Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Tricky spring on a surface question I have this relative simple-looking question that I haven't been able to solve for hours now, it's one of those questions that just drive you nuts if you don't know how to do it.
This is the scenario:
I have a spring that is on a flat surface, the springs details are like this:
sprin... | Basically at a point on the spring where y is displacement from the equilibrium condition, you'll get a differential equation $d^2/dt^2 (Y \times density) = -d^2Y/dZ^2 \times k$ the spring constant. (sorry I can't use Latex)! If we postulate that solutions look like $e^{ikZ +i\omega t}$, $ 2\pi\omega$ will be the frequ... | {
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movement of photons In a typical photon experiment the photon is depicted as moving across the page, say from right to left.
Suppose we were actually able to witness such an experiment, from the side (to position of reader to a page).
If the photon is actually moving from left to right can I, standing at 90 degrees to... | The simple answer is no, the eye can only detect photons by their direct interaction with the retina. In this case, the photon is not "visible", since it is not itself incident on the eye, nor emits "secondary" photons that indicate its position.
| {
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Vortex in liquid collects particles in center At xmas, I had a cup of tea with some debris at the bottom from the leaves. With less than an inch of tea left, I'd shake the cup to get a little vortex going, then stop shaking and watch it spin. At first, the particles were dispersed fairly evenly throughout the liquid,... | If you check Bernoulli's equation across streamlines (not along), you will see that particles with larger radius have higher static pressure than those with small radius, which actually drives the motion towards the center:
$${P\over\rho} + \int {V^2\over R}dn + gz = {\rm const}$$
When: $R \to {\rm small} \implies \int... | {
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Your favorite Physics/Astrophysics blogs? What are the Physics/Astrophysics blogs you regularly read? I'm looking to beef up my RSS feeds to catch up with during my long commutes. I'd like to discover lesser-known gems (e.g. not well known blogs such as Cosmic Variance), possibly that are updated regularly and recently... | Cosmic Variance
Science, Technology, and The Future
NOTE It would be great if someone who knows the blog well would write a few words about it. Just give a little more detail of what it's about. 3 sentences is more than enough. This is community wiki, so most people can edit it freely.
| {
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"source": "stackexchange",
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What would happen if you put your hand in front of the 7 TeV beam at LHC? Some speculation here:
http://www.youtube.com/watch?v=_NMqPT6oKJ8
Is there a possibility it would pass 'undetected' through your hand, or is it certain death?
Can you conclude it to be vital, or only loose your hand?
Would it simply make a small ... | What Gibbs said (+1), except that because the beam is highly relativistic, the probability of radiation being sent in directions other than down the beam line is very low. You can see this by looking at the problem in the center of mass reference frame for a typical collision. Because special relativity increases the m... | {
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What is the difference between a complex scalar field and two real scalar fields? Consider a complex scalar field $\phi$ with the Lagrangian:
$$L = \partial_\mu\phi^\dagger\partial^\mu\phi - m^2 \phi^\dagger\phi.$$
Consider also two real scalar fields $\phi_1$ and $\phi_2$ with the Lagrangian:
$$L = \frac12\partial_\mu... | I think the free Lagrangian alone does not give the physical content. We can also alternatively represent $\phi = \phi_0 \exp(i \theta)$. Then we have
$$ L = { 1 \over 2} \partial^\mu \phi_0 \partial_\mu \phi_0 + m^2 \phi_0^2 + {1 \over 2} \partial^\mu \theta \partial_\mu \theta $$
Here we can also ask whether we... | {
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Can spacetime be non-orientable? This question asks what constraints there are on the global topology of spacetime from the Einstein equations. It seems to me the quotient of any global solution can in turn be a global solution. In particular, there should be non-orientable solutions.
But does quantum physics place any... | Space could be non-orientable. All spacetimes are locally orientable. To be non-orientable a space has to have some loops that cannot be shrunk to a point. It is only when going round such a loop that non-orientability could reveal itself (For example you don't know that a Mobius strip is non-orientable unless you go r... | {
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Two slit experiment: Where does the energy go? In Physics class we were doing the two slit experiment with a helium-neon red laser. We used this to work out the wavelength of the laser light to a high degree of accuracy. On the piece of paper the light shined on there were patterns of interference, both constructive an... | Energy is indeed conserved. The link below gives a nice explanation...
http://skullsinthestars.com/2010/04/07/wave-interference-where-does-the-energy-go/
| {
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Stopping Distance (frictionless) Assuming I have a body travelling in space at a rate of $1000~\text{m/s}$. Let's also assume my maximum deceleration speed is $10~\text{m/s}^2$. How can I calculate the minimum stopping distance of the body?
All the formulas I can find seem to require either time or distance, but not on... | The formula you want is
$$v_f^2 = v_i^2 + 2a(x_f - x_i)$$
It's one of the basic kinematic formulas taught in high school (or even middle school) physics classes.
| {
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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... | You slightly misinterpreted your results. They don't just fall more slowly, they accelerate more slowly.
More magnets will cause the acceleration of the object to reduce. Once you have enough magnets to provide enough force to overcome the force on your object due to gravity, then it will stay up.
The same is true of y... | {
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Empty universe in the past, non-empty in the future My question is the following. Are there solutions to the Einstein field equations, which have the property that there is a hypersurface of constant time and to the past of that surface space is empty (Minkowski space-time) and to the future it is not (non-vanishing st... | If there existed at some point the same amount of matter and antimatter, should there not be a signature in the microwave background radiation? I would expect that the annihilation of electrons and positrons should still be a separate bump?
| {
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Why beauty is a good guide in physics? Dirac once said that he was mainly guided by mathematical beauty more than anything else in his discovery of the famous Dirac equation. Most of the deepest equations of physics are also the most beautiful ones e.g. Maxwell's equations of classical electrodynamics, Einstein's equat... | Although I agree, beauty can be seductive and may be related to our evolutionary development of "pattern forming" in the brain--we seem inclined to find symmetry beautiful. Effective theories are often ugly as sin---take a look at the Standard Model Lagrangian and tell me it is beautiful :)
http://nuclear.ucdavis.edu/... | {
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Polarization of the gluon I think that, by now, it's understood that the gluon propagator in QCD has a dynamically generated mass. Ok, so my question is the following: where does the extra polarization degree of freedom come from? Or, asking in another way: suppose you try to define an S matrix for QCD, apart from the ... | I'm not sure this is useful, but I suppose that the problem with an S-matrix for gluons is that the gluons are not free. That is, an S-matrix deals with free particles that interact, perhaps exchange bodily fluids (i.e. charge or whatever), and then escape to infinity. But the real questions with gluons have to do with... | {
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Determining Maximum Velocity of an object traveling horizontally I'm in the process of working on a physics related game. I'm looking to find the maximum velocity of an object given it's mass and the force acting on it when it is traveling horizontally. I believe there must be a method of calculating this but I'm una... | Suitable for game physics and BoTE calculations:
*
*Assume a functional form for the frictional resistances (all the apply from rolling, sliding and fluid (wind or water)), and solve for the total resistance equal to the driving force.
*If that does not limit the speed to a reasonable velocity and this even takes p... | {
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Does entropy apply to Newton's First Law or does "acted upon" always require an external factor?
First law: Every body remains in a state of rest or uniform motion (constant velocity) unless it is acted upon by an external unbalanced force. This means that in the absence of a non-zero net force, the center of mass of ... | If you ignore the microscopic explanation of entropy, entropy is just an internal state of a system, on par with the system's volume, or the number of particles in the system. If you have a gas with a fixed entropy (let's store it in a vacuum tube so it doesn't escape, and let's give the tube infinite insulation so it... | {
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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.
| I would actually emphasize the difference between the forces, rather than the similarity. Although we (as theorists) like to bundle the whole shebang into a "neat" $U(1)\times SU(2) \times SU(3)$ gauge structure (and possible some gauge version of gravity), it doesn't mean that reality has to be that neat (e.g. chirali... | {
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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... | Newton second law is known as fundamental law of mechanics, because it is supposed to solve the fundamental problem of mechanics, that is, finding the position of a particle at any given moment in time, i.e., to find
$$
x=f(t)
$$
Plot of $x=f(t)$ can only be a straight line (a special type of curve with curvature=0) o... | {
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"source": "stackexchange",
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Homework about spinning top I have a top of unknown mass that has a moment of inertia $I=4\times 10^{-7} kg \cdot m^2$. A string is wrapped around the top and pulls it so that its tension is kept at 5.57 N for a distance of .8 m.
Could somebody help me derive some equations to help with this? Or to get me in the right ... | This question and ones like it are trying to get at the 'transferability' of energy between different frames of reference. You begin in a linear domain and move to a rotational domain. Whether you are considering the problem in the linear or rotational sense the inherent physics remains the same (at least in elementa... | {
"language": "en",
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"source": "stackexchange",
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neutrinos by formation of "neutron pairs" Here :
http://www.newscientist.com/article/dn20084-neutron-star-seen-forming-exotic-new-state-of-matter.html
are news on superfluidity in a neutron star. The necessary bosons they say are pairs of neutrons. So far, so good.
But then they postulate the production of neutrinos i... | The phenomenon was first predicted in this paper:
"Neutrino pair emission from finite-temperature neutron superfluid and the cooling of young neutron stars"
Flowers E. G., Ruderman M., Sutherland P. G., 1976, ApJ, 205,541
PDF here
The process they are describing is actually $n^*n^*\to\nu\overline\nu$, where $n^*$ is a... | {
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Electromagnetic fields vs electromagnetic radiation As I understand, light is what is more generally called "electromagnetic radiation", right?
The energy radiated by a star, by an antenna, by a light bulb, by your cell phone, etc.. are all the same kind of energy: electromagnetic energy, i.e. photons traveling through... | Electromagnetic radiation consists of waves of electric and magnetic fields, but not all configurations of electric and magnetic fields are described as "radiation." Certainly static fields, like the Earth's magnetic field and the other fields you describe, are not called "radiation."
There is a standard technical defi... | {
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What is the usefulness of the Wigner-Eckart theorem? I am doing some self-study in between undergrad and grad school and I came across the beastly Wigner-Eckart theorem in Sakurai's Modern Quantum Mechanics. I was wondering if someone could tell me why it is useful and perhaps just help me understand a bit more about ... | I will not get into theoretical details -- Luboš ad Marek did that better than I'm able to.
Let me give an example instead: suppose that we need to calculate this integral:
$\int d\Omega (Y_{3m_1})^*Y_{2m_2}Y_{1m_3}$
Here $Y_{lm}$ -- are spherical harmonics and we integrate over the sphere $d\Omega=\sin\theta d\theta d... | {
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Does Wick rotation work for quantum gravity? Does Wick rotation work for quantum gravity? The Euclidean Einstein-Hilbert action isn't bounded from below.
| Wick rotation might work for backgrounds with an asymptotically timelike Killing vector isometry like asymptotically flat metrics and asymptotically anti de Sitter. It might also work when there's an asymptotic Killing vector which is either timelike to null at some horizon with what lying beyond truncated. Examples ar... | {
"language": "en",
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Colder surface radiates to warmer surface When radiation from a colder source arrives at a warmer surface there is some debate about what happens next. To make the question more concrete lets say that the colder source is at temperature 288K. The warmer surface is at 888K and has emissivity of 1.
3 possibilities
*
*... | The hotter object absorbs external radiation as well as it absorbs its own radiation inside the body before it reaches its surface.
The heat loss of a hot object (radiated power) is determined with the object temperature but the rate of cooling down (if there is cooling down $dT/dt < 0$) is smaller in case of addition... | {
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Did spacetime start with the Big bang? Did spacetime start with the Big Bang? I mean, was there any presence of this spacetime we are experiencing now before big bang? And could there be a presence/existence of any other space-time before the big bang?
| This relies on an empirical finding as to whether spacetime is finite or infinite. We already know that the Big Bang occured a finite amount of time ago.
If spacetime now is discovered to be finite then the Big Bang started at a point.
If spacetime now is discovered to infinite then spacetime at the Big Bang was also i... | {
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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... | The resistance between two electrodes each of radius r0 (not points) separated by a distance of 2S on an infinite plane is given by
arcosh(s/r0)/pi/resistivity
https://www.physicsforums.com/proxy.php?image=http%3A%2F%2Fimg11.hostingpics.net%2Fpics%2F843563pourforum11.jpg&hash=7b69021109a0ada9b50b7ba16cfd1414
See also ... | {
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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 ... | Possibly because the punch has less force behind it, if you meet it earlier. Can't say I ever heard of this conventional wisdom, but then again, I haven't been into many fights or rings.
| {
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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... | If you hold a spoon firmly and move it back and forth perpendicular to the face of the spoon at a certain rate you will cause stable cavitation and extreme turbulence that does not splash from the cup. I do this all the time when dissolving sugar in kool-aid but with practice I think it might cool the coffee faster. ... | {
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Difference between electric field $\mathbf E$ and electric displacement field $\mathbf D$ $$\mathbf D = \varepsilon \mathbf E$$
I don't understand the difference between $\mathbf D$ and $\mathbf E$.
When I have a plate capacitor, a different medium inside will change $\mathbf D$, right?
$\mathbf E$ is only dependent f... | The electrical field $\mathbf E$ is the fundamental one. In principle, you don't need the electrical displacement field $\mathbf D$, everything can be expressed in terms of the field $\mathbf E$ alone.
This works well for the vacuum. However, to describe electromagnetic fields in matter, it is convenient to introduce a... | {
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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... | Here's a recent science update to this question: Gravity propagates at the speed of light at least to a precision of one part in $10^{15}$. This has been measured directly in 2017 when a Binary Neutron Star Merger happened that was both seen in gravitational waves (GW170817) and in gamma rays (GRB 170817A). In particul... | {
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What does it take to become a top physicist? What does it take to become a top physicist?
Why do so many extremely talented young upstarts totally flop as they move to more advanced physics?
| Do not Despair :) .
What does it take to become a top physicist?
To start with one has to be a physicist. A physicist is one who studies physics because of a burning curiosity about how the material world works and tries to satisfy it by going to graduate school and accumulating knowledge .
Now a "middle of the drawer"... | {
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Has every possible interaction between elementary particles been observed? There are some interactions that are forbidden by conservation laws, e.g. an electron cannot turn into a positron by conservation of charge and a photon cannot turn into a positron electron pair by conservation of momentum.
My question is if eve... | *
*proton decay is un-observed, and suspected on the basis of various Beyond the Standard Model theories
*Nothing directly involving the Higgs had been published when the question was asked, but ATLAS and CMS have pretty definitive observations of the most easily measured channels. Some of the harder channels are sti... | {
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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... | Extra-dimensional scenarios may be described as "inspired" by string theory but they are independent hypotheses and they may be true even if string theory is not. However, one has to reduce the ambitions and standards of consistency.
Sociologically, it's surely true that the research of models with extra dimensions has... | {
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References about rigorous thermodynamics Can you suggest some references for rigorous treatment of thermodynamics? I want things like reversibility, equilibrium to be clearly defined in terms of the basic assumptions of the framework.
| *
*The pioneer of the rigorous treatment of thermodynamics is Constantin Carathéodory. His article (Carathéodory, C., Untersuchung über die Grundlagen der Thermodynamik, Math. Annalen
67, 355-386) is cited everywhere in this context, but probably you want some newer and more modern things.
*Buchdahl wrote a lot of p... | {
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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?
| This statement is true and a direct consequence of the 5th Law of Thermodynamics, the Onsager Relations for which Lars Onsager of Yale received the Nobel Prize in 1968.
In an electrical circuit, for DC, current takes the path of least reisitance;
For AC it takes the path of least inductance (impedance).
So a pulse of v... | {
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How do you derive Noether's theorem when the action combines chiral, antichiral, and full superspace? How do you derive Noether's theorem when the action combines chiral, antichiral, and full superspace?
| You can think of a generalized innerproduct, where terms get integrated over the "correct" superspace. In my view, the best way of deriving the propagators for chiral fields. It's much cleaner than lifting everything up to full superspace.
An example of this occurs in section 4.8 of Ideas and methods of supersymmetry a... | {
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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... | No, It was CG. The video-maker himself said it. Here: http://forums.cgsociety.org/showthread.php?t=957350
| {
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meaning of an integral in the continuity equation This is about continuity equation. What does the last integral mean?
$$\frac{\mathrm{d}Q_V}{\mathrm{d}t}=\iiint_V \mathrm{d}^3x \,\frac{\partial\rho}{\partial t}=-\iiint_V\! \mathrm{d}^3x\,\operatorname{div}\,\mathbf{j}=-\iint\limits_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\... | The last integral is a surface integral. It is the fluid (current) flux crossing the volume surface integrated over the whole surface. It is how much charge is leaving the volume per second. ($\partial V$ means boundary of V and you sum all local $j_\bot dS$.)
| {
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Magnetic moment of relativistic rotating ring Let's consider rotating charged ring. Theoretically mass of this ring has no limit as rotation speed increases. So what about magnetic moment of the ring? Is it limited by the value of speed of light?
| The magnetic moment of a rotating charged ring is
$$
m=IA=\lambda v A.
$$
Here $I$ is current, $\lambda$ is linear charge density, and $A$ is the enclosed area. This expression is true even relativistically. The quantities $\lambda,A$ don't depend on the rotation speed, so the magnetic moment is limited to $\lambda c... | {
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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.... | E. Zeidler, Quantum Field theory I Basics in Mathematics and Physics, Springer 2006. http://www.mis.mpg.de/zeidler/qft.html
is a book I highly recommend. It is the first volume of a sequence, of which not all volumes have been published yet. This volume gives an overview over the main mathematical techniques used in qu... | {
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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?
| $g$ becomes $ g \approx 9.7 \frac{m}{s^2}$ at a height of about 35km, so it would be ok to use the value $9.81$ for "down to earth" problems.
The relevant wikipedia article has lots of useful information, like for example the following approximation formula for different heights: $$ g_h=g_0\left(\frac{r_e}{r_e+h}\ri... | {
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Arguments for and against Many Worlds? I would like to hear the best arguments for and against the Many Worlds interpretation of QM.
| A good argument against is Occham's razor. Another is the fact that it is not an experimental testable hypothesis. The best argument I think against it is the fact that the only reasons for Many-worlds are based in human language, whose intuition is only developed for a classical setting, as such any human meta-reaso... | {
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Neutron star references? I'm looking for contemporary reviews on neutron stars. Seems like this area is pretty active, so even reviews from five or ten years ago are somewhat lacking, though certainly not worthless. Does anyone have recommendations? Newer is better.
Books are okay too, but I'd prefer one of those 70-is... | I would suggest these from Living Reviews in Relativity,
Rotating Stars in Relativity, by Nikos Stergioulas,
Physics of Neutron Star Crusts, by Nicolas Chamel and Pawel Haensel and
Relativistic Fluid Dynamics: Physics for Many Different Scales, by Nils Andersson and Gregory L. Comer
| {
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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... | Mathematical Tools for Physics, James Nearing
Also available in paperback from Dover. Undergraduate-level math methods book. Clear writing, many problems and exercises (usually without solution). IMHO better than Boas.
| {
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Where should a physicist go to learn chemistry? I took an introductory chemistry course long ago, but the rules seemed arbitrary, and I've forgotten most of what I learned. Now that I have an undergraduate education in physics, I should be able to use physics to learn general chemistry more effectively. What resource... | I think you should have a look at "Understanding Molecules: Lectures on Chemistry for Physicists and Engineers". I haven't read it myself but it looks promising.
| {
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Gamma Ray Bubble at the center of our galaxy seen by Fermi Telescope How could we measure high energy photons, whithout measuring them ?
I can't understand how we can "see" those Gamma Ray Bubbles if they are not reaching here
In this graph from Nasa you can see those "bubbles" are not reaching solar system:
Then how ... | Concerning the 8-shaped bubbles around the galaxy, see
http://motls.blogspot.com/2010/11/fermi-milky-way-cutting-x-ray-infinity.html
http://arxiv.org/abs/arXiv:1005.5480
They're not pictures of photons - X-rays themselves. The infinity symbol is a picture of X-ray sources: we are observing the X-rays that came from t... | {
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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?
| In principle, as the others say, you need to calculate the integral of the speed over time to determine the distance traveled.
But a non-constant speed doesn't necessarily mean that the function that describes the speed is complicated. For instance, you may be able to know the average speed simply analyzing the speed f... | {
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Snell's law starting from QED? Can one "interpret" Snell's law in terms of QED and the photon picture? How would one justifiy this interpretation with some degree of mathematical rigour? At the end I would like to have a direct path from QED to Snell's law as an approximation which is mathematically exact to some degre... | This appears to be explained in detail in Feynman's "QED the strange theory of light and matter" in Chapter 2, page 39 to 45, of the 2006 edition, in more or less plain English.
| {
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Are water waves (i.e. on the surface of the ocean) longitudinal or transverse? I'm convinced that water waves for example:
are a combination of longitudinal and transverse. Any references or proofs of this or otherwise?
| Maybe sea waves are longitudinal at sea but when they hit the shallows of the shore they become transverse waves and take the shape of a wheel and roll towards the shore.
Just guessing this from my years of surfing. The waves are up & down out in the deep but turn into tubes when they reach the shallows.
| {
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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?
| There seems to be a known explanation. I quote from Composition, Structure, Dynamics, and Evolution of Saturn’s Rings, Larry W. Esposito (Annu. Rev. Earth Planet. Sci. 2010.38:383-410):
[The] rapid collision rate explains why each ring is a nearly flat disk. Starting with a set of particle orbits on eccentric and mutu... | {
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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.)
| I don't know anything about the history of the Bel and related measures.
Logarithmic scales--whether for audio intensities, Earthquake energies, astronomical brightnesses, etc--have two advantages:
*
*You can look at phenomena over a wide ranges of scales with numbers that remain conveniently human-sized all the tim... | {
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Is it possible for one side of the universe to "meet" the other? I've variously heard the shape of the universe being described as multi-dimensional, like a helix or mobius strip, and super string theorem seems to say there are lots of universes all piled up next to each other in vibrating planes.
My question is, can t... | The short answer is no!
More about imagination how space of our universe looks (and how expanding) today and in past check here :WMAP
| {
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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?
| It does have an effect.
Also see this paper about modelling tsunami propagation.
As noted in the paper, the Coriolis force only becomes important over large distances.
Here's an article on MathWorld including many references.
| {
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estimating ion collisions from Vlasov equations Suppose you have a distribution function $ f_{\alpha}( \vec{r} , \vec{p} , t)$ obtained from Vlasov equations for a certain $\alpha$ species, say some ions.
Is there a rigorous way (in the domain of validity of the model, that is) to estimate a collision density function... | I am not sure to understand your question because the vlasov equation is only valid for a collisionless plasma ... The interactions between particles is done through the long range mean electromagnetic field. If you want to include the collision operator you need to work with the Landau's equation or Fokker-Planck one.... | {
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Uses of the 'Golden Ratio' in Physics What are some physics applications of the golden ratio?
$$\varphi~=~ \frac{1+\sqrt{5}}{2}~\approx~ 1.6180339887\ldots$$
Does it ever function specifically as a constant in any formulas or theorems?
EDIT: Original title said Golden Radio... facepalm. I originally asked this questi... | Googling arxiv comes up with lots of hits. For example:
NewJ.Phys.11:063026 (2009), Adisorn Adulpravitchai, Alexander Blum, Werner Rodejohann, Golden Ratio Prediction for Solar Neutrino Mixing :
It has recently been speculated that the solar neutrino mixing angle is connected to the golden ratio $\phi$. Two such propos... | {
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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... | The GE Mark V containment system used at Fukushima has a design basis that calls for the concrete containment vessel to withstand a complete meltdown. This is typical of reactors in the US. There are many penetrations of the vessel and some of them may be leaking, but that does not necessarily mean the vessel was breac... | {
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Why does the light side of the moon appear not to line up correctly with the evening sun? I live at roughly $(52.4^\circ,-2.1^\circ)$. On sunny evenings I've often looked at the Moon and the Sun and noticed that the light part of the Moon does not appear to line up with the Sun. For example, at about 17:00 GMT on 13 Ma... | I am puzzled by you question. When one has two points, the sun and the moon, one can always find a line connecting them, by definition of line.
If you mean why the earth is not part of that straight line, it is because the moon has an orbit around the earth, and the angle of the line earth-moon changes. It is the reas... | {
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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?
| I suspect that two charged objects orbiting one another due to gravitational attraction would radiate, but I can't support that assertion with a citation.
The question of whether or not a charge radiates when it is uniformly accelerated by gravity is an open question; read the link for an excellent discussion of why.
E... | {
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CPT violation and how could quark masses differ from anti-quark masses? A recent experimental paper measures a difference between the top quark and anti-top quark masses:
Fermilab-Pub-11-062-E, CDF Collaboration, Measurement of the mass difference between $t$ and $\bar{t}$ quarks
We present a direct measurement of the... | There is one simple, obvious, and almost certainly correct theoretical explanation: two-sigma effects show up all the time and, like most of them, this one is not real.
| {
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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?
| Several things are required to cause a nuclear explosion. It is not just about mass... In terms of a melt down, perhaps heat is the real issue, because it expands the gap between atoms and this diminishes the target cross section for a neutron to strike, thus lengthening the mean neutron pathway.
Other issues include i... | {
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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 ... | I know the answer :).
The most energy efficient way to get a hard boiled egg is to have a pot with a good cover on an electric range.
1)cover the bottom of pot with 1mm water, put eggs in and pot on the range and and turn it on to the maximum.
2)when the cover starts popping, turn off heat completely, leave it on the r... | {
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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?
| Cornelius Lanczos has a chapter on quaternions and special relativity in his "The Variational Principles of Mechanics". So, is has been used. But it seems more straightforward to consider the multivector algebra of spacetime so t,x,y,z really are on the same footing.
| {
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Can electricity transfer radioactivity? If a cable used to power something is exposed to a radioactive source will it over time make the entire cable radioactive?
| A cable cannot transport radioactivity away from the reactor using electrical current as a transport mechanism.
Nevertheless - if a material is exposed to a source of particles of sufficiently high energy (high energy particle beam, or neutron beam, for instance), the material can become activated (meaning that some o... | {
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Are regular light bulbs better for the eyes than CFLs or "tube lights"? I've heard that regular light bulbs with a filament are better for the eyes. Is the spectrum of one worse than the other? If so, are there any regulations for their use in industrial settings for worker safety?
| It is possible that children growing up under one kind of light would be more likely to become nearsighted (for example) than under another kind of light. But we don't know.
What we do know is that children who spend a lot of time under sunlight grow up with better vision than those who spend more time indoors:
http://... | {
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What properties do you need for building a tower? When I was a boy I used to daydream about building a tower so tall that the top of it would project into near space.
There would perhaps be a zero gravity area in the penthouse where my friends and I could bounce around and play space versions of various earth-based gam... | Towers supported from the bottom are a bit tricky.
Buckling
limits how tall a column can be. One needs to additional lateral stiffness to overcome this, usually by putting up guy wires. Even so there are going to be real limits, as Anonymous Coward has mentioned above, solids obtain their stiffness from chemical inte... | {
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A Basic Question about Gravity, Inertia or Momentum or something along those lines Why is it that if I'm sitting on a seat on a bus or train and its moving quite fast, I am able to throw something in the air and easily catch it? Why is it that I haven't moved 'past' the thing during the time its travelling up and down?... | Momentum is conserved. If you are on a frame (the bus) moving at a velocity that is constant, then everything else is as well. The momentum of every object is $p~=~mv$. This is whether or not there is something holding to the frame. In the absence of some force a body maintains a constant momentum.
| {
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Do cosmological and Doppler redshift produce different patterns? For a given black body radiation curve, would the changes to the spectrum resulting from cosmological expansion and those from Doppler effects be distinguishable on the basis of the shapes of the resulting curves alone? Or, put another way, starting from ... | The redshift due to cosmological expansion is identical to a Doppler shift in its effect on the spectrum of any source. To be specific, both phenomena "stretch" all wavelengths by the same factor.
There's a very good reason for this: in a suitable coordinate system, the cosmological redshift is a Doppler shift.
You'll... | {
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Will Earth Hour do damage to power supply system? There is always a debate around Earth Hour every year, and the opposite side of Earth Hour usually claims that
The (sudden) decrease and increase of the power usage in the start and end of Earth Hour will cause much more power loss (than the save of power), and even do... | It is unlikely that the Earth Hour will cause substantial damage to the power supply system. However, it will require a lot of energy and manpower to adjust the power plants to the changes.
First of all, generators are automatically taken off the grid if it is detected that the power supply is higher than the current d... | {
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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... | Quantum Chromodynamics, the electroweak theory, or general theory of relativity - or quantum gravity and string theory - are not methods to obtain new devices; they're theories meant to understand the truth about the Universe.
I find it unlikely that any of those things will become practically useful. It may still hypo... | {
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Is it true that the angular momentum of electromagnetic waves in an anisotropic medium is an integral of motion? Extending my previous question Angular moment and EM wave, does it make sense to talk about the angular momentum of electromagnetic waves in an anisotropic medium? It is not obvious that the angular momentum... | As was pointed out in an answer to your previous question, the polarization of your beam can be thought of as the "spin" angular momentum being carried by it. Circularly polarized light carries angular momentum, linearly polarized light does not (not counting the "orbital" angular momentum carried by the spatial profil... | {
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Introductory texts for functionals and calculus of variation I am going to learn some math about functionALs (like functional derivative, functional integration, functional Fourier transform) and calculus of variation. Just looking forward to any good introductory text for this topic. Any idea will be appreciated.
| The standard encyclopedic treatise of nonlinear functional analysis is the 5 volume opus of Eberhard Zeidler, "Nonlinear Functional Analysis and Its Applications". It covers a lot of material about variational calculus, for example, in volume III "Variational Methods and Optimization". The applications are usually appl... | {
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Why does Venus spin in the opposite direction? Given: Law of Conservation of Angular Momentum.
*
*Reverse spinning with dense atmosphere (92 times > Earth & CO2 dominant sulphur based).
*Surface same degree of aging all over.
*Hypothetical large impact is not a sufficient answer.
Assuming any object large enough... | Well, I Binged and found some references.
Seems that a collision is most probable, if it happened at a time when the whole system was malleable. But there is no solid explanation.
| {
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Hawking's alternative to Higgs Boson I have seen in popular media, claims that Hawking does not believe the Higgs boson exists due to microscopic black holes and even made a bet against it. This is based on something published in journal Physical Review D.
I don't have access to journal Physical Review D, and I can't ... | There is a book review which mentions this:
Famously, Stephen Hawking made his bet for $100 with Gordy Kane that neither LEP nor any other particle collider would ever see the Higgs boson because of virtual black holes. Perhaps unsurprisingly, Peter Higgs was very doubtful of the calculations that lead Hawking to this... | {
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Massless charged particles Are there any massless (zero invariant mass) particles carrying electric charge?
If not, why not? Do we expect to see any or are they a theoretical impossibility?
| There are no massless particles with no electric charge. All the fermions have mass and the leptons that are not neutrinos have electric charge. The quarks also have electric charge. The Bosons, W+ and W- have mass and are charged. So as far as we know all particles that have charge have a reasonable amount of mass. Ho... | {
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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... | It could go either way. If you are heating the liquid to the boiling point, then the foam will not limit boiling (unless it raises the pressure), but will limit convection/advection of air near the surface. Note that latent heat of water vapor is not the only method of heat loss from your pot. If air advects/convects o... | {
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Collision time of Brownian particles Let's assume two spherical particles $p_1$ and $p_2$ of finite radius $r_1$ and $r_2$, which are at locations $(\pm\frac{d}{2},0,0)$ a distance $d$ apart at initial time $t$. These particles diffuse with coefficients $D_1$ and $D_2$, respectively. How can I obtain the probability di... | Marek suggested I post my comment (which doesn't completely answer the question) as an answer. Here it is:
Suppose you have two Brownian motions with diffusion coefficients $D_1$ and $D_2$, which start at the same point at $t=0$. Let $x_i$ be the average displacement vector for particle $i$ after time $t$. Then, $\lang... | {
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Measuring the spin of a single electron Is it possible to measure the spin of a single electron? What papers have been published on answering this question? Would the measurement require a super sensitive SQUID, Superconductive Quantum Interference Device?
| The ion trap experiments by Hans Dehmelt might be of interest. Though the scientific focus was the precision measurement of the g factor, you can't get far with that without first knowing that your trapped electron has spin 1/2 - or if you don't know that, you'll find out pretty quick when theory doesn't match experim... | {
"language": "en",
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Why are mirror images flipped horizontally but not vertically? Why is it that when you look in the mirror left and right directions appear flipped, but not the up and down?
| Take a picture and look at it. Now turn the picture to face the mirror. Question one: who flipped the picture? Answer: you did. Now, face the picture back to you, and walk to the nearest refrigerator. Turn the picture to face the refrigerator. Wow! Refrigerators flip images too! Don't believe me? Take your flipped page... | {
"language": "en",
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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... | There are some recent efforts in trying to derive the mathematical structure of quantum mechanics from some reasonable and/or operational axioms. You may want to give a look, for example, at http://arxiv.org/abs/1011.6451 and references therein.
| {
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What are the conditions to be satisfied by a theory in order to be a quantum theory? This is in continuation to my previous question. It is not a duplicate of the previous one. This question arises because of the answers and discussions in that question.
Can we call a theory, quantum theory, if it is consistent with HU... | Apparently, No. To quote SEP
A second point is the question whether the theoretical structure or the quantitative laws of quantum theory can indeed be derived on the basis of the uncertainty principle, as Heisenberg wished. Serious attempts to build up quantum theory as a full-fledged Theory of Principle on the basis ... | {
"language": "en",
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Are there examples in classical mechanics where D'Alembert's principle fails? D'Alembert's principle suggests that the work done by the internal forces for a virtual displacement of a mechanical system in harmony with the constraints is zero.
This is obviously true for the constraint of a rigid body where all the parti... | I have a interesting example:
Consider two blocks moving in a line, and an electric intelligent rod connects them. Everything is frictionless. The rod can make measurements of the coordinates of the two blocks, and change length to always makes sure that $x_2 = 2x_1$. Then we assume the mass of the rod is negligible, s... | {
"language": "en",
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Why do all the planets of the solar system orbit in roughly the same 2D plane?
*
*Most images you see of the solar system are 2D and all planets orbit in the same plane. In a 3D view, are really all planets orbiting in similar planes? Is there a reason for this? I'd expect that the orbits distributed all around the s... | Nic and Approximist's answers hit the main points, but it's worth adding an additional word on the reason the orbits lie roughly in the same plane: Conservation of angular momentum.
The Solar System began as a large cloud of stuff, many times larger than its current size. It had some very slight initial angular momentu... | {
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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... | Conservation of angular momentum is invoked for the neutrinos because beams of neutrinos cannot be collimated for an experimental measurement. Neutron spin can be measured in a Stern Gerlach setup.
The interactions and decays were carefully examined in various experiments and the only consistent spin values are the ... | {
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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 light below a UFO is actually ionized air. A light beam would not be visible by itself. According to some witnesses mentioned by Feindt the ionized air below is rotating, creating a Taylor column, which could explain why the heavy flying saucer shaped vehicle doesn't fall down. According to Hill pulsating forces ca... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Making a "heavier-than-air" craft float How big would a hollow rigid object need to be to float, (not in water but in air) if all of the air was vacuumed out and the container sealed?
| Another way to look at this is to solve for what weight/area you are allowed to use. Assume a spherical craft. Surface area goes up in proportion to r^2. Volume (which will generate your lift) is proportional to r^3. If you do the math, you find that you are allowed to use (r x 0.4)kg/m^2, or about (r x 0.88) lbs/m... | {
"language": "en",
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Have CMB photons "cooled" or been "stretched"? Introductory texts and popular accounts of why we see the "once hot" CMB as microwaves nearly always say something about the photons "cooling" since the Big Bang. But isn't that misleading? Don't those photons have long ("cool") wavelengths because space expanded since the... | I think the best way to think about it is that the sentence "the photons have cooled" is simply describing a fact, not explaining that fact. At early times, the photons at any given location had a thermal (blackbody) distribution corresponding to a high temperature (as measured by observers at rest in the natural, como... | {
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How many bits are needed to simulate the universe? This is not the same as: How many bytes can the observable universe store?
The Bekenstein bound tells us how many bits of data can be stored in a space. Using this value, we can determine the number of unique states this space can be in.
Imagine now, we are to simul... | Multiply the area of the cosmological horizon by 4 - you'll get the needed information quantity in nats. Convert into bits by dividing by $\ln 2$. You'll get the needed value.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/8895",
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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... | Van Nieuwenhuizen's PhD advisor, Matinus Veltman, was arguably the first person to develop a computer algebra system in the early 1960s, and the program was used in the proof of renormalization of gauge theories.
| {
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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.
|
...(the idea) "that space is continuous is, I believe, wrong."
— Professor Richard Feynman
The Messenger Series: Seeking New Laws
A discontinuous space | continuous meta-space model fits observed facts, and provides refreshing insights into many aspects of life.
| {
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"source": "stackexchange",
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More on matter and anti-matter
*
*Does every particle that has rest mass also have an anti-particle with which it would annihilate?
*Does annihilation only occur between like particles? For example what happens if a antineutron (anti u, anti d, anti d) collides with a proton (uud)? What happens if a positron colli... | *
*Yes, for charged particles and some neutral particles. But there are so-called Majorana neutral particles that have no antiparticles (neutral pion or eta-meson, for example). In other words, a Majorana particle is its own antiparticle.
*At low energies a proton annihilates with an antineutron like a proton with an... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What is the Physical Meaning of Commutation of Two Operators? I understand the mathematics of commutation relations and anti-commutation relations, but what does it physically mean for an observable (self-adjoint operator) to commute with another observable (self-adjoint operator) in quantum mechanics?
E.g. an operato... | When two qm operators do not commute, it means that we are missing stuff in Nature. That is quantum mechanics is a theory of measurement but not of Nature because of non-commutation. Hence this means that the stuff we miss cannot be described by quantum mechanics, and this leads to the conclusion that qm is not a com... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/9194",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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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... | I solved the Ising model:
I. A. Stepanov. Exact Solutions of the One-Dimensional, Two-Dimensional, and Three-Dimensional Ising Models. – Nano Science and Nano Technology: An Indian Journal. 2012. Vol. 6. No 3. 118 - 122. (The paper is on the Journal site with a free access)
| {
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"timestamp": "2023-03-29T00:00:00",
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"question_score": "54",
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When water is about to boil Have ever noticed? When water is about to boil, no matters the kettle, there is some sound I have no idea where it comes from, sometimes long before it boils.
Is there any explanation for this phenomena?
| I don't know how good this explanation is, but it is certainly plausible. The sound must be from bubble formation/popping. It seems the difference between the noise in the beginning and when the water is really boiling well is because in the initial phase, bubbles don't reach the surface.
| {
"language": "en",
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"source": "stackexchange",
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Anti-matter repelled by gravity - is it a serious hypothesis?
Possible Duplicate:
Why would Antimatter behave differently via Gravity?
Regarding the following statement in this article:
Most important of these is whether ordinary gravity attracts or repels antimatter. In other words, does antihydrogen fall up or do... | I can't guarantee the authenticity of the article. But it seems to me quite bizarre since I fail to see how something (even antimatter) can behave differently than matter in a gravitational field without violating the equivalence principle.
A positron for example is a hole in the Dirac sea and it has the same mass as o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/9375",
"timestamp": "2023-03-29T00:00:00",
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In what order should the subjects be studied in order to get to String Theory I know:
*
*Quantum Mechanics (Griffiths Level, currently doing Sakurai Level)
*Mechanics (Newtonian+ Lagrangian/Hamiltonian but at level lower than Goldstein/Landau)
*Classical Electrodynamics (Griffiths + electro/magnetostatics from Ja... | You can try reading Zwiebach 'A first course in String theory' which is roughly at your level right now. Its very handwavy, but well thats the best you can hope for at this level.
Otherwise, to really learn the subject you will absolutely need
1) Grad level GR
2) Quantum II, + 2 semester long courses in QFT
And then ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/9468",
"timestamp": "2023-03-29T00:00:00",
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Laplace's equation: Why is $\ell$ to be a non-negative integer? I have got some mathematical difficulties in the following exercise:
Calculate the potential of the polarized sphere along the $z$-axis. There are no free charges.
For this, we need to solve Laplace's equation, by using the method of separation of variab... | Since this question has a physics context, reasoning by its underlying physics can give you an answer. First of all, it is easy to see the radial equation has two solutions: $\frac{1}{r^l}$ and $r^{l+1}$. Since the field outside of the sphere must contain multipole components decaying as $\frac{1}{r}, \frac{1}{r^2}, ..... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/9555",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Neutrino Speed in Supernova I've read that neutrinos in supernova can be affected by "neutrino refraction." Is this analagous to the refraction of light, and if so, is the speed of these neutrinos similarly reduced from their near c speeds via this index of refraction?
| First, check this reference on Wikipedia.
Now, it is generally true that the "speed" (or, more accurately, the dispersion relation) of any particle is affected by a medium, where it travels. Well, of course, if the particle interacts with the medium.
For neutrinos the "slowing down" itself is absolutely negligible eve... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/9609",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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$cm^3/g$ as a unit of adsorption I recently saw $cm^3/g$ as a unit for amount adsorbed. Usually, you see either $\mathrm{kg_{adsorbate}/kg_{adsorbent}}$ or $\mathrm{mole_{adsorbate}/kg_{adsorbent}}$. Does anyone know the meaning of this unit?
| I've only ever seen those units described as "specific surface area". It does have implications for adsorption, but I don't think it is the be all and end all.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/9657",
"timestamp": "2023-03-29T00:00:00",
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Why is $\frac{dx}{dt}=0$ in this average momentum calculation? In the following excerpt from S. Gasiorowicz's Quantum Physics, he derives an expression for the average momentum of a free particle. $\psi(x,t)$ is the wave function of a free particle, $\psi^*$ denotes its complex conjugate.
We try the following: since c... | The confusion seems to stem from a) not understanding what kind of objects you are dealing with and b) usual custom of not writing (all) arguments of functions when they are understood.
To clarify a) note that the position operator $\hat x$ does not depend on time, and so also its kernel $\left< x \right | \hat{x} \lef... | {
"language": "en",
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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... | Energy is the ability of a system to perform work on another system. In other words, it's a property of a physical system. The annihilation of an electron and a positron performs work on the electromagnetic field by creating two photons. We usually do not talk about these processes in the same language that we use in c... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/9731",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
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"answer_id": 3
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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?
| The short answer is no.
The subject of super algebras is a large one as its a fairly new subject and the terminology hasn't settled down to a form that is clear and transparent to both physicists and mathematicians.
A super algebra, in its most widest sense, is an algebra that has an odd-even grading, usually called a ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/9945",
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