Convert ECI coordinates to latitude/longitude?

I have been given output in (what I believe to be) ECI format (from OrbitTools):               TSINCE            X                Y                Z             0.00     4733.08693007    5370.64476064       0.09227655      360.00    -3928.94737512   -4784.93071195   -3602.13095174      720.00     2078.23905091    2928.47218732    6181.06427083     1080.00      343.60889986    -292.76288815   -7150.74620799     1440.00    -2682.96778230   -2415.73481378    6170.18900818      and need to convert the x,y pairs to latitude/longitude (to plot on a map where the object is above). I can't reason through the conversion. Is there a document that a laymen could get through or formula that would take a given time/point and yield a terrestrial latitude and longitude?


Terms allowed in Lagrangian density

I never fully understood why the Lagrangian density (let's say for a scalar field) was restricted to have only first order derivatives of the field in time and space in QFT. One reason I can think of is to ensure locality. But that doesn't restrict one from having a finite number of higher-order derivatives of the field, does it? Thanks!


Why does a moving electric charge have nonuniform electric field lines?

The electric field of a stationary electron is uniform, radially symmetric with straight field lines. However, the electric field of a moving electron still has radial and straight field lines, but they are no longer uniformly distributed, and the effect becomes more pronounced at higher speeds (that is, the field lines become more and more perpendicular to the direction of motion). I found this effect in this applet. Can someone physically explain to me the cause of this nonuniformity in the field lines? Thanks in advance.


Relation between Higgs boson and force of gravitation

I don't know and I can't handle it. I am so much curious about the recent discoveries in science. European Space Agency and NASA are doing great work. Hats up to these institutions. My nights are sleepless just thinking about the consequences of Higg's Boson. I am so excited for the thing that all the science fictions turning into reality will be happening in my generation. I am able to see it. Currently I am 28. So I am very optimistic about it when I went through the NASA and ESA's vision and missions down the years till 2025. I would be very much happy and grateful to know if someone can explain me a little about the relation between Higgs Boson and Force of Gravitation(Gravitons if exists). By any means does Higgs Boson supports String Theory?


Are voltages discrete when we zoom in enough?

Voltages are often thought of as continuous physical quantities. I was wondering whether by zooming in a lot, they are discrete. I feel like the answer to the above question is yes as voltages in the real world are generated by actions of electrons. Can someone give me a more formal proof or a disproof? Whether voltages are discrete of continuous can have some impact the correctness of devices such as the analog to digital converter. For example, if voltages in the real world are continuous, then the Buridan principle[1] says that there cannot be a perfect analog to digital converter because such a device makes a discrete decision from continuous inputs. [1] : Lamport, L. (2012). Buridan’s Principle. Found Phys 42, 1056–1066. http://link.springer.com/article/10.1007/s10701-012-9647-7 (It would be great if someone could also answer a related question http://electronics.stackexchange.com/questions/126091/is-there-an-adc-with-a- finite-bound-on-measurement-time)


How can you calculate the exact position of the Earth taking into account the gravitational attraction of Mars and the Sun?

I think there must be a formula to calculate the exact position of the Earth taking into account the gravitational attraction of Mars and the Sun. Is it possible with vectors?


Significant Figures (rules of addition)

It is a simple one but different teachers answer this question differently. $$34+1.4+0.2$$ what would be its answer with due regards to significant figures?


semiclassical exact expression (in one dimension only)

let be $ N(x)= \sum_{n} H(x-E_{n}) $ the eingenvalue 'staircase' function and let be a system so $ V(x)=V(-x)$ and $ V^{-1}(x)=\sqrt \pi \frac{d^{1/2}}{dx^{1/2}} N(x) $ then would it be true that the two function $\sum_{n}exp(-tE_{n})=Z(t)= \int_{0}^{\infty}dN(x)exp(-tx) $ and $ \int_{0}^{\infty}dx\int_{0}^{\infty}dpexp(-tp^{2}-tV(x))=U(t) $ would be equal ?? i have just compared the two results $\int_{0}^{\infty}dnN(x)exp(-tx)=\int_{0}^{\infty}dx\int_{0}^{\infty}dpexp(-tp^{2}-tV(x)) $ i have taken the Laplace transform inside and get the desired result assuming that the potential V(x) is EVEN


How did the energy/entropy/volume/pressure/temperature relationship exist at the Big Bang and how did it evolve thereafter?

According to the current Big Bang with inflation cosmological model? I was under the mistaken impression that there was very low volume, very high temperature/pressure, very low entropy and the Big Bang (perhaps prompted by the high pressure) resulted in an expansion of volume where energy didn't change much so temperature went down and entropy went up. Now I've learned about inflation and how there is no conservation of energy at cosmological scales and that the universe gained an exponential amount of energy during the inflationary period. How did this happen with a _decrease_ in temperature? Inflation was a period of supercooled expansion, was it not? Why was positive pressure not enough to cause inflation such that we need a negative pressure in the form of the inflaton field (or later dark energy) to explain the expansion of the universe? Thanks for your time


Conceptual quantum field theory

Often papers and books give some bold(deep physical insight) statements in quantum field theory which are not backed by mathematics, and seldom by citing papers. Being a student I don't grasp the real meaning of those statements, making me think that I don't really understand QFT. I have access to all the standard books in QFT, but is there a book/lecture notes that really aims to explain QFT in a way in which the ideas emerged, it's philosophy with a physical insight at a level of a graduate student ? I am mighty interested in doing theoretical high energy physics, and crave for a better understanding of QFT. Could somebody help me ....


Proportion of energy compared to mass in universe

In Wikipedia (http://en.wikipedia.org/wiki/Dark_matter), there is a picture that shows us the proportion of matter and energy in the current universe - CMB. It seems to suggest there is nothing that exists as energy form except dark energy - which we are yet to see - and every observable exists as matter forms. Is this correct interpretation? Of course, I know that matter's mass can be converted into energy by Einstein's basic and famous equation. If every observable exists as matter, is energy always converted to matter after being converted into energy from matter? Thanks.


Can someone explain the science behind MIT's 230% efficient LEDs?

I was reading Gizmodo the other day and I didn't quite understand the Physics behind this. Could anybody shed some light on how this effect actually works?


How is an ideal mirrored box of photons distinguishable from massive particles?

Suppose you have an ideal mirrored box that contains enough photons as to have a relativistic mass equivalent to the [rest mass + kinetic energy] of an electron. In other words, the two systems have the same total energy. How would I distinguish these two systems? They have equivalent gravitational pulls and I believe they have equivalent inertia. Are charge and spin the only distinguishing factors (I'm assuming the "box" itself has no properties of interest)?


why nontrivially space-like connected event horizons do not respect unitarity?

I want to understand the assertion that the gluing between distant event horizons is forbidden by unitarity. What is exactly the argument that unitarity will necessarily forbid topological nontrivial spacetimes?


representation of SU(2)

The question is regarding SU(2) group and SU(2) algebra. The SU(2) group can be generated by exponentiating the generators of SU(2) algebra $X_a$ as $exp(i t_a X_a )$ with $t_a$ being three parameters. Genreally we use half the Pauli matrices as $X_a$ when discussing SU(2) algebra as well as the group. But if we use the spin-1 representation of $X_a$ (which can surely be done at the Lie Alebra level) can they be exponentiated to give another rep. of the SU(2) group (which would be 3 dimensional)?


photons in expanding space: how is energy conserved?

If a photon (wave package) redshifts (streches) traveling in our expanding universe, is it's energy reduced? If so, where does it go?


With redshift, energy is lost. Where does it go?

A photon emitted by a distant source billions of light years away arrives here with a lower frequency hence less energy than it started with. What happened to the energy?


What are hidden variables exactly?

What are hidden variables in quantum mechanics? I am aware there are many types but what exactly do they mean or even "do" exactly? Do they mean that the quantum indeterminacy becomes hidden but still exists in reality somewhere but is hidden? Or does it mean that it is a hidden mechanism which means the reality underneath really is single world determinism or there abouts? I have done some searching but it really is not clear to me.


What's the physical meaning of the Fourier transform of magnetic flux density?

I have here below the distribution of the magnetic flux density $B$ across a 1 pole pitch in the airgap of a synchronous machine. The horizontal axis represents the distance along the arc length formed by a pole pitch across the airgap. ![plot of flux density distribution](http://i.stack.imgur.com/0NEXq.jpg) If I take the Fourier Transform of this flux density,how should I interpret the results? I am used to taking Fourier Transform with respect to time and not with respect to spatial data that I have here. Thanks a lot... **Update** I think it makes sense instead to use the Fourier Transform on a complete cycle (i.e. not the half cycle shown up) to look at the harmonics that we have in the magnetic flux density. This is what I get: ![enter image description here](http://i.stack.imgur.com/GxmWI.jpg) I guess from the Fourier Transform, this is the only information that is relevant.


Why would it be true that people with longer legs walk faster than ones with shorter legs?

When a person walks, the only force acting on him is the force of friction between him and the ground (neglecting air resistance and all). The magnitude of acceleration due to this force is independent of the mass of the object (longer legs have more mass). Hence the person should move with with a velocity independent of the length of his legs. But I have heard (also observed) that people with longer legs walk faster than ones with shorter legs. If that is true, then why? One can argue that the torque about the pivot due to friction is more in case of longer legs, But then the torque due to gravity (when one raises his leg to move), which opposes the frictional torque, is also more for longer legs. And why would these torques make a difference anyway, as they have no effect on the acceleration of the center of mass?


Is Space conserved

Can space be created or destroyed? Is space conserved? I am **not asking for matter,energy and time**. Its just a question about **conservation of space** PS: I am asking for **what was there before big bang**. Surely Big bang would require space in the first place...


Negative energy/mass bounds on de-Sitter spacetime

There exists a Positive Energy theorem for General Relativity in Anti-de Sitter and asymptotically flat spacetimes, but there is no equivalent theorem for de Sitter spacetimes > **Question:** Is there a lower bound theorem on negative mass-energy density > on de Sitter spacetimes? The intuition says that the absence of a positive energy theorem in dS has to do with the fact that for small enough positive energy densities, the cosmological expansion beats the gravitational attraction, which means that positive energy densities need to exceed a threshold in order to behave attractively from far away. Is this intuition correct?


Cause and properties of northern lights

If outside on a dark night in the middle to high latitudes, one might be able to see an aurora. It may be several hundred kilometers high and several thousand kilometers long, stretching around Earth in an arc. However, it is less than 1 km thick. What produces this huge display and what makes it so thin?


Quality loss when adding more components to a telescope?

I would think this would be inherently true, but I'm curious: (Assuming the highest quality _amateur_ instruments are used.) Is quality lost when, say, adding a T-mount adapter, diagonal or any other instrument between your eyes (or camera) and the primary focus? Maybe not discernible to our eyes, but could this be something to avoid when approaching astrophotography?


How can sunlight be white , but pictures of the sun be orange?

I was thinking about elementary physics today and realised: We learned and proved that sunlight is white. But i don't understand why when you look at a picture of a satellite orbiting the sun , it(the sun) seems yellow-orrange. How could this be? It is like there is a red light bulb in the room but what you see is green.


Topological insulator vs. topological superconductors in any dimension

My question today is simple. What is the difference between a topological insulator and a topological superconductor? How that difference depends on the dimensionality of space(time)? What is the difference in terms of the so- called edge states? PS: I only know that a topological insulator is some material that is conductor on the edge but insulator in the bulk...Is that definition right in ANY dimension?What about topological superconductors?


Why some particles interact with the Higgs field and others don't? Higgs doesn't explain that much: why some particles have mass and others don't? is like why some particles interact with the Higgs field and others don't?


Absorption of radiation due to temperature

I was wondering if the temperature of an object affects the amount of radiation it absorbs. For example, if I have a box that is hotter, will it absorb more energy as compared to the same cooler box?


Is it foolish to distinguish between covariant and contravariant vectors?

A vector space is a set whose elements satisfy certain axioms. Now there are physical entities that satisfy these properties, which may not be arrows. A co-ordinate transformation is linear map from a vector to itself with a change of basis. Now the transformation is an abstract concept, it is just a mapping. To calculate it we need basis and matrices and how a transformation ends up looking depends only on the basis we choose, a transformation can look like a diagonal matrix if an eigenbasis is used and so on. It has nothing to do with the vectors it is mapping, only the dimension of the vector spaces is important. So it is foolish to distinguish vectors on the way how their components change under a co-ordinate transformation, since it depends on the basis you used. So there is actually no difference between a contravariant and covariant vector, there is a difference between a contravariant and covariant basis as is shown here http://arxiv.org/abs/1002.3217. An inner product is between elements of the same vector space and not between two vector spaces, it is not how it is defined. Is this approach correct? Along with this approach mentioned, we can view covectors as members of the dual space of the contra-vector space. What advantage does this approach over the former mentioned in my post? _Addendum:_ So now there are contra variant vectors and their duals called covariant vectors. But the duals are defined only once the contravectors are set up because they are the maps from the space of contra vectors to $R$ and thus, it won't make sense of to talk of covectors alone. Then what does it mean that the gradient is a covector ? Now saying because it transforms in a certain way makes no sense.


How exactly is the Poisson bracket of the modes of a classical string defined?

In the theory of a classical bosonic string, we have expressions like: $$ \\{\alpha^\mu_m,\alpha^\nu_n \\} = - i m \delta_{m,-n} \eta^{\mu \nu} $$ were $\alpha^\mu_n$ are the Fourier modes of the string. How is this Poisson bracket defined? The definition from analytical mechanics involves partial derivatives with respect to the generalized coordinates and momenta. Since the modes $ \alpha^\mu_n $ are constants, their partial derivatives are zero, so there must be something I'm missing here.


Why is static friction called self adjusting force?

Explain what is limiting force of static friction.


Confusion concerning the use of wavenumber in exercise about Fabry-Perot etalon

In the exercise we are given that the spectrum of a light source consists of two spectral lines, which both have wavelengths around $500 \text{ nm}$ and the separation between them - given in wavenumbers - is close to $0.1 \text{ cm}^{-1}$. One part asks us to calculate the distance between the mirrors if we want the free spectral range of our Fabry-Perot etalon to satisfy $FSR(\text{in } \overline \nu) = 2.5(\overline \nu_2 - \overline \nu_1)$. Now, I know that the free spectral range ($\theta = 0$, $n_{air} \approx 1$) is given by $$FSR = \frac{c}{2d}$$ where $d$ is the distance between the mirrors and we have $$\Delta\overline \nu = \frac{c}{\lambda_2} - \frac{c}{\lambda_1} = \frac{c}{2\pi}\Delta k $$ So shouldn't then $$d = \frac{c}{2 FSR} = \frac{c}{2 \cdot 2.5c/(2\pi) \Delta k} = \frac{\pi}{2.5\Delta k} \approx 12.566 \text{ cm}$$ According to the solution this is wrong: They get $FSR = 0.25 \text{ cm}^{-1}$ and $d = \frac{1}{2 \cdot FSR} = 20 \text{ mm}$ I seem to be missing something. If they calculate the free spectral range in terms of the wavenumber, shouldn't they convert it to frequency by $$FSR(k) \to FSR(\nu) = \frac{c}{2\pi} FSR(k)$$ instead of $$FSR(k) \to FSR(\nu) = c \cdot FSR(k)$$ Does anybody see what's going on here (maybe the solution is simply wrong, but I'd like to know for sure)?


What's the difference between arc length and signed distance?

Suppose I give you a position function $x(t)$ where t is time and x is position. Then i ask you to find the total distance travelled from $t = 0$ to $t = t_f$. Which formula would give you that distance? $$\int_{0}^{t_f} \sqrt{1 + [x'(t)]^2} dt$$ $$\int_{0}^{t_f} |x(t)| dt$$ I know the first one gives you the arc length of the path (which is the total length of the path) and the second one gives me the signed distance, but why are they fundamentally different again?


Commercial large scale production of graphene

I am a third year undergraduate Physics student, and for my solid state physics course I am asked to give a short (10 minute) qualitative presentation on the current standings of graphene production, about what can be done right now, what is expected to be doable in the near future, what the current problems are that have to be solved, etcetera. However, I am having quite some trouble in finding suitable sources. It is of course such a hot topic that new papers come out basically every day, and it is hard to find 'objective' sources that don't just talk about how a specific company has found the new, best way to do it. I suppose this is a bit of a non-traditional question to ask, but I was wondering if someone could help me out by pointing me towards some reliable, recent sources. A review article would be optimal, but of course as it is such a swiftly changing field this might be difficult. What I plan on doing at this point is structuring my presentation along these rough lines To start with, talk about how the 'first' graphene was made, using the scotch tape. Everyone I will talk to knows this, but it is still nice to see, especially with good pictures. I will then move on to what can already be done: several techniques that exist and that are being implemented as we speak, and what exactly they produce (multilayer graphene instead of monolayer, for example), and what the problems are that 'we' are currently facing in producing good graphene. Then I would like to talk about what is on the horizon, and on what timescales we expect what. If anyone has any comments on this (improvements or things I should definitely include) I would also be very happy to read them.


Is antumbra part of shadow darker than penumbra part of shadow?

I'm exploring different types of shadows casted by objects.   I want to know if antumbra part of a shadow is darker than penumbra part. I've found two misleading pictures on Wikipedia:   First: ![Antumbra light](http://i.stack.imgur.com/c5pTC.png) Second: ![Antumbra darker](http://i.stack.imgur.com/ApN9C.jpg) Which one is correct? This example outside astronomy shows that antumbra is lighter than penumbra part of the shadow: ![Antumbra outside astronomy](http://i.stack.imgur.com/wABFH.jpg) btw. Are there any reliable online references on that topic?


Neglecting second order differentials

I am currently doing some Lorentz invariance exercises considering infinitesimal Lorentz transformations, and have been told to neglect second order differentials. It's not the first time I have come across seeing something like this, and I wonder which is the justification behind this, I mean, is this a justifiable exact procedure or just an approximation?


Do stationary states with higher energy necessarily have higher position-momentum uncertainty?

For simple potentials like square wells and harmonic oscillators, one can explicitly calculate the product $\Delta x \Delta p$ for stationary states. When you do this, it turns out that higher energy levels have higher values of $\Delta x \Delta p$. Is this true for all time-independent potentials? Certainly, it is possible to find two states $\mid \Psi_1 \rangle$ and $\mid \Psi_2 \rangle$ with $\langle \Psi_1 \mid H \mid \Psi_1 \rangle > \langle \Psi_2 \mid H \mid \Psi_2 \rangle$ and also $\Delta x_1 \Delta p_1 < \Delta x_2 \Delta p_2$. For example, choose a quadratic potential, let $\mid \Psi_2 \rangle$ be the first state and let $\mid \Psi_1 \rangle$ be a Gaussian coherent state (thus with minimum uncertainty) and fairly high energy. So I'm asking here just about the stationary states. As Ron pointed out in the comments, this question is most interesting if we consider potentials with only a single local minimum, and increasing potential to the right of it and decreasing to the left.


Relation between unitarity and conservation of probability

In a seminar, I heard that the unitary aspect of representations was important physically, because in quantum mechanics unitarity is closely tied to the conservation of probability. Could someone explain why this is so? After a bit of thought, one vague connection I can think of is that a matrix generated by a Hermitian matrix, $$U =e^{iH},$$ where $H$ is Hermitian is bound to be unitary . As Hermitian matrices correspond to observables, this must have some signficiance. Though, as I said, I still have the faintest idea.


What do "local" and "global" mean when talking about standard deviations in experimental particle physics?

I found the following sentence: The excess is most compatible with a SM Higgs hypothesis in the vicinity of 124 GeV and below, but the statistical significance (2.6σ local and 1.9σ global after correcting for the LEE in the low mass region) is not large enough to say anything conclusive. I am familiar with sigma, but not familiar with local and global. What do they mean?


Time passing near a black hole

Given distance $d$ from a normal black hole with mass $m$, how much seconds will pass at that distance while in infinite distance from the black hole $t$ seconds has passed?


What is the correct term to describe matter converting into energy?

Matter and energy are related; one can convert into the other. What is it called when this happens? For example, solids melt/liquefy into liquid, and liquid vaporizes into gas. Gas condenses into liquid, and liquid solidifies into solid. So matter [verb] into energy, and energy [verb] into matter. What are the correct verbs to use here? I am thinking that they are "energize" and "materialize", but I'm not sure, especially about "energize".


Lev Landau's "Theoretical Minimum"

The great russian physicist Lev Landau developed a famous entry exam to test his students. This "Theoretical Minimum" contained everything he considered elementary for a young theoretical physicist. Despite its name, it was notoriously hard and comprehensive, and in Landau's time, only 43 students passed it. I wonder if anyone can provide the list of topics, or even a copy of the exam? (I'm sure I'd have no chance to pass, but I'd like to see it out of a sense of sportmanship ;-). Also, I think it would make quite a good curriculum of theoretical physics (at least pre 1960).)


What are the differences between the terms flammable, inflammable, and non-flammable?

This question should perhaps go in Chemistry, to which I am committed, but since the Chemistry Stack Exchange forum is not yet in beta, I am wondering if you can help me from a physics perspective. I am wondering about the definitions of the terms _flammable_ , _inflammable_ , and _non-flammable_. Wikipedia says that _flammable_ and _inflammable_ are **synonyms** , meaning "capable of burning". In contrast, _non-flammable_ means "not capable of burning". To avoid confusion, it is recommended that use of the term _inflammable_ be avoided, since the prefix _in-_ here does not mean "not". This generally makes sense and sounds like good advice, but as I was reading a journal paper today, I came across a paragraph using these terms. I am wondering if you can help me by telling me your interpretation of the intent of this paragraph: > During the last decade room temperature ionic liquids (RTIL), being salts of > low temperature melting points, have been studied extensively. They may be > used as solvents for many processes and as electrolytes in electrochemical > devices. Batteries filled with such a type of electrolytes do not contain > any volatile components and therefore, they are not flammable. Room > temperature ionic liquids, being usually quaternary ammonium salts, are > characterized by negligible vapor pressure, which makes them inflammable. In > addition, they show a broad electrochemical stability window, generally >4 > V, which is necessary for the application in lithium-ion batteries with > high-energy cathodes. This is from page 602 in "Ionic liquids as electrolytes for Li-ion batteries-- An overview of electrochemical studies", Lewandowski, A.; Swidereska-Mocek, A. _Journal of Power Sources_ **2009** , _194_ , 601-609, which is available to subscribers here. The first part, **"...do not contain any volatile components and therefore, they are not flammable"** , seems to make sense; room temperature ionic liquids are promising in part because they do not ignite or burn easily, so they can potentially improve the safety of batteries. However, the next mention seems to say just the opposite: **"...are characterized by negligible vapor pressure, which makes them inflammable"**. So, my question is, does it seem to you that the term _inflammable_ has been used incorrectly in this paragraph? Does negligible vapor pressure imply that a substance is likely to burn readily or not burn readily? Thank you very much.


What is the physical meaning of a "complete" Hilbert space in QM?

What does the word "complete" means from the physical point of view? I do not understand what it physically means to say that a Hilbert space is a complete vector space.


Completeness of the state space and Hilbert space

I am wondering just why is it supposed that quantum states lie in a Hilbert space, which mathematically requires completeness? In other words, what does completeness (defined in terms of Cauchy sequences) imply physically?


How can a strong water current be cold

This is a layman question. If heat is the motion of atoms, how can a fast moving water current be cold?


What is the meaning of the gradient of a current vs time graph? In other words, what does the unit $As^{-1}$ or $Cs^{-2}$ represent?


What variables does the action $S$ depend on?

Action is defined as, $$S ~=~ \int L(q, q', t) dt,$$ but my question is what variables does $S$ depend on? Is $S = S(q, t)$ or $S = S(q, q', t)$ where $q' := \frac{dq}{dt}$? In Wikipedia I've read that $S = S(q(t))$ and I think that suppose, $q$ and $t$ are considered as independent coordinates. Then $S$ should depend on $q'$ also because, for the typical lagrangian $$L ~=~ \frac{q'^2}{2} - V(q).$$ I think we cannot find a function $Z(q, t)$ such that $$L = \frac{dZ(q, t)}{dt}?$$


Why do neutrino oscillations imply nonzero neutrino masses?

Neutrinos can pass from one family to another (that is, change in flavor) in a process known as neutrino oscillation. The oscillation between the different families occurs randomly, and the likelihood of change seems to be higher in a material medium than in a vacuum. Why does the oscillation of neutrinos directly imply that they must have a nonzero mass, since the passage of one flavor to another can only occur in massive particles? And What are the cosmological implications of these oscillations?


We have a ball projected at 20 m/s at an angle $\pi/6$ from the x-axis. Now we have to calculate x-coordinate of the ball when it's velocity is perpendicular to projection velocity. I am thinking about how to solve this problem. Is it related to the equation of trajectory? What I have figured out so far, is that it will be making angle $\pi/3$ from x-axis at this instant how to get the x-coordinate?


Does our existence cost us energy?

Anything when it needs to inform its presense such as electromagnetic presense of charged particles and gravitational presense of particles due to their mass does so by sending information of its existencs propogated in space via means of electromagnetic waves or hypothesised gravitational waves. So as a part of telling others of their presense to others, do the particles constantly lose their enegy ? I understand that they could also gain energy in same way, but if a particle was completely isolated would it lose its existence and turn into pure energy over time ? I understand that the mass and energy would together remain constant, but my question is that whether something would happen to a particle or would it remain a particle ?


Large gauge transformations

I would like to understand what is the importance of large gauge transformations. I read that these gauge transformation cannot be deformed to the identity, but why should we care about that?


Hawking radiation and reversibility

It's often said that, as long as the information that fell into a black hole comes out _eventually_ in the Hawking radiation (by whatever means), pure states remain pure rather than evolving into mixed states, and "the universe is safe for quantum mechanics." But that can't be the whole story! For quantum-mechanical reversibility doesn't merely say that information must _eventually_ be retrievable, after 1070 years or whatever; but also that, if U is an admissible transformation of a physical system, then U-1 is also an admissible transformation. So, just like it must be consistent with reversible microlaws for smoke and ash to spontaneously reassemble into a book, it must also be consistent for a black hole to spontaneously "uncollapse" into a star, or into whatever configuration of ordinary matter could have collapsed to form the black hole in the first place. And this "white-hole uncollapse process" must be possible in exactly the same amount of time as the black-hole collapse process, rather than an astronomically longer time (as with Hawking radiation). In both cases, the explanation for why we never see these processes must be thermodynamic -- i.e., sure they're allowed, but they involve such a crazy decrease in entropy that they're exponentially suppressed. I get that. But I'm still confused about something, and here's my best attempt to crystallize my confusion: > In order to explain how it could even be _possible_ for information to come > out of a black hole, physicists typically appeal to Hawking radiation, which > provides a mechanism based on more-or-less understood quantum field theory > in curved spacetime. (Granted, QFT also predicts that the radiation should > be thermal! But because of AdS/CFT and so forth, today people seem pretty > confident that the information, after hanging out near the event horizon, > _is_ carried away by the Hawking radiation in some not-yet-understood way.) > However, suppose it's objected that a Hawking radiation process seems > nothing whatsoever like the time-reverse of an ordinary black-hole formation > process. Then the only response I know would be along the lines of, "well, > do you believe that QM will survive unaltered in a future quantum theory of > gravity, or don't you? If you do, then consider the unitary U corresponding > to a black-hole formation process, and invert it to get U-1!" My question > is: why couldn't people have made that same straightforward argument even > _before_ they knew anything about Hawking radiation? (Or _did_ they make > it?) More generally, even if Hawking radiation _does_ carry away the > infalling information, that still seems extremely far from implying full > quantum-mechanical reversibility. So, how much does the existence of Hawking > radiation really have to do with the case for the compatibility between > quantum mechanics and black holes?


Using bra-ket notation?

Am I using Bra-ket notation correctly? I want to define a superposition of the states, $|0\rangle$ and $|1\rangle$. Is it simply? $|0\rangle + |1\rangle$ I can't find any non-technical information on it. I'm just a hobbyist.


What happens in a circuit, when the wire and the battery are superconducting. And shorted

When a wire with no resistance is connected to the terminals of an ideal battery, will a current exist in the circuit? If a capacitor is added to the circuit, will it be charged by the battery or will it remain uncharged? In all cases there is absolutely no resistance through the circuits.


Are there new states of matter at ultrahigh temperatures and densities?

Under extreme energetic conditions, matter undergoes a series of transitions, and atoms break down into their smallest constituent parts. Those parts are elementary particles called quarks and leptons, which as far as we know cannot be subdivided into smaller parts.Is there exist new states of matter?


Energy in electric field

I'm having some trouble understanding a homework question and would appreciate some help. The question is as follows: > Jenny charges a capacitor with the help of a battery. She then removes the > battery and halves the distance between the two plates. How does the energy > conserved in the capacitor change? I solved the question like this: $E=\frac{U}d$ and $U= \frac{W}Q$ $\implies W=EQd$ Hence, the energy doubles (as $E=\frac{U/d}2 \implies 2E=\frac{U}d$) where: $W$ = energy, $E$ = Electric field intensity, $Q$ = charge, $U$ = voltage, $d$ = distance This answer doesn't make any sense to me, considering the law of conservation of energy (So, Where did all that energy come from?) It also turns out that my answer is wrong, in fact the energy is halved. This also doesn't make any sense to me, what am I _missing_?


How to set the electric potential on a certain boundary to a certain value experimentally?

In electrostatic boundary value problems, usually the potential is set to some function or a constant on a certain boundary. It is never taught or told in textbooks how such assignment might be achieved experimentally. For example how to set experimentally the potential on the boundary of a ball of radius $R$ to some constant $V_0$, where $V_0$ could be $-100 V$ or $0 V$ or $5 V$ say?


What property of objects allow them to float?

I used to think that the shape of an object determines its ability to float (boat-shaped objects are more likely to float, and spheres tend to sink). But my friend, who is fond of making me look stupid, took me to the local lake showed me a sphere that floated and a boat-shaped object made out of iron that sunk. Is it based on the mass? I'm not sure that is possible, because I've seen really heavy things (like airplane carriers) float, and really light things (like my friend's iron boat) sink. What property of certain objects allow them to float, if any?


Photon statistics of an incandescent light source

We usually calibrate the cameras on our microscopes by capturing 20 images of a blurry (not sharp) fluorescent particle. For each pixel in this stack of 20 images we calculate the intensity variance. By plotting the variance against the intensity we obtain the scale factor that allows us to convert the ADU (arbitrary data unit) into detected photoelectrons. However, this approach relies on a light source with Poisson statistics. This is applicable for fluorescence light. **But can we also use light of a halogen lamp instead of fluorescent light?** I heard that photons leaving a heated metal surface have a particular statistic. I think the argument was that they are coming out in bunches and it has something to do with the workfunction. It would be nice if someone could give a good reference on this. ![Calibration results of an EMCCD camera](http://i.stack.imgur.com/9BX1D.jpg) The picture above shows the calibration curves for an EMCCD camera. The left graph corresponds to the readout mode you would use for bright images and has a readnoise of 15 electrons per pixel. The graph on the right shows the result for the low noise mode. In this mode the charge that has been accumulated under the pixels is transferred through an electron multiplication register. Impact ionization increases the number of electrons. The gain is usually up to 300x. The inset on the lower right is how a calibration image looks like. Note that this one is fake.


Finding the volume of this irregular shape I have

I have an approximately basketball-sized non-hollow piece of aluminum sitting in my house that is of irregular shape. I need to find the volume of it for a very legitimate yet irrelevant reason. What is the best way I can do this? In fact, what are **all** the ways I could feasibly do this without going to a lab? (I don't live near any labs)


Charge inside a sphere

Suppose I have a sphere of radius $r$ with all the charge residing on the surface, distributed uniformly i.e. charge density $\sigma$ is constant. I want to find the electric field created by this sphere. All problems of this sort I have solved by enclosing the sphere in a larger imaginary sphere with radius $R$, and then using the assumption that the electric field lines are in a radial direction, in combination with the divergence theorem. If I use that method for this question, I find that the Electric field inside the sphere is zero. I can't understand this intuitively. I would have thought that if you are in the proximity of charge, there will be an electric field. Why would the electric field lines extend outwards radially from the sphere, and not inwards too?


Generalized momentum conjugate and potential $U(q, \dot q)$

On Goldstein's "Classical Mechanics" (first ed.), I have read that if $q_j$ is a cyclic coordinate, its generalized momentum conjugate $p_j$ is costant. He obtained that starting from Lagrange's equation: $\frac {d}{dt} \frac {\partial L}{\partial \dot q_j}- \frac {\partial L}{\partial q_j}=0$ But this Lagrange's equation refers to a conservative system. What would happen if I considered a system in which the potential is $U(q, \dot q)$?


Derivation of the Poynting Vector without the Poynting Theorem

My professor worked out the Poynting Vector without using the Poynting Theorem-I can't remember how. I can't seem to figure out where the cross product would come in.


Physical significance of effective wave function

In Yanhua Shih's book on quantum optics, the coherence functions are expressed in terms of effective wave function. Here are the expressions for single photon wave packets. ![enter image description here](http://i.stack.imgur.com/Cr13p.jpg) To derive the coherence functions we have used Heisenberg picture where the field operators, not the wave functions, are time dependent. We can also take a look at the effective wave function for thermal source. ![enter image description here](http://i.stack.imgur.com/dSds4.jpg) So, it is confusing why we have a wave function with time as a parameter. What is the physical significance of effective wave function?


How to find the value of the parameter a in this transfer function?

> **Possible Duplicate:**   >  How to find the value of the parameter $a$ in this transfer function? I am given a transfer function of a second-order system as: $$G(s)=\frac{a}{s^{2}+4s+a}$$ and I need to find the value of the parameter a that will make the damping coefficient $$\zeta=.7$$ I am not sure how to do this but I might have found something that might have helped so I am going to take a stab at it. I found a transfer function in the book of a second order spring-mass-damper system with an external applied force in the book as: $$G(s)=\frac{a}{m\omega_{n}^{2}}(\frac{\omega_{n}^{2}}{s^{2}+2\omega_{n}\zeta+\omega_{n}^{2}})$$ I was thinking that I could writeZx: $$2\omega_{n}^{2}\zeta=4$$ and $$\omega_{n}^{2}=a$$ asd And then solve for a. Would this be possible?


"WLOG" re Schwarzschild geodesics

Why, when studying geodesics in the Schwarzschild metric, one can WLOG set $$\theta=\frac{\pi}{2}$$ to be equatorial? I assume it is so because when digging around the internet, most references seem to consider this particular case... and some actually said "wlog". But why? I don't think the motion is necessarily confined to a plane? Correct me if I'm wrong, but isn't the Euler-Lagrange equations for the coordinate $\theta$ $$\ddot\theta +\frac{2\dot r}{r}\dot\theta-\dot\phi\sin\theta\cos\theta=0?$$ I don't see why the motion can be "wlog" in $\theta=\frac{\pi}{2}$.


What is the wave function outside the barrier region?

I've been trying to learn how to apply WKB for several days now. I asked a similar question already about trying to find the wave function inside the barrier region. Now I would like to understand how to find the electron outside the barrier region. > _An electron, say, in the nuclear potential_ $$U(r)=\begin{cases} & -U_{0} > \;\;\;\;\;\;\text{ if } r < r_{0} \\\ & k/r \;\;\;\;\;\;\;\;\text{ if } r > > r_{0} \end{cases}$$ > > _What is the wave function outside the barrier?_ Here's my work so far: Outside the barrier region, $E>U(r)$ so $$\psi(r)=\frac{A}{\sqrt{|p(r)|}}e^{\frac{1}{\hbar}\int_{0}^{r}|p(r')|dr'}+\frac{B}{\sqrt{|p(r)|}}e^{-\frac{1}{\hbar}\int_{0}^{r}|p(r')|dr'}$$ where notice that the exponents are real. My question is: are the bounds for the integral correct?


Particles as a limit of classical field theory

A common academic exercise has been to show that classical mechanics is a limit of quantum mechanics, usually by putting $\hbar \rightarrow 0$. Similarly is it possible to show that a limit to field theory will lead to a particle ?   May be by considering a initial field configuration such that the "lumpiness" of the particle is there, and then as it evolves it maintains that. Clearly such an initial field configuration will continue to evolve as it is in a free field theory as two different modes don't talk to each other, but what about an interacting model ? Are there any instances in the literature which attempts to establish this connection ?


Why do some pressure cookers initially leak steam from the sides and after a while settle down and don't leak? Is it a positive feedback mechanism from the building steam which makes the sealing tighter and vice versa?


Relationship between balloon size and pressure

I see numerous websites talking about how a small balloon is at higher pressure than a big balloon. This is a fun counter-intuitive factoid... unless it isn't a fact at all. Young-Laplace gives $$T = \Delta p \frac R2 $$ Which means that for a given tension, increasing the radius does decrease the pressure. But why would the tension be constant? A latex balloon is like a 2D spring, right? So the tension in a inflated spherical balloon should be proportional to the surface area, correct? $$T \propto R^2 $$ But this gives $$\Delta p \propto R$$ Which means the bigger the balloon, the higher the internal pressure. Which, again, would be the normal intuition - but it would burst the bubble of some simplified explanations. (har har)


Calculating laser wavelength/power to cause emission of light in a gas?

I've become interested in volumetric displays. In particular I'm looking at a pair of lasers scanning a volume of gas such that the intersection of the lasers would supply enough energy to cause the gas to emit visible light. Since this is the start of my research I would like to investigate a number of gases in order to determine a number of gases which might be suitable for this application. I have, however, forgotten how to determine the amount of energy needed to cause an outer shell electron to emit a photon, and then trying to back-calculate the required wavelength(s) and power requirements of the laser emitters. I'm looking for some information on how to identify the required information for a given gas and how to calculate the energy required to cause visible light emission, and also information on how the wavelength of laser light impacts the ability of the gas to absorb the energy with the intended effect of emitting visible light. Links to introductory texts are always helpful, as are answers which help me get the terminology correct so that I can improve my searches for this information.


Quantum circuit, two control not gates

Consider the quantum circuit in the picture below: ![Figure 1](http://i.stack.imgur.com/s80aW.jpg) We have a Hadamard gate followed by a CNOT gate, this puts the 2nd & 3rd state in the bell state $\beta_{00}=\frac{1}{\sqrt2}(\mid 00\rangle +\mid 11\rangle$ This occurs because the CNOT gate flips the target qubit iff the control qubit is $\mid 1 \rangle$. The two qubits are now entangled. When we proceed to the second CNOT gate we only care about what state the second wire is in? Would someone be able to help explain how we can compute how the top wire acts in this situation? Or if someone would be able to explain in general how we treat qubits entangled such as this if we want to say something about them separately? At the end of the circuit we have two detectors $x$ and $y$, these will collapse wave function, two two lower qubits will carry on unchanged in their bell state, how would we describe the middle wire being measured by $x$?


Does quantum manybody theory with 2nd quantization completely equivalent to 1st quantization formulation?

by equivalent I mean:   1. the Hilbert spaces are isomorphic;   2. the operators can therefore be mapped 1:1


For a fixed power input, is it better to hit something with a light rod or a heavy rod?

My friends and I got into an argument about whether it was more damaging to hit an object with a heavy rod or a light rod. The sides of the argument go something like: "If you swing the light rod, you'll be able to swing it much faster and therefore do the most damage!" "Yes, but if it's too light there won't be enough mass behind it and it won't damage as much!" I have been toying around with this question for a few months and I have yet to come up with a satisfactory answer. I'm setting up the problem like this: **Person A** is swinging a rigid rod of mass $m$ and fixed length $L$ at **Object B** located at a fixed distance $d$ away. Imagine **Person A** is swinging the rod much like a baseball player would swing to hit a ball. **Person A** has a fixed power $P$ to input to the rod over distance $d$ before making impact with **Object B**. Given input power $P$, rod length $L$, and swing distance $d$, what is the optimal mass $m$ of the rod to maximize the damage of **Object B**? For simplicity, I'm modeling the power application to be over a linear rather than angular distance, and I'm modeling **Object B** as a spring with spring constant $k$ attached to a fixed wall. Effects of gravity should be ignored. Also, for now ignore the constraints of human strength and assume we can swing anything as heavy as we like.


Do greenhouse gasses make the world habitable?

An ageing gent says he does not accept this statement:               It's a fact that greenhouse gases, predominantly water vapour, keep the Earth      from being hostile and cold; that CO2 albeit in trace quantities is also a      greenhouse gas and therefore helps keep the planet warm...      I know no more about why he rejects this statement - maybe it is that water vapour alone would do the job. The gent in question has a first class degree and a doctorate in physics. Is there a debate within the physics community over this or am I misunderstanding?


Why is Avogadro's law always true?

Why is Avogadro's law always true? How and why do equal volumes of gases at equal pressure and temperature contain equal number of molecules? I know it is a fundamental principle in chemistry but I wonder how it works.


Increasing resistance, by heat?

I was wondering the magnitude of effect to a conductor's resistance when heated by a few degrees. Can this be controlled way of changing conductor's resistance, or fixing in a system?


Coverage of Quantum Electrodynamics (QED) in introductory Quantum Field Theory (QFT) books

Which QFT books also cover QED? I am not very familiar with QED, so I am looking for QFT books which cover QED too (I know they cover Quantum Chromodynamics (QCD).).


What is the difference between "kinematics" and "dynamics"?

I have noticed that authors in the literature sometimes divide characteristics of some phenomenon into "kinematics" and "dynamics". I first encountered this in Jackson's E&M book, where, in section 7.3 of the third edition, he writes, on the reflection and refraction of waves at a plane interface: >   1. Kinematic properties: (a) Angle of reflection equals angle of incidence > (b) Snell's law >   2. Dynamic properties (a) Intensities of reflected and refracted radiation > (b) Phase changes and polarization > But this is by no means the only example. A quick Google search reveals "dynamic and kinematic viscosity," "kinematic and dynamic performance," "fully dynamic and kinematic voronoi diagrams," "kinematic and reduced-dynamic precise orbit determination," and many other occurrences of this distinction. **What is the real distinction between _kinematics_ and _dynamics_?**


Heat & thermodynamics question based on heat loss

![enter image description here](http://i.stack.imgur.com/FkbmQ.jpg) A Sphere A is placed on a smooth table.Another sphere B is suspended as shown in the figure.Both the spheres are identical in all respects.Equal quantity of heat is supplied to both spheres.All kinds of heat loss are neglected.The final temperatures of A & B are T1 & T2 respectively,then   * T1>T2   * T1 = T2   * T1    * None of these Please give reasons for your answer.


Why is 55-60 MPH optimal for gas mileage of a passenger car?

My driver's education teacher back in high school said 55 MPH is optimal for gas mileage of a passenger car. Just last week, I read an article in a magazine saying 60 MPH is optimal. These numbers are pretty close, so there's some validity in the statement. What's the physics explanation for this 55-60 MPH sweet spot?


Toppling of a cylinder on a block

A uniform cylinder rests on a cart.The height and diameter is given.coefficient of static friction is given.How can i find the minimum acceleration of block such that the block topples? Morever what is the reason of toppling? ![cylinder on block](http://i.stack.imgur.com/eBbOx.png) Again, if i consider static friction to be the cause,then what is the point of rotation? If i consider the top to be te point of rotation,then why does the block topple with the lower end as point?I have conducted this experiment many times and if the block falls,it fell along the lower end.


Uncertainty principle - momentum so precise that uncertainty of position is outside light-cone?

Thought experiment: what happens if we measure momentum of a particle so precisely, that the uncertainty of its position becomes absurd? For example, what if the uncertainty of the position exceeds 1 light year? We know for a fact that the particle wasn't a light year away from the measuring device, or else how could the momentum have been measured? What if the uncertainty extended beyond the bounds of the universe? Isn't there some point at which we know for certain the particle was closer than what the uncertainty allows for?


Is Tube light polychromatic?

Is tube light/fluorescent lamp monochromatic or polychromatic? Please justify.


How do I calculate pressure drop across a reduction in pipe diameter?

If reducing from one pipe size to another through a reducing fitting, say 6.25cm to 5cm, how do I calculate the pressure drop? Also, how does this impact a change in volumetric flow rate (or does it affect the volumetric flow rate)?


The Time That 2 Masses Will Collide Due To Newtonian Gravity

My friend and I have been wracking our heads with this one for the past 3 hours... We have 2 point masses, $m$ and $M$ in a perfect world separated by radius r. Starting from rest, they both begin to accelerate towards each other. So we have the gravitational force between them as: $$F_g ~=~ G\frac{Mm}{r^2}$$ How do we find out at what time they will collide? What we're having trouble with is this function being a function of $r$, but I have suspected it as actually a function of $t$ due to the units of $G$ being $N(m/kg)^2$. I've tried taking a number of integrals, which haven't really yielded anything useful. Any guidance? No, this is not an actual homework problem, we're just 2 math/physics/computer people who are very bored at work :)


Solid in Liquid Heat Transfer

If there is a solid immersed in a large (but finite) pool of water, where the solid has temperature $T_s$ and the water has temperature $T_w$, with $T_w>T_s$, how can I calculate $T_s(t)$ and $T_w(t)$? (Suppose that the masses and the material properties of the solid are known.)


Graphene +1 extra carbon bond

I'm not a physicist just a curious mind, so please go easy! I was just watching a BBC Horizon Documentary that featured a piece on the recently discovered material Graphene. One of the facts mentioned on the documentary was that a sheet of graphene, despite being a lattice of carbon atoms just one atom thick, could hold the weight of a household cat without breaking. They showed an illustration of graphene's hexagonal structure and how a crude form of graphene could be created using Sellotape and piece of graphite. OK so here's my question.. From what I can remember from Chemistry lessons in school, carbon has a valency of 4, so it can bind to 4 more carbon atoms. Surely (in theory at least) a sheet of carbon could exist that adopts a square grid lattice, as oppose to graphene's hexagonal structure. If so wouldn't such a material be stronger than graphene? Also would such a lattice naturally form under any circumstance or does carbon always assume a hexagonal structure when reduced to layers?


Amateur Stargazing (30 degrees N)

When I look at the sky I easily recognize Orion, The Big Dipper, and the North Star (in relation to the Big Dipper). Besides these (and the moon^^), what **_easily identifiable_** (unaided eye) astronomical objects should I look for? (Latitude = 30 degrees North)


How did micrometeorite flux change with the age of the solar system?

Do we also have functions for the micrometeorite flux on the Moon, Mars, and even any random body in space as a function of solar distance too?


Minkowski to Euclidean

When dealing with solutions to Einstein's equations given by a 4d metric with signature $(-,+,+,+)$, we're able to move to Euclidean space using some transformation so that our signature is now $(+,+,+,+)$ and our metric is changed slightly different. What I'm worried about is what this does to the properties of my metric. When I go to Euclidean space, I am able to deduce some nice relations, however, $\textbf{do these relations hold for my original metric?}$ e.g. let's say I'm interested in the metric $$ds_1^2=-V_1dt^2+\frac{dr^2}{V_1}+W_1d\Omega^2,$$ where $d\Omega^2$ is metric on $S^2$. Now my metric in Euclidean space is $$ds_2^2=+V_2dt^2+\frac{dr^2}{V_2}+W_2d\Omega^2.$$ where $V_1(a,b,c)=V_2(i a,b,c)$ and for $V_2$ I have some cool relation (e.g. $V_2(a=b)=0$, for $i$ the imaginary number. How can I relate this to the properties of $V_1$ if $a$, $b$ and $c$ are real parameters? The reverse transformation gives $V_1(-i a=b)=0$, but I don't know how to interrupt this $a$ and $b$ are real. Perhaps I haven't throughout deeply enough about it yet and it's a naive question, but I don't think I yet comprehensively understand what this transformation means for the properties of our space.


Why isn't angle of launch used in this kinetic energy equation?

Question: A stick is thrown from a cliff 27 m high with an initial velocity of 18 m/s at an angle of 37 degrees above the horizontal. a) use the law of conservation of energy to determine the speed of the stick just before it hits the ground. solution: ![a busy cat](http://i60.tinypic.com/2qmdz74.png) Just wondering why the vertical initial speed vector isn't used? Should 18sin37 be used? I think I am confusing myself with projectile motion.


EM wave properties

Here are two small questions about EM wave properties: **Question 1:** Why do E and B propogate simultaneously? See picture ![enter image description here](http://i.stack.imgur.com/RcVwS.jpg) I mean why do not works a paradigm “changing E makes B and changing B makes E?” For such scenario we would have phase shift beatween E and B by $\pi/2$. I am asking because of f.e. maximum of B = dE/dt it is when E=0. So why not E = E_max*sin(x) and B=B_max*cos(x)? **Question 2:** But for standing wave we have phase shift beatween E and B by $\pi/2$ (by theory). http://www.youtube.com/watch?v=tbR93plA1WU ![enter image description here](http://i.stack.imgur.com/FlZVj.png) So do you know some experiments to confirm that maximums of B are really shifted by $\pi/2$ for standing wave?


Correlation between color of light visible to us and the intensity of transmitted light by the material

I wanted to know if there is any relation between the color of light observed by the eye and the intensity of light transmitted by a material. Let us assume that I have a table of intensities of light transmitted at different wavelengths by a material for 2 materials. Is it possible to determine which material will appear more colored and which is that color? I know that if a material transmits with more intensity at the wavelength of green light, it would be more 'greener' but what will be the effect of a range of wavelengths?


Hamiltonian Operator for Harmonic Oscillator

I have been solving the harmonic oscillator problem in quantum mechanics using Algebraic Method and since then I am consulting the books of Tannoudji and Griffiths for that matter. While studying both of them I ham having a small confusion while defining the Hamiltonian operator Tannoudji used this expression $\frac{H}{\hbar w}$ for defining the Hamiltonian operator where $H$ is classical Hamiltonian while Griffiths have not used this expression at all. The confusion is how this expression from Tannoudji came across and why Griffiths did not use this expression at all.


Why did the ancients fail to discover that the Earth orbits the Sun?

The ancients observed that the Sun and the 'fixed' stars rotated about the Earth. They were also aware that the Earth was spherical. They performed many astronomical measurements on the planets - which are far less 'obvious' than the Sun and the stars. Presumably they knew that the speed of rotation of the Sun and the 'fixed' stars differed and that difference happened to be one day a year. It would seem (in retrospect) obvious that this was no coincidence and no other heavenly motion was so clearly linked to any other. Could they not have deduced that the difference was due to the annual path of the Earth around the Sun?


Spectral energy distribution fitting tools or routines

I have observed magnitudes and fluxes for an object in different wavelengths from optical to mm. Now I need a tool, routine or something like that to fit a spectral energy distribution (SED) and derive some physical parameters from the fit. I'm looking for a ready tool which can be run remotely or installed locally. Mind you, I'm aware of this: http://caravan.astro.wisc.edu/protostars/


How to get a $\mathcal{N}=2$ SuperYang-Mills Lagrangian from a quiver

How can one write down the $\mathcal{N}=2$ SuperYang-Mills Lagrangian given a quiver graph? For concreteness consider the quiver $$(2)-(4)-[6]$$ where the node $(2)$ corresponds to a $U(2)$ factor of the gauge group, the $(4)$ node is a $U(4)$ factor and the $[6]$ node is a $SU(6)$ global symmetry (flavour). The lines correspond to two $\mathcal{N}=2$ hypermultiplets charged in the fundamental representations of one node and the antifundamental representation of the other node into which the line ends. In particular, how can one read the superpotential from this graph? How can one read the Kahler potential? Is this latter one always assumed to be canonical? In case you would like to choose an easier quiver to make an easier example it is perfectly fine.


Lagrangian Mechanics - Commutativity Rule $\frac{d}{dt}\delta q=\delta \frac{dq}{dt} $

I am reading about Lagrangian mechanics. At some point the difference between the temporal derivative of a variation and variation of the temporal derivative is discussed. The fact that the two are the same is presented in the book I am reading as a rule, commutativity, and possible non-commutative rules are mentioned too. I do not get it: given a path $q(t)$ and its variation $\delta q(t)$, the equivalence between the variation of the derivative $\delta \dot{q}$ and derivative of the variation $\dot{\delta q}$ seems to me a fact descending straight from calculus, not an arbitrary choice.


Could this mean that Schrodinger's Cat thought experiment is false?

Since it is uncertain on whether or not the cat could be dead or alive, it is concluded that it depends on the observer to make it either dead or alive. But lets look at a clock. It doesn't take observance of the gears to make it function. The clock ticks despite there being an observer. Could this mean that the famous thought experiment is false?


Hamilton-Jacobi Equation

In the Hamilton-Jacobi equation, we take the partial time derivative of the action. But the action comes from integrating the Lagrangian over time, so time seems to just be a dummy variable here and hence I do not understand how we can partial differentiate $S$ with respect to time? A simple example would also be helpful.


Can path integrals be used to understand entanglement?

I like path integrals. I prefer to try to understand quantum phenomena in terms of path integrals rather than Hamiltonian mechanics. However, most of the standard texts on quantum mechanics start from Hamiltonian mechanics and mention the path integrals as a side note. This makes it difficult for me to gain insight into common phenomena (with a few exceptions like certain areas of optics) from the perspective of path integrals formulations. I am aware of some exceptions to this rule (books on path integrals in particular), but I have only seen entanglement explained from the perspective of eigenstates of a Hamiltonian. I was wondering how entanglement would be interpreted if you started from a path integral formulation. I would be more than happy to hear from a quantum field theoretic perspective as well, but the usual quantum mechanical path integral would certainly satisfy my curiosity.


My conundrum with Gauss’ law in electrostatics

If I use Gauss’ law to calculate the electric field outside of a charged (conducting or insulating) sphere or a point charge, the fields are the same. However, as a test approaches a point charge, the field becomes infinite whereas the test charge approaching the surface of the sphere reaches a finite value of $Q/4πϵ_0R^2$, where $R$ and $Q$ are the radius and charge of the sphere. Why wouldn’t the field also go to infinity as I get infinitesimally close to the surface of sphere? Those are just “point charges” on the surface. What ultimately led me to this question was trying to physical understand why Gauss’ law predicts the same field for a charge point and charged sphere (obviously $r > R$). I don’t understand it.


All mirrors always shrink to 50% scale?

I have this geometric optics exercise here, in which a man is looking at himself in a mirror.   1. Determine the minimum height at which the bottom of the mirror must be placed so the man can see his feet (his eyes are at 1.7m).   2. How does this height vary depending on the distance from the mirror to the man's eyes?   3. What is the minimum length of the mirror so that the man can see his entire body (assume he is 1.8m tall). From the principle that the reflected angle is equal to the incident angle, we show that the minimum height of the bottom of the mirror is directly between the feet and the eyes (1), and that this does not depend on the distance to the mirror (2). The top of the mirror must be directly between the man's crown and eyes at the lowest, in order to reflect the top of his head, **therefore the mirror must be half the height of the man, at minimum**. Thus, the mirror reflects the man's image at a scale of 50%. But this doesn't depend on the distance from the mirror, and from what I can tell, doesn't even depend on the size of the mirror. These results, to me, indicate that no matter what kind of mirror you use or where you stand, your image should appear half way up the mirror, and at 50% scale.


Why is it difficult to differentiate between interference and diffraction? Is it because we don't clearly understand how both of these phenomenon takes place? My thoughts: From an answer to one of my earlier question here I could understand that light waves behave differently when it strikes a slit which is of several times bigger than its wavelength and when it strikes a slit of size comparable to it its wavelength.In the former case the different points on the slit acts as wave-front sources producing circular wave fronts which interfere to form the diffraction pattern but in the later case plane wave-front striking a slit after passing through it forms circular wave-fronts and two such wave-fronts from two different slits interfere to form the interference pattern. But, I'm not satisfied by that because I don't get any intuition about points on the slit acting as wavefront sources. So, what is actually happening?


Replacing diode in circuit analysis?

While analyzing circuits containing diodes in reverse bias I replace it with a pure insulator for simplifying things. Similarly can I replace a forward biased diode with a conductor and a varying resistance in series?


Is there a method to estimate the atomic yield of a supernova of a given size?

Given a supernova with stellar mass $M$, is there a theoretical method to estimating the isotope yield? If so, what processes are taken into account, and how accurate can the estimate be? Would it be more accurate if more properties were known about the star (e.g. metallicity)?


As stated in the heading: Is $\frac{\partial}{\partial \Phi(y)} \Phi (x) = \delta(x-y)$ correct? Here denotes $\Phi(x)$ denotes a scalar field. And if yes, why? Any reference where I can read about this would be great.


anti-matter activation energy

In chemical reactions, there are usually energy barriers that must be overcome before a reaction can take place. It seems that such a phenomena also exists at the atomic level as well. For instance, a certain amount of energy must be provided to two nuclei to bring them close enough together to fuse and release more energy than was input. In general, I read things like "energetically favorable" or "a lower energy state is available". However, in examining the behavior of anti-matter, it seems almost as if there is no such barrier between matter and anti-matter: they annihilate immediately on contact, converting most or all of their matter into energy. It seems like such a sharp divide between total annihilation with virtually no extra energy added to the equation, versus almost total stability for either matter or anti-matter by itself. Why such the big difference? Why does anti-matter seem to have no constraints to "decaying" into energy in the presence of matter (and vice versa) like other processes do? I know there are certain quantities like charge which must be conserved but it seems like a pretty abstract thing to say we don't all spontaneously decay into photons simply because charge must be conserved. Why isn't there some kind of energy barrier between matter and anti-matter which must be overcome before they can react? If anti-matter had negative mass, then it would have negative energy, in which the lack of such a barrier would make more sense. However, I don't know of any evidence that suggests anti-matter has negative mass. My naive guess would be that since a particle and anti-particle have opposite spin, they sort of "slam into" each other and cancel out, causing the particle to "break apart" into a free wave. However, since my understanding of spin is that it isn't really the same kind of spin we would observe at the macroscopic scale, i.e. actual physical rotation, this seems like an unreal explanation to me.


Many photons, one quantum field?

If a photon can be described as an excitation in a quantum field, is this the same field for all photons, or does each photon exist in its own field?


CP-symmetry and Ward identities and finite temperature

I have a few questions about Ward-identities which I summarize here. For each I am very greateful for answers and references to literature. Wikipedia states about Ward-identities: > _The Ward-Takahashi identity is a quantum version of the classical Noether's > theorem, and any symmetries in a quantum field theory can lead to an > equation of motion for correlation functions._   1. Taken seriously this means that Ward-Takahashi identities also exist for discrete symmetries like CP (if present in the Lagrangian) in contrast to a conserved Noether current. If so, I wonder if CP relations between amplitudes, such as $|\mathcal{M}|_{S_i\rightarrow S_f} =|\mathcal{M}|_{\bar{S}_i\rightarrow \bar{S}_f}$ which I can get by computing the amplitudes in perturbation theory and comparing, can be considered Ward-identities. $\bar{S}_{i,f}$ are the CP-conjugated states of ${S}_{i,f}$ respectively.   2. Since Ward-identities are considered to hold for the quantized theory, I wonder if they are invariant under the renormalization group running of parameters. If so, how does RGE running take these restrictions into account.   3. Finally I wonder if there is an established finite-temperature generalization.


NMR rotating frame

I'm reading about a linearly polarized field (in the context of NMR). The field is given by $$ {\bf H_{lin}}=2H_1({\bf i}cos(\omega_zt)).$$ This can be created by having a pulse field plus its mirror image; i.e. $${\bf H_1}=H_1({\bf i}cos(\omega_zt)+{\bf j}sin(\omega_zt)).$$ The mirror image field in the lab frame is obviously the same as ${\bf H_1}$ expect $\omega_z \rightarrow -\omega_z.$ Now, my question is what is the expression for the counter-rotating "mirror image" field in the ROTATING frame? I've having some trouble working through this...


Modeling non-quantum objects (in finance, sociology etc) using fermionic fields?

Please provide (if any) applications of fermionic field theory in non-physics macro contexts (finance, sociology etc). I see only bosonic fields being used mostly. The only (minor) application of fermionic fields that I have come across is in section 7.9.1 in Baaquie's Quantum Finance book where nonlinear forward interest rates are modeled using fermionic fields. Is there an intuitive reason for such asymmetry between bosonic and fermionic field usage at such scales?


How to calculate gravity path integrals about an AdS background?

Suppose I have some Lagrangian of some higher derivative gravity coupled to a may be matter fields. Now I want to fluctuate it to quadratic order about an AdS background and calculate the 1-loop partition function. Can someone point to a reference where such a thing might be done? This sounds like something standard which someone would have done... I can't see how one can even write down the fluctuated Lagrangian to quadratic order...And even if I wrote that down, how does one impose that the background is AdS? Then the issues of gauge fixing and ghosts are only added complication.. * * * I can imagine calculating the first order variation in the Christoffel symbols and Riemann and Ricci tensors but that goes only so far.


Learning about super-symmetric quantum mechanics and integrable systems

I'm an undergraduate interested in theory. I recently asked one of my professors, a physicist in the particle theory group at my school, if he'd be willing to take on an undergraduate for a senior project. He told me to check back in at the end of the quarter, and that he might have a project related to super-symmetric quantum mechanics and integrable systems that may be feasible for me to try out then. In the meantime, I want to familiarize myself as much as possible with the relevant math and physics so that I can impress him when I ask again. Do any of you have any books/online sources that you recommend I take a look at?


Matrix representation of a triplet state

The $SU(2)$ triplet state is typically given in the fundamental representation as a column vector, e.g. \begin{equation} \vec{\Delta} = \left( \begin{array}{c} \delta^{++} \\\ \delta^+ \\\ \delta^0 \end{array} \right) \end{equation} where I use this notation to be consistent with the references below. However, I'm reading through papers (in the context of the type II see-saw mechanism, but I don't think it has much relevance) and most references are using what they call the matrix representation of the $SU(2)$ triplet. My instinct was to assume that they were projecting the fundamental representation onto the Pauli matrices: \begin{equation} \Delta \rightarrow \vec{\Delta } \cdot \vec{ \sigma } = \delta ^{++} \sigma _1 + \delta ^+ \sigma _2 + \delta ^0 \sigma _3 \end{equation} However, this doesn't quite give me the correct result, which is given by, \begin{equation} \Delta = \left( \begin{array}{cc} \delta ^+ / \sqrt{2} & \delta ^{ + + } \\\ \delta ^0 & \- \delta ^+ / \sqrt{2} \end{array} \right) \end{equation} Is there some other way to get this "matrix representation"? Two sample references where they say they are using the matrix representation can be found here (pg. 124, equation 68) and here (pg. 4 equation 1).


Uniform Circular Motion: v = v_0 + (a_T)*t as a vector VS as a scalar equation

First, I'll explain my confusion, which may be enough for someone to clarify my misunderstanding. Second, to give context, I will give the homework problem (which I've solved successfully) which caused my confusion. Note: I'll use boldface to denote vector quantities. Also, I am in my third semester of Calculus. A particle accelerates around a track. Velocity is given by the below equation. $$ v = v_0 + a_Tt $$ When I substitute in values for this equation to solve homework problems, I use scalar values—in other words, I use magnitudes. I find $|\mathbf{a_T}|$ to use in the above equation. However, if the equation is written as a sum of vectors: $$ \mathbf{v} = \mathbf{v_0} + \mathbf{a_T}t $$ Then I take the magnitude of both sides . . . ($\theta$ is the angle between the positive $x$-axis and $\mathbf{a_C}$.) $$ \begin{align} |\mathbf{v}| &= |\mathbf{v_0} + \mathbf{a_T}t|\\\ &\text{. . . algebra . . .}\\\ &= \sqrt{|\mathbf{v_0|}^2 + 2|\mathbf{v_0}||\mathbf{a_T}|t + |\mathbf{a_t}|t^2}\\\ &\ne |\mathbf{v_0}| + |\mathbf{a_T}|t\ \ \text{*} \end{align} $$ But the starred equation is what I am using for homework problems and I get the answers with no problems. * * * http://i.imgur.com/vUDZuKb.png To summarize my solution:   1. Use $\mathbf{a}$ to find $|\mathbf{a_C}|$ and $|\mathbf{a_T}|$.   2. Substitute $|\mathbf{a_C}|$ into $a_C = \frac{{v_0}^2}{r}$ and solve for $v_0$.   3. Substitute $v_0$ and $\mathbf{a_T}$ into $v_1 = v_0 + a_T t$ and solve for $t_1$ when $v_1 = 0$. I also run into sign issues because I'm treating the value I get for tangential acceleration as the magnitude of a vector. This means that the value for tangential acceleration is positive, but it needs to subtract from velocity. There is a similar issue with the centripetal acceleration. The only way to deal with it properly seems to be to treat vectors counter clock-wise around the circle or pointing away from the circle as positive, and other vectors as negative . . . which is akin to treating the circle as a straight line almost . . . It feels like a hell of a lot of hand-waving, though I am sure that's because I don't understand what is happening.


"Magnetic mnemonics"

Over and over I'm getting into the same trouble, so I'd like to ask for some help.   1. I need to solve some basic electrodynamics problem, involving magnetic fields, moving charges or currents.   2. But I forgot all this rules about "where the magnetic field should go if the current flows up". I vaguely remember that it about hands or fingers or books or guns, and magnetic field should go somewhere along something, while current should flow along something else... But it doesn't help, because I don't remember the details.   3. I do find some very nice rule and use it. And I think "that one I will never forget".    4. ...time passes...   5. Go to step 1.  The problem is that you have to remember one choice from a dichotomy: "this way or that way". And all the mnemonics I know have the same problem -- I got to remember "left hand or right hand", "this finger or that finger", "inside the book or outside of the book". Maybe someone knows some mnemonics, that do not have such problem? ![By Bruno Touschek](http://i.stack.imgur.com/SxrgK.gif)


Is there literature on a continuous mass spectrum for the Higgs field?

Various masses for the Higgs field are compatible with experiment, but is it possible that the Higgs field is not observable because it has a continuous mass spectrum? Work in the 60s and 70s on free fields that have a continuous mass spectrum, often called generalized free fields, established that there is no simple particle interpretation if the mass spectrum is not delta function valued, which I take it can be described as due to destructive interference between the different mass components. [I'm taking that largely from R. F. Streater, _Rep. Prog. Phys._ , **38** , 771-846 (1975).] Is the possibility that the Higgs has a continuous mass spectrum to be found in the literature, or is there some sufficiently obvious anomaly or other reason why it is not considered in any detail?


Mie scattering intensity and spherical particles on

I am running an experiment where I shine infrared light on (almost) spherical particles on the micron scale (PM2.5 - PM10). I then look at the (90 deg) scattering properties to try and size the particles. I am looking for the theory of Mie scattering and its intensity, specifically how the scattered intensity depends on the surface area of the particles. Looking for suggestions of good literature on this, or just simple equations.


Why do cold metal plate make less noise?

I have a metal gate in my home so I have noticed that when it is a hot day and if I hit it it makes a lot of noise but when there is a rainy day and the weather and the gate re cold and if I hit the gate it makes very much less noise. I am assuming that when there is a cold day the metal is much dense so the vibration travel through it to the ground more easily as compared to that on a warm day, am I correct. ![enter image description here](http://i.stack.imgur.com/8jh1H.png)


Why the position of apparent horizon depend on choice of Sigma t of foliation?

Whether a 2d surface is a trapped surface is independent of choice of Sigma t of foliation. Why its outer boundary (apparent horizon) depends on choice of Sigma t of foliation?


I think there is something wrong with this problem. How do you know if the vertical acceleration is zero?

Suppose a block with mass 3kg is on a frictionless table and a force of 15N pulls it from an angle of 38 degrees above the horizontal. 1) What is the apparent weight of the block? 2) What is the minimum force for the block to take off? **Solution Given** $\sum F_y = n - mg - F\sin\theta = 0$ $\sum F_x = F\cos\theta = ma_x$ Solve for n, the apparent weight or the normal force. n = 20.16N The minimum force to take off when n = 0 $mg = F\sin\theta$ $F = \frac{mg}{\sin\theta}$ $F = 47.75N$ **Question** Why on earth is the force on the vertical direction 0? Shouldn't it be $\sum F_y = n - mg - F\sin\theta = ma_y$ There is a horizontal acceleration component, but no vertical acceleration.


Perturbation of coupled spin

I am given a system with Hamiltonian (all 1/2 spins) $$H_0=\alpha(S_1\cdot S_2)$$ I broke it down and found that there were four eigenstates: $|1,[0,\pm1]\rangle$ and $|0,0\rangle$. Each has an associated eigenvalues. I am then told that a weak magnetic field is applied giving a perturbation $$H_V=-\mu B_0\cdot(\sigma_1+\sigma_2)$$ I am supposed to use stationary state perturbation theory to find $E_n^{(1)}$. So I know that the perturbed energies are given as $$E_n^{(1)}=\langle \psi_n^{(0)}|H_V|\psi_n^{(0)}\rangle$$ I am a bit confused on what to use for the $\psi_n$ and then the $\sigma$ matrices. I know that the eigenstates are those given above, but I do not see how I can form a matrix from those and then I am unsure of what sigma would be in order to calculate the matrix element


Do photons interact only with single particles or can a single photon be absorbed by 2 or more particles simultaneously?

Say I have 100 particles in a vacuum that are spread out such that their movement caused by a time variant electromagnetic field does not have an effect on each other. That is the particles can not exchange any energy among themselves. The varying electromagnetic field must be experienced in quanta (a photon particle). Does this mean that it will take at least 100 photons worth of light to excite all the particles?


Michaelis-Menten derivation for 2 enzyme substrates

We know that the Michaelis-Menten derivation for the following reaction: $E + S \rightleftharpoons ES \rightarrow E + P$ However, what if the reaction took place in a different scenario whereby: $E + S \rightleftharpoons ES_1 \rightarrow ES_2 \rightarrow E + P$ What would be the derived Michaelis-Menten equation now? [ES2] is assumed to be at steady state assumption. What would be the derived Michaelis Menten Equation?


Dopant concentration and changes in band gap energy

Thanks to this lovely website, I was able to pop out reasonable values for my band gap energies from a translucent material. As expected, I found a decrease in band gap energy due to my treatments. Now, I also need some numbers put to dopant concentration. My dopants, in this case, are reduced forms of the semi-conductor material I am treating, but I think the concept can be generalized to all dopants. So my query is as follows: If I know how the band gap changes between a doped and undoped material, is there a formula that will give me the amount or density of the dopants in the material? For example, say my band gap before doping was 3.0eV and after doping it was 2.5eV, can I pull out how many dopant atoms were added to my material?


How is voltage generated due to difference in temperature in a thermocouple?

How is voltage generated due to difference in temperature between the two junctions of a thermocouple? What happens to the electrons at the junctions of the two materials and how do they behave when they are immersed in hot and cold medium?


Are intergalactic voids inertial frames?

I know earth is a non-inertia frame, so is the solar system, the milky way, the local group and even our super cluster. But what about all the space, the void that is left outside of the superclusters. From wikipedia "Interspersed among superclusters are large voids of space in which few galaxies exist. Superclusters are frequently subdivided into groups of clusters called galaxy clouds." When we talk of the voids the only movement we can talk about is the space expansion, not even a real movement as I have learnt after several debates and discussions. So are these voids actually inertial frames? If they are not, why are they not?


Lattice pattern

I'm trying to find and outline a non-primitive conventional unit mesh, I'd also like to find any mirrors planes and rotional symmetry axes. ![enter image description here](http://i.stack.imgur.com/vNPjZ.png) I first thought it would be like this: , but I was told the answer was smaller in a different thread. ![enter image description here](http://i.stack.imgur.com/dge86.png) This was the solution left by LDC3 ![enter image description here](http://i.stack.imgur.com/NM7pS.png) Which one is correct? I don't know if his is correct because I thought the conventional unit mesh connected to points that looked the same as the original small pattern I picked(the small hexagon in the middle) Also tried the axis of symmetry, but am unsure if 8 lines from the topside or 6 for a hexagonal pattern should come out. https://imgur.com/Bkjwhih I think for hexagonal structures there should be more lines like this https://i.imgur.com/GopAzmM.png Any help is much appreciated.


mechanism of annihilation

Can the annihilation of matter and antimatter be explained by the electro-weak interaction? Can pair-production be explained in the same way?


Configuration space of particles in the box

The notion of entropy says that we can count microstates that correspond to macrostate. But, I do not understand how this can be done. Does it imply that the state space is discrete (finite or countable)?


Mathematical definition of Bogomol'nyi–Prasad–Sommerfield (BPS) states

What is the mathematical definition of Bogomol'nyi–Prasad–Sommerfield (BPS) states, independent of any specific physical theory.


Leakage rate Calculation

I have to calculate leak rate for helium/air from an enclosure which is made of fabric. This is similar to helium balloons. There are small holes in the fabric. How should i proceed ?


Proton Radius Puzzle, Is it possible that proton's radius differ depending on how you measure it? What does that even mean?

I just read this NewScientist article, and I was stunned by its results. So I found the original paper here on arxiv. In the introduction of the paper it is stated: > The recent determination of the proton radius using the measurement of the > Lamb shift in the muonic hydrogen atom [1, 2] startled the physics world. > The obtained value of 0.84087(39) fm differs by about 4% or 7 standard > deviations from the CODATA [3] value of 0.8775(51) fm. The latter is > composed from the electronic hydrogenate atom value of 0.8758(77) fm and > from a similar value with larger uncertainties determined by electron > scattering [4] What Randolf Pohl _et al_ basically did, is that they measured the radius of the proton using more accurate techniques. While they were expecting to just get a more accurate result(few more decimal places), their proton radius is clearly smaller than all other experiments before. How they did the experiment is described in the paper I pointed to. The conclusion of the paper is: > The proton radius puzzle is real. A physical parameter should not depend on > the method of extraction. Yet here we have two highly precise methods based > on electronic and muonic hydrogen atoms that disagree significantly. The > possible origins of the disagreement are the subject of much of this text. > To summarize: the possibilities are > >   * The electronic hydrogen experiments are almost, but not quite, as > accurate as stated (Sect. 2.2). >   * The QED calculations are almost, but not quite, as accurate as stated > (Sect. 4.2). >   * The two photon exchange term that depends on proton polarizability has > not been correctly evaluated (Sect. 4.3). >   * The electron and muon really do have different interactions with the > proton (Sect. 4.4), so that there is physics beyond the Standard Model. > > > None of these possibilities seem very likely, but all must be pursued. My question is, what are the possible implications of this new result? Does anyone know how significant are the potential flaws in the experiments mentioned? It is stated in the paper that one possible solution might be Beyond the Standard Model theories; assuming the experiment is correct, do we really need BSM theories to explain the new results? If so, which specific branches of BSM will benefit from these results?


In the recent news, scientists at NASA have found “unprecedented” black hole cluster near Andromeda’s central bulge. I wonder why doesn't all these black holes merge and such each other in until just 1 remains? Is that even possible? Can one black hole suck in another black hole?


How to calculate the density of relic neutrinos?

May be not neutrinos, but antineutrinos? Or both types? In the last case, why they didn't annihilate and what is the ratio of relic neutrinos to relic antineutrinos? Is that ratio somehow related to the barion asymmetry? For reference: Relic neutrinos or cosmic neutrino background > Like the cosmic microwave background radiation (CMB), the cosmic neutrino > background is a relic of the big bang


General relativity theory

As I understand general relativity theory (please correct me if I'm wrong), time becomes dilated and space becomes compressed around mass, and this is responsible for gravity. I'm struggling with precisely how that results in gravitational force between masses. Can someone explain that to me (please keep any required math understandable to a lay person).


Einstein's theory tells us that gravity is a curve in space and time but how does that causes attraction in mass?

The sun is incredibly massive object and it causes the space around it to bend. This causes the planets to pulled to the sun or the planets move in an elliptical path around the sun. But I don't understand how the curvature in space can cause the pulling or what cause the planets to move in elliptical path?


Any use for $F_4$ in hep-th?

In high energy physics, the use of the classical Lie groups are common place, and in the Grand Unification the use of $E_{6,7,8}$ is also common place. In string theory $G_2$ is sometimes utilized, e.g. the $G_2$-holonomy manifolds are used to get 4d $\mathcal{N}=1$ susy from M-theory. That leaves $F_4$ from the list of simple Lie groups. Is there any place $F_4$ is used in any essential way? Of course there are papers where the dynamics of $d=4$ $\mathcal{N}=1$ susy gauge theory with $F_4$ are studied, as part of the study of all possible gauge groups, but I'm not asking those.


What does plasmon look like in 3D band structure graph?

Consider metal, and its reciprocal lattice representation with Fermi surface. What is the correct way to represent a plasmon in this system? M.b. rotating points on the surface? Or 3d membrane-like oscillation of surface? Or what?


Work done by gravity on Water

![enter image description here](http://i.stack.imgur.com/qeiCo.png) Now according to me we would see change in potential energy of system and equate it to the work done by gravity. But when we see this the first column lowers by $H/2$ and right one rises by $H/2$ and thus there should be no net work done. But it's not so. Work done by gravity is +ve. Where is it wrong?


Alternative career paths in physics?

What do you guys think of alternative career paths in physics away from academia free from the usual academic shackles? Examples: Garrett Lisi who spends his time surfing and skiing while not working on E8. Or Daniel Bedingham who is able to support himself part-time as an investment banker when not working on quantum mechanics. Or Julian Barbour who supports himself by translating Russian journal articles into English when not working on quantum gravity. Is it feasible to count upon Foundational Questions Institute to support such unconventional career paths using Templeton money?


Why put something in the middle of the pan would prevent soup coming out during cooking?

I see a website which teach people to put something on top of the pot during cooking soup to prevent the soup coming out during cooking. What is the physical theory behind that? ![enter image description here](http://i.stack.imgur.com/YAyKl.jpg)


Art : A Particular Mirror

There is a particular mirror used here (1 minute 26 seconds) in this video, which reflects light in a way I've never seen. I was hoping maybe one of you might know what kind of mirror this is, so that I may use it for my own personal use.


Real silicon atom structure?

Text books say that a pure silicon atom has four electrons in its outermost orbit. How do the scientists know it has four electrons?


Why doesn't rain fall down in streams (as opposed to drops)

Why is it that raindrops don't collide and 'stick together' on their descent to Earth, arriving in streams rather than separate drops?


Does water in the drain follow the distance-squared rule of force?

When I shower I notice that the soapy water spinning around the drain often takes the form of a spinning galaxy, complete with spiral arms. Does this indicate that the water's speed around the drain is inversely proportional to the square of its distance from the drain? Actually, I have heard that spinning galaxies themselves don't follow this rule, hence the discovery of dark matter, so does the spinning water follow whatever rule that the spinning stars do? Thanks.


In hydrostatics, is it possible for the bouancy to be greater than the weight of a body?

In the diagram we have two bodies, with density and volume $\delta$ and $V$, and a fluid $\ell$. $$\delta_1=0,7 \rm\frac{gr}{cm^3}$$ $$\delta_2=2 \rm\frac{gr}{cm^3}$$ $$V_1=100 \rm {cm^3}$$ $$V_2=10 \rm {cm^3}$$ $$\delta_\ell = 1,2 \rm\frac{gr}{cm^3}$$ The system is static. ![enter image description here](http://i.stack.imgur.com/E0db1.jpg) I need to find $(1)$ The tension of the rope $(2)$ the buoyancy $1$ receives due to the liquid. I solved it, but I'm getting strange results: Let $W$ be the weighs, $B$ be the buoyancy and $T$ the tension. Then, since the system is static: $$B_1+B_2-W_1-W_2=0$$ (the tensions cancel out) But $W_1= \delta_1 \cdot g \cdot V_1$, $W_2= \delta_2 \cdot g \cdot V_2$ and $B_2 = \delta_\ell \cdot g \cdot V_2$ (since the body is fully submerged): $$\eqalign{ 10\frac{{\text{m}}}{{{{\text{s}}^{\text{2}}}}}\left( {70{\text{gr}} + 20{\text{gr}} - 12{\text{gr}}} \right) = B_1 \cr 10\frac{\rm m}{{{\rm s^2}}}\left( {0,078\rm{kg} } \right) = B{_1} \cr 0,78{\text{N}} = B{_1} \cr} $$ It seems strange that the buoyancy is greater than the weigh of the body ($0,7 \rm N$), is that possible? Also, I can't figure out how to obtain the tension.


Resistance of a two-dimensional sample

In this review of the QHE, Steve Girvin makes the following statement (bottom of pg. 6, beginning of Sec. 1.1.1): > As one learns in the study of scaling in the localization transition, > resistivity (which is what theorists calculate) and resistance (which is > what experimental- ists measure) for classical systems (in the shape of a > [d-dimensional] hypercube) of size L are related by [12,13] > > $$ R = \rho L^{(2-d)} $$ where $R$ is the _resistance_ of the hypercube and $\rho$ its _resistivity_. For $d=2$ it is clear that the resistance and the resistivity of the sample are the same, and as Girvin goes on to say, this fact is crucial for the universality of the quantization of the resistivity plateaus in the QHE. My question is: **Is there a simple physical explanation of the above relationship?** Girvin cites two papers. Both are RMP: "Disordered Electronic Systems" by Lee and Ramakrishnan and "Continuous Quantum Phase Transitions" by Sondhi et al. I am hoping that someone can spare me the effort of going through these two papers by providing an answer.


Chaos is predictable?

I'm reading a book of computational physics [1] where the driven nonlinear pendulum is studied in deep. This is the equation used in the book: $$ \frac{d^2\theta}{dt^2} = -\frac{g}{l}\sin\theta - q\frac{d\theta}{dt}+F_d\sin(\Omega_dt) $$ Obviously the authors know when (whit which conditions) the pendulum switch to a chaotic regime. My question is the following: looking at the ODE, we can see (predict) the existence of chaotic behavior? If yes, this is valid for all the ODEs or only for a strict family of ODEs? [1] _Computational physics_ , N. J. Giordano and H. Nakanishi, Second Edition, Pearson Prentice Hall, 2006


For two planets in a 2:1 mean motion resonance , where will their periastron and apastron points be?

I want to animate the changing orbits of planets when they enter a mean motion resonance. Using a 2:1 resonance, I want to show a low-mass inner planet and a low-mass outer planet being tugged by a Jupiter-mass planet in the middle. I know the orbits of both become increasingly elliptical but I don't know in which direction the ellipse becomes extended. I want to include images of the planets' in orbit, too, so I want my points of periastron and apastron to be realistic relative to the position of the planets in their orbits. > Would the periastron point of the inner planet be near the point of 2:1 > resonance where my Jupiter-mass planet and the inner planet are nearest each > other, or on the opposite side, as I believe the case is with Neptune and > Pluto?   >  The same question for the outer planet, would it's periastron be closest to > the point where it is closest to my Jupiter mass planet, or on the other > side? Illustrating my question, I have an jpg illustration and animation in Flash at this location: Mean motion resonance animation (Flash) ![enter image description here](http://i.stack.imgur.com/8wpif.jpg)


Do perfect spheres exist in nature?

Often in physics, Objects are approximated as spherical. However do any perfectly spherical objects actually exist in nature?