistance of $3.2 \Omega$. The lamp shines when the voltage is $\geq 80V$.
*
*When the... | Yeah ok so this problem, is like I said a little silly. It seems like you have to assume the current drops to zero in the given time and therefore so does the flux. This gives you the first part, the induced voltage across the inductor. For the second part, it seems w... | {
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Confused about magnetic and geographic north I'm slightly confused about the "north-seeking" pole of a magnet: does it point towards magnetic north, or is it towards geographic north?
I ask because I've been finding different explanations in different places.
| 'Magnetic North' is a LOCATION, not the polarity of that location. It is so-named to distinguish it from 'True North'. Since the 'North-Seeking' pole of a compass needle points in that direction, 'Magnet North' (the location) has a south magnetic polarity.
| {
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"source": "stackexchange",
"question_score": "2",
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Confused about fire? Im confused about fire.
The way I see it :
*
*Heat creates (kinetic) energy in mass and this creates stronger vibrations of atoms.
*When those vibrations are strong enough the electrons interact stronger due to electromagnetic forces.
*This causes the electrons to fly away. This is the creatio... | Fire is a bunch of subatomic particles. Because they are not bound into an atom, fire technically is a plasma.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/51738",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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What exactly are we doing when we set $c=1$? I understand the idea of swapping from unit systems, say from $\mathrm{m\ s^{-1}}$ to $\mathrm{km\ s^{-1}}$, but why can we just delete the units altogether?
My question is: what exactly are we doing when we say that $c=1$?
| All we're doing is using a set of units where certain quantities happen to take convenient numerical values. For example, in the SI system we might measure lengths in meters and time intervals in seconds. In those units we have $c = 3 \times 10^8\ \text{m}/\text{s}$. But you could just as well measure all your distanc... | {
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Current without Voltage and Voltage without Current? At school I've always learned that you can view Current and Voltage like this:
The current is the flow of charge per second and the Voltage is how badly the current 'wants' to flow.
But I'm having some trouble with this view. How can we have a Voltage without a curre... | For e.g. a battery there is voltage even it is not connected anywhere.
Thus voltage(Potential difference between two points) exists without current(flow of charge with respect to time) but current doesn't exist without voltage .
| {
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Is Schrödinger’s cat misleading? And what would happen if Planck constant is bigger? Schrödinger’s cat, the thought experiment, makes it seem like as if measurement can cause a system to stop being in a superposition of states and become either one of the states (collapsed).
So does a system always exist in a superposi... | I'm pretty sure Planck's constant only refers to the size of quantum scale objects. If it were larger, all it would mean is that Newtonian physics would only apply at a larger scale.
And Schrodinger's cat only means that until observed, we cannot be sure of the state. It has a state, whether we know it or not. What we ... | {
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The viscous force between the layers of liquid is same, then why there is variation in the velocities of its layers? I have learned in my textbook that when the liquid flows the bottom layer of the liquid never moves because of friction, but the upper layers move with increasing velocities how it is possible if the vis... | Viscosity and friction are not the same thing. Viscosity is about how a unit of a fluid is sheared between regions of different velocity. Friction is about how one body has zero velocity with respect to another until a certain minimum amount of shear stress is applied.
| {
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Where does the mass term come from in the Proca Lagrangian? There are many good books describing how to construct the Lagrangian for an electromagnetic field in a medium.
$$
\mathcal{L}~=~-\frac{1}{16\pi}F^{\mu\nu}F_{\mu\nu}-\frac{1}{c}j^{\nu}A_{\nu}
$$
When moving to the Proca Lagrangian (and a massive photon), I kno... | In addition to the answer of Sam's, I would say there is no gauge invariance requirement for the massive field $A$, only Lorentz covariance.
| {
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Is it possible for a physical object to have an irrational length? Suppose I have a caliper that is infinitely precise. Also suppose that this caliper returns not a number, but rather whether the precise length is rational or irrational.
If I were to use this caliper to measure any small object, would the caliper ever ... | I think that because you have measurements that are real numbers not isomorphic to the natural numbers or countably infinite, you firstly have assumed the universe infinitely dense. Therefore any measurement as mentioned in some other answer's would justly be required to have infinite many decimal points.
This is seen... | {
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Representations of Lie algebras in physics Why is an invariant vector subspace sometimes called a representation? For example in Lie algebras, say su(3), the subspace characterized by the highest weight (1,0) is an irreducible representation of dimension 3 of su(3).
However, a representation of a Lie algebra is a Lie ... | To add to what @Qmechanic says, note also that for a representation $\rho:\mathfrak g\to \mathfrak{gl}(V)$ of a Lie algebra $\mathfrak g$ acting on a vector space $V$, a vector subspace $W$ of $V$ is called an invariant subspace of the representation provided $\rho(X)w\in W$ for all $X\in\mathfrak g$ and $w\in W$. A r... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Can low-gravity planets sustain a breathable atmosphere? If astronauts could deliver a large quantity of breathable air to somewhere with lower gravity, such as Earth's moon, would the air form an atmosphere, or would it float away and disappear? Is there a minimum amount of gravity necessary to trap a breathable atmos... | The moon has 85% of the gravity of Titan (which has a thick hydrocarbon atmosphere), so I cannot believe for 1 second that it's gravity is too weak to retain a viable atmosphere.
Factors like Sola winds stripping the atmosphere due to lack of protection from a magnetic field, is a valid explanation, but low gravity can... | {
"language": "en",
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Equivalence principle question I understand the equivalence principle as "The physics in a freely-falling small laboratory is that of special relativity (SR)." But I'm not quite sure why this is equivalent to "One cannot tell whether a laboratory on Earth is not actually in a rocket accelerating at 1 g".
| The equivalence principle (the version you mention) means that you cannot tell, locally, whether you are in a freely falling frame or in "outer space", i.e., in a region of space with no gravitational field. This version is the EEP.
There is another version, namely, WEP which says that the inertial mass is the same as... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What would be the effect of a slanted muzzle on the trajectory of a bullet? Let's say I cut off the end of a gun barrel at a 45° angle: What would the effect be on the trajectory of a bullet fired through that barrel?
Would the bullet be less stable (I guess)? Would it make the gun fire with an angle, and would that be... | Suppose you make the cut so that the slant is downward – i.e., the top part of the barrel is shortest, the bottom is longest. The bullet is driven down the barrel by the pressure of propellant gases on its base. As the base of the bullet leaves the barrel the propellant gases begin to act asymmetrically on the base. ... | {
"language": "en",
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"source": "stackexchange",
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Particle in infinite potential well which is doubled in size at $t_0$ I am currently studying for an exam in Quantum Mechanics and came across a solution to a problem I have trouble with understanding.
The Problem:
A Particle sits in an infinite potential well described by
\begin{align}
V(x) &= 0, & 0 \leq x \leq L \\
... | Under sudden perturbation the state does not change, but the basis does. This state gets expanded in the new basis whose coefficients evolve correspondingly. Normally it is covered in chapters with the time-dependent perturbation theory $\hat{V} = \hat{V}(t)$.
If the potential is time-dependent, the energy is not conse... | {
"language": "en",
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When do I apply Significant figures in physics calculations? I'm a little confused as to when to use significant figures for my physics class. For example, I'm asked to find the average speed of a race car that travels around a circular track with a radius of $500~\mathrm{m}$ in $50~\mathrm{s}$.
Would I need to apply t... | Keep precision all the way through to the number you report and then truncate accordingly at the end.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/52837",
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Dark Matter 'Stars' I'm aware that the Milky Way has a dark matter 'halo' around it, presumably a spherically symmetric distribution.
But I'm completely ignorant regarding the theories explaining dark matter... Is there any reason to not expect a star-sized object to also be made of dark matter?
I know they'll be extre... | If dark matter was self interacting, (and there is some evidence that it is self interacting) then it might form star-like clumps. Some groups even think that dark matter might be sort of copy of all the standard model particles.
If those star sized and massed clumps of dark matter were to pass through a nebula, it ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/52877",
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London into Australia in 90 minutes Me and my friend are having a debate on whether it would be possible for a human to travel at 15,000 miles an hour from London to Australia in the matter of 90 minutes. Would a human be able to survive travel in such at fast speeds knowing he will have to overcome immense amou... | The distance from London to Australia is about 17,000km. If you wanted to minimise the acceleration you'd feel during the trip you'd accelerate continuously for the first half of the journey (8,500km) then decelerate at the same rate for the second half. To work out what acceleration is required you use the SUVAT equat... | {
"language": "en",
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"source": "stackexchange",
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How to get "complex exponential" form of wave equation out of "sinusoidal form"? I am a novice on QM and until now i have allways been using sinusoidal form of wave equation:
$$A = A_0 \sin(kx - \omega t)$$
Well in QM everyone uses complex exponential form of wave equation:
$$A = A_0\, e^{i(kx - \omega t)}$$
QUESTION... | Consider the following derivative: $[\cos{x} +i\sin{x}]' = i \sin{x} - i\cos{x} = i(\cos{x} +i\sin{x})$. That sure looks like $[e^{ix}]' = ie^{ix}$. So the question from a physics point of view is why is the oscillatory behaviour of $\sin$ and $\cos$ so fundamentally connected to the behaviour of $\exp$ governing growt... | {
"language": "en",
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How does the correlation length of weather emerge? The question is pretty simple: If I know the weather where I stand, I can estimate the weather 5 meters or 1 km away away pretty well, but I'll have a hard time guessing what the weather is, say, 50 km away.
Therefore, it seems that the climatic system has a length-sca... |
Therefore, it seems that the climatic system has a length-scale. Where does it come from?
Let us not forget that the weather system is a classical case of chaotic dynamics: several interacting differential equations are at work, not just Navier Stokes. Think of tides, think of seasons, think of clouds/albedo etc.
But... | {
"language": "en",
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How scientists could say that such meteorite comes from Mars How could scientists affirm that a meteorite comes from Mars and not from another source ?
This is a probability or an absolute certainty ? How much percent ?
| Essentially, a chemical and mineralogical comparison is made between the meteorite and samples taken from the Martian surface and atmosphere - particularly from the article The SNC meteorites are from Mars (Treiman et al. 2000, Planetary and Space Science, vol. 48, pp. 1213-1230), that states:
Most telling is that the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/53311",
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"source": "stackexchange",
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Electric Flux Contradiction I am currently reading about electric flux; and from this passage I am reading, I am sensing a bit of a contradiction:
"If the E-field is not perpendicular to the surface area, then the flux will be less than EA
because less electric field lines will penetrate A. Consider the wedge shape s... | It is a misleading diagram due to the way the field lines are drawn and the way angle is defined. The angled surface has actually increased in Area, thereby inadvertently keeping the flux the same. The usual definition is that $\theta$ is zero when E and the surface are perpendicular.
$\theta=0$ , flux is proportional ... | {
"language": "en",
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What is the proof that a force applied on a rigid body will cause it to rotate around its center of mass? Say I have a rigid body in space. I've read that if I during some short time interval apply a force on the body at some point which is not in line with the center of mass, it would start rotating about an axis whic... | What you are talking about is called the instant center of percussion. To purely rotate a rigid body about an axis (the rotation axis) a force needs to be applied along the axis of percussion which is a) perpendicular to the rotation axis, b) on the far side of the center of gravity from the pivot and c) located a dist... | {
"language": "en",
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Why is ski jumping not suicidal? At least on television, ski jumpers seem to fall great vertical distances before they hit the ground - at least a few dozen meters, though I couldn't find exact distances via a quick search. And yet they almost always land on their feet as if they just fell two or three meters. (Here's ... | As @ChrisF correctly says, landing too far towards the end of the slope, hence towards the end where it becomes less steep and less parallel to the flight path of the jumper, would be very dangerous.
In ski jumping, every jump and slope is designed for a fixed jump length. This length is given by the K-Point which de... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/53530",
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Confused over complex representation of the wave My quantum mechanics textbook says that the following is a representation of a wave traveling in the +$x$ direction:$$\Psi(x,t)=Ae^{i\left(kx-\omega t\right)}\tag1$$
I'm having trouble visualizing this because of the imaginary part. I can see that (1) can be written as:$... | The wave function itself is not a "real" thing. I.e. it is not an observable quantity. What's "real" is the probability distribution which is associated with the wave function. The probability of finding the particle between points $x=a$ and $x=b$ (restricting to one dimension for simplicity) is given by:
$$P(a\leq x\l... | {
"language": "en",
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Why use Fourier expansion in Quantum Field Theory? I have just begun studying quantum field theory and am following the book by Peskin and Schroeder for that.
So while quantising the Klein Gordon field, we Fourier expand the field and then work only in the momentum space. What is the need for this expansion?
| I think it's also important to emphasize the physical significance of the Fourier modes in the context of QFT. The Fourier modes $a^\dagger(\mathbf k)$ and $a(\mathbf k)$ in the context of the quantized Klein-Gordon field, for example, create and destroy particles with momentum $\mathbf k$ respectively. Namely, if $|... | {
"language": "en",
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Identity as a trivial reducible representation In particle physics, I was taught that a representation of a group is a function $r: group \rightarrow matrices\,(n\times n)$ such that $r(g_1)r(g_2)=r(g_1g_2)$ and $r(e)=I_{n\times n}$. Then, that a representation is reducible when you can find a matrix $A$ such that $Ar(... | What you have constructed is a representation, but not a faithful one. Since your homomorphism $r$ is not injective, you lose some of the structure of the group. In fact, since $r$ is trivial, you lose all the structure of the group. While most useful statements about $G$ apply to $r(G)$ equally well, you cannot pull b... | {
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3D: Get linear velocity from position and angular velocity I want to find out the linear velocity of a point in 3D space, (Euclidean), given:
*
*Its position
*Its angular velocity
*The point it's rotating around (fulcrum)
(This is a problem I need to solve for 3D graphics programming with a physics engine).
The... | The relation between angular velocity $\vec{\omega}$, position $\vec{r}$ (assuming rotation around the origin) and tangential velocity $\vec{v}$ (which is what you are asking for) is given by
$\vec{\omega}=\frac{\vec{r}\times\vec{v}}{\mid\vec{r}\mid^2},$
where $\times$ is the cross product and $\mid\vec{r}\mid^2$ the ... | {
"language": "en",
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Why does Venus transit so slowly? I have calculated that because Venus is $d = 12,103.6~\mathrm{km}$ in diameter and moves at $v = 35.02~\mathrm{km}/\mathrm{s}$, it would take
$$ t=\frac{d}{v} = \frac{12,103.6~\mathrm{km}}{35.02~\mathrm{km}/\mathrm{s}} = 345.62~\mathrm{s} = 5~\mathrm{min}~46~\mathrm{s} $$
for Venus to ... | There are three main reasons.
1) While Venus is orbiting the Sun at 35.02 Km/s, the Earth is also orbiting the Sun in the same direction [both clockwise] at 29.78 Km/s. This factor will decrease the relative transit velocity of Venus as seen from earth.
2) Venus is travelling at 35.02 Km/s in an elliptical orbit. Hence... | {
"language": "en",
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Stability of nucleii and $A=5$ Why there is no stable nuclei with
$$A=5$$
in nuclide the chart and so in nature like we know it?
| As Jerry Schirmer said, helium-4 is an extremely stable nucleus. What does it mean quantitatively? It means that it binding energy is very high, namely 28 MeV. In other words, helium-4 is 28 MeV/$c^2$ lighter than the sum of masses of two free protons and two free neutrons.
The best candidates $A=5$ nuclei would have 2... | {
"language": "en",
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Difference between torque and moment What is the difference between torque and moment? I would like to see mathematical definitions for both quantities.
I also do not prefer definitions like "It is the tendancy..../It is a measure of ...."
To make my question clearer:
Let $D\subseteq\mathbb{R}^3$ be the volume occupie... | Torque and moment are essentially the same thing and are calculated in the same way - it's really the context that determines which word is used. 'Torque' is usually used when we're talking about the twisting effect on a shaft and 'moment' is usually used when we're talking about the bending effect on a beam. If yo... | {
"language": "en",
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Is it possible to calculate atmospheric pressure if given temperature (F) and elevation? I am working on a report at work and need to determine the atmospheric pressure for small intervals over a 24 hour period. Searching Google, I've found charts which give a base pressure of 14.65 psia at sea level. This is at 68F. T... | It depends on the precision you need.
A common and good approximation is the Hypsometric equation, that relates pressure and elevation in the standard Earth atmosphere (source Wikipedia):
$\ h = z_2 - z_1 = \frac{R \cdot T}{g} \cdot \ln \left [ \frac{P_1}{P_2} \right ]$
*
*$h$ = thickness of the layer [m]
*$z$ = ge... | {
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Is cosmic background radiation dark-matter and/or dark-energy? Dumb question alert: Is it possible that the cosmic background radiation might be the source of dark-matter and/or dark-energy? What is the mass of the background radiation in the known universe?
| No.
Neither dark matter nor dark energy can be seen in the electromagnetic spectrum---that's why it's "dark"---whereas the cosmic background radiation is electromagnetic radiation.
We are able to deduce a number of facts about about dark energy and dark matter from their effects on observable stuff (including the CMB i... | {
"language": "en",
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Dynamic structure factor Dynamic structure factor is the spatial and temporal Fourier transform of Van Hoves time dependent pair correlation function. It is written as
$$ S(k,\omega)= \frac{1}{2\pi}\int F(k,t)\exp(i\omega t)dt $$
$F(k,t)$ is intermediate scattering function.
My question is how did we use spatial and t... | A spatial Fourier transform means a Fourier transform in the spatial variable ($x\rightarrow k$), while a temporal Fourier transform is the same transformation, but in terms of the time variable ($t\rightarrow \omega$). The equation you have written is the (asymmetric) temporal Fourier transform of $F(k,t)$.
The spati... | {
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Equivalence between QFT and many-particle QM My understanding from my QFT class (and books such as Brown), is that many-particle QM is equivalent to field quantization. If this is true, why is it not an extremely surprising coincidence? The interpretation of particles being quanta of a field is -- at least superficiall... | Many body quantum mechanics is the non-relativistic limit of an underlying relativistic quantum field theory (QED in the case of electrons in atoms or metals, QCD in the case of nucleons in a nucleus). This can be made manifest by constructing a non-relativistic effective field theory which describes the low energy lim... | {
"language": "en",
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Why is electric potential scalar? I can't conceptually visualize why it would be so. Say you have two point charges of equal charge and a point right in the middle of them. The potential of that charge, mathematically, is proportional to the sum of their charges over distance from the point ($q/r$). But intuitively, my... | Because work and charge both are scalar quantity ie electric potential is scalar quantity
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/54900",
"timestamp": "2023-03-29T00:00:00",
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How is possible for current to flow so fast when charge flows so slow? How is it possible for current to flow so fast when charge flows so slowly?
We know electrons travel very slowly while charge travels at ~the speed of light.
| One needs to distinguish between two things when it comes to electricity, electric currents and voltages.
1) The electric current is flow of electrons in metal wires, (or in fluids like electrolytes). The electrons are moving in the wire at the drift velocity
$v=\frac{I}{enA}$
where: $I$ is the electric current; $e$ i... | {
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Dark matter and QFT My understanding is that the particle is a somewhat artificial notion in QFT (see: Quantum Mechanics: Myths and Facts), and that in general it is possible for a quantum field to have unstable excitations that don't look anything like particles. Is this an active field of research (what is it called)... | Maybe you mean something like Howard Georgi's unparticle theory, see here or here for example?
This is a high energy theory which extends the standard model by an additional scale invariant sector of particles whose properties such as energy, momentum, and mass can simultaneously be scaled up or down (therefore the ter... | {
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Deriving the reduced Green's functions in Polchinski's volume 1 In equation 6.2.7, Polchinski defines his reduced Green's functions $G'$ on the 2-manifold to satisfy the equation,
$$ \frac{-1}{2\pi \alpha '}\nabla ^2 G'(\sigma_1, \sigma_2) = \frac{1}{\sqrt{g}}\delta ^2 (\sigma_1 - \sigma_2) - X_0^2 $$
(..where $\sigma... | Recently, I just learned that this has to do with something called Hadamard form of the Green's function, which I am not familiar with. It's roughly about the singularity structure of the two-point function. In two dimensions, the Green's function is roughly a sum of a logarithmic divergent term and a regular term. In ... | {
"language": "en",
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Best method for building balsa-wood bridge I'm building a bridge out of balsa-wood strips for school, and wanted some advice. These are the specifications:
*
*Height: 2 to 6 in
*Length: 12 inches, plus 1-3 inches on each side resting on tables
*Width: 2 +- 1/16 in at the base
*Weight: <= 50 g
The objective is m... | Use paint thinner combined with glue. It thins the glue out so that the glue can get into all of the crevices that people can and CANNOT see. This makes the bridge much more compact and all aspects of the bridge, especially joints, will be bound together with more strength. My bridge was 20 inches long, 160 grams an... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/55219",
"timestamp": "2023-03-29T00:00:00",
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Distance traveled in a simple two body problem I'm trying to program an $N$-body simulation and I'd like to be able to test it with a known solution to a simple, two-body problem. I've looked at multiple sources, but I just don't know how to apply it to my simple test case.
Two objects at rest placed 10 meters apart wi... | First of all, this is by no means a trivial problem. The usual method goes something like the following. The force from mass 2 on mass 1 is:
$$F_{21} = G\frac{m_1 m_2}{(x_2 - x_1)^2} = m_1 \ddot{x}_1$$
Similarly:
$$F_{12} = -F_{21} = -G\frac{m_1 m_2}{(x_2 - x_1)^2} = m_2 \ddot{x}_2$$
Canceling masses and subtracting th... | {
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Number of strings in elementary particles I've seen many articles about the string theory and have a very simple question : I'd like to know how many Strings are in a quark or an electron?
| There are a lot of different ways to get quantum field theories that look like the Standard Model in string theory. In some string theory models (such as the heterotic models), every particle that the Standard Model treats as point-like (electrons, quarks, etc) is a single elementary string. But there are other more ... | {
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Interaction potential analysis from $\phi^4$ model In this paper, the authors consider a real scalar field theory in $d$-dimensional flat Minkowski space-time, with the action given by
$$S=\int d^d\! x \left[\frac12(\partial_\mu\phi)^2-U(\phi)\right],$$
where $U(x)$ is a general self-interaction potential. Then, the a... | It's not a gauge transformation, it's a field redefinition. Srednicki gives an example of this in exercise 10.5. In this exercise, a free field theory is turned into what looks like an interacting field theory by a field redefinition, however in perturbation theory, the scattering amplitudes vanish, confirming that t... | {
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"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Estimate number of hairs on human head A technique of vital importance at all levels in physics is estimation. This is obvious from the first chapter in any introductory physics textbook, but is also related to the working physicist. Checking orders of magnitudes during research presentations is common practice - I've ... | Firstly, I assume that we have 300 hairs per square cm on our head. This can be tested by waxing an area of 1cm^2 on your scalp and counting the number of hairs that are removed.
Step 2, we must calculate the area of the scalp, and we assume 100 hairs per square cm applies to the whole area of the scalp.
I assume the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/55598",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 5,
"answer_id": 3
} |
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