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Suppose I have a principal bundle, and some group G acting on the principal bundle. Is it always possible to find a G-invariant connection on the principle bundle? If G is compact, then I can imagine one can find such a connection by picking any connection to start with and then 'averaging' this connection over the group G. But what is G is not compact? Does an invariant connection still exist, in general? If not, what conditions do I need on G? | 0 |
I recently asked this question about whether or not profinite groups admit maximal subgroups: And indeed, profinite groups admit subgroups of finite index, so taking any minimum index subgroup containing the finite index subgroup gives a maximal subgroup of the profinite group. Now I wonder if it's true that all subgroups of a profinite group are contained in a maximal subgroup, i.e., can you have infinite chains of infinite index subgroups which do not split off to maximal subgroups periodically as you go up the chain? | 0 |
(There are a lot of questions about entanglement shown in the Similar Questions box. If there's already something about what I'm about to ask, please refer me there.) Suppose the particle paths are arranged to be of different length (e.g., detector A is close to the emitter but detector B is many miles away). And suppose that both detectors provide an exact time stamp of the detection event. Upon reading the logs of the two detectors, would you find that both detections registered at the same time, indicating that one particle got "stuck" in detector A until the other particle was detected at B? | 0 |
I learned that the possessive apostrophe -s is used for living beings and the "of" form for non living things: The dog's name is Sherlock The color of the flower is yellow However, I have noticed that these rules are often ignored in spoken language: The road's name is Privet Drive The name of the dog is Sherlock Are these mistakes made by non-native speakers or are these just theoretical grammatical rules that are not really strictly applied by native speakers in their spoken language as well? Does one stand out directly as a non-native speaker with these errors? | 0 |
I'm wondering if 'calls have grown for X to be Y-ed' is an acceptable substitute for 'there have been growing calls for X to be Y-ed'? To clarify, these are examples of the latter from the first page of Google search results: 'There have been growing calls by some eco-activists and developing countries for powerhouse states to foot the bill for climate change.' or 'There have been growing calls for St David's Day to be made a bank holiday in Wales' | 0 |
I know that loop-level three-photon vertex in QED is zero since the contribution from fermion and antifermion cancel each other. Also, from what I know this has something to do with gauge invariance of the QED. However, my question is "is this true even when the gauge invariance is broken?". If the gauge invariance is broken, I guess the photon will not only get a mass, but also there will be additional contribution from longitudinal mode of the photon which I am not sure whether this will change the story. | 0 |
I need a verb that describes asking someone to stop helping you, even though you know they mean well, because it's not helpful. So you ask them in a way that is almost pleading. It's stronger than just asking, but it's not quite pleading. I'm doing an analysis of a play, and one aspect of this analysis is that I have to categorize, line by line, what each character is trying to do in one action verb. It is proving to be harder than I thought. | 0 |
When a capacitor is charged, electrons flow from the battery terminal to the plate of the capacitor, as the electrons flow through the wire, they must be having some kinetic energy? So, when the electrons finally stop at the plates of the capacitor, what happens to their kinetic energy? We don't normally assume the kinetic energy to get stored in the capacitor, we only consider the energy stored in the capacitor to be due to the decrease in potential energy of the charge as it flows from one terminal of battery to the other, then where does the kinetic energy go? | 0 |
In the case of elastic scattering or absorption between photons and electrons, the incident light is either fully reflected or fully absorbed and hence it either retains its wavelength or ceases to exist. But how does inelastic scattering between them work? Specifically, if light has a wavelength, how exactly does that wavelength change in such a way that the light transfers only some of its energy and hence its wavelength increases? | 0 |
Let A and B be solenoids with the same pole facing each other. Then will their repulsion cause the set up to jump upwards? Please correct me if I am wrong: Solenoid A exerts a downward force on Solenoid B, which in turn exerts the same force on the ground. Then due to newton's third law, the ground exerts the same force and the whole thing is pushed upwards. If this force is greater than gravity, the set up will jump upwards. The connecting material makes sure the solenoid B is also carried upwards with Solenoid A. | 0 |
I am trying to find the minimum energy point of a catenary curve. Can anyone please let me know whether there is a potential energy or energy formula for a catenary curve ? Especially I would like to know when the end points of a catenary changes it's position, I would like to know how the energy of a particular point on a catenary changes and where that particular point will reach in position. | 0 |
I am confused in which category to put this sentence. It's a polite request, so it looks like it's an example of Imperative Sentence. But it does express the desire to have mango (even though not directly with the use of "I wish" or "I desire"), so feels like it may be Optative Sentence as well. And the listener of this sentence will most likely respond in "yes" or "no", that makes it a question. | 0 |
We know that thermal radiation is one of the ways energy can be transferred from one object to another. And we know, objects at any temperature emit electromagnetic radiation. So does that mean molecules and atoms are constantly losing energy? And why isn't this considered in the first law of thermodynamics? How can we even calculate the amount of thermal energy converted into electromagnetic energy (radiation). | 0 |
I searched a lot on the internet but I couldn't find any helpful answers, so here I am. I'm trying to create a chessboard figure, using xskak package that contains a label for each square. An example of what I'm trying to achieve is shown in the xskak tutorial on overleaf, linked here. I'll also add a screenshot of the image I'm referring to: Thanks! | 0 |
I've heard three seemingly contradictory facts, so apparently I'm not understanding at least one of them correctly. "Proper time along a path is the time elapsed for a clock that travels along that path." "Proper time along a null path is zero." "There are no preferred inertial reference frames, so if I travel at the speed of light, my own clock that I take with me will tick like normal for me." So how can it tick like normal but then not tick at all? Which of these three statements is incorrect? | 0 |
A jack of all trades is a master of none, but oftentimes better than a master of one is apparently accredited to William Shakespeare. Just to clarify - I mean the FULL quote, not just 'Jack of all trades' part. Is there a book, poem, or work by Shakespeare that proves he is the author? I have searched through the complete works of Shakespeare and couldn't find any phrase like this. | 0 |
Monoids represent maps from some mathematical object to itself. Groups represent the automorphisms of some mathematical object. What do abelian groups represent? One unsatisfying answer would be that they just represent automorphisms of nice enough mathematical objects. However it seems rather uncommon for the automorphisms of some object to form an abelian group unless they have very few automorphisms. Furthermore, the theory of abelian groups is very different from the theory of groups in general, and abelian groups appear frequently in other applications where they are not the automorphisms of some object in an obvious way, like homology groups. This suggests that maybe its just a coincidence that abelian groups are groups, and that they represent something else. What do they represent? | 0 |
Consider the following: "Saranghe" not only means "I love you," but it also means "Let's be together till we die." In Telugu, "Intiki veltunnava?" means "Are you going home?" What I'm wondering is whether I should capitalize the i in the transliteration of "intiki veltunnava? In other words, which one should it be? In Telugu, "intiki veltunnava?" means... In Telugu, "Intiki veltunnava?" means... If Telugu had a distinction between uppercase and lowercase letters, I could just use the equivalent version in the English transliteration, but Telugu is written in an abugida script, so that isn't really applicable. The transliteration introduces a new element that I can't figure out how to resolve. | 0 |
The Novikov self-consistency principle prevents a paradox in which a billiard ball is sent to its past through a closed timelike curve (allowed under general relativity) such that it collides with its past self and prevents it from entering. Imagine a setup where the ball, as soon as it exits in the past, hits a switch that closes a gate across the entrance. What's to stop that from creating a paradox? There's no alternate trajectory for the ball; the switch can be a plate that covers the exit so that the ball can't avoid hitting it. | 0 |
Momentum is the defined as the product of mass and velocity and can be thought as measuring how much motion something has. However, it is not clear to me why we need momentum and why force is not sufficient to explain nearly all the phenomena. Consider a larger mass moving at the same speed as an object of smaller mass. We say the object of larger mass is harder to stop, as it has more momentum. However, could we not just say the object of larger mass exerts more force, so it requires a greater force to stop it? The use of momentum is not entirely clear to me. | 0 |
I got a mouse which has wireless charging capabilities a while back. I would like to take advantage of this. However, I currently have an extremely nice mousemat from grovemade I grabbed in a sale a while back https://grovemade.com/mouse-pads/ which I would like to keep using. My idea is simply place a wireless charging mousemat below it. However, the grovemade mousemat has an aluminium plate in it and so the wireless charing will induce eddy currents. If you know how strong these eddy currents will be and/or whether that will make wireless charging impossible. I would appreciate any help. Thanks, Pioneer | 0 |
This post, currently closed, asks for the intuition behind Liouville's theorem, which states that every bounded entire function is constant; I find the answers unsatisfactory and hand-wavy. I am looking for a more focused, precise description of what is going on. Is there a geometrical understanding of what is going on? I try to visualize a non-constant analytic function, to understand why unboundedness is necessary along some direction, but it isn't working for me. | 0 |
There has been some recent buzz around generalized/higher form/categorical(?) symmetries in the physics community. I understand Seiberg's papers are a popular resource, and I am aware of McGreevy's review on the subject in the context of condensed matter. Nonetheless, what are some other resources I might look at if I want to learn about the subject? Specifically, where might I find problems on the subject (e.g., Andrew Lucas's lecture notes include one fairly introductory problem on the topic)? | 0 |
I'm reading Billingsley's Probability and measure. I'm reading about extremal distributions, and I'm at where he is proving that Gumbel is one of the extremal distributions. I'm having a hard time understanding the proof and I'll appreciate it if someone helps me figure out the proof. The text highlighted in yellow is what i don't understand (it is quite half of the proof). Thank you in advance. | 0 |
I'm new to optimization and I'm reading a paper that they reformulate an ILP problem into QUBO using penalty method. Let's say we use a solver to solve above QUBO, and the global optima of QUBO obtained from the solver is infeasible to the original ILP. (infeasible from my understanding is the QUBO solution does not satisfy all constraints of the ILP). My dumb question is: Can the local optima of QUBO obtained from the solver still be feasible to the original ILP? I don't have much background in optimization, so it would be nice if you guys can suggest some materials mentioning my question. Thank you in advance! | 0 |
If someone sets up a table at the edge of a conference room selling their wares, it could be described as a "stall" or maybe a "kiosk". But what if someone instead sets up something like a few chess boards that people can play on? The word "stall" doesn't really seem appropriate to describe this ("a chess stall"?) but is there any word that would be more appropriate? I thought of "sideshow" but that doesn't seem right either because it's not really a show, it's an interactive game activity. | 0 |
When using "too much", it is put after the verb & before the uncountable noun e.g. I drink too much coffee. However, this sounds strange in the sentence: I use too much social media. Instead I use social media too much sounds more natural. Can anyone explain why this one doesn't fit the rule? So far it seems that it only happens with the verb use. (Another e.g. would be I use my phone too much). | 0 |
The Gauss-Bonnet theorem for compact regular surfaces is often only enunciated for totally regular surfaces, with no singular points. But what if I wanted to state it on a surface with a finite number of singular points but otherwise regular, like a cube? How is the Gauss-Bonnet modified? I know somehow the curvature has to be concentrated on the vertices, but I'd like some help in making that notion precise. Thank you. | 0 |
Assuming "phreak" is a portmanteau of "phone" and "freak," giving us the term "phreaking" to describe the illicit act of hacking telephone networks, and "Phishing" pays homage to it by misspelling "fishing" to describe the practice of tricking someone into revealing sensitive information on computer networks, now we have "Vishing" (voice call phishing), "Smishing" (SMS text message phishing), and "Qishing" (QR code phishing) being used in the security industry. Is there a better term (besides "annoying") than "jargon" to describe these words? | 0 |
In one of his lectures, L Susskind stated that he cannot make sense of a metric with more than one timelike dimension. I also have trouble imagining it, but is there a good mathematical or physical reason why this is not possible? Let us assume all extra timelike dimensions are compactified, so we cannot directly observe them. What kind of trouble or unphysical problems would this create? I am not asking for non-standard physics here, but just a more formal reason than intuition as to why we assume the extra dimensions are necessarily spatial (I have a basic understanding of why string theory needs extra spatial dimensions, but I do not understand if it forbides extra time dimensions). The question is not limited to string theory though. | 0 |
I have seen several questions regarding the size of the absolute smallest black hole, the smallest stable black hole and similar. These made me wonder; what is the smallest stable black hole if it is immersed in a standard atmosphere? I assume there is some maximum rate at which the black hole can consume matter, and that this is related to its size. Therefore, since its Hawking radiation is inversely related to its size, logically there should be an unstable equilibrium point when these two equal each other. I could, of course, be completely wrong - however I'm afraid my knowledge of how to calculate anything regarding black holes is limited to working out the Schwarzschild radius. | 0 |
Imagine, there is a truck of mass 'm' accelerating with an acceleration 'a', this means that the truck definately carries some force 'F'(let). Now, imagine the truck collides with a man standing stationary on the middle of the road. So, the truck will hit the man with force 'F' and due to Newton's third law the man also exerts a force 'F' on the truck, then my question is that, why don't the truck's net force becomes zero, and why it continues accelerating? Kindly explain, where am I going wrong. Note- there is no external force other than 'F' acting on the system. | 0 |
We know that nothing including light can escape the gravitational pull of black hole. Now special relativity says that nothing travels faster than speed of light. Then how can effects of gravity due to the black hole be felt outside the black hole as nothing can escape black hole? This seems contradictory as anything is pulled inside the black hole due to gravity whereas nothing can escape a black hole. | 0 |
I've seen that the Leibniz formula of determinants can be reduced to the Laplace expansion through consolidating terms. What I haven't been able to find online is a connection between any of those and the geometric interpretation of determinants, which is the volume (or measure) contained between the parallelopiped formed from the column (or row) vectors. How do I prove that the Leibniz formula, which is based on terms composed of permutations has anything to do with geometric measures? | 0 |
I have just learned that linear frame dragging exists in General Relativity. I have also seen simulations where a periodically accelerated and decelerated mass causes a sort of gravitational dipole radiation, dragging nearby masses in the direction of the acceleration. My problem with this is that in my whole life I was taught that the leading order in gravitational radiation is quadrupole; dipole radiation can't exist because of conservation of linear and angular momentum. Is dipole radiation forbidden only in linearized General Relativity? What is the full picture here / what am I missing? | 0 |
I am trying to understand the jump operators in the Lindblad equation. Specifically, if there is any condition of boundedness we need to impose on them. I ask this because, as was pointed out in this post, there should be no assumption on the norm of the jump operators. But for example in this review, the jump operators live in the space of bounded operators. So is boundedness of the jump operators a necessary condition? In Preskill's notes, there is a derivation of the Lindbladian in terms of the operator-sum representation which gives some normalization condition that the jump-operator should fulfill in terms of the Kraus operators but I am not sure if this is relevant to my question. | 0 |
I think my formulation in the title may be a bit confusing. I mean a behaviour similar to "gaslighting" yourself into seeing/perceiving your own opinion from someone/something, even though that person/thing doesn't actually share your opinion. I've witnessed this a few times on social media when people interpreted satirical videos of political topics to match their own opinions/believes, even though the videos themselves were neutral/not actually picking a side in the political topic. Would be cool if there were a word for that. | 0 |
In textbooks on Category Theory, monoids pop-up all over the place, we several easy examples such as integers, lists and so on. I was then wondering about comonoids. What are some "simple" examples of comonoids appearing in mathematics? I've tried searching, but most texts either only mentions the concept of a comonoid, or provide some convoluted example. I'm trying to get a better feel for what a comonoid is, thus I'm searching for easy to grasp examples. | 0 |
A few days ago was the first time I ran into the word "Nigerien" meant to mean "something related to the African country of Niger" as opposed to "Nigerian" meaning "something related to the African country of Nigeria". Since this is very easily confused, for example by my spelling checker which didn't like "Nigerien" at all, and especially in spoken English, is that use actually correct, or is there a better word? And how would you pronounce it so that it doesn't get confused? (With the countries themselves, I thought NIger has an emphasis on the first syllable, and NiGERia on the second, but for Nigerien this sounds just wrong to me). | 0 |
If there is a circular metal loop and a changing magnetic field perpendicular to the loop, there is an induced electric field that causes the electrons to move and cause a current. But my question is why is there even a current? Why don't the electrons just move and rearrange themselves to cancel out the induced electric field, just as they do in case of electrostatic shielding? | 0 |
I am looking to replace the idiom "kangaroo court" in the following sentence: Class followed its usual script. The professor took center stage, exposing the deep racism, sexism, colonialism and homophobia of a previous generation and like well-rehearsed actors, us students assumed our roles as moral arbiters in a kangaroo court. I want the replacement to communicate the idea that the verdict or judgement is a forgone conclusion and that the trial/classroom is just a pretence of debate/justice as everyone already knows what the answer/verdict must be before discussion ensues. If no good replacement can be found you could rewrite the sentence entirely to help communicate the above point. Thanks a bunch. | 0 |
We know that a capacitor and an inductor both offer some opposition to the flow of current through an AC circuit and their reactance is a measure of the amount of Ohmic opposition due to these circuit components. I am aware of how these quantities arise mathematically. However, my question is, physically why do these circuit components provide a type of opposition to current flow in the case of AC circuits? What is the actual cause for this reactance to appear? | 0 |
Suppose you have a faucet that expels water at a rate r Liters/second. Will the rate at which water flows through some ring beneath the faucet be greater than r or equal to r? On one hand, if the rate at which water flows through the ring were greater than the flow rate of the faucet, wouldn't that violate conservation of mass? On the other hand, shouldn't water be traveling faster through the lower hoop, so it should have a higher flow rate? I've asked some people about this, and I've been told that the water column will inevitably become thinner as it falls such that the flow rate through the hoop will be the same as r. Is this true? | 0 |
I hope my question does not break the rules. I can't understand how this statement can be true in the book which I've mentioned: I cannot undestand why it's true because if I have two point charges with same sign and same magnitude then the electric field should be zero at point P: But according to gauss's law it's not zero and it equal to electric field due to one of these point charges. So this electric field is only caused by the charge inside the closed surface, not the charges outside it! | 0 |
I am doing a lab experiment (Franck-Hertz) at uni and am supposed to find the temperature, at which electrons are emitted from a barium oxide cathode (without the necessity of an external E-field that provides additional energy). I am attempting to calculate the temperature T = W/kB from the work function W (i.e. the ionization energy). Is there any source, that contains such data? I tried NIST Chemistry WebBook, but they only have data for BaO in the gas phase. I need some value for solid BaO. | 0 |
I am interested to see a derivation of Kepler's laws from Newtonian mechanics, which would be a suitable exercise or demonstration for a first-semester course in calculus. Therefore I'd like to avoid any use of the cross-product since this is usually only introduced much later in a calculus curriculum. I've looked at Newton's original derivations. They don't use any objects or theories which a first-semester calculus course couldn't use. But they do involve enough geometry that it seems "a bit much" for a first-semester calculus student. So I recognize that any such derivation will probably be hairy in one way or another. But in the off chance that there is some known elementary and simpler derivation, I wanted to ask. Thanks! | 0 |
Given a container filled with identical objects, how could I find the number of objects in the container accurately purely by analyzing the sound produced on shaking? More specifically, which acoustic parameter should I focus on? Some ideas I have had so far are: Looking at the number of amplitude "spikes" since the more objects there are, the more collisions there are Using Fourier Transform to break down the combined sound into its constituent frequencies, finding the number of distinct frequencies. Unfortunately, I am not sure if the frequencies will be measured for each object, since the objects are identical | 0 |
I have just switched to writing in LaTeX from markdown. I like to proofread by hand, and so in the past I used a template that increased the line spacing and changed the typeface to something monospaced just for proofreading. Now I cannot figure out how to change an entire document to being monospaced. I found several solutions that seem to only work on LuaLaTeX, but I would prefer to use pdfLaTeX. | 0 |
Circle k and a line p that intersect at points R and Q are given. Inside the circle point A is given. Construct all the circles that touch the line p and the circle k and pass through the point A. I tried to solve this problem using homothety, but it didn't work out so I guess that's not the proper way to solve it. I would appreciate any ideas. | 0 |
In the double-slit experiment, the interference pattern shows the probability of finding the particle (photon or electron) at a given volume. In a given experimental setting, this probability distribution doesn't change with time, so this probability distribution belongs to a stationary quantum state. I think that this doesn't mean that the Hamilton operator belonging to an experimental setting has only one eigenvalue and a single state that belongs to this eigenvalue because the pattern depends on the wavelength of the photon. If we used the superposition of two photons of different wavelengths, we would get a non-stationary interference pattern. Is there such a thing as "the superposition of two photons of different wavelengths"? Or the double-slit experiment can't produce non-stationary states? | 0 |
Phonons are typically used to describe quantised vibrations in solids. However, is it legitimate to talk about phonons for e.g. a sound wave propagating in air? Contrary to photons that are particles that can exist both in free space as well as inside an optical cavity, it seems like phonons are quasiparticles defined only in a solid (i.e. a cavity for sound). Is this the case? | 0 |
I've heard that because light takes time to travel from one place to another, we see objects in distant galaxies as they were when they released the light. new and advanced telescopes are able to see further and further into space, and therefore closer back in time to when the big bang happened. I've also heard that the laws of physics are slowly changing over time and that they might have been different in the early seconds of the big bang. In the future, could an advanced telescope be used to observe the light released by distant galaxies and other cosmic structures at the time of the big bang and observe physical laws that were different from the ones that we have in the present day? | 0 |
what would happen if I took a toroidal core, generated a static toroidal magnetic field in the core and then rotated the core around it's symmetry axis within a larger stationary toroidal winding around the same core? Just for simplicity imagine a toroidal transformer with a rotating core inside. Would I get DC current generated in the stationary coil? If yes can anyone explain by what law and formula? | 0 |
I haven't found satisfying answer yet. Beside those typical examples like how many colourings of a cube is there up to rotations or how many graphs are there on n vertices up to isomorphism etc., is there any "real" usage of Burnside's lemma in advanced math? All examples I could find seem to me more like funny riddles you can impress your friends with but they are not quite useful for anything. | 0 |
If I have n cards and n stacks of cards, how many ways can I split the cards between the stacks if the order of the cards in the stack is significant but the order of the stacks is insignificant and stacks are allowed to be empty. And is there an algorithm to find them. So for example, with two cards (a, b) and two stacks the possible arrangements are: [ab][],[ba][], [a][b]. ([b][a] is equivalent to [a][b]) this might seem like a silly problem but I am very much stuck and very much desperate | 0 |
Suppose I filled a bucket of water with a hose, now when it's filled, I remove the hose from the tap's end, while the other end is still submerged in water. Now if I throw the other end on the ground, it sucks all the water from inside the bucket spilling it out the ground till it's empty. Why does this happen? I assume there's something really simple about pressure and stuff going on which someone like me, who hasn't studied fluids in detail, can understand... | 0 |
I am trying to first construct a fractional linear transformation, to map the sector to a half or full circle. From there it seems straightforward using rotations, translations, and standard mappings between circles to half-planes to create a map that takes the sector to the right-half plane. My question is, how do I construct the fractional linear transformation? Lang's Complex Analysis shows how to construction fractional linear transformations to map a triplet of points to another triplet of points, but I don't see how that would be useful here. | 0 |
Good day all, I am looking for a way to estimate the composition of a thermal plasma formed by flowing gas between two charged electrodes. I understand that when plasma is formed this way, it would be composed of a number of species. Please is anyone able to point me in the right direction of finding an equation/correlation/data to allow me estimate the composition of the plasma for any gas? Thank you | 0 |
I remember my high school teacher explicitly saying that it took me a long time to do x was the correct form and I took a long time to do x was not. In recent years, I seem to remember hearing the latter quite often in common language, though. How applicable is the latter phrase compared to the former (a) in everyday speech and (b) in essay writing? | 0 |
I was discussing with some friends about English grammar, and we ended up confused about the accuracy of the sentences below "I know the motive for your rescheduling the class" "I know the motive for your rescheduling of the class" "I know the motive for you rescheduling the class" "I know your motive for rescheduling the class" Are all of them correct? Which one would be the most idiomatic? | 0 |
When I was young, a workmate convinced me that there was indeed a word which described the behaviour of someone who would congratulate themselves for behaving the way a person normally ought to, anyway. I don't want to write that word here, because some people might think part of it seems racist. So instead, I'll ask as plainly as I can: Is there a word that means "Congratulating oneself or others, for behaving the way one ought to behave?" | 0 |
Imagine a bicycle wheel level with the ground able to rotate around its center. Centered on one of the wheel "spokes" is a heavy marble which can slide from the center of the wheel to rim of the wheel and vice-versa. If the wheel is spun once very hard by hand, the marble will move from the center to the rim and return to the center as the wheel stops spinning. Question: Does the wheel spin longer with the heavy marble at the rim then if there was no marble on the spoke? I suspect it does spin longer. Please no formulas or highly technical discussion; a yes or no answer and a simple explanation would be appreciated. Thank you for sharing your knowledge of physics. | 0 |
This is a screenshot from a Khan Academy video on friction at the nanoscale. I understand how the force of friction on the purple block acts opposite to the direction of the force applied explained by the nanoscale diagram, but I don't understand how the Newton third law pair is explained by the diagram. Wouldn't the movement of the top layer of atoms move the bottom layer as well? In that case wouldn't the two layers move in the same direction? | 0 |
The motivation I was given for algebraic topology is to assign some algebraic objects as invariants to topological spaces. This way we can show that two spaces are not homeomorphic if they are assigned a different invariant. However it seems to me like in algebraic topology the invariants are always up to homotopy equivalence or maybe even only weak homotopy equivalence. This seems strange to me. Is there a reason why other kinds of algebraic invariants that can distinguish homotopy equivalent but not homeomorphic spaces not more widely studied? What is it about weak homotopy equivalence that is so special that seems to be the main focus of all algebraic topology? | 0 |
In the book General Relativity by M.P Hoson, the author tries to calculate the velocity of a particle radially infalling in Schwarzschild spacetime. The velocity is measured by the observer sitting at rest at infinity. For the same, he takes the ratio of proper distance and proper time of the particle, both measured by the observer. To calculate the proper distance, the path traveled by the particle should be spacelike, whereas, to calculate the proper time, the path traveled should be timelike. Since the particle can travel with only one of the paths, how does the observer simultaneously calculate the proper time and proper distance along the particle geodesic | 0 |
Provided everything remains constant, does the fringe separation, that is the distance between adjacent fringes become further apart for higher order maxima? Consider the above diagram. From the diagram it appears that the distance between adjacent maxima is getting larger with distance from the central maxima. My intuition agrees with this. However, I have heard that the distance between adjacent fringes is constant. Assume this is true. How so? Double slit interference pattern: Fringes are equally spaced and of equal widths. The above statement seems highly unintuitive. Shouldn't the spacing between adjacent fringes get larger, as the wave spreads out. How do I satisfy myself with the above statement? Proof? | 0 |
The below question was asked in national English exam in Turkey: Choose the best word or expression to fill the spaces in the passage. As Henry Hill, the actor Ray Liotta gives a complex portrayal of an Irish-Italian kid who succeeds in his youthful ambition ....... popularity as a wealthy gangster, only to have his position slowly eroded until it almost destroys him. A) to gain B)gaining C) to have gained D)having gained E) to be gaining My choice was b (gaining). But the correct answer is A (to gain). I thought the phrase "succeed in " takes gerund not infinitive. Why am I wrong for the answer. | 0 |
I'm studying X-Ray reflectivity at interfaces and the book I'm reading reads: ... The ideally flat, but graded interface, and the ideally sharp, but roughened interface, will be considered... I'm struggling to understand the difference between the two kinds of interfaces mentioned. Please consider that English is not my first language. Exactly speaking, what do they mean with graded and sharp? How do these two surfaces differ from each other? | 0 |
Imagine a system with a parallel plate capacitor with holes in the middle where the plates are charged before being disconnected and insulated. Neutral atoms are introduced between the plates and are subsequently ionized in some way. The created ions will gain momentum and travel through the hole after which their kinetic energy can be collected. As long as the kinetic energy gained by the ions is higher than the ionization energy we just gained energy. I know that this should not be possible so where am I wrong? | 0 |
Assuming we can't block neutrinos, and most of them pass through the earth, how do we know that the change in the neutrino detector is not just happened randomly? Is the detection of neutrinos more frequent when earth is closer to the sun, or are we just always seeing the same amount of neutrinos in the detectors because we have no way to block them? | 0 |
I'm doing mathematical analysis and I'm stuck with the following question: Give an example of a nowhere dense closed set of irrational numbers with no isolated points (that is, a perfect set of irrational numbers) I read this: Is this a perfect set? so apparently we can find such a set through specific enumeration of rational numbers, taking their vicinities union and taking its complement, but I struggle to find such enumeration that would not create isolated points. | 0 |
I came across this interview question online: Suppose you sit on the road side and observe cars driving by. Assume the distribution of cars driving by is according to an exponential distribution. Now you observe a first car after sitting for x mins, a second car after sitting for y min. Given those observations, can you estimate the parameter in the distribution? I don't see how I am able to solve it without additional information. Thanks | 0 |
I begin a PhD in coding theory next fall, and it concerns coding over certain types of rings (e.g. finite chain rings) instead of fields, and in consequence submodule codes. I have a fair amount of knowledge in comm. algebra and have had a standard undergraduate coding theory over finite fields course, so I was wondering: Is there a well-respected graduate text, or a good set of notes, covering more advanced tools in algebraic coding theory? Thanks, and let me know if I need to clarify anything. | 0 |
If I understand correctly, massive objects cause time dilation, and so time seems to pass more slowly for observers closer to a massive object than those who are farther away. Do cosmologists take the local gravitational effects of earth, the sun, and the Milky Way into account when calculating the expected speeds of stars orbiting distant galaxies? Do galaxies that are more distant rotate faster, by our observations, than those closer to us, even if comparing galaxies of similar mass? | 0 |
I am an undergraduate, studying physics. I have studied maths courses like Groups, Linear Algebra, Real analysis, Differential geometry and probability. I wish to get into mathematical physics, similar to what Arnold's book has to teach. But i find it a really difficult read since it's a graduate text in mathematics. Can anyone suggest me what stuff do i need to study before getting a good intuitive picture of Arnold's book. Or any resources that provide a road map, intuitive picture of the maths used in physics. | 0 |
Now I am studying elementary number theory, I am interested in arithmetic function, I have studied Burton's Number Theory but I can't find Dirichlet Convolution as a particular topic, I will be highly glad if anyone suggest some good book to study arithmetic function where I can find Dirichlet Convolution in details with some theorem like 'the set of all arithmetic function forms integral domain under pointwise addition and Dirichlet Convolution'. Thank you. | 0 |
I am trying to understand the concept of regular conditional distribution. I found the definition quit difficult to grasp . This is what i understood . A regular conditional distribution also called a probability kernel is a two variable function (x,A) -> K(x,A) x a scalar and A a set that verifies the following. when we fix x, we have a probability measure, when we fix A we get a measurable function. Can someone confirm this definition ? and give me an example of a non regular conditional distribution . | 0 |
The uncertainty principle holds for pairs of certain observables, such as position and momentum. All these observables have a relation to spacetime. Other particle properties, by contrast, such as mass or electric charge can be measured at arbitrary precision. Quantum theories do not even model them as observables, but as parameters to the field. So, what is the philosophical argument for why there is a uncertainty principle for some quantities, but not for others? | 0 |
I am currently using a software called "SCOUT" to thin film interference simulation, and I would like to know if there is a better software to do this type of simulations. My goal is to vary the thickness of a thin film in a multilayer, in order to create interference between the various thin films, and then create a specific color. So I want to freely change the thickness and get a graph of reflectance or transmittance corresponding to that change. The software should allow me to put my own materials with the respective reflectance and transmittance properties. I know some softwares, like "zemax" and "lumerical" but there are no videos doing what I intend. Does anyone have suggestions? Thank you! | 0 |
I've got a Literate Agda document, which contains a large number of unicode characters. It builds nicely with XeLaTeX and life is good. The problem is that arxiv only supports pdflatex, and I'd like to upload the file to arxiv. Are there any tools/scripts that can process a latex document written for xelatex and add the necessary commands to compile it with pdflatex? Things like declareUnicodeCharacter for each used character. Basically, I'm just looking for a better way than "start compiling with pdflatex, get an error, add the unicode character, repeat". Most of the unicode symbols are math symbols, so it shouldn't be too hard to map from the characters to TeX commands automatically. | 0 |
Hi, I'm taking a course of Electrical and Computer Engineering in my university. I don't understand why the partial circuit on the right side of the switch is ignored after the switch is closed. As you can see, the book says the network becomes (c) from (a) via the short circuit. What happens to the short circuit and the circuit on the right side? I think the resistor and the voltage source can still affect the network but it seems not.. | 0 |
I have two non-orthonormal basis vectors, and I want to represent a third vector as a pair of coordinates using the aformentioned basis vectors. How would I do that? The dot product, which usually transforms a vector into coordinates in each basis vector, doesn't work for non-orthonormal bases. How would I get coordinates in terms of my non-orthonormal basis vectors? I should also mention that I am coding, and so all my vectors are currently represented as pairs of numbers on an (x, y) plane. Please ask if you need any clarification, I explained it really poorly here. Also, I do not know very much linear algebra, so it would be appreciated if you answer in simpler terms :) | 0 |
If Alice is located just beyond the event horizon of a black hole, and Bob is at some other point in space with de minimis gravitiational effect, what, if any, effect would it have on the "spooky action at a distance" between these two entangled entities? I'm a wannabe sci-fi writer looking to exploit untested but possibly plausible concepts derived from my own madness and admittedly poor understanding of the universe. | 0 |
I am struggling with prooving convergence for an optimizer which uses adaptive step-size with heavy ball algorithm for convex and non-convex functions. In some literature, I could find a regret bound analysis/proof for convex functions and proving that the estimated gradient at t -> inf goes to zero. Could anyone please guide me through the process of convergence proof for non-convex functions or give me literature recommendations for the same. Thank you very much in advance. | 0 |
I need help understanding how particles do what they do and maintain the structures they maintain if so many of them exist for such a short time? In the case of the nucleus and pions, pions only exist for mere nanoseconds. So if they decay, and their properties change, what is holding that nucleus together? Are the nucleons continually exchanging a stream of pions that perpetuates the interaction that holds the nucleus together? Like I said... Explain like I'm five. | 0 |
I really like the greek letters of the default LaTeX font but I want the rest of the characters to be in Times New Roman using the Mathptmx font. I find the greek letters of the mathptmx package rather ugly since they're disproportionately bolder than the usual text. So may I know how can I change the greek characters only and retain the times new roman text? I have tried many suggestions from countless websites but to no avail. Alternatively, can I ask if there's a way to change the greek letters somewhat more similar to the greek letters in the books like those in University Physics by Young and Freedman? | 0 |
When observing interference fringes one often uses a lens after the diffraction grating to focus the fringes on a screen like this: At first sight, one might think that after the lens the path difference between the rays is altered. I think this is not the case, but don't see a clear argument why. Maybe one could apply Fermat's principle, but this - as far as I know - is restricted to the situation that we compare the path from a point A to a point B (in this case P). But here we start with parallel rays and not from a single point A. So, is it right, that it doesn't alter the optical path difference and how to explain exactly why? | 0 |
I had a debate with a buddy about this. He said you could get a chord by drawing the triangle formed by the two points and the center of the sphere and that chord corresponds to a single great circle arc. I can get to the chord but then projecting that chord on to a path on the surface of the sphere seems non obvious. So is it true that two points not colinear with the spheres center on the surface of a sphere have a unique great circle connecting them and if so how does one prove it? | 0 |
As the diagrams of categories can be represented as graphs of objects and morphisms, I was wondering if (the diagrams of) higher-dimensional categories could be represented as hypergraphs, and if not why? And in the more general sense, what would be the best west to represent higher-dimensional categories (thinking of diagrams, but also data structures to represent them in programming languages)? And if we reverse the question, are there classes of categories whose diagrams would be best encoded as hypergraphs? | 0 |
We know a way of measuring energy of a electromagnetic wave is the Poynting vector, which is independent of the frequency. But let's say we want to make two different electromagnetic waves, with different wavelengths and so different frequency, but with the same amplitude (so same Poynting vector). In my opinion the guy in the image is spending more energy for the wave with higher frequency. But the Poynting vector, doesn't care. So is there another property of Electromagnetic Waves that accounts for the energy that the guy used to make the wave? | 0 |
Two people, A and B, starts from two different points and move in a perfectly straight line in an infinite plane. When they move they leave a visible trace after them. Question: What is the probability that their path (of traces) will intersect at some point regardless of where they start? What I've tried so far is to draw two circles and split it in quadrants. That helped a little bit but didn't really solve the problem, just got an overview. Here's some examples of interesecting paths (first row) and non intersecting paths (second row) which gives you an idea of the criterias for when they intersect and don't intersect: How would you approach and solve this problem? | 0 |
I don't see why or how this could be argued against or if it really matters, but that's why I ask the forum. I am just trying to understand the nature of the fields in the universe. Am I correct in thinking that the entire universe is just a few fundamental fields laid over each other, getting influenced by the different particles that happen to interact with them? | 0 |
In a nuclear reaction, protons and neutrons are exchanged and the resulting elements have a number of different protons and neutrons that uniquely define the element that we are studying. However, can we say that a hydrogen atom without any electrons (what we would usually call an ionised atom of hydrogen) is really hydrogen? Or do electrons fundamentally indicate the element that results from the reaction? Can we really say that an atom of hydrogen without electrons is actually hydrogen? | 0 |
My textbook says: Similarly, non-polar (i.e., covalent or organic) compounds like naphthalene, anthracene etc. are soluble in non-polar (i.e., covalent or organic) solvents like benzene, ether, carbon tetrachloride, etc. and are very little soluble in water. My question is that if we have a non polar compound, then it seems as if it should not dissolve to any extent. However, the quote says that non polar molecules are a little soluble in water. Thus I want to know why non polar solutes dissolve in water at all, even if it is only to a very lesser extent? | 0 |
What is a word to describe how a cat looks when it's groomed? My husband described it as nappy, which I don't think would be the correct word. To give an image of what I am trying to describe, think of a medium-haired cat that licked its fur and looks messy, with wet fur sticking up a bit. It's a weird request and may be too specific, but I hope there's some kind of answer to what I am asking. | 0 |
I just read a quote in which someone, on behalf of herself and her spouse, wrote "Our heart goes out for ....". I Googled to know if when it comes to speaking about heart not as a body organ, is it possible to use it in the singular form, but I could not find any reliable source for that. So, what is the correct form for such situations and does it apply for other organs, specifically brain? | 0 |
If I shred a book into numerous pieces, and scatter them, so that the original text is completely unreadable, then for me, as a reader, the book has lost all its information. Its entropy has greatly increased. As a reader, the book's information rested upon a state of minimal entropy. However, my (limited) understanding of Shannon's information theory is that the 'information' in the shredded book has increased along with its entropy. Is there a way of reconciling the conventional/layperson's understanding of information as an ordered presentation of knowledge (like a well-written book) with the Shannon equation of information with entropy/disorder? Apologies if I have failed to grasp something fundamental. | 0 |
In the image above, we have the principle of induction cooking. An alternating current is run through the coil, which causes a change in flux. This change in flux induces eddy currents in the conductive pan, and by Joule heating/resistive heating (P=VI), this causes the pan to heat up. So the only thing that you need is a pan that can conduct electricity/the eddy currents right? As long as the pan does not have a too low or a too high resistance. However, why is the effect specifically optimal for ferromagnetic materials/conductors? How does the ability to magnetize somehow enhance the effect of induction heating? Does the magnetization of the pan itself somehow enhance the eddy currents or something? | 0 |
Often charge is defined as a measure of interaction with the electromagnetic field. However, electromagnetic field is often defined as a field produced by moving electrical charges, or relates to charges in some way or the other. Due to this circular definition, I am not able to understand what really is charge and its influence on electromagnetism, or any interaction. So what exactly is charge and what does it have to do with electromagnetism, or any other interaction? | 0 |
There is a word in German, ausgezeichnet which vaguely sounds like the English phrase "out of sight" but that is usually translated as "excellent". I could see some non-German speaker hearing it and, knowing that it meant "very good" from context, deciding to use it and approximating its sound with "out of sight". Note that I am interested in whether the German word and the phrase are related, not the general history of "Out of Sight" Is there any evidence to support this etymology? | 0 |
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