darklight03/StackMIAsub huggingface dataset:
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?
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
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.
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.
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).
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.
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?
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.
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?
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.
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.
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!
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!
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.
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?
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"?
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.
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.
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?
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!
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.
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 ?
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!! :)