Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Voltage drop along an idealized resistance-free wire in a circuit? If you connected the positive terminal of a battery to the negative terminal to a battery with a wire with (hypothetically) no resistance, and are asked to give the voltage drop of a segment of wire in the circuit, how would you determine this?
| If you have an ideal voltage source with 0 internal resistance and 0 external resistance (0 resistance of the wire) then the voltage drop is indeterminate since it is of the form $\infty \times o$. The question then is not well defined.
However in practice, we represent a practical voltage source by an ideal voltage so... | {
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Question on Conformal Field Theory Since every question has to be asked in a seperate topic,
I'm asking a question refering to the following topic:
Beginners questions concerning Conformal Field Theory
In particular I'm referring to the subsection "Implementing a symmetry on operators" of the answer given by Lubos Mo... | The point is that the adjoint representation may have vanishing central term.
As an example of this situation consider operators $R(L_n)$ and $R(C)$ on a Hilbert space $H$ which represent the Virasoro algebra $V$ i.e. it holds
$$[R(L_n),R(L_m)]=(n-m)R(L_{m+n}) +\frac{1}{12}\delta_{m+n,0}(n^3-n)R(C).$$
$$[R(C), R(L... | {
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Fourier transform and commutation of functions The book I am reading takes the unjustified step $$e^{-\frac{i}{\hbar}\vec{p}\cdot\vec{r}}f(\vec{p}) = f(\frac{\hbar}{i}\vec{\nabla})e^{-\frac{i}{\hbar}\vec{p}\cdot\vec{r}}$$
and similarly, he uses elsewhere $$e^{-\frac{i}{\hbar}\vec{p}\cdot\vec{r}}g(\vec{r}) = g(i\hbar\ve... | It follows from the rule
$$\frac{\partial}{\partial x^i} e^{a_j x^j}= a_i e^{a_j x^j},$$
which by repeated use leads to
$$f(\frac{\partial}{\partial x^i}) e^{a_j x^j}= f(a_i)e^{a_j x^j},$$
where $f$ is a polynomial. More general classes of functions $f$ can be reached by taking appropriate limits.
| {
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What is the significance of the QCD scale parameter $\Lambda$? I see that it appears as a constant in the relation for the running of the strong coupling constant. What is its significance? Does it have to be established by experiment? Is it somehow a scale for quark confinement? If yes, how? I ask because I saw this i... | Dear dbrane, $\Lambda_{\rm QCD}$ is the only dimensionful parameter of pure QCD (pure means without extra matter).
It is dimensionful and replaces the dimensionless parameter $g_{\rm QCD}$, the QCD coupling constant. The process in which a dimensionless constant such as $g$ is replaced by a dimensionful one such as $\L... | {
"language": "en",
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Group Cohomology and Topological Field Theories I have a two-part question:
*
*First and foremost: I have been going through the paper by Dijkgraaf and Witten "Group Cohomology and Topological Field Theories". Here they give a general definition for the Chern-Simons action for a general $3$-manifold $M$. My question ... | Dijkgraaf and Witten used $\mathcal H^3[G,U(1)]$ to define CS theory for gauge group $G$. Recently, group cohomology has found applications in condensed matter physics. It may classify the so called "symmetry protected topological phases"
of interacting bosons:
The $d$-dimensional symmetry protected topological phases ... | {
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Does Quantum Mechanics assume space and time are continuous? I was confused when I was listening to a Quantum Mechanics lecture online. Are space and time assumed to be continuous or discrete in Quantum Mechanics?
I can see the question is vague, but this is so since I am confused.
| Space and time are continuous, in quantum mechanics or otherwise. In particular, whenever our theories of any kind talk about time, it is always a real continuous parameter.
Similarly, spatial positions of particles in ordinary quantum mechanics are operators $\hat x$ whose eigenvalues are continuous, too. This fact is... | {
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How to calculate fuel consumption of car (mpg) from speed and accleration knowing mass, drag coeff and rolling resistance? How can I calculate the current (instantaneous) mpg of my car if I know the speed and acceleration of the car? From reading various answers for the "car going level or up/down hill" question asked ... | No, you cant. Because it is simple to know mpg we have to calculate fuel flow. Only measuring speed and acceleration you know variation distance time and need to calculate fuel flow also.
| {
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Why is it hard to solve the Ising-model in 3D? The Ising model is a well-known and well-studied model of magnetism. Ising solved the model in one dimension in 1925. In 1944, Onsager obtained the exact free energy of the two-dimensional (2D) model in zero field and, in 1952, Yang presented a computation of the spontaneo... | Two-dimensional theories simply have much more mathematical structure that makes many such models mathematically solvable - integrable.
In particular, in the long-distance limit, one obtains a scale-invariant theory that is typically conformally invariant as well. Two-dimensional conformal symmetry is - unlikely any h... | {
"language": "en",
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Why is heavier object more reluctant to get falling down? Is it because of the upward force that stops the object? for example-
| The big object has more inertia.
If you have a big object and a small object, the gravitational force on the big object is greater. Why, then, doesn't it fall faster?
The answer is that the big object needs more force to accelerate the same way. This is actually quite obvious if you view it in a different context.
... | {
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Glycerol: refractive index & absorption spectra in 0.2-0.4um range Could anyone suggest where can I find absorption spectra & refractive index of Glycerol?
I am specifically interested in UV range, 200-400nm, everything I was able to find out was for standard conditions only...
Is there any software which can get these... | This can probably be achieved with time dependent density functional theory, however it's nontrivial. Regrettably, I have no real experience in this area, however TD-DFT is a good place to start if you're interested in calculating UV/Vis and (hyper)polarisability properties almost from first principles.
Good electronic... | {
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What is "pure energy" in matter-antimatter annihilation made of? I used to read the term "pure energy" in the context of matter-antimatter annihilation. Is the "pure energy" spoken of photons? Is it some form of heat? Some kind of particles with mass?
Basically, what does "pure energy" in the context of matter-antim... | If I ruled the world, I would ban the phrase "pure energy" in contexts like this. There's no such thing as pure energy!
When particles and antiparticles annihilate, the resulting energy can take many different forms -- one of the basic principles of quantum physics is that any process that's not forbidden (say, because... | {
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Why is the steam from cooling towers not used? If I see the steam coming out of cooling towers at an altitude of 200 meters, I cannot help but think that this energy is wasted. My question is: Why isn't this steam cooled enough to become water and used to create hydroelectric power due to the drop from 200 meters?
| Let us see -- how much water per second is getting at the height?
Let's estimate it as 1 ton of water per second.
Then the energy you can extract form the water is:
$$ 1 [\mbox{ton/s}] * 200 [meters] * g \simeq 20000000 J/s = 2 \mbox{megaWatts}$$
Compared to hundreds or even thousands of megawatts produced and the pow... | {
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Phase Accumulation of Hankel-waves upon propagation Hankel functions are solutions to the scalar Helmholtz-equation $$\Delta\psi + k_e^2\psi = 0$$ in cylindrical and spherical geometry (with respect to a separated angular dependence). Thus, they are very important describing spherical and cylindrical waves. Here is an ... | A closed form solution (in terms of more elementary function than Hankel functions) does not exist. However, typically one is only interested in the regime where $k\rho \gg1$, i.e., the asymptotic region far away from the source. There one can use the asymptotic form of the Hankel functions
$$H^{1/2}_m (x) \sim \sqrt{\... | {
"language": "en",
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Assuming everything else is equal, which will stop first: a heavier car or a lighter car? If the friction from brakes, wind resistance and all such factors remain constant, which will stop first? A heavier car or a lighter car? How will the momentum of the car and gravitational pull on a heavier object influence the st... | The lighter car will stop faster because the lighter car has less energy to dissipate than the heavier one, while the tires more equal limits of friction with the road.
That's because tires gain traction non-linearly with vertical load.
(Even if the braking systems can't reach the friction limit of the tires, the bra... | {
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Are all superalgebras Clifford algebras? I believe the answer to be yes, but I realize that sometimes physicists place additional constraints that might not be obvious. If superalgebras are Clifford algebras, why make a literary distinction?
| On a mathematics stack exchange, you could succeed with such an "isomorphism". But in physics, superalgebras are interpreted totally differently than Clifford algebras. So not only you're forbidden to identify the two terms universally; but in reality, there is not a single example in physics that could be called both ... | {
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Online QFT video lectures I'm aware of Sidney Coleman's 1975/76 sequence of 54 lectures on Quantum Field Theory. Are there any other high-quality QFT lecture series available online?
| ... and from Lenny Susskind too there is
http://itunes.apple.com/us/itunes-u/supersymmetry-grand-unification/id384233338
and
http://www.youtube.com/view_play_list?p=202191442DB1B300
and this new course
http://www.youtube.com/watch?v=NZ-ElsvYKyo&feature=relmfu
| {
"language": "en",
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Are many-worlds and the multiverse really the same thing? Are many-worlds and the multiverse really the same thing?
Not too long ago, Susskind and Bousso uploaded the article "The Multiverse Interpretation of Quantum Mechanics" with the thesis that the many-worlds interpretation and the multiverse of eternal inflation ... | I see Lenny has done it again. I have to say I disagree with this paper. For the sake of argument, let's grant him the hat complementarity conjecture, which he has yet to justify or derive in any convincing way. By his own admission, complementarity scrambles states in the most efficient manner possible. Consequently, ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/10140",
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A question on a system of particles governed by laws of gravity and electromagnetic field Consider a system of many point particles each having a certain mass and electric charge and certain initial velocity. This system is completely governed by the laws of gravitation and electromagnetic field. If this system is left... | I think that singularities can occur in the electromagnetic fields (other than the ones occurring at the location of particles), if one allows the particles to move at speed $c$. That is, one can arrange for sonic booms or Cherenkov radiation.
This raises the question "is Cherenkov radiation smooth?" I suspect that the... | {
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Is the wave function objective or subjective? Here is a question I am curious about.
Is the wave function objective or subjective, or is such a question meaningless?
Conventionally, subjectivity is as follows: if a quantity is subjective then it is possible for two different people to legitimately give it different val... | The wave function is a solution of an equation.
It is as subjective and as objective as all mathematical solutions to equations describing physical fields, whether classical or quantum mechanical.
Certainly as a solution it is objective, a formula written on paper.
Subjectivity enters in the choice of the equation to ... | {
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Is there a "Size" Cutoff to Quantum Behaviour? We all know that subatomic particles exhibit quantum behavior. I was wondering if there's a cutoff in size where we stop exhibiting such behavior.
From what I have read, it seems to me that we still see quantum effects up to the nanometer level.
| There are definitely circumstances where we see quantum behaviors at rather large scales like, for example, in superconductors. In BCS theory cooper pairs are described by a macroscopic wave-function which, to my knowledge is valid for the bulk superconductor no matter how large it is.
| {
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state vector notation I've never taken a quantum mechanics class, but I find myself now using principles developed in the quantum theory of angular momentum. One particularly confusing aspect that I'm struggling with is the notation. Could someone please explain the meaning of a ket (or bra) with two arguments, i.e.: ... | It is just a label. Each element of the set $\left|j_1m_1\right>$ is a unique state vector. For example, $\left|1,1\right>$ and $\left|1,-1\right>$ are two independent angular momentum state vectors, just like any other state vector. Whenever you see the indices $j$, $m$, etc., see them as referring to a set of state v... | {
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Do quantum states contain exponentially more information than classical states? Do quantum states contain exponentially more information than classical states? It might seem so at first sight, but what about in light of this talk?
| The answer depends on what you mean by the information contained in a quantum state.
If you think of the wavefunction itself as a real physical entity then the answer is yes.
The problem with this view is that the information in a wavefunction is not accessible to us. We can only learn a small fraction of it through a ... | {
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Understanding the cause of sidebands in Amplitude Modulation I've read it many places that Amplitude Modulation produces sidebands in the frequency domain. But as best as I can imagine it, modulating the amplitude of a fixed-frequency carrier wave just makes that "louder" or "quieter", not higher-frequency or lower-fr... | A wave with amplitude modulation can be described with a carrier $A_0 cos(\omega_c t)$ and a modulating factor $\left [1+a_s cos(\omega_a t)\right ], |a_s| <1, \omega_s <<\omega_c$:
$A(t)=A_0 cos(\omega_c t)\cdot \left [1+a_s cos(\omega_s t) \right ]=A_0 cos(\omega_c t)+A_0a_s cos(\omega_c t)cos(\omega_s t)$
The first ... | {
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How can one reconcile the temperature of a black hole with asymptotic flatness? A stationary observer very close to the horizon of a black hole is immersed in a thermal bath of temperature that diverges as the horizon is approached. $$T^{-1} = 4\pi \sqrt{2M(r-2M)}$$ The temperature observed by a stationary observer at ... | It is simply not true that a non-vanishing stress tensor is incompatible with asymptotic flatness. The Schwarzschild spacetime is asymptotically flat, period. The semiclassical Hawking-calculation does not in any way change this background, unless you consider effects from backreactions.
Once you take into account back... | {
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Is 3+1 spacetime as privileged as is claimed? I've often heard the argument that having 3 spatial dimensions is very special. Such arguments are invariably based on certain assumptions that do not appear to be justifiable at all, at least to me. There is a summary of arguments on Wikipedia.
For example, a common argume... | I am not sure that being in 3+1-D is a privilege. Actually, all the troubles with Feynmann integrals come from 4D. Secondly, the QFT is integrable only in 2+1-D. From the mathematical point of view, the 4D differentiable manifolds are most problematic.
On contrary, I also heard that if the space is not 3D then the sign... | {
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Is there any proof for the 2nd law of thermodynamics? Are there any analytical proofs for the 2nd law of thermodynamics?
Or is it based entirely on empirical evidence?
| There is actually a very simple derivation of the Second Law in classical thermodynamics for an ideal gas, assuming only classical mechanics and the First Law. Here is a brief sketch -- whether this constitutes a "proof" depends largely on taste, the level of rigor desired, and how comfortable you are with thermo-styl... | {
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Retrocausal interpretations of quantum mechanics Can retrocausality resolve the paradoxes of quantum mechanics? The Copenhagen interpretation presumes something has no property until it is measured, but retrocausal interpretations explain that away by claiming that thing has a definite property before measurement, but ... | Retrocausal interpretations may explain Bell inequality violations for entangled particles and delayed-choice experiments, but can retrocausality explain how quantum computers can factorize large integers or compute discrete logarithms using Shor's algorithm? Even if retrocausal effects exist, they can't constitute a c... | {
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Michelson rotating mirror experiment Could someone explain the calculation required to answer this question. It is from a text book and the answer is recorded as 585Hz but I cannot replicate the answer.
In 1931 Michelson used a rotating prism with 32 faces to measure the time for light to travel through a 1.6km evacua... | Speed of light ---> about 3E8 m/s.
Round trip length ---> 3200 m.
Time for round trip ---> 3200/(3E8) = about 1.066E-5 = 10.66 uS.
The mirror turns 1/32 of a full turn in 10.66 uS; so it makes a full turn in (32 x 10.66) uS = 341uS = 0.341mS.
1/(0.341E-3 s) = 2932/s = 2932 Hz (based on c = 3E8 m/s).
If the authors made... | {
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Why photons transfer to electrons perpendicular momentum? Linear antenna directed along z, photons (EM waves) propagate along x. Momentum of photons have only x component. Why electrons in antenna have z component of momentum?
| Photons are quanta of electromagnetic waves which are transverse so if the momentum of the photon goes in the $x$-direction, then the magnetic and electric fields are in the transverse $yz$-plane, for example $B$ may be in the $y$ direction and $E$ may be in the $z$ direction. Because the electric field accelerates cha... | {
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What causes the Pauli exclusion principle (and why does spin 1/2 = fermion)? It seems to be related to exchange interaction, but I can't penetrate the Wikipedia article. What has the Pauli exclusion principle to do with indistinguishability?
| The exchange interaction is, on the contrary, one of the approximate low-energy consequences of the Pauli exclusion principle and the identical character of the particles.
The fundamental justification of these facts is offered by quantum field theory. Relativity requires observables to be linked to regions of spacetim... | {
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Effects on the lift of a Wing in a hermetically sealed torus To help settle an office discussion could someone please explain why this is/is not possible.
Assuming that materials could be found that are light and strong enough for its construction.
If you were to feed the back-end of a wind tunnel to the front forming ... | Actually, if the wing was tethered to the floor of the torus, the wing could 'kite'. The lift is produced by air flow over the wing. As long as there is a tether to counter the drag produced, the wing will lift in proportion to the air speed. Without the tether, drag and gravity would pull the wing backward and to th... | {
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How do you produce electricity from a wind mill? How does a spinning windmill produce electricity?What is the principle behind the windmill?
| The short answer, as Karsus Ren says, is that it's electromagnetic induction that generates the electricity: the relative movement of a conductor and a magnetic field.
As Vladimir Kalitvianski points out, strictly speaking, windmills don't generate electricity - wind turbines generate electricity, and windmills mill gr... | {
"language": "en",
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What do we consider "Perpetual Motion" I know this is a bad question to most serious Physics but I have a question about what is considered “Perpetual motion.” The Foucault pendulum in the UN consists of sphere that passes directly over a raised metal ring at the centre that contains an electromagnet, which induces a c... | The term "perpetual motion" signifies a machine that can keep moving indefinitely without any additional energy inputs, without losing kinetic energy. The Foucault pendulum you describe has additional energy inputs (from the electromagnet), to overcome friction and air resistance, as you say, so it's not a perpetual-mo... | {
"language": "en",
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Does spacetime really exist in quantum gravity? If there are no localized observables in quantum gravity, does spacetime really exist, or might spacetime really be an illusion?
| The answer is divided more on the lines of "TOE vs. non-TOE" than "quantum gravity vs. non-quantum gravity". In string theory, the metric tensor is an approximation that arises as an effective description of the graviton field (see also this post on TRF). But in non-unification theories of quantum gravity, like LQG and... | {
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Length of a curve in D dimensional euclidean space In a book I am reading on special relativity, the infinitesimal line element is defined as $dl^2=\delta_{ij}dx^idx^j$ (Einstein summation convention) where $\delta_{ij}$ is the euclidean metric. Next, if we have some curve C between two points $P_1$ and $P_2$ in this s... | You can derive the correct results when you use the key property of differentials $$dx_i=\dot{x}_i dt.$$ Note that
$\Delta L$ is invariant under reparameterization $t'=f(t)$ as you can check easily (this is in fact the reason why you can write it as $\int d\ell$ without any reference to a parametrization). However, to ... | {
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(Almost) double light speed Let's say we have $2$ particles facing each other and each traveling (almost) at speed of light.
Let's say I'm sitting on #$1$ particle so in my point of view #$2$ particle's speed is (almost) $c+c=2c$, double light speed? Please say why I am incorrect :)
EDIT: About sitting me is just exa... | This is what special relativity is all about..
In special relativity you cannot simply state that particle 2 is moving at c+c=2c in a reference frame where particle 1 is at rest.
Speeds add like this (easily found in wikipedia):
$$v_2^{'} = \frac{v_1+v_2}{1+\frac{v_1v_2}{c^2}}$$
i.e. the speed of particle 2 $v_2'$ in a... | {
"language": "en",
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Conversion of mass to energy in chemical/nuclear reactions Is mass converted into energy in exothermic chemical/nuclear reactions?
My (A Level) knowledge of chemistry suggests that this isn't the case. In a simple burning reaction, e.g.
$$\mathrm{C + O_2 \to CO_2}$$
energy is released by the $\mathrm{C-O}$ bonds formin... | Chemical reactions of any kind ---> No conversion. All mass (and energy) is conserved.
Nuclear reactions ---> Yes, mass is converted to energy, in both fission and fusion reactions.
What mass? Well, going by my college instruction, I would have said that a neutron is lost (converted to energy). But a quick surf of... | {
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Simple Harmonic Motion - What are the units for $\omega_0$? I'm trying to understand the units in:
$$mx''+kx=0$$
And the general solution is $$x(t)=A \cos(\omega_0 t)+B \sin(\omega_0 t).$$
Let $\omega_0 =\sqrt{\frac{k}{m}}$ - the unit for the spring constant $k$ is $kgms^{-2}$
or $Nm^{-1}$, where $m$ is in $kg$, so tha... | The importance of radians is "not" in its dimensions. It is necessary to mention whether $\omega_0$ is in radian/sec (and not just 1/sec) because angles can be expressed in various units - degrees, radians, etc (all which are dimensionless) and unless we know in which unit $\omega_0$ is expressed, we cannot do mathemat... | {
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Why is the gravitational force always attractive? Why is the gravitational force always attractive? Is there another way to explain this without the curvature of space time?
PS: If the simple answer to this question is that mass makes space-time curve in a concave fashion, I can rephrase the question as why does mass ... | It is not true at all that gravitation is always attractive. In fact, if it were always attractive, the universe would not be expanding at an accelerated rate right now and an inflationary period would not have occurred.
Currently the only known source of expansion components of gravity is the cosmological constant, wh... | {
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Partially polarized light in laboratory Does anybody know a way to create (in laboratory, but with no super-sophisticated equipement) a beam of light with partial linear polarization whose degree of polarization can be adjusted (at least over the range 0-0.5)?
| Start with unpolarized let. Let it scatter off a surface at a variable angle.
You could also try scattered sunlight (i.e., light from the blue sky). The degree of polarization depends on the angle between the direction of the Sun and the direction the light is coming from. Apparently under the right circumstances you ... | {
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How is thermodynamic entropy defined? What is its relationship to information entropy? I read that thermodynamic entropy is a measure of the number of microenergy states. What is the derivation for $S=k\log N$, where $k$ is Boltzmann constant, $N$ number of microenergy states.
How is the logarithmic measure justified?
... | The connection between thermodynamic and information theoretic entropies is a deep connection, and has been an active research area for more than a century.
To get more information, you can look at
*
*This well written comprehensive review at Stanford Encyclopedia of Philosophy, including the link with macroscopic ... | {
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What are the properties of two bodies for their collision to be elastic? For example, must the shock wave in each body be of a particular form which influences the shape and material properties of the bodies?
I suspect part of the the answer is that the objects must be spherical, and the round-trip of the shock wave in... | For a collision to be elastic, by the usual definition, no internal degrees of freedom of the colliding bodies can be excited/de-excited by the collision.
The internal degrees of freedom that might change in a collision include vibration, rotation (although some might argue about this), electron orbitals, electron spin... | {
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On a bicycle, why does my back tyre wear so much more quickly than the front? This question is cross-posted from Bicycles.SE, but it is really one for those that know a bit about physics.
Why does the back tyre of a bicycle wear out quicker than the front tyre?
I have my uneducated suspicions but I would appreciate an ... | On most bicycles, your center of gravity is not halfway between the front and back wheel - it is closer to the back wheel (image source: http://www.esquire.com/cm/esquire/images/d1/bike-080210-lg.jpg).
This means that the back wheel carries more of the weight. Now assuming that you inflate the tires with the same pre... | {
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If you view the Earth from far enough away can you observe its past? From my understanding of light, you are always looking into the past based on how much time it takes the light to reach you from what you are observing.
For example when you see a star burn out, if the star was 5 light years away then the star actuall... | No. Because you cannot reach the speed of light, even if you had started travelling away from Earth the day you were born, you could never catch the light carrying the image of your being born.
| {
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Could we enable ourselves to send messages to and receive messages from the future? Based on John Isaacks' question, "If you view the Earth from far enough away can you observe its past?" and the responses, it appears that we could use mirrors to see into the past. Using Vintage's example, a single mirror on the moon ... | Bouncing light off a distant mirror allows you to "see into the past" because it takes the light a while to get to the mirror and back. You can achieve the same goal much more efficiently by just recording the event or information, and then just letting the recording go into the future the usual way.
| {
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How does stuff glow in the dark? Many things have glow in the dark properties (glow sticks, paint, toys ..), and I am wondering what is the physics behind them. How do these materials store light energy and emit it later when dark?
What dictates the wavelength(s) of the glow? Is there a limit on how much energy can be ... | This phenomenon is called phosphorescence. Electrons in the material are pushed into excited states by light, and then drop back down, emitting light with a characteristic frequency corresponding to the energy of the transition. It is analogous to fluorescence, however whereas fluorescence is a very rapid process, phos... | {
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How come an anti-reflective coating makes glass *more* transparent? The book I'm reading about optics says that an anti-reflective film applied on glass* makes the glass more transparent, because the air→film and film→glass reflected waves (originated from a paraxial incoming wave) interfere destructively with each oth... | Perhaps it will help to recall that energy is a nonlinear function of the electromagnetic field. The superposition principle applies to the electromagnetic field, not the energy or power. So if two waves are superimposed out of phase, 1 - 1 = 0, we can say they are both happily traveling "independent" of each other... | {
"language": "en",
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Non-interchangeability of time-like intervals I am reading Landau's Volume 2 of the course of theoretical physics. I have a doubt after reading the first few pages of it which I explain below.
Landau first defines intervals and on pages 5 and 6 shows that two events having time like interval between them can never occu... | I don't know what Landau says, but space-time interval doesn't distinguish order. To derive the non-interchangeability of time-like intervals, Lorentz transformation must be explicitly used.
| {
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Why is it that when driving in a car, and a lightning bolt strikes, my AM radio gets cut off for a while, but FM stays on? I noticed this one day, a lightning/thunder occurred and my Fabulosa Spanish music died for a second. But not FM?
| AM radio typically transmits at around 1 MHz, FM radio at about 90 MHz. Measurements of the RF spectrum of lightning strikes show a falloff with frequency of about 20 dB per decade in that frequency range, so with FM about 2 decades above AM, you'd expect AM to have about 40dB higher interference from a lightning stri... | {
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What is the terminal velocity for a mobile phone You may have seen the story of the iPhone which was dropped from perhaps 13,500 feet by a skydiver - it survived.
This made me wonder how to work out the terminal velocity for something like that. Obviously calculating terminal velocity for a sphere can be relatively str... | From the equilibrium between drag and weight:
$$
\frac{1}{2} C_x \rho v^2 S = m g
$$
we can write the terminal velocity as
$$
v = \sqrt{\frac{2 m g}{C_x \rho S}}
$$
where $m$ is the mass of the phone, $C_x$ its drag coefficient,
$S$ its section, $g$ the acceleration of gravity,
and $\rho$ the density of air.
Now, t... | {
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Do eyeballs exhibit chromatic aberration? Fairly straightforward question. If not, why not?
I suspect that if they do, it is not perceived due to the regions of highest dispersion being in one's region of lowest visual acuity.
| Here is an interesting webpage on the aberrations of the eye:
http://www.telescope-optics.net/eye_chromatism.htm
According to http://kaschke-medtec.de/SS10/Exercise5.pdf the eye has quite a large chromatic aberration of 2 dptr across the visible range.
I heard (the rumor?) that for this reason the color bands in the fr... | {
"language": "en",
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'Getting in' to research physics? I'm going to be choosing a university course soon, and I want to go into a branch of physics. A dream job for me would be to work in research, however, I do realise that this isn't for everyone and is difficult to reach. So what is the best way to go about achieving this aim? What thin... | Take the physics courses you plan with your advisor not with an eye towards getting through easily but with a passion for the subject. If you are passionate about the work you do, if you enjoy studying hard problems and finding even harder ones, the road towards research will be easier, because professors are looking f... | {
"language": "en",
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Books that every layman should read To add to Books that every physicist should read:
A list of popular physics books for people who aren't necessarily interested in technical physics.
(see also Book recommendations)
| Dr. Posin's Giants, by Daniel Posin even children can read this one....
The Strange Story of the Quantum Banesh Hoffman a real scientist and a good, if a little colloquial in that breathless American 1940's way, writer
Men of Mathematics Eric Temple Bell includes many of the greatest physicists
Understanding Ph... | {
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Time dilation and dimensional compactification Is time dilation a form of dimensional compactification?
As a probe approaches a black hole, toward a point on the equator of the event horizon, does general relativity predict that the time dimension is compactified like the extra dimensions of string theory? Will this c... |
Is time dilation a form of dimensional compactification?
As far as I know, no, it isn't. Compactified dimensions have a finite extent, and as used in string theory they're typically periodic. For example, the Earth's surface has two compactified dimensions: you can't travel more than a certain distance in any one dir... | {
"language": "en",
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Helmholtz Free Energy relation Ok so in a lecture my professor gave us this definition:
$dF=\left(\frac{\partial F}{\partial T}\right)_{V,N}dT+\left(\frac{\partial F}{\partial V}\right)_{T,N}dV+\left(\frac{\partial F}{\partial N}\right)_{T,V}dN$
Now we were given that:
$F=E-TS=-pV+\mu N$
$\left(\frac{\partial F}{\parti... | This seems to come from the derivatives of the second given form of $F$, namely
$F = -pV +\mu N$
assuming $p$, $\mu$ do not depend on $V$, $N$.
| {
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In dimensional analysis, why the dimensionless constant is usually of order 1? Usually in all discussions and arguments of scaling or solving problems using dimensional analysis, the dimensionless constant is indeterminate but it is usually assumed that it is of order 1.
*
*What does "of order 1" mean? 0.1-10?
*Is... | Here are two examples of where dimensional estimates fail:
Divergent expressions
I have a laser pointer pointed at a wall directly facing me, 1 meter away. I turn the laser pointer by 90 degrees over the course of 1 second. What is the average speed of the laser spot during the turn? The dimensional analysis argument i... | {
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Will the earth never cool, but only get hotter? Since the earth is in a vacuum and therefore there is no thermal transfer of heat to anything else, how can it even cool down? It seems like its average temperature would always be constant, ignoring outside sources of heat.
However, if you then consider that there is co... |
"Since the earth is in a vacuum and therefore there is no thermal
transfer of heat"
"there is constant radiant heat transfer from the sun to the earth"
You might like to think about those two statements !
Since the rate of heat flow from the earth into space increase as the temperature increases then you have a sta... | {
"language": "en",
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Why are infinite order Lagrangians called 'non-local'? And in what sense are they 'non-local'?
| Clearly, an interaction involving $\phi(x+h)$ deserved to be called nonlocal. But since $\phi(x+h)=\sum_{k=0}^\infty \phi^{(k)}(x) h^k/k!$, any nonlocal interaction can be expressed as a power series involving arbitrarily many derivatives. Therefore an action (or Lagrangian) is called nonlocal if it involves infinitely... | {
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Does the wavelength always decrease in a medium? I was studying a GRE Physics Test problem where optical light with a wavelength of 500 nm travels through a gas with refractive index $n$.
If we look at the equations for wave motion and index of refraction
$$c=\lambda_0\nu\quad\text{(in vacuum)}$$
$$v = \lambda\nu\quad\... | The index of refraction of a material can be less than 1 at high frequency, this is called "anomalous dispersion" and it happens as you cross an energy level of certain materials. It means that the phase velocity of light of a certain frequency is higher than c.
If the index of refraction is constant, as it is for long... | {
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Explain the direction of waves on sea shore Why do waves on the seashore move towards the shore even when the tide is going out?
| Suppose it was the other way round. In that case, the waves would be starting at the coastline. And suppose these waves would be caused by wind as are "normal" waves.
The wind pattern, in this case, would have to be very specific! But, let's assume. As the waves reach outward, they will, instead of growing smaller, gro... | {
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How to measure faster than light electric energy? According to relativity,nothing can break light barrier.But a recent preprint shows energy transmission of commercial electric power (f=60Hz) is faster than light. (It is not the drift velocity of electrons because energy transport depends on the electromagnetic field i... | In physics where where you make time critical measurements you often use the fast nim signal, which is essential a dc signal. To make e.g one signal arrive later at your electronics you use delay boxes, that is just cable inside a box. You can also use small pieces of cable to make a small delay, and it is usually wri... | {
"language": "en",
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"source": "stackexchange",
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Solid objects inside the event horizon - can they remain "solid"? So, once something is inside a black hole's event horizon, it can only move towards the center. This is fine for a point-object. But 3D solid objects rely on molecular forces to stay in one piece. These forces act in all directions inside the solid. But ... | Inside the event horizon notion of 'center' ceases to exist. The 'distance from the center' has no meaning either. Actually, black hole has no 'center' at all! The singularity that exists in spacetimes containing black holes is space-like - so it can be interpreted as a certain moment of time for an infalling object. T... | {
"language": "en",
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How can it be that the beginning universe had a high temperature and a low entropy at the same time? The Big Bang theory assumes that our universe started from a very/infinitely dense and extremely/infinitely hot state. But on the other side, it is often claimed that our universe must have been started in a state with ... | It's an example of adiabatic expansion. If you have a container full of gas and you expand the container, the gas cools. Entropy is preserved.
Adiabatic processes preserve entropy. Any decrease in entropy due to lowered energy, and correspondingly fewer possible velocities for the particles, is offset by an increase in... | {
"language": "en",
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Plotting a wave function that represents a particle The problem is this:
A particle is represented by the wave function $\psi = e^{-(x-x_{0})^2/2\alpha}\sin kx$. Plot the wave function $\psi$ and the probability distribution $|\psi(x)|^2$.
This the problem 2.1 in the book Fundamental University Physics Volume III by ... | The real purpose of this exercise seems to be exactly finding out the meaning of $\alpha$, $k$ and $x_0$. So just try modifying them all one by one and see how this affects the wave function. For instance, you will see that a very small $\alpha$ will give you a narrow-peaked distribution, while a big $\alpha$ leads to ... | {
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Confusion with the torque Consider an imaginary vertical plane. Now say, a body is falling freely (under earth's attraction). If you consider any axis that is perpendicular to that plane. We get a non-zero value for torque. Then why is it that body is not moving in a circular path about that axis?
| When you exert a torque on something, its angular momentum changes. This doesn't necessarily mean things are moving in a circle, or even rotating. You can have torque and changing angular momentum even when things are going in a straight line.
Most of the time, when we discuss torque and angular momentum in basic p... | {
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Rainbow around Sun From the perspective of a person, a rainbow is formed when the Sun is behind the person, and there is a critical angle made by the rainbow.
However, on several occasions, usually at noon when the Sun is higher, I saw a ring around the Sun made of the colors of the rainbow. Is that a rainbow? Is wit... | Well, the definition of a rainbow is "an arch of colors formed in the sky under certain circumstances" according to my Apple dictionary. More literally, it would need to be caused by rain, so you're correct that you'd see it 180° away from the sun.
But, if there are thin cirrus clouds made with tiny ice crystals, you ... | {
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General relativity at 0K Relativistic gravity affects particle in motion, does it affect particle that are resting too? How? and if not could one say that the matter at 0K is not affected by gravity?
I'm not a physicist; is just a thought and probably really naive.
| Yes, gravity affects particles at rest, and particles at rest affect gravity.
In GR, the interaction between spacetime and matter and energy is described by Einstein's equation,
(from Wikipedia).
The term $T_{\mu\nu}$ on the right is the stress-energy tensor. Matter at rest contributes to the $T_{00}$ term, even if ... | {
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Surface tension of solutions and mixtures The inspiration for this question is over on cooking.stackexchange, asking more about actual measurements for commonly consumed liquids, but I'm interested more generally as well.
What determines the behavior of surface tension for solutions and mixtures with respect to concent... | About the surface tension of mixtures, this is quite complex, and the answer is certainly not straight. However, it looks like the surface tension of the mixture of two fluids is always in between the surface tension of the pure fluids somehow (so it is simpler than azeotropes for the boiling temperatures of mixtures).... | {
"language": "en",
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On Einstein's original paper: speed of light in different reference frames On Einstein original paper "On the electrodynamics of moving bodies", on section 2 of the first part (Kinematics), the following thought experiment is described: a rod is imparted constant speed $v$ in the direction of the $xx$ axis (growing $x$... | When setting up this description, the author states:
We imagine further that at the two ends A and B of the rod, clocks are
placed which synchronize with the clocks of the stationary system, that is to say
that their indications correspond at any instant to the “time of the stationary
system” at the places where... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/14615",
"timestamp": "2023-03-29T00:00:00",
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Fluid Mechanics from a variational principle It is possible to define a good variational principle to describe Fluid Mechanics? If so, what is the correct treatment of the issue. I guess something like:
$$I=\int d^4x \left(\frac{1}{2}\rho v^2-P-\rho g x\right).$$
| Well, this is a huge topic, cf. e.g. Refs. 1-2 and e.g. this Phys.SE post.
*
*The simplest action functional for fluid dynamics in the Lagrangian flow picture is
$$\begin{align} I[{\bf r}] ~=~&\int \!\mathrm{d}\tau~\mathrm{d}^3{\bf a}~{\cal L},\cr
{\cal L}~=~&\frac{1}{2}\dot{\bf r}^2 - \varepsilon\left(\rho({\bf a})^... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Graphene space elevator possible? I just read this story on MIT working on industrial scale, km^2 sheet production of graphene.
A quick check of Wikipedia on graphene and Wikipedia on space elevator tells me
Measurements have shown that graphene has a breaking strength 200 times greater than steel, with a tensile stre... | The real economics will come into play via electricity. Space based solar transmitting electricity down graphene cables solves our energy crisis basically forever. Once you build the first cable, building more is an order of magnitude cheaper. Once you make that initial investment, the solar farms become trivial, altho... | {
"language": "en",
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"source": "stackexchange",
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Indirect band gap semiconductor for LEDs? Can someone please explain why Indirect band gap semiconductor can not be used for LED creation. Can you also please give me some reference link for details.
| Because they do not emit light.
And they do not emit light because: massless photon has (almost) zero momentum. In indirect semiconductor holes and electrons have different momenta. Thus, to recombinate and fulfill momentum conservation law they need to do something with this uncompencated momentum. While in direct gap... | {
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Water under high pressure If you were to sink a container to the bottom of a deep ocean and seal it there, then bring it up to the surface, would it retain its pressure?
The answer for a gas is obviously yes, but what about for a liquid like water which is incompressible? Once the crushing weight of the water column ab... | The problem in your post is that you don't consider the force resisting the water pressure, which is exerted by the walls of your container.
To do this, imagine a two-chamber container, with outer walls infinitely strong, but with a piston in between them which is maintained at its central position by some force that y... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/15148",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
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Schwarzschild metric Why, if the Schwarzschild metric is a vacuum solution ($T_{\mu\nu}=0$) , do textbooks state that $T=\rho c^{2}$ when approximating Poisson's Equation from the Einstein Field Equations?
Thank you.
| Because the approximation for Poisson's equation is weak field. In order to get a self-sourcing gravitational field, like the Schwartschild solution, you need a region with a strong field. You can always imagine that the source for the Schwarschild solution is right on the event horizon of the black hole it describes.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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What does it take to understand Maxwell's equations? Assume I want to learn math and physics enough to reach a level where I understand Maxwell's equations (The terms and reasoning in the equations I.e. why they "work"). What would I have to learn in order to have the tools I need to make sense out of it?
I'm kindof lo... | I advise to start with Purcell's "Electricity and Magnetism", then read Griffiths' "Introduction to electrodynamics". As for mathematics, in order to understand Maxwell's equations you need to know vector calculus, not to mention differential equations.
Edit: The review of vector analysis can be found in the first chap... | {
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Is an electron/proton gun possible? In the 1944 SF story “Off the Beam” by George O. Smith, an electron gun is constructed along the length of a spaceship. In order to avoid being constrained by a net charge imbalance, it is built to also fire the same number of protons in the other direction, dissipating the mass of t... | The general way of making proton beams is to ionize hydrogen and separate the protons and electrons with electric fields.
Notice that with an other material
*
*you have to get the protons out of a nuclear context, which requires much more energy (MeV rather than eV)
*you leave behind a increasingly neutron rich (i.... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/15290",
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"source": "stackexchange",
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"answer_id": 1
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A telescope with a bunch of small mirrors Together with colleagues we got this question. Imagine to take small mirrors, the size for example of a dentist mirror, and stick them to a wooden frame with a parabolic shape. Each mirror is flat, and once set of the frame it can be aligned properly with screws so that it redi... | Somehow all answers so far failed to mention that a segmented mirror consisting of flat segments could in principle yield a high optical quality (diffraction-limited) telescope provided the mirror segments are small enough.
Spherical (or hexagonal or any other compact shape) flat mirrors would work perfectly provided:... | {
"language": "en",
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"source": "stackexchange",
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To what extent is the "minimal substitution" or "minimal coupling" for the EM vector potential valid? In all text books (and papers for that matter) about QFT and the classical limit of relativistic equations, one comes across the "minimal substitution" to introduce the magnetic potential into the equation (Schrödinger... | As explained on Wikipedia, the reason this procedure is called "minimal coupling" is that it effectively ignores all but the first multipole moment (i.e. the charge) of the charged particle. But as long as you stick to monopoles, it's an exact expression, not an approximation.
You can get it from the Lagrangian for a r... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/15436",
"timestamp": "2023-03-29T00:00:00",
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"question_score": "22",
"answer_count": 2,
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Could the acceleration of universe expansion be caused by gravity itself? Dark energy is suggested to be a repulsive force in the universe causing an accelerated expansion. If the amount of mass outside our observable universe is greater than inside (higher mass density), would it not cause an accelerated expansion fro... | The simple answer would be no. If that were the case every thing in the universe would have the exact same gravitational pull. Meaning gravity on the moon, earth and sun would all be the same value and that is simply not the case.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/15546",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 5,
"answer_id": 3
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simulations at constant pressure-volume and constant volume-temperature I have read some papers where the authors perform simulations at constant pressure
and constant volumen or sometimes constant volume constant temperature. My question
is when is it better to use one or the other? For which systems it would be ok to... | The choice doesn't depend on the system but on the properties you want to measure (which means that it depends on the computational experiments you need to perform).
In NPT:
Pressure is constant.
Volume (and density) is changing.
In NVT:
Pressure is changing.
Volume (and density) is constant.
So, for example, if you w... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/15577",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Why is the energy density of the electric field produced by two unlike charges positive, even though their potential energy is negative? Consider two stationary charges, one positive the other negative. Their potential energy is clearly negative. So you would expect that the energy density of the associated electric ... | Potential energy of interaction is about interaction and can be negative.
The electric field created by two charges for a third one is a vector sum of two fields:
$\vec{E}=\vec{E}_1(\vec{r}_3-\vec{r}_1)+\vec{E}_2(\vec{r}_3-\vec{r}_2)$.
It defines the corresponding force. From it you can derive the potential energy of ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 4,
"answer_id": 2
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Why are nuclear reactors dome/bell shaped? Just what the title states.
What is the reason that a Nuclear reactor has a characteristic dome/bell shape?
| The containments of PWRs and BWRs are indeed different:
PWRs have the containment buildings you are talking here about. That's because in PWRs, the containment contains much more than in a BWR and is much larger. In a PWR, the reactor building is itself the containment vessel (hence the term containment building) and ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 4,
"answer_id": 3
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Measuring a Rod in Motion with two Synchronized Clocks An explanation of special relativity I'm struggling with, goes like this:
A rod traveling by a "stationary" observer has its length measured by use of two stationary synchronized clocks (synchronized from the perspective of the observer). The resulting length will... | You need two clocks if you don't know the velocity of the object a priori. Using a single clock will tell you only the time it takes to get past a particular point (that is, the rod's length divided by its velocity).
If you have two clocks with a known distance between them, you can determine the velocity (given by th... | {
"language": "en",
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"source": "stackexchange",
"question_score": "1",
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Could a ship equipped with Alcubierre drive theoretically escape from a black hole? Could a ship equipped with Alcubierre drive theoretically escape from a black hole?
Also, could it reach parts of the universe that are receding faster than the speed of light from us?
| Theoretically, yes. Assuming that our physics for black holes is correct enough to tell us that the escape velocity of a black hole is just greater than the speed of light. If you think about going faster than the speed of light as going back in time, this also serves as a way of "escaping" the black hole, for you woul... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/15960",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "24",
"answer_count": 4,
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Is the cooling rate of a (very) cold object, sitting next to an AC higher or lower? In more detail:
If i have two soda cans, both are cooled to exactly 4 degrees celsius,
And i put one in a 25 degrees room, and the other next to an AC vent set to 16 degrees.
After three minutes, which one should be colder than the othe... | Tricky. The 25C room is a static environment, whereas in the 16C AC-blowing room, the can environment is forced to be at 16C.
After 3 minutes, which is a short amount of time, I think we need to take into account many factors, like - among others - if there is moisture in the air. The can that is blown on by the AC wil... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/16076",
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"source": "stackexchange",
"question_score": "3",
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Which subjects in physics should I choose if I want to help tackling today's energy and environment related problems? I was wondering what subjects a freshman in mathematics ought to choose in the future if s/he wanted to help working on energy and environment-related issues we are currently facing, and will very likel... | You should research Pons/Fleischmann cold fusion, which also goes by the name LENR (Low Energy Nuclear Reactions). This field is taboo to all mainstream researchers, but the effect is obviously real, and extremely important.
Unfortunately, there are frauds in this field, like Rossi. Avoid the frauds, and try to find th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/16119",
"timestamp": "2023-03-29T00:00:00",
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"question_score": "5",
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Why you need a graviton when you have the Higgs boson? Since I studied General Relativity I had this question running on my mind. As I see it (just taking lectures of Quantum Field Theory right now)
"Why you need a gauge boson for gravity when the Higgs brings things mass?"
You know, mass is the cause for physicist to ... | There is also the confining strong interactions (quarks, gluons, color charge) which give hadrons mass independent of the Higgs (interaction, mechanism).
There is also the dominant decay mode of the first detection of the Higgs boson which turned out to produce a pair of gluons, not to mention the masses of other funda... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/16206",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "29",
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Are specific heat and thermal conductivity related? Are there any logical relationship between specific heat capacity and thermal conductivity ?
I was wondering about this when I was reading an article on whether to choose cast iron or aluminium vessels for kitchen.
Aluminium has more thermal conductivity and specific ... | There is not really a general answer to your question because both, the specific heat capacity and the thermal conductivity are not due to a single process in the material.
Both are in general terms a "sum" over the individual components in the material that can store thermal energy or transport thermal energy.
For m... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How do we perceive hotness or coldness of an object? Some objects, especially metallic ones, feel cold on touching and others like wood, etc. feel warm on touching. Both are exposed to same environment and are in their stable state, so some kind of equilibrium must be being reached. What is this equilibrium?
And how do... | The elaborate mechanism for heat detection in human skin is mainly carried by somatosensory system, which is responsible for temperature, touch, pressure sensing.
Somatosensory system contains thermoreceptors which are chiefly responsible for thermo sensing. wiki
These thermoreceptors are able to detect absolute, to a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/16333",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
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On the topic of action and reaction So, let's say we have a spacecraft in deep space. It activates its rocket engines, to keep it simple. The engine reaction channels exhaust through the aft nozzle, right? How does that chemical reaction actually induce a change in the velocity of the spacecraft? The particles have to ... | Imagine a box with fuel burning inside it creating pressure.
That pressure acts equally on all the sides of the box so no net force, no accelration, no movement.
Now remove one of the walls - what happens to the balance of forces?
Opening the door in a spacecraft is exactly the same as an engine (just with a very short... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/16422",
"timestamp": "2023-03-29T00:00:00",
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Is there any anti-gravity material? I want to know if there is any anti-gravity material. I am thinking of making flying vehicles which are made up of anti-gravity material so that they will not experience any gravity on them and can easily take off and be more fuel efficient. Is there any such thing? Or any workaround... | Forget anti-gravity material. As far as we know, there is none--gravity is always an attractive force. But there is a workaround: Use something with the appropriate properties, i.e. something that does have repelling force. Electromagnetism! All you need to do is separate enough charge, say a few grams of electrons, pl... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/16474",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 5,
"answer_id": 2
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Y Intercept of photoelectric effect graph? In a graph of $\mathrm{KE=hf-W}$ (the photoelectric effect equation), why is the work function equal to the y intercept? I mean I can see why it is using the equation $(y=mx-c)$ but conceptually, why is the work function - the minimum energy required to cause emission of elect... | The photoelectric effect graph just says that the outgoing electron is emitted with the energy of the photon minus the ionization energy, the energy it takes to rip an electron from the metal. Energy out equals energy in minus energy consumed in ionization.
The energy of the photon is proportional to f. If you make f z... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/16649",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
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Is it (theoretically) physically possible to project an image into thin air? Is there some law of physics that strictly prohibits the projection of 2D or 3D images into thin air (such as holograms in movies) or is a solution to achieve this still up for grabs by an eventual discoverer?
| The most common way used to "project images on thin air" is by optically creating a virtual image. That's what 3D TVs and holograms do. (Note that 3D TV create a only a "static" virtual image : the point of view of the scene does not change if you move around ; unlike holograms). But one can tell none of those technolo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/16718",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 5,
"answer_id": 4
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How long does it take for expanding space to double in size? I have been reading about Hubble's constant and trying to make 'sense' of the theory of the expanding Universe. Is is possible that space in the universe expands uniformly? If so, absent of other forces (ie gravity), how long does it take for the distance b... | The increase of the size of the Universe isn't quite exponential yet but it's getting close to it. It will become (nearly) exponential when the dark energy (cosmological constant) constitutes (nearly) 100% of the energy density. So far, it is only 73 percent.
Because the expansion hasn't been quite exponential so far, ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/16781",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 4,
"answer_id": 0
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given the infinitesimal generator can we deduce the symmetry? for example given the differential operator $ \partial _{x} $ we know that it belong to the translation $ y=x+a $ for some 'a'
given the differential operator $ x\partial _{x} $ we know that we are dealing with dilations $ y=ax$
however for any particular fi... | An infinitesimal generator $X$ is a vector field, which satisfies Leibniz rule
$$X[fg]~=~ fX[g]+g X[f].$$
In the $1$-dimensional case, the generator is of the form $X=p(x)\frac{\partial}{\partial x}$, where $p=p(x)$ is some function. Assume furthermore that there exists a bijective smooth function $h=h(x)$, such that ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/16829",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
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A physical understanding of fractionalization all! Is there a physical understanding of fractionalization in condensed matter physics? The textbook approach is theoretical, not physical. I'm thinking of spin-charge separation for electrons, the fractional quantum hall effect, and things like that. The theoretical appro... | Beyond one dimension, fractionalization is always associated with emergent gauge theory. Emergent gauge theory can (some times) be understood from string-net condensation. In this case, quasiparticles with fractional quantum numbers are
always defects that correspond to "ends of strings" (see a discussion here).
One wa... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/16863",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 1,
"answer_id": 0
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Time, what is it? If you ask any person about time, she/he will give you some answer.
I suspect that it is extremely difficult, (if not impossible) to define time.
Is there a definition of what it is in physics? Is it an "axiom" that has to be taken as it is, without explanations? I also noticed that the tag "time" ha... | Each paradigm shift leads to a change in the conception of time. Newton introduced the notion of absolute time. That was hardly a mainstream view before him. Special relativity overturned the nature of time, and so did general relativity after that. When quantum gravity is cracked, the nature of time will need to be re... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/17056",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "14",
"answer_count": 6,
"answer_id": 4
} |
The fine structure non-constant If the fine structure constant is different in different parts of the universe, then what would happen if we travelled to those regions?
(I realise this is completely impossible as they are impossibly distant, so this is just a thought experiment).
If we hop in our spaceship and travel t... | If we move to a region where the fine structure constant is different, as we see by measuring the electrons and protons in this region, we would feel the new value of the fine structure constant also, gradually, as we moved to the new region. The reason is because the electrons in our bodies are quantum-mechanically in... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/17092",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 1,
"answer_id": 0
} |
Inertial Mass of a scalar field Does it make sense to talk of the inertial mass of a scalar field? By the equivalence principle, it must be equal to its gravitational mass. We know that the scalar field contributes towards the stress-energy tensor, so, shouldn't it have an inertial mass too?
| Yes, of course, if you produce a localized concentration of energy carried by a scalar field, it exhibits all the properties that this total energy $E=mc^2$ should exhibit.
It will enter the right hand side of Einstein's equations so it will curve the surrounding spacetime and create a gravitational field. It will be ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/17134",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
} |
Why doesn't this perpetual motion machine using magnets work? See image:
If I'm not totally dumb the car would move when the right magnet would not be attached to the car, at same distance of the booth magnets.
So why would it not move?
| A simple symmetry argument might help here. Try to abstract everything away from your picture that is just a distraction. In the end it might look like this:
Why should this move to the left or to the right? It cannot and therefore adding a person and wheels does not change the problem.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/17177",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
"answer_count": 2,
"answer_id": 1
} |
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