darklight03/StackMIAsub huggingface dataset:
How is quantum entanglement different from a controlled experiment where a pineapple is smashed at a high speed to a perfectly symmetric object and measuring one of its piece in air for spin, speed, direction etc. and finding correlations with other pieces of pinapple in mid air? In quantum mechanics information cannot travel from piece A to piece B at faster than light to explain the correlation so the result is seen as unexpected (at least to people outside the science community like me) and at any time a piece can have any property but once the properties of a piece is measured the wave function will collapse and the properties of other piece or pieces becomes clear. But isn't the correlation simply due to how the piece or particle was generated? No information needs to travel because the particle is simply continuing to react to the same common generation event? If we can call it information isn't it already with all the particles or pieces of pineapples in air already? I (am a beginner, used to be interested in physics but nobody gave me answers so lost interest eventually and took a career in finance. this one was one of my questions) also view quantum mechanics as deterministic rather than probablistic but think the probablistic approach is necessary because we cannot measure all the variables with our very limited measuring and processing capabilities. For example, a roll of die by a machine is deterministic if we measure and process everything from the light fluctuation in power, air movement in real time, mass of the die, initial position, curvature, area of contact, etc. but because that is too complicated we use it as random with a probability. I feel in quantum physics we are doing the same thing as it is simply more practical, but everybody I talk to truly believe I am wrong. Mentioning this as it is related to the question, that is, the properties can be calculated without measuring in quantum mechanics if we have virtually unfathomable knowledge, measurement capability and processing power. We don't have that so in my view too probablistic quantum mechanicsm is the way science can progress, so no question about that, but is it established that quantum mechanics cannot be deterministric in reality? Just want to know where and why I'm wrong. Thank you in advance.
It occurred to me that the limits of possibility to the nature of the universe is it is either deterministic ie we are all at the will of natural laws that determine the outcome of events from the moment of inception and we are philosophically dust in the wind. Or is the world random and our future is uncertain and indeterminate we have freewill and there is nothing governing our future but our free choice or is it both of these scenarios happening concurrently. I am no expert, but from what I gather from quantum mechanics is that the cause of events at the quantum level is indefinite and the outcome of these uncertain and probalistic. There is the principle of uncertainty in which determining the property of a particle results in an uncertainty in determining the nature of another property of this particle is it this principle that makes it difficult to get precise measurement that is a factor in us being able to predict the outcome of events in a linear deterministic equation that gives us the unpredictable nature of quantum mechanics ie there is an equation governing the outcome of events at the quantum mechanical scale and classical scale but we are unable to feed that equation with precise data to enable us to accurately predict their outcome ,kind of like how dynamically chaotic systems are mathematically determined by there initial condition but a small perturbation or difference in initial conditions results in a different outcome. I know its that old chestnut I am not a mathematician or physicist but there can only be three possible scenarios any response will be welcome even if its disparaging.
The proofs presented in lectures, textbooks ect. are usually cleaned up versions that show just the necessary steps for logically proving the theorem, not the thought process that went into the proof. To give a concrete example, I'm working through an (overall quite good) MIT Open Course Ware class on real analysis. I just paused a lecture where the professor said: Now, when you write a proof, as you'll see, it's going to be magic that somehow this h does something magical. That's not exactly how you come up with proofs. How it comes up is you take an inequality that you want to mess with, you fiddle around with it, and you see that if h is given by something, then it breaks the inequality or it satisfies the inequality, which whichever one you're trying to do. And proceeded to just write the finalized proof. Because that's not the part I care about. The main thing I want to learn is the part were you do the fiddling around to come up with the proof to begin with. Verifying proofs other people made is (relatively) straightforward, and the property being proven (Q doesn't have the least upper bound property) is important but I'd be willing to take it as an assertion if I was just trying to learn about Q rather than how to do analytical proofs. I would really like to see examples of someone who is good at proofs showing their work in creating a new one including the dead ends, fiddling around ect. I have tried to teach myself this step by just going out and proving things, and have made a little bit of progress but thing I would greatly benefit from more examples of deriving proofs.
In gel electrophoresis, there needs to be an electric field created in the gel. I realized that I have some gaps related to my understanding of electromagnetism because I cannot fully understand in what conditions a field gets created. Are the electrode plates on either side in contact with the gel or insulated, and if so, how does this affect the field? My understanding is two insulated plates with different voltages would still create a field between them. Is the issue that the surface charges in the gel would align themselves to cancel out this field on the gel inside? Thus, do you need to actually pass a current through the gel in order to create an electric field inside? I think this is related to the nature of the electric field in a current carrying wire (where I treat the gel as a really thick rectangular wire), which I also realize I don't understand. Namely, do the electrodes need to span the full width of the gel rectangle to create a uniform field across the width? More generally, what are the possible ways to create an electric field on the interior of a conductive object such as a gel? Do you have to pass a current through it from one side to the other? My other thought is that a changing magnetic flux would also create an electric field, although it would be of a odd shape. But would this induced electric field exist on the interior or also be subject to some cancelling effect as is the electrostatic case?
Recently I saw a conversation between Sean Carroll and Slavoj Zizek concerning the MWI. One of the questions that drove Slavoj concerned with this question of Ontology vs. Epistemology, as the way Sean had described the current understanding of MWI is that we merely 'don't know' where we are on the wavefunction which seems to keep the openness of reality at the level of epistemology rather than ontology. The question I have concerns entanglement with new information that an object encounters as it is coming in from outside the object's light cone. In my understanding when entanglement-measurement occurs, some pair (or more) objects in the wavefunction take on a correlated value, but then the price of this is that other values become randomized (so electrons take on opposite spins, but then the spin of each electron is not determined). What I am wondering is as we pass from before the moment of entanglement with new information coming in from outside the lightcone to after that moment, some of the information will be consistent (or not consistent) with our current history - that information gets zipped with (or excluded from) the entanglement event, but all the sort of 'random' information that is really new... is it the case that the wavefunction of our object has a different space (or location on the wavefunction) for each of these random timelines before the encounter with new information - or is that space created at the moment of entanglement with the new information? That is... is it the case that our original object is actually already always split into all of its future possible timelines in a way such that various points on its original wavefunction can be assigned to various final 'futures' - or is that split not possible in principle or in the mathematics from the beginning of the calculation (so that in reality many futures pass through the same original point on the wave function)?
I would like to forecast demand count time series of taxi fleets at different locations on the map at different points in time. I.e. multivariate demand Time series forecasting. Given hierarchinal demand time series. where the region level time series is the sum of district level time series at each point in time and district level time is the sum of city level time series at each point. sum of all the city level time series at each point in time should equal region level time series. There are also covariate time series (both numerical and categorical) associated with each city's demand time series. e.g. rainfall level, temperature, traffic level, taxi supply amount, date information like weekday or weekend, holiday information and Time invariant features like type of city. (e.g. industrial, CBD, residential etc. ) Note: The city level time series are quite sparse ( have many zeros). How do I go about using a bayesian framework/statistics to model and predict the mutivariate (city-wide) demand time series? The reason for choosing the bayesian framework is to estimate uncertainty in the prediction. Build a strong prior sequentially over time which can capture the fundamental data distribution/patterns without being affected by noise in instantaneous data. incorporate the various pieces of covariate information together to enhance prediction accuracy. Here are my thoughts: Use summary statistics of covariate time series and response time series like ACF to compare similiarities between and try to explain causation. Try to improve dataset quality by (probably using bayesian a hierarchical model using partial pooling) to combine sparse and low quality (lowly correlated time series to response time series) covariates to model a better covariate. Use bayesian sequential learning to sequentially accumulate learned patterns over time into the prior distribution. Could someone give me your thoughts and suggestions on how to go about doing this? Thanks.
When a mathematician says that two categories are the same thing, they may mean there is an equivalence or an isomorphism between them. I am wondering if there is a precise way we can say that two categories that are isomorphic are different categories. I have no idea what I mean, but perhaps it has something to do with models of categories in Set. I just feel there may be justification sometimes when two mathematics feel that two isomorphic categories should be considered independently. Is this possible? Does it ever come up in discussion? For example, consider this language on modules "The concept of a Z-module agrees with the notion of an abelian groups." This language "agrees" really means there is an isomorphism of categories. It seems like the theory of categories simply deletes any way of seeing them differently, but is there another way of seeing them where one might say"No, we consider them differently!" I think this might have something to do with the way computer scientists talk about monads in a different way than mathematicians. If you've ever looked at these two literatures, they are nearly incompatible at times. This may have something to do with the notion of "up to isomorphism" in category theory. When, in category theory, do we say, "no, I won't forget details that are deleted when we work 'up to isomorphism'"? Is there category theory that doesn't work "up to isomorphism"? Which category theory concepts and constructions only work up to isomorphism and which, if any, go beyond this?
Consider a loop gap resonator for electron paramagnetic resonance which has static (but sweepable) magnetic field in one direction, "x", and a GHz RF magnetic field in a direction "z" that is perpendicular to the static field." I had assumed that I had built the loop-gap such that the H_z field was constant over the sample volume. We get a reasonable EPR signature from it, can identify some hyperfine components, etc. I finally got around to doing a finite element for the field and to my surprise, the calculation appears to show that I am generating positive and largely constant Hz on much of the "left" side of the resonator and exactly the opposite Hz on the "right" hand side of the resonator (i.e. negative Hz, with zero field in the middle). I am now completely confused. I would not have thought such an RF field could give any EPR signature because the spin contribution on the left should cancel that from right. If so then my FEM model is wrong and I need to look there. But maybe not... in which case I need to look into fixing whatever is driving the wrong eigenmode because obviously I will get more signal if all the Hz is uniform. So that's my question can you get an EPR signal from an Hz which is flat over two areas of the resonator but such that the average Hz is zero? Or maybe in math terms: Given a computation of the RF field in a resonator and a theoretical spectrum of a species, how can I determine the corresponding EPR spectrum of the sample? E.g. does it depend on |H_z| or H_z ?
In everyday talk we say things like: we must use the fundamental theorem of calculus to calculate this integral; we must use the results of analysis to proof the fundamental theorem of algebra; we must have a function that maps well formed formulas to numbers and that is bijective (Godel beta function); we must have a ring with the fundamental theorem of algebra to be able to proof this result; etc... Sometimes it seems that, when we say this, we are saying that the theorem in question must be made an axiom, then we will try to investigate what results hold with it, or without it, like in the case of the fundamental theorem of algebra. Sometimes it seems that we are saying that to proof some theorem we need to use a central theorem that mobilizes a particular set of axioms, this seems to be the case with the fundamental theorem of calculus, or the case of a theorem that say that some function or property exist and we must use it. In this last case, which is the case I am interested, it seems that the construction we are trying to make needs another construction, that in turn needs a set of axioms. But it's not the case that, if we simply fix it as an axiom, we could see what thing depends or not on it, for fixing it as axiom would turn the axiom system redundant (meaning: one or more axioms could be eliminated). So, my question is: what means to say that a theorem depends on another theorem? Is there some logical analysis of what means to say this?
Constant motion can not be detected by neither particles (because of inertia) nor mechanical waves ( because they need a medium ). However when you consider light for example and assume it does not need a medium to travel through you could detect constant motion. For example, when someone is traveling at the speed of light in the x direction, and fire some photons in the x direction the person would see light as standing still while someone who is not moving will see the light passing at c. So why would we consider constant velocity to always be relative and so on undetectable. Clarify: Its obvious that the discovery was made, however for Einstein to actually get anywhere he needed to assume c to be constant. Which is exactly what I am wondering about, how did he come up with this. So that is why I am asking about constant relative motion and trying to come up with a thought experiment which proves the distinction between being stationary and constant velocity reference frames. However every single object with or without inertia which includes particles and mechanical waves are shown to give no proof of one or the other the one being in constant velocity. Which brings me to a light wave traveling through no medium and then would suddenly give us a way to detect constant motion, because now the so called ether wind is not causing the wave of light to go slower because the "wind" is moving in the opposite direction, no, it is now possible to say that light moves at a different speed for one of the two experiments on board the two and then proof that the one where c is slower, is the one actually moving and the one other one stationary. So from knowing this to be forbidden there is only one logical conclusion c must be constant for all observers, its the part where knowing this to be forbidden to c is constant for all observers is where I am stuck. Ps: please don't just give me a mathematical proof, this doesn't really help me, Much appreciated!
A 'blunt' statement is when someone says things to the point and factual. But wouldn't 'sharp' (or some other word that implies frankness or sharpness) be a better word than 'blunt'? As blunt has the meaning that it is not sharp. When someone says something that is not direct or something soft (and if I am to make phrases or rules in English) then I am more likely to use 'blunt' for such a thing. All I am saying is the real meaning of the word is not appropriate(actually opposing) for the phrase. Being direct is never 'soft' and can hurt and blunt real meaning is more close to 'soft' and cannot hurt you (compared to a sharp object). Blunt: (of a cutting implement) not having a sharp edge or point. "a blunt knife" (of a person or remark) uncompromisingly forthright. "a blunt statement of fact" Etymology here points to some interesting meanings and usages but none quite explain the usage in phrases . Edit: what I am trying to say explained better in comments by other users "why blunt means what it does, when it doesn't sound like a piercing effect" The most common, physical meaning of 'blunt' is 'dull', 'rounded', or lacking edges - the antonym of this context is, as you say, 'sharp'. But when 'blunt' is used more metaphorically to mean 'direct' or 'unnuanced', the antonyms are very different. Also "Blunt knife hurts more" is creepy thinking and language usages do not take shape on those lines. It is usually simple popular opinions that turn to usages/phrases.
According, to definition, provided, as I understand by Newton, there are frame of reference, where all constantly moving bodies keep their velocity constant, untill the force is not applied to such bodies. Some sources, in particular Russian Wikipedia inertial frame of reference article, state, that there is no inertial frame of reference in the world (translated from Russian): Absolute interial frames of reference are mathematical model, and do not exist in real world Or, for example this answer from this forum: When you ask for a "perfect" or "true" inertial reference frame you are asking for something that cannot be answered in physics. But each time sources either do not explain why, probably considering it obvious, or the explanation is not satisfying for me. I do not know, do I understand the reason correctly. Is the condition of frame of reference to be inertial applied for any time? Do constantly moving bodies in such frame should always move constantly if the force is not applied, so if the force even only once is applied to the body, which is linked with inertial frame of reference, that frame will never be intertial? Or frame can variate: for some period it can considered absolutely inertial, even in real world, for some period not? Is there no inertial frame of reference because there is no constantly moving bodies, i.e. every body have at least tiny, yet acceleration? If yes, why all bodies have acceleration? Due to mass, and the fact, that gravity force goes to infinity? Okay, I understand, that massless particle will move at speed of light, but what if there is a particle, that doesn't not affected by gravity or eletric field, i.e. will be "fixed" at space? Will it have intertial frame? Also what about particle with speed of light? Since their speed is constant, don't they have interial frame of reference? (Extra) Also, since the motion, even non-constant (i.e. with acceleration), as I understand is relative, then for some frame of reference, attached to the accelerated body, there are "constantly" moving bodies, that "actually" move with acceleration, but relatively to such frame - constantly. I do not understand why this frame is not inertial? Because, by definition, bodies should move constantly and without a force being applied to them? But how do we know is the force applied? No, if someone punches a ball, okay, but what about fields of something like this?
I am in advanced UG (in Elec Engg). I was consolidating a mental model to help in (most of) engineering applications. I read Griffith recently. I learned that there exists no magnetic charge, (although, as Griffith said - how cute the scenario would have been, if they did.) Intuitively so; as Magnetic fields are engendered by time-variance of electric phenomenon (in field or charge (as current)), I never expected their existence. But, why the world needs a concept that is "charge"? The Gauss law, firmly relates the charge concept to the field. Intuitively, the field fluxes out of charge. It may seem that charge is engendering the field. But, let's believe in absence of such concept; the field is inexplicably (concentrated) sourced at "some" places - say S. Here is an argument - It is ambiguous whether the charge carries the energy or field. In the absence of charge concept; the field carries the energy; then the source to this energy are S. Energy is a transient phenomenon; Charge concept could represent the source to these new perturbations in the field. Coming to the title of the question. There is no magnetic monopole. Why is there an electric mono-charge? Clearly, charge represents transfer of energy from other domain of energy into electrical domain. Transfer of energy is relative. Can't we say the other half of the charge exists in the other domain of energy? (imaginary pole). I have an argument to address the polar nature of charge as well. But, I have already revulsed enough physicists here. (Excuse me, I was just thinking.)