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I often come across materials discussing convergence spaces and their relevance in various contexts. It's commonly mentioned that the existence of a natural convergence on the space of continuous functions (turning them into exponential objects) makes the category of these spaces a suitable environment for studying homotopy. However, I've found only a limited number of resources that actually delve into this idea (mainly this and this). As someone who doesn't engage with algebraic topology on a daily basis, this leaves me with a few questions. Are there any works that effectively highlight the significance of these spaces for the typical algebraic topologist? If not, could the issue possibly be attributed to an "excessive" use of filter-related terminology? I would greatly appreciate any insights or references that could shed light on this matter. | 0 |
Say we're drawing marbles from a box. The marbles can be labeled X, Y, or Z and can be either black, brown, or white. The probability of drawing a marble with each letter label is unknown but fixed and marbles are replaced after each draw. A marble labeled X is half as likely to be brown as the other colors. A marble labeled Y is half as likely to be black as the other colors. A marble labeled Z is half as likely to be white as the other colors. Say on our twentieth draw from the box you see a black Y for the first time. Question I came up with: What is the best estimate for the probability of drawing a marble labeled Y from the box? | 0 |
In the "talk" tab for Wikipedia Heat Engine article, someone is questioning whether an internal combustion engine can be modeled as a heat engine - and therefore is limited or is not limited by Carnot efficiency. The arguments are that the input is chemical energy, not heat. And also that IC engines dont operate on a closed cycle. Fresh air enters and is expelled each cycle. There are some answers there as well, but I'd like to get input from you guys to settle this matter once and for all! Is it ok to model IC engines as heat engines? And in a wider sence; can you model a solar cell as a heat engine and calculate carnot efficiency with T_c being the air temperature, and T_h being temperature of the sun. (I saw this in a textbook once, I believe.) https://en.wikipedia.org/wiki/Talk:Heat_engine (section headline: "Internal combustion engines can't be considered heat engines") | 0 |
If I were sorting, for example, audio recordings based upon the performer, then "Vince Guaraldi" and "Bob Seger" would be sorted as "Guaraldi, Vince" and "Seger, Bob" On the other hand it's not immediately clear to me how I should sort a recording by "Vince Guaraldi Trio" or "Bob Seger & The Silver Bullet Band." My instinct is that this is now an entire proper name for a group and shouldn't be split up (just like I wouldn't sort things under "Zeppelin, Led"), but in both cases the group name is created to highlight the most famous member. Both of my print style-guides are silent on this; the MusicBrainz style guide, is clear that e.g. "Guaraldi, Vince, Trio" is correct, but I'm not sure if that's just a quirk of a single site, or if it is something more universally done. | 0 |
I am thinking about the following question: when I look at the atomic emission spectrum of a specific element and I am only interested in the visible section of this spectrum and the method of retrieving it is via putting the element inside a flame, does the type of the flame in any significant way impact the observed spectrum? For example, does it matter wheter I excite lithium with a standard propane flame or instead a hydrogen or acetylene flame? I am trying to find ressources on this online but so far I haven't found any spectrum of any element that was measured using anything else than "the flame method" which I suspect refers to using propane gas (or other falmes with less known composition) as the exciting medium. I was tasked to find such spectra measured using different types of flames but since I couldn't find anything on this I am wondering if this question makes sense in the first place. | 0 |
Suppose we have a loop of copper wire moving perpendicularly through a constant finite rectangular magnetic field directed into the screen . When the loop enters the field, the induced current would be counter-clockwise and when it leaves the field the induced current would be clockwise according to Lenz's law if we view the loop moving through the field from above. But the question here is that when the loop is moving through the middle of the field where it is neither entering nor leaving the field, can we say that the magnetic flux is changing and thus producing an induced current in the loop? The field is constant throughout, so will the change in flux be zero? But if not, how can we tell in which direction the current will be flowing? How could Lenz's law be applied to such a case? | 0 |
I'm studying about electric field and referring to an article about electric field in wikipedia And in here, there are some doubtful sentences: The electric field is defined as a vector field that associates to each point in space the electrostatic (Coulomb) force per unit of charge exerted on an infinitesimal positive test charge at rest at that point First, in this sentence, i'm doubtful about 'electrostatic force'. As i know, moving charges also make electric field. This implies there are two kinds of electric fields: electrostatic fields and fields arising from time-varying magnetic fields. And i think, in here, there is electric field which is not belonging to 'electrostatic field and field time-varying magnetic fields'. For example, steady current, not in wire, makes electric field but don't make time varying magnetic field.. Is there something I'm thinking wrong? I think above sentences are uncomplete | 0 |
In the vacuum state, particles and antiparticles can spontaneously emerge as virtual pairs due to the uncertainty principle. These virtual particles have a brief existence before they annihilate each other. This process is a manifestation of vacuum fluctuations. Similarly, in particle interactions, intermediate states involve virtual particles that can exist for a short time before contributing to the overall interaction process. These virtual particles mediate the exchange of momentum and energy between the initial and final states of the particles involved. If the intermediate state is represented by virtual particles, should we distinguish the actual physical process of the in-between, intermediate state from the vacuum state? Are intermediate states just mathematical constructs only useful for calculating; or they have a physical significance within the framework of quantum field theory? We cannot think of the intermediate state as the vacuum state despite having the same description involving virtual particles that cannot be observed due to their brief existence? | 0 |
I am what most of the world considers a "non-native" speaker of English. I, however, consider myself a "native" speaker of English because: I grew up speaking English since birth, English is the language that I am most fluent at, I have never formally studied English, I just picked it up as a child as the first language that I acquired. Recently, a "non-native" friend of mine asked me whether it is "a helicopter" or , "an helicopter", and I realised that I would personally say "a helicopter" when the stress in the sentence was on the noun helicopter, but when the stress was elsewhere, I would say "an helicopter". Is this correct in the main standard dialects of English or is this some bad habit I have picked up? | 0 |
In all of the treatments of elementary Euclidean geometry which I've seen so far, the section about triangle congruences introduces S.A.S. criterion as the basic postulate from which A.S.A. and S.S.S. criteria are deduced. I remember reading somewhere that one could choose any one of these three as "the congruence postulate" and deduce others from it. I am able to produce proofs for S.A.S. by taking A.S.A. as an axiom and vice versa, but S.S.S. seems to be the "odd" one since I cannot reach either S.A.S. or A.S.A. by taking it as the axiom. I was unable to find anything online that shows such a proof so my question is whether the premise that any one of these three criteria can be picked as the axiom is true or not. If it is, how can we prove, for example, S.A.S. through S.S.S.? | 0 |
How would little, native English speaking kids say "Tell me a story about the bear!"? In my language, they might say something like "Tell me the bear!". Does "Tell me the bear!" sounds like a valid "little English" question from a little kid who is catching up the language? Context: Each language has different logic, and the kids build up the logic differently. I am very much curious about how young kids in native English environment build up the logic of the English language. For example, in my language, they might say something like "Tell me the bear!" instead of "Tell me the story about the bear!" Do English-speaking kids make similar mistakes, like saying "Tell me the bear"? What are the common mistakes they make in this context? | 0 |
I hope this question hasn't already been asked, but I looked and couldn't find a question with a similar title. It is my understanding that Maxwell's equations and the Lorentz force law form the foundation of classical electromagnetism. These are fundamental because (in the classical limit) they are always obeyed, in contrast to Ohm's law, which is still a valid empirical law, but is restricted to a specific scope. As I understand them (correct me if I have made a mistake), these describe basic assumptions used to create a model of electromagnetism: the net outflow of electric field lines through a closed surface is proportional to the amount of and polarity of the charge inside the net outflow of magnetic field lines through a closed surface is zero a magnetic field that changes with time will create a circulating electric field an electric field that changes with time will create a circulating magnetic field, taking into account the polarization current the electromagnetic force on a charged particle depends both on the electric field and the magnetic field I've encountered some equations pertaining to phenomena described by QED, but I was wondering if there is a set of fundamental equations like Maxwell's equations and the Lorentz force law that describe all of the core requirements for accurate predictions in its model. In other words, can I summarize QED the same way as I have done above for classical electromagnetism? | 0 |
I am currently reading "No-Nonsense Quantum Field Theory" by Jakob Schwichtenberg and in several derivations in the book it'll pull a partial derivative operator out of an integral, or change the order of full and partial derivatives on a function, etc. without explanation. So my question is: Are the differential and integral operators commutative? Is this always true? And if not, what are the conditions for it? Furthermore, in the more general sense of abstract algebra, if/when are unary operators commutative? A proof to accompany a given answer would be much appreciated, or at least the citation of one which is free and public. It's certainly intuitive that this is true, at least in the special case of the calculus and physics in this book, but I'm not sure why it is in a more fundamental, mathematical sense and I'm also curious about the general case of all unary operators. This is the kind of thing I would love to try to solve and research on my own but I simply don't have the time right now and I'm having trouble finding a straightforward answer online, so any help would be greatly appreciated. Thank you! | 0 |
I would like to learn Mathematics for understanding GR, Differential Geometry, Riemannian Geometry and related research papers rigorously. I would like to carve out a clear path to understand these topics by listing out all the necessary prerequisites. I have undergrad Math under my belt such as: Real Analysis, Algebra, Topology and ODEs. I am missing intro to PDEs at this point. I have also created a diagram of the prerequisites in which each bubble represents a subject along with textbooks written in blue. Please take a look at the attached image/file. UG means "Undergrad" in the diagram. Specifically, I need help with the following questions: Is my goal (the center bubble) well defined? I know it may not be specific enough yet, but I have tried to list down some topics I am interested in RED color. Have I listed all the subjects? Am I missing any subject? Is Lie Groups worthy of mention here? Or, would it just fit under Algebra? Is Hyperbolic Geometry worthy of mention here? Is it relevant? How do I learn it? Any textbooks for it? Would anyone please help me break down the following subjects into specific topics that are necessary for my goal: Manifolds, Riemannian Geometry, Real Analysis (grad version), PDEs (grad version), Algebra (grad version). | 0 |
I was explaining the tidal locking phenomenon to a friend. First I started with the formation of solar system and how at the beginning the planets were actually like balls of magma-esque rocks. And then how the force of gravity would eventually affect their shape and mass distribution and consequently, moment of inertia. But I myself wasn't satisfied with this abstract argument and tried to come up with a more intuitive one. So I said: imagine a fresh egg. Its yolk is at its center (almost) and the mass is evenly distributed. Then after a few days, the earth's gravity pulls the yolk down and moves it closer to the shell. This changes its moment of inertia. But I didn't know how to continue and pull a tidal locking explanation out of this. So I said never mind!! There are large-scale forces and objects involved in tidal locking that I cannot scale them down to something more accessible and easier to demonstrate. Now this has gotten on my nerves. I thought a lot about it and also searched [fruitlessly] quite a lot to find an intuitive, accessible way to understand this phenomenon. We may not be able to demonstrate the effect of gravity on a small scale, but can we use another force that behaves like gravity (e.g. static electricity) to design an experiment for tidal locking? | 0 |
I've recently started using Texmaker to edit on my LaTeX documents (up to now, I mostly used Overleaf or TeXworks), so I am still new to this program's shortcuts. I have been looking for a shortcut in specific that I can't seem to find, and I would like to know whether this is something this specific LaTeX editor has. I am working on a lengthy file that has several chapters saved as separate .tex documents, which are all called by a single main.tex document. As such, any time I want to edit a specific part of the compiled .pdf file, I need to know in which line of which of my subfiles that specific part of the document was encoded - which is always a bit annoying to find. In Overleaf, this is made simple, since double-clicking on the corresponding line of the .pdf I wanted to edit would link me to the corresponding code line in the document. Does Texmaker also support a similar shortcut? And if so, what is it? | 0 |
This is a question that a high school student asked me and I couldn't give him a satisfactory answer. He started by saying that An object appears red because the energy corresponding to a "red" (don't take it literally) photon isn't equal to that of the energy gap of the elctronic energy levels of the object. And now if I take the same object in complete dark and shine a red laser from above why don't I see a red beam coming out from the bottom surface the object ? My first reponse was that 'since the object is opaque it reflects most of the red light falling on it' but he wasn't convinced and I think that he is basically trying to ask what causes an object to be more reflective than refractive from the atomic point of view . Can someone help me with this ? | 0 |
I would like to find the distance function for a curve comprised of all points within a lune that are of equal perpendicular distance to both circular arcs. In other words, what's the minimum distance by which a given point inside of the lune would need to move in order to become equidistant to both arcs? My use case would require both arcs to be of equal radius, if this helps. Constructing a signed distance function for the lune itself is fairly straightforward, but this particular problem seems considerably harder. I've been mulling over it for a few days without any real idea of how to approach it. Can anyone point me in the right direction? Edit For clarity, the curve marked in red is what I would like to find the distance function of: | 0 |
I am searching for a book on group theory that follows in the style of textbooks written for math students (since I was one), but that covers all (or at least most) topics that would be needed in physics, such as in QFT for example (Think of the topics in Zee's Group theory in a nutshell). My problem with Zee is that it is too verbose and not as mathematically rigorous as I'd prefer (I can understand the concepts better when they are presented in a formal mathematical way). And my problem with other standard group theory books for math is that they usually do not cover all the topics needed for physics (Lie Algebras, Poincare groups...) A single or many-book-combination recommendation that would fill in these criteria is welcome. | 0 |
Please correct me if I am wrong. Electron is fundamental and is zero dimensional (probably made up of strings). Electron is bound to the nucleus. Electron in an atom has velocity and position which are statistically distributed. Electron mainly interacts electromagnetically. Temperature is the measure of statistical kinetic energy of particles. In the nucleus of an atom, proton and neutron have temperature because they are a bag bound by color forces , valence quarks and a sea of quarks and anti-quarks. Quarks interact electromagnetically. Saying that protons and neutrons have temperature means that there is a randomness in the kinetic energy of the constituents of proton and neutrons. Electrons are bound to the constituents of protons and neutrons through electromagnetic force. Therefore if there is randomness in the kinetic energy of the constituents of protons and neutrons then the electrons must be experiencing wobblyness in its orbit, that is , it must be experiencing some kind of little randomness in its motion around nucleus. And therefore the electron must have a little temperature in the atom. My question is : Does the electron have a temperature in the atom? | 0 |
I am a veteran of the wars in Iraq and Afghanistan. When talking about the people opposing us, I have always referred to them as the "enemy." Now, as I get a little older, and a little more aware (specifically, as I became a determinist), I have lost any hostility I feel towards them, and I feel that calling them the "enemy" demonizes them in a way I no longer wish to do. So, I was hoping there was some neutral term applied to enemy combatants, even if it's historical or in another language. I think opponent comes close, but it's not quite there. I was hoping there was a word like "interlocutor" meant for combatants of war. I have checked the OED (paywall, I think, I get it through my library), and the words I think that come closest are two obsolete words "contrary" and "adverse." (obviously those words are still in use today, just not in the noun sense of a contrary or adverse being someone who opposes you). Does anyone else have any better matches? One note, some may suggest I call them by the name they go by, such as the Taliban. The problem is that the Taliban is one of dozens of different groups of fighters and we rarely knew who belonged to which. So, I was hoping for a neutral term I could apply to all of them. | 0 |
I recently received a newsletter from an entity I previously thought to be credible which is embarking on a brand/campaign around the concept of ambition which makes me wonder if my understanding of the word is "off". Can the following be examples of Ambition? Starting a new hobby. Getting out for a walk on the beach. I would have thought that while the above are goals/things a person may strive for - they are not ambitions because they are not substantive enough to qualify as an ambition. Similarly I see an ambition is a goal you strive to reach, while the "Ambition" campaign in question is about the journey (and indeed with no expectation of completing the journey) In other words I think "Planting a new garden" would qualify, but "Planting some plants in my garden" would not, or "Completing a marathon" would qualify, but "getting out for a walk on the beach wouldn't". Do I misunderstand the meaning of the word? | 0 |
I got a bit confused about independent clauses,so I decided to ask ChatGpt, which has given me three different answers for the same sentence I think he is getting too old, suffering from Alzheimer's disease. The sentence is: I bring a natural positivity and a can-do attitude, allowing me to effectively solve challenging problems even under pressure. Here are my questions about that : First of all "allowing me to effectively solve challenging problems even under" is that a gerund clause functions as an adjective for the main clause describe it Now regarding the clause I have two possible analyses The first one is that: "allowing me to effectively" is a gerund phrase that acts as a subject. "solve" is the main verb. "challenging problems" is the direct object. "even under pressure" is a prepositional phrase that acts as an adverb The second one would be: . "allowing me" is a gerund phrase to start the caluse "to effectively solve" is an infinitive phrase "challenging problems" is the direct object to solve "even under pressure" is a prepositional phrase that acts as an adverb Does anyone have a clue which analysis is right and why? | 0 |
I was reading a paper on black-hole information loss and it mentioned backreaction. I had never heard the word before so I googled it and was surprised to find no cohesive definition that I could understand. The best I found was this wikipedia article which gives a definition akin to "a backreaction is a field that is often used to calculate forces in quantum systems." However, it gave no strict definition or real physical justification. I was wondering if someone who understood the topic could explain them to me better, because right now they seem to me to be more like quantum epicycles than anything. P.S. I also found this article talking about back-action in quantum measurement which used the term back-reaction once. I could't quite figure out precisely how they were related though. | 0 |
I am currently studying Linear Algebra Done Right (LADR) by Sheldon Axler and also How to prove it by Daniel Velleman. Currently I am in the chapter of Bases in LADR and I already read the chapter on equivalence relations in How to prove it. I tend to be somebody who looks for analogous things and something that I wanted to verify was whether there is a resemblance of Vector Subspaces and Equivalence Relations: Can one think of subspaces being equivalence classes? What I would suggest would be to say that vectors in a subspace form an equivalence class if they can be written as a linear combination of the basis vectors of that subspace. Moreover, there is a theorem which says: Every subspace of V is part of a direct sum equal to V. Wouldn't then the vector subspaces be analogous to a partition? Am I thinking along the right lines? Doesn't that mean that there is a sort of universal structure of mathematical topics? | 0 |
A common construct for comparison (making parallels) is "the X of A is similar to that of B". Quoting an example here ... the animals' situation is similar to that of the plants. which is equivalent to the situation of the animals is similar to that (i.e. the situation) of the plants. I often wondered whether this construct can be extended to make parallels in more complex scenarios, where one needs to compare or contrast two relationships (between two pairs of objects). A contrived example is as follows: "The difference between werewolfs and vampires is similar to that (i.e. the difference) between wolfs and bats." Here, what I am trying to compare are two relations: the one between werewolfs and vampires and the one between wolfs and bats. As the two relations are each between a pair of objects, should one say "... is similar to that between X and Y"? If not, what is the proper way to express such comparisons/parallels? (I thought about using such patterns from time to time, but haven't seen it used. Hence the question here.) | 0 |
I have the following diffraction pattern produced by a fabry-perot etalon The red represents the center of that pattern. Taking the mean intensity of the pattern as a function of the radius from the red dot and applying a cut-off radius results in This clearly shows a superposition of at least two diffraction patterns. Is there any way to automatically decompose the patterns? I originally tried Fourier analysis but that resulted in a complete mess as the peaks appear to be Gaussian, not sine functions. I can fit Gaussian to all the individual peaks. But then my question is if there is an algorithm or method that would allow me to determine which gaussian belongs to which diffraction pattern. I have quite a few more diffraction patterns some of which are more complicated and I wanted to see if there is a way to automate this? | 0 |
Two up quarks in a proton lead to an imbalance, which results in the proton having the ability to attract electrons. Two down quarks in a neutron lead to balance in the electromagnetic force, leading to no interactions happening with electrons. The strong force and electromagnetic force appear to be directly related. Unless I am misunderstanding something, it appears that a particular arrangement of quarks leads to a specific kind of baryon that has a specific kind of electromagnetic behavior - meaning the strong force is indirectly leading to the behavior of the electromagnetic force. I don't understand why the electromagnetic force is considered to be a separate force than the strong force for the following reasons: Quarks clump together to form baryons due to the strong force, not the electromagnetic force. I understand that quarks have electromagnetic charges, but I don't understand whether the cause for this is due to it "fitting into the math" or it actually being a fundamental property of the quarks. I understand that the strong force overpowers the electromagnetic force, but how do we know for certain that quarks even have charges? Any insights or references would be greatly appreciated! Thanks for reading. So, my question is: why is the electromagnetic force considered separate than the strong force? | 0 |
I am trying to simulate the reflection of a sound ray, that goes from a sound source, bounces off a wall, and is received by a microphone. The wall has a an absorption coefficient, and a specular reflection coefficient, both of which vary by frequency. Thus, the sound reflected by the wall specularly can be characterized by a certain frequency response curve. LTI filters are characterized by a frequency response and a phase response. Thus, we can treat the contribution of the wall's specular reflection as a LTI filter (applied to the source signal) if we know the correct phase response. The reflection path (shown in red above) corresponds to a time delay proportional to the length of the path. If we assume a constant time delay across the frequency spectrum we get a linear-phase filter, that is symmetric about the time-delay corresponding to the reflection path length. However, this filter clearly has "anti-causal" components: the filter is nonzero before the red line. Thus, the filter begins to have an effect on the signal before the length of the reflection path would suggest that it should. It seems that either the assumption of constant time delay across the frequency spectrum must be wrong then? If so, I wonder what the correct phase response of the filter is. | 0 |
I have a couple questions on the mechanism for how solar projection through a telescope works: I recently took a small telescope focused at infinity, aimed it at the sun, and held a sheet of paper behind the eyepiece. It projected a focused image of the sun onto the paper. When I changed the focus away from infinity in either direction, the picture became less focused. I'm confused as to why this works since I always thought a focused telescope produces a virtual image that can never be projected onto a screen (and your eye turns it back into a real image for your retina). How can one focus setting for the telescope make an image that your eye can see and that can also be projected onto a paper? If the image coming out of a telescope can be projected onto a paper, I assume it is a real image. However, I find that no matter how far or close I move the paper, the image remains in focus. I always thought that a real image is projected onto a single focal plane at a fixed distance from the lens, so how does this work? Any help would be greatly appreciated. | 0 |
Suppose we have two bodies at different temperatures, and we let them interact thermally in such a way that the process is not quasistatic (e.g. two different metal spheres touching). Do we arrive at the same final temperature as if the same spheres had equilibrated via a quasistatic process? If so then, rigorously, why? Of course I expect the answer to be yes but I can't convince myself of why in the context of thermodynamic theory. Edit: I think I see that since I can establish that in a final equilibrium, they have equal temperatures, then I can imagine a quasistatic process taking them to this final state? It seems thus that in the case of non-quasistatic heat transfer, ceteris paribus, we have the same entropy change as for the corresponding quasistatic heat transfer? | 0 |
Clarification: the word "important" is ambiguous. Here, I use "important" to mean that we want to know the value of a quantity accurately. For many optimisation problems, it looks as if we are more interested in finding the minimum value, rather than finding the argmin. For instance, in machine learning models, we care about how well the model can predict, and we do not care about the internal argmin inside the black box that makes this possible. For a linear programming problem, say, for an airport, we do not really care about the exact way to schedule flights to get the maximum efficiency. We just want to come up with a plan which can be completely different from the optimal one, but have similar efficiency in terms of saving time. This is due to the existence of many equally good solutions. Note: one might argue that we do need to know a solution. Of course we do. But we don't care which solution we get, as long as it is a good solution. So it is unimportant to know the solution itself accurately; only the objective value is important. Nevertheless, argmin is discussed a lot in literature (like parameter estimation in statistics). However, I have not seen anywhere why this is useful. Could anyone give an example application where the argmin is more important than the min? | 0 |
Some English nouns are identical to their verbs (and their adjectives) both in spelling and pronunciation, for example: "This is fake"; "to fake"; "this is a fake" "To tear"; "a tear" "To parody"; "a parody" "A misfire"; "to misfire" There are some examples where the (disyllabic) noun is spelt exactly like its verb but the noun is pronounced with the opposite stress (at least, in the standard accents which I hear day-to-day in the UK), for example: "An escort"; "to escort" "My recall of the event is faulty"; "I cannot recall what happened" "To repeat"; "a repeat" (this last one is a bit weak since people use either stress pattern in different contexts) This phenomenon is observed with some verb-adjective pairs too: "To perfect"; "this is perfect" In all three cases, I would be interested in: The corresponding formal linguistic term (if there is one) Examples! Although I know there are plenty more than I've shown here, they elude me. What's worse is that there's a fair few I've thought of but can no longer recall. Bonus: are there any examples of noun-adjective pairs that are pronounced with opposite stress? | 0 |
Imagine a situation where I'm moving at the same velocity as the electrons in a conducting wire. In this scenario, from my frame of reference, the electrons appear to be stationary and thus there is no current from my POV. Now, for a brief moment, these "stationary" electrons come into contact with (or pass right next to) a light bulb in the vacuum of space and closes the circuit for a brief moment, causing it to illuminate, and then we all continue moving together. (water this down as much as possible to reach "spherical cows in a vaccuum" state for the purposes of this problem) Question: From my perspective, the light bulb lights up even though the electrons (which I observe as stationary) aren't "flowing" in the traditional sense. How is this phenomenon explained? Would I effectively be seeing a light bulb illuminating without any observable current thus creating something out of thin air (obviously no). Or rather, what do i have to "give up" for the laws of physics to be consistent. | 0 |
I am trying to check if my understanding is correct. This is not really a question but a request for validation. I hope this is allowed. When painting with a heat reflective paint there are two options A- The room does not contain a significant heat source. This will always lead to a reduction in ambient temperature as heat from the outside is not allowed in. Heat by convection and conduction will still penetrate but overall the energy transfer will decrease. B- The room contains a heat source emitting IR rays. The rays will keep bouncing over the painted walls until it is absorbed by the air or the body of the heat source itself. Depending on the ratio between the external and internal IR sources, a IR reflective paint can lead to either increase or decrease of ambient temperature | 0 |
In algebraic number theory, we would like to study rings of algebraic integers but sometimes they are not PIDs and thus they don't possess good properties. Because of this, we have introduced the notion of Dedekind domains, in which rings of algebraic integer are included and one can study the nice properties of Dedekind domains to understand algebraic integers. While doing algebraic geometry and commutative algebra, I have encountered polynomial rings in several variables, whose properties are quite different from polynomial rings in one variable, as the former ones are just UFDs while the latter one is a PID. So this "degeneracy" of polynomial rings from PID to UFDs reminds me of the similar case of rings of algebraic integers but I don't think they are related since the dimension of polynomial rings depends on the number of variables , which does not fit the definition of Dedekind domains.But I wonder if there is a way to classify polynomial rings of several variables(especially those over an algebraically closed field) into a specific type of rings, such that this type of rings has nice properties just like Dedekind domains and from which one can classify the prime ideals as well as determine the irreducibility of polynomials easily? | 0 |
I came across a question a while back. It stated that a oil droplet was suspended vertically within an electric field. The man who suspended it had left to eat a very LONG lunch, and came back to see that it was splattered on the top plate (nothing with the setup had changed), and the question asked us to state a physical reason for such an event. I thought it was because of a transfer of momentum from electrons moving from the negative plate on the bottom to the positive plate on top, which just so happened to collide with the oil droplet. Someone else answered saying that the droplet evaporated slightly, which caused it's mass to decrease and so the force acting upon it managed to accelerate it more than that of gravity, causing it to move upwards slowly. That was the correct solution, but I'm just a bit confused, since wouldn't it lose some charge when it evaporates as well? So overall the q/m ratio would still be the same? They said it was unlikely that it evaporated some of its charge, so I'm just wondering how the charge within an object is distributed. Is it distributed evenly throughout, or is it more concentrated in some areas? | 0 |
I have learned some basic measure theory as covered in the first chapter of Durrett's Probability: Theory and Examples, which includes the construction of Lebesgue integral (from simple functions to bounded to positive to integrable ones), as well as some basic properties such as Fatou's Lemma, monotone convergence theorem, dominated convergence theorem, the Fubini theorem, etc. I will be officially taking Real Analysis (measure theory), next year. However, as sometimes functional analysis turns out to be sometimes illuminating for my undergraduate research in mathematical optimization, I want to have a basic pass through the most fundamental concepts of functional analysis. I have read some posts here stating that it's possible to learn functional analysis before measure theory, but the other order is preferred due to the need for integration. Since I don't have much time nor want to stumble upon something that requires measure theory, does anyone has some recommendation on a list of topics or theorems that might be needed for a basic read on functional analysis? Thanks in advance! Edit: I have some basic background in general topology. | 0 |
Google dictionary (based on Oxford dictionary) has an entry for the verb "reveal" as follows: make (something) known to humans by divine or supernatural means. And it includes one example: "the truth revealed at the Incarnation" Based on the definition, I find it hard to understand the role of "the truth" in this example whether it's an object (as denoted by "something" in the definition) or a subject (that is supposed to "make(something) in the def.)? My best guess is that it's an object because after checking other dictionaries such as Collins, Merriam Webster, Cambridge, etc., I found that they all define "reveal" to be a transitive verb. So I guess that the "to be" may be omitted in this case and the full sentence should be: "the truth IS revealed at the Incarnation". However, no resources I found have mentioned such type of ellipsis like this one. So my question is, is my guess correct. If it's indeed correct could you give me some resource covering such type of ellipsis? | 0 |
If I have a stick that has a spinning disc on the end of it, and I try to rotate the stick, I will feel more inertia the faster the disc is spinning because I have to transform its rotational energy into a different axis. It seems intuitive to me that this would apply to electromagnetic fields as well, since you have to move all the energy in the field to another axis. So if you had an MRI machine on an airplane and the plane tried to rotate, would it rotate more slowly when the machine was powered vs unpowered? If so, does this depend on whether the axis of the field is aligned with the axis of rotation? If they were aligned so that the dipoles are parallel to the body of the plane, could it roll without extra inertia? I may be describing the Einstein-de Haas effect or gyromagnetism, but I am confused whether they are describing the same thing as me in different words or just a related concept. | 0 |
Often we define a quantum phase of matter as a set of ground states of a gapped family of Hamiltonians, where the gap does not close anywhere in the family. Equivalently, we can define it as a set of states which are related by constant depth quantum circuits with local gates (equivalence of these two definitions is shown by the adiabatic theorem). Now consider a family of states which are ground states of a gapless family of Hamiltonians, and assume they have similar correlations and can be considered a "phase of matter" in the sense that all their observables vary analytically with the parameters of the Hamiltonian. Can we use the circuit definition of a phase of matter in the same way as the gapped case? That is, is it reasonable to define a "gapless phase of matter" in terms of states which are related to each other by a constant depth-quantum circuit? Maybe there are counter-examples to this which demonstrate this is not true. In particular, it seems reasonable to define gapless phases of matter in this way as (a) local unitaries do not change long-ranged entanglement properties, which intuitively define phase (b) unlike the Hamiltonian case, we do not need to worry about excitations to higher energy levels. Is there any literature on this at all? | 0 |
This question might be very silly, but I am really confused about it from several days. Look transverse waves on a string propagate along the string due to the electromagnetic (EM) forces between adjacent particles of the string. So when one of the particles is displaced, it will drag nearby particles and thus the disturbance travels. In case of electromagnetic waves, the electric field values oscillate with time. But is there anything physical that connects the electric field at a point to that at its nearby points (just like we had for strings)? If not, then why does this information travel? And if yes, then what is that "thing"? Also, I would like to add that for strings the direction of displacement at nearby points was completely determined by the source point, but for EM waves the direction of electric field at one point does not necessarily imply that the electric field at nearby points will be in the same direction (take the case of unpolarised light). Why is that? | 0 |
I am working on automated templates, and I want to use latexmake with luaLaTeX, as suggested in a comment on this question, where I attempted a similar setup with XeLaTeX. However, I am facing challenges with the configuration. My goal is to automate the process of typesetting my documents with luaLaTeX using latexmake, and I believe this will save me a significant amount of time. I have tried variations of latexmake main.tex -lualatex -outdir=output -auxdir=auxil in the terminal but it tells me that lualatex is not recognized as an argument For the code examples, I have a template that works and needs lualatex but needs several compilations. Hence the need for a latex maker. I also have tried to read the documentation for latexmake but I didn't find any solution and there isn't much content about this library online. If someone could provide guidance on how to configure latexmake to work with luaLaTeX, it would be greatly appreciated. Thank you! | 0 |
For context, I watched PBS Spacetime's video on virtual particles (link goes to relevant timestamp) where they say that virtual particles aren't mathematically necessary, because the lattice version of nonperturbative QFT doesn't use them, and yet still makes all the same predictions as perturbative QFT. I was satisfied with that, until I had a brief exchange with someone in the comments of this answer where he says that, in most cases, it's impossible to actually do computations in nonperturbative QFT, and, when I asked if this was just due to not having sufficiently efficient algorithms, he said Note that in particular that even establishing the existence of a non-perturbative Yang-Mills QFT (which is what the standard model / QCD / QFD are) is a millennium problem. which implies that we don't currently even have a nonperturbative version of the standard model and that it's unclear whether one exists. However, PBS Spacetime is, in my experience, typically a reliable source for high-level explanations, so I wouldn't have expected them to mention nonperturbative QFT as the reason not to think virtual particles are physical if that theory wasn't actually useful for nontrivial calculation. Is it that most physicists think there probably is a nonperturbative version of the standard model and it just hasn't been discovered/created yet? | 0 |
Let S be a compact orientable surface and U an open connected subset of S with finitely many ideal boundary points (or ends). U has a prime ends compactification which is a surface with boundary (following Mather). Let b be one of these ideal boundary points and Z(b) its impression in S. If Z(b) has more than one point, then there is a circle C(b) of prime ends associated to b. Each prime end e of C(b) has its impression Y(e) (another impression, the intersection of the closures of the sets of a chain that define e). This seem to be known by experts, but I could not find it written anywhere. Does anybody knows how to prove it? Knows a reference? I think I can prove it using scaffolds, a powerful tool created by Mather to prove various properties of prime ends. But it is a lot of work. Any good hint? Thanks. | 0 |
In the situation above, we have a power line which uses an alternating current. This alternating current causes a change in magnetic flux through the loop below the power line, which induces a current according to Lenz's law/Faraday's law, which eventually goes to the farmer's equipment. This is classed as power theft. However, I was wondering, does this power tapping by the farmer in some way reduce the power delivered by the power line or cause an energy loss from the power line? If so how? If it doesn't, then how is this situation exactly consistent with conservation of energy? Does the induced magnetic field in the farmer's loop somehow cause energy to get lost in the power line? (Where does the energy from changing magnetic flux come from in the first place?) | 0 |
I have a hard time understanding time dilation and special relativity; each explanation seems to contradict the other, and don't explain the apparent paradoxes they cause. Say clock A orbits clock B at a very high speed. According to the explanations I've heard, B would perceive A as ticking slower than B, because of time dilation. But since A has equal right to claim to be stationary, it should observe B as orbiting A, thus ticking slower than A. If at any moment the clocks' time would be measured, would their respective elapsed time be different? In other words, is one clock actually slower than the other? This seems unreasonable, since the respective situations of the clocks are identical. If the answer is no, what exactly happens if the clocks suddenly stopped orbiting each other and become stationary relative to each other? If each clock has perceived the other as ticking slower for a while, would the clocks instantly jump to the same time? This also seems unreasonable, since orbiting each other for a longer time then would imply a different outcome when stopping, even if the events of stopping are identical. How can this be resolved? | 0 |
Usually when we introduce postulates it is so they are of some use to us. I do not see the reason for these two. The Line Separation Postulate: Each point on a given line divides the line into three disjoint sets: the set containing the point, and the two half lines on either side of the point. The Plane Separation Postulate: Each line within any plane divides the plane into three disjoint sets: The line and the two half-planes on either side of the line. I understand the postulates and what they are saying, but I do not see how they can be used. And I have not yet found a proof that uses them in the book. I guess I am not convinced of their fruitfulness so if anyone can help convince me these are useful/necessary postulates that would be of great help. | 0 |
Suppose that, as a manager, I am creating a campign to evaluate employees based on the NPS (Net Promoter Score) of their sales - the objective is to reward high perfoming employees. However, due to the different nature of each role, some employees have a lot more sales than others. What is the best way to create a ranking system? The data available is: NPS for each sale for each employee (the value can be null, if the survey has not been answered by the customer). I thought about using a bayesian ranking system, but I think that it would be unfair to low seeling employees which sell little beacuse of their specific role. In a more abstract sense, how can I compare samples of varying sizes without skewing the comparison towards bigger or smaller samples? | 0 |
I've noticed while playing Minesweeper that when I have too few bombs, I get very easy to play games. In other words, I get games that can be solved with very simple algorithms. When I play games with too many bombs, I get unsolvable games or games that can't be solved without guessing. There seems to be a region in the middle(not too few, not too many), where some games are solvable but require increasingly complex algorithms. I've also read that Minesweeper is NP-complete, which I take to mean that there is no upper bound to how complex these algorithms can be as n, in an n-by-n game of Minesweeper, is allowed to grow. This seems relevant to information processing(halting problem?) but not exactly sure how. First, is my phrasing correct? And second, where can I search for clarification in my thinking? | 0 |
In an office, there are typically various different kinds of environments in which each employee carries out their work. Some have their own rooms, some have cubicles, some only have a desk in an open landscape etc. I'm looking for a word for the place where an individual employee carries out their work, regardless of if it's in a room, at a desk etc. Things I considered: Workstation - probably the best I've got so far, but it sounds kind of techy to me (associating with a workstation computer perhaps) - does this work also for someone not using a computer such as writing by hand (!), manning a reception etc? Workplace - to me this sounds like a common word for the entire office/building? Am I wrong? Furniture - kind of encompasses all kinds of surfaces you can work at, but it sounds too broad (and plain silly!) Equipment - to me this sounds more like advanced/specialized lab gear (labs, fume hoods, ...)? Does anyone have a good suggestion? Imagine e.g. this sentence: "All employees in the office are guaranteed their own [ ... ] where they can carry out their work". And I don't want to go too broad with abstract terms such as "location", "spot", etc. | 0 |
There are Two different defintions for the event horizon of a black hole. The Absolute horizon and the Apparent horizon. An apparent horizon is a surface that is the boundary between light rays that are directed outwards and moving outwards and those directed outward but moving inward. While and Absolute Horiozn is a boundary defined with respect to the external universe, inside which events cannot affect an external observer at infinity. Normally these horizons coincide but they can differ during event such ad black hole mergers. Technically, knowing exactly where the Absolute horizon is requires knowing the entire future history of spacetime. So it seems to me therefore that in a universe destined to even in a big crunch, black holes wouldn't technically have Absolute horizons, only Apparent horizons. | 0 |
I interpret the expression 'If P then Q' as asserting that if P is true Q is automatically true. So, we would say 'If P then Q' is true only when it indeed is the case that P being true implies Q is true. However, in logic, the truth of 'If P then Q' is determined solely on the basis of the truth values of P and Q individually and not by verifying whether Q follows from P, or is implied by P. So I just don't get how we can decide the truth of if-then statements by just looking at the truth values of P and Q. For it to be true don't we need to prove somehow that the truth of Q follows from the truth of P? In one of the logic books that I read, they explained conditional statements in this manner: 'If P then Q' asserts that it is not the case that P is true and Q is false. I liked this. It makes me understand the truth table of conditional statements well. However, by this explanation, I'm not able to see why would one use the words 'If then' then. How the idea that it is not the case that P is true and Q is false follows from the meaning of words 'if then' (or 'implies' for that matter). Should I completely forget about the meaning of if-then sentences as used in ordinary language and assign them a new meaning? | 0 |
One possible formulation of the second law of thermodynamics is that the work extracted during the change of a thermodynamic system between two thermodynamic states is at most equal to the free energy difference between those two states. One possible derivation of this empirical result from statistical mechanics is the derivation of Jarzinski relation in the canonical ensemble. Also, the Jarzinski relation was also derived in a stochastic setting by Crooks. For the sake of further simplifying the statement of the Jarzinski relation, I consider a Brownian particle fluctuating within a double-well potential in one dimension, i.e subject a Langevin equation on the real axis with known potential and noise. What I can say for this system is that the particle will be undergoing transitions between the two wells with a rate that is exponential in the barrier height of those two wells. Also, the equilibrium distribution of the particle will be a bi-modal having a peak at each potential minimum, and the height of each peak is given by the barrier height. Now which additional useful information does the Jarzinsky relation tell me about this simple system ? | 0 |
I'd like to prove: Given two points A and B and a straight line connecting them AB, any smooth curve passing through A and B will, at some point, have a derivative that exceeds the slope of AB. My proof uses the Mean Value Theorem. So, any curve passing through A and B has, at some point, a derivative equal to slope of AB, call this point C. Consider lines AC and BC. Together with AB, they form a triangle. Noting the angles a and b, we know that the slope of either AC or BC exceeds the slope of AB, and, by the Mean Value Theorem, there exists a derivative on any curve passing through either A and C or through B and C that equals the slopes of the lines AC and BC. Therefore, any smooth curve passing through A and B will, at some point, have a derivative that exceeds the slope of AB. Perhaps this is trivial, but for me it is important. | 0 |
I'm trying to understand where heat energy goes in a substance. I've seen that mainly it's translation at lower temperatures, rotation at mid range, and vibration at high range, but I'm not sure of that. Someone made the claim that an atom can expand as it is heated, which I don't think is right, but in a way, this is a good description of black body radiation? Does anyone know some approximation of percentages for how much heat energy goes towards motion (translation, rotation, vibration) and how much is radiated as blackbody? And, does this change between the different phases: solid, liquid, gas, plasma? I'm just looking for a general concept here, so no constraints. If there's some special constraints to note, then please list them and the energy distribution within that particular system for comparison. | 0 |
Recently I saw a video talking about the Yoneda lemma from category theory being used in neuroscience. It was my first introduction to category theory. In category theory we have objects and maps between the same objects called morphisms. For example we have one type of object called set and its morphism would be the function. A function is a map from one set to another. Another example would be the object vector field with its morphisms being linear transformations. This just looks like we are renaming the same stuff. Is a vector space not just a type of set we construct to obey our desired axioms? If so then introducing linear transforms would be truly just renaming stuff. And if they are not sets, why not allow non linear transforms? | 0 |
My first name is "Jean-Baptiste". "Baptiste" is not a second or middle name, however I noticed that it's not unusual for native English speakers to address me just as "Jean". I don't mind it at all, I'm not offended and find it actually charming, but it would be quite unusual for a speaker of my native language (France's French) to call me like that (either native speakers address me with my full first name, or they use various nicknames - and the nickname is never "Jean"). So I'm curious as to why many native English speakers seem to spontaneously call me "Jean". The two hypotheses I have is that either my full first name might be a bit difficult to pronounce (so just saying "Jean" is easier), or because they mistakenly think that "Baptiste" is my middle name - as compound first names are unusual in English (correct me if I'm wrong). I'd tend to think it's the second option, as I noticed that it also happens in writing, but I'd be interested in having the insight of people who know English language and English-speaking cultures better than I do. Maybe I'm completely on the wrong track! When it happens, I usually don't have the opportunity to ask people why they are calling me like that (e.g. in a professional context we usually don't have the time for that, plus in this kind of situation I don't want to make people feel like they offended me), that's why I ask this question here. Thank you, | 0 |
An event horizon appears in the Schwarzschild metric when considering a positive point mass in General Relativity. But for a negative point mass in the negative mass Schwarzschild metric, which repulses test particles, no matter how big the negative mass is, no repulsive event horizon forms. Intuitively, a big negative point mass should also create a repulsive event horizon, i.e., a region of spacetime that cannot be traversed from outside, due to respulsive gravity. If I make the negative mass big enough, I should create a region in which masses are so much gravitationally repelled, that they cannot enter (a repulsive event horizon). Why can't a repulsive event horizon form in General Relavity with negative mass? Is there any other metric which contains a repulsive event horizon with negative mass? | 0 |
I am interested in calculating the power received by an object near a black body radiator. Say, for example, I had a piece of paper perpendicular to the earth's surface normal. If I make assumptions about the earth's temperature, I can calculate its black body radiation. If I had a range of wavelengths I was interested in, I could calculate the power in that spectral range. Now if I assume my paper is itself a blackbody in the spectral range of interest, then I believe I could say that if it were placed very, very close to the earth, then the power it absorbed would be the power emitted per unit area by the earth multiplied by the area of my paper. This is based on the image below. My question is, what if I start to move my paper up? Is there anything I can say about the power it receives at different ranges from the surface of the earth? (Assume we are not so far from the earth that it can be treated as a point source). What I would like to be able to say is that the paper receives that maximum possible power when it is very, very close to the earth's surface. I am unsure how to prove this or if it is even true. Any kind of bounding limit on the received power I could derive would be helpful | 0 |
I would like to ask correspondence between Euclidean and non-Euclidean geometries. In the science and hypothesis, Poincare says that non-Euclidean geometry can be translated into Euclidean geometry with the following correspondence. ref)https://mathshistory.st-andrews.ac.uk/Extras/Poincare_non-Euclidean/ Space -> The portion of space situated above the fundamental plane. Plane -> Sphere cutting orthogonally the fundamental plane. Line -> Circle cutting orthogonally the fundamental plane. Sphere -> Sphere. Circle -> Circle. Angle -> Angle. Distance between two points -> Logarithm of the anharmonic ratio of these two points and of the intersection of the fundamental plane with the circle passing through these two points and cutting it orthogonally. Etc. Etc. Does he talk about Poincare's disk here? I cannot understand the meaning "Sphere cutting orthogonally the fundamental plane". If possible, can you please illustrate this? In addition, he says an theorem of Lobatschewsky's geometry: "The sum of the angles of a triangle is less than two right angles," can be translated thus: "If a curvilinear triangle has for its sides arcs of circles which if produced would cut orthogonally the fundamental plane, the sum of the angles of this curvilinear triangle will be less than two right angles." I would appreciate if you explain the above meaning more easily. Thank you for your help. | 0 |
When it comes to topologies, my understanding is that we designate elements of that topology as 'open.' In the context of a metric space, a topology is formed by selecting open sets, as defined with respect to a given metric. Moreover, a normed vector space is equipped with an induced metric derived from its norm. This metric allows us to associate it with a metric space and, consequently, with a topology. In the realm of topology, a closed set is one for which the complement is open. In the context of metric spaces, it refers to the set containing all points to which sequences converge. Now, in regard to normed vector spaces, when discussing Banach spaces, it's often mentioned, as seen in Riesz's lemma, that a certain subspace is 'closed.' I wasn't familiar with a concrete definition of what a 'closed' vector space entails. To the best of my knowledge, this term has been used to describe the property of addition and scalar multiplication remaining closed operations. Furthermore, are the concepts of 'open' and 'closed' equivalent in these structures? Does dimension play a role? In the case of finite dimensions, all norms are equivalent, and open sets are the same regardless of the induced metrics. | 0 |
My wife, a native Spanish speaker, today asked me about why a youtuber would call themselves 'craftypants'. I explained that -pants was added to something as synecdoche, so for example an intelligent person might be called a 'smarty-pants', a poor-humored person a 'grumpy-pants', etc. However, I then realized that while this is common in the US, in the UK 'pants' by itself usually means what this Yank would call 'underwear', while what I call 'pants' would appear over there as 'trousers'. How do such expressions as 'fancy-pants' sound to speakers in the UK? Are they understandable in meaning but recognizable as being North American? Does putting a -pants ending on a word remove the association with intimate clothing? Does it just sound bizarre? Do parallel expressions like grumpy-trousers exist? Are some combinations acceptable in polite speech, but others (e.g., pissy pants) not? Edit: There is much discussion in comments, and some in answers, about whether -pants is synecdoche. That's fair, and I am happy to have the point challenged. However, that's not my question. Even if I am wrong, my question is how "-pants" sounds to UK speakers, and whether it is clear or not that it is different from "pants" (underwear). | 0 |
I've studied in my physics class, absorption and emission spectra for gases or more "spread out" molecules like what is done in atomic absorption spectroscopy (learnt that one in chemistry). As in what discrete wavelengths of light a singular atom absorbs and why it only absorbs those specific wavelengths because of what energy levels its electrons are available to jump to. I was wondering if this worked generally the same for solids and liquids? Like, when you have something painted black, is the black paint designed to be composed of molecules that absorb enough wavelengths of light to make it look black (it wont be entirely black of course), or is it more that when light hits the surface of the paint, it travels as far as it can through it before using up all its energy to cause electron (and to an extent proton) vibrations? Is it both? Sorry if this comes off as confusing, I've tried to convey my question(s) as best I can. | 0 |
I have been reading into X-ray and gamma spectroscopy. I have found that they can both be done with scintillation detectors and work off similar principles. That is to say that when a sample is bombarded with high amounts of radiation, electrons will be excited, and electrons from other shells will fill the spot of the excited electrons. The ejected photons from this event then hit a scintillator, turning it into light (usually a NaI crystal), which is then turned into an electrical signal via a photomultiplier tube. It is then possible to ascertain the identity of the element using modern analysis tools. My question is: Is it possible for a scintillation probe meant for gamma spectrometry to be used to perform X-ray spectroscopy and identify the chemical composition of samples What would be different and have to be modified for such a setup to work with X-rays instead of radioactive isotopes? | 0 |
Now this might be a very dumb question but this has been bothering me from some days. Imagine I want to create the real number line and for that I start with the rational numbers. So I start to put the numbers on the line (like toppings on a pizza). Now I know that between any two rational numbers I can add another rational number. So I keep on adding infinitely many rationals between any two rational numbers by adding more and more digits in the decimal expansion. I can keep on doing this forever but I don't think I will ever reach a point where I can't put a rational and only an irrational number can go there i.e. I don't think there will be any gap between two rationals which can be only fit in by an irrational (or is it ?) So where do irrationals actually fit in on the line ? I know this entire argument can be done the other way starting with irrationals too. | 0 |
In accordance with special relativity, if we take into account length contraction then ideally the Planck length which is the smallest possible length possible should be frame dependent. Well we know that the number of particles are invariant in different frames. So, a frame travelling with some relative velocity will see the same number of particles but their length contracted by a factor. According to this logic, the Planck length should change with different frames. Yet it is defined by using the fundamental constants G,c and h which obviously do not change with frame. This could only imply two things :- One of the fundamental constants G,c,h are frame dependent (which I do not believe could be since they are fundamental constants) The shortest possible length cannot be written only in terms of fundamental constants The second conclusion seems more apt but is it right or is there something more to this? | 0 |
I am a Canadian, but I study in Edinburgh, Scotland. I have discovered a peculiar feature of my speach that seems to surprise most people from here. When ill befalls others, I use the phrase "that's too bad" to express my honest heartfelt sympathy with the victim. I have been surprised to find that most people here interpret the phrase "that's too bad" more negatively, closer to "well- sucks to sucks" and such. I have posed this question to a few folks from both Canada and the UK, and the Canadians seem to "agree" with my usage, and the British folks seem to take it negatively. Maybe I just have a small sample size. My question is: is this a feature that others know about/have evidence for? Or is my sample size just small, and it's pure chance. | 0 |
What is the simple relationship expressed verbally between flux, circulation, div, and curl, as captured by Green's, Stokes', and Gauss' Theorems? Below is what I've been able to assemble: Can you confirm or improve it? Given a vector field, we can measure its instantaneous rate of change in multiple ways, the two most important being div (a scalar) and curl (a vector). Each of these can be accumulated in a region. These theorems shows that this accumulation equals a property of the region's boundary: Flux (through a boundary) equals the accumulation of divergence (in the bounded region). Circulation (around a boundary) equals the accumulation of curl (in the bounded region). More fundamentally, neither flux nor circulation is limited to boundaries: they, or their equivalents, can be measured in non-closed curves as well. Only in that case, there is no relationship to any accumulation. That is: Flux can be measured across a simple curve or surface that is not closed. But this has no relationship to divergence. Likewise, a quantity equivalent to circulation can be measured through a simple curve or surface that is not closed, but if the curve isn't closed, it's called a line integral or work integral (or, for a surface, a surface integral). Neither has any relationship to curl. | 0 |
I have been frequently stuck on this question since first realizing it in the shower. While watching the hot water drop from the above shower head, and then watching cold water drop, I realize they both appear to be moving at the same speed. This puzzles me, because I know that when an object is hot, its atoms are moving fast, or otherwise have energy that is propelling them to "move fast". Correspondingly, when an object is cold, its atoms are moving slowly, since they do not have as much energy to propel them to "move fast". I was wondering, if cold water appears to be moving at the exact same speed as hot water, then where does my misunderstanding come in? What law of physics and thermodynamics am I misunderstanding, or otherwise unaware of? Thanks for any answers! | 0 |
The title might be a bit misleading, but basically I've been self studying differential equations so I could apply them in electronic circuit design. I was wondering what books could be recommended on differential equations, the Fourier, Laplace, and Z transforms, PDEs up to solving the wave equation, convolutions, filtering, and both discrete and continuous approaches to signal processing. One book that's caught my eye was Differential Equations: A Modern Approach with Wavelets by Steven Krantz, but I'm not sure how relevant wavelets are in modern signal processing. But regardless, if there are any books you've enjoyed a lot, please let me know! Also, if possible, I was wondering what a good book on information and coding theory would be, specifically with a focus on communications? I just want some physical reference books on these topics I'm learning by other means, since holding physical books is different from using an ebook. Thank you for your time! | 0 |
I'm looking for an existing word that roughly means "the process or idea of replacing bad/negative elements/deeds with good/positive elements/deeds, such as when a negative thing is eliminated at the same time that a positive thing is added". In terms of words that would not fit this goal are words that could (to some people) mean only the elimination of bad or the addition of good without the other half. Here is an example sentence showing the usage: I live my life with _____ so that I'm not just removing bad habits, but I'm filling the hole created by removing the bad habits with the addition of good habits, which both maintains my ability to fight returning to the bad habit while also creating a positive element at the same time. | 0 |
I am trying to do ray tracing for an endoscope, but I don't see how it could form a sharp image that could be viewed at the eyepiece. In the diagram the box in the middle is the "fiber", but the light from the object (the dot on the left) comes out of the fiber as if they originate from two locations (top and bottom), and if viewed through the eyepiece at the end, wouldn't two images form (the two dots on the right)? Also, if just looking at the image end of the fiber by eye directly without eyepiece, one should still see the image of the object, right? I don't see how it would work with ray tracing in this case either. And should the image in this case be inverted or upright, or left/right flipped, or does it depend? | 0 |
I've been struggling with this one... I'm trying to figure out whether it's okay to use the expression "call of the blood" to describe the phenomenon of doing something naturally (or coming to like it naturally) because it's in your blood, because your ancestors did it/were skillful at it, etc. For example, my ancestors were always good at horse riding, and I should also be good at that, at least like that because it's in my blood- in English, could I call this the "call of the blood"? We do have this expression in Russian. The words themselves seem pretty self-explanatory, but since there are so many expressions involving the word "blood", I thought to ask the native speakers and English language specialists here. (What I found during my research online were the similar-sounding expressions "call out for blood", or "blood for blood", but theseare not what I need in terms of the meaning.) So, can I say "call of the blood"/"the blood call"? | 0 |
It is said that most of what we call "mass" of nucleons are in fact from the kinetic and binding energies of quarks, and that the rest mass of quarks, from the higgs mechanism is much smaller compared to the nucleon. There are other examples, like the binding energy of a nucleus, that show how energy contributes to the mass of things in the subatomic world. My problem arises from the fact that it is also said that the gravitational effects are not really affected by how fast the object goes. Thus, a object won't get infinitely attracted to a planet even it goes at the speed near light. This seemed different from the previous examples, since in those cases the energy did affect the mass(in the classical way), which is basically what builds us up. What would be a appropriate way of understanding this discrepancy? Thank you for your time in advance. | 0 |
I've been playing around with the concept of entropy and how it can be manipulated when I came onto the complex workings of quantum waves. To my understanding, everything we know as a particle is a wave on a quantum field. Those waves are the result of energy being introduced to, and then propagated through, the field---ei. The waves carry energy. Further, the wave's entire existence is defined by the energy it carries, no energy, no wave. This caused me to ask the question, is there anything in our reality that is fundamentally real? Is there anything that exists that is not just the extrapolation of the process of moving energy from a to b? To be clear, I think that, to a certain extent, the fabric of space-time counts, but it's not what I'm really looking for. Space-time is what our reality is built upon, but it does not constitute it. It is the physical stuff that is built upon and held within space-time that makes reality, and it is from that that I ask if there is anything that is fundamentally real. | 0 |
I just watched a rather unreliable (or so I think) Physics YouTuber who asserted that absolute acceleration is impossible to measure, because it is impossible to ever calibrate an accelerometer accordingly, and I'm rather stumped by this argument. My understanding for all these years has been that acceleration can be absolute, and it can be measured easily with an accelerometer, but the YouTuber asserts that all accelerometers that are calibrated are done so in a frame that may or may not be accelerating, and to "correct" for this acceleration means having knowledge of an "absolute" inertial frame, which is defined using the accelerometer in the first place, thereby making the logic circular and invalid. Is he correct? Or is there a hole in his explanation? Or is this just an engineering problem, with a fairly easy fix in pure physics? What am I missing? | 0 |
In a recent conversation with my professor, he explained to me a misconception I had, in that given how physicists says that the Higgs "gives" the mass of all other particles, I was under the impression that a particle's interaction with the Higgs field is what gives it the property of mass. However, my professor explained that the Higgs boson was simply the first term in a perturbative series where each term can be recursively defined as the one before it. So knowing the first term allows us to calculate all the other terms. The other terms were the masses of all other particles and the first term was the mass of the Higgs boson, so discovering the Higgs's mass allowed us to calculate ("gave us") the masses of all other particles. This topic came up because I am doing research in QFT with him and in the book we're using I recently got to the part where it describes self-interactions and Yukawa interactions of fields (not yet quantized) using perturbative analysis. So, my professor used the Higgs as an example of this which I may have heard of and I had to explain my misconception to him. My question is: Where exactly does this perturbative series come from, what was it attempting to describe, and what does it and its derivation look like mathematically? it's difficult to read the literature on this and, to be frank, I don't quite have the time. Any help is greatly appreciated. Thank you! | 0 |
We know that a static charge only produces an electric field and a charge in motion (be it constant velocity or accelerated) creates both magnetic and electric field. But recently I came across that "changing electric field changing magnetic field, and a charge moving with uniform velocity doesn't create a changing magnetic field, and hence electromagnetic waves aren't emitted". Now I am confused since I can't find a clear explanation of accelerated vs uniform velocity in case of charge anywhere. Let's assume a source charge in space and the corresponding electric field associated with all points. Now if the charge starts moving (irrespective of uniform velocity or accelerated), since the position of the source charge is changing, the electric field associated with all the points in space are experiencing a change in both direction and magnitude and hence electric field is changing. So according to "changing electric field creates changing magnetic field theory" shouldn't electromagnetic waves be generated in this case? I really am finding it hard to understand the concepts. It seems that the electromagnetic waves are generated, only if the field lines are disturbed according to the following picture, but I am finding it hard to reconcile between the two concepts. | 0 |
The diffusion coefficient is known in the traditional physical literature as an empirical parameter of Fick's law. Here the observation is that spatial gradients of densities are suppressed by a rate proportional to the gradient of the density, and the diffusion constant is identified as the constant of proportionality. An other empirical definition is the identification of the constant of proportionality between the mean squared displacement and the square root of time of colloids. One insight of the paper on Brownian motion by Einstein was that these two definitions are consistent with each other. However in the last decades we additionally learned from the computational physical literature that if we take N classical particles interacting via Lennard-Jones pair forces, we consistently observe the linear MSD vs square root of time dependence. However I never came across an attempt to derive this result analytically, that is, for a set of known LJ parameters (sigma, epsilon, T, V, N,..), is it possible to analytically show or derive this linear correlation ? | 0 |
According to my environmental science textbook and various sources on the web, the thermosphere has the second highest density of any part of the atmosphere. It falls only behind the troposphere which can be explained as the most dense because the force of gravity holds gas particles there. But here is where I get lost, The thermosphere is located at a higher altitude than the stratosphere or mesosphere and has a higher temperature. It collects most of the thermal energy released in radiation from the sun. The thermosphere is more dense than the two layers directly below it (stratosphere and mesosphere.) But why is that? Pressure and temperature would be higher, but those shouldn't effect density. If density is mass/volume, then shouldn't the density be lower in the hottest part of the atmosphere due to Charles' Law? I can't really find any reason why it would be more dense other than this theory from Einstein that adding thermal energy to a gas particle would increase its mass. (can someone explain why this would be, I get increasing its kinetic energy but thats cause of speed increase, not mass.) Attached is a graph detailing temperature, density, and pressure in the different altitudes, I've been turning about this for a few hours and any input is greatly appreciated!! :) | 0 |
Consider a simple chemical reaction, such as the association of two hydrogen atoms within the gas phase to form one hydrogen molecule. It is known that this reaction is related with energy release in the form of heat because the hydrogen molecule is more stable than the two hydrogen atoms. Within a gas containing hydrogen atoms and hydrogen molecules, kinetic energy can be stored in several modes, including translation, vibration and rotation. If the energy of the reaction is to be released as heat, then directly after the reaction the temperature should slightly increase locally near the reaction. This local increase of temperature results in a transfer of energy to the "bath", and this transfer of energy is the heat. Which one of the above mentioned modes of kinetic energy do you think is first activated directly after the reaction ? If I imagine two hydrogen atoms that decide to make a covalent bond at some "t", then directly after time "t" they feel a strong bonded radial force, and directly before they feel a weak "dipole force". So they should be pulled toward one another, possibly overshooting the equilibrium distance of the molecule, then relaxing back. So I guess the energy is dissipated in the vibration mode. For my understanding, I would first like to focus on the case without radiation. | 0 |
I have been reading this article about the quantum vacuum state, and in the section that I linked to, there is a video showing an experiment that shows visibly that quantum fluctuations are actually happening (see the video in the link). The quantum fluctuations are visible because they amplified them using Spontaneous parametric down-conversion Now from what I learned here, quantum fluctuations (or virtual particles) do not exist (and links therein). They are just tools of perturbation theory in QFT when taking into account interactions to make the mathematics work. Another reason I learned is that the fluctuation-dissipation theorem states that when a system is in fluctuation, the energy dissipates as heat or other forms of energy. So then, the vacuum cannot be fluctuating. I seem to be confused now. Is the video fake or is what the video/wiki claiming not true and is something else entirely? This question is sort of a follow-up to my previous question. | 0 |
I'm trying to figure out if a hexagonal grid can embed rectangular coordinates in whole numbers of "Y-steps". In the image below, one "Y-step" is the spacing between red hexagon centers in the Y dimension. For some arbitrary hexagonal grid size, how many hexagons do I need to produce some whole-valued number of "Y-steps" in the X dimension? Another way to ask this might be: Select four hexagons whose centers create the corners of a square. In the hexagon grid orientation shown below, how many horizontal hexagons are needed to create such a square, and then how many vertical "steps" are needed in the Y dimension? Both X and Y values need to be whole integers. In case it helps, this site provides great info in hexagonal coordinates, but I've not figured out how to pin down a way to solve this. We are using the "pointy top" orientation. | 0 |
I would like to perform something that resembles a curve fitting optimization but for which i could not find much info. Lets say i have a function that yields a time series. What i would like to do is tune the parameters of this function so that the time series it yields has a specific shape. For instance i want it to output a step, or two steps back to back. What i don't know (or care about for that matter) is the height of the steps. For a single step, a naive solution would be to simply take the average of the output and compute the RMSE of the output to it's average and minimizing it. However this gets more and more complicated for more complex shapes (the two steps example is already a pain with this method) Would there be a mathematical tool that would facilitate this? | 0 |
Classical mechanical systems observable on a dynamical scale are subject to Newton's laws. In this case, knowledge of the Hamiltonian allows us to minimize energy taking into account inertia. This allows us to calculate trajectories, find equilibria and derive many properties. Classical mechanical systems consisting of large sets of particles are subject to Boltzmann's law. In this case, knowledge of the Hamiltonian allows us to minimize energy and maximize entropy. This allows us to calculate phase space weights and derive many properties. Is it possible to proof that the two approaches are equivalent in some cases ? That is, proofing all assumptions made in micro-canonical and canonical formalisms based on Newtonian mechanics ? Or that the average properties generated by Newtonian trajectories are equivalent to Boltzmann average properties ? Or is it maybe possible to observe some kind of transition between the two cases if they are not equivalent ? | 0 |
I have observed that when an insect is electrocuted in a bug zapper, there are typically a few sparks or flashes of light. Sometimes the insect will catch on flame in a tiny fire, and the body will burn for a few seconds before stopping burning. The lights and flames stop after a few seconds, but the insect body often, instead of falling, remains in position still connecting two wires. Given that the body is still in position connecting two wires, why is it that after a few seconds, sparks or flashes of light stop appearing, and any fire is extinguished? Does that mean that electricity is no longer flowing through the insect's body, and if so, why does the electricity stop flowing if the body is still connecting the two wires? | 0 |
Is it okay (in terms of usage) to use present participle clause for an action that follows another action as a result? For instance, the following sentence seems correct to me: The bomb will explode, sending shrapnel everywhere. Yet the following sentence does not correct at all to me: I will run one mile to reach my target, grabbing him. I don't know how I feel about this sentence, I think it feels fine: The cat leaped into the air, landing in the river. This sentence feels pretty wrong: I noticed my target, shooting until I hit him. But this sentence feels fine: The man took off from one end of the street, reaching the other side just in time. And then obviously this sentence feels not great: I will live a good life, dying. But then this sentence feels fine: I will live a good life, dying when it reaches its conclusion. What's the differentiator here? Are my feelings correct? | 0 |
The following problem has bugged me for a while, ever since I noticed it. On the Visible Spectrum Wikipedia, the following is the visible spectrum: Now, in Photoshop, or really any colour picker, the hue slider looks something like this: Or sometimes this: I noticed that in both of these, the colour loops back to red. Why is this? I believe that this doesn't happen on the visible spectrum. The visible spectrum goes from a violet-ish colour to a maroon-ish colour, with a whole range in between. But where does the magenta colour from the hue slider fit in? I take it that it is possible to have a purely yellow object, or a purely teal one, as it is on the colour spectrum, yet are magenta things and pink flowers inherently reflecting multiple wavelengths of light, from opposite ends of our particular viewing spectrum? All of this seems awfully odd to me, so I was hoping someone might be able to clear it up. | 0 |
I understand why the temperature of the hot reservoir has to be minimally higher than the temperature of the hot working fluid during the isothermal expansion phase of the Carnot cycle (to limit new entropy being produced in the working fluid that we have to get rid of). But during the isothermal compression phase why do we need the cold reservoir to be only minimally cooler than the cold working fluid? The working fluid looses the same entropy independent of the temperature of the cold reservoir, so why do we need to minimize the new entropy created in the cold reservoir? What is wrong with just letting the cold reservoir get more and more entropy as long as the working fluid returns to the same state as before the cycle? | 0 |
So, as I was browsing a bunch of the tachyon questions throughout the years in this forum, and an oddity of these hypothetical faster-than-light particles came to mind. Ordinary particles with mass always have an inertial frame of reference where they are at rest, thus their rest mass can be measured. Lightspeed particles, while never at rest, have an invariant velocity, so different frames of reference can agree on their energy. Not so for tachyons. Tachyons not only are never at rest (like lightspeed particles), but their measured velocity is frame-dependent (like ordinary particles with mass). So, my question: Question: Is there anything analogous to a rest mass that can be used as a common point of reference when working out the mass of tachyons, or is it completely frame-dependent? And, no, we cannot say the tachyon's frame of reference, because they cannot be treated as observers (same as with lightspeed particles, we cannot treat a photon as an observer). | 0 |
Electricity is used for many things. One of the biggest uses is transporting energy, almost instantly, from a power plant to the machines in my home and many others'. I was wondering if a similar energy transport grid could be created using a fluid under pressure. The power plant would use its energy to pump a fluid into the main pipe, which extends all over the country, with many sub pipes coming out to each house. The high pressure liquid would act like high voltage electricity, ready to be tapped into by a user. At home, one would open a valve in the pipe, causing high pressure fluid to come out. This jet could be used to spin a rotor mechanically, in other words, energy was transmitted almost instantly from the power plant to my home. We would probably need to have the used fluid go back into another pipe which goes back to the power plant to be pumped again. In other words, something similar to an electric circuit but using fluid instead of electrons. Knowing about the analogy between electric current and hydrodynamics, I was wondering if my strange idea could be practical or at least physically valid. | 0 |
I hope this isn't the completely wrong community for my question, please let me know. I did search for 'varifocal' and got some hits, it seems (still getting used to these glasses, so it is a bit hard to use my PC) So, it seems that when you get these glasses - we call them varifocal in UK, not sure if that is the international name? - they have these three zones with different strength, but for some reason, there are two blurry areas in the lower right and left corners. The top has the distance vision all across, but the computer- and reading strengths are only in the middle. I haven't been able to find an explanation online so far; does anybody here know of a good, technical reason for not simply providing three zones in the full width? | 0 |
Even though a black hole has a Scwarzschild radius that indicates a finite small distance to the center of the hole, the distance traveled by an infalling particle seems a lot bigger than the Schwarzschild radius due to the extreme curvature of spacetime. An infinite curvature even seems to imply an infinite distance. Two particles falling into the hole, one after another, end up spatially separated. This holds true for all particles that fall into it. This seems to imply that the distance traveled is actually infinite. I mean, if particles end up spatially separated because of spaghettification, and they all fall the same distance to the singularity, only an infinite distance will do, so it seems. What (if) is the flaw in my reasoning? EDIT I'm not sure if the linked question is a duplicate as it asks about the time it takes to freely fall to the singularity. I'm asking about the distance traveled, and I read in a comment by @MichaelSeifert that there is a good explanation for why the concept of distance isn't well-defined in this case. I can't see why that is so. What if you, the freely falling indestructible observer, have an infinite rope, one end of which you attach somehow just above the horizon? Can't you see how much rope has rolled off from your device when you hit the singularity? | 0 |
Short introduction to my understanding: As far as i understand, virtual particles are usually defined to be the internal lines in Feynman Diagrams. But we know that those are just useful tools to calculate amplitudes in interacting quantum field theories. In a free theory I have no interactions, hence no internal lines and no virtual particles. Virtual particles show up when, in interacting QFTs, we have the so called contact interactions showing up in the perturbative Dyson-Schwinger equations as deltas. My question: Can we regard virtual particles solely as mathematical tools needed to make predictions in perturbative interacting theories because we don't fully understand how interacting theories work? (I mean how they work in a non-perturbative setting) If the latter is true, and from my actual understanding I think it is true, what is our "hole" in the understanding of full interacting QFTs? | 0 |
I was reading about effective field theories and wondering how much an EFT can tell you about the ''underlying'' theory which is then reflected in the EFT. Can one extrapolate back from what one sees in the EFT to derive features of the theory for the high energy degrees of freedom? As an example, general relativity is considered to be an effective field theory for quantum gravity, but that does not tell us much about what the correct quantum gravity theory would look like, with many people arguing that this underlying theory would be a string theory and not even a field theory. However, are there cases where one can say more or come to definite conclusions about the underlying theory? What is the systematic way for doing this? For example, in lecture notes of Pich on EFTs with Nambu-Goldstone modes, he mentions that one can ''uncover fingerprints of new physics scales'' from couplings in the EFT. | 0 |
So, just to expand on the question in the title, I know group representation theory, and especially character theory, are quintessential tools for anyone hoping to study finite groups. That said, from what I've seen and read, some people study characters in and of themselves (say, density of zeroes, Brauer characters, etc), while another set of people uses them as tools for studying questions concerning the groups themselves (i.e., it's not clear from the get-go that characters will even get used; they are a part of a toolkit). My question is: what's the intersection between these two sets of people? Can a person spend some time working on Brauer characters and blocks and then move on to study, say, the subgroup structure of finite simple groups? Or are the areas far enough apart that character theorists simply don't have enough baggage to work in general problems on finite groups and vice-versa? Sorry for being a bit "vague", perhaps... I'm just very curious about the distinction (if it even exists at all!), since I really love both topics! Thanks so much in advance! | 0 |
(Honestly I fear this is borderline off-topic... be gentle with the downvotes ;-)) Most of the packages I've written are for personal use but a couple of them are used by some other people. These packages change relatively often as I'm constantly implementing requested features. Right now I tend to ship out the most recent stable version by e-mail but then I get either answers of people that are not interested any more, or requests from other people who aren't in the mailing list yet. I do not want to upload the packages on CTAN for two reasons: There's maybe a dozen users. It's highly unlikely the packages will be useful to someone else. I find there is enough bad code on CTAN without me contributing to it. For now I've got an institutional home page but that may change any minute, so posting the code there for download (which I've done) might not be a long-term solution. Any advice? (My personal texmf tree is on Dropbox, if that may spurt a solution.) | 0 |
It seems correct to write "A host of tools exists..." or "A range of tools exists...", i.e. the verb reflects the fact that you are referring to one collective noun. But, if I want to continue to talk about that collection of things, it often seems natural to say ". They aim to solve..." or ", which attempt to model...", i.e. now I am referring to the capabilities/intentions of the things within the collection. Which is strictly correct? And putting strict grammatical rules aside, which is an English speaker most likely to say? a) "A host of tools exist, which aim to solve..." b) "A host of tools exists, which aims to solve..." c) "A host of tools exists, which aim to solve..." My instinct is to avoid the construction and write "Several tools exist, with the aim of solving..." | 0 |
It is currently understood that gravity is not actually a force, and a fact that is often used to show this is that an object in free fall doesn't "feel" that it is accelerating and is thus an inertial frame. However, it seems to me that Newtonian mechanics can already predict that this will be the case. Since all the parts of the object are being accelerated by the same amount simultaneously (at least approximately, like near the surface of the Earth) there won't be a tendency for this object to contract, and thus "feel" that it is accelerating. This isn't the case, for example, when I push the same object. In my understanding, the force needs to be communicated from the point I apply it to all the rest of the object, and this delay is the cause of a contraction/increase in internal forces or tension, allowing it to effectively "feel" that is accelerating. Now, suppose that there is a uniform field that accelerates any particles with constant acceleration. Like gravity, a free object in this field will not be able to detect that it is accelerating, since all of its particles are accelerating equally at the same time. My question is: Is this object inertial, or is it only inertial if this field is a gravitational one? | 0 |
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