Convert running speed uphill to equivilent speed on flat

Given a certain running pace uphill, I want to be able to determine an equivalent pace running with no elevation change. Assumptions: similar effort in both cases (say for example running at 90% max heart rate), ignore wind, slope is constant for simplicity, ignore physiological and bio-mechanical factors, weight of the runner is 135 lbs if that matters. Example: Elevation change +236 feet, distance traveled 1 mile, elapsed time 6 minutes 55 seconds. What could I theoretically run for 1 mile with no elevation change given the same effort?


What is the effect of polarization on diffraction by a narrow slit?

Consider the well known demonstration of diffraction by a narrowing slit. (See for example the demonstration at the 30 minute mark of this lecture at MIT by Walter Lewin) It is my (possibly mistaken) understanding that the light emerging after the slit becomes substantially slimmer than one wavelength is polarized.   This would seem to imply that light of perpendicular polarization would not be transmitted, thus implying a fairly substantial and dramatic difference in the results of the experiment with parallel and perpendicularly polarized light. That is, instead of spreading out, the light polarized in the wrong direction would essentially just shut down as the slit narrows below one wavelength. Is this true?


following up dark matter accretion in supermassive black holes

A while ago, there was some conspicuous evidence that supermassive black holes didn't seem to be eating dark matter at the expected rate of 70%-30%, in fact, only 10% of the black hole mass increase could in principle be attributed to non-baryonic mass. Was there some follow-up evidence for or against this observation? because it is 2012 and every astrophysicist that is out there seems to be happy and dandy about dark matter, despite this huge clue (together with MOND, and the negative results from CoGENT) that dark matter doesn't actually exist


What does an electromagnetic wave look like at a fixed moment in time?

I am curious what the electric and magnetic field's of light look like when time is stopped. A "photograph" or illustration/description of these fields at a moment in time is what I desire. Also, does the picture change at various points in the wave? I assume that this is like a "time exposure" of a light wave.


How can super massive black holes have a lower density than water?

I heard on a podcast recently that the supermassive black holes at the centre of some galaxies could have densities less than water, so in theory, they could float on the substance they were gobbling up... can someone explain how something with such mass could float? Please see the below link for the podcast in question: http://www.universetoday.com/83204/podcast-supermassive-black-holes/


Exciting Surface Plasmons using ATR

I'm very new to the topic of surface plasmons and I have been reading about different methods of exciting them. There is one method in which a prism is set up to allow phase matching of an incident light ray to the required wave vector for exciting a surface plasmon. The light goes through total internal reflection in the prism and then either tunnels through the metal (on which we want to excite the surface plasmon), or a lower indexed dielectric to excite the surface plasmon. This might be a lack of understanding of attenuated total internal reflection, but apparently this field harbors no energy and 100% of the incident light is reflected. My question is how is energy conserved (how can it excite surface plasmons)? Is it because the energy of the attenuated field only time averages to 0? But then how can all the light be reflected?


Is this static mechanical balance possible without trickery?

On damnlol.com, I came across this picture: ![enter image description here](http://i.stack.imgur.com/Bwxxl.jpg) http://www.damnlol.com/hello-god-i-have-a-fault-to-report-7549.html My question is: Is this possible without glue? If not are there similar situations in which something like this is possible ?


The concept of center of mass behind dropping water from a faucet?

> Water, dripping at a constant rate from a faucet, falls to the ground. At > any instant there are many drops in the air between the faucet and the > ground. Where does the center of mass of the drops lie relative to the > halfway point between the faucet and the ground? (a) Above it (b) Below it > (c) Exactly at the halfway point When I looked at this, I thought the answer is (b) below it since if the water drop and the ground are in a system, then the center of mass will be nearer to the heavier object, which is the ground. But when I looked up the answer it was (a) above it. Could you please explain why? Thank you!


Determining wave function for term symbol 1D

I am trying to follow a book (Introduction to Ligand Field Theory by Ballhausen in 1962 on pg 15), but it isn't clear how they make a particular leap. **Background** I want to find the wave function for the term $^1 D$. We know that $\psi(L,M_L,S,M_S) = \psi (2,2,0,0)$ is made up of three micro states: $(2^+,0^-)$, $(2^-,0^+)$, $(1^+,1^-)$. Thus, a linear combination must be taken of these micro states. Now in the book they say they must be orthogonal to $\psi(3,2,1,0)$ and $\psi(4,2,0,0)$. Presumably these are picked because we just determined those via lowering operators in the previous section. I don't take it that there is another reason those two wave functions are mentioned. $(2^+,0^−)$ means that electron 1 has $m_s=+1/2$ and $m_l=2$ and that electron 2 has $m_s=−1/2$ and $m_l=0$. We write that $\Psi=|(\psi^+_1)(\psi^−_2)|$ where we have written the short form of the determinantal antisymmetrized normalized wave function, which comes from the diagonal element in the Slater determinant AND separated the orbital- and spin-dependent parts of the wave function (spin is denoted by super plus or minus sign). **Problem** Anyway, I understand that $\psi(2,2,0,0) = a (2^+,0^-) + b (2^-,0^+) + c(1^+,1^-)$. Then they write "and we get $a \sqrt{3} - b \sqrt{3} + c \sqrt{8} = 0$ and $a + b = 0$." I'm totally lost how they made this leap and why these must be equal to zero. Does this have to do with the orthogonal wave functions just mentioned? Where did the numbers in the sqrt come from? And the minus sign! Greatly appreciated.


Does someone falling into a black hole see the end of the universe?

This question was prompted by Can matter really fall through an event horizon?. Notoriously, if you calculate the Schwarzschild coordinate time for anything, matter or light, to reach the event horizon the result is infinite. This implies that the universe ages by an infinite time before someone falling into the black hole reaches the event horizon, so could that person see the universe age by an infinite time? To be more precise, suppose the observer starts falling from rest at time $t = 0$ and some initial distance $r > r_s$. If we wait for some time $T$ then shine a light ray at the falling observer. Will the light ray always reach the falling observer before they cross the event horizon? If not, what is the formula for the longest time $T$ that we can wait and still be sure the ray will catch the observer? If $T$ is not bounded it implies that observer could indeed see the end of the universe. I can think of a qualitative argument for an upper limit on $T$, but I'm not sure how sound my argument is. The proper time for the observer to fall to the event horizon is finite - call this $\tau$. The proper time for the light ray to release the horizon is zero, therefore the light ray will reach the observer before they cross the event horizon only if $T < \tau$. Hence $T$ is bounded and the observer won't see the end of the universe. I think a more rigorous approach would be to determine the equations of motion (in the Schwarzschild coordinates) for the falling observer and the light ray, and then find the condition for the light to reach the falling observer at some distance $\epsilon$ from the event horizon. Then take the limit as $\epsilon \rightarrow 0$. In principle this seems straightforward, but in practice the algebra rapidly defeated me. Even for a light ray the radial distance:time equation isn't closed form (Wolfram claims it needs the $W$ function) and for the falling observer the calculation is even harder.


Renormalization scheme independence of beta function

I have some questions about renormalization. To my understanding, in order to deal with infinities that appear in loop integrals, one introduces some kind of regulator (eg, high momentum cutoff, taking $d\to d+\epsilon$, etc.) so that we get a finite answer, which blows up as we remove the regulator. Then we renormalize various coefficients in the Lagrangian in a regulator-dependent way so that, in scattering amplitudes, a finite piece remains as we remove the cutoff. The regulator seems to always require introducing some arbitrary scale (eg, the momentum cutoff or $\mu^\epsilon$ for dim-reg), although I'm not sure why this must be the case. Now, this finite piece is completely arbitrary, and depends on what scheme we want to use (eg, on-shell, minimal subtraction, etc). The beta function is then, roughly speaking, the rate of change of this finite piece under changes in the scale in the regulator. My question is, what exactly is the invariant information in the beta function? Under changing renormalization scheme, it obviously changes, but it seems that this roughly corresponds to a diffeomorphism on the space of couplings (is this always true? for example, in on-shell renormalization, if we set the mass to the physical mass and the coupling to the corresponding exact vertex function at zero momentum, these seem to be independent of scale - do the beta functions vanish here?). Also, it seems to depend on exactly what regulator we are using, and how the dimensionful scale enters into it. There are certain quantities, such as the anomalous dimension of a field at a fixed point, which must be independent of all these choices, but I don't understand why this is the case. Finally, and this is more of a philosophical question, what exactly do the infinities in the loop integrals mean in the first place? Why is it that we can remove them by any of these various regulators and expect to get the same answer? I've read something about Haag's theorem, that interacting theories live in a different Hilbert space than the free-field Fock space, and that this is somehow related, but I'm not sure why. Thank you.


Why does a particle fall in a straight line?

In Lagrangian Mechanics we choose the path of least action. Given a uniform gravitational field, and a particle of finite mass; and fixing two points the start & end-point we consider all paths connecting the two points and minimise the action. This turns out to be a Brachistone, as first shown by Bernouilli. When we fix the end-point vertically below; the Brachistone is in fact astraight-line. But is there a principle in Lagrangian Mechanics that allows me to choose the point vertically below? Of course, we know from Newtons Mechanics that this must be the case. But how do we determine that end-point entirely within Lagrangian Mechanics?


Is pressure invariant under Lorentz transformations?

In an article from the reference there are following words (page 2): "...pressure P is a Lorentz invariant... the result follows from standart properties of the relativistic stress-energy tensor...". What properties are used by the authors of an article? For example, I used the expression for stress-energy tensor of an isotropic body: $$ T_{\alpha \beta} = (\varepsilon + p)\frac{v_{\alpha }v_{\beta}}{c^{2}} - g_{\alpha \beta }p. $$ If pressure is determined as a 3-trace of this tensor, it's obviously that it isn't Lorentz invariant.


Topological vs. non-topological noetherian charges

What (if any) is the relationship between the conserved (non-topological) noetherian charges and topological charges? Namely, is there any "generalization" of the Noether's first theorem that includes topological charges as subcase and it provides some relationship between these two classes of charge?


Showing constraint is nonholonomic

One example of a nonholonomic constraint is a disk rolling around in the cartesian plane that is constrained to not be slipping. These leads to the constraint $dx - a \sin\theta d\phi = 0$ and $dy - a\cos\theta d\phi = 0$ Where $\phi$ is the angle of how far the disk has rotated, $-\theta$ is angle that velocity makes with respect to $x$. We know that these aren't exact differentials because to put it in form $Mdx + Ndy = 0$, we don't have $\partial M/\partial y = \partial N / \partial x$. But that doesn't mean we can't find some integrating factor to multiply it by and make it an exact differential? So I don't see how we know that is it nonintegrable? If I take $f(x,\phi)[ dx - a \sin\theta d\phi] = 0$ and try to manipulate it to get something analogous to $\partial M/\partial y = \partial N / \partial x$, then I get a tricky PDE, which I don't know how to solve.


Why can we allow the speed of light being infinite in case of Surface Plasmons?

I have a problem with understanding of these sentences: > We have indicated in the opening paragraph of the Introduction that surface > plasmon polaritons are solutions of Maxwell’s equations in which the effects > of retardation—the finiteness of the speed of light—are taken into account. > An important subclass of surface plasmon polaritons are surface plasmons. > These can be viewed as the limiting case of surface plasmon polaritons when > the speed of light is allowed to become infinitely large. > > Nano-optics of surface plasmon polaritons (1.1.2) - Anatoly Zayats et.al. How can we allow c be infinite? Why is it correct in case of surface plasmons? The article is available online, easy to find with Google Scholar


How many seconds should you accelerate to complete the run on time?

Your goal is to complete your 10,000-m run in less than 30.0 min. Apparently you've started too slowly because at 27.0 min, you still have 1100 m to go! Part A You can accelerate at 0.20 m/s2. For how many seconds should you accelerate (and after this have constant velocity) in order to complete the run on time?


How quarks converted into leptons

![Pion Plus Decay](http://hyperphysics.phy- astr.gsu.edu/hbase/particles/imgpar/pidec1.gif) Since the charged pions decay into two particles, a muon and a muon neutrino, seems quarks disappeared!, The decay proceeds by the weak interaction $W^{+}$ and can be visualized in terms of Feynman diagrams. Isn't it why Quarks are not directly observed!? I read somewhere: > If you are consistent thinker you can go even further and question existence > of quarks themselfs then you will not have a problem with fractional charge


Calculating threshold energy of particle reactions

{..everything that follows is in the domain of relativistic kinematics..} Say a particle A collides with a particle B at rest and produces particles C and D. What exactly is the definition of "threshold energy" for a reaction ? Is it the energy that A should have so that so that the heavier of C and D is produced at rest? Given the masses of all the particles, how does one calculate the threshold energy that A must have to cause this reaction ? I intuitively feel that a threshold energy scenario would mean that C and D are moving along the same direction in which A was coming in. I think it is an unnecessary "waste" of energy for C and D to develop momentum in the two transverse directions of A's motion. But I can't prove this in general. I would like to know how this situation is analyzed.


How thermal imaging cameras work

As far as I see from wiki, 'consumer'-grade(non-cryogenic) thermal imaging cameras use microbolometer sensors to get integrated IR intensity over some 5-12um range. But I had an impression, that having just integrated IR intensity you can't get surface temperature precisely, especially with 0.1C precision we see on consumer cameras. IR thermometers (pyrometers) for example use 2-band IR measurement, but I don't see this principle being used in thermal imaging. Or there is some sort of 'know-how' matrix of IR band filters in front of the sensor?


Induced voltage by a rotating ring

Two concentric rings dielectrics and uniformly charged are suspended on the same floor. The outer ring has a radius R and mass M, while the other has radius r << R and mass M. The outer ring that has overall charge Q, is made to rotate around the axis passing through the center and perpendicular to the plane of the ring itself, with angular acceleration α. Calculate the angular acceleration α' of thr inner ring. * * * My solution is the following: The outer ring produce a variation of magnetic flux on the inner ring equal to               (μ * Q * π^2 * r^2 ) / ( α * R )  (*)      The inner ring produce a self-induced variation of magnetic flux for the law of Faraday-Lenz equal to               (μ * Q * π^2 * r' ) / α'   (**)      Comparing the ( * ) and ( ** ), I obtain               α' = α * R / r      Is it my solution right?


Questions about angular momentum and 3-dimensional(3D) space?

**Q1:** As we know, in classical mechanics(CM), according to Noether's theorem, there is always one conserved quantity corresponding to one particular symmetry. Now consider a classical system in a $n$ dimensional general coordinates space described by the Lagrangian $L(q,\dot{q})$, where $q=(q_1,...,q_n)$ and $\dot{q}=(\dot{q_1},...,\dot{q_n})$ are general coordinates and general velocities, respectively. If the system has $SO(n)$ spatial rotation-symmetry, e.g.$\forall A\in SO(n),L(Aq^T,A\dot{q}^T)=L(q,\dot{q})$, then we can get $\frac{n(n-1)}{2}$(number of the generators of group $SO(n)$) conserved angular momentum. **My question is as follows** , now note that our spatial dimension is $n$, when $n=3\rightarrow $ number of angular momentum$(\frac{n(n-1)}{2})$$=$spatial dimension$(n)$$=$3, otherwise, number of angular momentum$\neq $spatial dimension, so why spatial dimension 3 is so special? Is there any deep reason for number 3 or it's just an accidental event? Or even does this phenomena have something to do with the fact that we "live" in a 3D world? **Q2:** In quantum mechanics(QM), a Hermitian operator $J=(J_x,J_y,J_z)$ is called an angular momentum iff $[J_x,J_y]=iJ_z,[J_y,J_z]=iJ_x,[J_z,J_x]=iJ_y$. **And my question is as follows** , in QM, we can have 1-component momentum operator $\hat{p}$ , or 2-component momentum operator$(\hat{p_x},\hat{p_y})$, and so on. But Why we have never encountered a angular momentum with only two components $J=(J_x,J_y)$? Can we define a 2-component angular momentum? Like in the **CM** case, again the **number 3** is special in **QM** case, why? Thanks in advance. **By the way:** More questions concerning the **definition of rotation groups** for angular momentum can be found here , who are interested in may have a look, thanks.


Tension in an Atwoods machine conceptual?

![enter image description here](http://i.stack.imgur.com/jLunv.gif) Assuming $T_1$ is the force that acts on box $1$ and $T_2$ is the force that acts on box $2$. Exactly what causes the Tension? Why does $T_1 = T_2$? The problem is we are told to memorize that $T_1 = T_2$ for mass less ropes, but I do not understand why, especially in an Atwoods machine. When I think about it, I know it has something to do with the force $m_2g$ which causes the box with mass $m_1$ to rise, and vice versa. But I cannot apply physics terminology to this, or really understand whats going on.


Geometric Interpretation of these equations of motion?

I was reading my Engineering Mechanics book, and it derived some strange looking integrals I'll have to apply. I could memorize them, but I'd rather understand them - then I won't have to memorize. A few words mentioning Leibniz notion, and viola - we have these relationships: $$\int_{v_0}^vdv=\int_0^ta_cdt$$ $$\int_{s_0}^sds=\int_0^t(v_0+a_ct)dt$$ $$\int_{v_0}^vvdv=\int_{s_0}^sa_cds$$ I can manipulate them given appropriate data, but they don't really _mean_ much to me. (I _do_ easily understand things like $a=\frac{dv}{dt}$,however). I anyone could point me to website that discuss or even just show me how to derive these, I would really appreciate it - I find it easier to understand geometric interpretations, but I would appreciate any knowledge you would be willing to share.


Aside from Noether's theorem, what other concepts would explain energy conservation?

Energy is defined more in the mathematical sense, and tends to show true with observations in the physical world. But why is energy conserved aside from "Noether's theorem"? In a closed system that has an energy $E$, we know that system will always have this much energy, but why? In the cosmological scale I heard that energy is not conserved, why? Is the universe creating more energy? OR Is the expansion of the universe due to the energy at the beginning that caused it's creation? Could anyone explain their point in layman terms? Without using difficult Mathematics, I'm not as "qualified" to understand such rigorous equations yet.


Contact angle of liquid drop on surface

How do you explain point 44 of the attached pdf document on surface tension? Here's the link. How is the direction of surface tension found out? (I know it tangential but in which direction along the tangent?) Also why is surface tension for solid-air surface considered when balancing the forces on liquid? Any help will be appreciated.


Would HgTe be a topological insulator?

In "Quantum Spin Hall Insulator State in HgTe Quantum Wells", researchers observed a 2D topological insulator by sandwiching HgTe between CdTe. Is the CdTe really necessary? Would Vacuum/HgTe/Vacuum itself be a topological insulator?


How to design an experiment that shows that a rectangular pulse can be expressed as a series of infinite sinusoids?

Is it possible to design a physical experiment that shows that a time limited signal, such as a rectangular pulse is composed of infinite continuous sine/cosine waves?


Which is more fundamental, Fields or Particles?

I hope that I am using appropriate terminology. My confusion about quantum theory (beyond my obvious unfamiliarity with its terminology) is basically twofold:   1. I lack an adequate understanding of how the _mathematics_ of quantum theory is supposed to correspond to phenomena in the physical world   2. I still have an incomplete picture in my mind of how cause and effect relationships occur at the quantum level of reality.  This is why phenomena such as "entanglement" make absolutely no sense to me. So, in an attempt to come to some understanding of all of this, I would like to know that if what we conceptualize as a "field" is merely an interaction among particles (bosons and fermions in the case of quantum fields), and particles (themselves) are actually fluctuations in "fields", then which comes first in the hierarchy of cause and effect relationships, particles or "fields"?


Literature request for books / review papers on gravitation, gauge theories and related mathematics

Similar to this reference, are there more such references / works [including textbooks] available in the literature? (A list would be greatly welcomed and appreciated.) With great appreciation.


The multiverse of eternal inflation

I don't have a clear picture of what is "by definition" the multiverse appearing in the models of eternal inflation. A long time ago I heard that it is a quantum state, but in the cosmology books I have looked into (all treating the subject superficially, may I suspect it's because the object is still not clearly defined?) they define a non spatially homogeneous scalar field on it, entering in the slow-roll inflation regime in some areas, and creating a nucleation this way... So it must also be a manifold, so we can define a coordinate chart on it. Then how many dimensions is it? Because they is also this picture where it solves the landscape problem of string theory and each bubbles becomes a particular vacua of ST (but I am not sure about that neither as I have not read enough of string theory so far). Well to summarize I have a really blurry picture of this mysterious multiverse, so if someone could share his clear definition of it (assuming it exists) I would be really thankful. ps: is it even a physical object? in the sense obeying itself to some physical laws (which ones?) not like Newton's universe for example? is it dynamical?


Role of the canonical ensemble and electric charge in AdS/CFT

If we consider a charged black hole in AdS spacetime, we can either do thermodynamics in the grand canonical or the canonical ensemble. In the former, we fix the electrostatic potential $\Phi=A_t(r=\infty)$ at the boundary of the bulk such that $\left<Q\right>=-\frac{1}{\beta}\left(\frac{\partial S}{\partial\beta}\right)_{\beta}$, where $S$ is the Euclidean action. In the latter, we fix the charge $Q$ of the black hole and we do not consider $\Phi$ at all. The phase diagram of the black hole is highly dependent on the choice of ensemble, see for example this paper by Chamblin, Emparan, Johnson and Myers. One could therefore expect that this choice also has an influence on the CFT side. In the AdS/CFT dictionary, the charged black hole gives a global $U(1)$ symmetry on the CFT side. Here $\Phi$ in the bulk corresponds to a chemical potential $\mu$ on the CFT, so that we usually consider the grand canonical ensemble when using the correspondence. My questions are as follows:   * Do we ever consider the _canonical_ ensemble in AdS/CFT?    * If so, what would $Q$ determine on the CFT side (in the same way $\Phi$ determines $\mu$)?    * If we work in the grand canonical ensemble, does $\left<Q\right>$ play any role on the CFT side, or do we only need $\Phi$? EDIT: For my last question: I just looked into holographic superconductors and it seems that from $\Phi$ one can derive both the chemical potential and the charge density of the CFT. The charge density seems to coincide with $\left<Q\right>$ in this case (up to some constant factors), but we don't need $Q$ to calculate it as we can derive it from an asymptotic expansion of $\Phi$. Specifically see page 8 of this paper by Horowitz. I don't think this answers my first 2 questions though.


Difference between the two equations for acceleration

I came upon this while studying S.H.M. Well,is there a difference between writing $$a=\frac{dv}{dt}\;$$ and $$a=v\frac{dv}{dx}\;$$ do they differ on the basis of one being a vector and the other being a scalar equation?Please explain.


Hawking radiation and entropy

What is your opinion of the hawking radiation mechanism, does that actually lower the entropy of the black hole?


Angles in cosmology

We have several definitions of distances in cosmology. Take angular diameter distance. $$d_A = a(t)\int \frac{dt}{a(t)}\;.$$ If an object has proper length $L$ then the angle $\theta$ it is seen at is $$\theta = \frac{L}{d_A}$$ This is similar to the way an angle $\theta$ and arc length $s$ are related in a circle with radius $r$ $$ \theta = \frac{s}{r}$$ On cosmological scales distances are so vast that the arc length $s$ is indistinguishable from the proper length $L$ of the star or galaxy observed. All this is fine. But when it comes to the cosmic microwave background, we look at temperature correlations between two directions $\vec{n_1}$ and $\vec{n_2}$ with an angle $\theta$ between them on the sky today. $$ C(\theta) = C(\vec{n_1}\cdot\vec{n_2})$$ These angles are not small necessarily. For the quadrupole there is $90$ degrees between the two directions. Subsequent Higher multipoles have smaller angles. With such wide angles we should no longer use $$\theta = \frac{L}{d_A}$$ but instead use $$tan(\theta) = \frac{L}{d_A}$$ Where am I going wrong with this line of thought?


What is the gamma five matrix $\gamma_5$?

This Wikipedia page explains that for each of the four main gamma matrices $\gamma^{\mu}$, you can find the covariant matrices $\gamma_{\mu}$ with the equation $\gamma_{\mu} = \eta_{\mu\nu}\gamma^{\mu}$. But that formula doesn't make any sense for $\gamma^5$ because $\eta_{\mu\nu}$ does not have that many indices. So what is $\gamma_5$?


I have a length of string and I want to know the maximum tension the string can support. I tie one end of the string to the ceiling and the other end to a glass of mass 100 g. The glass is cylindrical, with a cross-sectional radius of 4 cm and a height of 15 cm. I fill the glass with water (density of 1 g/cm3) and discover that the string breaks when the glass is 2/3 full. What is the maximum tension in N the string can support?


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 HUP? For example, suppose there is a finite and self consistent theory of gravity which incorporates the uncertainty principle. Can we at once call this theory a quantum theory of gravity or does it have to satisfy other conditions too? This question may be too basic but it is intriguing my mind.


What allows the Wave Disk Generator to be so efficient?

Researchers at Michigan State University recently invented the Wave Disk Generator that is supposed to get 60% fuel efficiency. What allows it to be so much more efficient than a traditional Internal Combustion Engine? I am aware that there is better mixing of fuel and air, but surely this alone does not produce the extreme efficiency.


Strong interacting v.s. Strong Coupling v.s. Strong Correlated

One of the active research areas in present is Strong interacting, Strong Coupling, Strong Correlated regime of the phases of matters. It seems to me that some physicists in the fields often mix the usages of these twos: **Strong Coupling, Strong Correlated**. However, in my viewpoint, they are NOT the exactly same, I regard that > $\bullet$ **Strong Coupling** : implies the large coupling of interactions > comparing to the free part of theory. Say, suppose there is a Lagrangian > description, then the action $S$ $$ S=S_{free} +g S_{interact} $$ the > **Strong Coupling** means $g >>1$. So this can be the confined phases of > QCD, where coupling $g$ of quarks and gluons runs large. \-- > $\bullet$ **Strong Correlated** : in my view, usually implies the > **fractionalization of the elementary particles into fractional quantum > numbers**. For example, this happens at 1+1D Luttinger liquids, where spin > and charge can separated their degree of freedom from the elementary > constituents(electrons), but the system needs NOT to be **Strong Coupling**. > i.e. this example is **Strong Correlated** but NOT **Strong Coupling**. This > is about the fields of **Strong Correlated Electron** on arXiv. \-- **My question** , so what are other **examples of systems** that are: > **1\. YES Strong Coupling and YES Strong Correlated** > > **2\. YES Strong Coupling but NOT Strong Correlated** > > **3\. NOT Strong Coupling but YES Strong Correlated** See also this relevant post.


Did physical models of galaxies come before they were actually observed?

Black holes were first predicted by astrophysics, then observed. Was the existence of galaxies first predicted by astrophysics, or first observed by astronomers?


Energy of a simple pendulum like device

If there is a device in which a ball is attached to a pivot by a rod of length R and it is left to oscillate by dragging it to one side so that it is completely horizontal, at any point on its decent the ball has some velocity and also has some angular velocity about the pivot. In this case is the rotational kinetic energy about pivot equal to translational kinetic energy of the ball ? Why/ Why not ? If they are same then what is better way to deal with the calculations of such problems, the rotational KE about the pivot or translation KE of the ball alone ?


Transformation from waves to matter

Let $|\psi \rangle$ represents a wavefunction through and $\langle \psi |$ represent the dual   vector. Now there are things such as matter waves, could $|\psi \rangle$ represents a matter wavefunction, (of course representation is a definition), which is analogous to that of the massless wavefunction $|\psi \rangle$? If so, what would the $\langle \psi |\psi \rangle = n \in \mathbb{R}$ represent, an object? and the outer product $|\psi \rangle \langle \psi | = \rho$ would that be similar to the probability of localization of matter? I guess what I am trying to do is understand mathematically how I would be able to represent matter and how, if any, way there is to represent this in an analogous matter with the bra-kets. Seems there should be a relation as if waves are representable and matter is a wave, then matter is representable. Thanks, Brian


What role has our Moon played in creating a persistent geomagnetic field?

The question comes from a comment by Mark Rovetta on my earlier question about the Earth's core going cold.


Can we excite a nucleus by means of very intense low energy gamma-photon irradiation?

The phenomenon of multi-photon ionization of atoms has been studied, both theoretically and experimentally, for several decades. Intense laser beam devices are the apparatuses used for the experimental study of this phenomenon. **QUESTION:** Would it be possible to use similar excitation processes with nuclei, using "low energy" $\gamma$-photons in order to manufacture nuclear isomers for industrial and medical applications?


Can you prepare the superposition of two arbitrary light beams?

More specifically, how do you physically prepare the superposition of two beams of polarized light? Suppose beam A and beam B, the two input beams, each have unknown polarizations.   Beam C, the output beam, must be the superposition of beams A and B.   How do you do it? You can create an overlap of two beams with a half silvered mirror at 45%.   You can also creat a localized overlap by crossing the beams with a small angle.   In both cases you get a mixture, not a superposition. How do you get the superposition? Bonus Points: How do you prepare $ a|A \rangle + b|B\rangle $?


When I ride my bike, does half of the energy go into the earth?

When I ride my bike, does half of the energy go into the earth because of Newton's third law? Does the energy in the earth transfer into heat upon my brakes when I utilize them? If the earth was 2000 times less massive than it is, and I applied the same energy to my pedal, would my bike move (relative to an observer not connected to earth) at the same speed as it would if the earth was normal? I think if you think about it these two questions are the same.


photoelectric cell

In the photoelectric cell my teacher says that the electron emission from the cathode depends on the frequency of the incident photon and it doesn't depend on the light intensity (I = nhU/ta , Right?) so if the light intensity increased the photoelectric current won't change . but what if this increase in the light intensity is due to an increase in the frequency(energy) of each photon. to make a correct statement shouldn't the light intensity be replaced with rate of photons? so that if the number of photons increased even to millions and if the frequency of each was less than the threshold frequency , the photoelectric current won't be affected.


Tidal force of Sun?

As I understand, satellites and the Moon orbiting Earth are in free fall. Isn't the same true for Earth orbiting the Sun? My question is then: How can the Sun's gravity affect tides? Aren't the molecules in the oceans in free fall relative to the Sun?


Maximum Shear on a Beam - beam with fixed support on one end and hinge on other end

A beam $\displaystyle 3m$ long with fixed support on one end and hinge on the other end is subjected to a uniform load of $10\ kN/m$. What is the maximum shear of this beam? The solution is this one: $\displaystyle Max.Shear = \frac{5\omega{L}}{8}=\frac{5\left(10\right)\left(3\right)}{8}=18.75\ kN$ where $\omega$ = distributed load $N/m$ $L=$ length My question is, how did he get this equation? All I know is that hinges have two forces acting on them. Can anyone derive this equation?


Future light cones inside black hole

In Caroll's Spacetime and Geometry, page 227, he says that from the Schwarzschild metric, you can see than from inside a black hole future events all lead to the singularity. He says you can see this because for $r<2GM$, t becomes spacelike and r becomes timelike. I don't understand his reasoning though. Why does r being timelike mean you can only travel towards the singularity?


How to show that in 1D scalar potential well there isn't pairs production (Dirac particle)

Let's have the potential $U = -V_{0}$ for $|x| \leqslant a$ and $U = 0$ for $|x| > a$. The stationary Dirac equation for bound states gives $$ tg(\frac{p_{2}a}{\hbar}) = \frac{2\Gamma}{1 - \Gamma^{2}}, \qquad (1) $$ where $$ \Gamma = \frac{p_{1}}{p_{2}}\frac{E + mc^{2} + V_{0}}{E + mc^{2}}, \quad p_{1}c = \sqrt{m^{2}c^{4} - E^{2}}, \quad p_{2}c = \sqrt{(E + V_{0})^{2} - m^{2}c^{4}}. $$ How to show that there isn't pair production independently on well's parameters $V_{0}, a$? My attemption. I assume that if scalar potential acts on particle and antiparticle by the same ways, there exists only one case when the production is possible. It is when $E_{1} = E_{2} = 0$, where these energies refer to the particle and antiparticle energies correspondingly. For case $E = 0 (1)$ gives me $$ \sqrt{V_{0}^{2} - m^{2}c^{4}} = -mc^{2}tg\left(\frac{\sqrt{V_{0}^{2} - m^{2}c^{4}}a}{c\hbar}\right), $$ and theoretically it doesn't have solutions for all possible values of $a, V_{0}$. But it seems that it has. Can you help me?


Does Light (EM Signal) undergo accelration during reflection?

Since Average acceleration is defined as, Average acceleration over a period of time is the change in Velocity divided by the Duration of the Period. Does Light (EM Wave) undergo acceleration during reflection from mirror or any other surface?


What happens when a photon hits a mirror?

When a photon of light hits a mirror does the exact same photon of light bounce back or is it absorbed then one with the same properties emitted? If the same one is bounced back does it's velocity take all values on $[-c,c]$ or does it just jump from $c$ to $-c$ when it hits the mirror? Or, is the phenomenon of a mirror better explained using a wave analogy? If so, what is this explanation?


Bloch sphere representation

Suppose you know that a qubit is either is in state $|+\rangle$ with probability $p$ or in state $|-\rangle$ with probability $1-p$. If this is the best you know about the qubit's state, where in the Bloch sphere would you represent this qubit?


Why are orbits elliptical?

Just wanted to know why planetary orbits get to be elliptical? I'm not debating how stable these orbits are (obviously almost completely stable), but why don't planets revolve in the special ellipse known as a circle? Wouldn't the centrifugal/-pedal forces between the planet and Sun make the planet revolve around the Sun in a perfect circle? Is there a 'third force' that attracts planets at a specific point (a hypothetical reasoning for elliptical orbits)? I'm not trying to disprove Kepler over here, but I don't exactly get it.


How to calculate the radius of a rain drop with variable mass?

I need help with the following problem, please help me get started as I do not know where to begin with One spherical raindrop is falling in the atmosphere. Mass of the raindrop increases proportional with it's area. There's no counterpoise in it's move. I should show that radius of a rain drop is increasing linearly with time.


What field of physics play a major role in water pipe function

Background: I'm a legal MMJ patient and I've been looking into water pipers/bongs recently. I understand that this question can be a little controversial but where I live this is all legal as long as you have the proper prescription. Last few years there has been quite a lot of "scientific" bongs that has been hitting the market and in my to medicate as healthy as possible I would like to understand how they work. I know about vaporizers and I have a few of them, this is a physics question. So to my question. What are the major fields that come into play when talking drag/resistance, smoke cooling and smoke filtration? My theory is that it is fluid dynamics. Are there any good books to read to fully understand the mechanics behind the water bong? Thank you


Practical matter of the Higgs-Mechanism

My maybe very naive question is, of what practical importance will the discovery of the Higgs-Mechanism be for our technological advance in the near future?


What good is extraordinary matter to the consumer?

> **Possible Duplicate:**   >  Practical matter of the Higgs-Mechanism This video claims that for everyday matter you only need electrons, upquarks, and downquarks. So are all these other fermions useless? Has anyone ever made a shovel out of strange-charm-muon atoms or something?


What's next after Higgs Boson discovery?

> **Possible Duplicate:**   >  Practical matter of the Higgs-Mechanism As everybody knows that the Higgs Boson was discovered on July 4th,2012, I am so curious about it.   1. What are the possible outcome applications of Higgs Boson?   2. How Higgs Boson is related to Quantum Mechanics?   3. Does Higgs Boson fits in General Theory of Relativity?   4. Does Higgs Boson fits in String Theory? Please share the knowledge. I am very curious about it.


Not-so-hot black shirt

As it is getting warmer here by the minute I was asking myself: **Are there materials, that are black (in th visible range) but reflect (most) invisible light?** Furthermore, I asked myself **what fraction of heat could be kept** away using this material in daylight. For bonus points, it would be great if it could be used as some kind of fabric. I am not looking for a specific material but am curious, as e.g. metals do reflect all light up to a certain frequency and thus would not suffy. Therefore it would be nice to understand the underlying mechanism. In the winter of course it would be nice to reverse this, so to have white shirts, still getting hot in the sun.


Equal and opposite electron flows in a magent?

If the electron flow in a magnet is say from South pole to North pole, then I can understand why you can't put the two north ends of magnets together, as the two flows of electrons repel each other. But then why can't I put the two south pole ends of a magnet together? If the electrons flow out the North pole and into the south pole, then what force is repelling the two south poles?? If the answer is to say there are two electron flow, in opposite directions, then why don't they just cancel each other? There must be "something" else flowing in the opposite direction of the electrons that causes the two south poles to be repelled. Edit: Perhaps electron flow was bad choice of words. Every diagram of a magnet I see shows the lines of flux flowing from out of North pole and into South pole. Given this flow of "whatever", it is easy to understand why the North poles would repel each other. It is also easy to understand why the North pole of one magnet is attracted to the South pole of another. My question really is why do the South poles also repel each other? If the magnetic field is really flowing "into" the south pole, then what force causes the two South poles to Repel each other.


Motional EMF and EMF?

What is the difference between motional EMF = $-vBL$ , and Faraday's law of induction $\displaystyle\mathcal{E} = \left|\frac{d\Phi_B}{dt}\right|$? Aren't they the same? What is the relation of Lorentz force to motional EMF?


The relation between the movement of electrons and energy

So, I've been enjoying reading a lot of helpful posts, but now, I found myself in the need of asking something. I have a hard time grasping the general concept of electricity / how the relation between the movement of electrons and energy corresponds. But so far I've reach this conclusion / guess: 1) The movement of electrons, should rather be called mechanical energy, than calling it electric energy. Why? Electrons move by pushing to each other, typical mechanical energy example. That electrons has a electric charge, doesn't make the movement of them electric energy. 2) Every single electron has their own electric field. When there is a potential difference between minus and plus (electroncurrent), we say that there will be created an uniform field, because of the field lines between two parallel conducting plates with oppositely charges. Meanwhile, when electrons move in the same direction, they create a magnetic field. **And now comes my guess:** My statement: It is the effects of the magnetic and electric field in the wire, that do the work on electronic devices. We know that fields of all kinds can exert a force on any given object within its reach. So my guess is that this electromagnetic field the wire creates, can effect: a smaller wire in a computer, the wires that goes to the screen, the way the screen lights up. So you could say that the energy / what I would believe people in general thinks is 'electricity' exists not only inside the wire, but also outside. So when a device is 'using' / 'transforming' the energy to other energyforms, you could think of it this way. 1) Remembering that a current exists in a closed circuit. 2) When you exert a force from a battery or whatever, the electrons move very slowly themselves, but all in all as a system, they move at the speed of light. When they do this, the electromagnetic field will be a natural follower of this event. So when we transform energy/ use energy, it is the constant need for making the electrons move around, in order to create the electromagnetic field. And when there is no force to push the electrons around, the electromagnetic field disappears - and no work is done, and no money spent. This would also mean / or be the reasoning behind why devices / light or what so ever, starts in splitseconds. Because the electromagnetic field comes at the speed of light, because the electrons move the way they do. And using the expressions as potential energy, is just a way of saying that you create a strong difference between minus and plus (electroncurrent.) And the electromagneticfield will be "tapped" when there is devices nearby, but the current logically remains the same, buut, the electromagnetic field will be weaker near plus, because it has already done a lot of work. But we might be taking about fractions of seconds, so we probably wouldn't register it.. (is this right or just totally wrong reasoning??) So saying electricity, could in daily life relate to: the movement of electrons or the effects of electromagnetic field exertion on electronic devices. Many thanks in advance!


Reading list in topological QFT

I'm interested in learning about topological QFT including Chern Simons theory, Jones polynomial, Donaldson theory and Floer homology - basically the kind of things Witten worked on in the 80s. I'm looking for pedagogical reviews rather than original articles. Though these things sit at the interface of mathematics and physics I'm interested in them more as a physics student. I remember someone asking for a suggested reading list for topological QFT in mathoverflow. The suggested papers were almost uniformly rigorous mathematics written by mathematicians. I am not looking for something like that.


References for Chern-Simons action $ \int d^3 x ~\epsilon^{\mu \nu \rho} A_{\mu} \partial_{\nu} A_{\rho}$

Can you recommend to me good references on this action? From basics to more advanced stuff.


Correlation between outstanding hints in experimental particle physics

The 115 GeV ATLAS Higgs with enhanced diphoton decays has gone away but there are several other recent tantalizing hints relevant for particle physics, namely   * CoGeNT's 7-8 GeV dark matter particle that seems to support DAMA's and other signals   * D0's fourth-generation top prime quark that may be there at 325 GeV if a 3-sigma signal is right   * CDF's "new" force Z prime boson at 144 GeV which could be there if another 3-sigma bump is real   * Tevatron's top-antitop asymmetry above 400 GeV which seems very large   * A related CDF top-quark anomaly and maybe others I missed. My question is simple: > Is there some sensible theoretical basis (e.g. paper) that would > simultaneously explain at least two of the observations above if they were > real?


Absorption/Extinction formula of nanoparticles

I know the absorption/extinction equations in nanoparticle physics should be: $$Q_{abs}=\frac{1}{2}\mathbf{Re}\int \mathbf{J}_{tot}\cdot\mathbf{E}_{tot}^\ast dV=\frac{\omega}{2}\mathbf{Im}(\epsilon)\int|\mathbf{E}_{tot}|^2dV$$ also, for the extinction, it reads: $$Q_{ext}=\frac{1}{2}\mathbf{Re}\int \mathbf{J}_{tot}\cdot\mathbf{E}_0^\ast dV$$ But I see in some papers people use the following equations: $$Q_{abs}=\frac{\omega}{2}\mathbf{Im}(\mathbf{d}\cdot\mathbf{E}_{inside}^\ast)$$ where $\mathbf{d}$ is the total dipole moment of nanoparticles. Also, for the extinction, it reads: $$Q_{ext}=\frac{\omega}{2}\mathbf{Im}(\mathbf{d}\cdot\mathbf{E}_0^\ast)$$ I failed to derive the two equations. Can anyone give some help? Or, some reference papers would be also very helpful. Thanks a lot for the help.


Only gravitation and Newton's $2^{\mathrm{nd}}$ law needed to derive Kepler's laws?

It is known that Kepler's laws of planetary motion can be derived from Newton's laws of motion and his law of universal gravitation. However, are all of Newton's laws of motion necessary? According to this website, all of Kepler's laws can be derived from gravitation and the Newton's second law ($\mathbf{F} = m\mathbf{a}$). Does this mean that Newton's first and third laws are irrelevant for planetary motion? Perhaps Newton's third law (action-reaction) is necessary to take into account the motion of the Sun as induced by gravitational pull from the orbiting planets, but when deriving Kepler's laws the Sun is assumed to be fixed...


Gauss’s Law inside the hollow of charged spherical shell

Use Gauss’s Law to prove that the electric field anywhere inside the hollow of a charged spherical shell must be zero. My attempt: $$\int \mathbf{E}\cdot \mathbf{dA} = \frac{q_{net}}{e}$$ $$\int E \ dAcos\theta = \frac{q_{net}}{e}$$ $$E \int dA = \frac{q_{net}}{e}$$ $E\ 4\pi r^2 = \frac{q_{net}}{e}$ and since it is a hollow of a charged spherical shell the $q_{net}$ or $q_{in}$ is $0$ so: $E = 0$. Is my reasoning on this problem correct? Essentially $E$ is $0$ because there is no charge enclosed.


Lorentz Transformations and Aberration

Why does the azimuthal angle, $\phi$, remain unchanged between reference frames in special relativity? Edit: Here is a link from "Radiative Processes in Astrophysics": http://i937.photobucket.com/albums/ad216/Kyanise/Capture-5.jpg. I think this comes from the aberration formula, showing dependence only on the polar angle, $\theta$. The aberration formula is: $\tan \theta = \frac{u_\perp}{u_{||}} =\frac{ u' \sin \theta '}{\gamma (u' \cos \theta ' + v)}$ where ' indicates a property of the moving frame. But I'm not even sure why this is true. I know it comes from the transforms of the velocities, but why should $\tan \theta = \frac{u_\perp}{u_{||}}$ anyways? I mean $v$ can be in any direction, right? How come there is no dependence on $\phi$?


Question about the vacuum bundle on A- and B-model

Let us consider the topological string A- and B-model (twisted SUSY non-linear sigma model on CY 3-manifold $X$). They are realization of $N=2$ SCFT and there are ground-states vector bundle $\mathcal{H}$ and vacuum line bundle $\mathcal{L}$ over the moduli space of the theory. In the A-model, $\mathcal{H}=H^{even}(X,\mathbb{C})$ and $\mathcal{L}=H^0(X,\mathbb{C})$. In the B-model, $\mathcal{H}=H^{3}(X,\mathbb{C})$ and $\mathcal{L}=H^{3,0}(X,\mathbb{C})$. The genus $g$ string amplitude is given as a section of $\mathcal{L}$ in either theory. Mirror symmetry is an identification of the geometry of A- and B-model ground-state geometry on distinct CY 3manifolds. My questions is following. In the A-model, it seems the splitting of the bundle $$ \mathcal{H}_A=H^{even}(X,\mathbb{C})=\oplus_{i=0}^3 H^{2i}(X,\mathbb{C}) $$ does not vary over the moduli space of the theory (Kahler moduli space). On the other hand, in the B-model, the splitting $$ \mathcal{H}=H^{3}(X,\mathbb{C})=\oplus_{p+q=3}H^{p,q}(X,\mathbb{C}) $$ varies over the moduli space (variation of Hodge structure). Moreover, $\mathcal{L}$ is the trivial line bundle in the A-model, while it is not in the B-model. Isn't this contradiction?


What is the extent of the Galactic Magnetic Field?

What is the extent of the `Galactic Magnetic Field`? What does the `Galactic Magnetic Field` look like from afar (such as half-way between the `Milky Way Galaxy` and `Andromeda Galaxy`)? Does the `Galactic Magnetic Field` interact with other galaxies's magnetic field? Also, is there an `Inter-Galactic Wind` interacting with all of the above (in similar nature to how the `Solar Magnetic Field` interacts with the `Galactic Wind`)?


Does time exist in a vacuum?

Imagine a perfect vacuum devoid of all matter and radiation. Irrespective of whether such a space can even exist, my intuition tells me that time would not exist within such a space. What this thought experiment tells me is that the human concept of time is basically that it's a measure of motion. Whether its a car speeding down a highway, skin on your face as the years go by, or photons, it's really all about motion. Now what about something like a gravitational field? Could that also be excluded from acting within a perfect vacuum?


Caculating thermal stresses in a composite rod

**The Question** > Between two rigid walls separated by a distance $l_1+l_2$, two rods of equal > cross-section area $A$, and length, coefficient of linear expansion and > Young's modulus $l_1, \alpha_1, Y_1$ and $l_2,\alpha_2,Y_2$. Suppose the > temperature of the entire system is raised by $T$ kelvins. What is the force > the two rods exert on each other?   >  ![enter image description here](http://i.stack.imgur.com/XhGMT.png) **Concepts Involved**   1. Tendency to expand of the two rods   2. Stress generated due to the constraint on total length which limits their expansion   3. Different increases in length of both the rods owing to different young's modulus and original lengths  **My efforts** Let at the increased temperature, the length of Rod 1 be $l_1+x$ and that of rod two be $l_2-x$. The "natural length" of both the rods at that temperature is $l_1(1+\alpha_1T)$ and $l_2(1+\alpha_2T)$. Therefore the longitudnal stress developed in each is:- $\delta l_1=l_1\alpha_1T-x$ and $\delta l_2=l_2\alpha_2T+x$. For the rods in equilibrium, the forces they exert on each other need to be equal. Therefore, using $F=\delta l/l\times AY$, and equating their forces we get:- $$\frac{Y_1l_2(l_1\alpha_1T-x)}{Y_2l_1(l_2\alpha_2T+x)}=1$$ This can be solved for $x$ which on substituting in $F=(l_1\alpha_1T-x)/l_1\times AY_1$, we should get the force. But no matter how much I rearrange this equation, it does not match with the given answer. **Is there a fault in my arguments/equations or calculations?** Sorry if there is trivial mistake.


Why do we set $x^0 = ct$ instead of $x^0 = t$?

When we deal with Special Relativity and we start considering spacetime instead of space and time each at once, we usually see books saying that we consider a space with four coordinate $x^\alpha$ with $x^0 = ct$. We also consider this manifold to be $\mathbb{R}^4$ and give to it the metric tensor $g = \operatorname{diag}(-1,1,1,1)$. Now, why $x^0 = ct$ and not just $x^0 = t$? One possible answer might be "so that all coordinates are measured with the same units", but isn't there any deeper meaning?


Why Is String Theory Called A Theory

> **Possible Duplicate:**   >  Laws of Atomic Theory - how is this possible? Generally in science, a theory is effectively a fact. The **theory** of evolution is not a guess, or a hypothesis. It's currently understood to be a fact, backed up by evidence from numerous scientific fields spanning many decades. String **theory** on the other hand seems much more contentious, much less settled in the scientific community. Why isn't it called the string hypothesis?


How small of a depletion signal can the best modern mass spectrometers detect?

So I know the answer to this question varies widely across mass spec techniques, masses, and, of course, budgets, but my question is about the _best_ case scenario for all of these variables (although I'm not really looking at proteins or anything of that size). I realize that the concept of depletion spectroscopy relies heavily on very sensitive mass spectrometers, and I'm curious about the lower limits of signal detection for such methods. Thus, I'm interested in the sensitivity, not resolution ("mass resolving power"), which seems to be a statistic that is difficult to find for most of the systems that I've looked at. Some related follow-up questions are what mass spectrometry methods can and cannot be used with depletion spectroscopy and what methods/manufacturers are the gold standard in the field of mass spec? Thanks in advance for your answers.


Electrical eddy current visualization or simulation

Eddy currents are induced in a metal plate when it experiences a changing magnetic flux. Is there a realistic visualization or simulation of eddy currents available? The only picture I found, on wikipedia, is a cartoon schematic.


Using Einstein's Relativity: Who is younger?

Suppose we have a person **A** and a person **B**. Person B travels very close to speed of light and never returns. He's constant in speed. Then, we can say two things:   1. B is younger than A.   2. A is younger than B (since we can consider B's reference as inertial). Who is correct between the two?


How many sigma did the discovery of the W boson have?

When the W boson was discovered in the 1980s, nobody spoke of sigmas. How many sigmas was it at that time?


About electric current analogy

my teacher gave me this analogy to the electric current , the wire is like a pearl necklace where the pearls can move, the current or the movement of electrons is like putting your fingers between 2 pearls separating them then you start taking one pearl from the right of your finger and push itto the left of your finger starting making the pearls to move, is this analogy right?


Why is Standard Model + Loop Quantum Gravity usually not listed as a theory of everything

I have often seeen statements on physics.SE such as, > The only consistent theory of everything which we know of to date (2013) is > string theory. Why exactly is this so? Adding the Loop Quantum Gravity Lagrangian Density (the Einstein-Hilbert-Palatini-Ashtekar lagrangian density) to the Standard Model Lagrnagian Density should be able to describe all the interactions and fermions, in my opinion. Maybe it isn't as elegant as string theory since it doesn't really unify all the forces/interactions and fermions but it is still a complet description, right? Because once the Lagrangian Densities are added, one obtains the following "Complete Lagrangian Density": $${{{\cal L}}_{\operatorname{complete}}} = - \frac{1}{4}{H^{\mu \nu \rho }}{H_{\mu \nu \rho }} + i\hbar {c_0}\bar \psi \not \nabla \psi + {c_0}\bar \psi \phi \psi + \operatorname{h.c.} + {\left\| {\not \nabla \phi } \right\|^2} - U\left( \phi \right){\rm{ }}+\Re \left( {\frac{1}{{4\kappa }}\mbox{}^ \pm\Sigma _{IJ}^\mu {{\rm{ }}^ \pm }F_{IJ}^\mu} \right) $$


Am I right in saying that $gmm/r$ is motion due to potential energy?

I was watching a video about the swarzchild radius and it said that potential energy is $gmm/r$. This cannot be right though because potential energy goes up with distance not down. I'm assuming he meant motion due to potential energy. Also what is the intuition behind the equation $gmm/r$?


Stringy corrections of Einstein's vacuum field equations

From string theory, the vacuum field equations obtain correction of the order $O[\alpha'R]^n$ such that they can be written as $$ R_{\alpha\beta} -\frac{1}{2}g_{\alpha\beta}R + O[\alpha'R] = 0 $$ where $\alpha' = \frac{1}{2\pi T_s}$, when including just the first order term for example. What is the physical interpretation of these corrections, what do they look like more explicitely, and how can they be obtained?


maths question on levers

> Someone holds a 2kg weight in their hand at a distance of 35cm from the > elbow (fulcrum) and the downward force (load) due to the weight is 20 > Newtons. Calculate the effort in Newtons that the muscles of the forearm > must apply at a distance of 5cm from the fulcrum to hold the weight up. Show > calculations. Anyone any ideas please, I kinda grasp the concept but am unsure of how to show workings


Decomposition of two particle wavefunction into product of single-particle wavefunctions

Suppose you prepare a two-particle system such that $\Psi(\vec{r}_1,\vec{r}_2, t_0) = \Psi_1(\vec{r}_1, t_0)\Psi_2(\vec{r}_2, t_0)$. So then, initially $\Psi(\vec{r}_1,\vec{r}_2,t_0) - \Psi_1(\vec{r}_1, t_0)\Psi_2(\vec{r}_2, t_0) = 0$ But now you let the system evolve in time and $\Psi(\vec{r}_1,\vec{r}_2, t)$ can now no longer be decomposed into a product of two single-particle wavefunctions. What then does, physically, does $\Psi(\vec{r}_1,\vec{r}_2, t) - \Psi_1(\vec{r}_1, t)\Psi_2(\vec{r}_2, t)$ represent?


Entropy increase and end of the universe

While taking thermodynamics our chemistry teacher told us that entropy is increasing in day by day (as per second law of thermodynamics), and when it reaches its maximum the end of the world will occur. I didn't see such an argument in any of the science books, is there any probablity for this to be true?


Rotationally invariant body and principal axis

Suppose a rigid body is invariant under a rotation around an axis $\mathsf{A}$ by a given angle $0 \leq \alpha_0 < 2\pi$ (and also every multiple of $\alpha_0$). Is it true that in this case the axis $\mathsf{A}$ is a principal axis of the rigid body? If so, how to prove it? Do you have any references for a proof?


Full refraction in fibre optics

Well in a problem I had to calculate the maximum amount of "reflections" in a glass fibre optic pipe (index of refraction = 1.3, width of 20 micrometer and length of 1 meter). I am a bit blocked on how to calculate this. I considered first the critical angle $sin(\theta_{cr}) = \frac{1}{n}$ Which came out to be 50 degrees. I thought: well at critical angle the whole light beam is reflected. $\theta_i = \theta_o = \theta_{cr}$. And the length of each "reflection" would simply be $\frac{d}{\tan(\theta_{cr})}$. Resulting in $\frac{l}{d}$ reflections in the pipe. However this came a bit over 60 000 reflections. While the answer should be around 42 000. What am I missing here?


Does tritium hydride exhibit measurable spontaneous fusion via proton tunneling?

In a fascinating 30 June 2013 article in _Nature Chemistry_ , researchers from the University of Leeds found that when molecules of hydroxyl ( **OH** , a fairly stable radical) and methanol ( **CH$_3$OH** ) are cold enough to adhere to each other in deep space instead of bouncing apart, they combine to form methoxy molecules ( **CH$_3$O** ) and water at rates hundreds of times higher than at room temperature. The reason for this unexpected increase in reactivity is both elegant and simple: By being cold enough to cling together loosely for long periods, the integral of very low quantum tunneling rates becomes large enough to enable appreciable rates of combination of the two molecules, despite the reaction having a high classical energy barrier. Now what I find interesting is that there is a simple equivalent of this "let's stay close for a while" situation in nuclear chemistry. Specifically, it is the formation of an ordinary chemical molecule of two nuclei that have a high energy potential for fusion. The chemical bond becomes the analog of the gentle "let's say close" binding of cold hydroxyl and methanol molecules, and the nuclear fusion reaction becomes the analog of the exothermic recombination of the two molecules, albeit with an enormously higher energy barrier. This analogy leads to only two or three interesting candidates: **TH** , tritium hydride; **TD** , tritium deuteride; and **T$_2$** , a molecule of two tritons. **TH** would seem by far the most interesting, since the probabilities for protons to tunnel over atomic distances are orders of magnitude higher than those of deuterons or tritons. The details will be complicated by the larger fusion cross sections of **D-T** and **T-T** in comparison to **H-T** , however. So my question: Has anyone ever specifically looked for this effect -- that is, for higher rates of spontaneous fusion in **TH** that can be attributed to increased tunneling probabilities due to the proton being kept at an atomic distance from the triton for an indefinitely long time? I did a cursory online-only look for relevant articles, without much success. Nonetheless, my best guess is that spontaneous **TH** fusion rates were likely calculated out to the $n^{th}$ degree decades ago, and likely experimentally verified to the same degree. After all, everything in nuclear chemistry is about tunneling probabilities. Nonetheless, the close analogy of long-term atomic-distance binding of nucleons to this more recent finding on increased tunneling between cold-bound molecules is intriguing. I was curious whether anyone out there is familiar with the topic and can talk about it in this forum.


Identifying objects, for dummies

If I'm a tyro and have a latitude, longitude, time, date, height from the horizon, and compass direction, what means can I use for identifying what I see there? Realize that, as a tyro, I don't have any astronomy books or programs, and don't want to buy any; I might download a free program for my occasional inquiries about the sky, but would prefer a Web site.


Generated wavelength of free electron laser

Could you please help me understand how one can measure output frequency of free electron laser **(provided that we know size of magnetic domains and electron energy)**? This should be a function of magnetic domains size & electron velocity? But electron velocity should drop due to photon emission - does that means that FEL have a "wideband" spectrum? Why military users focus on Röntgen radiation while UV in air transparancy window might have less air absorption? Bold is still unanswered :-)


> **Possible Duplicate:**   >  Age of the Earth and the star that preceded the Sun How were the heavy elements from iron to uranium made? References: http://www.phy.anl.gov/accelerator_rd/index.html Review of proposed Tech: http://www.annualreviews.org/doi/abs/10.1146/annurev.nucl.55.090704.151604


Do bubble universes have a centre?

This question is motivated by Big Bang Physics/Cosmology. If eternal inflation is a good description of the universe and we live in a bubble universe then presumably our bubble nucleated at a spacetime point. Does this mean it is (approximately) a finite hypersphere and therefore has a centre?


Assuming that the Cosmological Principle is correct, does this imply that the universe possess an empirically privileged reference frame?

OK...before everyone blasts this with references to the relativistic invariance of the physical laws, time dilation, etc let me add some context. Also, I am an _amateur_ with an interest in physics, so I don't know the details of the physics. However, I have read enough about the cosmological principle and cosmic time to develop this "confusion" . Based on evidence gathered to-date, it appears that the universe is both isotropic and homogenous to a high degree, as evidenced by observations and the usefulness of the Freedman-Lemaitre-Robertson-Walker (FLRW) metric. This principle, when combined with the FLRW metric, allows space-time to be divided into non-intersecting slices and therefore establish a "cosmic time." Now, the existance of such a time in no way suggests that it is the "right" time or a true "now", hence violating relativity -- although some presentist philosophers (e.g., W.L. Craig) have tried to make this argument, but it is not generally accepted in philosophical circles. However, this leaves me confused about an apparent disconnect between relativity and the cosmological principle: Isotropy only holds if we are at rest relative to the cosmic microwave background radiation (universal rest frame), o/w anisotropy is present - yet each reference frame is supposed to allow equally valid observations. How can these two be reconciled when most reference frames would lead us to conclude that the universe is NOT isotropic? It seems that only by appealing to the idea of being at rest relative to "universal rest frame" can we explain away any discrepancies from isotropy as due to "peculiar motion". However, doesn't this give this "universal rest frame" and its associated time an _empirically_ privileged status, even though physical laws work just fine in every reference frame? For example (pardon any abuse of astronomy): if look off in some part of space and see only quasars, and then in another part of space and see only brown dwarfs, but I measure both as apparently the same distance from me, then can I conclude that we are in motion, since otherwise we would have an empirical contradiction (kind of like finding dinosaur and human remains in the same strata)? Any help on where I am going wrong would be helpful. Intuitively, I don't think there should be a way to establish absolute ordering between space-like separated events, but the above reasoning suggests otherwise.


can hydrogen stay frozen in vacuum?

I've look into the hydrogen state diagram, and it seems that it can be frozen under pressure. > **Question:** Does this mean that hydrogen cannot be kept frozen in a vacuum > chamber?


Different directions of frictional force when objects are rolling

My textbook has two instances of rolling bodies (smooth rolling). In the first, the body is rolling on the horizontal floor with some acceleration of its centre of mass. In this case, the book says that the friction will act in the direction the ball is accelerating. In the other instance, the ball is rolling down an incline. In this case, the book says that the force of friction acts opposite to $mg\sin\theta$, the component of the gravitational force parallel to the incline. I don't understand the difference. I mean, in both the cases, the ball experiences an acceleration due to a force. Why does the direction of friction change? For me the second case was more intuitive. The friction and gravity both induce torques of the same sign on the body. But I'm lost on the first case. The force that produces the acceleration and the frictional force clearly induce opposite torques which should cancel. Or atleast cancel partially. Also, my intuition says that for the first case, friction should act opposite to the direction of acceleration. I tried to get answers on the web, but I couldn't find anything that was explained in a lucid manner. Some websites mentioned that the direction of friction is affected if the force is applied at the axle. I don't see why that should be.


Darwin term and Zitterbewegung

I've noticed that in the discussion of the fine structure of Hydrogen atom standard QM texts claim that the Darwin term, which corrects energy of $\ell=0$ (or $s$-) states only, is related to the zitterbewegung of the relativistic electron. I'm quite familiar with the zitterbewegung phenomenon, but it is not clear to me how it leads to the correction to the Hamiltonian in the form: $$H_\text{Darwin}=\frac{\hbar^2}{8m^2c^2}\nabla^2 V$$ Furthermore, this article: http://arxiv.org/abs/atom-ph/9607005 claims that the Darwin term has its origin in the spin-orbit coupling rather than zitterbewegung. Who is right? Question:   1. What is the physical origin of the Darwin term?   2. What is the history behind the Darwin term?


The definition of Density of States

The density of states (DOS) is generally defined as $D(E)=\frac{d\Omega(E)}{dE}$, where $\Omega(E)$ is the number of states. But why DOS can also be defined using delta function, as $$D(E)~=~\sum\limits_{n} \int \frac{d^3k}{(2\pi)^3}\delta(E-\epsilon_n(\mathbf{k}))?$$


In What Frame of Reference does the Special Theory of Relativity Operate?

> **Possible Duplicate:**   >  Time Dilation - How does it know which Frame of Reference to age slower? This has bugged me for years. According to the theory of relativity, the faster an object moves, the slower time goes for that object, relative to a stationary observer. However, it is my understanding that motion is necessarily relative to a frame of reference. If you have two objects in space moving away from each other at a combined velocity of 20mph, the rate at which each is moving is totally conditional on what frame of reference you specify.   1. If object A is your frame of reference, than object A is moving at 0mph, and object B is moving at 20mph.   2. If object B is your frame of reference, the opposite is true.   3. If something else is your frame of reference, then the two objects will have some other two velocities, which, when summed, equal 20mph. If this is true, how does physics know how much to slow down time for each object? It's as if they don't actually have set velocities.


Deriving Feynman rules from a Lagrangian for vertex factors for "more complicated" interactions

I am trying to derive Feynman rules from a given Lagrangian and I got stuck on some vertex factors. What for example is the vertex factor that corresponds to the four-scalar interaction that is decribed by the following Lagrangian? \begin{equation} L = -\frac{1}{4} g_3^2 \phi^\dagger \lambda^a \phi \chi^\dagger \lambda^a \chi + \frac{2}{9} g_1^2 \phi^\dagger \phi \chi^\dagger \chi \,, \end{equation} where $\phi,\chi$ are complex scalar (color triplet) fields, $\lambda^a$ are the Gell-Mann matrices, and $g_1,g_3$ are the coupling constants corresponding to $\text{U}(1)$ and $\text{SU}(3)$ respectively. If we would have only had the second term here, say, then the vertex factor would simply be found by "dropping" the fields and multiplying by $i$. But now there are two terms contributing, and in the first term the Gell-Mann matrices even mix the color components of the scalar triplets. So how do I proceed in this case? And could anyone give me some general strategies on how to derive vertex factors for "complicated" interactions? For example, I also find it tricky to get the sign right if there is a derivative in an interaction. (If you are interested in the context of this Lagrangian, for $\phi = \tilde{u}_R$ and $\chi = \tilde{d}_R$ this Lagrangian describes the interaction between two up squarks and two down squarks in a supersymmetric theory.)


Radiofrequency attenuation in cold plasma

The missile plume can be considered a cold plasma. If a radio signal passes across the plume it's attenuated. Obviously the attenuation depends on the frequency of the signal. Where can I find some information about the behaviour of the RF across the cold plasma? Thanks


Solution Maxwell's equations cylinder

I face some trouble solving Maxwell's equations inside a cylinder with perfect conductor boundaries (in 3D) ? We work with cylindrical coordinates $(r, \phi, z)$ and we make the assumption that fields have a sinusoidal "$e^{i\omega t}$" time dependence. Note that we have a $\phi$ symmetry. First, and in any coordinates system, by taking the rotational and injecting one equation in the other we reduce Maxwell's equations to the following, $$ \nabla\times\nabla\times E = -\partial_t^2 E = \omega^2 E $$ In vacuum, from the $curl curl$ identity, it leads, $$ \nabla\times\nabla\times E = \nabla(\nabla . E) - \nabla^2 E = - \nabla^2 E $$ Where $- \nabla^2 E$ is the laplacian operator applied to each coordinate. Now, in cylindrical coordinates, we can only compute the $z-$coordinate since, in this case we get the wave equation, $$ \nabla^2 E_z = \omega^2 E_z $$ For the other coordinates, the change of coordinates introduce other terms such that (for the $\phi-$ coordin. ate)$\frac{E_r}{r^2} - \frac{2}{r^2}\frac{\partial E_\phi}{\partial\phi}$. Then, a fastidious step consists in performing a separation of variable which leads us quite easily to the solution for every separated variable and also to the Bessel differential equation which brings its solution, the Bessel function. Together with boundary conditions we can get the solution according to $z$ but what about the other coordinates ?


Doubt in law of mutual interaction

Book: Classical mechanics (textbook) by Douglas Gregory (cambridge publications) Law of mutual interaction states that when two particle (let it be P1 and P2) interacts, the particle (P1) induces an instantaneous acceleration (a21) on particle P2 and the particle P2 induces an instantaneous acceleration (a12) on particle (P1). If the (inertial)masses of the particles are same, then the magnitude of acceleration be the same, and the ratios of acceleration will be constant ( for this case it is 1)(consistency relation) That is what Newton's third law says. > My question is, for different (inertial)masses the ratio will be constant ( > but not unity) ( it does not satisfy consistency relation) Am i right? > > If yes My question is consistency relation is important in classical > mechanics?


What restrictions on time boundary conditions does it have to use Fourier transform to solve wave equation?

The wave equation can be solved using Fourier transform, by assuming a solution of the form of $$\mathbf{E}(x,y,z,t)~=~\mathbf{E}(x,y,z)e^{j\omega t}$$ and then reducing the equation to the Helmholtz equation.   * What are the presumed _restrictions_ on the solution, when solving the equation this way? (e.g., on _time_ boundary condition) I mean can this method give the most general solution (given some boundary conditions)? What _features_ does the solution obtained this way have?   * Does it have any difference with solutions obtained using Laplace transform? (The very same above questions, for Laplace transform.)


What would be the effect of an excess of up quarks on stellar formation?

Suppose you had 80% up quarks, and only 20% down quarks. How would this affect stellar formation?


What is crystal field anisotropy or effect ? It forces the magnetic moment to point in particular local direction..

Can you give a basic explanation of what is crystal field anisotropy ? What is the reason to arise ? In spin ice it forces the dipoles to point in the local 111 direction. For partially filled rare earth atoms hund rule requires S and L max. This leaves (2s +1)(2l+1) degeneracy which is partially lifted from the LS coupling. When inserted in anisotropic field inside crystal the expectation value , or mean value of L is 0 = 0 and the L is quenched leaving only S so is forced to point in some local direction, but this is if the field removes the deneracy ? Is it this or it is much more complicated ?


Lightning and nuclear fusion

I'm going to be brief, I just saw a Discovery Channel show that showed a lot of interesting phenomena around lightning (like elves, how cool is that(!)), and got me wondering. 1) Thinking of lightning as a purely mechanical phenomenon, I would think the elves are the "other side of the momentum balance". What I mean is this: somewhere in some cloud formation, an event happens that triggers a lightning flash. This means a ton of electrons (and other, associated particles) that start a _very_ fast journey to the surface of the Earth. Their momentum must be balanced by particles going in the opposite direction, hence elves. Am I right? 2) Taking this further, is it possible that the "trigger" for the lightning flash could be atomic/molecular fusion forced by extremely high electrical fields, that may only exist for a nanosecond, causing a ton of energy to be transferred to the electrons around the atoms/molecules, and we have lightning. I would then think of the energy necessary to force the fusion to occur as a quantum fluctuation as in $$\Delta E \Delta t \leq \hbar$$ 3) Is every arc caused by a particle collision, somewhat like in a particle accelerator? It seems logical to me: there are more than enough particles in the air to collide with, and all the light could well be some form of Brehm or Cherenkov radiation. The question I seem to be asking is where to find good scientific theory/information about lightning. Some say we know a lot about it, but I haven't found any good papers explaining it. I have a pretty good background in physics (1st year Master student) and am not afraid of serious literature. Thanks!


Strings with negative pressure

This question is inspired by the following comment: > the strings in string theory are relativistic and on a large enough piece of > world sheet, the internal SO(1,1) Lorentz symmetry is preserved. That's why > a string carries not only an energy density ρ but also a negative pressure > p=−ρ in the direction along the string. by Lubos at the end of his answer to the question "What is tension in String Theory?". I don't see how having a $SO(1,1)$ symmetry for the worldsheet leads to a negative pressure. I have the following questions:   1. Why does a string carry negative pressure?   2. Can a gas of strings then be treated as a substance which has a negative equation of state: $$ w = \frac{p}{\rho} = -1 $$   3. If this is possible then the next natural question is: what are the implications for the cosmological constant problem? **Background material to give some context for questions 2 and 3:** One part of the cosmological constant problem is an explanation of what form of matter could seed cosmological expansion. A cosmological constant term $\Lambda$ in the action for GR is equivalent to having a medium which satisfies the negative equation of state (relation between density and pressure). One simple example of matter with a negative equation of state is a homogenous, isotropic scalar field [for details see any book on cosmology with a chapter on inflation]. If strings carry negative pressure and if a string gas can be treated as matter with $w\sim-1$ then one would have a far more natural alternative to a scalar field.


How to get discretization coefficients of matrix $A$ in Finite Volume Method (FVM)?

First we have Discretization of the Transport Equation $$ \frac{\partial \rho \phi}{\partial t} + \nabla(\rho U \phi) - \nabla (\rho \Gamma_\phi \nabla \phi) = S_\phi (\phi) $$ In Finite Volume Method it looks like: $$ \int_t^{t+\Delta t} \left[ \frac{\partial}{\partial t} \int_{V_p} \rho \phi dV + \int_{V_p} \nabla \cdot (\rho U\phi)dV - \int_{V_p} \nabla \cdot (\rho \Gamma_\phi \nabla \phi)dV \right]dt = \int_t^{t+\Delta t} \left(\int_{V_p}S_\phi(\phi)dV \right)dt $$ and after transformations: $$ \int_t^{t+\Delta t} \left[ \left( \frac{\partial \rho \phi}{\partial t} \right)_p V_p + \sum_f F\phi_f - \sum_f(\rho \Gamma_\phi)_f S.(\nabla\phi)_f \right]dt=\int_t^{t+\Delta t}(SuV_p+S_pV_p\phi_p)dt $$ and time discretization: $$ \frac{\rho_p\phi_p^n-\rho_p\phi_p^o}{\Delta t}V_p+ \frac{1}{2}\sum_f F\phi_f^n-\frac{1}{2}\sum_f(\rho\Gamma_\phi)_f S.(\nabla\phi)^n_f+ \frac{1}{2}\sum_f F\phi_f^o-\frac{1}{2}\sum_f(\rho\Gamma_\phi)_f S.(\nabla\phi)^o_f = SuV_p + \frac{1}{2}S_pV_p\phi_p^n+\frac{1}{2}S_pV_p\phi_p^o $$ For every cell we can make equation: $$ a_p\phi^n_p+\sum_N a_N \phi_N^n = R_p $$ But how we can get elements of matrix $A$ if we don't know $\phi$? $$ [A][\phi]=[R] $$ Here Hrvoje Jasak wrote that every coefficient $ a_p $ includes the contribution from temporal derivative, convection and diffusion terms. But what formula of $a_p = ...$? http://powerlab.fsb.hr/ped/kturbo/OpenFOAM/docs/HrvojeJasakPhD.pdf


Calculate loudness of sound: why am I getting contradictory answers?

I know of events that are happening about 45 KM away from me which are said to be 210 or 213 dB at 75 meters distance from multiple sources. I think that I can hear them, so I did the obvious: $$ \frac{I_2}{I_1} = \left( \frac{d_1}{d_2} \right)^2$$ $$ I_2 = I_1 * \left( \frac{d_1}{d_2} \right)^2\text{ dB}$$ For my values: $$ I_2 = 213 \left( \frac{75}{45000} \right)^2\text{ dB}$$ $$ I_2 = 213 \left( \frac{1}{600} \right)^2\text{ dB}$$ $$ I_2 = \frac{213}{360000}\text{ dB}$$ $$ I_2 \approx 0.6 \cdot 10^{-3}\text{ dB}$$ Well, **0.6 e-3 dB** I should not be able to hear! However, going by the rule of thumb "twice the distance, minus three decibels": $$ 75 * 2^x = 45000 $$ $$ 2^x = 600 $$ $$ x = \log_2(600) $$ $$ x \approx 9.2 $$ $$ 213 - 3 \cdot 9.2 = 213 - 27.6 = 185.4 $$ The value of **184 dB** seems too loud, and additionally does not agree with the previous method. Lastly I tried tool for estimating Sound Levels With the Inverse Square Law from the usually-terrific HyperPhysics website. This tool gave a value of **157 decibels**! Another on-line tool gives the same result. **Which result should I trust?**


does light experience time?

If we positioned a mirror 1 light year away from earth and shot a particle of light at the mirror so that it would reflect and come back to earth, how long would it take for us to receive that particle of light back to earth and if I jumped on this particle of light for the trip how would it effect how much time has gone by for me and the people waiting for me back on earth


Double-slit experiment with alternating on-off switch

Suppose we perform a double-slit experiment with a detector placed at a position of minimum intensity (maximum destructive interference), off-center where the path lengths differ by half a wavelength. The light source is alternately turned on and off (or blocked and unblocked near the source) and the intensity over time is recorded. I interpret the uncertainty principle to mean that there will be a peak in intensity at the times when the switch is flipped (whether on-to-off or off-to-on). i.e., it will look something like this (in ASCII art):                __________'-----'__________'-----'__________      Is this correct? I have had trouble convincingly explaining my reasons for thinking so. What will be the measured intensity over time and why?


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 US has ignited over the years (most underground, but two notably in Japanese cities). So how much radiation exposure in the US was caused by the 105 nuke tests in the Pacific? Should the inhabitants of the West coast have taken iodine pills? I'd also like to know how much fallout these bombs produced, as compared to the reactor steam releases in Japan, 2011.


Rigid body dynamics joints

I can't seem to find any info on connected rigid bodies by a joint. Can someone explain the basics to me? I'm trying to do a little research to find out how feasible it would be to implement 3d ragdoll physics for my first person shooter game.


What is the Units for Thermal conductivity?

What are the units for thermal conductivity and why?


why does what get pushed away when centripetal acceleration is towards the center

If centripetal acceleration is towards the center, then why - when you spin a bucket of water (a classic demonstration) - does the water not get pushed out but rather stays in the bucket without spilling?


What is the covariant derivative in mathematician's language?

In mathematics, we talk about tangent vectors and cotangent vectors on a manifold at each point, and vector fields and cotangent vector fields (also known as differential one-forms). When we talk about tensor fields, we mean differentiable sections of some tensor power of the tangent or cotangent bundle (or a combination). There are various natural differentiation operations, such as the exterior derivative of anti-symmetric covariant tensor fields, or the Lie derivative of two vector fields. These have nice coordinate-free definitions. In physics, there is talk of "covariant derivatives" of tensor fields, whose resulting objects are different kind of tensor fields. I was wondering, what is the abstract interpretation of the general notion of a covariant derivative in terms of (tensor products of) tangent vectors and vector fields.


Is there a better, faster way to do this projectile motion question?

The question is > In a combat exercise, a mortar at M is required to hit a target at O, which > is taking cover 25 m behind a structure of negligible width 10 m tall. This > mortar can only fire at an angle of 45 degrees to the horizontal, but can > fire shells of any velocity. Find the minimum initial velocity required to > hit the target. ![diagram](http://i.imgur.com/yoTXyv8.png) I solved it as follows. Forming a parabola with $ r_v $ against $ r_h $: $ r_v = u_vt + \frac{1}{2}a_vt^{2} $ (1) $ r_h = u_ht + \frac{1}{2}a_ht^{2} $ but $ a_h = 0 $ so $ r_h = u_ht $ $ t = \frac{r_h}{u_h} $ (2) Substituting (2) into (1): $ r_v = u_v\frac{r_h}{u_h} + \frac{1}{2}a_v\frac{r_h^{2}}{u_h^{2}} $ (3) and because the angle of inclination is 45° $ u_v = u_h = \frac{u}{\sqrt{2}} $ (4) From (4) and (3): $ r_v = r_h^{2}\frac{a}{u^{2}} + r_h $ (5) Let the distance between the mortar and the building be $ d $. Then when $ r_h = d + 25 $, $ r_v = 0 $. (6) From (5) and (6): $ 0 = (d + 25)\frac{a}{u^{2}} + 1 $ so $ u^2 = -a(d + 25) $ (7) Substituting (7) into (5): $ r_v = -r_h^{2}\frac{1}{(d + 25)} + r_h $ (8) We also know that to clear the building, when $ r_h = d $, $ r_v > 10 $. (9) From (9) and (8): $ 10 < -d^{2} \frac{1}{(d + 25)} + d $ After simplifying... ($ d + 25 $ is positive) $ d > \frac{50}{3} $ (10) Rearranging (7): $ d = -\frac{u^{2}}{a} - 25 $ (11) And then from (10) and (11) and with $ a = -9.8 $: $ \frac{50}{3} < \frac{u^{2}}{9.8} - 25 $ Simplifying, and with the knowledge that $ u > 0 $: $ u > 20.2073... $ So the minimum initial velocity required to hit the target is **20 m/s** (2 s. f.). Huzzah! My question is: **is there a faster way to solve the problem?**


Help understanding the solution to a problem regarding kinetic energy of a group of point charges

The problem provided by my professor goes as follows: "Now consider a situation in which all charges are equal to q and they simultaneously become "unglued". What speed will each charge have when a hexagonal configuration has doubled in size (each side has a length). The work done was found to be $$U=\frac{kq^2}a\left(\frac{5}2+\frac{2}{\sqrt2}\right)$$ So far I have done: $$\Delta K=-\Delta U$$ $$K_f=U_i-U_f$$ $$6\cdot\left(\frac{1}2mv^2\right)= k\frac{q^2}a\left(\frac{5}2+\frac{2}{\sqrt3}\right)-\frac{kq^2}{2a}\left(\frac{5}2+\frac{2}{\sqrt3}\right)$$ However, the solution is: $$6\cdot\left(\frac12mv^2\right)=k\frac{q^2}a\left(\frac{15}2+\frac{6}{\sqrt2}\right)-\frac{kq^2}{2a}\left(\frac{15}2+\frac{6}{\sqrt3}\right)$$ Can anyone explain why?


Is it possible to build an optical system that increases the perceived surface brightness?

So is it possbile to build a system from lenses and mirrors that can make faint gas nebulas brighter or can be used as nightvision? If you increase the size of the aperture of a telescope it will collect more light, but the exit pupil will be also bigger, so not all light will enter the eye. In order to direct all light into the eye you'll need to shrink the exit pupil and you'll need a stronger eyepiece. But this will increase the magnification too and the collected light will spread on a larger image so the surface brightness will remain the same. Is it possible to work this limitation around?


Quantum mechanics - how can the energy be complex?

In section 134 of Vol. 3 (Quantum Mechanics), Landau and Lifshitz make the energy complex in order to describe a particle that can decay: $E = E_0 - \frac{1}{2}i \Gamma$ The propagator $U(t) = \exp(-i H t)$ then makes the wavefunction die exponentially with time. But also, $H$ is non-Hermitian. My question: Do we have to modify the basic postulates of quantum mechanics (as described by Shankar, say, or the earlier sections of Landau & Lifshitz) to describe unstable particles?


What temperature can you attain with a solar furnace?

A solar furnace is a device that concentrates the sun's light on a small point to heat it up to high temperature. One can imagine that in the limit of being completely surrounded by mirrors, your entire $4\pi$ solid angle will look like the surface of the sun, at about 6000K. The target will then heat up to 6000K and start to radiate as a blackbody, reaching thermal equilibrium with the sun. The question is: is there any way to surpass this temperature, perhaps by filtering the light to make it look like a BB spectrum at higher temp, then concentrating it back on the target?


when an object moves downward, is its height negative?

the question is: A ball is thrown directly downward with an initial speed of 8.00m/s from a height of 30.0m. After what time interval does it strike the ground. so i went through the problem and got the answer 1.79 sec. but after reviewing some notes from my teacher, I got the idea that in equations where an object is dropped down, the height has to be counted as negative. so I went through the problem again using -30m, but now my answer doesn't check out when plugged back in to x - x0 = V0 (t) + 1/2 at^2 Is there something I'm missing about this idea that height or distance is negative in drop-down questions?


How to do this index notation differentiation?

I am studying classical Maxwell fields and I am stuck on this differentiating part. How can I derive the result given below ? $$\dfrac{\partial}{\partial(\partial A_{\mu}/\partial x_{\nu})} \left(2\dfrac{\partial A_{\sigma}}{\partial x_{\lambda}}\dfrac{\partial A_{\sigma}}{\partial x_{\lambda}}-2\dfrac{\partial A_{\sigma}}{\partial x_{\lambda}}\dfrac{\partial A_{\lambda}}{\partial x_{\sigma}}\right)$$ The answer is $$4\dfrac{\partial A_{\mu}}{\partial x_{\nu}}-4\dfrac{\partial A_{\nu}}{\partial x_{\mu}}$$ where $A$ is vector potential and $x$ is four-vector.


What are "parity considerations" in deciding the form of the Hamiltonian?

In "introductory Quantum Optics", by Gerry and Knight, the Jeynes model is considered. In this model of electron-EM field interaction the electron is approximated by a two state system ($\lvert g\rangle$ and $\lvert e\rangle$), and the form of the dipole operator $\hat{d}$ is said to be constrained by parity consideration not to have on-diagonal terms: > Only the off-diagonal elements of the dipole operator are nonzero, since by > parity consideration $\langle e\rvert\hat{d}\lvert e\rangle=0=\langle > g\rvert\hat{d}\lvert g\rangle$. Why? What does parity have to do with it?


Is the axial gauge with a $\xi$ term useful in Yang-Mills theory?

i) Do people use axial gauge with a $\xi$ term? When $\xi\neq 0$, ghosts do not decouple, but maybe it's still useful? ii) Is it proved that the term $\frac 1 {2\xi}(n.A)^2$ in the Lagrangian does not renormalize, for $\xi=0$ and $\xi\neq 0$?


Understanding the relationship between electricity and magnetism

I keep on hearing that magnetism is just another form of electricity and vice versa. If that's the case why can't we use magnets as batteries, and why aren't my batteries magnetic?


Frequency of a Tuning Fork

**Question:** Which of the following affect the frequency of a tuning fork?   * Tine stiffness   * Tine length   * The force with which it's struck   * Density of the surrounding air   * Temperature of the surrounding air **Answer Attempt:** Based on the formula for the frequency, I know that tine stiffness (or density) affects it, and so does the tine length. I believe the temperature and density of air can have a slight affect as well. What about the force with which it's struck?


If a material is built to handle tension, would removing the tension damage it?

If an object is designed to cope with large forces such as tension, would removing these forces risk damaging the object? For example: The neck of a guitar is built to handle the tension of steel strings (~800 Newtons), if you removed/reduced the tension (removed the strings) for a long period of time would this risk damaging the guitar neck?


Stopping potential in the photoelectric effect, collector work function

In this question I am talking about the following situation: ![enter image description here](http://i.stack.imgur.com/Q4brH.gif) Now, I know that the max kinetic energy of the electrons emitted is $KE_{max} = h\nu - e\phi_{em}$ where $\phi_{em}$ is the work function of the emitter electrode (on the left in the diagram). And my lecturer agrees with that, but he tells us that the stopping potential $V_0$ can be found using $eV_0 = h\nu - e\phi_{col}$ where $\phi_{col}$ is the work function of the collector electrode (on the right in the diagram). The emitter and collector electrodes are made from different metals. What I don't understand is why the stopping potential doesn't depend on the kinetic energy of the emitted electrons. **EDIT** I have attached the slide from the lecture course ![Lecture slide](http://i.stack.imgur.com/vJ2aF.png)


Dependence of intensity of a LED on forward bias voltage

Due to increase in forward bias voltage, the intensity of light increases but after a particular value the intensity decreases. Why?


Fermi Energy and the Electric Potential

In an extrinsic semiconductor the electric potential is: $$\phi = \frac{1}{q}(E_{\mathrm{F}} - E_{\mathrm{Fi}})$$ where $E_{\mathrm{F}}$ is the Fermi energy, $E_{\mathrm{Fi}}$ is the intrinsic Fermi energy, $q$ is the electron charge and $\phi$ is the electric potential. I am not sure where this equation comes from. I understand why a potential will be created qualitatively, but where does this equation come from quantitatively? From what I understand , the expected value of the electron energy is the Fermi energy. You take $E_{\mathrm{Fi}}$ as the reference for the electron potential. This is the equilibrium condition of an intrinsic semiconductor. If you dope the semiconductor, you introduce an imbalance and that causes the generation of an electric field, hence the new expected value $E_{\mathrm{F}} - E_{\mathrm{Fi}}$. Is that correct?


From where does the sound come from when two charged objects meet in real life?

I am sure all of us have played with rubbing things and producing static electricity and when I was charging my comb by rubbing it on my hair and watching it attracting a small piece of paper, I heard a very feeble noise just like an electric buzz sound. I could feel the electron "cloud" all around the comb and the paper it I could find no reason as to why a sound should be produced. From where is that sound coming from?