Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Why are snowflakes symmetrical? The title says it all. Why are snowflakes symmetrical in shape and not a mush of ice?
Is it a property of water freezing or what? Does anyone care to explain it to me? I'm intrigued by this and couldn't find an explanation.
| Not quite an answer but the first attempt to explain the shape was published by astronomer Johannes Kepler in 1611, the original is in Latin - "Strena Seu de Nive Sexangula" (A New Year's Gift of Hexagonal Snow). There is an English translation ("The Six-Cornered Snowflake") available at Amazon and elsewhere.
| {
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Stopping Distance (frictionless) Assuming I have a body travelling in space at a rate of $1000~\text{m/s}$. Let's also assume my maximum deceleration speed is $10~\text{m/s}^2$. How can I calculate the minimum stopping distance of the body?
All the formulas I can find seem to require either time or distance, but not on... | Another equation of motion problem,very easy.
$$v^2 = u^2 + 2.a.s$$ where $$v = \textbf{final velocity} $$ , $$u = \textbf{initial velocity}$$ , $$a=\textbf{ acceleration or in this case negative acceleration}$$ , $$s = displacement$$ . This equation is time independent. Now, to find $s$ , put the values: $$s = \frac{... | {
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"url": "https://physics.stackexchange.com/questions/3818",
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Will tensile strength keep a cable from snapping indefinitely? Trying to secure a wall hanging using magnets; me and a coworker came up with an interesting question:
When the hanging is hung using 1 magnet, the weight of it causes it to quickly drag the magnet down and the hanging drops. Using n magnets retards this p... | Ultimately, the weight will fall.
If the weight falls, it will collide with the floor and convert its gravitational potential energy into heat, resulting in an increase in entropy, so the process of the weight eventually falling is thermodynamically favored.
One possible (and somewhat ludicrous) mechanism is quantum ... | {
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Haag's theorem and practical QFT computations There exists this famous Haag's theorem which basically states that the interaction picture in QFT cannot exist. Yet, everyone uses it to calculate almost everything in QFT and it works beautifully.
*
*Why? More specifically to particle physics: In which limit does the ... | Lubosh wrote: "... perturbative QFT clearly works...". No, it miserably fails in the initial approximation ("bare" particles, no soft radiation predicted) and in course of search of the solutions by iterations (infinite corrections to the initial approximation). That is why there are so many questions to it!
What is co... | {
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Renormalization and Infinites Measuring a qubit and ending up with a bit feels a little like tossing out infinities in renormalization. Does neglecting the part of the wave function with a vanishing Hilbert space norm amount to renormalizing of Hilbert space?
| I am maybe a bit uncertain what you are asking, but from what I understand the answer would be no. Renormalization is a procedure for absorbing infinities in an interacting field theory. A quantum bit is really just a state, but referred to in information theoretic terms. The two physics are not directly related as ... | {
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A reference request for real world experimental data I always use to wonder how the experimental physicists discover new particles every now and then whose dimensions/properties/mass/charge several order of magnitudes below that of anything that is visible/perceptible. So as engineers do, I guess they also set up a ext... | You can download raw (or processed) data from various observational cosmology projects (e.g. COBE and WMAP) here:
http://lambda.gsfc.nasa.gov/product/map/current/
As a project, you could use this to re-compute the famous angular power spectrum of the cosmic microwave background radiation.
| {
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Why are there only derivatives to the first order in the Lagrangian? Why is the Lagrangian a function of the position and velocity (possibly also of time) and why are dependences on higher order derivatives (acceleration, jerk,...) excluded?
Is there a good reason for this or is it simply "because it works".
| This question actually needs a 2 steps answer:
*
*Why Lagrangian has only derivatives to the first order?:
Lagrangian has been defined in such a way, that problem to be solved would produce a second order derivative with respect to time when Euler-Lagrange equation is produced. It includes an implicit derivation o... | {
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How to avoid getting shocked by static electricity? sometimes I get "charged" and the next thing I touch something that conducts electricity such as a person, a car, a motal door, etc I get shocked by static electricity.
I'm trying to avoid this so if I suspect being "charged" I try to touch something that does not con... | Removing the radicals from the surface will protect you.
http://dx.doi.org/10.1126/science.1241326
Drink your anti-oxidants;-)
| {
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Why is the relationship between atomic number and density not linear? What are the factors that affect the density of an atom?
| At an atomic scale, there are two things that go into the density, which is $\rho=\frac{\mbox{mass}}{\mbox{volume}}$. First, we have the number density, which is $n=\frac{\mbox{number of atoms}}{\mbox{volume}}$. Then we also have the mass per atom, $\mu=\frac{\mbox{mass}}{\mbox{atom}}$. It is easy to see by combining ... | {
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Physical meaning of Legendre transformation I would like to know the physical meaning of the Legendre transformation, if there is any? I've used it in thermodynamics and classical mechanics and it seemed only a change of coordinates?
| See
http://en.wikipedia.org/wiki/Legendre_transformation#Applications
In theoretical physics, the basic or defining mathematical properties of the Legendre transformation are used to switch between one form of the energy - or "potential", as the generalized energies are called in thermodynamics - to another.
This is... | {
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How to explain the weak force to a layman? I'm trying to explain in simple terms what the weak interaction does, but I'm having trouble since it doesn't resemble other forces he's familiar with and I haven't been able to come up (or find on the web) with a good, simple visualization for it.
| The weak force "looks" different because in the first (and still most important) reincarnation we have encountered it - namely beta-decay (including the decay of the neutron) - the force seems to be a contact interaction: it has an extremely short range, essentially zero.
However, any phenomenon that differs from the i... | {
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What would happen if $F=m\dot{a}$? What would happen if instead of $F=m \frac{d^2x}{dt^2}$, we had $F=m \frac{d^3x}{dt^3}$ or higher?
Intuitively, I have always seen a justification for $\sim 1/r^2$ forces as the "forces being divided equally over the area of a sphere of radius $r$".
But why $n=2$ in $F=m\frac{d^nx}{dt... | There is a deeper reason for $F~=~\frac{d^2x}{dt^2}$ Within the Galilean group it is an invariant with respect to all changes of frame $x’~=~x~+~vt$. The acceleration of a body is not something which can be made to vanish by boosting to another Galilean frame as
$$
F’~=~\frac{d^2x’}{dt^2}~=~\frac{d^2x}{dt^2}~+~\frac... | {
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Why is quicksilver (mercury) liquid at room temperature? This is a nice question when you find it out, and I am really looking for a proper answer.
Take quicksilver (Hg) in the periodic table. It has one proton more than Gold (melting point 1337.33 K), and one less than Thallium (melting point 577 K). It belongs to the... | Gold has its 6s valence shell unfilled, so is more reactive than Hg. thallium has a valence electron in the 6p shell which again is unfilled. The valence shell of mercury, 6s2 is filled, and is drawn closer to the nucleus because the proximity causes the electron to move at relativistic speeds thereby causing its rest ... | {
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Glass melting at near absolute zero? I read this report and summarise here but my question is - if quantum mechanics will make glass melt at temperatures near absolute zero and it is near absolute zero then wouldn't this be a huge issue for satellites and space shuttles?
http://www.sciencedaily.com/releases/2011/02/11... | A preprint has appeared for this:
Accepted for publication in Nature Physics., Thomas E. Markland, Joseph A. Morrone, B. J. Berne, Kunimasa Miyazaki, Eran Rabani, David R. Reichman, Quantum fluctuations can promote or inhibit glass formation
http://arxiv.org/abs/1011.0015
While the article does apply to glasses in g... | {
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What is the wavefunction of the observer himself? I am aware about different interpretations of quantum mechanics out there but would mostly like to see an answer from the perspective of Copenhagen interpretation (or relative quantum mechanics if you wish).
Let an observer being a man with brain consisting of molecules... | Look in the mirror and you will see your wave functions squared ;-).
No, I am joking. In the mirror you see an inclusive picture, not elastic one.
The observer himself consist of so many degrees of freedom with so tiny differences between energetic levels that it is impossible to keep it in a pure state. There are perm... | {
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Black holes in a head-on collision Assume two uncharged non-rotating black holes traveling straight at each other with no outside forces acting on the system. What is thought to happen to the kinetic energy of these two masses when they collide? Is the excess energy lost through gravitational radiation? What would th... | Some energy is lost to gravitational radiation. Some probably ends up in the final black hole (i.e., $m_{\rm final}$ could be greater than the sum of the two initial masses). Figuring out the proportions of these two is not trivial, I would imagine.
The gravitational waves striking matter would not have any terribly dr... | {
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Bose-Einstein condensate in 1D I've read that for a Bose-Einstein gas in 1D there's no condensation. Why this happenes? How can I prove that?
| It is necessary to clarify that a uniform, non interacting Bose gas (considered to be confined in a periodic box) in thermal equilibrium does not have a macroscopic occupation of the zero momentum mode if $d<3$. This is not quite accurate for $d=2$ as macroscopic occupation is achieved at T=0, or rather the critical t... | {
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Mathematical background for Quantum Mechanics What are some good sources to learn the mathematical background of Quantum Mechanics?
I am talking functional analysis, operator theory etc etc...
| The most important background is the extension of linear algebra to infinite-dimensional vectorial spaces. So you introduce Banach and Hilbert spaces, $L^p$ and note that only $L^2$ (that's the space of quantum waves functions) is a Hilbert space.
You must study linear operator on $L^2$, and $l^2$: many attentions mus... | {
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Noether's theorem vs. Heisenberg uncertainty principle In continuation of another question about Noether's theorem I wonder whether there exists some kind of relationship between this theorem and the Heisenberg uncertainty principle.
Because both the principle and the theorem relate energy with time, momentum with spac... | Expanding on Marek's comment, they are related, but not in a deep way. They are related by the notion from Hamiltonian mechanics that every dynamical variable can be interpreted as an infinitesimal generator of some canonical transformation, or the quantum mechnical notion that every Hermitian operator generates a unit... | {
"language": "en",
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Gravitational and gauge-gravitational anomalies in ${\cal N}=1$ $D=4$ supergravity coupled to a SUSY gauge theory with chiral matter When people talk about the first superstring revolution they often mention the miraculous cancellation of anomalies via the Green-Schwarz mechanism. My question is whether such a string-t... | In 4D, we can have an axion mechanism. We have the axion-gauge coupling $\int d^4x\, d^2\theta \, \Phi W^\alpha W_\alpha$. But there are no gauge or gravitational anomalies in MSSM!
| {
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Resistance between two points on a conducting surface Suppose we have a cylindrical resistor, with resistance given by $R=\rho\cdot l/(\pi r^2)$
Let $d$ be the distance between two points in the interior of the resistor and let $r\gg d\gg l$.
Ie. it is approximately a 2D-surface (a rather thin disk).
What is the resis... | I'll tackle the 3D case. I am using the SI system. It should be noted that the electrical resistance of an electrical element (in given case a homogeneous medium) measures its opposition to the passage of an electric current (in given case direct current). The resistance of a homogeneous medium between two electrodes i... | {
"language": "en",
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Should you really lean into a punch? There's a conventional wisdom that the best way to minimize the force impact of a punch to the head is to lean into it, rather than away from it.
Is it true? If so, why?
EDIT: Hard to search for where I got this CW, but heres one, and another. The reason it seems counter-intuitive ... | This movement causes the temper of the neck muscles, and strengthens the spine. The punching power is also distributed by the muscles. The soft flesh does not absorb any impact energy and is simply overwhelmed.
How much more energy is absorbed by the neck less energy will be transmitted to the brain.
Similarly a handba... | {
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Cooling a cup of coffee with help of a spoon During breakfast with my colleagues, a question popped into my head:
What is the fastest method to cool a cup of coffee, if your only available instrument is a spoon?
A qualitative answer would be nice, but if we could find a mathematical model or even better make the experi... | According the fastest way would be keep a flat rectangular thick strip in the coffee with an ice cube at the other end the heat will flow by conduction. And since the temperature difference between the two is large a lot of heat energy will be absorbed by the ice cube to melt.(Taking perhaps a colder object might be be... | {
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How fast does gravity propagate? A thought experiment: Imagine the Sun is suddenly removed. We wouldn't notice a difference for 8 minutes, because that's how long light takes to get from the Sun's surface to Earth.
However, what about the Sun's gravitational effect? If gravity propagates at the speed of light, for 8 m... | the fact that distortion travels 'as soon' as a mass is removed or not is not implied in any way by gravity being due to a distortion of spacetime. In fact distortions of spacetime are as limited to travel to the speed of light as any other physical influence.
| {
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If we are willing to accept tachyonic string modes, are there valid projections other than the GSO projections? One reason superstring theory has often been touted as being an improvement over bosonic string theory is that we can impose GSO projections to remove the tachyonic mode. If we insist upon the no tachyon cond... | In ten dimensions this question was answered long ago in the three papers listed below.
The first one found several new possibilities using orbifold projections including a theory without spacetime supersymmetry and with no tree-level tachyon, the latter two papers classified modular invariant spin structures in a ferm... | {
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Do extra-dimensional theories like ADD or Randall-Sundrum require string theory to be true? What I mean is could it turn out that the world is not described by string theory / M-Theory, but that nevertheless some version of one of these extra-dimensional theories is true?
I have no real background in this area. I just... | In 1974 String theories are shown to require extra dimensions. An object similar to the graviton is found in superstring theories.
However these alternative dimensions or realities must be exactly the same as each other, even to the last grain of sand. For example There can not be different version of you in those univ... | {
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Electricity takes the path of least resistance?
Electricity takes the path of least resistance!
Is this statement correct?
If so, why is it the case? If there are two paths available, and one, for example, has a resistor, why would the current run through the other path only, and not both?
| If you turn on the water at your sink it comes out the nozzle, not the pipe.(unless you have a leak) Or in the case of a rocket if you ignite the fuel it comes out of the opening. These all have the path of least resistance, if you have two different paths the flow of energy will go through both of them until one of th... | {
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What is Fermi surface and why is this concept so useful in metals research? What is Fermi surface and why is this concept so useful in metals research?
Particularly, I can somewhat appreciate the Fermi energy idea - the radius of Fermi surface which is a sphere. But is there any quantitative use of more complicated Fer... | One more thing about geometrical properties of the Fermi surface. Its structure defines material transport properties like conductivity. It is actually equal to the integral of the mean free path along those wave vectors that define a Fermi surface.
Knowing this is very important. How do you sample the Fermi surface of... | {
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Is it really possible for water to be held in a "cone shape" for a brief period of time? I just saw this "trick" where a cup of water is turned over onto a table without spilling (using a piece of cardboard. After removing the cardboard from underneath the cup, the person then removes the cup in a particular way (lif... | We used to do the trick with the glass of water and a piece of paper when I was a child. You fill the glass, to the rim it is more successful, cover with a dry piece of paper or a bit of flat aluminum foil, put your hand flat over it, and upend it slowly. Slowly remove the hand. The water does not empty. The paper stay... | {
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Conjectures that have been disproved with extremely large counterexamples I would like to migrate this Math Question into physics. The question is:
*
*Are there conjectures in Physics which have been disproved with extremely large counterexamples? If yes, i would like to know some of them.
| Lots of properties that were found to hold locally (in space and time) turned out to be only local approximations.
Flat earth hypothesis - long journey.
Galilean transformations - breaks at large velocities.
Global curvature of spacetime, locally it is flat - large distances.
Spacetime is not expanding - breaks at la... | {
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How does Newtonian mechanics explain why orbiting objects do not fall to the object they are orbiting? The force of gravity is constantly being applied to an orbiting object. And therefore the object is constantly accelerating. Why doesn't gravity eventually "win" over the object's momentum, like a force such as fric... | The force of gravity has little to do with friction. As dmckee says, what is happening is that the body falls, but precisely because it has enough momentum, it falls around the object towards which it gravitates instead of into it. Of course, this is not always the case, collisions do happen. Also systems of astronomic... | {
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Relationship between magnetic resonance linewidth and spin relaxation First of all, what is the mathematical relationship between measured linewidth (usually in units of magnetic field) and spin relaxation time? I see papers talk about spin relaxation times in terms of linewidths but I have no idea how to correlate the... | The theory is rather generic Fourier transform: if you have a perfectly non-decaying oscillation $e^{i\omega_0 t}$ (with real $k$) then the transform gives a perfectly sharp spectrum as a delta function $\delta(\omega - \omega_0)$. But if the excitation decays $e^{i\omega_0 t} e^{-k t}$ then we get $\delta(\omega - \om... | {
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Are elementary particles ultimate fate of black holes? From the "no hair theorem" we know that black holes have only 3 characteristic external observables, mass, electric charge and angular momentum (except the possible exceptions in the higher dimensional theories). These make them very similar to elementary particles... | The short answer is no. Have a look at the wikipedia article on dissipation of black holes.
quote: Unlike most objects, a black hole's temperature increases as it radiates away mass. The rate of temperature increase is exponential, with the most likely endpoint being the dissolution of the black hole in a violent burst... | {
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Physics for mathematicians How and from where does a mathematician learn physics from a mathematical stand point? I am reading the book by Spivak Elementary Mechanics from a mathematicians view point. The first couple of pages of Lecture 1 of the book summarizes what I intend by physics from a mathematical stand point.... | You want the book by V.I. Arnold, Mathematical Methods of Classical Mechanics. It takes a very rigorous, axiomatic approach to Lagrangian and Hamiltonian mechanics, and it should be accessible to, and enjoyable by, a broad spectrum of mathematicians.
For more details see this review by Ian Sneddon, which also covers Wa... | {
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Do we take gravity = 9.8 m/s² for all heights when solving problems? Why or why not? Do we take gravity = 9.8 m/s² for all heights when solving problems?
| The approximation of 9.81 m/s^2 is a generalisation. The exact value is most likely different at a specific location, due to the distance from the centre of the earth to the point being evaluated.
The reference to "surface of the earth" is also a relative since the earth is known not to be perfectly round due to cent... | {
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Special Relativistic Time Dilation -- A computer in a very fast centrifuge Ok, I've stumbled onto what I think is a bit of a paradox.
First off, say you had some computer in a very fast(near light speed) centrifuge. You provide power to this computer via a metal plate on the "wall" of the centrifuge's container, so it... | If you want your computer to run fastest, leave it at rest ;-).
| {
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List of freely available physics books I'm trying to amass a list of physics books with open-source licenses, like Creative Commons, GPL, etc. The books can be about a particular field in physics or about physics in general.
What are some freely available great physics books on the Internet?
edit: I'm aware that there... | Quantum Mechanics for Engineers
*
*http://www.eng.fsu.edu/~dommelen/quantum/
I stumbled across this book the other day when I was looking for a text on nuclear physics. It seems like a handy resource.
To quote the preface:
The book was primarily written for engineering graduate students who find themselves caught u... | {
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Paradoxical interaction between a massive charged sphere and a point charge Suppose we have a sphere of radius $r$ and mass m and a negatively charged
test particle at distance d from its center, $d\gg r$. If the sphere is electrically neutral, the particle will fall toward the sphere because of gravity. As we deposi... | As a brainstorming answer, lets calculate the binding energy in another way:
suppose we have N electron in the sphere, the electrostatic energy to bring a new electron into the sphere is $Ne/R$. If we add a new electron, only the net electrostatic potential $Ne/R$.
the net potential on far-away electrons is
$N( e - m_... | {
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Does a photon interfere only with itself? I sometimes hear statements like:
Quantum-mechanically, an interference pattern occurs due to quantum interference of the wavefunction of a photon. The wavefunction of a single photon only interferes with itself. Different photons (for example from different atoms) do not inte... | Lubos Motl's answer is correct, of course, but I would like to point out a physical system in which it appears that photons from different sources are interfering with each other.
Consider two external-cavity lasers, nominally identical but running independently. HeNe lasers will work just fine. On the first laser, m... | {
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Does hot air really rise? "Heat rises" or "warm air rises" is a widely used phrase (and widely accepted phenomenon).
Does hot air really rise? Or is it simply displaced by colder (denser) air pulled down by gravity?
| Just one word for you, the convection. Have you heard about it?
Convective heat transfer, often referred to simply as convection, is
the transfer of heat from one place to another by the movement of
fluids. Convection is usually the dominant form of heat
transfer(convection) in liquids and gases
We are just to... | {
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I need help with finding distance traveled How do I find the distance traveled of an object if the speed is not constant?
| Integrating velocity is OK, but usually I do simpler things to know the answer.
It depends on the context. Traveled you said?
An odometer is the ideal instrument. Cars, bycicles, pedestrians can use one.
I can use a GPS in cars, bykes, pedestrian, airplanes and sea turtles, etc, complemented by Google Maps.
Trucks hav... | {
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Is causality synonymous with continuity? In general relativity, we use the term "time-like" to state that two events can influence one another. In fact, in order for an event to physically interact with another one, they have to be inifnitely close both in time and space.
As far as I know (correct me if I'm wrong) this... | The answer is "no" if you take precise definitions of "continuity" and "causality". Then these are different concepts.
Indeed. The "background" for general relativity is a manifold which necessarily have some topological structure -- it locally "looks like" an Euclidean space and you just take standard Euclidean topol... | {
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Why are Saturn's rings so thin? Take a look at this picture (from APOD https://apod.nasa.gov/apod/ap110308.html):
I presume that rocks within rings smash each other. Below the picture there is a note which says that Saturn's rings are about 1 km thick.
Is it an explained phenomenon?
| The rings have formed where they are because there is greater gravity there. The reason is the shape of the gas giant. It is far from circular. It is wider at its equator. Centripetal force causes a thicker equator. Therefore because the thickness is far wider at the equator, the gravitation at the equator is more than... | {
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Why is the decibel scale logarithmic? Could someone explain in simple terms (let's say, limited to a high school calculus vocabulary) why decibels are measured on a logarithmic scale?
(This isn't homework, just good old fashioned curiousity.)
| It's just because sounds that the human ear is capable of hearing range over a very large range of amplitudes. If you talked about the power delivered to the ear, rather than the log of the power delivered to the ear, you would need to use numbers like $10^{12}$ to talk about airplane engines. So, rather than deal wi... | {
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What is the closest general-relativistic equivalent of a "time slice"? In a newtonian universe, one can talk of a "time slice", that is, the state of the universe at a given point in (global) time. In a "typical" classical universe, a time slice would contain enough information to fully compute the state of the univers... | See my answer to this question, which is complementary to yours. The question there is what is a foliation, which as it turns out is the closest thing in GR to a time slice. In a word, foliation of spacetime is a choice of time slicing of spacetime. Unlike the idea of geodesics which are unique after choosing initial c... | {
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Why do tsunami waves begin with the water flowing away from shore? A sign of a tsunami is that the water rushes away from the shore, then comes back to higher levels. It seems that waves should be both + and - polarized and that some tsunamis should go in the opposite direction. That is the first indication of them wou... | Dear Carl, the recession of the sea level is an inevitable consequence of the mass conservation: the extra water in the tsunami has to come from somewhere. It comes from both sides - from the region in front of the wave as well as behind the wave.
So if the sea level is most elevated somewhere, it must obviously be low... | {
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Coriolis effect on Tsunami The Japanese tsunami, moving at about 700 km/h, affected areas as distant as Chile's coast, 20 hours after the earthquake. How does the Coriolis force affect tsunami? Also, I saw an image of a boat caught within a large whirlpool. Is the whirlpool's rotation due to Coriolis force?
| Your adjective "large" in "large whirlpool" may be very misleading. If you mean hundreds of meters, no effect of the Coriolis force may be visible by a naked eye at this scale. The origin of the whirlpool had to be different.
Quite generally, tsunami is all about waves, and if one has a wave, molecules of water are mov... | {
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What are the modern marvels in Physics that seem crazy but true? What are the modern marvels in Physics which are crazy but true? Ideas which are ridiculed and dismissed in the beginning but passed the test of time?
| Relativity and Quantum Theory. That whole division of the waters thing, of the infinite and infinitesimal, leaving our everyday world of beer and sandwiches in the middle. But I still don't understand mass, or gravity or momentum.
Cataclysm Theory and Continental Drift. Loads of stuff.
Some of the replies seem a bit sh... | {
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Can a nuclear reactor meltdown be contained with molten lead? If lead can absorb or block radiation, would it be possible to pump molten lead into a reactor core which is melting, so that it would eventually cool and contain the radiation?
Is there something that can be dumped into the core that will both stop the reac... | Meltdown containment: Sounds like an option would be boron mixed with wet wet cement pumped through long flexible tubing with a water flush to keep it moving and a pump replaceable and far away from the meltdown far away from being affected. Forget recovery (containment). Pile it high and thick over the top. Dig deep u... | {
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For an accelerated charge to radiate, is an electromagnetic field as the source necessary? For an accelerated charge to radiate, must an electromagnetic field be the source of the force?
Would it radiate if accelerated by a gravitational field?
| If you mean an external EMF, the answer is "The radiation is determined with an external filed". The charge acceleration is proportional to the external field, and a single accelerated charge radiates.
If you mean the radiated field influence on the charge motion and subsequent radiation, the answer is "No" because th... | {
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How much radiation exposure in the US was caused by the 105 nuke tests in the Pacific? Between 1947 and 1962 the US conducted 105 tests of nuclear weapons in the "Pacific Proving Grounds". I'm wondering how much radiation exposure resulted on the west coast of the US. These were part of the 1056 nuclear bombs that the ... | There are a lot of works contained in proceedings related to the IAEA, but one very interesting publication is a study of deposition of long lived isotopes as monitored at Tsukuba since 1956. The period of study includes all of the nuclear weapons testing period, and also capturing the Chernobyl accident. The report ... | {
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Why does nuclear fuel not form a critical mass in the course of a meltdown? A BWR reactor core may contain up to 146 tons of uranium. Why does it not form a critical mass when molten? Are there any estimates of the critical mass of the resulting zirconium alloy, steel, concrete and uranium oxide mixture?
| My guess would be that the moderator (normally the water, graphite already would have caused the accident) is missing and that is still vital in a compacted mass. The uranium oxide is not enriched to military grade, but I can't speak for MOx-elements.
Should be difficult to say without some decent figures about leftove... | {
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What is the most energy efficient way to boil an egg? Starting with a pot of cold tap water, I want to cook a hard-boiled egg using the minimum amount of energy. Is it more energy efficient to bring a pot to boil first and then put the egg in it, or to put the egg in the pot of cold water first and let it heat up with ... | My cookbook says an egg should simmer in water for about 10 minutes. If you wait till the water simmers and then add the egg, the water will start boiling again in a few seconds, then needs to simmer for the 10 minutes. The heat of vaporization loss takes place for about 10 minutes.
If the egg is placed in cold water f... | {
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Light bending surfaces and energy funneling properties In the last year there has been fuzz regarding metamaterials studied for the purpose of cloaking, and it seem to me they are somewhat glorified 2D waveguides, but in any case it seems a reasonable application of this to funnel radiation captured over a wide area of... | Assuming that you have a source whose temperature is T, the best any optics system can do (in applying the energy from the source to a target) is in such a way that the target may be heated up to the temperature T. This is because of a basic law of thermodynamics: heat flows from hot things to cold things and never vic... | {
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Quaternions and 4-vectors I recently realised that quaternions could be used to write intervals or norms of vectors in special relativity:
$$(t,ix,jy,kz)^2 = t^2 + (ix)^2 + (jy)^2 + (kz)^2 = t^2 - x^2 - y^2 - z^2$$
Is it useful? Is it used? Does it bring anything? Or is it just funny?
| You've stumbled on a fertile area. Though not strictly what you were asking about, I can tell you that perhaps the most interesting relationship between orthogonal groups and quaternions comes from looking at spinors. As you may know, the symmetry group called $Spin$ double covers the group of rotations, and is the m... | {
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Where's earths death bulge, destroying everything in it's path? I was watching a BBC documentary on space last night. It was talking about gravity, and it said that the reason we only ever see one side of the moon, is because the earths gravity is strong enough to actually stretch the moon into a longer shape, creatin... | It would be good if you read an article about tides, and the bulge the sun/moon combination makes on the earth, seas and crust. Earth tides are interesting, the whole crust moves reaching 55 cms at places.
| {
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If the universe were a fractal Inflation seems to solve many of the problems of cosmology like horizon problem, flatness problem etc. Now suppose, I am a devil's advocate and tries to find holes in this beautiful theory. I argue that the early universe were having a fractal geometry. For any generic initial conditions ... | The universe is a fractal according to inflation, or very nearly. The product of inflation is very close to a scale-invariant spectrum, which is a fractal spectrum, in that rescaling the fluctuations gives almost the same result. This fractal-ness is amplified to the current filamentous fractal structure of galaxies an... | {
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Gravity and the Standard Model Gravity is ignored in the SM. The proton rest mass is ~0.938 GeV/$c^2$. LHC protons will move with 7 TeV energy, presumably with a relativistic mass about 7,450 times rest mass. A cosmic ray with the highest energy was detected at about $6\times 10^{21}$ eV. If it was a proton, its relati... | This question is a bit open ended. There are theories and maybe some experimental hints of extra large dimensions and black hole or AdS amplitudes with heavy ion collisions. The jury is of course still out, but there might be some gravity physics creeping into the standard model + QCD in the TeV energy range and abov... | {
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Representation of quantum transformations as matrices I was reading Quantum Computation explained to my mother, which makes the following claim
Postulate 2 A closed physical system
in state V will evolve into a new
state W , after a certain period of
time, according to W = UV where U is a
n × n unit matrix of ... | If we assume time evolution preserves the Hilbert space norm, then Wigner had shown it can only be a linear unitary transformation, or an antilinear antiunitary transformation. If time evolution is continuous in time, it can't possibly be antiunitary as there's no continuous deformation of the identity operator to an a... | {
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What future technologies does particle physics and string theory promise? What practical application can we expect from particle physics a century or two from now? What use can we make of quark-gluon plasmas or strange quarks? How can we harness W- and Z-bosons or the Higgs boson? Nuclear physics has given us nuclear p... | Here are some possible applications of neutrinos
Submarine neutrino communication
Demonstration of Communication using Neutrinos
Searching for cavities of various densities in the Earth's crust with a low-energy electron-antineutrino beta-beam
| {
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Definitions and usage of Covariant, Form-invariant & Invariant? Just wondering about the definitions and usage of these three terms.
To my understanding so far, "covariant" and "form-invariant" are used when referring to physical laws, and these words are synonyms?
"Invariant" on the other hand refers to physical quant... | This is a good question because I think physicists nowadays don't understand the difference between form invariant and covariant.
The equations of physics are form invariant under a Lorentz transformation, but they're not co-variant as in they don't vary with the Lorentz transformation.
| {
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Why there's a whirl when you drain the bathtub? At first I thought it's because of Coriolis, but then someone told me that at the bathtub scale that's not the predominant force in this phenomenon.
| The whirl happens in the draining tube, whose optimal solution to drain the bathtub is a laminar flow allowing for some rotation in the tube. What you see in the surface is the match between the solution of flow in the tube and the solution of flow in the surface.
Angular momentum of the flow gets modified a lot as the... | {
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How might a resonant antenna and black body radiation interact? How does an antenna behave when it is cooled so that its black-body radiation is emitting energy at its resonant frequency?
Edit: To clarify, its not how they're related in general, but how might thermal radiation and resonance interact with each other whe... | They're not related. The black-body radiation as well as the resonance curve may look like "bumps" but they are very different bumps mathematically. The black body radiation gets emitted at all frequencies, and the "uncertainty of the frequency" is maximized, in some sense. On the other hand, resonances are peaked arou... | {
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Alternative career paths in physics? What do you guys think of alternative career paths in physics away from academia free from the usual academic shackles?
Examples: Garrett Lisi who spends his time surfing and skiing while not working on E8.
Or Daniel Bedingham who is able to support himself part-time as an investmen... | Before closure, thanks for informing me of the foundational question institutes ' existence :) .
According to the link :
It has run two worldwide grant competitions. The first competition provided US $2M to 30 projects
Any researcher who can compete is free to try for those 30 grants. On the other hand academic and res... | {
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Does the foam on top of boiling maple sap affect the rate of evaporation? This is a serious question from someone engaged in evaporating large quantities of water to turn sap into syrup at this time of year.
Probably some background will help. When sap boils vigorously it creates quite a bit of foam, which will overflo... | I'm new at making syrup but the foam issue seems to relate to boiling water in a pot. A pot of hot water will rapidly boil with a lid, in this case a layer of foam, while an uncovered pot will barely form bubbles at the bottom of the pot. The foam seems to form a layer of insulation that allows the sap to reach a hig... | {
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Measuring acceleration of earth due to its fall around the sun Every orbiting of a satellite around a mass is nothing else but a constant fall - and therefore acceleration - towards this mass. In a way it is a "falling around" that mass.
My question Is it possible to measure this acceleration on earth due to its "falli... | The answer depends in part on what you mean by "measure". You can certainly calculate the acceleration using the laws of kinematics and dynamics, as Lawrence B. Crowell points out in his answer. Does that, in your mind, count as "measuring the acceleration"?
Here's a much more direct recipe that I think would uncontrov... | {
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How many Gs would a driver of the Bugatti Veyron experience on the Ehra-Lessien track when cornering before record attempt? Apologies if too specific.
Watched a documentary National Geographic Megafactories Bugatti Veyron
I told an colleague (engineer) about the need to warm the car up and then unleash it on the long s... | Neglecting friction, the force experienced is the Centrifugal Force $F=\frac{mv^2}{r}$ (it would be less if you included friction since the car actually slips) vectorially added to the orthogonal gravitational force $F_g=mg$, i.e. $F = m\sqrt{\left(\frac{v^2}r\right)^2 + g^2}$ where $g = 9.81 \frac{m}{s^2}$1. Divide th... | {
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Are the basic postulates of QM the only set of postulates that can give rise to a sensible semi-probabilistic physical theory? Are the basic postulates of QM, such as complex Hilbert space, unitary evolution, Hermitian operator observables, projection hypothesis etc., the unique and only set of postulates that gives ri... | No, in fact our current postulates allow certain ambiguity in the description of the same physical system (or at least of the possible set of measurements we can extract from them), suggesting that there might be a more concise underlying theory (or set of postulates) that groups such descriptions under a equivalence c... | {
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What reflective media do laser shows use? I am having a hard time in finding out what exact light media laser shows use. I am trying to build a laser show myself. I know that the laser light is reflected off these particles in such a way that that it makes the laser line "viewable" in all directions
Can somebody explai... | Note that there is a huge difference between standard particles (elementary, atoms, or molecules) and droplets. Droplets are quite macroscopic and having a definite spherical shape, they would act as nontrivial optical medium (think about rainbows caused by water droplets) which could selectively prefer some directions... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Where does the energy go, when light is blocked by polarisation I've been looking around about LCD monitors, and how they polarise light. When a pixel needs to be black, the light is "twisted" so that it can't go through the polarising sheet in front.
What happens to this light? Does it relfect back into the screen? Su... | It is possible to "block" light based on its polarization in a number of ways. In the situation you are describing, where the light hits a polarizing filter, it is simply absorbed by the filter. The filter does indeed heat up, and in fact if you put your hand near the screen you can usually feel that it is quite warm.
... | {
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How to measure the spin of a neutral particle? If a charged particle with charge $q$ and mass $m$ has spin $s \neq 0$ we can measure an intrinsic magnetic moment $\mu = g \frac{q}{2m}\hbar \sqrt{s(s+1)}$. This is how spin was discovered in the first place in the Stern-Gerlach Experiment.
But for a neutral particle $\mu... | another way to measure 'spin' is through scattering experiments as the scattering cross sections depend on the spin-spin interactions- the most famous example is two types of hydrogen molecules called ortho and para -hydrogen whose scattering with neutrons yielded different cross sections-see any standard textbook on n... | {
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What is the difference between $|0\rangle $ and $0$? What is the difference between $|0\rangle $ and $0$ in the context of $$a_- |0\rangle =0~?$$
| $|0\rangle$ is just a quantum state that happens to be labeled by the number 0. It's conventional to use that label to denote the ground state (or vacuum state), the one with the lowest energy. But the label you put on a quantum state is actually kind of arbitrary. You could choose a different convention in which you l... | {
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Can a disk like object (like UFO's) really fly? UFOs as shown in movies are shown as disk like objects with raised centers that emit some sort of light from bottom. Can such a thing fly?
My very limited knowledge in physics tell me that a disk like object may not be able to maneuver unless it has thrusters on sides and... | The lift works on the craft body by interaction between the curren on which flows through the body surface and the magnetic field of the body center. ”The law on the left Fleming."
| {
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"timestamp": "2023-03-29T00:00:00",
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"question_score": "5",
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What is a Kustaanheimo-Stiefel transformation? What is a Kustaanheimo-Stiefel transformation? Which applications has it in physics? Can you point me to a reference, where this transformation is explained?
| http://arxiv.org/abs/0803.4441
The Kustaanheimo-Stiefel transform turns a gravitational two-body problem into a harmonic oscillator, by going to four dimensions. In addition to the mathematical-physics interest, the KS transform has proved very useful in N-body simulations, where it helps handle close encounters. Yet ... | {
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Is it possible to know the exact values of momentum and velocity of a particle simultaneously? I know that by Heisenberg's Uncertainty Principle that it is not possible to know the exact values of position and momentum of a particle simultaneously, but can we know the exact values of momentum and velocity of a particle... | The argument that Heisenberg's Uncertainty Principle prohibits that we can know the exact values of momentum and velocity of a particle simultaneously is already discredited in the old textbook by Feynman on Quantum Electrodynamics.
Two observables can be simultaneously determined if the operators commute. For velocity... | {
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Supergravity calculation using computer algebra system in early days I was having a look at the original paper on supergravity by Ferrara, Freedman and van Nieuwenhuizen available here. The abstract has an interesting line saying that
Added note: This term has now been shown to vanish by a computer calculation, so tha... | (This is not really an answer, but here I have not yet enough reputation to post comments. If someone wants to move this to a comment, I won't object.)
1976 is not a particularly early date for computer calculations: Fermi, Pasta, and Ulam used computer simulations in the early 50s for their 1955 paper.
| {
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Why does a rotating tire use the static, rather than the dynamic coefficient of friction? The explanation I have heard of the difference between static and dynamic friction is that static friction is stronger because bonds form when one object is put on top of another object and these have to be overcome to get the mov... | I am not sure why you are rejecting the static friction on the basis on long the parts are in contact. A "bond" is not a chemical bond that might take time, but rather an interaction between adjacent molecules, or atoms. It propagates at the speed of light, so there is plenty of time for the adjacent molecules to "bond... | {
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Why do they store gold bars with the narrow side down? I watched on TV as they where showing gold bars stored in bank vaults and I noticed that they always stack them with the narrow side down and the wide side up. Like this:
So there has to be a mechanical reason why is that. Any ideas?
| The primary reason I have usually heard is that this makes it easier to lift them.
Pure gold is quite smooth, and very dense, and would be near impossible to lift from the other side.
| {
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What are constraints on a "purity" operator in quantum mechanics? Consider the normalized state, written in some orthonormal basis as:
$$\psi = A |0\rangle + B |1\rangle$$
Let's define a "purity operator" for a basis as any operator whose expectation value gives 1 for a pure state in this basis, and 0 for the most mixe... | From the example you've given, it's clear that you're using the wrong terms to describe what you want. Purity and mixedness apply to density operators and not to state vectors -- if your system is described by a state vector $|\psi\rangle$, it is already pure.
What you seem to want to know is whether there is an operat... | {
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"source": "stackexchange",
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What is meant by positive and negative gravity/energy/spacetime-curvature? I have recently come across some cosmological assertions (based on empirical data) about the universe being self contained in the sense that it is entirely capable of coming into existence from a zero-energy initial state. This is based on the o... | No answer I'm afraid but I'd add my naive request to that of Mumtaz. It's true that I did hear this "negative energy" claim from a popular science TV program but since it was made by Stephen Hawking himself one cannot dismiss it. He seemed to suggest that in the co-emergence of space and mass-energy to form the univers... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/9201",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Laplacian of $1/r^2$ (context: electromagnetism and Poisson equation) We know that a point charge $q$ located at the origin $r=0$ produces a potential $\sim \frac{q}{r}$, and this is consistent with the fact that the Laplacian of $\frac{q}{r}$ is
$$\nabla^2\frac{q}{r}~=~-4\pi q~ \delta^3(\vec{r}).$$
My question is, w... | Vladimir's answer is off by factor of 2. The laplacian is $\nabla^2(\frac{1}{r^2}) = \frac{4}{r^4}$ A potential that falls of as $\frac{1}{r^2}$ is a dipole (In general, if it falls off as $r^{-n}$ its an ($2^{n-1}$)-pole, e.g $\frac{1}{r^3}$ bheaviour is quadrupole, etc).
Is this a dirac delta? To find out, check : $... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
"answer_count": 5,
"answer_id": 1
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Testing General Relativity Ever since Einstein published his GR theory in 1916, there have been numerous experimental tests to confirm its correctness--and has passed with flying colors.
NASA and Stanford have just announced that their Gravity Probe B activity has confirmed GR's predicted geodetic and frame-dragging e... | Sure there are. The theory has been tested within only a teeny tiny part of the range of its predictions. For example it predicts gravitational redshift in the range of 0% (no redshift) to 100% (black hole), but experiments to date have shown a maximum gravitational redshift less than 0.01%. It matters less how many te... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/9474",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Far-field intensity from scattering of small particles Howdy, I'm building a simulation for looking at the light field underwater. In order to verify my simulation, I'm looking for some data showing the far-field intensity that comes from single scattering from many small particles in suspension. I suspect Mie theory p... | I was able to find experimental and simulated data for the plane intensity from multiple scattering of small (1, 5 and 10 $\mu$m spheres in the Thesis of Edouard Berrocal. His thesis can be downloaded here.
| {
"language": "en",
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"source": "stackexchange",
"question_score": "7",
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Is this a weather phenomenon or an instrumental artifact? The radar image of the midwest provided by Weatherunderground at 10:30 PM Central time, May 8 2011 has odd patterns.
Are these patterns real? Perhaps caused by large scale convection over cities? Or are they artifacts of radar placement?
Here is the image that ... | No proposed urban rainfall effect is dominant enough to cause that picture. But limited radar range, with radars being located in larger cities would easily explain it. The urban rainfall enhancement effect would have to be pretty extreme for it to be otherwise.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/9612",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
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"answer_id": 1
} |
Protons' repulsion within a nucleus Do the protons inside the nucleus repel each other by the electrostatic force? If they do, why doesn't the repulsion drive the protons apart so that the nuclei get disintegrated?
| There is an electrostatic repulsion between the protons in the nucleus. However, there is also an attraction due to another kind of force besides electromagnetism, namely the so-called "strong nuclear interaction".
The strong nuclear interaction ultimately boils down to the forces between the "colorful" quarks inside t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/9661",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Feedback on the paper, 'CCC-predicted low-variance circles in CMB sky and LCDM' by V. G. Gurzadyan and R. Penrose Ref: CCC-predicted low-variance circles in CMB sky and LCDM
To all cosmology / theoretical physics / related or similar researchers and academics,
Are there some updates concerning the issue of these concen... | Since the first paper that I associate the circles with the voids.
in the paper, about Fig 4
The distortions could be the result of
... or more likely, ...Indeed, the
presence of giant voids could
particularly influence such images
Gurzadyan V.G., Kocharyan A.A. (2009)
The concentric features reminds me a ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/9850",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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"answer_id": 2
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Why is there an absolute entropy? Why is there an absolute entropy? Given any non-discrete probability distribution, we don't really have an absolute entropy because the entropy depends on the parametrization of the distribution (e.g. Beta vs. Beta-prime) which was arbitrarily chosen. Another way to put it is that in... | The measure isn't arbitrary. In classical mechanics, the symplectic structure of phase space defines the Liouville measure. In quantum mechanics, the Hilbert space norm plays this role.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/9894",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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"answer_count": 1,
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} |
How to calculate the effect of roof items on gas mileage? I have a kayak and a bike. I routinely put them on top of my car and drive 60-70 mph for hundreds of miles. I am curious how much this affects my gas mileage.
| The best way: just do it. Go out and drive on the highway for some distance with the kayak and bike on top of your car, and measure the amount of fuel used, then do the same trip without the items on top of your car and measure the amount of fuel used in that case. The trip would have to be long enough that you can get... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Is Shor's algorithm a demonstration of the many worlds interpretation? David Deutsch is very fond of pointing out Shor's integer factorization algorithm is a demonstration of the many worlds interpretation. As he often asked, where else did all the exponentially many combinations happen?
Are there any other alternative... | Absolutely no! In the computational basis given by $\{|x\rangle \}_x$, it certainly looks like there is a massive parallelism going on. This is the wrong, wrong, wrong way of thinking about it. Everything clears up once you realize the "correct" preferred basis for Simon's algorithm is actually $\left \{ \frac{1}{\sqrt... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/10062",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "19",
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} |
5MHz RF pulse frequency analysed in software Is there software available that can analyse a 5MHz RF pulse to give a plot of frequency spectrum.
The signal data is visible on a LCD screen or a print out could be obtained.
| Thanks for your solutions they have confirmed my initial thoughts.
A 5MHz pulse of 3 or 4 cycles will have a bandwidth of 1 or 2 MHz but it is the profile of the spectrum that I need.
I also need a windows utility to digitise the pulse, so I may try Getdata or Dagra either can produce a file for input to excel but the... | {
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"url": "https://physics.stackexchange.com/questions/10204",
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"question_score": "3",
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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... | Consider an EPR experiment where an entangled pair of electrons is created. One of them hits a detector which finds its spin to be up. The other hits a detector at some distance. The first detector sends a light signal to the vicinity of the distant detector. That signal arrives before the other electron. Near tha... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 6,
"answer_id": 4
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What happens if you connect a hot resistor to a cold resistor? Kind of an extension to this question:
If you heat up an object, and put it in contact with a colder object, in an ideal insulated box, the heat from one will transfer to the other through thermal conduction and they will eventually reach an equilibrium tem... | 4kTBR is an approximation.
For very high frequencies or very low temperatures, quantum effects kick in. That's what limits the amount of power transferred, not the RF properties of real resistors.
Look it up on Wikipedia - Johnson Noise
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/10293",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 3,
"answer_id": 2
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Graduate Physics Problems Books Need to brush up on my late-undergrad and early-grad physics and was wondering if anyone can recommend books or lecture notes (hard copy, or on-line) that also have solutions.
Two that I have come across are:
Princeton Problems in Physics with Solutions - Nathan Newbury
University of Ch... | "Problem Book on Relativity and Gravitation" - A. Lightman, W. Press, R. Price, S. Teukolsky
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/10325",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "24",
"answer_count": 11,
"answer_id": 3
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Inflating a balloon (expansion resistance) I am doing a quick calculation on how to calculate the pressure needed to inflate a perfectly spherical balloon to a certain volume, however I have difficulties with the fact that the balloon (rubber) has resistance to stretching and how this affects the pressure needed. It ha... | The complete stress tensor, while accurate, is largely unnecessary for solving this problem, as it is a thin walled pressure vessel
Assuming the balloon is spherical, the strain can just be calculated from the current and initial radii.
$$\epsilon=\frac{r}{r_0}-1$$
The stress can be found using the modulus of elasticit... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why does the road look like it's wet on hot days? Often, I'll be driving down the road on a summer day, and as I look ahead toward the horizon, I notice that the road looks like there's a puddle of water on it, or that it was somehow wet. Of course, as I get closer, the effect disappears.
I know that it is some kind of... | Mirage is an optical phenomenon very common in sunny days. It's caused by the redirection of the reflected light rays form the object, in other words, is a real physical phenomenon and not just an optical illusion. The sun light in the direction of the road gets refracted do to the temperature gradient (continuous chan... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/10464",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "26",
"answer_count": 5,
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Helmholtz decomposition in the plane Prove or disprove the following proposition:
For any smooth plane vector field $\mathbf{H}=\left(H_x,H_y\right)$, there exist scalar potentials $\phi$, $\psi$ such that
$H_x=\frac{\partial \phi }{\partial x}+\frac{\partial \psi }{\partial y}$
$H_y=\frac{\partial \phi }{\partial y}-\... | We can certainly find a $\psi$ that solves the following partial differential equation
$\frac{\partial ^2\psi }{\partial x^2}+\frac{\partial ^2\psi }{\partial y^2}=\frac{\partial H_x}{\partial y}-\frac{\partial H_y}{\partial x}$
It then follows that
$\frac{\partial }{\partial y}\left(H_x-\frac{\partial \psi }{\partial ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/10525",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 2,
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Does a magnetic field do work on an intrinsic magnetic dipole? When you release a magnetic dipole in a nonuniform magnetic field, it will accelerate.
I understand that for current loops (and other such macroscopic objects) the magnetic moment comes from moving charges, and since magnetic fields do no work on charges ($... | See Appendix B on page 47 and further of this article:
Note that the failure of the “rest mass” m to be constant resolves a paradox concerning
what one is taught in elementary physics courses: On one hand, one is (correctly) taught
that an external magnetic field can “do no work” on a body, so a body moving in an e... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/10565",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "43",
"answer_count": 7,
"answer_id": 3
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How do laser rangefinders work when the object surface is not perpendicular to the laser beam? I find the functioning of a laser rangefinder confusing.
The explanation usually goes like this: "you shine a laser beam onto the object, the laser beam gets reflected and gets back to the device and time required for that is... | Simply what it means is if you can see the laser dot on the wall the rangefinder can see it 1000s better! Don't think of it as a reflection coming off the fur of a bear at 300 yards. That seems stupid but if you aim a laser at a bear at 300 yards and had a telescope, you would and could see the dot on the bears fur. Th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/10695",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 4,
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Can heat be transfered via magnetic field in a vacuum? Say you want to store hot coffee in a container surrounded by a vacuum. To remove all sources of conductive energy loss the container is suspended in the vacuum by a magnetic field and does not have a physical connection to the sides of the vacuum chamber,
My quest... | I would say the first point to stress here is that heat by definition is the transfer of energy. 'Heat loss' can occur via convection, conduction or radiation. Clearly, the first two can be essentially reduced to zero by surrounding your coffee (or whatever) with a perfect vacuum. Creating a perfect vacuum is pretty mu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/10745",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 5,
"answer_id": 3
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Where is spin in the Schroedinger equation of an electron in the hydrogen atom? In my current quantum mechanics, course, we have derived in full (I believe?) the wave equations for the time-independent stationary states of the hydrogen atom.
We are told that the Pauli Exclusion principle is a consequence of two electro... | A description of electron spin and the Pauli exclusion principle needs to go beyond the Schrödinger-equation to the spinor-valued Dirac-equation.
I don't remember my atomic physics course very well but at the level of your analysis I think you just add the rule of the two parallel spin orbitals explicitly.
For a discus... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/10837",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
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