darklight03/StackMIAsub huggingface dataset:
This is a question from an interested amateur. Math welcome (as I or another may investigate it some day) but don't expect me to understand it in your answer. Consider a star emitting light. In order to talk about it simply, think of a point light source, and ignore spatial perturbations (for the sake of phrasing the question). At at time t, the light emitted at a single instant at now-t forms a sphere at a distance from the source. What is the density of photons in the surface of that sphere? Perhaps the reply is that the energy is traveling as a wave, but I understand light energy is quantized - that is, the energy has no representation described by infinitesimals, but will be in minimum quantities. How much must the sphere expand so that there are gaps in the image when sampled at different locations on the 'instant-sphere' image? Or, is there an explanation as to why the energy is quantized, yet can manifest at any separation (due to distance) despite the energy density falling below the quantization when the sphere is of sufficient size? What if the source is a candle? Is the original source always sufficient to 'map' adequate photons to any sphere that may be created in the dimensions of our universe? Are there objects we cannot see because they are so far away (or dim) that we are 'in-between' the photons that form their expanding image? Of course, I may simply not understand, but the explanation would be welcome.
I play football. However, I dislike going and sometimes I just dont want to play it. But whenever someone tells me that i do not have to do it or that I can stop when I want, I put all the work into it. One reason I can assume is that my father played ball and I am the last son, he and my mother want me to play but I have "mixed" feelings to say the least. Whenever I constantly tell my parents that I dislike football, they obviously get very saddened and I dont care about that in particular. The strange thing is that when I get the choice alone and with nobody around, I always play ball because it makes me happy. But whenever I'm told that I have to, it feels like a chore. I can't explain this to my parents and I feel the need to get this off my chest as I am heading out soon.
As we know, In a circuit, simple or complex, electric fields created by surface charges move electrons which creates current which creates magnetic field which can be coupled to other lines and induce voltage if it is changing by time, which also creates current and this current also creates magnetic field and voltage drop along where it is coupled so on and so forth. Voltage and electric field are related just like currents and magnetic fields are. Changing electric fields create magnetic fields and the opposite is also true. I mean what is the independent variable here? Everything is like being affected by one another continuously. Is it power or energy or fields? What variable or thing I must I hang on to or take as starting point for better analysis of circuits?
Currently the proven theory is the quantum field theory. This theory defines fields in "all spacetime" and particles are disturbances in these fields. These particles are punctual and interact through virtual particles. But string theory is not clear to me. This defines the strings (bosonic or fermionic) as the smallest entities and these "strings are in a spacetime" but they are not defined unlike the fields in all spacetime. How is it possible? How is the zero point energy then described? So we must understand that at every point in space there is at least one section of string? Here the difference is analogous to the first quantization with the second quantization. Is a string field already confirmed in all string theories? Is there talk of virtual strings? If I take a field, for example the Dirac field or the EM field, these are defined in all time space. It may be that there are disturbances that we interpret as particles, but if there are not, the field exists the same and has a zero field energy value not equal to zero, with virtual particles being created and destroyed. Or for example, the higgs field directly has a non-zero energy in all space. Do we have a defined string in all space?
I am wondering how heat loss happens in sound waves through air. First of all, for wave energy to be transformed into heat, absorption should happen by a medium. But why wont absorption implicitly translate to faster vibrations which would state that even though wave energy was translated into heat vis absorption, that again must have transfered back into wave energy. My logic is that some particles that absorb wave energy will in turn increase their their own kinetic energy, and those that dont absorb wont. So some particles will vibrate more, some wont. Then due to this difference between particles, redistribution energy will occur and since particles that absorbed energy, they might not actually vibrate in a pattern but randomly start moving who knows where. I believe this random motion and not in direct vibration pattern is why we say energy of wave was lost due to heat conversion. Correct ? But I wonder why absorption(even though it increases KE of particle) does not implicitly give it more vibration in the same pattern as it had before the absorption ?
We call G the formula that in the formal axiomatic system employed by Godel to formalise arithmetic has the meaning of: "I am not provable in this system". We know that this formula G is true in that axiomatic system since we can exclude that it is false. But why can we say that it is also true in arithmetic itself? After all, within arithmetic such a formula is only a set of symbols, and even if well formed it can still be a false formula. How can we say that such a formula is also true within arithmetic and not only in the aforementioned formal system that formalises arithmetic? We come to this conclusion because the formula G also within mathematics retains the meaning of: "I am not provable in this system" or are there other reasons for considering it true within arithmetic?
In security, we speak about different strategies of protection. Mainly, there are three to consider. First kind, usually called shell protection corresponds to the act of preventing the intrusion before the access. For instance, a door, fence, password on a website or silver galvanization of the utensils. That's usually very powerful and easy to maintain. Occasionally, there's a breach and then, we have problems, unless there's also the other kind of security implemented. Here, we're talking about smoke dispensers, mazes, ambulating patrols, honey pots, fake repos etc. What would be a good term for that? (Extra great if it's formal'ish.) The one I've been using is impregnation protection but I'm not sure if it makes sense, let alone is correct linguistically, let aloner comprehensible to regular people. (The third is deterrent protection and not relevant to this question.)
I have seen videos that interview accent experts, like on why Americans do bad English accents (a reason given is a lack of exposure). But are there something like references that one could point to to rate accents? I would think at least one should survey native speakers to get a rating (I met a Kiwi who said he would get mistaken for British by Americans even). Maybe AI could do ratings nowadays if trained on enough. I figure one would need to do individual ratings for each case, even if a reference existed, like having to break down examples, showing where they messed up. If ratings were compiled somewhere that'd be easier though. Like something one could use to show how bad Americans doing accents in lotr were, except like wormtongue, which one may figure influenced having less in the hobbit.
As oppose to a cylinder in two pieces rotating against each other, as in O'Neill's cylinder, what if the cylinder were all one piece and an external thrust, like rockets, set the cylinder in motion, rotating it, would it rotate indefinitely? Would inhabitants of the cylinder experience artificial gravity indefinitely, or would their movement against the rotation of the cylinder slow it, or would movement with the rotation of the cylinder even it out? Or would neither effect the closed system because they'd be pressing against the cylinder from inside the cylinder? Would friction from the air inside slow the cylinder over time, or would the air turn with the cylinder and artificial gravity? If any of the above would slow the cylinder, how frequently would the rockets around it have to add more momentum to keep the craft spinning? Would it at least be a number of years?
What does it mean, "gravity is so strong that not even light can escape from a BH..."? This can physically interpreted IMHO that beyond the event horizon of the BH, light is phase transitioned (accelerated) to a FTL superluminal energy that breaks known physics. The inner of the BH therefore appears in our spacetime as "Nothing"! Exactly as the rest of vacuum space appears to us, basically as nothing. Someone could therefore infer that vacuum space we generally describe us nothing is actually something and considering the physics of BHs it points to the possibility that vacuum space could be a superluminal FTL (i.e. faster than light speed c) unknown type of energy. There is light, matter and vacuum in our universe. Seems to me that vacuum could be a different energy than matter and light, defying our known physics which we mastered over millennia and concern more about matter and light and their interactions. The vacuum is still a mystery today. Much to learn in the future. Maybe sci-fi Star Wars creators imagination was right after all when saying "...prepare for a jump to hyperspace!".
classical electromagnetism , from my understanding can be derived completely from coloumb's law , charge invariance, superposition principle and postulates of special relativity. Biot savart law and lorentz force law are all consequences of it . For derieving faraday's we need not do any experiments, flux rule : e=-d(phi)/dt (e is induced emf and phi is magnetic flux) can be proved from motional emf . From flux rule , it can be understood that emf is induced when area of conducting loop changes in constant magnetic field or magnetic feild is a function of time with constant area. As the flux rule rule is derived from no experimental information other than lorentz force law biot savart law ,we should be able to prove that changing magnetic feild induces emf and hence current is induced . It seems that magnetic feild cannot induce current because it acts on moving charges (which in our case is not moving).experiments shows that it is non conservative electric feild that induces current , but why do we need to do experiment because we already proved it in flux rule. My question is that this information of inducing emf was in flux rule , but it seems that we can not prove induced non conservative electric feild from basic priciples (coloumb's law , special relativity,charge invariance....)
The photoelectric effect is most probably seen when the incoming light has lower energy than the energy needed for both Compton scattering and pair production to happen. The probability of the photoelectric effect to occur also increases when the matter that light interacts with has a big atomic number and high atomic/electronic density such as Lead, Tungsten, and even better Uranium. Given the energy difference between Gamma and X-Rays, and the for high probability, photoelectric effect requiring low energetic photons to occur, how is it possible that X and Gamma rays are both prevented by the photoelectric effect that is observed in those materials? Is it that energy levels of photons that photoelectric effect has to occur on materials like Tungsten are on the high energy boundary of X-Rays and Low Energy boundary of Gamma Rays, and thus rest of the matter-photon interaction effects such as COMPTON and PAIR PRODUCTION are almost always on the GAMMA Spectrum then?
I was watching Susskind lectures in string theory. There he explains that open strings can both, split at any point, and also join at the ends when the ends touch at a single point. I have one question about each of these two processes. Is not the likelihood that the two ends of a string end up at the same spatial position of measure zero? Or the two ends do not need to really meet at the same point, but only be close and then they will be attracted to each other to make it closed? If and open string breaks at an arbitrary point, would not this create particles of arbitrary mass? as the rest mass is proportional to the length? but we know particle masses do not form a continuum. What am I thinking wrong?
If we shine a light that has less energy than the work function energy of the electron of an atom on a metal, the electron is not released but excited and electron gives off this excess energy as heat or collisions or light. We know that the intensity of incoming light does not affect whether the electron will be released from the metal or not, only the energy of the incoming photon determines it. So, Assume that we hit an electron with an energy lower than the work function energy so that the electron gets excited and builds up with energy. WHAT IF Before that excited electron releases its build -up energy as heat or light or collisions we hit it again with a light that again has an energy lower than work function energy, why isn't it released from the metal?
Current in a wire is defined as the amount of charge that passes through a cross-section of that wire in a single second. By this definition alone, it is clear that a current relies on the motion of some charged particle. I believe it is possible that electrons could transfer energy to each other in every direction and when the current starts flowing those energy transfers are more directional. This could lead to electrons always having the same velocity independently of the current. Is this the case? I came up with this wile trying to understand magnetic force around wire, if electrons are traveling in the same direction their spins would also be in the same direction, which could cause magnetic field similarly that would spinning ball in viscose liquid cause flow of that liquid.
In cubical homology you have to consider the group of degenerate cubics and use the group of cubes module degenerate cubes (Massey). If you not do that you get the wrong homology for one point space. In singular homology (simplices) every textbook explain you do not need to do that because you are going to get the same groups. It is easy to check that you get the correct homology groups for a point space without exclude degenerate simplices. But I would like to know a GENERAL PROOF of that. That is the equality of both groups in general order and spaces (excluding or not degenerate simplices). Because it seems that textbook writers consider that evident for I have seen the statement many times but no proof at all and I am not willing to take it by faith. I have read an old paper by Tucker available in internet by googling: Degenerate cycles bound. But I dont know how to apply that to singular homology Thank you very much
I have a set with unknown cardinality. The cardinality can be from a number a to a number b. How can I indicate the number a (or b)? The question in texts is: "What is the least value of n(A)" (A is a set with a few possible cardinalities) How can I properly express this in mathematical notation? I used the notation(If you call it a "notation") least of n(A) I have seen this question: Mathematical notation for the maximum of a set of function values The things that differ is that I need the notation to express the minimum (or max) number a function can give for a constant x, not the min (max) for a range of x Also, the set of all possible sets isn't given and is there to be found out by the question solver. (as it implies, each solver may generate a different one) n(A) is the cardinality of the set A I do not have a strong mathematical background. so please avoid very confusing notations. thanks in advance
Clearly particles individually pass through slits, be it a single or a double slit experiment. The fact that wave interference is evident in their trajectory may be due to their interaction upon entering the slits. If water particles, or sand particles can together form waves, one can assume they will act in such way that their individual trajectories will reflect the wave they form, and once that wave, if it were to pass through a couple of slits will alter their individual trajectories to satisfy the interference pattern we see on the plate in the double split experiment. In other words, the interference pattern in the double slit experiment (based perhaps on the my sorely naive point of view), are the result of particles, that together form a wave, and upon the entrance to their respective slits, their altered trajectories through the slits reflect their wave relationship. I need to know if any of this is absurd.
[Note I am asking up to, but not including, consciousness as this bleeds into philosophy and is a much messier question] Assuming that the laws of physics have remained constant across space & time since the big bang, has the way the universe evolved been entirely predetermined? While impossible to know the physical parameters & interactions across all space and time, these unknown states would have been acted upon by consistent forces since their onset. Thus, while not knowable, the universe grew along only a single possible path forward, meaning from the instant of the big bang to (cosmic) now, everything has been entirely determined? Phrased another way, was there any physical process that introduced true randomness that caused the universe to have multiple different potential paths? Note that I don't mean things that seem random - such as paths of specific gas molecules when dispersing - since these are ultimately entirely predictable given sufficient knowledge of states & environment. Or is my premise somehow wrong?
If the Hamiltonian manifold for the moving surface of the standing wave is smooth then it must be minimum surface of revolution. The frequency of the string is the capacity of the manifold that is a periodic solution to the Hamiltonian. The frequency cannot be a rational number frequency = velocity/wavelength because the solution to the Hamiltonian is a real given by the Dirac measure. There is only one Hamiltonian so I think string tension and length are determinative. All I want is the mean curvature of the manifold. You are being asked here to prove the manifold is not symplectic. Obviously, you cannot. I say you must conclude curvature is constant. You have no way out of this except to say I have not explained this to you well enough that the string makes coherent theory. Do you have a calculus for the string as a moving surface?
I. I thought he was swimming - I thought he swam for a while but found out it was a lie I thought he is swimming - I thought he was swimming now, but he's not. I thought he swam - I thought he once swam (don't know when). I thought he has swam - I thought he has already swum recently (a couple of minutes ago). I thought he had swam - I thought he had already swum recently (a couple of hours ago). I thought he ... but i changed my mind, and now i dont think in this way If I can't frame my thoughts in this way, how should I do it? Specify proposals, add new ones? But is it possible to designate meaning with the help of time?
If electric fields are created by an accelerated charged particle, such as an electron, and magnetic fields are generated by electric fields in motion, what are the individual fields that make up Electromagnetic Radiation oscillating between? What is the Y axis in their sinusoid function measuring, and how does that continue to oscilate in the absense of moving charge once the photo is emited? Is the electronic field aspect oscilating between a negative and positive charge relevant to overall energy levels, or is it confined to one side of that? I am asking as I have an incomplete understanding of how a photon, without a charge, continues to oscilate at the speec of light. I fully expect that I have an oversimplified understanding of both repsective fields, and I hope to learn what unknown forces are at play.
Hi there Wise people of the internet, I am trying to do analysis some data gathered from a gamma scintillator setup, its stored in root. So i have to do some coincidence measurements, and i found that in Krane, you normally use a TAC (Time to Amplitude Converter) to check for it. However, this gaussian peak expected there has count per channel in y axis. Should i just divide the counts that i recieve for each channel by channel number? I dont see how that will be useful.(this will disproportionately eat away any meaningful data stored in higher channels, which corresponds to higher energy,after calibration, breaking expected stable background of chance coincidence) I am kinda new to detectors. Any help is much appreciated and also any resources/references will also be. Regards
There is a group in which is embedded the set of rational functions considering the formal composition binary operation? More generally how (and when) can we extend a non-commutative monoid (or semi-group) into a group ? I was looking at the interesting case that the natural numbers can be extended to de integers by the matters of considering it as a monoid over the sum and constructing a group of the fractions and then extended again into the rational by applying the almost same method considering the multiplication operation this time. Thinking in this context i try to apply the same ideia to the set of rational function (with rational coefficients - quotients of two rational polynomials) but considering the composition binary operation as it is associative, has a neutral element, etc... But obviously isn't that simple and after searching for a answer i discover the concept of group completion of but not much more and specially not much for the non-commutative case. I'm thinking in a abstract way, thinking in a rational function as a pair of finite sequence of rational numbers, as was already noted in comments that not all rational polynomial are invertible, but. Considering that the case is analogous to the fact that not all integers are multiplicatively invertible
I am stuck writing this sentence: Relics such as Fortran, B, D and other programming languages continue to stay alive, stories of programming languages in the graveyard, and those that spurred magic have antecedent the continues quest of improving programming. EDIT: Clarity. Think of this as a battle cry among programming language developers. In this battle cry, stories of both success, and failures emerge overtime and historically, nevertheless, the journey is not even complete or done. Essentially, events, programming languages in the graveyard, and programming languages that made magic and allowed some companies to achieve technology never seen before, the combination of all of this has thus, "......" the continuous quest of improving programming. I am trying to make the reader, from also previous text and stories discussed in the text, to understand that, technologies that left a MARK in an industry or across industries as a result of a different programming language have caused: a curiosity and quest to build even better programming languages that can move industries forward. I HOPE THIS IS CLEAR ENOUGH.
I've read quite a few things about rarefaction waves in terms of giving weak and entropy solutions to certain PDE problems with fixed initial time data. I understand that the consideration of these solutions provide some sense of density that decreases with the passing of time, but I've not heard much else. My concerns are: Why are these kind of solutions specially noticed as one of the very first examples given in several books?. Maybe it's some sort of "unwritten" but written tradition to expose these solutions. Are they directly applicable in some specific physics topic or something? I'm pretty sure they are since every attempt I've done to try to research about the topic results in some content including the word "density". Any thought, suggestion or reference could be very helpful to me ;)