Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Why can't "missing mass" (=dark matter) be photons? After a star lives and dies, I assume virtually all of its mass would be photons. If enough stars have already lived and died, couldn’t there be enough photon energy out there to account for all the "missing mass" (=dark matter) in the universe?
And if there were enou... | Photons are easily detectable. We can count how many photons are there at any distance of us by just counting the photons reaching us from there. It is impossible that the hidden photons ramble the whole universe but mysteriously avoid us.
| {
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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 ... | Imagine a container containing just ice at $-1^\circ \rm C$. When you heat it, the energy goes into kinetic motion of the molecules, and its temperature increases. Similarly, if the container is filled with liquid water at $1^\circ \rm C$ its temperature will increase for the same reason.
But now imagine the container ... | {
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Other Gross-Neveu like theories? By "Gross-Neveu like" I mean non-supersymmetric QFTs whose partition function/beta-function (or any n-point function) is somehow exactly solvable in the large $N_c$ or $N_f$ or 't Hooft limit.
(..supersymmetric examples would also be helpful to know of if in case there are no other th... | There are many quantum field theory models which are exactly solvable in the Large $N$ limit, such that the $\mathbb{C}P^N$ model, the Thirring model, the $O(N)$ vector model etc. Please see the following review by Moshe Moshe and Jean Zinn-Justin covering many of these models. The main idea is that Feynman diagrams (f... | {
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"source": "stackexchange",
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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.
| One of the Gaussian equations for a compound lens system describe this :
$$
\phi_{\text{tot}}=\phi_1 + \phi_2 - \phi_1\phi_2\tau
$$
where $\tau = \frac{t}{n}$ is the reduced distance between the lenses (or lens systems), $n$ is the index of refraction of the medium between them (the gas or liquid which you describe), a... | {
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Do new universes form on the other side of black holes? I have four questions about black holes and universe formations.
*
*Do new universes form on the other side of black holes?
*Was our own universe formed by this process?
*Was our big bang a black hole seen from the other side?
*Are there solid reasons why th... | It's not exactly a duplicate, but have a look at my answer to Entering a black hole, jumping into another universe---with questions.
For certain types of black holes it's possible to find a trajectory that takes you inside the event horizon then back out again, but when you emerge you'll find there is no way (without t... | {
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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... | Before answering the question more or less directly, I'd like to point out that this is a good question that provides an object lesson and opens a foray into the topics of singular integral equations, analytic continuation and dispersion relations. Here are some references of these more advanced topics: Muskhelishvili,... | {
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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... | The choice of postulates is somewhat arbitrary in the sense that given a set of postulates you almost always can find an alternative set. The choice is guided by subjective criteria such as simplicity, closeness to experiment, or theoretical elegance.
However there are situations where some postulates/theorems do not m... | {
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How can Sub-Atomic Particles be Visualized? Can you see or accurately visualise sub atomic particles or are they known only by maths and/or inference?
| We can image the sub-structure of nucleons by a number of different techniques involving high energy scattering. The results are generally presented in terms of "parton distribution functions" or "structure functions".
One such experiment that I had some small relationship with (though not enough to be an author) was N... | {
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Averaging decibels Wikipedia:
The decibel (dB) is a logarithmic unit that indicates the ratio of a
physical quantity (usually power or intensity) relative to a specified
or implied reference level.
If I measure some physical quantity in decibels, then what is the preferred way to calculate the mean of the measur... | The "physically natural" quantity to average is the actual power, or energy, but it depends exponentially on the number of decibels. So if you were averaging the power or energy, the result would be pretty much equal to the power or energy of the largest (loudest) reading in decibels.
So even though it's physically les... | {
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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... | The point charge $q$ moves in a potential field $\phi$ (generated by the capacitor), so the point charge has potential energy $U=q \phi$. It is accelerated by a force $\boldsymbol{F}$ along the gradient of that potential ($\boldsymbol{F}=q \boldsymbol{E}= -q \boldsymbol{\nabla} \phi$). For any such situation, you can ... | {
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Beyond WKB approximation for energies In the first term the energies are given by the Wentzel–Kramers–Brillouin (WKB) formula
$$ \oint p dq = 2\pi \left( n+\frac{1}{2} \right) $$
However, can this formula be improved to include further corrections? For example the wave function in the WKB approach can be evaluated to... | In the following, I'll describe to you how in principle one can compute higher order corrections to the Bohr-Sommerfeld condition.
In order to find higher order corrections to the Bohr-Sommerfeld formula, we need to include higher order corrections of the wavefunction of the form:
$\Psi(x) = \sum_n \hbar^n a_n(x) exp(\... | {
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Is the Lagrangian density in field theory real? As the Lagrangian in classical mechanics corresponds to energy, it must be real. But is that the case in quantum field theory? I mean, it should still correspond to some sort of energy, but what about all the "$i$"s here and there, such as in the Dirac Lagrangian $i\bar{\... | In quantum field theory, the Lagrangian density is an operator, not a number. So it doesn't make sense to say it has to be real; "real" is a term that applies to numbers, not operators.
What does have to be true is that $\mathcal{L}$ has to have real expectation values in all physical states, and that in turn means it ... | {
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When is the right ascension of the mean sun 0? I understand that the right ascension of the mean sun changes (at least over a specified period) by a constant rate, but where is it zero? I had naively assumed that it would be zero at the most recent vernal equinox, but when I try to calculate the equation of time using ... | No, the right ascension of the mean Sun is NOT zero at the vernal equinox. It is in fact nearly identical to the ecliptic longitude of the mean Sun (the difference is due to UT vs ephemeris time), and this is defined such that it coincides with the ecliptic longitude of the apparent Sun when the Earth is at perihelion.... | {
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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... | In case you want to take it from the partition function,
$U = k_B T^2 \frac{\partial}{\partial T} \left( \ln Q \right)$
and
$Q(N, V, T) = \frac{1}{N!} \left( \frac{2 \pi m k_B T}{h^2} \right)^{\frac{3N}{2}} \left( V - Nb \right)^N e^{\frac{a N^2}{V k_B T}}$,
which gives the same result as the other answers.
| {
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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... | Another way to look at it is to imagine that time is a curved dimension, in sense it will be cyclic.
To visualize that imagine a plane of two dimensions, then the third usual dimension will be a perpendicular line to this plane.
Now consider this line to be bent in a circle, thus this dimension will go around and aroun... | {
"language": "en",
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"question_score": "40",
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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... | Unfortunately, anything that reduces noise without slowing the system down is going to do it by sacrificing rigidity.
If it is within your engineering parameters, you might introduce a damper on the pistons that engages within a millimeter or so of the ultimate extension of the piston. By slowing the piston down befor... | {
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Who used the concept of symmetries first? Who "invented" the concept of symmetries? This article is quite extensive, but it blurs the history with the modern understanding.
https://plato.stanford.edu/entries/symmetry-breaking/
Some of the concepts can be traced to Galileo and Newton, but I'm quite certain the modern no... | For any application of symmetries throughout history, one can always find an earlier, more rudimentary application, so there is no first person, at least not as far as records go. The very first mathematics/physics/natural sciences results were geometric in nature, so the symmetries of the objects played a crucial role... | {
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"source": "stackexchange",
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Energy from man-made tornadoes Peter Thiel just paid $300,000 to Canadian inventor Louis Michaud who is working to construct useful "man-made tornadoes" or "atmospheric vortex engines" which could be components of future power plants.
Less ambitiously, they could replace chimneys and reduce the losses. More ambitiously... | I accidentally stumbled over this question and wanted to post an answer, after some brief reading on http://vortexengine.ca/english.shtml, despite it was asked already over a year ago.
I think the basic idea of the concept is founded on a major confusion between cause and effect regarding meteorological phenomena. Whil... | {
"language": "en",
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"question_score": "13",
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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... | consider a system of gas particle inside a perfume bottle. Now lets say you spray the gas out, and the system of particle now gets spread all around in a Random manner. Well,now lets see this particles as waves(matter waves) ,just like the electron clouds. I admit, I don't have any deep understanding of quantum mechani... | {
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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 ... | I am not sure, but maybe you can use a micro-thermocouple (https://www.variohm.com/images/datasheets/Micro-Thermocouples.pdf) For example, 44 AWG wire is 0.05 mm diameter, if I am not mistaken.
| {
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"source": "stackexchange",
"question_score": "8",
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Separation between slip rings of DC generator
This is a DC generator which converts mechanical energy to Direct Current. The commutators in a DC generator are separated (as you can see in the image). It is explained in our book that it prevents the change in direction of current. But I don't understand.
Even if we don... | Imagine a that one of the carbon brushes is connected to a positive terminal of a DC voltage source (eg: battery) and the other brush to the negative terminal.
A current, $I$, will flow through the rotor winding from the positive terminal to the negative terminal. As the current flows through the magnetic field $B$ set... | {
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Is the superposition principle universal? In David J. Griffiths' Introduction to Electrodynamics, he claims that the superposition principle is not obvious but has always been found to be consistent with the experiments. So I was wondering have we found some physics quantities which do not follow superposition principl... | Any physical quantity that can be organized as a vector space obeys the superposition principle. I would go as far as to say that the superposition principle arises from the fact that a vector space is closed under the weak operation $+$ of the field $\mathbb{(R,+,\cdot)}$.
| {
"language": "en",
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"source": "stackexchange",
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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... | If you inject the gas very slowly, the system will remain in thermodynamic equilibrium
source
By looking at the diagram above, you can heat up the gas as you inject it and keep it on the bottom right of the quadrant, thus gaseous.
| {
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What is the current radius of cosmological event horizon? Doing some crude calculations (using the value of $H_0$ at this point of time only, since it is time dependent but not distance dependent thanks to Johannes answer) what is the radius of cosmological event horizon at this point of time? (not looking for the chan... | The Hubble length $c/H_0$ does not coincide with the radius of the observable universe.
Your calculation assumes a Hubble parameter that doesn't change over time. This is not correct: the Hubble parameter $H$ changes over time, and $H_0$ (the Hubble constant) indicates the current value of $H$. To refer to $H_0$ as a ... | {
"language": "en",
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Reasons for violation of universality in statistical mechanics The Universality in statistical mechanics is nicely explained by the renormalization group theory. However, there are fair amount of numerical and theoretical studies show that it can be violated in models such as Ising model, spin glass, polymer chain and ... | Your reference $3$, for instance, is an Ising model modified by randomness. It is of course not clear how universality works in such complex systems. Another link studies (finite size) clusters, far from the ideal infinite system of the analytical solution.
In general, recall that universality is a feature of phase tr... | {
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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... | A test charge "feels" only an external field. If another charge is approaching, it will experience a stronger field due to $1/R^2$ field strength dependence.
| {
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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)$$
(cf. last formula on p. 101). He then says that these eigenfunctions... | You need nothing more than your understanding of
$$
\int_{-\infty}^\infty f(x)\delta(x-a)dx=f(a)
$$
Just treat one of the delta functions as $f(x)\equiv\delta(x-\lambda)$ in your problem. So it would be something like this:
$$
\int\delta(x-\lambda)\delta(x-\lambda)dx=\int f(x)\delta(x-\lambda)dx=f(\lambda)=\delta(\lam... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/47934",
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Do particle pairs avoid each other? Please end my musings Can you explain what happens when a particle and its antiparticle are created. Do they whiz away from each other at the speed of light or what? I suppose that they don't because otherwise they would never meet and annihilate each other, but then, if I had just b... | This is a clarifying answer.
Here are particle antiparticle pairs in a bubble chamber photo from Fermi lab, created by the reaction
gamma + proton -->electron positron pair + proton
The gamma is unseen before it hits the proton ,because it does not ionize and when it hits the proton, most of its energy is taken up... | {
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When are leap seconds added in various time zones? I understand that technically when a leap second is added, it is added after midnight UTC, but I'm unclear how the addition is handled in other timezones. For precise reckoning of course (e.g. astronomical ephemeris), it must be added at the same instant (e.g. at 1 AM ... | Yes, the leap second are added at the same "instant" in the whole world, whatever is the part of the day on a given place. This is documented by a rather typical screenshot of some "clock" in 2008 according to Chicago's U.S. Standard Central Time:
The confusing second was added right before 6 p.m. – in as big a city a... | {
"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?
| I think it can be safely stated that no one really knows the answer to this, because like you've said, there's so much unknown stuff in the Universe. There's that dark matter and dark energy stuff that's pretty mysterious as of today.
Here's a Wikipedia article on the zero-energy-universe, btw.
http://en.wikipedia.org/... | {
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Conformal Quantum Mechanics I heard the term Conformal Quantum Mechanics used today.
*
*What exactly does this mean?
*Why would one want to study this?
| It's slang for conformal field theory for manifolds of $D=1$ dimensions. (If you take the dimension to be time, 1-D QFT describes the time evolution of a system living in zero spatial dimensions, i.e. at a single point, so it's not really field theory but QM.)
It is special in the sense that normally, CFT representati... | {
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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 ... | It actually is providing an image, you just cannot see it because of contrast. The light you have in the picture is flooding the room with enough ambient light that the image that is actually formed has no contrast.
*
*Pinhole camera image quality heavily depends on the pinhole size.
However, the smaller the pinho... | {
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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... | In the rotating frame of the earth's surface, there are two fictitious forces acting on you, a centrifugal force and a Coriolis force. These are both quite small in absolute terms, and the centrifugal force is also not noticeable because it simply feels equivalent to a slight change in the over-all direction and magnit... | {
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Charge conjugation in Dirac equation According to Dirac equation we can write,
\begin{equation}
\left(i\gamma^\mu( \partial_\mu +ie A_\mu)- m \right)\psi(x,t) = 0
\end{equation}
We seek an equation where $e\rightarrow -e $ and which relates to the new wave functions to $\psi(x,t)$ .
Now taking the complex conjugate o... | The key here is that the gamma matrices are given by their commutation relationships and those do not determine a unique representation for the matrices.
If you start from the Dirac equation
$$\gamma^\mu (i\partial_\mu - e A_\mu) \Psi = m \Psi$$
and make the following generic transformation $\Psi = U \Psi'$ with $U$ a... | {
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Phase difference of driving frequency and oscillating frequency Suppose a mass is attached to a spring and is oscillating (SHM). If a driving force is applied, it must be at the same frequency as the mass' oscillation frequency. However I'm told that the phase difference between the driving frequency and the mass's fre... | For resonance to occur (at $\gamma$=0 and $\omega=\omega_0$), the system must be able to absorb all the energy input coming from the external driving force, and this results in incessant growth in the amplitude. For this to happen, the external force, which does not have to be in sine/cosine form, should be positive (p... | {
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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... | It's just that magnitudes can't be ordered, I mean: things like $meter>second$ don't make sense.
In every physical equation, or inequation, both sides must be in the same unit, so what you're doing is actually checking that the units at the right are the same as the ones in the left. That must be true, as you're saying... | {
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Rigorous approaches to quantum field theory I have been reading Quantum Mechanics: A Modern Development by L. Ballentine. I like the way everything is deduced starting from symmetry principles.
I was wondering if anyone familiar with the book knows any equally elegant presentation for quantum field theory. Weinberg's ... | I have not read it myself, but did you take a look at Zee's book? I heard that while it is not very technical, it is great on a conceptual level.
| {
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Why do we weigh less when falling?
I don't want to go to science world to find out because it would be a long round-trip.
I understand that acceleration/deceleration would effect the weight and I can also imagine that someone at terminal velocity would weigh nothing but I can't get my understanding in terms of forces ... | As an alternative example, think about how it feels to drive a car.
*
*When the car is standing still, you will sink into the seat and feel the seat pressing against you (= normal weight).
*When you press the throttle and the car accelerates, you will be pressed further back into the seat and will in turn feel the ... | {
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Cyclic Coordinates in Hamiltonian Mechanics I was reading up on Hamiltonian Mechanics and came across the following:
If a generalized coordinate $q_j$ doesn't explicitly occur in the
Hamiltonian, then $p_j$ is a constant of motion (meaning, a constant, independent
of time for a true dynamical motion). $q_j$ then ... | It's an old question and already has a fine answer, I just wanted to quickly add a more physical example.
Take a 2D particle in a central potential in polar coordinates, the Lagrange function is
$$ L(r,\dot r,\theta,\dot\theta) = \frac 1 2 \left( \dot r^2 + r^2 \dot\theta^2 \right) - V(r) \;. $$
Now the angle $\theta$ ... | {
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Do perfect spheres exist in nature? Often in physics, Objects are approximated as spherical. However do any perfectly spherical objects actually exist in nature?
| If we are considering the states of matter we are familiar with (fermions), since these structures are inherently discretized (solids, liquids, gases), they will not exhibit perfect spherical symmetry.
We can loosen the definition of perfect and construct a cutoff where variations in the radius are negligible below so... | {
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What happens to heat waste produced by energy generation? What happens to heat waste produced by energy generation on earth that must be there according to the laws of thermodynamics? So, it never dissipates and remains on earth?
| Take for example a conventional coal fired power plant as used widely in most countries.
About 40% of the energy from burning the coal is converted to electricity, and the remaining 60% is lost as heat to the environment.
The 40% of the energy that gets converted to heat is used by us consumers and eventually gets conv... | {
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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 conductivity of a nanotube depends on the chirality / diameter of the individual nanotube and the conductivity. The chirality determines whether a nanotube is classified as either metallic or semiconducting.
The highest conductivity that has been measured for a carbon nanotube is ~100 MS/m, which is equivalent to... | {
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why is orbital moment quenched while atoms forming solid atom has well defined spin(up and down) and orbital(s,p,d,etc) momentum, but when forming crystals, why the spin degree continues to be good quantum number while orbital momentum is quenched?
| Orbital angular momentum is a good quantum number for the atomic problem because the Coulomb potential between the electron and nucleus is rotationally invariant, but the potential an electron feels in a crystal is not. A non-spherically-symmetric potential can couple states with different $l_z$, and so if $\psi_{l_z}$... | {
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Force and Torque Question on an isolated system If there's a rigid rod in space, and you give some external force perpendicular to the rod at one of the ends for a short time, what happens?
Specifically:
What dependence does the moment of inertia have?
If it rotates, what is the center of rotation?
Does it matter that ... | The moment of inertia of a rod with a perpendicular axis of rotation through the center of mass is $$I=\frac{1}{12}ml^2$$ where m is the mass and l the length.
If you apply a torque $$\tau=r\times F$$ (all vectors), then $$\tau=I\alpha$$ lets you calculate the angular acceleration alpha.
If the rod deforms, energy will... | {
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Why does smoke go out the window of the car - and what if there's wind blowing instead of the car moving? When driving a car while smoking with the window open (safety and legal issues aside), I've noticed that the smoke tends to go outside the window.
*
*Why does the smoke go outside?
*If the car is standing still... | To the first question: no idea, honestly. My intuition says that air should come by the front windows and out from the rear ones. Probably air creates difference of pressures in the neighboorhood of the window and suck air out, just like a vaccum cleaner: it sucks air by making it go out... Making theoretic studies may... | {
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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 $e^{\frac{i}{\hbar}k_ix^i}=e^{\frac{i}{\hbar}\int k_idx^i}$. ... | Just as V is the potential energy, $\vec{A}$ is the potential momentum. This is also true in a crystal.
| {
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What is the result of a classical collision between THREE point particles at the same precise instant? Classical Mechanics is said to be deterministic, a statement that nearly always is followed by that quote from Laplace, something like
If at one time, one knew the positions and velocities of all the
particles in t... | Taking the case of point particles and "contact" collisions seriously actually causes trouble even in the two dimensional case: the instantaneous forces are necessarily infinite even if the impulses remain finite.
The solution to that problem--to recognise that all real particles interact via fields over non-zero dista... | {
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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... | I think the other answers cover your question about the change in flux. As to why $U/R_{tot}$ is used instead of $U/R_{lamp}$... it's not quite clear whether you're expected to find the current at a particular point on the circuit, or what point that might be. If I had to pick one current to characterize the circuit, i... | {
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Why does unbroken supersymmetry imply the absence of tachyons? Just a quick question, same as in the title. I'm trying to understand stable D-branes.
| In theories with unbroken supersymmetry, the energy can be written as
$$E=\sum_i c_i Q_i Q_i $$
where $Q_i$ are some Hermitian supercharges and the coefficients are positive. This is a sum of squares of Hermitian operators which is why it's positively semidefinite. It can't be negative.
Tachyons obey $E^2-p^2=m^2$ for ... | {
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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 $c=1$?
| Not much, although in a given reference frame, velocity being equal to zero is (usually) a fixed point on the scale. So you still have two points, which is enough to define this scale.
When looking at the Lorentz Transformations for something like $SO(1,3)^{\uparrow}$ (the space that special relativity takes place in),... | {
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How to guarantee that a kilogram of antimatter will quickly annihilate another kilogram of matter? What I mean is, suppose we could somehow get a kilogram of antimatter and contain it safely. Now lets say we want to make a bomb using this kilogram, now, we have two ways, either store another kilogram of matter inside t... | You face exactly the same problem as the makers of the first explosives. Although these days we use explosives that react intramolecularly, the original explosives like gunpowder were made from a mixture of an oxidising agent (potassium nitrate) and a reducing agent (sulphur and charcoal). To get the gunpowder to go ba... | {
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How do transformers work? A transformer is basically a primary inductor connected to a voltage $U_P$ which you want to transform. You also have an iron rod and a secondary inductor. So when there is a current $I_P$ the iron rods becomes magnetic. When you connect the primary inductor to AC, that means that you'll have... | It's always handy to have some background information:
In Europe the mains voltage is 230 Volts, which is too much for a lamp for example, so it needs to be lowered to for example 12 Volts. This is done by using a transformer.
The primary winding is connected to the mains voltage of 230 Volts. The AC in this primary wi... | {
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What is $v \, dp$ work and when do I use it? I am a little confused, from the first law of thermodynamics (energy conservation)
$$\Delta E = \delta Q - \delta W $$
If the amount of work done is a volume expansion of a gas in, say a piston cylinder instrument at constant pressure,
$$\Delta E = \delta Q - p \, dv$$
Here ... | I hate answering my own question but I'd like to share this with you as it is definitive:
$$\mathrm{d}h = \mathrm{d}u + \mathrm{d} (p v)$$
$$h_2 - h_1 = u_2 - u_1 + p(v_2 - v_1) + v (p_2 - p_1)$$
Now, for a pump working in the compressed liquid (subcooled liquid zone), it is noted that the change in specific volume $v$... | {
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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... | Consider that
$$ \mbox{Force} \propto \mbox{Velocity Gradient} $$
Equal force means, the same velocity gradient, i.e. linear distribution of velocities across the flow. The flow near the boundary has zero velocity and so velocity increases linearly the further away you go from the boundary.
| {
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what is use of relativistic action? this is relativistic action:
$$S=\int_C \mathcal {L}dt$$
where the $\mathcal{L}$ is $-m_oc^2\gamma^{-1}$
what is use of relativistic action!?
| The use of an action is do derive all the dynamical equations of a theory from the least-action principle, $\delta S=0$ (action is minimized along the right path). Quantum mechanically, the use of an action is to derive the transition amplitudes from an initial state to the final state by summing over histories weighte... | {
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Evaporating Black holes and entropy
*
*I'm told that for Black Holes, when they radiate (Hawking radiation) particles and anti-particles) split at the event horizon, one going to infinity, the other into the BH. They then lose mass. How is that possible? Wouldn't their masses increase, since they are absorbing partic... | 1) In the tunneling picture, there are two scenarios:
i)a virtual particle/antiparticle pair is created just outside of the horizon. The negative energy particle then tunnels into the horizon and the positive energy particle is radiated away.
ii) a virtual particle/antiparticle pair is created just inside of the hori... | {
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Coulomb gauge fixing and "normalizability" The Setup
Let Greek indices be summed over $0,1,\dots, d$ and Latin indices over $1,2,\dots, d$. Consider a vector potential $A_\mu$ on $\mathbb R^{d,1}$ defined to gauge transform as
$$
A_\mu\to A_\mu'=A_\mu+\partial_\mu\theta
$$
for some real-valued function $\theta$ on $... | It means that the gauge ambiguity is practically removed in the Coulomb gauge if you deal with a "nice" $\mathbf{A}$ (which is your purpose).
However, it does not mean you only deal with the radiation (propagating solutions). Transversal $\mathbf{A}$ is different from zero for a uniformly moving charge too.
| {
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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 ... | The hypotenuse of a right angled triangle with legs 1 is irrational.
Alternatively, consider a pyramid. As you take measurements of the 'base length' towards the apex, you get a continuous sets of values. One of these must be irrational.
Of course, you can then start an argument about what 'physical' object is, and if... | {
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Exact diagonalization of graphene's tight binding Hamiltonian While directly diagonalize graphene's tight binding Hamiltonian, which is numerical. We have to use a finite-sized graphene.
So how to deal with boundary conditions? The usual solutions are zigzag or armchair condition, but to make our model more realistic t... | You're mixing two things here. One is what the structure of the boundary is, e.g. armchair or zigzag. The other is what the wavefunction does at the boundary.
For your finite size cluster of carbon atoms, you have to decide what shape it has, which basically means deciding how many lattice sites you include and where y... | {
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Resonant inductive coupling and Schumann resonances I was reading about WiTricity (http://en.wikipedia.org/wiki/WiTricity) a technology developed by MIT to wirelessly transmit electricity through resonance, and I have this question:
Given the phenomenon of resonant inductive coupling which wikipedia defines as:
the n... | You Must reflect the signal, "back upon itself"for it to amplify.Like a reflective inner surface of a tube surrounding it.Like a Laser does.Then you must pin the charge, in Maxwell Ultra Capacitors.The Resonant coupling is a sustained resonance.A resonant tank circuit would work.Positive to North, and Negative to South... | {
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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 gravity of a planet holds the atmosphere in place. The moon doesn't have enough mass / gravity to do so. If you moved air to the moon there's so little gravity the air would simply float away.
| {
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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 way it makes sense to me is that if you shoot a ray of light across a room inside an accelerating rocket ship, the ray will fall some distance (relative to the room). Therefore on Earth the ray of light must also fall (ostensibly "due to gravity"), otherwise you would know whether you are in a ship or not based on ... | {
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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... | I think the main effect would be that the muzzle velocity will be lower.
This is because the expanding gases of the gun power will have a shorter distance along which they push the bullet. Once the back of the bullet emerges out the short side of the barrel, the gases will escape and depressurize, loosing the ability t... | {
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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... | I have been taught and continue to teach that you should record (and use) the answers to your intermediate calculations (and/or conversions) with one extra significant digit beyond the number of significant digits that will be in your final answer.
| {
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Which theory predicts that dubbed tires have more friction? The physical reasoning I suppose could be that more contact areas mean more and higher friction. But is there an actual formula or a more mathematical explanation?
Application for bicycling was my question https://bicycles.stackexchange.com/questions/14319/cou... | For a rolling tyre the resistance (it's not really friction) is due to viscous losses in the rubber as the tyre is deformed.
If you take a piece of rubber and put work in to stretch it then get work out as it relaxes, the work you get back is less than the work you put in. The balance goes into heating the rubber. If t... | {
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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... | Gagarin flew around the world in 90 minutes 50 years ago, apparently without serious health problems.EDIT: OK, it was 108 minutes.
| {
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Is time dilation an illusion? It is said that we can verify time dilation by flying a very accurate clock on a fast jet or spaceship and prove that it registers less time than the clocks on earth. However, the clocks on earth would be moving relative to the clock on the spaceship, and since time always dilates and neve... | You're referring to what is commonly known as the twin paradox. The Wikipedia page provides several different ways of analysing the situation, but one way to look at it is this -
When the clock on the spaceship leaves earth, it'll experience an acceleration (even if it's a really small acceleration for a long time, or... | {
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Thought experiment regarding an object approaching a mirror Here's a thought experiment I came up with in class today when my mind drifted (I however highly doubt I'm the first to think about this since it is pretty rudimentary) :
Let's say superman approaches a (flat) mirror at 200,000 km/s. At what speed does superma... | Superman's image approaches him at c, it will be blue shifted a bit towards xrays.
Luckily Superman has xray vision so he should be able to see himself.
For the side question of what you would see at c, try this link.
http://www.space.com/19268-star-wars-hyperspace-physics-reality.html
| {
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"timestamp": "2023-03-29T00:00:00",
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"question_score": "15",
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What grounds the difference between space and time? We experience space and time very differently. From the point of view of physics, what fundamentally grounds this difference?
Dimensionality (the fact that there are three spatial dimensions but only one temporal) surely cannot be sufficient, as there are tentative pr... | What makes the difference is that the order of Time is made by the presence of memory. That is, consciousness creates the "arrow of Time".
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/53116",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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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... | Part of your scale comes from the observer, the time and space averaging of the observations.
You say the weather 10 meters distant is pretty similar to here, but look a bit closer, and it is not. The wind 10 meters from where you are can be quite different from where you stand. A sunny rock can be dry and hot 1 meter... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/53189",
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How accurate are our calculations about distant stars keeping in mind their enormous distances? Since many stars are hundreds of light years away from the Earth and therefore, what we observe of them today is really their distant past, how can we say anything with certainty about their composition, size and nature? Bet... | Well, we don't claim to know the status of the star at the present time. If the star is close enough (within our galaxy, or local neighbourhood), we measure the distance in light years, or parsecs. If they're further away than that, it's easier to quantify their distance in terms of a redshift.
When we say that a star ... | {
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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... |
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 which is perpendicular to the force and which goes through the center of mass.
To my understanding, your question is flawed. If a single force... | {
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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 ... | A main part is because they are landing on a slope. It means that for most, if not all, of the jump they are travelling parallel to the ground. The jump looks impressive because a) it is and b) the camera angles don't show this clearly.
This slope means that when the jumper lands they can carry on moving forwards with ... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
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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 trick is in hiding information about phase of wave in this kind of representation. There is a nice appendix from a book about holography :
http://onlinelibrary.wiley.com/doi/10.1002/9783527619139.app1/pdf - part A.3
It stays that:
For general wave function $ y = A · cos (\omega t − kr + \alpha) $, $kr$ and $\alph... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is enstrophy? In turbulence, the enstrophy of a flow in a domain $\mathcal{D} \subset \mathbb{R}^{D}$
$$
\mathcal{E} = \int_{\mathcal{D}} |\vec{\nabla} \times \, \vec{v}|^2 d^{D}x
$$
appears sometimes, it's cool and has cute properties in 2d (see this answer about turbulent flows), etc.
Now, what does it represent... | From mathematics point of view, it is a surface integral of the scalar quantity |Curl v $|^2$. The physical meaning of it, in the context of fluid dynamics in 2-D or 3-D, is that it has the units $(m/s)^2$ which when multiplied by the density of a fluid represents some form of energy. As for the meaning of the intgral ... | {
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"source": "stackexchange",
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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(... | Well if you're just looking for one example of a reducible representation of a group, then that's a fine one. However, representation theory of groups has a bunch of wonderful complexity that is illuminated by studying other examples of reducible representations with a lot more structure.
For example, addition of angu... | {
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Why does the presence of a battery change whether a circuit is in parallel or series? If I take a closed circuit with two capacitors and a voltage difference, the circuit is apparently in parallel, but if I introduce a battery, the circuit is in series. Why does the presence of the battery make a difference?
Here's a ... | If you look at the structure of the circuit on the left, and where voltage must be, you will see that the wire connecting C1 and C2 ensures that the plates connected to point A are at one voltage, let's call it VA, and the other plates connected to voltage VB.
So this can be thought of as two batteries , each with vol... | {
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Maxwell-Boltzmann velocity PDF to CDF I asked on Math.SE and was advised to try here instead.
I need to draw from a Maxwell-Boltzmann velocity distribution to initialise a molecular dynamics simulation. I have the PDF but I'm having difficulty finding the correct CDF so that I can make random draws from it.
The PDF I a... | The solution is to realise that that function is merely a Gaussian. In fact Each component of the velocity vector has a normal distribution with mean =0 and st-dev $\sqrt {kT/m}$.
All that is left to do at that point is to get the Gaussian CDF (well known) and sample from it, making sure to plug in our mas and temperat... | {
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"source": "stackexchange",
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What would the collision of two photons look like? Could someone explain to me what the collision of two photons would look like? Will they behave like,
*
*Electromagnetic waves: they will interfere with each other and keep their wave nature
*Particles: they will bounce like classical balls
I assume that energy o... | A lowest order QED Feynman diagram for the process photon + photon $\rightarrow$ electron + positron looks like shown below (the time axis is the horizontal axis).
From the point of view of energy conservation, this process is only possible if sum of the energy of the photons is above twice the electron mass. In the ce... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/54323",
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"source": "stackexchange",
"question_score": "18",
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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... | Moment is bending due to linear force and the distance from the axis is perpendicular whereas in torque rotation takes place beyond 360 degrees.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/54383",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
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"answer_id": 5
} |
Can we make images of single atoms? I was wondering how far in imaging physics had gotten. Do we hold the technology to actually take a picture of, say, an alpha particle, or even a single atom?
I realise we aren't talking about camera pictures, so what kind of imaging techniques have taken images/is most likely to be ... | Yes - depending on what you mean by image (if you squint you can read IBM in individual atoms)
Atomic Force Microscopy measures the position of individual atoms.
There is a presentation of IBM's nantotech research
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/54431",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "14",
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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?
| I can only elaborate on what's already been said, but no, dark matter and dark energy do not exist as part as the CBR. The CBR we conventionally think of was constructed based on observed EM radiation. Dark matter and energy are only detected currently through their gravitational effects, and won't show up as radiation... | {
"language": "en",
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Proper notation for normalized scalar? I have not been able to find a resource to tell me the standard notation for a normalized scalar value. Normalized vectors (i.e. unit vectors) are typically denoted by placing a hat over the variable, something like:
$${\bf \hat{e} = \dfrac{e}{||e||} }$$
However, does the same a... | There is not, to my knowledge, a uniform standard on this subject. I have seen normalized quantities expressed by adding a twiddle (tilde) over the character (as in $\tilde{A}=A/A_0$), but I this notation is often reserved to indicate a time-varying quantity, instead. Unless someone knows of a strong standard in this... | {
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Is light affected by gravity? Why? I would like to know if light is affected by gravity, also, I would like to know what is the correct definition of gravity:
"A force that attracts bodies with mass" or "a force that attracts bodies with energy, such as light"?
Is light massless after all?
| I'd like to answer the first question "Is light affect by gravity? Why?" because I remembered an adorable thought experiment.
In the spirit of the equivalence principle consider an observer in a closed box. As we all know, the observer inside that box would be unable to tell (neglecting tidal effects) the difference be... | {
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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... | When we bring a test charge let us say (+q) to a certain point, we exert some force. Our exerted force has to be equal or greater to the force exerted by the electric field in order to overcome it. Thus the forces being opposite and equal cancel each other and hence the direction is undetermined.
Since it is a compulsi... | {
"language": "en",
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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.
| As you may've noticed, the drift velocity of electric charges is $\sim {10}^{-5} \frac{\mathrm{m}}{\mathrm{s}} ,$ which is much slower than the flow of electric current.
So, how could electric current travel near the speed of light? It's because the charges' electric field is propagating near the speed of light.
| {
"language": "en",
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"source": "stackexchange",
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Can a black hole bounce? Is there a limit to the amount of matter that a black hole can accrete per second and if so could a certain sized black hole bounce off a dense enough surface?
| Let's answer the first part of your question first. In general, astrophysical objects are limited in the amount they can accrete by the Eddington limit.
What happens is as matter is accreted onto the object (black hole in our case), it heats up due to conversion of gravitational potential energy into kinetic thermal e... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/55222",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Schrodinger equation in term of Fokker-Planck equation From Wikipedia on the Fokker-Planck equation:
$$\tag{1}\frac{\partial }{\partial t}f\left( x^{\prime },t\right) ~=~\int_{-\infty}^\infty dx\left( \left[ D_{1}\left( x,t\right) \frac{\partial }{\partial x}+D_2 \left( x,t\right) \frac{\partial^2}{\partial x^2}\right... | Hints:
$\underline{(0) \Rightarrow (1)}$: Don't try to accomplish everything at once. Do it slowly in as many steps as you need to be sure that you are calculating correctly and understand everything. The trick is to integrate by part. Be very careful to keep track of what depends on $x$ and what depends on $x^{\prime... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/55288",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why does electromagnetic waves travel slower in well isolated conductor? Wikipedia writes, that
Propagation speed is affected by insulation, so that in an unshielded copper conductor ranges 95 to 97% that of the speed of light, while in a typical coaxial cable it is about 66% of the speed of light
Why does insulation... | That's because adding shield means that there is now distributed capacitance between core & shield in addition to the inductance of the central wire.
Current/voltage transitions gets slower because charging/discharging "capacitor" on each segment through "inductor" of the wire takes time -> propagation speed decreases... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/55366",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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How to choose a solution from all possible solutions of general relativity So there are so many solutions for general relativity - then how does one "choose" the solution that is right one? By checking with observation? (though I also know that it is currently unknown which one is the correct solution.)
| Generally speaking we start with a known stress-energy tensor and boundary conditions and look for solutions for the curvature. When doing this we're not usually overloaded with possible solutions, and it's normally pretty obvious which solutions are physically relevant.
Where multiple physically relevant solutions exi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/55435",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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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 ... | First estimate roughly the no. of hairs in 1mm^2 and consider the distance between two hairs is uniform all over the head and calculate the area of the whole head and subtract the area of the head having no hair.then multiply that with the hair contained in 1mm^2.
hair is supposed to distribute uniformly.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/55598",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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"answer_id": 4
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How to evaluate commutator with angular momentum? I need to evaluate the commutator $[\hat{x},\hat{L}_z]$. I believe the $L_z$ is referring to the angular momentum operator which is:
$L_z = xp_y - yp_x$
using this relationship i end up with:
$[x,L_z] = x(xp_y - yp_x)-(xp_y - yp_x)x$
my next step is substituting in for ... | Usually I find it easiest to evaluate commutators without resorting to an explicit (position or momentum space) representation where the operators are represented by differential operators on a function space.
In order to evaluate commutators without these representations, we use the so-called canonical commutation rel... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why can't we store light in the form of light? We can store cold (ice), heat (i.e. hot water bag) and electrical charge (batteries). We can even "store" a magnetic field in a magnet. We can convert light into energy and then, if we want, back to light. But we can't store light in form of light in significant amounts. ... | Isn't that what we call "heat" is just a form of electromagnetic waves in the infrared spectrum? So we may say that we can store an electromagnetic wave in a certain media, like water in a thermos. But the first thing, we do not use a thermos filled with hot water as an energy storing container, we just use it for a ve... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/55768",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "27",
"answer_count": 7,
"answer_id": 6
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A Book about the Bohr-Einstein debate? A book about the Bohr-Einstein debate?
Is there any book that details the correspondence between the two? The only books I could find are popular science books, I wonder if there is a book that lists the correspondence in a more 'raw' form.
| The following essay by N.P. Landsman: "When champions meet: Rethinking the Bohr–Einstein debate." Studies In History and Philosophy of Science Part B: Studies In History and Philosophy of Modern Physics 37.1 (2006): 212-242” contains an extensive bibliography on the debate.
In particular the main references containing... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/55905",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 1,
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distance of electron from proton An electron is projected, with an initial speed of $1.10 \times 10^5 \text{m/s}$, directly towards a proton that is essentially at rest. If the electron is initially a great distance from the proton, at what distance from the proton is its speed instantaneously equal to twice its init... | You have written down the right equation. Use the electric potential energy between the electron and the proton and write:
$\frac{1}{2}mv_1^2-\frac{e^2}{4\pi\epsilon_0}\frac{1}{R} =\frac{1}{2}mv_2^2-\frac{e^2}{4\pi\epsilon_0}\frac{1}{r}$
Put $v_2=2v_1$, ignore the $1/R$ term since $R$ is very large, so that the electro... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/56109",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
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Absolute zero and Heisenberg uncertainty principle I got to read Volume I of Feynmann's lectures. It said that at absolute zero, molecular motion doesn't cease at all, because if that happens, we will be able to make precise determination of position and momentum of the atom. We do know that Heisenberg uncertainty prin... | The uncertainty principle is a fundamental property of quantum systems, and is not a statement about observational success. No particle either free or in crystal can have zero momentum otherwise a nonsensical infinity is required for the standard deviation of position $\Delta x$, in the uncertainty principle $\Delta x ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/56170",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 2,
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Influence of charged particle's own electric field on itself I read this in my textbook: A charged particle or object is not affected by its own electric field.
Since I find this completely unintuitive and my mind is yelling "wrong! wrong! how could a particle even distinguish between its own field and the external fie... | A correct treatment of the self-force problem, 100% rigorous and free of the paradoxes associated with the conventional textbook treatments is given here.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/56233",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "14",
"answer_count": 4,
"answer_id": 3
} |
How to determine the direction of a wave propagation? In the textbook, it said a wave in the form $y(x, t) = A\cos(\omega t + \beta x + \varphi)$ propagates along negative $x$ direction and $y(x, t) = A\cos(\omega t - \beta x + \varphi)$ propagates along positive $x$ direction. This statement looks really confusing bec... | $y(x,t)=A\cos(\omega t+\beta x+\phi)$ in this equation $\omega t$ and $\beta x$ symbols of the coefficient are same i.e( ++ or --) then the wave is negative direction travelling wave.
$y(x,t)=A\cos(\omega t−\beta x+\phi)$ in this equation $\omega t$ and $\beta x$ symbols of the coefficient are alternative i.e( +- or -... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/56338",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "22",
"answer_count": 4,
"answer_id": 2
} |
Calculating the mass equivalency of a song? I've recently become fascinated with the idea of sound energy having a theoretical equivalent mass. I've read over this thread:
Do light and sound waves have mass
I understand this part: $m_{eq}=E/c^2$ and $E=A\rho \xi^2\omega^2$
Where I am getting tripped up is the way to me... | A song has no mass equivalence. The sound waves from playing a song do---to the extent that they carry energy, and you can relate an equivalent mass1 to energy.
To cut to the chase, it would probably be easiest to look up how much power (energy per unit time) your speakers produce, then multiply that by the duration o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/56589",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
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Tensor perturbation inflation During inflation the metric is de-Sitter so $dt^2-d\underline{X}^2 $.
I know that the eqn.motion governing GW's from inflation (tensor perturbations) is
$$2H\dot{h}+\ddot{h}-\nabla^{2}_{i}h~=~0,$$
derived from varying
$$S^{(2)}~=~\int \frac{a^{2}(t)}{2}~\partial^{\mu}h ~\partial_{\mu}h... | De Sitter space is a special case of the Robertson-Walker spacetime. If you want, you can even work out what the coordinate transformation is.
If your question isn't answered by this, could you please amend it to make it clearer exactly where your hangup is?
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/56677",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
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