darklight03/StackMIAsub huggingface dataset:
I have confused myself about the following variant of Maxwell's demon and I can't seem to find out where the energy went. Consider this: You have a chain (one dimension) of spins (up/down) with a nearest-neighbor coupling. Energy is minimized if spins are aligned. Let us say the energy difference between alignment and not-alignment is E. The zero temperature state is either all up or all down. If we heat the state up to a temperature T, some of the spins will flip with a probability given by the Bolzmann-factor, depending on the ratio T/E. So far so good. Now the finite temperature state has energy because the states aren't all aligned, but the distribution is thermal and it's no useful (free) energy. However, if you knew which spins are misaligned, you could selectively flip them. Let us say the system is such that you can flip them by shooting a photon with energy E at the spin. Eg, you shoot at the middle spin in a series of three. If it's up,up,up then the photon will be absorbed and you end up with up, down, up. If it's up, down, up, the photon stimulates emission and you get up, up, up plus two photons of energy E. If you have up, down, down, the photon doesn't change anything about the total energy. The same happens if you exchange all ups with downs. Now the thing is this: If you do not know which spins you have to flip, your chances of gaining or losing energy by shooting photons at the chain are the same. You just convert one thermal state into the other. But if you knew which spins to flip, you could topple them over selectively and get energy out of the system. Essentially, you extract it from the thermal bath that did heat up the chain. That's possible (I think) because you are using information to reduce the entropy of the system. My question is this: How do I see that the energy needed to measure the spin orientations in the chain is at least as large as the energy I can gain by flipping them selective once I have measured? It isn't clear to me why it should not be possible to measure them with some very low-energetic probe, eg measuring the local magnetic field with the Hall effect.
Consider an American actor who is tasked with mastering British Received Pronunciation for an upcoming role. If he has a talent for vocal mimicry, as many actors do, he should have no trouble picking up the "rules" of RP just from listening to people speak it: the non-rhotacism of the dialect, the aspiration of intervocalic t, the characteristic intonation patterns and prosody of RP, and so on. For the most part, he should have no trouble speaking RP like a native. Yet he would never in a million years figure out on his own that lieutenant should be pronounced "leftenant," for example, or that controversy is often pronounced with the accent on the second syllable, unless he hears those specific words pronounced. To my knowledge, there are no general characteristics of RP that account for the mysterious appearance of an f in lieutenant (or, if you prefer, there are no general characteristics of General American that account for its absence). You just have to know how those specific words should be pronounced, because you'll never figure it out on your own. Do linguists recognize a distinction between the "rules" of a dialect on the one hand and its individual pronunciation "quirks" on the other? Is there a term for this phenomenon? Is it considered merely a variation on regional preferences for certain words over their synonyms (e.g., rubbish vs. garbage), or is there something else at play here? (Disclaimer: I take no position on whether the BE or AE pronunciation of any of these words should be considered the "quirky" one; I simply note that one couldn't easily intuit one pronunciation just from knowing the other.)
In a previous Phys.SE question, Does a spaceship travelling at near lightspeed see the universe aging slow or fast?, the answer (which was followed by a proof involving co-moving reference frames) was given as The short answer is that yes, an astronaut moving relative to the cosmic microwave background would measure a shorter time since the Big Bang than an observer stationary wrt to the CMB. However, an observer in such a spaceship will consider the time of any object which is at the CMBR co-moving reference frame to be moving slower than itself. Is this not a conflicting result? For example, let's say the spaceship and a CMBR Earth communicate as they pass by each other. Each would have an estimate of the age of the universe, and each would have an estimate of the measured age of universe that the other would give, based on their own measurement of the age and the time dilation that they assume the other would experience. Here are the results The CMBR observer is fine - both his estimate of the universe's age that the spaceship would give and the estimate actually given by the spaceship match and are less than his own estimate of the universe's age. However, the spaceship expects the CMBR observer to have a lower estimate of the age of the universe because their clock is (according to spaceship observer) ticking slower than his own. What the spaceship observer does not expect is that the CMBR observer's estimate is larger than his own estimate of the age of the universe, yet that is what happens. How is this resolved without implying a preferred reference frame?
I tried to make rain with a bottle and a balloon but it failed. The bottle was small, only a couple inches wide and the threaded part that I had the balloon on was less than an inch. In particular it was the size of this hydrogen peroxide bottle: It was originally a hydrogen peroxide bottle but all the hydrogen peroxide was out of it when I did this experiment. I stretched the balloon a little bit and put it over the threaded part of the bottle. But right before that I put hot water in the bottle. I knew that some water was evaporating. Also there was regular air(including dust particles) inside the balloon(I did this outside during a dry spell during the summer). This gives plenty of opportunities for the water to condense to form a cloud in the balloon and eventually, rain. However I left it out there for several days and nothing happened. The balloon didn't inflate from the water vapor bouncing off of the balloon. The water didn't condense enough to be noticeable. Rain didn't form. I thought that maybe there was too little water and too little air so I went to a much bigger bottle(about a gallon in size). The balloon started to separate. I also had a control of an open bottle in the same conditions while doing this experiment. The water level did not change in the open bottle even when the humidity was low. So why didn't the balloon inflate if the fact that both the water and the air were hot should have increased the vapor pressure, thus causing the balloon to inflate? Why didn't the water condense into a cloud that I could see through the latex of the balloon if it were inflated? Why didn't the water get to the critical size for raindrops if there were plenty of dust particles in there for the water to condense on to form water droplets and eventually raindrops? Why didn't the water level in the open bottle change? Is there anything I can do to improve this rain in a balloon experiment besides having a source of heat underneath the water?
The principle conservation of energy is often taken as an obvious fact, or law of nature. But it seems to me the definition of energy is far from obvious, or natural: http://en.wikipedia.org/wiki/Energy lists lots of different types of energy. So if I want to apply this principle in some concrete experiment, I have to go through all the forms of energy and consider whether this form of energy is applicable to each particular entity in my experiment. This seems like a rather cookbook-oriented approach (and the wiki list doesn't even claim to be complete!). Now I wonder: ---> to what extent can these different energies be derived from some single simpler definition? For example, if my model is that everything is made up of atoms (I don't want to consider anything at a smaller scale, I fear that would muddle the discussion and miss the main point. Also, I'm considering only classical mechanics.) which are determined by their position, momentum, charge and mass (?), is there a clear and exhaustive definition of the energy of a such a system? EDIT: In light of comments and answers, I think I need to clarify my question a bit. Is it true that the electric potential and gravitation potential (for atoms, say) will explain all instances of conservation of 'energy' occurring in classical mechanics? If no, is there some modification of "electric potential and gravitation potential" above which will yield yes? My question is not really about mathematics - Noether's theorem for example is a purely mathematical statement about mathematical objects. Of course mathematics and my question are related since they both involve similar kinds of reasoning, but I'm ultimately after a physical or intuitive explanation (which is not possible using only mathematics since this involves choice of a model, which needs to be explained intuitively) or assertion that all these energies (chemical, elastic, magenetic et.c. (possibly not including nuclear energy - let's assume we're in the times when we did not know about the inner workings of atoms)) come from some simple energy defined for atoms (for example).
I'm nearing the end of the semester of an introductory-level complex variables class. (Very introductory -- it's the version of the class that's only required for engineering and physics majors, as it doesn't require two semesters of undergrad analysis that are prerequisite to the complex variables class for math majors, at my school.) One of the many fascinating things I've seen this semester has been, speaking in broad terms, the behavior of analytic function, and the way that a harmonic function and its conjugate 'synchronize' (for lack of a better word) to create analyticity. Despite the examples I've seen of harmonic functions being steady-state solutions to heat problems and showing up in descriptions of electric fields and whatnot, I feel like I lack any sense of what the 'harmonicity' of harmonic functions is all about. On a side note: I do recall one day, however, where I was working through an example having to do with the level curves of a harmonic function and its conjugate, where I believe the significance what they points of intersection where always orthogonal. This 'mesh' notion created, for me, a visual image of how the the two functions work together to give an analytic function its synchronized, predictable nature. (But, as with most things, I could be mistaken in my understanding of this; these weren't points being stressed in the book, and it was in a chapter later in the book than what we'll cover in the class.) So, my question is that of how one ought finish this statement:"I was considering a problem, and I intuitively knew the solution would need to be a harmonic function because the problem had the property..." I stress the word 'intuitively,' by the way. If you feel this misses the point of harmonic functions and how I should think of them, then by all means please answer however you feel is appropriate.
I'm quite perplexed by the notion of 'observation' in regards to the collapse of a particle's probability wave. Does a particle's wave only collapse when it is involved in a strong interaction (such as a collision with another particle, like bouncing a photon off another particle to determine the other particle's position) or does any interaction with another particle or field also cause this collapse? For example, I presume traditional detectors such as those mentioned when talking about the double slit experiment are devices that do exactly as I stated above and (in the case of the double slit) have a stream of photons (like a curtain) going from the top of the slit to the bottom which the electron (or particle being shot at the slits) has to pass through and therefore get smashed into by the photons. So given an environment where there was no other gravitational or electromagnetic influence, or where the effects of such have been taken into account, what would happen if you had a region of space within which a massive neutral particle 'is' (ie, it's probability wave fills this volume), and then shot a beam of photons across the bow of this region (so as to pass nearby, but not intersect), and then have a photo-sensitive plate on the other side to see if the photons passed straight by, or were pulled towards one direction slightly by the warping of spacetime caused by the massive neutral particle (gravitational lensing on a mini scale)? Does this even make sense? And if the photons were being pulled slightly towards the massive neutral particle, would the waveform collapse at this point, since if the mass of the neutral particle was known, the amount by which the photons path had been bent could confirm it's position couldn't it? Or perhaps take the above and use an electromagnetically positive particle as the target and an electromagnetically negative particle as the beam you shoot by it to see if it is effected by the electromagnetic field caused by the target particle if that makes more sense. I might be making some silly errors or assumptions here, I'm only a layman with no formal education or in depth knowledge, so be gentle :)
First I will have to explain my question. Look at the image below. This shows doppler shift when an object is moving horizontally to the direction of the wave. Keep the word 'horizontally' in mind. Now this happens because: I will quote Jim from his answer for Redshifting of light from a moving light source We all know that light is a wave, when you turn on your headlights and drive in reverse, the light is doppler shifted because of the motion of source. When not moving, each cycle of the light wave is emitted from the same position; it has a specific set of wavelengths. The distance between one crest of a wave and the next crest is equal to the speed of light, c, times the period of the light (which is determined by the oscillations in your headlights and won't change when you are in motion). When you drive backwards, the distance between one crest and the next becomes the period times c plus the period times your backwards velocity (approximately); the second crest is not emitted at the same location as the first, so it extends the wavelength. From your perspective, the emitted wave would not be red-shifted at all, but from a stationary observer's perspective it is. So now my question is, imagine a car which has a torch attached to one of its windows. The torch is switched on and the car begins to move. When the car moves, its movement is in the opposite axis from the propagation of the wave. So each crest will be released from a different location while the first crest is already on its way in a straight line. I will try to represent this graphically. The representation is very estimate. It just shows how would the light bend as each crest is released from a different location. Please explain this to me. Will the light actually bend? Why or Why not? Edit What I have concluded from the answers is that first a photon is emitted and then it continues as a wave and is in no way attached to other photons. Is this right? If I got this then I got the answer for my question.
I'm a math student, starting a PhD in the near future. My field of research will be mostly in the field of applied mathematics / numerics. Topics will deal with Kinetic Theory, Moment Equations, Fractional Diffusion, Spetral Methods. I think I have a solid background in numerical computing, especially for PDEs. Now for my Masterthesis I've dealt with numerical methods for fractional diffusion equations. Since (fractional) diffusion is related to Brownian motion / CTRWs, a lot of authors named mathematical finance as a field that is impacted by their research. The problem is, that I have absolutely no background in finance / econ whatsoever, but I would really like to get into this topic. I think it would open me a lot of opportunities to gain a little expertise in that field. I started to read some mathematical finance papers, referenced in the papers I encountered and noticed quite quickly, that I lack the non-mathematical background. The goal of this question is maybe a bit ambition. I would like to get to know the field of mathematical finance over the next three years. Start with the basics and then move quickly to mathematical finance with a focus on computing / simulation. Since I will do this on top of my work, I would also appreciate books that I can pick up every other day/evening and just read a little. What interests me espacially are processes that are related to Stochastic DEs, Brownian Motion, Ramdom processes. Especially topics that might rely on the same basics as diffusive processes / kinetic theory. For example, some buzzwords I encountered where stylized facts, options, derivatives (in finance). Maybe you could split up your recommendations in the categories finance/econ, general mathematical finance and random processes / SDEs in finance. If you have general remarks regarding my proceedings please feel free to contribute (for example, what do you think about visiting certain lectures offered at my university, broadening my mathematical background, relating my research to the field of finance, software I should get to know like R, etc.) Thank you very much!
Suppose I have plotted the body angles of a flying aeroplane.I have two such plots. One of a normal plane, and the other plot in which a primary sensor of the aeroplane is removed. So with the absence of a sensor you are expected to see an instability in their flight. Below are the two graphs--- The first one is the control flight, and the second one is the experimental (sensor removed.) Lets look at the second graph --- you can see that the roll of the flight is sinusoidal. Even the pitch is slightly. But the sinusoid fluctuation of the roll is more prominent. And I see this fluctuation in all my experimental graphs (sensor-removed) that I have obtained, and none in the control (normal) graphs. Now, I would like to quantify this fluctuation. One way of quantifying it would be to plot the mean and standard deviation of roll in both cases and show that the standard deviation is very high in the second case. But this is not correct because, the standard deviation might also be very high in the first case ---- this can happen when the flight rolls a lot, but does not necessarily fluctuate. It could roll in one direction, maintain that for some time, then roll in the opposite direction or the same one. Its not fluctuating, but standard deviation will be high. So, I am looking for another parameter, to quantify this fluctuation in the graph, something like a fourier transform perhaps. Something that would accentuate the instability bit. Suggestions people?
During an episode of Archer, he criticized a journalist's grammar for her misuse of the word 'child-murderer'. She meant one who murders children, and Archer argued in using the hyphenated form, she implied the accused man is a child who murders. Is this correct? I searched "child-murder" and "child-murderer", only to find columns eschewing the hyphen in nearly all cases. Instead, the columnists, relied on context as to whether they are referring to a child who murders or one who murders children. I, however, am purely interested in the proper use of the hyphen in this situation, as it could possibly extend to other situations as well. The trouble seems to arise from child not having an adjective or descriptive form. With 'teen', one does not run into this problem: Teenage murderer vs teen murderer However, if one uses 'adolescent murderer', it becomes unclear as to whether one means an adolescent who murders or... you get the picture. This problem arises from adolescent being both an adjective and noun; a hyphen can resolve the ambiguity. But once again, how should the hyphen be used? I found a similar question: What is the plural of 'only child'? I err on the side of only-children, in the event that 'only children' reads as 'just/simply/merely children'. Some suggested entirely new phrasing, while others say that the context is sufficient. I don't believe one should change his entire sentence when proper use of the hyphen can get his meaning across just fine, and even when context is suitable, proper grammar is still rule of law.
I'll try my best to explain my question with examples because I don't have much knowledge on the theory. So say that I had a block of water in air, a cube of water, that is dropping. If the cube wasn't too big, I believe that as it will drop, then the air from underneath it will rush to either side of it, as the water displaces the air on it's way down. Now lets change the situation. Say I had the cube of water, but now its suspended in the air in a tank (like a fish tank), as shown in the picture. Here, I believe that there is the weight force of the water acting evenly downwards, but the air pressure may be different, as the whole system is bounded by the walls. Logically, I believe that the air would then rush through the center of the water cube, forming a bubble, allowing the water to rush down to the bottom. Though this may be completely wrong, I'm not sure. So my question is, is that is there any possible shape for the water to be originally in, so that all the forces sort of balance so that there is no distortions in the shape, and that then the air will be compressed under the force? I understand that perhaps at the microscopic level, if we take into account the random motion of molecules, and other factors, that there will inevitably be some sort of inbalance, but macroscopically what would be the perfect shape? I'm not even sure if any of this makes any sense. Thanks for any help understanding.
Saw a question about faster than light travel... I still have the same question though none of the answers offered any resolution for me. It is so summarily assumed by all physicists and commentaries that exceeding the speed of light would turn back the clock. I can't see the relation. Doubling the amount of any speed halves the time taken to travel a given distance. Keep doubling the speed and that time is halved (or otherwise divided). Divide any quantity (time in this case) and you always end up with a fraction of it but never zero and certainly never a negative amount as would be the case for the causality conflict. So it seems to me that whatever speed one attains, there is always a positive time element in the travel no matter how tiny!! The speed of light is only unique to me in that it is the fastest observed speed but is otherwise just another speed quantity set by nature (just like the speed of sound etc) could it be that other elements in nature are travelling faster than light but we lack the means to detect or measure them (like the rebellious neutrino)? I also don't understand time as an independent element that can be slowed sped up etc. It seems to me that time is simply a relative measure of the ever-changing state of matter relative to other states of matter. If every thing in the universe stopped- that is all state of matter everywhere frozen, all electrons frozen in place etc wouldn't we observe that time had stopped? Isn't it therefore our observation of the changing state of matter around us that gives the perception (perhaps illusion) of time? I can therefore only understand time as a subjective sense of changing states relative to an observer! It should be the rate of change of these states that slow down or speed up (in relation to the observer or instrument) and not the universal rate of change or universal time that changes! It would also debunk any notion of time travel, as it would involve the manipulation of every particle in the universe to a previous of future state... Disclaimer.. I hate calculations, stink at them and have no idea what mathematical formulas are used to arrive at the accepted conclusions so I'm not trying to dispute any findings etc by the experts, just trying to align my lay understanding to their conclusions.