title: Does quantum mechanics allow faster than light (FTL) travel?

text: Let's suppose I initially have a particle with a nice and narrow wave function[1] (I will leave these unnormed): $$e^{-\frac{x^2}{a}}$$ where $a$ is some small number (to make it narrow). Let's also suppose that the wave function travels along x axis with constant speed $v$ and it smears out with constant speed $v_s$. So after time $t$ wave function looks like $$e^{-\frac{(x-vt)^2}{a+v_st}}$$ Now, if speed $v$ is close to $c$ and $v_s$ is big enough too, we could get a situation where the centre of mass moves at subluminal speed (this is the group velocity, I suppose), but the front[2] of the function moves at superluminal speed. If I measure either the particle's position after some time $T$ or time when it reaches some point $A$ i will mostly and averagely conclude that it has travelled with speed $v$. But in some (less probable) cases it will seem that it has travelled faster, even FTL. Is this a normal thing in quantum mechanics or I understand it all wrong? Maybe there is some constraint not only on $v$, but also on $v+v_s$? ## A little background When talking about superluminal tunneling speeds I usually hear explanations like this: > That speed is apparent. In those cases only some frontal part of the wave > function gets through the barrier. Although it's center of mass seems to > have travelled FTL, that function would still stay under the initial wave > function if it continued it's way without the barrier. The center just > shifted because of dropping the rear part. I have never actually understood why does it solve the problem, because the position of center doesn't change the fact that signal in some cases may arrive FTL. This is where my question comes from. **EDIT:** Sorry, the question was not about what some classic QM models allow, but actual quantum physics. I understand that Schrodinger's equation allows me any speed, I want to know if this situation is allowed in actual quantum physics. I guess the use of term QM was wrong. Sorry, my bad. ## Question reformulated Is it possible to send a particle that's slowly _spreads_ and with some small chance (in some rare cases) measure it arriving FTL? (provided that the mean arrival value still stays under $c$). I am aware that this is possible when tunneling through a barrier (and the mean value can even move to superluminal by _train dropping cars_ ), but is the same possible without any barrier? Maybe I could equivalently ask, if quantum uncertainties allow occasional exceeding of $c$. [1] If you say that I had some chance to measure it at any point in the very beginning and that it wasn't entirely localized, we can replace the Gauss' function with a square or triangle one that gets wider along the way. [2] If you need, we can define the _front_ of the wave, for example first of the points where second derivative is zero. It's position is $vt+\sqrt{\frac{a+v_st}{2}}$.


title: Is it correct to sum over either index of the metric the same way?

text: I don't know if the following is correct, i want to compute the following derivative $$\frac{\partial }{\partial (\partial_{\mu}A_{\nu})}\left(\partial^{\alpha}A^{\beta}\partial_{\alpha}A_{\beta} \right)$$ So I first introduce the metric in order to lower the first two indices $$\partial^{\alpha}A^{\beta}\partial_{\alpha}A_{\beta}=\eta^{\alpha\gamma}\eta^{\beta\delta}\partial_{\gamma}A_{\delta}\partial_{\alpha}A_{\beta} $$ and then $$\begin{align}\frac{\partial }{\partial (\partial_{\mu}A_{\nu})}\left(\eta^{\alpha\gamma}\eta^{\beta\delta}\partial_{\gamma}A_{\delta}\partial_{\alpha}A_{\beta}\right) &= \eta^{\alpha\gamma}\eta^{\beta\delta}\frac{\partial }{\partial (\partial_{\mu}A_{\nu})}\left(\partial_{\gamma}A_{\delta}\partial_{\alpha}A_{\beta}\right) \\\ &=\eta^{\alpha\gamma}\eta^{\beta\delta}\left(\partial_{\alpha}A_{\beta}\delta_{\mu \gamma}\delta_{\delta \nu}+\partial_{\gamma}A_{\delta}\delta_{\alpha\mu}\delta_{\beta\nu}\right) \\\ &=\eta^{\alpha\mu}\eta^{\beta\nu}\partial_{\alpha}A_{\beta}+\eta^{\mu\gamma}\eta^{\nu\delta}\partial_{\gamma}A_{\delta} \\\ &=2\partial^{\mu}A^{\nu}\end{align}$$ I was troubled because in the metric sometimes the first index is the summed one and other times the second. Is it correct that $A^{\alpha}=\eta^{\alpha \beta}A_{\beta}=\eta^{\beta \alpha}A_{\beta}$?


title: Angular velocity and the speed of light

text: So, accelerate a particle to just under the speed of light, then send it round a bend, technically it accelerates due to the change of direction, will its speed exceed or match $c$? Keep it simple, I'm only a high school teacher!


title: Where to find information on the pulsar map written to Voyager's golden record?

text: Where might I find details about the pulsar map written on the Voyager's golden record? ![enter image description here](http://i.stack.imgur.com/bFopN.png) > This diagram defines the location of our Sun utilizing 14 > > pulsars of known directions from our sun. The binary > > code defines the frequency of the pulses.


title: How do the day/night temperature variations of moons compare to those of their planets?

text: Does the planet's eclipse have a significant impact on the flux of light hitting the moon? Does tidal locking have any effect on the day-night difference of the planet?


title: Get time from sun Azimuth

text: I want to know if I can determine the time where the sun's azimuth is at a given value. In other words, I want a function that takes the sun azimuth along with longitude or time zone and outputs the time. Is there anything like this?


title: Is there a simple yet accurate formula for where on Earth the Sun and Moon are directly overhead?

text: I'm trying to improve a site that shows the region of the Earth currently under daylight, and I need a formula that, given the current time, tells where (latitude/longitude) the sun and moon are overhead, accurate to 1 mile. Can anyone come up with one? Ideally I'm hoping to get something JavaScript can calculate at a "reasonable speed" without recursion, loops, or extra libraries. I've tried several things (eg, Fourier series on the Sun/Moon's RA/DEC), but nothing seems quite accurate enough. Note: I realize my calculations for sun/moon rise/set ignore refraction and lunar parallax: for now, I'm focusing on finding the overhead positions. I realize I can pull data from a non-JavaScript CGI program (and have tried that), but it seems like a lot of unnecessary network access. EDIT: Thanks, Dustin and everyone. Actually, I'm aware of http://ssd.jpl.nasa.gov/?horizons and even wrote programs to download and parse their data (https://github.com/barrycarter/bcapps/blob/master/bc-email-horizons.pl and https://github.com/barrycarter/bcapps/blob/master/bc-parse-horizons.pl) with the hope of finding simple formulas (https://github.com/barrycarter/bcapps/blob/master/bc-fourier-cont.m and others), but got nowhere. I realize I could hardcode the data into my JavaScript but that would make the script unnecessarily large. Currently, I rebuild the script every minute (https://github.com/barrycarter/bcapps/blob/master/bc-sun-always-shines.pl) using interpolated JPLs data (the sun/moonfakex/y.txt files in https://github.com/barrycarter/bcapps/tree/master/data), but this seems insanely complicated. This may be an inherently difficult and/or pointless question: to get accuracy of 1 mile, you have to calculate the position within 52 seconds of arc, which is considerably smaller than the 30 minute (1800 seconds) width of the sun and moon themselves. The ultimate goal is to let people zoom into their city on google maps and watch the sunset "sweep" over their city (ie, predict the sun is setting over a certain part of the city and have people in that part of the city confirm it), but given refraction and parallax, this may be impossible.


title: Is there any site/place which gives access to astronomical signals acquired from space?

text: I am an engineer and I'd like to know if there are any places which provide access to any kind of astronomical signals acquired from space using radio telescopes.


title: What conditions should an asteroid or comet impact need to meet in order to start an impact winter?

text: Is there a way to calculate if an impact from a given asteroid (say 5 miles in diameter, solid rock to which we know the mass) would start an impact winter? If yes, I would like to see a real example of an existing asteroid, if possible some calculations, and the conclusion that an impact winter would be imminent. I'm not sure if I'm not forcing the boundaries of available knowledge, but I would like to be able to understand and deduce if a given asteroid impact would start an impact winter. I know what that is, and I've read the Wikipedia article _Impact winter_. I'm interested in a specific example, if possible.


title: What limits the velocity of ships such as voyager 1?

text: Voyager 1 travels at a small fraction of light speed. I've read it's fueled by hydrazine, which is a cheap combustive. Questions:   1. What factors limit the speed of voyager 1 and similar rockets? Are there equations that sum it up?   2. What would be required to accelerate a rocket to relativistic speeds, and how practical it is?


title: Time Dilation in relation to Acceleration

text: What I am looking for is a layman's explanation on the equations required to work out Time Dilation at high speeds including acceleration and deceleration of velocity. Or I would greatly appreciate it if you could point me in the direction of a website which explains each step required and all the variables involved in solving this problem if you feel that to outline it here would be too much work. Many thanks.


title: Inflation and scalar spectral index

text: I've been reading that the results from the Planck satellite constrain a number called the "scalar spectral index" to be 0.96 rather than 1 at the 5-sigma level. This is supposed to be big news, but I don't understand why (my ignorance, of course). For instance, with an index of 0.96, can we say how many e-foldings occured during inflation? What else does it tell us?


Can protons in the nucleus of an atom be aligned by electromagnetic fields? If so can it be done around $-135°C$ zero?


title: Why are trajectories in General Relativity speed-dependant?

text: I'm a secondary student who never studied any general relativity level maths (yet!), but I heard that in general relativity objects with mass and energy deform space-time, and therefore bodies move in the shortest path in this deformed space. At least this is what I think this article means. Wikipedia - General Relativity > There is no gravitational force deflecting objects from their natural, > straight paths. Instead, gravity corresponds to changes in the properties of > space and time, which in turn changes the straightest-possible paths that > objects will naturally follow. The curvature is, in turn, caused by the > energy–momentum of matter. Here's my question: If this is the case how come objects moving initially in the same direction but at different speeds, have end up having different trajectories? I mean, the length of a path doesn't depend on the speed you traverse it with? Unless some relativistic phenomena is at work?


title: Questions about the Jeans length

text: I have a couple of questions about the Jeans length. Suppose the universe has a homogeneous energy density, except there's a spherical region that is overdense.   * I understand that if the region is smaller than the Jeans length, then pressure, which travels at the speed of sound (compared to the speed of gravity $c$), can build up fast enough to counteract the gravitational collapse. But if the region is bigger than the Jeans length, it collapses. What exactly does it mean? Does the region get smaller and smaller until it vanishes? Wouldn't this create a black hole, since you're stuffing all the energy of the overdense region into a smaller and smaller place?   * Or, if the region is collapsing, wouldn't it eventually be smaller than the Jeans length, at which point it stops collapsing?   * And what happens if the region is underdense, rather than overdense?


title: Vaporization in function of relative humidity

text: I am wondering how the relative humidity affects the vaporization?   I saw on an other post that it doesn't affect it, but in my personal experience, it takes much more time to dry clothes when the relative humidity is high, so it's hard for me to believe that it does not have a big effect. What is the effect of relative humidity on evaporation speed?


title: Can coherent light also be polarized?

text: I need to know if it is possible to polarize coherent light using a Wollaston prism. And would the resultant (2) beams of polarized light still be individually coherent?


title: Arbitrary tensor covariant derivative

text: what are the rules for performing covariant derivatives on tensors of arbitrary rank? I found a few examples of Tensor derivatives: $$\nabla_{c} T^a {}_{b} = \partial_{c}T^a {}_{b}+ \Gamma^a{}_{cd} T^d {}_{b} - \Gamma^d {}_{bc}T^a {}_{d}$$ $$\nabla_{c} T {}_{ab} = \partial_{c}T {}_{ab}- \Gamma^d{}_{ac} T {}_{db} - \Gamma^d {}_{cb}T {}_{ab}$$ $$\nabla_{c} T^{ab} = \partial_{c}T^{ab}+ \Gamma^a{}_{cd} T^{db} + \Gamma^b {}_{dc}T^{ad}$$ It seems to me, that you take the partial derivative of the tensor in question, and add tensor terms like to $\Gamma^{x}{}_{yz}$ along with the original tensor with the index labeled slightly differently for each index. The terms are +ve if the index is contravariant and -ve if the index is covarient. Why is this true? The indices orientation confuses me, could someone tell me a general rule or formula which I can follow for any tensor rank. Cheers


title: Atom Theory vs Quantum Physics

text: This never really occurred to me until now, so maybe it does not categorize a really important question, but according to Quantum theory anything that "is not observed is probability until it is observed when it condenses down into matter." So with that said i would like to know if that theory has any any contradictions with atom theory. Atom theory is pretty straight forward but because you cannot see atoms on a macro or even a microscopic scale (only nano or smaller), how does that work with quantum physics. You cannot observe atoms with your eyes even if you're looking at something with mass, so does that mean (supposedly) that atoms are only probability until you can observe them with the proper equipment, even though on a smaller scale thats what the things you are observing are made up of?


title: Hydrogen atom in quantum mechanics

text: I have problems following the calculations in Griffiths' _Introduction to Quantum Mechanics_ (Chapter 4.2.1): If you apply the Schrödinger equation to the Coulomb potential you get the following differential equation: $$\tag{4.56} \frac{d^2u}{d\rho^2} ~=~ [1-\frac{\rho_0}{\rho} + \frac{\ell(\ell+1)}{\rho^2}]u. $$ A few steps later my books substitutes $u(\rho)$ without explaining why this is allowed: The next step is to peel of the asymptotic behavior, introducing a new function $v(\rho)$: $$\tag{4.60} u(\rho) ~=~ \rho^{\ell+1}e^{-\rho}v(\rho). $$ How is this function still related to the Hydrogen atom? To me it looks like something total random.


title: Special Relativity - speed of light question

text: Just a basic question: I know that if you are traveling at $x$ speed the time will pass for you slower than to an observer that is relatively stopped. That's all just because a photon released at the $x$ speed can't travel faster than the $c$ limit. I want to know what happens if you have two bodies, $A$ and $B$ moving towards each other. If $A$ releases a light beam, and $B$ measures it (the speed of the photons), the speed measured is still the same? The only difference will be the wave length? And if we have the opposite case, $A$ and $B$ are moving away from each other, we get the red shift, but the speed measured will be still the same? _I just want to know if I got it right..._


title: Rotation of Rockets

text: I referred the Roll program in space shuttles. But, I can't understand the mechanism. So, They rotate during the launch in order for proper alignment. I know that only tilting, gimbaling or using additional vernier thrusters would align the space shuttles in proper direction. But how does this rotation of a space shuttle help in alignment? What's the mechanism behind this..?


What are the mathematical prerequisites to understand this paper? > Blumenhagen et al. Four-dimensional String Compactifications with D-Branes, > Orientifolds and Fluxes. _Phys. Rept._ **445** no. 1-6, pp. 1-193 (2007). > doi:10.1016/j.physrep.2007.04.003, arXiv:hep-th/0610327. I know quantum field theory and some string theory (at the level of string theory demystified) What else should I know in order to be able to read this paper?


title: Could negative dimension ever make sense?

text: After some quick check I found that negative dimensions are not used. But we have negative probability, negative energy etc. So is it so likely that we won't ever use negative dimension(s) ? ## Update I understand there're also dimensions that are not integers e.g. dimension 1½ (?) for fractals or so. Could there also be a dimension such as dimension i (imaginary)?


title: Black holes and entropy

text: 1)I'm told that for Black Holes, when they radiate (Hawking radiation) particles and anti-particles) split at the event horizon, one going to infinity, the other into the BH. They then lose mass. How is that possible? Wouldn't their masses increase, since they are absorbing particle or anti- particles? 2)Also, their entropy varies as their masses, and since entropy increases, wouldn't their masses also be increasing, along with their area? How does that reconcile with case 1? Thanks


title: What is the difference between the properties of Electron spin and Photon polarization/helicity?

text: What is the difference between a photon's polarization/helicity and an electrons spin half? I know that the photon is spin 1 but isn't its polarization analogous to spin half? This question stems from wondering why there isn't a classical wave equation like maxwell's equation for the electron.


title: Nonpertubative renormalization in quantum field theory versus statistical physics

text: I am trying to work my head around how renormalization works for quantum field theory. Most treatments cover perturbative renormalization theory and I am fine with this approach. But it is not the most general framework and is not intuitively related to the Wilsonian approach. I am also a bit lost with respect to the meaning of the associated notions in the QFT context like the anomalous dimension. So, I essence what I am asking what is the intuitive picture relating the coarse graining idea of statistical physics with the framework of quantum field theory. Also, how could one picture/understand the notion of proliferation, coupling constants, beta functions, fixed points, anomalous dimension and conformal invariance with respect to the way the ideas are interpreted in statistical physics. I find it easy to visualize the entire procedure in the latter context but not in the former. A complete analogy might not be possible but I am only asking to what extent it can be achieved.


title: Measuring life through radiation

text: Dramatic title, I know. But it's shorter than _Measuring a person's effective mass through radiation and comparing it to their weighed mass_ and I figured this would get people's attention. I just thought of this a while back. If we were to collect the EM radiation a person emits, we could find a measure for their rest energy and therefore we should be able to use $E = Mc^2$ to calculate a corresponding mass $M$. Now I reasoned that this would not yield the same result as an actual measurement of their 'weighed mass' $m$ with a weighing scale due to the fact that humans are living creatures and there's loads of biochemical processes going on inside of us to try and keep our temperature at a certain stable level, among other things. Then I started thinking about the meaning of the mass we could calculate from the radiation and more specifically about the exact meaning of the difference $M-m$. If all of my above reasoning is correct, I should think this gives us some measure for the amount of energy (maybe power might be a more appropriate quantity) we need to keep us alive. Obviously, in this context it might make more sense to talk about energies (so to transform $m$ to an energy $e$ instead of transforming $E$ to a mass $M$) but hey, they're equivalent and I'm quirky. Anyway, to get to my question: is there any truth in my reasoning or have I made a mistake? If there is truth to it, I'm guessing other people have explored this already and I'd be interested in any results.


title: How is the direction of time determined in general relativity?

text: In special relativity every frame has its own unique time axis, represented in Minkowski diagrams by a fan-out of time vectors that grows infinitely dense as you approach the surface of the light cone for a given rest frame. Viewed from any other frame, these same time vectors shift about exactly the same fan-out topology, so no one frame perspective is any more "correct" than any other one. In general relativity this does not quite seem to be the case. If nothing else, all those worldlines extend over billions of years and so presumably end up having a quite precise average time orientation for any given local region of space, even if you select a complicated overall topology. Conversely (and I assume equivalently), if space is viewed interpreted as manifold, the idea of an average "flatness" that is orthogonal to this long-term time axis appears to be assumed, since it would look quite odd to see the entire universe slanted relative to its own time axis, yes? So:   1. Am I understanding this correctly? Does GR applied over eons necessarily end up defining and distinguishing a unique and well-defined overall time axis?   2. If so, how is this unique time axis ascertained in experimental practice? Is it taken to be some sort of very large center-of-momentum average, as the billions-of-years bundle analogy would seem to suggest?   3. If a distinguished time arrow does exist in GR, does the existence of that axis imply any experimentally meaningful implications for its associated SR frame?


title: How to compute configurations (entropy) of a system?

text: If we have a system $X$ consisting of subsystems $X_1$ and $X_2$. We also know that $X_1$ and $X_2$ have eigenstates $H_1 = 1 \times 10^{20}$ and $H_2 = 1 \times 10 ^{22}$. Can we calculate the entropy given the above data? If yes, what's the basis?


title: Do residents of the Hudson Bay area have more time?

text: Apparently there is a gravity anomaly in the Hudson Bay Area in Canada: gravity is "missing" or it is slightly less than it is in the rest of the world. Does that mean that things in the Hudson Bay Area would theoretically be at a higher gravitational potential, and consequently clocks would run faster there? Would people living there have "more time" than people in other parts of the world - even if over their lives it only amounted to a few nanoseconds?


title: Why does air circulate on an airfoil --- The Kutta Condition

text: ![enter image description here](http://i.stack.imgur.com/flYBz.png) Why does the air circulate on a flowing airfoil, thus giving rise to increased velocity (circulation + relative airspeed) above the wing and hence decreased pressure.


title: Why friction force is force of constraint?

text: My understanding about constraint force is that it is a force which limits the geometry of particle's motion. For example, situations such as the particle trapped in a track or limited in domain can be assumed constraint force. But in this point of view, I couldn't understand why friction is constraint force. In lagrangian formulation, we divide forces into two part, F= F(applied) + F(constraint) If particle moves in one dimension, and assuming there exists sliding friction, that particle can move anywhere. The sliding friction never restrict the domain that particle can move. so I think the sliding force is applied force, rather than constraint force. can anyone clarify why friction is constraint force??


title: Zero field cooled / field cooled susceptibilities

text: I'm studying magnetic properties of nanoparticles in a liquid carrier and trying to understand better zero-field-cooled/field-cooled curves. We use the Stoner–Wohlfarth model and Chantrell calculations to model ZFC/FC curves but I'm having some issues to follow the calculation. Does anyone understands the model and can help or knows any reference that can help with that?


title: Milky way rotation data

text: Can anyone tell me where I can download sample rotation curve data for the Milky Way in csv format?


title: Inverse of a series (solid state)

text: I am working with the expression involving the equilibrium displacement ($y_n$) for the $n$th particle in a 1D harmonic lattice in terms of the normal modes coordinates $A_k$. Let me show you the expression: $$ y_n(t) = \sqrt{\frac{2}{N}} \sum_k A_k(t) \sin(kan) $$ where $k$ is the wave vector and $a$ the lattice spacing. My question is, how can I invert the series in order to express the $A$'s in terms of $y$'s?. I was thinking about an inverse Fourier transform but since $\imath$ is not involved I'm not sure.


title: Does moving something horizontally in gravity do no work?

text: > Bill’s job is to lift bags of flour and place them in the back of a truck, > which is parked next to him. Sally is loading the same bags of flour into a > similar truck that is located 10 m away. Sally wants a raise because she > says she is doing more work than Bill. Does the physics definition of work > support her claim? **Attempt** : By the definition Work is Force multiplied by the Displacement in the direction of the force. Sally does the same amount of Work when she lifts the bag. But, when she cares the bag for 10 m to the truck there is no force exerted on the bag in the direction of the truck. Therefore, she does the same amount of Work. Is my reasoning correct? Why the Force exerted in the direction of the truck is zero?


title: What is the mechanism for the production of the electromagnetic radiations due to accelerated charge particles?

text: I have recently read in Griffiths that when a charge particle get accelerated the electromagnetic field associated with it get " ditatched " from it and this detatched electromagnetic field is what we call as electromagnetic radiations...But how physically the electromagnetic field gets detatched from the charge ? I have also read that the electromagnetic field or entity is as real as a foot ball or a book or any other thing that we actually feel to be existing physically ...But I don't understand how ? before Griffiths I have read that the electric field or the magnetic fields are only assumed entities that can be regarded as important tools to explain the interactions of the charged bodies..But how can they have " real " physical existance ?


title: Calculating velocity change after impact?

text: Let's say there is no gravity here and objects won't crush. We have 2 rocks with $m=10\text{ kg}$. First rock has velocity $v_1=0\text{ m/s}$ and second $v_2=10\text{ m/s}$ (flying in leftward direction). The second rock hit first causing force for a time $t=0.001\text{ s}$. $F=ma \rightarrow F=\frac{mv}{t} \rightarrow F=\frac{10*10}{0.001} = 100000\text{ N}$ $a=F/m= 100 000/10 = 10 000\text{ m/s}^2$ So acceleration is $10 000\text{ m/s}^2$ in time $0.001\text{ s}$ meaning change in velocity would be $10\text{ m/s}$? It would mean first rock would travel at velocity $10\text{ m/s}$ (flying in leftward direction) and the second would stop $(10-10=0)$ but it seems against all logic. I probably messed up something here so anyone can help?


title: Can a spinor be defined as any quantity which transforms linearly under Lorentz transformations?

text: Recently I’ve come across a few papers from China (e.g. Xiang-Yao Wu et al., arXiv:1212.4028v1 14 Dec 2012) that make the following statement: > ...any quantity which transforms linearly under Lorentz transformations is a > spinor. It’s my understanding that e.g. a 4-momentum vector also transforms linearly under a Lorentz transformation. Is the first statement simply false, or should one take it to be true in the sense that a 4-vector is capable of being written in spinor notation? Perhaps the first statement might be a confusion between Lorentz transformations and spin matrices? In the chapter on spinors in Misner, Thorne and Wheeler’s Gravitation (p. 1148) they show that while a vector transforms under a spin matrix (aka rotation operator / quaternion / spinor transformation) as: $$X \to X' = RXR^*,$$ a quantity that transforms as $$ξ \to Rξ'$$ is known as a spinor. Advice please? UPDATE After further web-searching, I’ve come across references making statements that seem to throw some light on the issue   1. Andrew Steane’s recent and very readable (to such tyros as myself) “An introduction to spinors” (http://arxiv.org/abs/1312.3824 13 Dec 2013), in which he writes (p.1, 2nd para): “… One could say that a spinor is the most basic sort of mathematical object that can be Lorentz-transformed.” (But see (3), here below).   2. I’ve also now traced back the original quotation, repeated word-for-word, through a number of earlier papers (Chinese and Russian) to: V. V. Varlamov arXiv:math-ph/0310051v1 (2003), in which he cites – as do all the later papers – one of the earliest writers on spinors, B. L. van der Waerden, Nachr. d. Ces. d. Wiss. Gottingen, 100 (1929). Varlamov also wrote a densely mathematical and well-referenced paper “Clifford Algebras and Lorentz Group” (math-ph/0108022, 2001), which inclines me to give more credence to the original statement, even though it was parroted by a number of later authors.   3. However, it appears that Dirac himself suggested an even more general entity than the spinor: “A new kind of quantity with components which transform linearly under Lorentz transformations must be introduced, and I call it an expansor. It is rather more general than a tensor or a spinor in that the number of its components is infinite, but enumerable.” P. 1205, section 1946:1 DEVELOPMENTS IN QUANTUM ELECTRODYNAMICS (p. 21 of the section). The Collected Works of P. A. M. Dirac: 1924-48: 1924-1948 By (author) P. A. M. Dirac, Volume editor Richard Henry Dalitz. Cambridge University Press, 26 Oct 1995 - Science - 1310 pages. Further, on p. 1163 of the above, Dirac notes that “the present theory of expansors applies, of course, only to integral spins, but probably it will be possible to set up a corresponding theory of two-valued representations of the Lorentz group, which will apply to half odd integral spins.” These two-valued entities were subsequently supplied by Harish-Chandra, who called them “expinors” (“Infinite Irreducible Representations of the Lorentz Group”, Published 1 May 1947 doi:10.1098/rspa.1947.0047Proc. R. Soc. Lond. A 1 May 1947 vol. 189 no. 1018 372-401). I haven’t access to van der Waerden’s classic, so cannot check whether he made the claim referenced by Varlamov (but have little reason to doubt him). So what can I conclude? The subsequent work by Dirac and Harish-Chandra seems to invalidate the van der Waerden claim, as later cited by Varlamov, at least for infinite dimensional IRs of the Lorentz group. So perhaps the queried definition does apply fairly generally, but not universally? If so, it would be good to have an expert clarify the distinction. PS Gratitude to Qmechanics for tidying up the original posting.


title: Magnetic hot air balloon

text: Normally, hot air balloons are limited to 60,000 ft (related question), the limits being the mass of the physical structure containing the air, and the heat source. If one constructed a magnetic bubble and filled it with plasma (AKA mini- magnetospheric plasma propulsion) which was kept hot with a really powerful ground based microwave source (~3MW for a 1 ton payload, from my back of the envelope calculations), could it reach space (Kármán line, atmospheric pressure 32 mPa)? Or would something stop it working at a particular altitude, e.g. the plasma would cool down too fast, or become detached from the magnetic field, or the electrical conductivity of the air at some height would neutralise the plasma, or some other reason I don't know yet? If it is possible, how accurate are my estimates (I don't know how efficiently microwaves would heat a plasma, nor how much power would really be lost by something like this).


title: What does "foliation" mean in the context of a "foliation of spacetime?"

text: I've seen foliation used in the context of "foliation of spacetime" here and elsewhere in papers and such. Generally defined in reference to a "sequence of spatial hypersurfaces." But I don't know what that means either. Again, I can imagine what these terms mean because of the English language meaning of the words. But what do these mean specifically in reference to the physics of spacetime?


title: What is physical in the principle of local gauge invariance?

text: Modern theories of interactions in particle physics are gauge ones. I know how the gauge fields are introduced in equations ($D = \partial + A$). I just do not see any physical motivation in it. I am afraid it is done by analogy with QED and that's it. I conclude that it is not the only possible way of description of interactions. But maybe there is something essential that I am missing? **EDIT:** As the main failure of gauge way of "introducing" interactions I can point out its intrinsically perturbative character. One cannot switch off **permanent** interaction without severe problems. dbrane answered to that in comments "... you can treat gauge field theories non-perturbatively and still gather valuable insights ..." Let us see. First question: With what does $A$ interact - with bare or real electron?


title: How to describe a well defined "zero moment" in time

text: Suppose you have to specify the moment in time when a given event occurred, a "zero time". The record must be accurate to the minute, and be obtainable even after thousands of years. All the measures of time we currently have are relative to a well defined zero, but the zero is not easy to backtrack exactly. One possibility would be to take a sample of Carbon with a well defined, very accurate amount of 14C, and say: the event occurred when the 14C was x%. At any time, measuring the rate of decay, you would know when the event occurred. This however, requires a physical entity to measure, which may be lost. Another way would be to give the time lapsed after a well defined series of solar eclipses. In order to define precisely the context, you would say a list of (say) five consecutive eclipses and the places on Earth where they were total, and then a time gap from the last of the set. At any time in the future, you can backtrack the specified conditions into a celestial mechanics program and find when the event occurred. Is there a standardized or well recognized method to do so?


title: Are fundamental forces conservative?

text: I wonder whether fundamental forces are conservative. First of all, I'm not sure if we can talk about conservative forces, since to study electromagnetism, weak and strong interactions we need QFT. For gravity, I'd that it's not conservative, because energy conservation doesn't even apply.


title: Ground-based anti-matter detector on the cheap?

text: Given today's revelation of the detection of terrestrial gammay-ray flashes (TGF) produced by thunderstorms and the associated pair production of an electron and a positron, how feasible is it to set up ground-based gamma ray detection station on the cheap using a Geiger-Muller tube? The electron/positron pair travels along the magnetic field of the earth and bounces back (additional question: why do they bounce back?) This is how Fermi could detect the positrons: they interacted with the satellite which happened to be in the way. The loss of energy due the interaction slow down the positrons which interact with electrons and produce two 511keV photons flying in opposite directions (source.) My question is: is it feasible at all to capture and detect positron annihilation as the pairs bounce back using a G-M tube? Given that there are 1500 thunderstorms a day I'm assuming each location on earth has a good chance of being a "bounce site" at least a few times a year.


title: Could Static Electricity cause Fire in a room full of Flammable Gases

text: I am working on a Project and one of the major part of it is a GAS Detector, The GAS Detector detects the large number of flammable gases, but in order to test the Detector I am required to release certain gases in a room from the GAS cylinder with different flammable gases. There is no such thing in a room which could cause ignition, still i wonder if the Static electricity produces in a room somehow, can it cause the fire or some harm due to this gases ?? Is there even the slightest possiblity that it could be harmful ? I just want to know if it may cause so that I could tell my Professors why I am testing the GAS sensor with the Hydrogen gas present in air.


title: How to convert RL Circuits?

text: _**How do we convert a parallel RL circuit into its equivalent series RL circuit ?_**


title: Charge signs in current

text: I've had recently an argument with my friend about different charge carriers in an electric current. Suppose that electrons and holes are moving in the same direction. It effectively means we have half of the electrons moving in one direction and half in another direction. Thus, he says, the current is zero. So in general:   1. If charge $Q$ moving, say, to the **right** and charge $Q$ of the **same sign** is moving to the **left** the current is **zero**.    2. If charge $Q$ of one sign and charge $Q$ of the **opposite sign** are moving in the **same direction** the current is also **zero**. But why? Why then when we have a **positive** charge $Q$ moving to the **right** and **negative** charge $Q$ moving to the **left** the current is $|2Q|/t$ and not zero? I don't see why the directions are so important and why in some cases the charge "cancels" while in others it doesn't. Moreover, it seems more intuitive that the charge will "cancel out" in the last situation that I have described (because then we have an algebraic sum $+Q-Q=0$).


title: Interpretation of rank 2 spinors

text: While inspecting the $(\frac{1}{2},\frac{1}{2})$ representation of the Lorentz group and defining a right-handed spinor with upper dotted index and a left- handed spinor with lower undotted index and therefore $$v^{\dot{a}}_b = v^{\nu} \sigma_{b \nu}^{\dot{a}}= \begin{pmatrix} v_1+iv_2&-(v_0+v_3) \\\v_0-v_3&-(v_1-iv_2) \end{pmatrix}$$ and $$v^{ \dot{a} b} = \epsilon^{bc} v_c^{\dot{a}}$$ with spinor metric $$\epsilon^{bc}= \begin{pmatrix} 0&1 \\\ -1&0 \end{pmatrix}$$ it can be seen that the rank 2 spinor $v^{ \dot{a} b}$ has exactly the same transformation properties as a 4-vector $v_{\mu}$. But in the same way it can seen that for example $v^{\dot{a}}_b$ transforms differently. Are there any physical interpretations of those objects? Do they describe specific particles (not vector particles?)? Any help or reading suggestion would be much appreciated.


title: Why is developable surface developable (ie. can be flattened onto a plane without distortion)?

text: The course _Differential Geometry_ told me that developable surfaces, of which the Gaussian curvature is $0$, can be flattened onto a plane without distortion. Some says this is because a developable surface can have the same metric as a plane. But I still think **metric** here is a little abstract, since I can't figure out the connection between metric and the physical nature or the structure of a paper. I cannot connect well between the physical phenomenon of paper folding and its mathematical description of Gaussian curvature or metric. Is there a good physical explanation of this? Thanks.


title: Helicity and Chirality

text: Does the concept of both **helicity** and and **chirality** make sense for a massive Dirac spinor? A massive electron in chiral basis is written as a column made up of $\psi_L$ and $\psi_R$. What are the significance of this? These cannot be decoupled from each other due to the presence of mass term in the Dirac equation? But we know electrons will look either left handed or right handed depending upon from which frame we are looking at it. Then, in a given frame it is either left handed or right handed. Then what is the meaning of $\psi_L$ and $\psi_R$ separately?


title: How is this process not quasi-static yet reversible?

text: Consider a (adiabatic) canister with a piston containing some gas kept in a vacuum. There are two weights on the canister which equalize the pressure of the gas on the piston. Assume the system is at equilibrium. I remove one weight from the piston. The system will go out of equilibrium. After some flux, it will again settle into equilibrium. Clearly, this is not a quasi-static process. But its a reversible one, isn't it? If I put the weight back on the piston, the system will again achieve its initial state. How can a non-quasi-static process be reversible? **EDIT:** According to Wikipedia, a reversible process "is a process that can be 'reversed' by means of infinitesimal changes in some property of the system without entropy production". So, if a process can be reversed _without_ the means of infinitesimal changes without entropy production. Would that qualify as reversible? (as in the example given above)


title: How does light get into a stable optical cavity in the first place?

text: It is supposedly possible to trap a beam of light bouncing back and fourth between two mirrors in a stable configuration. As I understand it, this means the configuration will _prevent further spread of the beam angle_ so it stays between the two mirrors, since it certainly couldn't decrease the beam spread as that would violate the 2nd law of thermodynamics. Wikipedia has an enlightening section on this, and I found this illustrative, showing the region of stable configurations: ![enter image description here](http://i.stack.imgur.com/53qYL.png) As has come up in other questions, this method has been used by researchers to get beams of light to bounce between mirrors over 100,000 times. Wouldn't any given photon make it back to the point where it was emitted in the first place? Then, since it's not possible to have a one-way mirror (would also violate thermodynamics), then it would ultimately cause the destruction of the photon because it exits the cavity. That would imply that in order to get 100,000 bounces, the mirror's area would have to be 100,000x the area of the emission point. Is that how it's done? Or is there a better way that researchers have to keep the light in such a cavity from being destroyed at its emission point? Maybe if you were using a laser, you could let the photon physically go back into the laser and stimulate more emission or bounce off the back wall?


title: How reflected objects are composed and who is responsible for that?

text: Please refer to this image. The scene contains an object close to a mirror in the wall and a window, note that the reflected object is receiving more light than the object itself. I read some articles about the Law of Reflection and the Ray Principle but did not get a straight answer on how the mirror(or my eyes) knows how to compose that virtual image in a way it appears to receive more light. According to the definition of the Plane Mirror, the light rays do not actually pass through the virtual image, then why the virtual image is being composed with more light and who is responsible for that? The mirror? My eyes?


title: Can a curvature in time (and not space) cause acceleration?

text: I realize that the curvature of space-time causes acceleration (gravity). Is it possible to have a curvature only of space, or a curvature only of time? If so, would a curvature only of space, or a curvature only of time, also cause acceleration?


title: Application of wavelets in computational electromagnetics

text: I am a first-year graduate student (electrical eng.); wavelets is one of the courses that I am taking presently. As part of the course, I plan to explore application of wavelets in computational electromagnetics (CEM). The idea behind it is to study a few applications where wavelets are used in CEM, code/simulate them and explain their computational advantages over conventional CEM methods like Finite Element, etc. I have a very nominal knowledge of the numerical techniques used in CEM, and time constraints forbid me from exploring or going into depth. Can anybody please suggest a few specific application problems of CEM which I can work on? I understand Maxwell's equations quite well. Also, any references/books/online resources of the suggested application would be extremely helpful to proceed.


title: Textbook on Diffusion and Diffusion NMR Spectroscopy

text: I am looking for textbooks ( Mathematical / Theoretical Physics ) that cover diffusion in general. Although it is not necessary that your recommendation covers it, I am also particularly interested in a theory textbook that covers the fundamentals of diffusion NMR spectroscopy (how diffusion enters the Bloch equations and so on).


title: Why would air try to escape from under a pot?

text: I put a wet Calphalon pot down flat on a wet synthetic countertop. None of the surfaces or liquids was hot. Bubbles started appearing a second or two later from under the rim of the pot in one area. (Video.) It looked as though air was trying to escape form under the pot and forming bubbles because of the water, perhaps as if the air pressure was greater under the pot than everywhere else. Anyone know why?


title: Why does only one twin travel in the twin paradox?

text: The wikipedia page repeatedly says that the twin travelling in space is the only one which travels, and also is the only one which faces acceleration and deceleration. So it does not age, while the twin which remains in one place ages. However, this seems wrong as there is no such thing as staying in one place. The twin which presumably stays on earth is travelling at the same **relative** velocity, relative to the twin in the spaceship. Since the spaceship twin's acceleration is just the rate of change of velocity, so when the spaceship twin's velocity changes relative to the earth twin, the earth twin's relative velocity compared to the space twin also changes, and so the earth twin experiences the same relative acceleration as the space twin (in the opposite direction). In fact, the space twin sees the earth twin as accelerating away from him, then decelerating and coming back, while he thinks his spaceship is at rest all the time. So then why should the earth twin age more than the space twin? Why not the other way around?


title: In calculating resistivity of skin do I use the body's surface area?

text: > Most of the resistance of the human body comes from the skin, as the > interior of the body contains aqueous solutions that are good electrical > conductors. For dry skin, the resistance between a person’s hands is > measured at typically $500\: \mathrm{k \Omega}$. The skin varies in > thickness, but on the average it is about $2.0\: \mathrm{mm}$ thick. We can > model the body between the hands as a cylinder $1.6\: \mathrm{m}$ long and > $14\: \mathrm{cm}$ in diameter with the skin wrapped around it. > > (a) What is the resistivity of the skin? So for this, I used the equation $R = (\rho*L)/A$. For Area, should I use the entire surface area of the body a.k.a cylinder?


title: What would be the basis vectors for this 2D crystal structure?

text: ![enter image description here](http://i.stack.imgur.com/hvaL7.jpg) In the above image, I have a 2D crystal structure. The lattice vectors are described by:               a = {-1/2, -Sqrt[3]/2};     b = {1, 0};      and the location of atoms A and B are given by:               \[Tau][A] = {2/3, 1/3};     \[Tau][B] = {0, 0};      Now the problem I'm tasked with is to plot the locations of the atoms A and B, which I have done as seen above, where A is red and B is blue. I also have to plot the lattice vectors which I have done in blue arrows as seen above, and lastly I have to plot the basis vectors and this is where I don't know what to do. I don't know what the basis vectors are. Googling has led me to discover that a lot of people use lattice vectors and basis vectors interchangeably, and overall, I have no clear definition to work with. Sometimes people say basis vectors are orthonormal, sometimes they need to be linear combinations with integers, sometimes with any real numbers. I'm frustrated by the looseness with which all kinds of sources use these terms, and ultimately I don't have a clear reference to go with.


title: There must be free positive charges, moving oppositely to electrons for the wire with current to stay neutral

text: All popular expositions (e.g. these ones) of relativistic electromagnetism claim univocally that electrons in motion become more dense due to the speed. They teach that Lorentz contraction of charges causes charge imbalance and wire with current charged. Thereby, no teacher says that the wire becomes negatively charged (because electrons move) in the lab frame, where we had it originally neutral, when no current was flowing. That is a question: is wire neutrality conserved, once we create a current of electrons in it? It must be the case because, as Feynman points out, the lighter electrons better react on temperature changes and would charge the wire when heated. But, then answer how neutrality is persisted after you say that electron contraction takes place and it increases their density? Might be "some light" positive charges start moving in opposite direction, to compensate the growth of negative charge? I see that all discussions of "magnetism as electricity+relativism" avoid concerning this, most basic and most interesting case. Instead, they jump immediately to the case where you have an electric balance for a test charge in motion. Once finished with this, you are encouraged to answer how it is possible that density of charges is increased whereas volume of the loop is intact?


title: Can Increasing the Turbulence Inside a Pipeline Economically Increase Flow?

text: > "The velocity gradient in turbulent flows is steeper close to the wall and > less steep in the center of the pipe than it is for laminar flows (Blatt > p.97)." Does this mean that some degree of turbulence near the wall of a pipe may actually improve the energy efficiency of pumping a fluid? I realize that turbulence tends to increase the energy required, but perhaps just the minimum amount in the right place might prove advantageous. Have surface modifications to increase turbulence been investigated for potential efficiency? "The eddy viscosity is generally much larger than the dynamic viscosity (Blatt p.111)." This would suggest that larger diameter pipes would be better candidates for turbulence assisted flow, since the volume to surface area ratio is larger. Icebreakers bubble air past their hulls to lubricate the ice scraping against their hulls. Specially tailored turbulence might be able to lubricate the sliding the bulk of the fluid as virtually "extruded" past controlled turbulence. The efficiency of the turbulence would likely be velocity dependent. Relevant Information: The Darcy-Weisbach equation is used to describe the pressure loss over a given segment of pipe. Blatt, Middleton, and Murray, "Origin of Sedimentary Rocks," 2nd Ed.


title: What happens to the electron companions of cosmic ray protons?

text: If primary cosmic rays are made mostly of protons, where are the electrons lost, and does this mean that the Earth is positively charged? Does the sun eject protons and electrons in equal number?


title: A lightning protection device physics

text: Here is a description of the principle of the operation of a new lightning device: _During a storm the ambient electric field may rise to between 10 to 20 kV/m. As soon as the field exceeds a thresold representing the minimum risk of a lightning strike, the OPR lightning terminal is activated. **It draw its energy from the ambient electric field the energy required to generate high voltage pulses, creating and propagating an upward leader.** No other power sources are required, and no radioactive components are used._ It remains unclear to me the physics of the drawing the energy from the electric field. Obviously, you can not draw the energy from the electrostatic field, no matter how strong it is. So i suppose that the electric field must oscillate more or less. The question is: Which is a minimal frequency of the oscillations so that such device can work properly? A full description of the device


title: Does Earth's rotation change at a constant rate?

text: Follow-up to Is Earth's orbit altered by recoil from take-off/launch/recovery of aero/space vehicles? and How much meteoric/space dust does the moon accumulate daily? Is the length of the day increasing? I understand the addition of mass probably slows Earth's rotation. As Earth gains mass does it's gravity attract space/meteoric dust in an increasing quantity? Ergo, Does Earth's rotation change at a constant, or accelerating rate?


title: Why is the Yang–Mills existence and mass gap problem so fundamental?

text: Ref: Yang–Mills existence and mass gap Can anyone please explain why the Yang–Mills Existence and Mass Gap problem is so important / fundamental to contemporary mathematics (and, presumably, theoretical / mathematical physics)? If possible, please include the following in your answer / response: (1) Why the problem is so fundamental / important - for both mathematics and theoretical / mathematical physics; (2) How the solution to the problem would impact research in the above two fields; (3) (If applicable) What progress has been made so far in resolving it; (references to papers, books, other resources would be helpful). I'm an upper-level undergraduate in theoretical physics, and so am seeking an answer / response at such level.


title: Why is $\frac{dx}{dt}=0$ in this average momentum calculation?

text: In the following excerpt from S. Gasiorowicz's _Quantum Physics_ , he derives an expression for the average momentum of a free particle. $\psi(x,t)$ is the wave function of a free particle, $\psi^*$ denotes its complex conjugate. > We try the following: since classically, > > $$ p = mv = m\frac{dx}{dt} $$ > > we shall write > > $$ <p> = m\frac{d}{dt}<x> = m\frac{d}{dt}\int{dx \psi^*(x,t) x \psi(x,t)} $$ > > This yields > > $$ <p> = m\int_{-\infty}^\infty{dx\left( \frac{\partial\psi^*}{\partial t} x > \psi + \psi^* x \frac{\partial\psi}{\partial t} \right)} $$ > > Note that there is no $dx/dt$ under the integral sign. The only quantity > that varies with time is $\psi(x,t)$, and it is this variation that gives > rise to a change in $x$ with time. I seem to have trouble understanding the difference between the position $x$ and the average position $<x>$. Why can it be assumed that $\frac{dx}{dt}=0$? What _is_ x?


title: What is the value of the fine structure constant at Planck energy?

text: At low energy, 511 keV, the value of the fine structure constant is 1/137.03599... At Planck energy $\sqrt{\frac{\hbar c^5}{G}}$, or 1.956 $\times$ 109 Joule, or 1.22 $\times$ 1028 eV, it has a value around 1/100 . Does anybody know a more precise value, maybe with error bars? Clarification: The idea is to take the famous "semi-official" plot for the standard model: go to page http://www-ekp.physik.uni-karlsruhe.de/~deboer/ then click on "our research" then go towards the end of the page: the graph is the link "Unification plot.ps (update from Phys. Lett. B260 (1991) 447)". Now take the left graph (not the right one for supersymmetry). The upper curve shows the fine structure constant, but scaled with some funny numbers suggested by GUTs. The precise question is: what value for the fine structure constant would this normal QED/standard model graph show at Planck energy if these funny GUT numbers would not be in the graph? My estimate is about 1/100, but I would be interested in a more precise value. It is clear that this question _assumes_ , like the graph itself, that both QED and the standard model are correct all the way up to Planck energy.


title: Why does compressing a piston increase the internal energy?

text: When we compress a piston, its total internal energy increases, however I don't understand why. As the piston compresses, the temperature should change, as the total energy density increases. As a piston compresses, work is done to compress the gas. However, this is solely fighting a differential in pressure, as well as the force to accelerate the piston. It seems none (or very little) of this energy should be imparted to the gas - so why does the internal energy significantly increase? The last one is somewhat explicable, however, when we pull back on a piston, uncompressing the air, we're not taking energy away from the air. While the overall energy density changes, the total energy itself shouldn't, as no process is removing energy. However, it does - so where is the energy going? Ultimately I think this comes down to: where does the energy go, _and how does it get there?_


title: Physics and Skin Color: What differences do physicists observe between different skin colors?

text: I majored in social sciences, so I haven't taken a science class since 1999, so forgive me if I don't ask this right. What difference would skin color make from a physics perspective? Would there be any difference in the energy emitted, reflected or absorbed? Would it affect what is emitted, reflected or absorbed? Can physics provide an analysis of why paler skin is more prone to melanoma? Does melanin in an of itself have any physics applications? Is is used in physics experiments, etc.?


title: Relative Motion

text: I read the following: http://www.feynmanlectures.caltech.edu/I_15.html#Ch15-S4 > "Now let us see what happens to the moving clock. Before the man took it > aboard, he agreed that it was a nice, standard clock, and when he goes along > in the space ship he will not see anything peculiar. If he did, he would > know he was moving—if anything at all changed because of the motion, he > could tell he was moving. But the _principle of relativity_ says this is > impossible in a uniformly moving system, so nothing has changed." In my point of view Feynman uses the principle of relativity as a kind of an _axiom_ for his derivation of time dilation. **Question:** How do we know that the _principle of relativity_ is true and can use it like an axiom for new phenomena? If we had treated Newton's laws of motion as axioms we would never have found out how nature actually works. In other words, what is the law behind the fact that you cannot know how fast you are moving? How can you use this assumption as axiom for e.g. the behavior of clocks as Feynman does further down in the link? P.S.: Feel free to edit since I'm not a native English speaker. Nevertheless I want to improve my English and it would be great if you pointed out my errors.


title: Does a UV completion of gravity necessarily need to be so drastic as String Theory or LQG?

text: First of all I, it is my understanding that the problems one encounters with the non-renormalizability of gravity are very similar (if not the same) as one encounters in any non-renormalizable theory. As long as you are doing your calculations well-below the scale that suppresses irrelevant operators your calculations should make sense. As you approach that scale that suppresses irrelevant operators there is new physics that comes in at that scale - if you try to push your effective theory to the scale of new physics, perturbation theory will break down. This to my knowledge is the story that underlies the failure of Fermi-theory that necessitates introducing W bosons, and the failure of the standard model with out a higgs that necessitates the introduction of a higgs. My questions is, is gravity, a priori, any different then the above 2 scenarios? That is, we need new physics to come in at the planck scale to UV complete the theory (or, put it another way, unitarize graviton scattering), but could it be as simple as one to a few new particles? Or for other reasons does it have to be something as drastic as String Theory or Loop Quantum Gravity? By drastic I mean paradigm shifts where its not some small modification to the current theory consisting of a few new particles, but more of an complete overhaul.


title: Feynman's sum over histories?

text: The concept requires all possible path's to be mapped out, and any remaining paths not cancelled out represent the most probable path of the object. Considering this:      i) If "infinite" paths are mapped out (since there are infinite paths for every movement) , isn't it guaranteed for every path to be canceled out? Every path has an opposite, and if infinite paths are mapped, the opposites are guaranteed to be present. ii) How do you map out infinite paths? Nothing infinite can be completely mapped, on the basis that it is infinite.


title: What's the basic premise of General Relativity?

text: What is the basic assumption(s) required to explore general relativity? For example, if one merely assumes that the speed of light $c$ is the same for all observers, and the laws of physics are the same for all observers, then it's possible using a mix of algebra and some calculus to derive every SR result from time dilation to length contraction, $E = mc^2$, and so on. What is the basic premise of general relativity? I assume that all of SR is included but is there anything else?


title: How exactly are the degrees of freedom seen by a falling into a black hole observer related to the ones seen by a staying outside observer?

text: This is some kind of a follow up of this nicely to the point answer to a provocative (but nevertheless upvoted!) question, about the legitimacy of black hole physics. The answer mentions, that the interior and exterior of a black hole are not completely decoupled, and about this exact relationship I'd like to learn some more not just hand waving details. Of course I know the complementarity principle, which says that the perspective of what happens near the event horizon of a black hole an infalling observer who does not note anything special when crossing the event horizon and the description of the physics near the horizon by a staying outside observer who sees the infalling observer getting frozen on the horizon, are both equally legitimate descriptions of the same physics. Is there some kind of a map, or exact dictionary by which one can transform back and forth between these two descriptions of the same physics, that describes the complementary principle for black holes mathematically? An aside: I always thought that the holographic principle is soemething different from the complementarity principle in this context, so this should not be the trivial answer to my question (?) ... Maybe I have managed to confuse myself now :-) Clarification after some comments I am not just up to a coordinate transformation between spacetime inside and outside the even horizon, but I'd like to learn about how the degrees of freedom used by an infalling observer and the ones used by a staying outside observer to describe the same physics transform into each other.


title: Magnetic force doesn't do work and therefore can't change the KE of a particle?

text: I am having a real hard time understanding the principles behind a question I've come across during test prep. Here is the question: > Q: A proton and an electron are traveling in the uniform magnetic field with > identical velocities. If the movement of both particles is perpendicular to > the magnetic field lines, is the following true? > > _The proton will experience a greater kinetic energy change than the > electron._ On one hand I think if there is a $\mathrm{KE}$ change for the particles, they would have to be both changed equally, since an input of force to each particle would be converted into $\mathrm{KE}$. On the other hand, since $\mathrm{KE} = \frac{1}{2}mv^2$, and both particles are traveling at the same velocity, it seems the proton's much large mass would mean it has a greater $\mathrm{KE}$ change. However, neither of my thoughts were on target, as the answer reads as follows: > False, because the magnetic force does not do work, so it cannot change the > kinetic energy of either particle. How does this make sense? Won't the particles change velocity when exposed to the magnetic field, and therefore change $\mathrm{KE}$?


title: "Derivation" of the Heisenberg Uncertainty Principle

text: Ok, so I posted this in the mathematics StackExchange, but got no response. The question I outline below is my textbook's "derivation" of the Heisenberg Uncertainty Principle. The "derivation" my textbook uses involves wave packets. Suppose there are seven waves of slightly different wavelengths and amplitudes and we superimpose them (textbook is talking about wave packets). The wavelengths range from $\lambda _9 = 1/9$ to $\lambda _{15} = 1/15$. Their wavenumbers ($k = 2\pi / \lambda$) ranges from $k_9 = 18\pi$ to $k_{15} = 30\pi$. Note, the waves are of the form $$y(x,t) = A\sin(kx - wt)$$ The waves are all in phase at $x = 0$ and again at $x = \pm 12, \pm 24$ etc. My question is the last line. How does my textbook (from which I copied what they wrote) know that they are all in phase at $x = \pm 12$ etc. ? If you can do this in simple terms that would be great (i.e., no fourier transform math since I have yet to learn about it). Is there some rule to know when $n$ number of waves are in phase? (They have all 7 waves graphed, but not on top of each other. Did they do some mathematics or find this from the graph? Note, looking at this graph its hard to tell that all 7 waves are in phase at $x=\pm 12, \pm 24$, etc). Second question, my textbook goes on to say that the width of the group $\Delta x$ of superposition is just a big larger than 1/12. There's a graph of the superposition (looks like a beat graph) but did they determine this number from the graph or is it somehow related to the numbers given above? Then it shows a plot of the amplitude of the waves ($y_0$) vs. $k$. It ``shows'' that the width at $y_0 = 1/2$ is $4\pi$. Just fyi, this is a physics textbook which goes on to say that $\Delta k \Delta x \sim 1$ (using the numbers above, $4\pi * 1/12 \approx 1$) and $\Delta w \Delta t \sim 1$ (by similar arguments). It then uses these as a basis to state the Heisenberg uncertainty principle.


title: What is the meaning behind the neutrino oscillation parameter?

text: As far as I can tell, there are 6 parameters that describe how a neutrino oscillates: 2 mass squared differences, 3 mixing angles and another parameter I don't understand at all (delta). Thus I have three questions: 1) I understand that the 2 mass differences is enough information for the three masses, but we cant yet measure the actual mass. Is this limit due to current technology or is the mass squared difference the most fundamental information about the mass we could possibly acquire? 2) What exactly do the mixing angles physically represent? Are they all of the same importance, and if so why has the theta-13 angle been studied so relatively little? I have also read that a non-zero theta-13 angle hints towards an asymmetry between matter and anti-matter. How so, and why the 13 angle in particular over the other angles? 3) What is the delta parameter? I know that current technology does not have the capacity to measure it, but the next generation (hopefully) will. What does this parameter represent and what implications would measuring it have?


title: Can we create a force shield using a gas that acts like a non-Newtonian fluid?

text: Most people know that if you mix cornflour with water it creates a liquid that if a force is acted upon it it solidify for an instant then returns to a liquid state. will we be able to create a gas than can 1 be contained or produced easy in a set area and 2 that can be carried easy.To act like a non Newtonian fluid for example: If a soldier was in a skirmish and had no cover, the soldier could deploy this gas surrounding him, and acting like a bullet proof shield. The bullet would hit the gas and the gas would (were the bullet hit) become solid suddenly both stopping the bullet and protecting the user Is this possible ?


title: Is it possible to defy time using speed?

text: I have always wondered if we were to travel at past the speed of light (even beyond the current capability) would we be able to slow down time around us? I have asked my teacher at school and he has said that it is possible. Now I am not saying he is wrong. I would just like a second opinion.


title: Cosmological constant doubts

text: I have read about cosmological constant given by einstein in universe in nutshell as well as in general and special relativity. But still I am not able to understand the aim to use it or to introduce it. Can someone explain in brief.


title: What is the effect of total internal reflection on polarized light

text: Total Internal Reflection causes phase change of a light beam. I searched for effect on a polarized light beam by Total Internal Reflection but could not find much. I am assuming polarization does not get altered. I am unable to understand the reason why atoms in glass are able to change phase but unable to change the orientation of electric field of an EM wave. I am re-studying optics after 20 years so please excuse me for being rather naive.


title: Energy of electron spinning in a magnetic field

text: When an electron travels in circles in a uniform magnetic field, it must lose energy because all accelerated charges radiate, and must therefore spiral down to the center. Is this energy compensated by the magnetic field? Or where does this energy go?


title: Optical absorption -- what are the common ranges and mechanisms?

text: So let's say you do some reflection/transmission spectroscopy of a material. It's clear that it's absorbing in some range. What would be your first step in identifying the source of the absorption? The two main clues I would look at would be   1. The range it occurs in (if your incident light is in the x-ray range, it's clearly not phonon absorption, for example)   2. The shape of the absorption (is it a peak? Or an absorption 'edge', where it isn't absorbing below some energy, and absorbs everything above, for example) But I'd like to know if there are other ways as well. Additionally, does anyone know of a 'map' of the ranges you'll typically find different types of absorption in? I saw one on wikipedia once, but it only had three types, and now I can't find it of course. For example, a few types of absorption I can think of off the top of my head are   * Interband electron transitions   * Intersubband electron transitions   * Impurities   * Phonons   * Vibrational modes   * Atomic transitions I understand that a lot of these will be material-dependent, but often the same mechanism in different materials will yield absorption in the same order of magnitude range. What ranges would one typically see these (and other) absorption mechanisms in? Thank you!


title: Metric coefficients in rotating coordinates

text: Let $(t,x,y,z)$ be the standard coordinates on $\mathbb{R}^4$ and consider the Minkowski metric $$ds^2 = -dt^2+dx^2+dy^2+dz^2.$$ I am trying to compute the metric coefficients under the change of coordinates given by: $t' = t$ $x' = \sqrt{x^2+y^2}\cos(\omega t + \phi)$ $y' = \sqrt{x^2+y^2}\sin(\omega t + \phi)$ $z' = z$ where $\phi = \tan \frac{y}{x}$. I know one way to do this is to compute write each of the original coordinate maps as a composition of these new coordinate maps and then take derivatives to express $(\partial_{t'},\partial_{x'},\partial_{y'},\partial_{z'})$ in terms of $(\partial_t,\partial_x,\partial_y,\partial_z)$. This is rather cumbersome though and it seems like there should be a more elegant way to do this. Can anyone suggest a cleaner way to transform the metric?


title: Why is an Aircraft Runway NOT like a Teaspoon?

text: If the aircraft runway were like a teaspoon (by this I mean, flat in the beginning, then curving downwards and finally upwards), would it not work in favor of the propulsion of the aircraft? In spite of this, why are the runways flat?


title: Stationary wave on a string

text: The problem says: > _A string lies on the x-axis, and is fixed at $ x=-a $ and $ x=a $. At $ t=0 > $ we impose a transversal velocity given by $ a^2-x^2 $. Assuming that the > velocity of the wave is $ c $, find the solution to the wave equation._ So here's what I did so far: I set up the solution in complex form as $$ \tilde{y}(x,t) = \tilde{A}e^{i(kx-\omega t)}+\tilde{B}e^{i(-kx-\omega t)} $$   Then imposing the condition of fixed string, I got the values for $ k_n =\frac{n \pi}{2a} $ and $\omega_n =\frac{n \pi}{2a}c $ In the process I got the relation $\tilde{A}=-\tilde{B}e^{2ka}$ Now my problem is when I plug back into the original equation, I get something like this: $$ \tilde{y}(x,t)=\tilde{B}e^{-i\omega_n t}(e^{ik_nx} -e^{i(k_nx + 2k_na)})$$ I know that $2k_na=n\pi$, but that gives me two possible results for $e^{i2k_na}$, 1 and -1. That confuses me a bit, and I don't know how to continue from here. I've seen the example of the plucked string that goes from 0 to $L$, and that's much simpler than this case. I guess I just don't know what to do with the constants introduced by the fact that the string goes from $-a$ to $a$. Any help is appreciated.


title: Average value of consecutive measurements of two observables

text: Suppose we had two boxes named "1" and "2", and suppose we can measure observables $A_1$ and $A_2$ from these boxes, respectively. $A_1$ and $A_2$ commute, meaning we can find a basis of simultaneous eigenstates of $A_1$ and $A_2$. However, a measurement of $A_1$ can affect measurements of $A_2$ because we prepared an entangled state $|\psi \rangle$ for the two boxes. Now, lets measure $A_1$ and then measure $A_2$. We let $X$ be the product of the value returned by measuring $A_1$ and $A_2$. We repeat this experiment a million times for a million identically prepared pairs of boxes. Is the average value of $X$ equal to $\langle \psi | A_1 A_2 | \psi \rangle$? What if $A_1$ and $A_2$ didn't commute? What if we had $N$ boxes with observables $A_1, ... , A_N$?


title: algebraic quantum field theory

text: I am a grad student .I wonder why it seems there have no professors in US doing algebraic quantum field theory compared to Europe? Are they focusing on other model like topological quantum field theory ? Thanks


title: How to find percentage error of equivalent resister?

text: The resistors of $R_1=100\pm3Ω $ and $R_2=200\pm4Ω $ are connected in parallel.Then express equivalent resistance with percentage error. I know how tho find percentage error if resistors are connected in series connection. Can any one help me to find the percentage error if resistors are connected in parallel connection??


title: Why doesn't the LHC accelerate electrons?

text: Electrons   * have a much bigger charge density as the protons (and especially lead nuclei),   * aren't compound particles as the protons (and especially lead nuclei)   * are able to get a much bigger energy with the same fields as the protons (and especially the lead nuclei). Why seems common for the big colliders after the LEP to use protons (and much bigger nuclei)? Reacting comments: Yes, to get good experimental data about quark matter they need a lot of hot quarks (= collided big nuclei). But to create new particles, the _energy per degree of freedom_ needs to be maximized, and this maximum is at the single particle with the highest charge density, and this is the electron.


title: Coulomb & Electric Fields (Highschool Physics)

text: If an electric field is said to have a strength of $10^{-15} N/C$, what does this mean? N is Newtons, C is coulomb - I'm not sure how they link? So then I am asked to calculate the force on the electron and show unit, direction and number. I know force is = QE where Q is electric charge in Coloumbs and E is electric field strength in newtons / coloumb. The electric field has force of $10^{-5}$. So I do $(1.6 * 10^{-19}) * (10^{-5})$ and I get $1.6 * 10^{-24} N $- the correct answer is $1.6 * 10^{-14} N$ Left. I am off by a large factor, and I don't know how the left direction was derived. I hope I formatted everything clearly here.


title: Differential equation for speed relate to the homogeneous cosmological background in FLRW metric

text: How to derive DE for the speed (which relate to the homogeneous cosmological background) of the observer which moves with constant proper acceleration in spatially flat FLRW universe?


title: Intrinsic Viscosity

text: I'm presently undergoing an Experiment for the determination of the viscosity of Ficoll-70 using Ostwald viscometer to calculate the time and a digital weighing balance to determine the weight of a specified volume of the solution at different concentration. I have reached a result but unable to correlate with any data provided by the journals or thesis on this area. It's because they all have given the value of 'Intrinsic Viscosity'. How different is the Dynamic viscosity from the Intrinsic one? Can I calculate the dynamic viscosity of a solution if I know its Intrinsic viscosity ?


Do Dirac Gamma Matrices act like Tensors? Is it true that $$ \gamma_\mu = \eta_{\mu\nu}\gamma^\nu~? $$ Also what about $\sigma_{\mu\nu}$, where $\sigma_{\mu\nu}$ is defined to be: \begin{align*} \sigma_{\mu\nu} = \frac{i}{2}[\gamma_\mu,\gamma_\nu]~? \end{align*}


title: Optically thick media

text: What does "optically thick media" mean? Does this property depend on the length of an enclosure? Why is the diffusion approximation for the radiative transfer equation applied to optically thick media?


title: Does AC current produce EM waves?

text: Does AC current in simple wires produce electromagnetic waves? AC current entails very rapid changes in polarity and therefore the electrons in the metal will feel rapidly changing forces which should make them accelerate before attaining a constant drift velocity. Will this rapidly changing accelerations produce any electromagnetic wave, since the acceleration should be sinusoidal if the voltage source is, and hence the emitted electromagnetic wave should also be sinusoidal? Am I correct? If yes, why do we not account for energy lossd through EM waves in simple AC circuit analysis?


title: California "firenados"

text: There are spectacular rotating towers of fire that can be seen in recent television images of fire in California. In this video, we see that these fire towers can rotate either clockwise or counter clockwise. What is the mechanism behind these "firenados?"


title: how dense fluid affect the buoyancy force?

text: I read a story regarding the Archimedes' principle in a magazine of popular science and I am thinking of the following question: how does the density of the fluid change the buoyancy force for the same object? As we know, the Archimedes' principle tell that for any object in a fluid, the buoyancy force equals to the weight of the fluid displaced by the object. It is pretty straightforward. Now, if I have an object partially floating on the surface of a liquid, so we have $$ F_b = \Delta V \rho g $$ where $\Delta V$ is the volume of the displaced liquid and $\rho$ is the density of the liquid. So what happen if we place the same object into a denser liquid? Physically or intuitively, since the liquid is denser, it is harder for the object to 'inject' into the liquid, so the buoyancy force should be bigger, so less part of the object submerge into the liquid. But if you look at the math, it seems not like this. Well, now $\rho$ is bigger, but the volume of displaced liquid will be smaller because it is harder to submerge the object into a denser liquid too. So how do we that for denser fluid, the same object will experience bigger buoyancy force instead of being the same? So my question is from intuition, the same object in the denser liquid should submerse less than the case in less dense liquid. But from the math, it buoyancy force could stay the same or more. So how to prove from the math that our intuition is correct?


title: Scalar potential, vector potential, and spinor potnetial

text: In Particle Physics, I've seen Scalar potentials which look like this $$ V = a \Phi^2 + b \Phi^4$$ $\Phi$ is scalar (a number). What about vector potentials, and spinor potentials? How are they constructed? I know that when constructing expressions, a number of symmetries should be respected but I don't understand the whole story.


title: Why does paper become translucent when smeared with oil but not (so much) with water?

text: When I smear oil onto a scrap of paper and rub it in, the paper becomes quite translucent; but when I attempt the same with water it doesn't as much. Why?


title: How can I cheat an XRD sample (~10 mg) from a total 1g required? How can I use for the background.

text: How much can affect (in terms of hump) my X-ray diffraction pattern the "amorphous" glass or maybe someone can suggest me other material to compensate for the small amount of the sample. Note: my sample is a powder.


title: How is the poincare conjecture(and perelman proof) helpful in studying the properties of the universe?

text: Can someone tell me how the poincare's famous conjecture or its proof by perelmen can be helpful in deciding some properties like the shape of the universe?


title: How do we prove that multiverse exist?

text: Scientists are talking about our universe not being the only universe, but even if that is true, how can we prove the existence of multiverse? We are being 'confined' in this universe and there is no way we can know what is happening outside, right?


title: max velocity of SHM

text: So I think my algebra is wrong somewhere. Lets say you have an object that goes under SHM with some initial conditions (amplitude is 5m. The piston is at 5m at t = 0 and period is 20 seconds). Okay so $x(t) = A sin(\omega_0 + \phi)$. $\phi$ for us is 0. The frequency = $0.05 Hz$, angular frequency = $\frac{\pi}{10}$ and period of the piston = $20s$. The maximum velocity is is when the first derivative $x'(t) = \omega_0 A cos(\omega_0 t)$ The maximum velocity is when the cosine function is 1 at x = 0. So the maximum velocity is $v(t) = A\omega_0$ so that means $cos(\omega_0 t)= 1$ but $\omega_0 = \frac{\pi}{10}$ so the missing value is t. But thats trivial to find, since cosine function is 1. So $t = 20s$ So here is my issue. The maximum velocity can only be at x = 0 (when kinetic energy is max, and potential energy is zero). But the value t = 20s represents the object at x = Amplitude. So what am I doing wrong? edit: I just realized that if $x(t) = A sin(\omega_0 + \phi)$ then the initial conditions are not satisfied. When t = 0, sin function goes to 0 and hence everything is 0 but that dosnt satisfy initial conditions. When $t = 0$, displacement should be $5m$ However, if i replace $sin$ with $cos$ then everything works. Is that okay?


title: What's the point of having an einbein in your action?

text: One often comes across actions written with an extra auxiliary field, with respect to which if you vary the action, you get the equation of motion of the auxiliary field, which when plugged into the original action lets you retrieve a more familiar looking action without the auxiliary field. An example is $\begin{equation*} S=\int d\tau e^{-1}(\tau)\eta_{\mu\nu}\frac{dx^{\mu}}{d\tau}\frac{dx^{\nu}}{d\tau} \end{equation*}$ which when solved for the einbein $e$ gives you the familiar square root form of the action. Why would you want this extra auxiliary field apart from having an action which is not in an annoying square root form? Why, for example, does GSW mention on Page 18 of "Superstring Theory" that "the role of $e(\tau)$ is to ensure the action is invariant under reparametrizations of $\tau$" when you can have reparametrization invariance even in the square root form of the action?


title: Electron momentum distribution and wavefunction in momentum space

text: Does there exist any relationship between the electron momentum distribution used in above threshold ionization and the wave function in momentum space? In other words, starting with the wavefunction in momentum space $\phi(\mathrm{p})$ how can I derive an expression for $\partial^2P/\partial E\partial\theta$, where $E=p^2/2$ is the kinetic energy of the detached electron and $\theta$ is angular coordinate?


title: $\Omega_{r}$ from WMAP results?

text: To do some Friedmann-Lemaître cosmology calculations, I would like to know an estimation of $\Omega_{r_0}$ ($\Omega$ radiation today). WMAP 7 give estimation of $\Omega_{b}$, $\Omega_{c}$ and $\Omega_{\Lambda}$ but nothing about $\Omega_{r}$ : http://lambda.gsfc.nasa.gov/product/map/dr4/best_params.cfm Where can I find the best value of $\Omega_{r}$ available today ? Thank you very much.


title: Why airplanes fly: the final truth

text: The questions about the reasons the aircraft fly are frequent among scientist, since the high school until now, even if I work on the other side of fluid mysterious world (the Low Reynolds numbers regime), I've always asked to my professors, advisors, colleagues, what is their own explanation of the flight. I know about the controversy about the push downward, considered a common fallacy by the NASA website, and about the Anderson argument, denying the erroneous principles of equal times, and the overstimated role of the Bernoulli theorem. My best "global" and simple explanation is taken from Anderson, and consists in the following: _Somehow the air reaching the first edge of the wing, after the interaction with it, is going donward. This must be the result of some kind of force, and therefore, for the third Newton's Law, there must be an opposite force of equal strenght in the opposite direction, which pushes the aircraft up._ First: why does the air go down? Answer: the angle of attack and shape of the airfoil, together with simple pressure and stagnation arguments. Second: which is the role of the Bernoulli theorem here? If the air is pushed down by means of the "geometry", we don't need the difference of velocity between the upper and the lower part of the wing, but just we have this as a consequence of the change of pressure (due to the shape). Is that right? My second question, actually, is about the most common and sophisticated explanation: the Starting Vortex Balance. The main argument is: due to the Kutta condition (a body with a sharp trailing edge which is moving through a fluid will create about itself a circulation of sufficient strength to hold the rear stagnation point at the trailing edge) the vorticity "injected"by means of the viscous diffusion by the boundary layer generated near the airfoil, to the surrounding flow, transforms in a continuum of mini-starting- vortexes. This leaves the airfoil, and remains (nearly) stationary in the flow.It rapidly decays through the action of viscosity. By means of the Kelvin Theorem, which in the 2D case is nothing but the statement that the vorticity is constant along every particle's path, this vorticity must be balanced by the formation of an equal but opposite "bound vortex" around the airfoil. This vortex, being causes an higher velocity on the top of the wing, and a lower velocity under it, causing the arising of the lift by means of the Bernoulli phenomenon. Now, I wonder: 1) We are assuming that the vorticity leaving the wall (the no-slip condition make the airfoil wall a sheet of infinite vorticity) by diffusion, leaves the boundary layer and enters in the region where the Reynolds number is high enough to allow us to apply the Euler Equation, then the Kelvin Theorem (valid only for inviscid fluids). I usually explain this using the vorticity equation, that is a local version (in 2D) of the Kelvin Theorem: $$\partial_t\omega+\boldsymbol u \cdot \nabla \omega=\nu \nabla^2 \omega$$ in the boundary layer the viscosity terme dominates, whereas in the outer layer it can be neglected. When the vorticity arrives in the outer layer, vorticity is conserved and we can say that the structures arriving from the boundary layer must be balanced (in terms of vorticity) by the fluid in this region. And we can do this only because the circulation, which is the actual constant, is a line-integral, and if we don't cross the airfoil/BL region we don't have problem of any sort. Is this correct? 2) In this explanation the Bernoulli theorem seems to be a cause, generating the lift through the difference of velocity. Is this right? Thanks in advance. I feel always a kid, asking about that issue. And at the same time, I feel an actual ignorant but curious scientist.


title: Future of colliders and technical limitations

text: Are there any technical limitations (theoretical or technological) that prevent quark based colliders? ie. Colliding two quarks together.


title: Why should the Standard Model be renormalizable?

text: Effective theories like _Little Higgs models_ or _Nambu-Jona-Lasinio model_ are non-renormalizable and there is no problem with it, since an effective theory does not need to be renormalizable. These theories are valid until a scale $\Lambda$ (ultraviolet cutoff), after this scale an effective theory need a UV completion, a more "general" theory. The Standard Model, as an effective theory of particle physics, needs a more general theory that addresses the phenomena beyond the Standard Model (an UV completion?). **So, why should the Standard Model be renormalizable?**


title: Batting averages of the Large Hadron Collider

text: As I understand it, the Large Hadron Collider's function is to throw particles into each other while avoiding hitting the nucleus? If quantum mechanics dictate the position of a particle can only ever be an educated guess how accurate or reliable is the collider's standard results for a successful observation? Does it miss more than it hits? What happens if the nuclei collide, would their impact result in a nasty reaction that would destroy the collider at the least? I can go on, has it ever done so and what was the effect?


title: Some questions about flavour and R-symmetry in $2+1$ ${\cal N}=3$ theory

text: * I have heard this fact that for ${\cal N}=3$ theories in $2+1$ with $N_f$ ${\cal N}=3$ matter fields the flavour symmetry group is $USp(N_f)$, $U(N_f)$ or $SO(2N_f)$ depending on whether the gauge representation in which it is lying is real (like adjoint) or complex (like fundamental) or pseudoreal. I would like to know of the proof (or reference) for the above. The following questions stem from, this paper.   * If I use the notation of $\phi_1$ and $\phi_2$ for the N=2 chiral multiplets in which the N=3 splits into (why? how?) then at least for the fundamental case why is $\phi_1$ and $\bar{\phi_2}$ in the same flavour representation? I guess I can legitimately use the notation of $\phi_1$ and $\phi_2$ to denote what is called $\tilde{Q}$ and $Q$ on page $7$ section $2.2$ of the above. Their notation seems to denote that there is some relationship between the fields $\tilde{Q}$ and $Q$ which I think is not true.     * If $\phi_1$ and $\phi_2$ ${\cal N}=2$ multiplets are in the same ${\cal N}=3$ multiplet then why are $\phi_1$ and $\bar{\phi_2}$ in the same flavour representation and their respective conjugates in the conjugate flavour representation? Apparently this has got to do with two facts,   * that the coupling is $(\phi_1 T^a \phi_2)^2$ in the deforming potential to ${\cal N}=2$ (..equation 2.9 in the paper linked above..)   * and that the SU(2) R-symmetry of ${\cal N}=3$ rotates in a spin-1/2 representation the 2-tuples $(\phi_2, \phi_1)$, and $(-\bar{\phi_1}, \bar{\phi_2})$ (..equation A.2 page 31 of the above linked paper..)  And what is the explicit action of the $SU(2)$ R-symmetry which rotates the above 2-tuples? And around the above equation A.2 why is are these two 2-tuples called "scalrs"? Aren't they full ${\cal N}=2$ chiral multiplets?


title: How are the masses of unstable elementary particles measured?

text: I am interested in knowing _how_ (Q1) the particle's masses are experimentally determined from accelerator observations. What kind of particles? They must be as far as we know _elementary_ **and** _unstable_ (very short lifetime) **and** _not subject to the strong interaction_ (for example, Higgs particle, Z boson, etc.) I'm not interested in neutrons (not elementary), electrons (stable) or quarks (hadron). I'm not particularly interested in neutrinos either, since I think that best constraints come from neutrino oscillations and cosmological observations. Since the particles I'm asking about acquire their masses through the Higgs mechanism, I would like to know what is actually or more directly measured _the mass or the Yukawa coupling_. (Q2) I also wonder what is actually measured the _propagator's pole_ (this the magnitude reported as mass for stable leptons) or the _running mass at certain energy scale_ (this is one of the magnitudes reported as mass for quarks). (Q3) This question may be considered a follow-up of How Can We Measure The Mass Of Particle? Thanks in advance. **Edit:** In connection with the answers: From all your answer I deduce that the mass reported for the Higgs, W and Z is the mass (rest energy) that appears in the energy-momentum conservation law. I guest that this mass corresponds to the pole of the free propagator of the Higgs, W and Z, respectively (and not to the running mass). I also deduce that what is more directly measured is the mass of the Higgs and from that value one deduces the self-coupling of the Higgs (and not in the other way around). These were my Question 3 and 2. Do you agree with my conclusion?


title: Primordial black hole: how dense does matter need to be to feed it?

text: Primordial black holes are a dark matter candidate. Suppose you put a primordial black hole the mass of an asteroid in Earth's core. Will it grow? NO! The black hole will be on the order of a proton in size. At this scale, Hawking radiation is so powerful that particles will be repelled by the BH. When the BH finally explodes, the energy released in the final few seconds is about a 7.0-8.0 earthquake (we are so far from the core that we wouldn't feel much). A large enough BH would be able to grow, but the process emits so much energy (~10% of in-falling mass) that Earth would become a ball of white-hot plasma before much mass was consumed. But what happens in a denser medium? In white dwarfs and neutron stars, this paper stated that a single hole would rapidly consume it's host (without giving any justification): http://arxiv.org/abs/1209.6021 Is this claim valid? Has any paper examined the physics of a tiny BH devouring it's host and calculated an (approximate) formula on when the hole would begin to grow as a function of the star's central density and black hole mass? And whether this would happen fast enough to destroy the star in 10^9 yr time scales?


title: Natural refrigeration

text: I have an electricity-free pot-in-pot refrigerator that uses evaporative cooling to keep the inside cool. However, I live in a very humid place, so the rate of evaporation will be low and hence this won't be as effective for cooling. Are there ways to increase the rate of evaporation? Is there a way to decrease the pressure of the water between the 2 pots (without using electricity) in order to increase the rate of evaporation? And of course, I have constraint on how big of a refrigerator I can keep, so increasing the pot's size (and hence the surface area of the water) isn't the ideal option. Thanks!


title: Blood Viscosity

text: When measuring blood viscosity, the literature claims that we generally use a cone-and-plate viscometer. Why is this; is there any way to explain this mathematically in terms of the shear rate, etc? Does it have to do with the fact that the shear rate is constant in this device? Why won't it work with a parallel-plate viscometer?


title: Could the acceleration of universe expansion be caused by gravity itself?

text: Dark energy is suggested to be a repulsive force in the universe causing an accelerated expansion. If the amount of mass outside our observable universe is greater than inside (higher mass density), would it not cause an accelerated expansion from our viewpoint?


title: Behaviour of free electron with constant velocity

text: Can a free electron with a constant velocity V то move eternally at this rate in the inertial frame? The question arises from the fact that a moving charge creates near its trajectory varying electric and magnetic fields. Whether kinetic energy of electron is spent for it?


title: magnetic fields and symmetry

text: When we compute the magnetic field for some configuration (with enough symmetry), we usually use the fact that the magnetic field is orthogonal to any plan of symmetry for the distribution of current , or belong to any plan of antisymmetry (vice versa the electric field) , is there any intuitive explanation why these statements must hold ?


title: Do all phases of ice look the same visually?

text: I recently read about different phases of ice on Wikipedia. But I can't find any pictures of the different ice phases. Do they all look alike visually? If you weren't able to measure the pressure and temperature, would you be able to tell one phase from another in any way?


title: How is time distributed through space?

text: I was greatly confused when I saw video saying that if two wormholes were separated by _time_ instead of _distance_ , it would allow time travel. My question is what did they mean by this statement? What do they mean by time instead distance? How is time distributed through space?