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I am very poor at English, so I used ChatGPT to translate my question. My question is here (Is my idea right?): Is it possible to conceive concepts like a coordinate system in a completely empty space? I believe that without some reference, even establishing an origin becomes impossible. In a space where there is just one object (please consider the object is very small), it is possible to consider an origin. You can regard the location of that object as the origin. However, I think it's not possible to conceive axes in this context. In a space with exactly two objects (please consider the objects are very small), it is possible to establish an origin and one axis. You can choose a location of one object as the origin and define an axis with a positive direction towards the other object's location. Nevertheless, I believe it's not possible to conceive the other two axes. It is only when there are three objects (please consider the objects are very small) in a space that one can begin to consider a coordinate system. | 0 |
I have been looking up at available database that had dielectric constants for metals since I need them for my research and wanted to get an idea of what the values were before I focus on actually calculating them numerically if ever it is needed for my research. Thankfully I was able to find this website https://refractiveindex.info/?shelf=main&book=Ti&page=Johnson However I noticed that there are two values for the relative permittivity when it came to metals and I was wondering why this is the case. From what I know so far, metals should have a negative permittivity, so I was confused as to why it shows that Titanium also has a positive permittivity. Can someone enlighten me as to why this is the case for the permittivities that I found on the website. Apologies as well for the question since I dont know a lot yet about the properties of materials when it comes to permittivity and permeability. | 0 |
If a quantum particle is described by a certain wave function and we express it as superposition of for example its possibles energy states, after we measure it the wave function collapses and we observe the quantum particle as having a certain energy. I have a couple questions. No matter what happens to that particle or what I do with it everytime that I observe it again it's going to be in that same energy state? If after measuring energy I now try to measure something else like position could the energy state change when I measure it again? In general I'm trying to understand what it means that the wave function collapses because by what I've studied it sounds like it's undoable but that doesn't make much sense to me. So far I thought that when we observe a particle's energy for example we measure a certain energy but then if we measure it again right after we could measure any of the other possible energy states but I'm told this is wrong. How does it actually work then? | 0 |
Reading Harris' Modern Physics, specifically the classic example of Anna holding two lightbulbs on a moving train. I find myself confused about this passage: Before moving on, we emphasize a vital point: The preceding arguments had nothing at all to do with Bob's specific location in his frame or the time it takes light to reach his eyes. The issue here is not which beam reaches Bob first, which does depend on where he stands, but rather which begins first, which has nothing to do with where he stands. Attempting to blame the effect on optical illusions is the comfortable yet incorrect way out of accepting a counterintuitive notion. The truth is more challenging. Bob could be standing right next to one flashbulb when it flashes and have an assistant, Bob Jr., standing next to the other flashbulb when it flashes. Each records the time of his flash and neither has to wait for the light to reach his eyes. They record different times. Anna, in her frame, causes the bulbs to flash simultaneously, but Bob and Bob Jr., from their frame, determine that she causes the bulbs to flash at different times. I guess my understanding of the relativity of simultaneity was dependent on thinking about the path that light took to travel to Bob. If Bob/Bob Jr can be right next to the lightbulb, I am failing to see how that's any different then them being on the train with Anna. | 0 |
Context: I would like to talk about how a book questions the reader's traditional, conservative values about family structures. I want to say we are introduced to a shared household wherein there isn't a typical nuclear family structure, the children are not trained in table manners and everything is loud, lively and disorganised. This contrasts the presumed reader (at the time)'s traditional beliefs that a house should have a nuclear family, children should be taught table manners, etc. The sentence I want to say is, "The reader is positioned to feel [insert word], as their beliefs are subverted and challenged." Words I've tried so far: Unsettled Uneasy Disturbed These are the closest words I could find but I feel like they have a more negative association, and creates a malaise in the reader. I feel that the effect of the book is more subtle and just lightly 'shocks' the reader, positioning them to just take notice of their preconceived beliefs, rather than evoke a negative reaction. Destabilise Bewildered These words suggest that the representation of these households are completely weird and confusing, however, that is not the case. It's not so weird that a reader wouldn't comprehend it, these households are just different to the mainstream households. Source for definitions: Google dictionary | 0 |
Background: I tile lidar and photogrammetry products as part of my job. Project areas are typically single polygons outlining an area, and can be quite irregular in shape. Overall there is a lot of data and I am required to achieve a maximum file size per tile by creating square tiles that cover the project area. I know from experience what this tile size is but it differs by product. Although tiles are square, they are allowed to hang over the edge of the polygon. I'd like an algorithm to take a polygon and a square tile and return the tiling which has the fewest number of tiles that completely cover the polygon. The square tiles must not be off-grid or rotated, they must be orthogonal. If possible I'd like actual code, preferably in python and utilizing arcpy, however I'm willing to accept any answer that provides the algorithm I'm after. Bonus - multiple polygons representing disjoint areas need to be tiled using one tiling scheme. Tiles that don't cover any project area aren't needed, but all tiles must be on the same grid. | 0 |
Levitated pits were introduced after after solid pits. In this design the tamper is separated from the fissile with an airgap. From the Nuclear Weapon Archive: The original Fat Man pit design used a Christy solid plutonium core, surrounded by a close fitting natural uranium tamper. The Sandstone devices all replaced the contiguous tamper-core approach with a "levitated core" in which the core was suspended within a larger hollow space within the tamper so that a gap existed between them. The collision between the tamper and core would create more efficient compression of the core than the explosive-driven shock in the wartime design. Other vague descriptions I found: The first improvement on the Fat Man design was to put an air space between the tamper and the pit to create a hammer-on-nail impact. Efficiency of the implosion can be increased by leaving an empty space between the tamper and the pit, causing a rapid acceleration of the shock wave before it impacts the pit. I recently started studying shockwaves and I don't understand this. How does leaving an empty space increase schokwave acceleration? If I remove the airgap, the mass of the core won't change but now I can use the extra volume for more explosive. Inside the pit, compression of the fissile is the result of work performed by the explosive charge, so how is it possible that I can increase compression by reducing explosive volume ?? | 0 |
In table tennis it is often desirable to produce as much spin on the ball as possible using a glancing contact. (The rubber covering of a table tennis bat is typically highly elastic and has a high coefficient of friction.) Anecdotally, the view is sometimes expressed that acceleration at the point of contact is more important than speed. I take this to mean that when the ball is hit with the bat at the same angle and travelling in the same direction, it is possible for a bat at a lower velocity but with some acceleration to impart more spin on the ball than a bat travelling at a constant higher velocity (higher than the maximum speed of the accelerating bat) without acceleration. Is this true? If so, why, and how can the optimal contact (in terms of speed and acceleration) to produce maximum spin be determined? | 0 |
One English rule is to hyphenate two or more words when they come before a noun they modify and act as a single idea, called a compound adjective. This is the most common use of the hyphen I've seen. For example: A non-cloud platform Some cloud-based platforms What happens when there are three adjectives before a noun? Should I hyphenate all three? This example looks awful, but maybe that's because it's joining two compound adjectives that we usually see by themselves: Non-cloud-based platform That compound adjective would look better without the two hyphens. For most groups of three or more hyphenated words, they tend to form expressions that behave like compound adjectives, e.g. up-to-date, hit-or-miss, trial-and-error, etc. but they would also look alright as phrases by themselves. The three-word compound adjective in my example doesn't fall into that category. | 0 |
I heard that Lagrange mechanics can be derived from Newtonian mechanics, and Newtonian mechanics can be derived from Lagrange mechanics. I've heard many times that they have equal explanatory power. But I encountered that there is a tricky point in deriving the law of conservation of angular momentum in Newtonian mechanics. On the other hand, theories that use the principle of least (or stationary) action derive each conservation law from the Noether's theorem by assuming each symmetry. So, is my understanding appropriate? That is, while Newtonian mechanics itself derives conservation of linear momentum without any additional assumptions, and requires some manipulation to derive conservation of angular momentum, but Lagrangian mechanics cannot derive both without the assumption of symmetry, or derive both if the assumption is made. Then, it seems that it can be explained by Lagrangian mechanics, but there is something that is not correct in Newtonian mechanics, or it seems that more assumptions are made in Newtonian mechanics than in Lagrange mechanics. Which of the two makes sense? I'd also like to ask if Newton's third law conflicts with Lagrange mechanics, and if it's possible to find a set of Newtonian laws that have the same explanatory power as Lagrange mechanics. However, I want to know (even short) to just the above two questions. | 0 |
I have problems in understanding the terminology used in Sylvester's Criterion about the "sign" of a matrix. I got the "positive-definite", the "negative-definite", the "indefinite" and "non-definite" (the last one is when the determinant is zero, whilst the penultimate refers to two eigenvalues with different signs). What it's really unclear are those two: positive semi-definite: "all its eigenvalues are non negative" positive semi-definite but non positive definite: "there is one zero eigenvalue and the rest are non negative". I would really understand why one has to complicate the terminology in such a horrible way. Why shall we use "non negative"? Just say "Positive". Also, what's the difference between "all its eigenvalues are non negative" and "there is one zero eigenvalue and the rest are non negative"? I don't get this. If zero is counted as "neither negative nor positive" then wouldn't positive semi-definite mean positive definite? It's all so messy. | 0 |
My current level of maths does not allow me to understand any of the proofs I was able to find online for the Fundamental Theorem of Algebra. I find it very unsettling having to continue learning about polynomials without being able to grasp such a fundamental property of them that is there exists a complex root for any polynomial with complex coefficients. My question is, is there a way I can reach the same conclusion of the Fundamental Theorem of Algebra for polynomials with real coefficients instead of complex coefficients. In other words, to prove that at least one complex root exists for a polynomial with real coefficients. Does restricting the coefficients to be real instead of complex make things any easier? If the answer to my question above is no, then I would appreciate it if you could provide any sources that I could've missed, that explain the Theorem by using the least amount of mathematical notation and advanced concepts as possible. If I cannot figure this out, I am going to have to accept the existence of a root as an axiom going further, which is something I really don't want to do. | 0 |
I've been thinking about the critical point of water, which has three distinct and specific properties: critical temperature, critical pressure, and specific critical volume. However, when I draw a PV and TV graph I can't seem to think of any way in which to bring the water to its critical point because in order to get one property to its final state you have to change one of the others. For instance, if you already have the water at its critical temperature and pressure, you would have to decrease or increase one of those values to get it to its critical volume. To this end, I'm wondering whether it's even possible to bring water to its critical point - because once you achieve two of the three intended properties, it seems impossible to me to get the third property to the correct state without changing one of the other two. | 0 |
I am reading up on Christol's theoreom and an important part is that k-uniform transducers (where k is somehow related to prime numbers) preserve the algebricity of a formal power series (taking the coefficients as a sequence). So basically, we start with a formal power series that has roots (my friend told me that algebraic means there are roots or zero crossings), run the coefficients through a k-uniform transducer and, when we use the values that come out as coefficients for a power series, that power series is again algebraic. There is a lot I still need to understand here clearly (like, what is a "formal" power series vs a "business casual" power series...), but I'd like to start by understanding what is so special about a power series having roots. Just for context, I have nearly no formal background in mathematics but came across Christol's theorem and thought it was very cool and maybe related to my area of work (computer science, temporal logics, and automata). Any help is appreciated! | 0 |
Is there a conceptual problem in formulating of Liouville's theorem and the BBGKY Hierarchy for classical field theories? I always see treatments of Lioville's theorem only in the context of classical mechanics. I also know that most references treat linear response theory only for classical mechanics and do not touch upon linear response theory aspects of classical field theories such as Kubo formula. One can definitely take the continuum limit of a classical mechanical system and obtain some sort of Lioville's theorem or BBGKY hierarchy for the continuum field theory. I would like see if this is discussed in some rigorous way in any reference. In particular, I'm looking for references which discuss aspects such as the phase space for classical field theories, BBGKY and Green-Kubo Formula. I'm not a mathematician so a good systematic treatment I'm comfortable with for classical mechanics is David Tong's lecture notes and the text by Evans and Moriss. I'm looking for similar treatments for classical field theories. | 0 |
When we calculate the excess pressure on the concave side of the meniscus of the liquid surface formed in a capillary tube, we balance the force by the atmospheric pressure, force by the pressure on the the side of the fluid , and the force due to surface tension, to derive the expression for the excess pressure on the concave side of the meniscus, but, my question is, when we balance the forces acting on a body, we balance the net external forces on a body for it to be in equilibrium, but here the surface tension force is an internal force on the surface, applied by the surface molecules themselves, then why do we include it in the equation for balancing the net external force on the meniscus? | 0 |
I'd like to get some clarity about how nice the problem of decomposing semigroups using the wreath product is compared to the problem of decomposing groups, and where this apparent difference in niceness comes from. Looking at the Krohn-Rhodes theorem for finite semigroups, one can decompose a finite semigroup as a wreath product of finite simple groups and really basic "reset automata" semigroups. If I understand the Krohn-Rhodes theorem correctly, if one applies it to a finite group, you don't get any "reset automata" semigroups, so it gives us a decomposition of our group as the wreath product of simple groups. Is this correct? On the other hand, Meaning of factorization of groups and looking into the extension problem for finite groups leads me to doubt that the case for finite groups is that simple. So is it not as simple as "there's some kind of wreath product-like construction that allows us to reconstruct a group from its factors"? I'd greatly appreciate some clarity about this. | 0 |
I have been trying to define the notion of a product of second-order classes using (finitary) second-order and if needed third-order logic. It seems to be possible to define the product of finitely many classes, because I can just express this using a finite second-order sentence. The problem is that, when I try to define an infinite product, I seem to need to be able to refer to an indexed family of classes. More specifically, so that I can use an infinite index class. But something tells me this should not be possible to do in higher-order logic, because intuitively, it seems to involve some circularity. Do you know if it is possible? Also, someone suggested me that type theory should help me with this problem, and if so, do you know why? | 0 |
Im reading make: electronics, and I have investigated a little bit about displacement current and how a change in electric flux can create a magnetic field in a vacuum. A can understand that, however there is one effect which I don't comprehend the physics behind it. The effect that I'm talking about can be resumed in the next quote from the book: "A sudden change in voltage on one plate in a capacitor induces an equal change in voltage on the other plate, as if is reacting in sympathy". An image from the book showing the voltages in both plates of the capacitor in respect to time. My theory: So my theory is that since there is a current displacement there is also a change in magnetic flux, and this change in magnetic flux can generate a similar voltage on the other plate, since the plate has thickness and thus inside the plate there is an area that is perpendicular to the direction of the magnetic field, which will lead to a magnetic flux, and if you change the magnetic flux a voltage is created (according to Lens and Faraday). However, I don't know if this is right, and at the same time trying to find information on the internet about it is impossible. If anybody has an answer I will be delighted. | 0 |
I am seeking answers from experts in mathematical logic about the amount (if any) of university mathematics I need to know in order to understand mathematical logic and later hopefully do meaningful (independent) research on the subject in general and Godel's Theorems in particular. I am proficient in high school math and have a bachelor's degree in Physics. I have also recently taught myself some calculus, linear algebra, and parts of real analysis as I assumed you must need at least undergrad math to eventually get proficient in a certain math discipline. Earlier I had decided to learn up to grad level math but after I glanced through some logic books it appears they make close to zero use of even undergrad math. Also, I have come to know that philosophers too do research in mathematical logic, and as far as I know, they don't study any university math. So, my question is should I first teach myself undergrad (and grad math) or just dive into mathematical logic as I don't want to later find myself in a position where I have to study all that university math before I can make further progress in logic? If that is the case I would consider enrolling myself in a math program first and doing the research later in the conventional way. | 0 |
My understanding is that the word means a rephrasing of something the person has said in expressing the same sentiment or idea. But I think people use the word to mean essentially, say something in a similar way to mean something else. A simple example: Marge is talking to a bullied Bart: "If they beat you up, I do not think they are your friends." Someone who wants to borrow this sort of phrasing to apply to the situation where someone has more extremely pushed an acquaintance off a roof and this is reported in the news as "Woman's friend pushed her from roof" and says, "To paraphrase Marge Simpson, 'If someone pushes you from the roof, I don't think she is your friend.'" In the above, is "paraphrase" being misused and if so, what is a better word for such borrowing/reuse with modification of a phrase? | 0 |
I'm currently working as a (undergrad) TA for a mutlivariable calculus class and while covering the topic of multivariable differentiability, one of our students suggested that it'd be nice to have some actual functions we could use as examples to navigate how the theorems can be used to both establish differentiability and to flip them back around to deduce things about the partial derivatives if they're not differentiable. In particular, we were discussing a sufficient condition for differentiability which, roughly, states that if all of the partial derivatives of a scalar field are continuous at a given point, then the field is also differentiable at that point. But more specifically I was warning them about how the contraposition of this statement does not forbid a function from being differentiable while having discontinous partial derivatives, as this beautiful example shows. The previous example has all of its partial derivatives be discontinuous, but then a student asked if I knew any scalar fields which only had one or two discontinuous, while the rest remained continuous at the given point. Here's where I ask for your help :) I have looked around in some of the literature but haven't been able to find good enough example of this, although in principle this should be possible (from what I understand). Also, if you have other interesting examples that show how differentiability can be wrinkly or deceiving I'd really appreciate it (and our students would too)! | 0 |
I have read this question (no answer, just comments): Light, including pulses of light, consists of many photons. A very short pulse has a wide range of frequencies. See The more general uncertainty principle, regarding Fourier transformsA single photon can also have a long or short duration, and a narrow or wide range of frequencies. I have never heard of single photons with a wide rage of frequencies. Each photon is always supposed to have a single quantified energy/frequency, otherwise the quantum effects would not occur. Can you refer to studies that show single photons with a range of frequencies? Relation between attosecond light pulses and photons? And this: This is very fast for a pulse of light, and it is actually so fast that the pulse of light is no longer a periodic electric-field oscillation, and instead it lasts only for a few cycles. But it is still not fast enough. What is an "attosecond pulse", and what can you use it for? Now we have had single photon emitters for a while and the photon is the smallest amount (quantum) of EM energy. But then the question remains, why are attosecond pulses better (for example to track electron orbitals) then single photon emissions? Very naively thinking, if you shoot single photons at the electron (atom), you are using the smallest quantum of energy to do so. Then why is attosecond pulse generation superior to single-photon emitters? Question: How can an attosecond pulse be shorter than a single photon (quantum) emission? | 0 |
In practical engineering we are limited in the upper temperature of thermodynamic cycle due to the material properties. So, after the max temperature is fixed, we want to make our cycle as close as possible to a Carnot cycle with the same max temperature. It is clear that the compression and expansion should be adiabatic and we are technically close to the realization of this. Also, we have to cut lower right angle of the Carnot cycle, because each next turbine stage should be larger in diameter, and building them becomes economically or technically impractical at a certain point. But the process of heat addition is a bit more tricky to understand. Consider the case of Humphrey and Brayton cycles in the same range of temperatures: The heat addition process is more vertical in case of faster heat addition, but according to Carnot process it should be more horizontal to be more efficient (i.e. close to isothermal). However, we do know that faster heat addition is more efficient (detonation engines are more efficient), so Humphrey cycle should be more efficient. Can't solve this puzzle... | 0 |
I have viewed the definitions of the Hubble Sphere and related cosmological concepts, as well as various explanations, yet Im still struggling to comprehend a full visualisation of this, which I would prefer instead of taking its word for it. To phrase the question that would most help me, the following follows: so from the moment that a celestial object crosses the hubble sphere boundary, as in going out of our hubble sphere scope, the images of that object will never reach us, the observer, from that point on, and we are left with a developing and cascading history of prior images only just reaching us now. If what I said is accurate, and requires no correction, my question now is how will the developing and changing history of past images for this celestial object play out in our view for the next millions of years until that moment in the old present where it crossed the Hubble Sphere boundary? How would it appear to us, the observer, over such a long term period? My intuition is telling me that such a celestial object will continue to age in our view of its past images, but also becoming increasingly redshifted until phoof, it is no longer visible due to being outside of the Hubble sphere. | 0 |
I understand that infalling objects reach the speed of light at the event horizon. Any associated clock would be observed to stop, according to SR. But isn't the key here 'observed'? An infalling observer at the event horizon would observe a remote clock to stop. Who is to say which clock stops. No clocks actually stop in SR, because it is symmetrical. But there is gravitational time dilation. In this case clocks really slow down. But you would expect the force of gravity to be infinite at the singularity. It is here you would expect gravitational time dilation to be infinite and clocks would really stop, not just be observed to stop. The force of gravity is nowhere near infinite at the event horizon, so why would clocks stop here rather than just slow down? Do properties at the singularity transfer themselves to the event horizon? Perhaps because there is no physical singularity? | 0 |
This paper has the following abstract: We theoretically consider a graphene ripple as a Brownian particle coupled to an energy storage circuit. When circuit and particle are at the same temperature, the second law forbids harvesting energy from the thermal motion of the Brownian particle, even if the circuit contains a rectifying diode. However, when the circuit contains a junction followed by two diodes wired in opposition, the approach to equilibrium may become ultraslow. Detailed balance is temporarily broken as current flows between the two diodes and charges storage capacitors. The energy harvested by each capacitor comes from the thermal bath of the diodes while the system obeys the first and second laws of thermodynamics. Can someone explain the importance/meaning of the claimed result for a layperson? In particular, how does this not violate the second law, if it's "thermodynamic fluctuations" being harvested? | 0 |
I am working on this problem. A hexagon is inscribed in a circle. The length of five of its sides is a, while the length of the six side is b. My question is : a. How to find the area of this hexagon? b. how to find the each of the diagonals's length? What I have in mind is that, since only one side is different from all other sides, the figure is still symmetric. Then I can calculate the area of the two trapezoids. I think I should use the condition that it is inscribed in a circle. However, I am stuck with how to find the angles or what other fomula should be used here. Then for the length of the diagonals, I am thinking that once I got the two trapezoids, I got them. Anyway, I think I lack of the knowledge of some intermediate theorems. Thank you for the help in advance! | 0 |
This question closely ties into a question I had about verbless clauses. However, I am writing a new one at the suggestion of a user. Polarity-sensitive aspectual-related words are those such as 'still' and 'already.' I have established that modifiers like 'obviously,' which I believe to be evaluative in nature, can function as modifiers in an adjective phrase, as determined by the answer to my question linked above, where I confused them to be part of verbless clauses. But can 'still' and 'already' also be modifiers in an adjective phrase? Below is an example similar to the one from my previous question, using 'still' instead of 'obviously.' I have highlighted in bold what I believe to be the complete adjective phrase. He was crying, still sad because of the passing of his father. | 0 |
According to my current understanding of special relativity, photons do not experience the passage of time. It is as though the universe is completely 'paused' for them. I know that objects with mass cannot accelerate to the speed of light. But isn't the whole point of relativity to predict the motion of an object from a different frame of reference? The universe also tends to increase its size with time. In that case, consider the following thought experiment: Let's go back in time to when the universe was relatively young. There was once a photon which, when created, observed the universe to be completely stationary as it didn't experience the ticking of time. As the time does not tick, the universe doesn't expand (relative to the photon) and instantaneously, it exits the universe. So my question is, what part(s) of the above statements is false? | 0 |
I made the claim on a manuscript that all manifolds possess an acceleration field. The referee rejected the idea saying "The nature of this acceleration field has not been seriously discussed and the theory lacks justification in physics". This confused me as I understand that a field, in physics, is a region of space for which each point is associated with a specific physical quantity. Velocity is a physical quantity. If we impose an evolution parameter, then don't all points on this manifold have a velocity (vector) quantity? Is that not sufficient to claim the manifold has a velocity field? Can we not also take the second derivative of the position with respect to our evolution parameter and say that every point on a manifold has an acceleration (vector) quantity? Does that not also qualify as a field? Is there an argument to be made that all smooth, differentiable manifolds do not possess an acceleration field? | 0 |
I am looking for a word that describes something whose meaning is instantly recognizable, that is so simple as to be offensively lazy, and yet completely apropos. Such a word might describe Kazimir Malevich's painting Black Square: Chef's kiss conveys artfulness and minimalism, but not to the point of laziness or offense. I like sophomoric for its literal translation "wise fool", but the word is not used to suggest brilliance. Cunning has the right connotation of artfulness, but its connotations of subtlety, and further, deception, make it inappropriate. Stupidly/offensively obvious almost works, but is boring. Unsubtle is ok; blunt better. Both don't convey the artfulness that I'm looking for. I love the divine feel of manifest; I'm wondering if this is the best I can do. I'm tempted to coin kazimirean, but of course that's too indulgent. | 0 |
Let's bring a positively charged rod near a conductor. Now since some electrons in outer shells are not strongly bound to atoms,they will get to the side near the rod. But why does it mean that dipole is formed in that conductor? We take the vertical cross sections of the conductor. Now,in each vertical layer,there will be atoms. So electrons from each vertical layer will get to the side of the rod. If that happens,except from the region closest to the rod,there will be positive charge in every cross section. Hence,apart from the very region towards the rod,the entirety of the conductor will be positively charged since electrons have left from each of the cross sections. As we can see dipole(positive at one side and negative on another side) hasn't been created,rather negative at a very small region and positive charges throughout the rest of the conductor. The logic that the rod will push the positive charges at the extreme end also doesn't work since atoms are firmly immovable. So why is it still said that dipole is created as a result of electrostatic induction whereas we have proved that it isn't the case? | 0 |
In basic physics lectures, the teacher or professor in my class never explains the behavior of rotating two or many body particles. In my experience and intuition doing physics, two-particle or many-body systems tend to rotate about their center of mass. For example, the earth-sun rotates around its center of mass, or two black holes rotate around its center of mass; also in ideal conditions, without air friction, a stick when a force is applied to it at the end edge, stick will rotate around its center of mass. Can anyone explain the physics of a system of mass that tends to rotate around its center of mass? I tried to solve this problem and read some reference books, but I don't have any conclusion. most of the books I read just explain what rotation or torque is. Or, is my intuition wrong? | 0 |
I'm hoping maybe this is the right spot for this question, if not, I would love for someone to suggest a better spot I am attempting to use SOLIDWORKS flow simulation to simulate the airflow through a ram air duct. Think like a venturi tube on an airplane, but the convergent divergent duct is embedded in the structure rather than being a protrusion. The issue I'm having, is that for the area ratio of the entrance to the throat, I don't get the velocities I expect at the throat when doing an external flow sim. When I build just the duct itself and put lids on it and do an internal sim I get the numbers I expect. Is there any deficiency in the Flow Simulation when using the external simulation and the flow must through a completely bounded flow area? Or is the simulation giving me true results and the flow through the duct is that degraded by being embedded in the larger structure moving through the air? | 0 |
Intuitionistic logic can't prove as many sentences as classical logic, for example: Peirce's Law; Reductio Ad Absurdum; Double Negation Elimination; and Tertium Non Datur, which are all equivalent in classical propositional calculus and they can't be proved in intuitionistic systems. I can prove their equivalences in some famous system, but I can't prove that we can't prove all of them in intuitionistic proof system especially without using semantics. I would like to prove this fact only using syntactic properties, i.e. proving these formulas are not in the set of provable sentences or proving that there aren't any proof of them in the set of proofs of intuitionistc proof system, without interpretation into some semantics: Kripke models or Heyting algebra. Where can I read this topic? is there any great book for this proof? | 0 |
I'm using pandoc in my website to allow my content creators to use Word, which would simplify developmnent immensely. The only issue I have is that Pandoc seems to output very little information about document styling. It's possible for me to manually re-add these with CSS later, but that somewhat defeats the pupose of using Word. Hence my question. Can I get pandoc to spit out more information about how my document is structured, such that I can apply more generic styles and have the document looking comparable to how it was written. Example, I've got a table with user-defined centre-aligned text (the person centred the text in Word). When I export my document to HTML using the following command: pandoc --from docx --to html --embed-resources --reference-doc ./reference.docx --section-divs. (I'm streaming in the contents of the file via stdin, as it isn't guaranteed to be in a consistent location)`. When the HTML comes back, the contents of the table elements are simply paragraphs. I'd like them to be wrapped in <center> tags or the equivalent - just something to identify that they need to be centred. There's a number of examples like these that I'd like to introduce, but momentarily, centring text is a priority. Thanks for any pointers | 0 |
When there is wind at a surface, and a rotating cylinder is placed there, mounted in a way that it is free to reorient itself, can it be predicted if the cylinder will align itself in a certain way? Perhaps it is easier to first consider the same scenario but without a surface. So, simply, a rotating cylinder in wind. Can it be predicted if it will prefer to orient itself in a certain way? A cylinder with its axis perpendicular to the wind direction, will for example experience lift. Is there anything to suggest a rotating cylinder, free to orient itself in any direction, will prefer to orient itself perpendicular to the wind (its axis perpendicular), such that it also develops lift? And, what if a surface is then added? May be possible to make an analogy to how cylinders rotating in the same direction repel while those rotating in opposite direction attract. In this case, the surface with wind over it may "appear" similar to the surface of a rotating cylinder. | 0 |
It is very common in physics, when we refer to the most diverse theories, on the most diverse length scales, we also refer to their energy scale. It is through the energy scale that we classify a theory as being classical, quantum, or relativistic, for example. Likewise, on such a scale, we know whether we are dealing with sub-atomic or sub-nuclear particles. Thus, when constructing a theory, it seems to be of vital importance for the physicist to understand where such a theory lies on the underlying energy scale. However, for a young physicist student, it is not always easy to make such a correlation and find available material that deals with the subject in a didactic way. So, the question of how to determine the energy scale of a physical theory and classify it in the energy scale of physical phenomena remains somewhat nebulous, without many students realizing the importance of knowing how to classify the energy regime of a given theory. From this, as the question in the title of this topic already delivers, I would like to know how, given any physical theory, one can determine its energy and classify it according to the cosmic energy scale (I don't know if I can call it so: "cosmic energy" scale.). I would like, if possible, indications of references that deal with the subject. | 0 |
I was walking by the sidewalk during the night when I noticed a swarm of flies circling a street lamp. It was difficult to see at first, so I tried looking in different angles. The security gate came in by pure chance between me and the streetlight. Now the insects became crystal clear. I tried to capture this in camera, and the same effect can be observed. Now the object between me and the streetlight doesn't matter. My umbrella, or even my hand also works. I would like to know why exactly the blocking of the dominant light source allows the less dominant ones to be seen. The light from the less dominant ones were still present before blocking the light. What roles does blocking play here? Many a times me and my friends have to abandon astrophotography camps in the night due to an overly bright moon or street lamp nearby. Can this same method be utilized to capture a clear image of stars in the night sky? | 0 |
My teacher gave us the assignment to find the moment of inertia of any shape you want. So I decided to find the moment of inertia of our milky way galaxy. I found out that our galaxy is shaped like a warped disk, not a flat. After I found out that, I looked for the equation of the shape and density distribution of the Milky Way to find its I. But, to me, Nasa's and some high university papers had so many big wards that I could bearly understand what they were talking about(I'm Korean.. ^^). I'm sure that I can understand the equation if I had it, but I just can't find any information about them. I would really appreciate it if someone could tell me what you know about this equation(shape & density distribution) Thank you! (Img)Dorota M. Skowron, A three-dimensional map of the Milky Way using classical Cepheid variable stars | 0 |
I was watching this video on Hall effect, and to demonstrate that it is not electric fields that are bending the electron beam, the presenter puts a metal plate between the magnet and the beam. So, my question is, say there was a charge instead of the magnet. How will the metal plate shield the electric field produced by a charge? My reasoning till now was, say, you put a positive charge in front of the metal. Since the electric field inside the metal is zero, negative charges will develop on the face near the charge, and to maintain charge conservation, a positive charge will develop on the other face of the metal. So, in effect, the plate has done nothing. There are still positive charges pointing toward the beam, and the beam will still perceive a force from the charge. So, how is the metal plate acting as a shield? ( If I assume that the plate is grounded, then I can say that the plate will serve as a shield. But in the video, it is not grounded.) | 0 |
Some visuals are so obvious that you would think proofs are not needed. But then trying to proof them rigouresly is a whole other kettle of fish. I was stumped by the following puzzle I made for myself: (really it is no homework question) How do you proof that the axis of an ellipse are perpendicular? Yes you can see it, it is obvious but seeing in itself is no proof. Yes you cannot construct a countermodel, but again that is no proof. I am really stumped with this one, it is so obvious, and easy to see, but a proof? As definition of an ellipse I want to use: (reused from Wikipedia) An ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the points is a constant. As definition of the axis i want to use: (all made up by myself, so maybe incorrect, the second one, defining the minor axis, was a real struggle ;) The first axis of the ellipse is the line containing the longest segment possible between two points on the ellipse. The second axis of the ellipse is the line containing the midpoint of the two focal points and the shortest segment possible between two points on the ellipse, | 0 |
Good afternoon everyone, I am currently resetting my mac and reinstalling everything in a clean way. I would love to have guidance here if possible. I currently installed TexLive and TextDist but now i am guiding myself with this : https://github.com/James-Yu/LaTeX-Workshop/wiki/Install If anyone could explain to me this section : Setting PATH environment variable After installing TeX Live, you must add the directory of TeX Live binaries to your PATH environment variable except on Windows. See the official document. LaTeX Workshop never touches the variable. If VS Code cannot find executables of TeX, it means that the setting of your system is broken. For the ways of setting environment variables on Windows, see link or link. On macOS and Linux, see the documentation by the rbenv dev team. Very detailed information is also available on stackoverflow for macOS. Notice that you have to restart VS Code and the operating system after changing the variable. If you can not fix the setting of your system, you can also override PATH with the env property of LaTeX tools in LaTeX recipes. Notice that, to set the PATH environment variable for VS Code Remote Development, you usually have to edit .bash_profile or .profile instead of .bashrc. See the document for WSL and an issue for Remote SSH. If you want to know about environment variable itself, please read Wikipedia and stackexchange. I do not really understand how it is important and what to do if anyone could help here ! | 0 |
I often have to translate sentences such as: The Department of Environment has offices everywhere in the country, and we would love for you to join us [us as in "the whole department, and not a specific team]. Or: The Police Department is assigning as many resources possible to the case, but we [the Police Department] cannot counter these threats alone I've been told quite a few times that a switch from the third person singular to the first person plural like that is to be avoided in French (supposedly because "we" could refer to anything and cause confusion, even in simple cases like these), and was wondering if the same kind of rule applies in English. I couldn't find any grammar or style guide to help me with this. All help is appreciated, thanks. | 0 |
I have a great interest in synthetic geometry since I was in senior high school. Although I have graduated from university I still like them now. When I was in high school, I read many textbooks and exercise books about synthetic geometry of mathematical competition and learned many interesting things like harmonic range and inversion transformation. But I think people must have invented something new. I am really curious about what new techniques synthetic geometry has developed other than I learned in old textbooks and I want to know if there are any reference on modern synthetic geometry. Also I want to learn how synthetic geometry studies other curves such as conic curves, especially ellipses. I have read the book Geometry of Conics, and the Conics Books by Apollonius, but I hope I could read more such books with deeper results, like those ordinary mathematical competition books with various theorems and interesting and difficult exercices. On a Chinese forum I find out that there are many people discussing modern synthetic geometry and writing short essays on various topics, but I hope I can read some systematic reference books. Thank you in advance. | 0 |
I have a problem I fail to research properly, so I hope you may at least push me in the right direction (or maybe even provide me an answer right away?). I know how linear regression works, that it attempts to find a linear curve such that the sum of all residual errors to the square of the given data points is minimal (least squares). Now, how does one go about, when data points have deviations attached? I have a set of data points, where every point has a unique deviation. The linear regression should still work as usual, but how do I get the resulting error bar of the linear regression curve? Also, since deviations fluctuate, I'd assume some sort of weighted method would make more sense in order to prioritize those data points with less deviation relative to those with larger deviation. What weighted method would make most sense in my case? Thanks a lot for your reply! | 0 |
I've read other answers about how vinyl records reproduce sound, but they don't quite address a main thing I'm curious about. Play Middle C on a piano or a Clarinet, its the same note that can be played at the same volume because the main note is the same. You can tell the instruments apart because there is a different timbre in the instruments due to the components of the other harmonics present in the sound that differ between the instruments. You can break this down using Fourier Analysis. Part of the reason for these differences is the natural frequency of the materials involved. Strike metal with a small hammer, you typically get a higher pitched sound than if you strike a similar volume of wood. A vinyl record has its own natural frequency, yet it can sound just like instruments neither of which sound like each other. Somehow the natural frequency of the vinyl doesn't matter. What's going on there? | 0 |
If an isolated conductor has a net zero charge and is not in an external field, would the free charges still move to the surface of the conductor eg. a conducting sphere? Wouldn't this create an electric field inside the conductor pointing radially outwards as there would be positive ions within the conductor and negative charges on the surface? And then wouldn't the electrons move back to join the positive ions? [I understand how free charges will move in a conductor to cancel any external field, cancelling the external field inside the conductor, but then wouldn't there still be a field pointing radially outwards?] I also don't understand this in terms of energy - why is it a lower electric potential energy position for the charges to go to the surface - wouldn't it be lower energy for the electrons to go back to the positive ions? Gauss's law talks about there being no charges inside a conductor, but wouldn't there still be all the positive ions left there if the conduction electrons have gone to the surface? My guess is that people are usually talking about any NET charge going to the surface of a conductor. But wouldn't an isolated conductor at equilibrium (as in the general textbook questions on this) be net neutral and so then not have charge on the surface? | 0 |
I understand my question sounds stupid but hear me out. I wondered if protons or any charged particle could generate photons and I found this wonderful answer that says yes: Does shaking an atom produce photons? The issue now is that the more I thought about it the more I became confused and here is why. If any shaking charged thing can make a photon, well, which way does the photon choose to go into? I don't have a clear understanding of photons so maybe that's the problem, so to better answer me I'll give my understanding. Photons are packets of energy that represent an oscillating electric and magnetic fields. Please correct me on that if i'm wrong, I'm mostly using the visual model of a photon when i describe it. How does a photon decide in which direction it moves in? Is it just completely random? | 0 |
I've gotten some contradictory answers on where the definition of the element within a set comes from. From a quick Google search, I got this strange idea that the definition of the element comes from the definition of a set. I reached this conclusion because some websites state simply that the element is A member of a set But I feel this results in some type of circular logic (At least I think that's what this logical fallacy is called). Since the definition of a set is A set is a collection of objects whose contents can be clearly determined. The objects in a set are called the elements of the set. (Robert blitzer college algebra) I am almost certain that the issue here lies in the definition of an element I found, But I can't seem to find a definition of the element that is independent of the set so to speak. I hope you guys can help clear this up for me thanks | 0 |
Suppose the situation where an object undergoes linear motion at a constant velocity on a frictionless surface. This motion is often introduced as inertial motion, which is the motion described with Newton's first law. On the other hand, suppose the situation where a person applies a force to an object on a surface with friction, adjusting the force to balance the kinetic frictional force and causing the object to undergo linear motion at a constant velocity (here assuming no torque). In terms of the fact that net force exerted to the object is zero, I know there has been recognition that the motion of the latter case can be interpreted as inertial motion according to Newton's first law. However, is such motion really an example of inertial motion? Such motion seems to be rather different from the motion of the former case (close to Galileo's original thought experiment in which the essence of inertial motion is highlighted in idealized situation with no friction). Or is it just a problem of how we define inertial motion? | 0 |
I have an understanding of electrical circuits, however I am very interested to know more about electromagnetic waves radiation. In particular I want to know how an oscillating voltage causes the electrons move inside a conductive antenna. Voltage is only a difference in electrical potential in our local circuit, it is only difference between electrical potential of two nets (ex ANT and GND) so how the ANT net can itself cause movements of electrons inside an antenna? (because in some circuits the antenna is only connected to ANT.) I want to know which physics model explains this phenomenon? as far as I know circuit theory doesn't explain this behavior. so It should be something else. I know there are some formulas to model electromagnetic radiation, however I want to build an intuition around this, I don't need formulas to solve problems. Also I know that speed of the light has relation to design of the antenna, so I think the theory should include speed of the light as well. I prefer to not get very deep in physic subjects, so I am looking for the most higher level theory/model which is able to fully explain this :) | 0 |
This is a discussion I was having with a friend: Its very likely that the temperature of the water you place a tea bag in while change the flavor of the tea (although I don't know why exactly from a physics perspective) But suppose I have water at a certain temperature: If I let the teabag naturally sit and soak in the hot water.... compared to taking a spoon and pressing/squeezing the teabag as soon as it lands in the hot water: will the flavor of the tea be different? From a diffusion perspective, I know that squeezing the tea bag in the hot water changes the color of the water much faster compared to letting the tea bag rest. But based from a physics perspective, looking at the interaction of the water and the tea molecules - will accelerating the diffusion process of the tea by pressing/squeezing change anything about the tea? (e.g. intensity, flavor). Are there any physics related equations (e.g. statistical mechanics, thermodynamics) that can explain this (if this hypothesis is true)? Thanks! | 0 |
I downloaded a latex template for Wiley journal articles, and can open the template file but cannot seem to get Texstudio/Miktex to find the .cls file. The template comes with a latex file which uses the class as an example, and if I open that right in the extracted ZIP folder, all is well; however, if I save-as anywhere else, I get a "cannot locate name.cls file". I have made sure that I saved the extracted ZIP folder within a directory listed in the MikTex path (have tried two different locations) and I have refreshed the filename database (multiple times) but still the same error occurs. This also happens if I open a blank file and attempt to use the class. I have closed and opened TexStudio a number of times, but I am unsure of what else I can try. | 0 |
During the last few days I have been interested in the gravitational hierarchy problem and the different explanations for it/solutions to it. Among the most "concrete" (insofar as anything this complex can be concrete) explanations are several realisations of the so-called "brane cosmology". In these, whether they be the original ADD model or some string theory model, the standard model particles/modes are confined to a brane (either due to them being open strings or some other effect) while gravity/gravitons can freely propagate into the so-called "bulk", therefore allowing gravity to "leak" away from "our" spacetime thereby explaining why it's so weak. Common to these theories is that while these dimensions can be taken to be either compact or non-compact (but often are assumed to be compact) they are "large" extra dimensions. Now in your "garden-variety/lift pitch"-string theory the necessary extra dimensions are assumed to be very, very small and compact. My questions now revolve around the parallels of these Kaluza-Klein compactified theories and the brane cosmology ones in regard to the hierarchy problem: Can standard model particles/modes access the extra dimensions? I seem to recall that this should only be possible at "high enough" energies but I am unsure. Can gravity/the graviton access the extra dimensions even at low energies? If so, why? What is the mechanism/explanation for this? If neither of the above yields a similar solution to the hierarchy problem as in the brane cosmology scenario, how is the hierarchy problem solved in these "classical ", small-extra-dimensions Kaluza-Klein types of theories? | 0 |
So imagine the classic science experiment where you take an empty aluminium can and a rubber bar that you charge with fur. At first, that can is electrically neutral. Two different cases now that I want to discuss: If I put the can on a desk made out of wood, the can will be attracted by my charged rubber bar due to influence. So the electrons in my rubber bar push away the electrons being in the can as far away as possible (the other side) and so the rubber bar only "sees" the protons. If I put the can on a desk made out of a metal which is grounded, what happens then? Still influence? Or is the electrically neutral can now positive due to electrons escaping to ground? Would love to hear some thoughts. Best regards | 0 |
Can we determine the truth value of the statement "if A then B" knowing only that B is definitely false whenever A is true, for example, "If you live in Paris, then you live in London." From what I understand about truth tables, this on the face of it is indetermined because it could be true or false based on whether you live in Paris and not in London, or you don't live in Paris. But at the same time, the fact that we know that whenever A is true B has to be false, seems to go against the purpose of implication, that whenever A is True B has to be True, and from that alone, the conditional statement can't be anything other than false? The book I'm reading says that the statement in the above example is false. | 0 |
The existing English language term needs to refer to a robot that can navigate environments and it incorporates a human who is present virtually inside the robot from a remote location. The human navigates the robot and communicates with the environment in real-time. The closest example are the so-called telepresence robots being tested for use in classrooms or offices, but they are not exactly what I am describing. I feel like there is a term for such a machine vessel that 'embodies' a human, or that there should be such a term. The terms robot or cyborg do not describe this vessel. I can imagine in the near future a humanoid robot that is not driven by AI but by a human from a remote location using VR with ability to sense the environment (e.g. sense of touch). For example, this would benefit persons with significant mobility disabilities by allowing them to be present and interact with environments, the idea behind the current telepresence robots but in a much more integrated way between the remote human and the machine, and more interactive with the environment. So, to recap, is there a word for such a machine vessel virtually occupied by a human? | 0 |
In the picture below, mountains farther away blends into the color of sky, this is "atmospheric perspective", caused by atmospheric scattering. This effect is also called "fog". But dark blue appears in the middle of the [green -> light blue] gradient somehow. Why? Is there a physically-based model to explain that? In many video games, they used linear gradient to simulate the fog. The color what we see is a linear interpolation between the color of the object and the color of sky. It looks like the gradient in the right side of the picture. But that isn't realistic because of the missing "dark blue" color, so mountains in video games usually looks too grey. My guess: The dark blue color is caused by Rayleigh scattering. The white color at the farthest mountain is caused by Mie scattering. Somehow combine them makes the fog both blue and white. But I have no idea how. | 0 |
In a room at normal room temperature, certain materials, such as metal, glass, ceramic, or rock, will feel cold to the touch, but others, such as wood or plastic, do not so much. Which physical properties do the former materials have in common that cause them to be cold to the touch but the others lack? The fact that wood is porous? Solid plastic pieces still do not get/feel as cold even though they are not porous. Most sources point to thermal conductivity, but how can that alone be the answer? Rock and rock-like materials (such as glass and ceramic) have a very poor thermal conductivity whereas metal has a very high thermal conductivity. I know that because rocks take a long time to heat up and cool down in a fire, but metal takes not very much time. Which physical properties (might be more than one) determine whether a material at ambient temperature will be perceived as cold or not? | 0 |
As a forward, I'm no a physicist or a student of it. In fact I'm pretty ordinary. So if I mischarecterize some concepts, bear with me. So I was reading up on some of the new technologies and then I had a moment. I am wondering if you could use quantum entanglement to transmit data across a vast distance, theoretically even light years, in an instant. I was debating this in a youtube clip where there was a whistle blower from the antarctic and they were speaking on this. My "opponent"(I guess?) Stated that measuring any entangled particle removes the connection, but quantum computers can use gates that flip an electron spin without disrupting the connection. Another objection was multi light year transmission, but I thought that should be fine since according to the theory, it's instant, no matter the setting. So basically I'm wondering with the current tech that we have, technically couldn't we set up an experiment to send a byte of data via quantum entanglement by changing the state of an electron, using a gate to measure it on the other end, and translating that to a binary digit? In other words, do we have Faster-Than-Light communication on the horizon? | 0 |
My understanding: electrocaloric effect relies on polarized molecules lining up to an external electric field, which lowers the local entropy and thus heat is given off to the surroundings. When the field is removed, the molecular dipoles again arrange randomly, which increases the local entropy, thus heat is taken in from the surroundings. I ask about a macro level system. Here I have micron sized particles, each particle made of two hemispheres using different materials from the triboelectric series. These serve as my "molecules". Upon initial shaking, the surfaces rub and so each particle has a dipole. Before shaking: After shaking: Now I turn on an electric field and vibrate the container a little so the particles loosen and align themselves to the field. This vibrating is kind of like of how they used to hammer the living hell out of heated iron in a strong magnetic field, so the magnetic domains align as the object solidified. Now I can't think of any reason why this won't display the electrocaloric effect. And since here we don't rely on the molecule shapes, crystallization, polarization and the intermolecular forces that prevent the dipoles from completely aligning themselves, I think this could display interesting levels of cooling and heating. Of course, I'm a nobody, so to you experts I hand over my question. Will this work, and if yes, can we quantify the effect using any equations? | 0 |
I'm looking for a word that effectively conveys an attitude showing a preference for having a child related to oneself ... ie, a lineally/genetically-related child. In particular, a word that would fit the following example: Michael had a _____ attitude, he wanted children of his own and / or possibly a noun form: Michael was a _____ unlike Sam who was a non-_____ which would be helpful in distinguishing between people that prefer to have their own children and those that are happy to adopt, foster, etc. I had considered "autogenic" ... "auto" meaning self, and "genic" meaning "produced by" ... and even "progenic" (or "progenetic" possibly) which might work here, "pro-", I take to mean "following" or "in favour of" which in combination with "genic" / "genetic" relates to genetic lineage or heritage. However, I'm not sure I've constructed them appropriately, or whether they're right or not. | 0 |
Scientocracy (to my understanding and as my intended meaning) is government by results, i.e., eschew policy debates to instead argue and then agree on metrics, run an experiment and then transition to whichever solution produces the best outcome as determined by the agreed upon metrics (of course, if cultural, climatic or other considerations make a new policy ineffective in a certain place, the policy should be revoked or adapted there). My question is what is the 'ism' associated with this? Scientocracism isn't a word, and ends with racism, so that doesn't really work. Technocracy (a related, if more loaded term) has the same problem. An example sentence would be: I believe in representative democracy, but I also believe in [] because while I think that we should be able to elect people to represent our interests - and fire them when they fail - I also believe in results. | 0 |
In the preface to Landau and Lifshitz's Statistical Physics, they comment the following In the discussion of the foundations of classical statistical physics, we consider from the start the statistical distribution for small parts (subsystems) of systems, not for entire closed systems. This is in accordance with the fundamental problems and aims of physical statistics, and allows a complete avoidance of the problem of the ergodic and similar hypotheses, which in fact is not important as regards these aims. After explaining that they will consider (macroscopical) subsystems of the whole closed system, they claim A fundamental feature of this approach is the fact that, because of the extreme complexity of the external interactions with the other parts of the system, during a sufficiently long time the subsystem considered will be many times in every possible state. But this is very similar to the ergodic hypothesis, is it not? From my Stat Physics lecture notes, Given a sufficiently large time, any closed system will approach arbitrarily closely any point in phase space I don't understand how considering subsystems overcomes the need for this hypothesis, neither what advantage it has. It seems to me that the authors are using the complexity of the interactions between the subsystem and the rest of the system to grant credibility to the claim that the subsystem will eventually have populated the entire phase space. But why isn't this equally credible to stating the ergodic hypothesis? | 0 |
Im not necessarily talking about emf (and also not considering rotation) , but rather the potential difference created due the induced electric field to balance the lorentz force on the electron. For example if the disk is moving toward the right and the magnetic field is into the screen then the lorentz force is acting on an electron downwards pushing it down. now due to the excess of electrons downwards an electric field is created top to bottom which increases until the lorentz force is equal to the force due to the electric field on the electron, resulting in an electrostatic condition. So my question is does this actually happen? if not why dosent it happen? Im a bit bothered by this because according to faradays law there should be no emf induced in the disk but according my reasoning there should be a potential difference. Is there a difference between emf and potential difference? | 0 |
As I understand it, the (real) index of refraction is given by the ratio of speed of a monochromatic light wave in vacuo versus speed in medium. When it comes to the question of propagation of a light pulse in a (dispersive) medium I know that I need to calculate the group refractive index to obtain the propagation speed of the pulse. My question specifically now is, if it is possible to use radiative transfer theory to calculate light pulse propagation in a scattering environment embedded within a medium (not vacuum)? If the former is possible, can that speed be said to be the effective group velocity of the mixture of the scatterers and medium? Further can this effective group velocity be used to calculate an effective group refraction index? Background: Although I have no working experience with radiative transfer theory I can imagine that it would be possible to use it for calculation of attenuation related values such as the imaginary part of the index of refraction, but I cannot see how it would be possible to get at the real part of the index of refraction. | 0 |
I've recently watched this video about an electromagnetic ring accelerator. I get how it works: it uses controlled electro-magnetic coils to accelerate metal balls' Passing trough one of the coils has two stages: when the coil passes enters the coil, the coil is powered on, generating an electro-magnetic field, accelerating the ball towards the center as the particle passes trough the origin of the coil, the coil is quickly powered off and the ball continues forward What I am curious about is exactly what forces act on it. Searching online there appear to be some inconsistent answers, but it always either is the magnetic force or the Lorenz force law. From what I understood the magnetic force is purely for describing magnetic attraction, either between two magnets or a magnetic (ferromagnetic?) object and a magnet, while the Lorenz force law is the combination of the magnetic and electric laws. Could somebody explain which of these two is and what exactly their formulas are in the context of the balls passing trough the coils? | 0 |
For example, ZFC and ZF. I have come across the notion of pure and applied mathematics, and how the development of the former can (and is usually intended to) lead to the furtherance of the latter. In this case, how do we know that the axioms we do pure maths with are "sound"? For me, there is no point in doing something as rigorous as maths unless we are certain it could at least possibly provide a practical use to us, however subtle that use may be: otherwise, it is just an elaborate (and hugely unproductive) mind game. I suppose my question boils down to why we do maths and what it is. If its a way of abstractly describing physical natures and phenomena (like Plato thought), I'd have thought you could test axioms with the scientific method, in which case there would be no confusion surrounding, for example, the millennium problems. There is so much nuance about axioms and proofs, truth, falsity and their natures that really interests me, and I would like to know more about, but I don't know where to start. I have heard of "metamathematics" as related a field of study, which is why it's included in the title, but I honestly don't know much about it. I also appreciate that ZFC and ZF may be bad examples, in which case please point out why. Thank you! | 0 |
In Slavery in Massachusetts, Thoreau writes: But it chanced the other day that I scented a white water-lily, and a season I had waited for had arrived. It is the emblem of purity. It bursts up so pure and fair to the eye, and so sweet to the scent, as if to show us what purity and sweetness reside in, and can be extracted from, the slime and muck of earth. I think I have plucked the first one that has opened for a mile. What does for a mile mean in this sentence? I looked up for in a dictionary, and methinks the author might mean the first lily that he came across, and that was opened, after walking a mile. Or does Thoreau mean something else here? | 0 |
Shouldn't acoustic oscillations created by primordial matter anisotropies create multiple peaks and troughs when those oscillations are frozen by decoupling ? It's not unthinkable to imagine that the exact calculations of the expected amplitudes of each will lead to a result where the first peak is much more significant than the rest, but do those other peaks and troughs theoretically exist, just at very small currently non measurable amplitudes ? In other words, the BAO peak corresponds to the first peak in the CMB power spectrum, but am I wrong in assuming the other peaks and troughs are theoretically also present in present matter distribution, just at negligible amplitude ? As a bonus, if the answer is indeed yes, why are the other peaks so negligible ? I understand that the first one has the greatest amplitude, but why are the remaining ones so vanishingly small as to remain undetected in current matter distribution, despite being nowhere near insignificant in the CMB power spectrum ? | 0 |
A current-carrying loop of wire is placed in a uniform external magnetic field as shown. If the current in the wire is traveling counterclockwise in the picture, what do you predict the loop will do when released? The answer provided for this question: From the RHR for loops, place the heel of the right hand in the plane of the loop so that the fingers are curled in the direction of the current. The extended thumb points in the direction of the B-field. Since it is anti-parallel to the external B-field, the loop will flip over and then remain at rest. I don't understand what causes that. When you apply the Right-Hand Rule or Flaming Left-hand Rule I prefer, the force induced is inward around the loop. How come it makes it flip over? I must be missing something deep here. What is the underlying concept that causes the wire to flip over? | 0 |
If I take a pair of classical particles with some energy interacting via Lennard-Jones potential, then the motion of the two particles will be in such a way that the distance oscillates around the equilibrium point (if the energy is not too high compared to barrier depth). If I consider a large number of Lennard Jones particles packed into a crystalline lattice, then intuitively I expect that each pair of particles should have a distance close to the equilibrium distance of the pair potential. In other words the "lattice constant" should be close to the equilibrium of the pair potential. But is it actually the case ? Can we consider a pair of neighbors in a Lennard-Jones lattice to be roughly an equilibrium of the pair potential with small corrections of further particles ? | 0 |
The situation: I'm trying to generate my resume with Latex, and get a pdf with all the text - no problems here. When I copy all of this text into a plain .txt file though, the formatting transforms all whitespaces (newlines etc.) into a single space, it seems. For example, lists are not vertically placed anymore, but placed sequentially. Does this maybe have something to do with how Latex files are built up (compiled) differently than ordinary text documents, causing it not to have any classical newlines characters, for example? In that case, would there be some way to insert those, allowing for a proper copy-and-paste functionality? I tried to make use of the pachage cmap, which assists with Unicode mapping, but could not get it to work. Anyone who knows a fix to this, possibly with cmap, or possibly another package? | 0 |
I'm working on performing a linear stability analysis on a system with fluid undergoing applied vibrations. Now, usually these systems are analyzed with no fluid velocity. Under these conditions, it can be shown that the system reduces to the form of a Mathieu equation (or a modified Mathieu equation in the case of viscous fluid). For Mathieu equations, it's known that there are discrete regions where the system response is either Harmonic or Subharmonic resonance, which is in line with the Faraday instability that's observed on the fluid interface. However, what happens when the system equations cannot be reduced to the form of Mathieu equations (for example, for complex fluids or fluids with flow)? Can the system allow resonance at frequencies outside of Harmonic and Subharmonic, or is there something more fundamental that says that these are the only allowable options? Should I also consider the possibility that the response might not even be periodic? Analysis procedure for inviscid Newtonian fluids Analysis procedure for viscous Newtonian fluids | 0 |
All explanations of jet propulsion that I've seen are formulated as "due to conservation of momentum, air with momentum coming out of one end means the rocket must gain momentum in the opposing direction". However it can't be the case that particles simply exiting some area with a momentum means all of a sudden something else must gain opposing momentum. If we had a straight pipe open on both ends, particles suddenly exiting one side (maybe a chemical exploding inside or the like) does not mean the pipe will all of a sudden start moving in the opposing direction. You need one side of the pipe to be closed in order for the pipe to move opposingly. Similarly it can't be the case that particles suddenly exiting an inflated balloon or rocket means the object must propel in the opposing direction due to some 'rule'. I'm assuming what is actually happening is a case of 'particle collision averages'. In the case of a balloon the air inside is constantly bouncing off the walls in all direction. So when I let go of an inflated balloon I have disturbed this average. There are now particles hitting a side of the balloon with no opposing force, as the particles opposing that wall are now simply exiting the balloon. Assuming my above formulation is correct, does this mean all statements regarding conservation of momentum are simply a rule of thumb for this above 'particle collisions average' explanation? | 0 |
I was trying to find some references for modelling the equations of motion of a simple dynamical system (say a pendulum on a moving mass) when I realized that the very vast majority of the material you find online or even in textbooks suffer from the following problems: Reference frame poorly defined, wildly assigned or even implicit. No idea which point is considered to be origin, which direction positive, etc. Free body diagram completely unprincipled and/or confusing. Confusion between magnitude of a vector (e.g., Force) and the vector itself (not mentioning switching back and forth) No general form for basic laws of motion. Sometimes when the authors apply Newton's second law, for instance, they are applying it implicitly along some dimension. Constants are stated and used without derivation or motivation, e.g., moment of inertia are mysterious constants that you would look up from a table And many more problems. Does there exist any textbook on modeling classical dynamical systems (pendulum, masses, multi-link robot) from scratch? | 0 |
While reading the Wikipedia article on infinite sets I found the following quote: A set is infinite if and only if for every natural number, the set has a subset whose cardinality is that natural number. If the axiom of choice holds, then a set is infinite if and only if it includes a countable infinite subset. This raised an interesting question; without AC, is it possible to have a set where, given any natural number, you can find a subset with cardinality great than that number, but not necessary one equal to it? For example a set where all definable subsets have even cardinality? Edit to clarify the question: are there sets that satisfy the intuitive meaning of infinat but not the definition as quoted above? FWIW, id be interested in both the case where "subsets larger than n exist" requires those subsets be finite and where they don't. (Though I suspect the second case is uninteresting as most of the interesting properties would be trivially true.) | 0 |
Let's say the origin is an equilibrium position for a particle. If we have a case such that a slight displacement of the particle in x direction makes it return to the mean position (stable equilibrium) and a slight displacement of the particle in y/z directions makes it go further away from the mean position (unstable equilibrium). The directions of displacement for which particle is in unstable equilibrium are more than directions of displacement for which particle is in stable equilibrium. I have seen this question but the answer didn't clearly state whether there will be an equilibrium type defined for that position or will that position have no type of equilibrium (and the comments on that answer about Unstable equilibrium "winning" over Stable equilibrium confused me even more). So what will we actually call the equilibrium type at the origin? Or will we just define its equilibrium associated with direction (like stable in x direction and such)? | 0 |
My understanding from popular science articles is that the boundary is a field theory that has no gravity and has one less spatial dimension than the bulk. However, I am not sure I understood this picture correctly. I just read a recent article at quanta magazine that states: "A solar system in the central anti-de Sitter region, for instance, can be described as a collection of particles scattered around the boundary that obey only quantum theory and have no sense of gravity or space-time at all". So my question is, did the quote mean no curved spacetime, or there is not even a minkowski spacetime associated with the physics in the boundary? I dont even understand how it is possible to have a quantum theory of particles without either space or time. | 0 |
I am trying to understand Turing's halting problem proof by applying the same paradox to a similar problem where, instead of determining if a given code will halt, you instead determine if it will return True or False (assuming it will always return eventually). Obviously such a machine can exist, as it is simply a standard compiler. However, when run through the paradox: We assume h is a function that determines if the return is True or False We construct a machine P around h in the following way: def P(i): return not h(i, i) P(P) As we can see, if P returns True then P returns False, and vice versa. Thus compilers cannot exist, as a compiler is an example of h. Can someone please help me find the error in reasoning? | 0 |
According to this and this answer, and as far as I understand these answers, dark matter halos cannot collapse to a black hole because, due to uncoupling from the EM field, they are unable to radiate their kinetic energy, and hence, getting closer to some gravitational center point also means that they get faster and so they resist further "collapse". But what about the motion perpendicular to the galactic plane? I would naively expect the dark matter to gravitationally fall down on the galactic plane on both its sides, until it concentrates there. Depending on whatever the type of dark matter may be, this may cause other forces (e.g. weak interaction) to take over (possibly at nuclear distances) or it may oscillate until it becomes spherical again. One way I imagine that this might happen is a small-scale alternating velocity variation in the dark matter field, so that dark matter is alternately falling to/moving away from the mid plane from location to location, and these regions simply pass by one another infinitely. If this alternating pattern in the velocity field exactly balances, the dark matter halo is able to maintain a spherical shape. But even the slightest imbalance might result in a global oscillatory motion between spherical and disc-like. Have the available observations been investigated with respect to these possible oscillations of the dark matter halos? And isn't it likely that such oscillatory motion (if it existed) would eventually stop due to second order dissipation (dark-matter to ordinary matter to radiation). | 0 |
I am working in an algorithm to order a bed of close-packed spheres. In the case where I have got four spheres, I understand that the fifth sphere position and radius is determined by the positions and radii of the four other spheres. It seems that there would be different solutions: one that produces a sphere that is similar in size to the other four, and a second solution in which the four spheres are encompassed in a bigger sphere. What interests me is the first solution. Any ideas what equation system solves this? The input data for the systems would be the positions of the original four sphere centres and their respective radii, and the output would be the position and radius of the fifth sphere. It is also important to notice that the four original spheres can but do not need to be tangent between them. Thanks a lot in advance! | 0 |
From what I understand, each particle has an energy called kinetic energy. When we consider a system of particles, in addition to their individual kinetic energy, there is an energy associated with the systems which depends on their relative configuration which we call the potential energy. Mathematically a system of particles can be analysed at the individual particle level by assuming that system of particles induces a field and associate potential energy for each particle and then sum up over particles to get the potential energy for the system of particles. So I thought that potential energy is some sort of energy associated with the field (which is a mathematical construct). But later I studied that fields are real and they have their own energy. So is the potential energy the same as field energy, if not how are they related? Additionally, just as the energy of a particle is decomposed as potential and kinetic energy, can we do the same for the field, i.e., potential field energy and kinetic field energy? If so, then how is the potential energy of the particle related to the potential energy of the field? Also, potential energy in my mind is related to the shape a system of particles takes. Changing shape releases or absorbs energy. Entropy is a concept which is also related to the structure/order of the system. So how does the entropy relate to the potential energy? | 0 |
Can we answer the question: "What are all the types?" i.e. can we recursively generate all the types in a given type theory according to a certain set of rules? Pardon for asking such a weird question. Question/personal background: I'm leaving this question intentionally vague with regards to what I mean by "type theory" because I guess I'm just interested in the status of this question for type theories in general. My background is pure math and I am comfortable with proofs in ZFC and FOL but I can't write a single line of code in any programming language. I hope to understandthe basics of using type theory for proof like Lean does, and started reading about type theory yesterday in preparation, although I've heard snippets about type theory in passing elsewhere. | 0 |
Let's say you're looking at your keyboard on your phone.. let's take the letter g. Light from g is going in every direction.. we know this because we can see g from all angles above the phone. So light from g is also hitting your eye where you would see all the other keys,screen and background objects however we don't see g in those areas.. just wherever g is located. What happened to the images of g everywhere else but where we see it? We should be seeing g in all places but something happened and we don't.. if you're getting what I'm saying I you should be as perplexed as I am.. also knowing this now think about how a camera can take a picture with light from all objects being scattered in all directions.. it shouldn't be able to take a picture like it does.. how on earth was it even made???? It shouldn't be able to work but it does!!! Does this prove something else about life? | 0 |
In the same vein/spirit as the UIPAC books for standardising systematic names and formulae of chemicals, the SI units for units of physical measurements, or the INN for generic drug names, have there been efforts to write every statement in mathematics (eg. axiom, postulate, result, theorem) in a standardised language? This standardised language might be a formal logic like those touched upon in mathematical logic textbooks or monographs, or it might simply be a set of standardised terms or statements in a natural language like English. (I'd like to emphasise that a standardisation effort need not necessarily be one in a formal language.) I'd like to know if there existed, or there exists currently, a consortium, an organisation, an initiative etc. like this.. I tried searching for this on google but couldn't find one so far... Ermm, do put aside the debate on whether such an effort is desirable or not.. I just like to know if there is/was such an effort, not whether it is a good/bad thing.. I've come across TPTP.org, but not sure if this is the largest/most well-known/most followed/most active effort so far in mathematics.. Do let me know if there's any better.. | 0 |
In google translate, the word "bizarre" means "very strange or unusual, especially so as to cause interest or amusement.". But I believe that this description is more suited for "eccentric". For example, the character of Jack Sparrow from Pirates of the Caribbean is eccentric. On the other hand, AI chat GPT says that "bizarre" usually means something odd and unsettling. And I have seen people make use of the word "bizarre" for criticizing something, rather than an expression of fascination. In Meriam-Webster site, "bizarre" means odd or eccentric in stye. This means "bizarre" and "eccentric" share the same meaning? But "Jack Sparrow is such a bizarre person" and "Jack Sparrow is such an eccentric person" don't seem to resonate. I got different vibes from them. Or is it just my feeling? Both means "unconventional"? What are their subtle differences, and can I have one example for each that would enlighten me about their differences? | 0 |
Almost every text on Category theory uses categories such as Ab, Grp, and so on as examples to work with but can category theoretic methods actually help us understand the structures better? In particular, does Category Theory aid us in proving some significant abstract algebraic results that are otherwise tedious to prove? Furthermore, is there any structural insight about abstract algebraic objects that is not readily apparent from algebra itself but becomes crystal clear with a category theoretic approach? I do not have a specific format for the answer in mind. As category theory is quite general, the answer may also include ways to say use results from other branches such as analysis or topology, so as to prove an abstract algebraic result which was tedious to prove using an algebraic approach. In this light, any insight about the relationship between category theory and abstract algebra is welcome. | 0 |
I find it amusing why the infimum norm or supremum norm defined on function spaces work actually? It's difficult for me to reach to an intuition where I would see the infimum or supremum as a natural way to represent distance between two functions. Is there any intuition which can motivate the norms defined on function spaces ? How do we make sure that two functions having the same infimum or supremum don't deviate too much from each other and that the function which is a limit under such a norm satisfies the properties the functions in the sequence have ? What is the norm measuring in function spaces I went thorugh the above question but could not find an intuitive way to address the last question in the first paragraph of my post . Disclaimer : I am not a pure maths student , please pardon my immaturities . I was just trying to find an intuition here. | 0 |
Im working on a nonlinear control based on Lyapunov theory and its working really well. I am able to implement it on a dynamical model of the system in simulink. However I think it has a really big limitation and that is: I cant guarantee that the real system will have the exact parameters that I am modelling. I want to make my lyapunov controller into a more robust controller by adding parameter estimation too it. I see some texts based around system identification, but I do not need to go that deep, I know what the system looks like. I just need some kind of method to zero in on the drift between my modelled and real components. Is this possible? I am controlling an DC to AC power converter. Physical System model: Model: Controller: | 0 |
Often metaphors are likenesses where there's a direct connection. For example on the news somebody describes a crash/ earthquake/ explosion as It was like a bomb going off. What about where the two things are not similar. Her painted toe-nails were an explosion of colour. (Exploding feet anyone!) This poem Cherry Ripe by Thomas Campion is full of insinuations rather than direct likenesses. There is a garden in her face Where roses and white lilies blow; A heavenly paradise is that place, Wherein all pleasant fruits do flow: There cherries grow which none may buy Till 'Cherry-ripe' themselves do cry. Those cherries fairly do enclose Of orient pearl a double row, Which when her lovely laughter shows, They look like rose-buds fill'd with snow; Yet them nor peer nor prince can buy Till 'Cherry-ripe' themselves do cry. Her eyes like angels watch them still; Her brows like bended bows do stand, Threat'ning with piercing frowns to kill All that attempt with eye or hand Those sacred cherries to come nigh, Till 'Cherry-ripe' themselves do cry. My question is: Are there technical terms that distinguish between: (a) Direct likeness. eg sky-blue eyes (b) Not really like at all. eg eyes like angels (c) Over-arching 'big metaphor'. eg garden in her face | 0 |
I am using TeXstudio with LaTex on Windows I also know about Git. In fact, I use Git to collaborate on RStudio but on TeXstudio I cannot. While typing on TeXstudio on my own without collaboration, I had my first problem saving different versions of .txt files on the same project, which sometimes confuses me. When I was writing my PhD thesis, I would send the PDF to my professor, which he could not edit. How do I solve these two problems? WHAT I WANT I have read different posts on reproducibility on TeXstudio, but I cannot figure out my foot on any. I want a step-by-step guide on achieving reproducibility and collaboration on TeXstudio using Git. I want to be able to revert to my previous changes without saving multiple documents. | 0 |
Goldblatt gives a brief overview of adjunctions in his "Topoi", and one of the exercises asks to characterise the partial arrow classifier in terms of some universal arrow. Well, I gave it some thought, and I'm not even sure where to go from there. The main problem I have is that in the "there exists" part I have only one arrow (the PAC itself), and in the "such that for every" part I'm given two arrows (the "top-left" components of the PAC pullback), and I'm just not sure how to construct a category and a functor into/from it that'd allow for both. I tried something along the lines of the diagonalization functor used for (co)products derivation via adjoints, but it didn't get me far (or anywhere, frankly). So, how would I do that? Again, my exposition to adjoints is limited to several pages of "Topoi", so I likely miss some otherwise well-known results. | 0 |
In statistical thermodynamics we can prove that the evolution of a system minimises some potential with units of energy (e.g. energy). This can be done purely statistically, by using the first two laws of thermodynamics, and showing that the state where the appropriate potential is minimised is the most likely one. Therefore, minimisation of energy is just an argument about entropy. Is there a similar (or any other) proof of the principle of least or stationary action? I have seen it referred to as an axiom, but is there at least a possibility that there exists an underlying theory from which it can be derived? Can it be shown that systems where action is stationary are the most likely ones? Also, it is interesting that the Lagrangian has units of energy as well. Edit: To clarify on the first paragraph. I was referring to quasistatic systems that satisfy a sepcific set of conditions. Energy is minimised in the stable state of an isolated system (where entropy, volume, and the number of particles is conserved). For a system where the temperature, pressure, and the number of particles are constant, the Gibbs free energy is minimised etc. | 0 |
I am at a loss to understand the justification behind the following statement being false and would appreciate someone explaining what this particular argument is saying: The set of all finite subsets of a countably infinite set is uncountable. Answer: False. Any countable set has a bijection with the naturals, and one can list the subsets in order of the sum of their values. Every finite subset has a finite sum and therefore will appear in the listing. I am not sure how this argument proves the falsehood of this statement, or what the process of its logic is. Do we not have to say something about how different subsets will have the same sums? I would appreciate a more formal version of the above argument so I could understand what point it is making. | 0 |
In common parlance, we say "s/he pretends s/he doesn't understand", for people who ignore the context of the conversation and require hyper-specific definitions to keep the conversation going. (hyper-simplified) example of the above, in the form of a dialogue: Q: Hey, how's your day? A: In what sense? Q: Uh, let's say for the sake of argument, how's work? A: What do you mean by that? In terms of what? Q: What are you up to? A: I do lot's of stuff, you have to be more specific - is there something in particular you're interested in? Q: Nope just in general, are you enjoying it? A: Sorry I don't understand, define "enjoying it" in the context of work and so on... Is there a term for what the person (A) is doing? | 0 |
Based on the double slit experiment we know that in the case of a single particle system the wave function or state vector of position is in a superposition of possibilities before measurement. But does this rule apply in the case of the vacuum state? Is it in a superposition of (non degenerate energy) possibilities before measurement? A physicist has replied to this question, in a personal correspondence, by noting that: It is thought that in quantum field theory, different vacuum states are essentially classical, and don't get superposed quantum mechanically. The reason is their effectively infinite spatial extent, so the distinct vacuum configurations are mathematically very distant. Yet I am not well convinced by his answer. Isn't a quantum state, either a single particle or a vacumm, a nonlocal object in the Hilbert space and independent of physical space? So why the vacuum state is an exception from the general rule of quantum theory that applies to position or momentum quantum state? Why being "mathematically distant" rules out being "superposed" in the case of vacuum. This is not trivial to me. Is there a theorem about this? Should we suppose that there are multiple Hilbert spaces and therefore in a single Hilbert space there is only one quantum state for vacuum? and "by mathematically very distant" we need to consider another Hilbert space with its own vacuum state? | 0 |
I have the following books about QFT: Peskin-Schroeder Lancaster-Blundell Iliopoulos-Tomaras I would like to know if there is a QFT that is as concise as Dirac's book about general Relativity. What I found useful about Dirac's book was that it developed most mathematical machinery "from scratch" with very little comments. I would like a "quick reference" QFT book that allows one to study the matter from a more mathematical perspective, rather than using a lot of physical analogies as in the books I have read. As an example, I would like to see "This is the QED Lagrangian. Those are the consequences", but a more classical, experiment driven approach is appreciated if it is strictly functional to the development of the theory and if it is kept as concise as possible. Ideally the book should be: More or less "self-contained", allowing a student with all prerequisites to learn introductory QFT from scratch (at least to renormalization) As concise as possible (ideally also in the number of pages) I would also like lecture notes or papers, it does not have to be a book. | 0 |
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