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The Higgs mechanism allows massless fields to acquire mass through their coupling to a scalar field. But if the masses cannot be predicted because the couplings have to be fixed, what really is the utility of the Higgs mechanism? Instead of saying "Here are a priori couplings; the Higgs mechanism generates mass.", I co...
Van Eck phreaking, the ability to reconstruct distally the text on a CRT or LCD screen using the leaking em from the target computer, was in the news about five to ten years ago. It is talked about as if it is easily done, but I see little hard confirmation. The NSA has something called project TEMPEST to study this, b...
The work done during a process between two equilibrium states can be described by thermodynamics. Even when process itself is out of equilibrium, the thermodynamic laws can still be used, though calculating the work is much more difficult. But if the initial or final states, or both, are not in equilibrium, can the wor...
Hello this is my first question. For an open string you can pick different boundary conditions for the endpoints along different directions of space time. For example, you can choose Dirichlet conditions in some directions and Neumann along others. This gives us D-branes. My question is, why can't you choose Neumann b....
Noether's theorem is one of those surprisingly clear results of mathematical calculations, for which I am inclined to think that some kind of intuitive understanding should or must be possible. However I don't know of any, do you? Independence of time $\leftrightarrow$ energy conservation. Independence of position $...
One statement I've heard many times is that QFT is "defined" by the lattice, or that the "only" definition of QFT is on the lattice (when such definition exists, e.g in pure Yang-Mills theory). I've heard that from many people I respect, but I have my doubts. Specifically - the lattice is an algorithmic definition of t...
I was hoping for an answer in general terms avoiding things like holonomy, Chern classes, Kahler manifolds, fibre bundles and terms of similar ilk. Simply, what are the compelling reasons for restricting the landscape to admittedly bizarre Calabi-Yau manifolds? I have Yau's semi-popular book but haven't read it yet, no...
Let us consider a classical mechanical system of N particles in a constant external field. We have 3N coordinates and 3N velocities, so totally 6N unknown variables. We have 6N ordinary differential equations of the first order for them or 3N equations of the second order. It is known that such a system has 6N-1 conser...
I've read that for a Bose-Einstein gas in 1D there's no condensation. Why this happenes? How can I prove that?
With regard to the recent arXiv article: J. D. Shelton, Eddy Current Model of Ball Lightening http://arxiv.org/abs/1102.1224 I wonder if this is a reasonable explanation of ball lightening, or if there is such an explanation. The paper is somewhat technical and E&M is one of my worst subjects. Please feel free to edit ...
I know that in string theory, D-branes are objects on which open strings are attached with Dirichlet boundary conditions. But what exactly is a brane? Are they equally fundamental objects like string? If so then do they also vibrate? If the visible universe itself is not a brane then what is the dynamics of these brane...
My professor in class went a little over chaos theory, and basically said that Newtonian determinism no longer applies, since as time goes to infinity, no matter how close together two initial points are, the distance between them will increase greatly. But why isn't this merely a matter of the imprecision of our measu...
Once you understand the formalism, I think it's clearest to say the critical dimension of the space-time arises because we need to cancel the central charge of the (super)conformal ghosts on the worldsheet. But suppose I need to explain this to a person who only knows very basic QFT. How would you explain the concept ...
I’m trying to better my understanding of the thermodynamics and momentum balance of pipe flows. The following situation, however, is making me scratch my head and I’ve found no help in my books. Consider a pipe of constant section in which an ideal gas is flowing with negligible friction. Somewhere along this pipe ther...
Consider gWZW action $S_{gWZW}(g,A)=S_{WZW}(g)+S_{gauge}(g,A)$, where $S_{WZW}$ is usual WZW action being sum of sigma model and WZ terms for field $g$ taking values in group $G$ and $S_{gauge}=\int d^2\sigma\text{Tr}(A_+\partial _-gg^{-1}-A_-g^{-1}\partial _+g-g^{-1}A_+gA_-+A_+A_-)$ is gauge action which depends on fi...
In my opinion, the Grassmann number "apparatus" is one of the least intuitive things in modern physics. I remember that it took a lot of effort when I was studying this. The problem was not in the algebraic manipulations themselves -- it was rather psychological: "Why would one want to consider such a crazy stuff!?" ...
I am a computer scientist interested in network theory. I have come across the Bose-Einstein Condensate (BEC) because of its connections to complex networks. What I know about condensation is the state changes in water; liquid-gas. Reading the wikipedia articles on the subject is difficult, not because of the maths, bu...
What are some good sources to learn the mathematical background of Quantum Mechanics? I am talking functional analysis, operator theory etc etc...
Moshe's recent questions on formalizing quantum field theory and lattices as a definition of field theory remind me of something I occasionally idly wonder about, and maybe this site can tell me the answer. Are there any mathematicians working on defining quantum field theory by beginning with a rigorous definition of ...
I'm trying to learn how to do a many-body path integral for both fermions and bosons, and I'm stuck. I'm following Altland and Simons - Condensed Matter Field Theory, chapter 4. On page 167, equation 4.27 is \begin{equation} Z = \int \prod_{n=1}^N d(\bar{\psi}^n,\psi^n) e^{-\delta \sum_{n=0}^{N-1}[\delta^{-1}(\bar{\psi...
I was watching the documentary Carl Sagan did about gravity (I believe it's quite old though) and wondered about space being "flat" and that mass creates dents in this plane as shown at about 3 minutes in this clip (http://www.youtube.com/watch?v=Y-db4iC0aHw) Is this simply a metaphor or is it something more than that?...
With the form $y(x,t)=A\sin(kx-\omega t+\phi_0)$, there are two variables, How do I find the velocity? I don't know I can apply derivative with two variables.
Imagine a linear decrease in concentration from left to right. Using Fick's first law, $J = -D \frac{d \psi}{d x}$ for all x, from left to right, we have the same flux amount because the decrease is linear. So $J(x) = m$ According to Fick's second law, $\frac{d \psi}{d t} = -D \frac{d^2 \psi}{d x^2} = \frac{d J}{d x}$...
Recently it has been studied non-abelian anyons in some solid-state systems. These states are being studied for the creation and manipulation of qubits in quantum computing. But, how these non-abelian anyons can arise if all particles involved are fermions? In other words, how electronic states can have different stati...
One thing I know about black holes is that an object gets closer to the event horizon, gravitation time dilation make it move more slower from an outside perspective, so that it looks like it take an infinite amount of time for the object to reach the event horizon. It seems like a similar process should slow the forma...
Absorption spectra are a result of light of a certain wavelength exciting an atom from a lower energy level to a higher one and at the same time being absorbed. However, the atom should eventually go back down to its lower energy state, and at the same time emit a photon of same frequency it absorbed earlier. Overall, ...
Can I use a normal metal antenna to emit visible light?
I have heard before that the 4th dimension is time, however, another theory makes a lot more sense to me. This is that the 4th dimension is the third dimension stacked on top of each other in a similar in which 3d objects are just many 2d planes. I have seen many articles related to the 4thdimension being time, but how...
The mass of a nucleus if less than the mass of the protons and nucleus. The difference is knows as binding energy of the nucleus. This nuclear binding energy is derived from the strong nuclear force. Now my question is that does the strong nuclear force provide this energy? How does the mass decrease if the force pro...
Possible Duplicate: What experiment would disprove string theory? We carefully observe things, observe patterns and then build theories that predict. String theory is frequently criticized for not providing quantitative experimental prediction. What are the problems that prevent this theory from producing quantita...
In continuation of another question about Noether's theorem I wonder whether there exists some kind of relationship between this theorem and the Heisenberg uncertainty principle. Because both the principle and the theorem relate energy with time, momentum with space, direction with angular momentum. When this is a gene...
Inspired by this question, let me ask a similar question. Is it possible to do the same (give a description of M-theory your grandmother could understand)for M theory? While I know even experts don't understand it properly, I still hope some basic ideas may be expressed. Is it just a hypothetical non-perturbative formu...
Liquid and solid chemical fuels in rockets are very expensive and inefficient. I have heard of solar sails but what are the most realistic space travel fuels that will be used in the future to get close to the speed of light?
If I understand correctly, according to Einstein's General Theory of Relativity, mass results in a distortion in space-time. In turn, the motion of the mass is affected by the distortion. A result of the interplay between mass and space-time is that the 'force' of gravity may be explained away. Masses are not subject t...
Can someone summarize, with references if possible, all of the alternatives to the simplest model (that requires only a single scalar Higgs field with the Mexican Hat potential) of spontaneous electroweak symmetry breaking?
What impulse should be applied to an object of mass m, having a known coefficient of friction u to get to a distance d ? Thanks! Update 14.02.2011: I still wasn't able to find an answer to this. Could you please share the solution? I need an "Idiot's solution" for this. I'm not experienced enough to find a formula by ...
Stephen Wolfram in his book A New Kind of Science touches on a model of space itself based on automata theory. That it, he makes some suggestions about modelling not only the behaviour of matter through space, but the space itself in terms of state machines (a notion from computing). Here, the general topology of space...
I'm contemplating particle-hole symmetry, and as an example I am looking at either an electron moving along a hypothetical lattice of hydrogen ions, or a hole moving along a hypothetical lattice of helium atoms. According to some lecture notes I found, the hopping integral I get when I treat this in a tight-binding an...
Could you please suggest the software, where I can load my 3D model and see how it behave on various conditions (speed - preferably including supersonic, temperature, pressure)? Both free & commercial variants are interesting.
Witten (and earlier, Bodner) hypothesized that strange matter (up, down, strange quarks) should be more stable than "regular" nuclear matter(The strange matter hypothesis). That is that the typical hadrons in matter are metastable, and will eventually decay into strange matter because it can exist at lower energy confi...
What is the current status of the swampland? Have people expanded the list of swampland criteria? If let's say I wish to figure out if the Standard Model belongs to the swampland, are there any concrete steps I can use to go about it, at least in principle? If let's say technical difficulties aren't an objection, and w...
If we try to work out the details of string theory over a worldsheet with genus 1, does that mean we have periodic time on the worldsheet? But if we have periodic time, and in some portions of the worldsheet, the target space time $X^0$ increases with $\tau$, won't it have to decrease with $\tau$ somewhere else on the ...
When radiation from a colder source arrives at a warmer surface there is some debate about what happens next. To make the question more concrete lets say that the colder source is at temperature 288K. The warmer surface is at 888K and has emissivity of 1. 3 possibilities We ignore such radiation because it cannot happ...
When people talk about the first superstring revolution they often mention the miraculous cancellation of anomalies via the Green-Schwarz mechanism. My question is whether such a string-theoretic mechanism is also at work when the 4D gravitational and gauge-gravitational anomalies are tackled? In this context, would it...
Is this just a historical artifact - that the particle physics community decided at some point to call all of the pre-oscillation physics by the name the "Standard Model"? The reason I ask is because I often see articles and books say something to the effect "the strongest hint of physics beyond the SM are the non-zero...
Let $X$ be a manifold with $G_2$ holonomy and $\Phi$ be the fundamental associative 3-form on $X$. Let $\Phi$ be the dual co-associative 4-form on $X$. Now consider a particular associative 3-cycle $Q\in X$, which is Poincare dual to the co-associative 4-form $\Phi$, i.e. $*\Phi=\lambda\times PD(Q)$, where $\lambda\i...
Can we describe our universe without it? Example; Explaining a muon able to hit Earth, by its time dilation only? Or a spinning disc contracting? Does it exist, and if it does, does it do so from all frames of existence, that means, if you observe a Lorentz contraction, will the person in that frame, 'experience' it to...
I am currently taking a graduate level class on lasers. The primary focus of the class is on the design and engineering aspects of lasers, e.g. resonator design. However the first portion of the class is an overview of the quantum mechanics of laser processes in semi-classical terms: transition probabilities for a 2-le...
Hopf algebra appears in recent papers that systematize renormalization of quantum field theory (QFT). For example see Connes' work and citing papers or a paper referenced here on PSE: R. E. Borcherds, "Renormalization and quantum field theory" http://arxiv.org/abs/1008.0129 This seems to be an effort that is separate f...
I was thinking the other day about what sort of exotic materials one would find in the depths of a planet. I have heard theories about how an enormous diamond might be found in the centre of gas giants. Current theories have a ball of iron at Earth's core - would that be like the iron up here on the surface or does the...
It is known that in F-theory compactifications on CY 4-folds one can get gauge groups with very large ranks. The largest single factor* gauge group for compact CY 4-folds I found in the literature is the mind-blowing SO(7232) in this paper: http://arxiv.org/abs/hep-th/9706226 . One can imagine that there exist 4D compa...
I'm a mathematician studying Arnold's Mathematical Methods of Classical Mechanics. On p. 83 the following definition is given. Let $M$ be a differentiable manifold, $TM$ its tangent bundle, and $L:TM \to \mathbf{R}$ a differentiable function. A map $\gamma: \mathbf{R} \to M$ is called a motion in the lagrangian syste...
This is something I don't ever seem to hear about, except regarding QCD ("lattice QCD"). What about QED? Is numerical integration always inferior to hand-calculating Feynman diagrams in perturbation theory? What about numerical simulation of the full time-evolution of a quantum field (rather than just calculating corre...
Did spacetime start with the Big Bang? I mean, was there any presence of this spacetime we are experiencing now before big bang? And could there be a presence/existence of any other space-time before the big bang?
I have several questions regarding the "big bounce" theory. It appears to be popular among LQG researchers. My questions are as as follows. 1) How one reconciles it with the fact that it is now experimentally established that the universe is expanding in an accelerating manner? 2) The entropy of the universe should hav...
My sister is in 10th grade. She doesn't seem to understand the concept of time varying functions (current, light, sound wave forms etc). I explained her in easiest possible terms. She got it but not very comfortable with the concepts. So, instead of explaining. I simply wanted her to take a stopwatch & measure "somethi...
Supposing it's possible to see some distant galaxies with an earth telescope, then, at the tip of the telescope lens there are photons comming from the distant galaxy... So, if I extend my hand in a dark night without visible moon, and far from city lights, photons from distant galaxies are in my hand skin... if it is ...
Specifically, does the focal length change? How can this be rationalized?
Venus ($0.815$ Earth mass) supports a $\rm{CO_2}$ atmosphere of $93 \ \mathrm{bars}$ at its surface. Earth's $\rm{N_2/O_2}$ atmosphere has a surface pressure of one bar. What are the factors that limit the mass of atmospheric gases on a planet?
I'm studying Richardson Model in second quantization. There are many initial points that I don't understand: We supposed that an attractive force between 2 electrons exists, due to electron-phonon interaction: an electron generates a phonon that is absorbed by the other electron, and we prove that the resulting potent...
The famous AdS/CFT calculation of the shear viscosity/entropy ratio for strongly coupled $N=4$ SYM relates the shear viscosity to the absorption cross section for fluctuations of the metric onto a black hole in AdS which in turn can be related to the absorption cross section for a massless scalar field. On the AdS side...
I know the basics of solar system like how earth moves around sun, and that we have so many planets, elliptical orbit of earth, and how far is sun from earth etc etc. I want to take a step back and understand how mankind has been able to construct this knowledge of solar system piece by piece.Questions: -- Sun is somet...
I know the basics of solar system like how Earth moves around Sun, and that we have so many planets, elliptical orbit of earth, and how far is sun from earth etc etc. I want to take a step back and understand how mankind has been able to construct this knowledge of solar system piece by piece. Questions: -- Sun is some...
How has the distance between sun and earth been calculated? Also what is the size of the sun?
How is the speed of light calculated? My knowledge of physics is limited to how much I studied till high school. One way that comes to my mind is: if we throw light from one point to another (of known distance) and measure the time taken, we could know the speed of light. but do we have such a precise time measuring to...
Suppose we have a cylindrical resistor, with resistance given by $R=\rho\cdot l/(\pi r^2)$ Let $d$ be the distance between two points in the interior of the resistor and let $r\gg d\gg l$. Ie. it is approximately a 2D-surface (a rather thin disk). What is the resistance between these two points? Let $r,l\gg d$, (ie a ...
I often encountered the term "localization" in the context of instantons, as for example in the work of Nekrasov on extensions of Seiberg-Witten theory to ${\cal N}=1$ gauge theories. Could someone give a "intuitive" explanation of the concept of localization as well as a "simple" concrete realisation of it?
This question has led me to ask somewhat a more specific question. I have read somewhere about a coincidence. Numbers of the form $8k + 2$ appears to be relevant for string theory. For $k = 0$ one gets 2 dimensional string world sheet, For $k = 1$ one gets 10 spacetime dimensions and for $k = 3$ one gets 26 dimensions ...
In quantum gravity, ADM wavefunctional solutions have to satisfy the Wheeler-DeWitt equation. This leads to timelessness. What happens if we have a time periodic solution? In classical general relativity, a time periodic solution just means that and no more. But when combined with a timeless wavefunctional, if the same...
First, discrete examples. In a computer screen I can specify any "2D" point with just one single number (pixel order starting count from first at upper left, and going on, left2right and up2down like reading till last one at right bottom corner) Then I don't need two numbers to specify position, just one. Same can ex...
The Schrodinger equation governs the possible time evolution of a wave function, expressed as a partial differential equation. Isn't this equivalent to the simpler equation $$\omega = \hbar k^2/2m$$ i.e. any wave function that satisfies this dispersion relation will also satisfy Schrodinger's equation, and the equatio...
A truly reversible thermodynamic process needs to be infinitesimally displaced from equilibrium at all times and therefore takes infinite time to complete. However, if I execute the process slowly, I should be able to get close to reversibility. My question is, "What determines when something is slow?" For definitene...
On a principal bundle, at each point you have a tangent vector space. At a given point, the vectors tangent to the fiber form the vertical vector space. Then the vector space at that point is a direct sum of the vertical vector space and what's called the horizontal vector space. This is all standard stuff in gauge th...
The quarks and leptons chiral states have hypercharges of $0,\pm 1/3,\pm 2/3, \pm 3/3, \pm 4/3, \pm 6/3$. The value of $\pm 5/3$ is prominently missing. Is there a theoretical principle which picks out these values? In looking for papers on arXiv with hypercharge 5/3, I've found only a handful of papers. One is a prepr...
If someone (or some robot) on the moon were to point a laser at the Earth, how many watts would the laser need, to be easily seen with the un-aided eye from Earth? Obviously this depends on a number of factors. Assume the beam is made divergent enough to cover latitudes 60S to 60N, wavelength 532nm, and the beam origin...
We know that an operator A in quantum mechanics has time evolution given by Heisenberg equation: $$ \frac{i}{\hbar}[H,A]+\frac{\partial A}{\partial t}=\frac{d A}{d t} $$ Can we derive from this that $$ A(t)=e^{\frac{i}{\hbar}Ht}A(0)e^{-\frac{i}{\hbar}Ht} \qquad ? $$ L.M.: I added $i/\hbar$ in front of $[H,A]$.
There's a conventional wisdom that the best way to minimize the force impact of a punch to the head is to lean into it, rather than away from it. Is it true? If so, why? EDIT: Hard to search for where I got this CW, but heres one, and another. The reason it seems counter-intuitive is that I'd think if you move in the ...
Now in disordered organics, the band picture is thrown out the window, from what I can tell (due to lack of symmetry). But don't HOMO/LUMO levels basically take the place of conduction/valence bands in molecules? In a organic system (a lot of molecules with no order), then, I am correct to believe that the HOMO and LUM...
Why String theory ? simple cosmological model is not sufficient for study of nature of universe
A proper time interval $\Delta\tau$ for a given observer is a relativistic invariant. However, the calculation of $\Delta\tau$ requires reference to some arbitrary coordinate time t: $$\Delta\tau = \int_{t_1}^{t_2} \! \frac{\mathrm{d}t}{\gamma}$$ Doesn't the invariance of $\Delta\tau$ require a "preferred" reference co...
During breakfast with my colleagues, a question popped into my head: What is the fastest method to cool a cup of coffee, if your only available instrument is a spoon? A qualitative answer would be nice, but if we could find a mathematical model or even better make the experiment (we don't have the means here:-s) for th...
What would be the vertical velocity of this ski jumper (ski flyer), after he first touches down, after he breaks the record with a $246.5m$ jump? What g force would he experience as he slows down? Video (the last video) I think he gets at least 6 seconds of airtime from $26$ to $32$ second mark. The ramp gradient at ta...
Covariant quantisation in string theory is accomplished by giving the commutator relations $$[X^\mu(\sigma,\tau),P^\nu(\sigma',\tau)] = i \eta^{\mu\nu} \delta(\sigma - \sigma').$$ Although string theory is not a field theory this approach is identical to the quantisation of fields $X^\mu$ in 1+1 dimensions. From this ...
This question arises in a somewhat naive form because I am largely unfamiliar with String Theory. I do know that it incorporates higher space dimensions where I shall take the overall dimensionality to be 10 in this question, for concreteness. Now the traditional Hawking-Penrose Singularity results apply to the the Gen...
First, what do you call this in English? Second, how does it work? Why do I have not only light at the gas barrier between the two wires? Thanks!
As I remembered, at the 2 poles of a battery, positive or negative electric charges are gathered. So there'll be electric field existing inside the battery. This filed is neutralized by the chemical power of the battery so the electric charges will stay at the poles. Since there are electric charges at both poles, ther...
That is, are they identical to their anti-particles? (Any results of double beta decay experiments?)
It has been said that our universe is going to eventually become a de Sitter universe. Expansion will accelerate until their relative speed become higher than the speed of light. So i want to understand what happens after this point: so from our point of view, we see a progressively shrinking event horizon (each galax...
I'm reading this silly Time article: http://www.time.com/time/health/article/0,8599,2044517,00.html And they say "Even at its best, the 20-year-old telescope never had the acuity to peer so far into space, where the rapid expansion of the universe causes light waves to shift to a deep red." Doesn't that imply that thin...
When you look a the Polyakov or Nambu-Goto action, you see a $T$ for tension, but no mass. When you look the action of a relativistic particle, you see the $m$. See here. So here's the question. Where is the mass in the String theory actions? For a classical relativistic string I would expect that the equations of moti...
From answers to a previous question, a finite degree polynomial in the distribution $i\Delta^+(x)$, with Fourier transform $2\pi\delta(k^2-m^2)\theta(k_0)$, is a distribution, even though a product of distributions is not in general well-defined. So far I've not been able to find, or be myself sure enough, whether $\ex...
$$\mathbf D = \varepsilon \mathbf E$$ I don't understand the difference between $\mathbf D$ and $\mathbf E$. When I have a plate capacitor, a different medium inside will change $\mathbf D$, right? $\mathbf E$ is only dependent from the charges right?
Are there any objects out there that have since vanished, but because of their distance and the travel time for light, can be seen with the naked eye? Or are those things only visible with magnification? How much magnification at least?
If Betelgeuse were to go supernova would the sky be twice as bright, or day time extended, depending on what time of year it happened in. Basically when it does supernova how bright and large will it appear in the sky, and how do you work out the apparent brightness and size for something that hasn't happened yet?
I have a numerical method for computing solutions to the Dirac equation for a spin 1/2 particle constrained to an arbitrary surface and am interested in finding applications where the configuration space has a complicated geometry, i.e., not just $R^2$ or the sphere, but a more general curved surface possibly with spec...
The size of our observable universe must have grown over time in the early universe. Conversely with the accelerated expansion, I have heard that eventually our observable universe will shrink down to our local group of gravitationally bound galaxies. So then the observable universe must go through a maximum at some ...
This is a summary from Physics World of the paper: L J Wang et al. 2000 Nature 406 277-- "Wang and colleagues begin by using a third continuous-wave laser to confirm that there are two peaks in the gain spectrum and that the refractive index does indeed change rapidly with wavelength in between. Next they send a 3.7-mi...
There are lots of models of gravity-mediated SUSY breaking with various spectra as well as various general gauge mediation models. Are there any "smoking gun" experimental signatures that could distinguish between the two scenarios? Would this be possible to do at the LHC or would we need an ILC-type machine to do that...
The phenomenon of high temperature superconductivity has been known for decades, particularly layered cuprate superconductors. We know the precise lattice structure of the materials. We know the band theory of electrons and how electronic orbitals mix. But yet, theoreticians still haven't solved high Tc superconductivi...
When computing the first order perturbative corrections to string theory over a curved background, we find the background has to be Ricci-flat if the dilaton is constant and we have no fluxes. Such is the case for Calabi-Yau compactifications. However, to fourth order in perturbation theory, we find nonzero contributio...

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