darklight03/StackMIAsub huggingface dataset:
I read an article that referred to the idea that a double slit experiment near the event horizon of a black hole observed by someone inside the black hole creates a paradox because the inside observer can break the interference pattern, thereby bringing information of their presence out of the black hole. This seems odd to me. The significant part of "observation" here, as far as I understand, is that it requires interaction. The inside observer can't interact with the particle to measure it's position. He can only detect it's position if something outside the black hole interacted with the particle, which means the superposition would have collapsed whether or not he was there. Am I missing something? Edit: Link: https://www.sciencenews.org/article/black-hole-paradoxes-quantum-states
I have often heard that two physically distinguishable mixed quantum states produce different density matrices. However, how would I prove it? I know that they have to differ on the main diagonal, because these elements correspond to measurement probabilities in the standard basis. Moreover, I have seen someone using density matrices to show that two mixed states are physically indistinguishable. Does this process always work? In other words, is it true that for any two physically indistinguishable quantum mixed states, the density matrix is the same? And how to prove it?
I'm learning some math by myself and I thought of this question that has to do with how useful complex numbers are: I'm looking for a specific example of an equation that has the following properties: The equation is true, i.e., its LHS and RHS are always equal, no matter the values of its variables, if any. The LHS and the RHS are algebraic expressions (no limits, derivatives, integrals, sin, cos, etc...) The equation only involves real numbers. Its shortest equality proof involves complex numbers. The proof ends with no complex numbers. It has a longer equality proof that doesn't involve complex numbers. It's a short equation (this property is subjective). Please, let me know if my question is wrong or if no such equation can exist.
I want to understand in some detail why superconducting qubits need periodic calibration. The usual, hand wavy explanation is environmental effects that tend to vary from time to time. However, I suspect that the actual picture is more complex than that. I want to understand in particular which effects are purely external, like the earth magnetic field (in lack of a better example) and which are internal to the superconducting device. I am especially interested in those factors that are internal to the qubit itself, like manufacturing defects and physical characteristics that may change in time. A good reference on this subject would be appreciated.
A spanning tree of a graph is a subgraph obtained by deleting only edges of the graph and which is also a tree. Why does one study "spanning tree" in graph theory? What are "spanning trees" real life application? We know the number of spanning trees of a graph is equal to any cofactor of the Laplacian matrix of the graph. Why is one interested in knowing number of spanning trees of a given graph? I would like to know enough in order to motivate a undergraduate or graduate student.
Hi I was trying to determine the basis of the topology on the following collection in R {[a,b), a <b}. Here is what I tried : Knowing that the basis for a subspace topology is equal to the set of all intersections of {[a,b), a <b} with the basis of the topology it is a subspace to. Now I also know that the basis for the euclidean topology on R is {(a,b), a <b}. Can I just take the intersection of {[a,b), a <b} and {(a,b), a <b} to get the basis? If so what does this equal? Or am I totally wrong? Thanks in advance.
I understand that Berry curvature sinks and sources correspond to Weyl points. However, I'm curious about the identity of points exhibiting a Berry curvature spiral, highlighted by red circles in the figure below. Could these be Dirac points? Is it possible to differentiate between Dirac and Weyl points based on the direction of the Berry curvature rotation? It's worth noting that these two spirals exhibit opposite rotation directions.
I read that a sound wave (a scalar wave) produces monopole radiation, an eletromagnetic wave (a vector wave) produces dipole radiation, and a gravitational wave (a second order tensor wave) produces quadrupole radiation. How do I make sense of multipole radiation physically? The Wikipedia article on multipole radiation is informative on the mathematics, but I can't seem to get a physical picture. Note: my question is different from this post, which asks about the pattern of lowest order multipole radiation produced.
first post here. I've been looking into acoustics a bit recently and I'm wondering if for a compressed solid, acoustic impedance should change along different axis in certain cases. Consider a cubic lattice of atoms with pressure being applied to the top and bottom, compressing the lattice. Atoms would be spaced further apart in planes parallel to the applied pressure. I'm hypothesizing that acoustic impedance would be higher for a sound wave travelling through the lattice perpendicular to the plane of applied pressure and lower for a sound wave travelling through the lattice parallel to the plane of applied pressure. Could we consider density as a vector to solve our impedance equation if the above holds true?
We know that Maxwell's electromagnetic theory was originally an ether theory. Later, the ether was denied. But Maxwell's electromagnetic theory can be transformed into a theory of "field". The theory opposite to Maxwell's theory is the theory of action and reaction. Or it could be the theory of action-at-a-distance (Wheeler-Feynman absorber theory). According to Maxwell's electromagnetic theory, electromagnetic waves can exist independently of their source or have their own degrees of freedom. According to the theory of action-at-a-distance, electromagnetic waves cannot exist independently of their source. Electromagnetic waves do not have their own degrees of freedom. These two theories have been debated for hundreds of years. Is there a formula that can distinguish which of these two theories is right or wrong. Just like Bell's formula?
Consider a few sentences: I read a lot. ?I read much. I don't read a lot. I don't read much. Do you read much? This seems to suggest "much" is a negative polarity item, but then we can say things like "Much of it has to do with you not being here." So how much of a negative polarity item is "much"? I am particularly interested in existing literature on this.
While reading the CMU FLAC overview, I stumbled upon the above image. While I have seen Greek numerals before, I had no idea that there was an entire algebraic symbology developed in Greek (though this isn't too surprising). To try and find more about this particular notation, I reverse Google Image searched it and found nothing (well, I was greeted to snippets written in the Tengwar, but that's besides the point). What is this notation? Can you direct me to an overview of the system?
As a thought experiment, say, for the sake of simplicity, we have a meson. This meson, which is traveling near light speed, is traveling towards a black hole. And skirts the event horizon in such a way where the anti-quark ends up inside it's event horizon, but the quark does not. What would happen? Would this create a free quark? That seems like the only logical thing to happen, but I know that would also break color confinement.
The operational principle of frequency combs is that you generate very short pulses (in time domain), and that in the frequency domain (due to Fourier's transform) the spectrum of such pulses is a comb. But this is just maths. And how it works from the physics perspective? Let's say I have a monochromatic continuous laser pointer that outputs only ONE wavelength. In front of the pointer I place a shutter that chops the beam into short pulses. How can those pulses have multiple optical frequencies (with many different wavelengths)? Or is my idea too simplistic and I'm forgetting something?
If so, then why? We know that a current carrying closed loop in a uniform magnetic field experiences no force but when it's suddenly pulled by an external force, according to Lenz law a magnetic force will start acting on it to oppose the external force and eventually reach steady state at infinity. How can this be? Edit: Iam sorry for not specifying the doubt clearly, here is the question in which I was confused as to how there can be a magnetic force acting on the ring
What does the Stark-Lo Surdo effect consist of in the interaction of the electromagnetic field and the active medium in a laser? I thank those who want to give a clear and concise answer. In my student notes from the seventies, I found the topic I was looking for, the calculation for which I attach. But what happens in practice (since I don't have an optics laboratory available)?
Am getting the following error when I try to do tlmgr install package: tlmgr.pl: package repository http://mirrors.rit.edu/CTAN/systems/texlive/tlnet (not verified: pubkey missing) It appears I need to get the keys somewhere, but I haven't been able to find them on CTAN. Where else can I find them? If it's any use, I just updated my system on Arch, so maybe some other fellow Arch users had a similar problem?
Any regular curve may be parametrized by the arc length (the natural parametrization or the unit speed parametrization). But I haven't seen an analogous development for regular parametric surfaces. I hope we can do this at least for orientable surfaces with no umbilical points. For such a surface, there will be two orthogonal lines of curvature through each point, and I suspect that there is a parametrization whose parametric curves coincide with lines of curvature. But I'm not sure how I should approach showing the existence of such a re-parametrization. Is there a such parametrization? If not, what are the conditions that we should impose to have such a parametrization?
When talking about black holes and singularities, most books say that combining relativity and quantum mechanics gives the answer of infinity in some equations. They also say that: Infinity is the answer you get when the universe is trying to tell you that you have made a mistake. Why can't equations have answers of infinity? For example, a singularity is infinitely dense, so why can't other things about it be infinite?
In the original version of Sequent Calculus by Gentzen for classical and intuitionistic propositional logic there is a structural difference: the classical version admits succedents with multiple formulas but the intuitionistic version admits only succedents with one formula. I'm searching for another formulation of Sequent Calculus in with succedents are restricted to one formula both for classical and intuitionistic logic. In particular I'm searching for a formulation in which Sequent Calculus for classical logic is obtained by Sequent Calculus for intuitionistic logic by adding some rule (i.e. excluded middle). Can someone suggest me some reference?
It is often said that the achievability proof for Shannon's coding theorem relies on the channel being discrete and memoryless. At the same time, following the classical proof (using random coding and AEP), I can't find any part of the proof that explicitly uses the fact that the channel is memoryless (except arguably perhaps the guaranteed existence of a supremum of the mutual information?), as AEP has been shown to work for any stationary and ergodic channel. Further, Shannon's original paper does not seem to make any mention of memory in the proof as far as I can tell. Is it true that the classical achievability proof relies explicitly on the channel being memoryless? If so, where in the proof is the memoryless assumption used?
Quick question with probably a simple answer. For context, I am currently in undergraduate classical mechanics studying potential energy. My question is, if a conservative force is one in which is only a function of position, can radioactivity be a conservative force? The example I thought of was if we take two identical particles which are undergoing radioactive decay, and we put one in the upper bound regions of the atmosphere, and the other at sea level, can we say that radiation is a function of position? I guess this also poses the question, can atmospheric pressure/temperature affect radioactivity? Feel free to slaughter my logic/understanding. Thanks :)
I know work done is equal to product of force, displacement and cosine of angle between them. But that formula works only when we assume that the force is constant during displacement and it acts so long the body moves and also when the direction of force and displacement is constant. But how should I calculate work done if the direction of force or displacement is changing. So in this case there would be no constant angle between them and so dot product won't work as I don't know the cosine value and at this point I have got stuck.
I have an object that takes a shape similar to a catenoid, which is known for its zero mean curvature. According to Laplace's law, the pressure difference is proportional to the mean curvature. This implies that if the mean curvature is zero, then the pressure difference is also zero. However, I am aware that when there is a non-zero pressure difference between the inside and outside of the object, which has left me puzzled. Is it possible to have a shape resembling a catenoid but with a constant pressure difference? Furthermore, how can I relate the curvature to the distance, r(z), from the z-axis to any point z on the boundary of this shape?
Reading through Einstein's Brownian motion paper "On the Movement of Small Particles Suspended in Stationary Liquids Required by the Molecular-Kinetic Theory of Heat", it seems the final argument is that he can calculate the Avogadro's constant by using data on the diffusion rates, particle size and fluid viscosity. But its hard to see the connection that ultimately atoms must exist. Can someone lay out a flowchart of step-by-step reasoning leading to that conclusion? I see all the math steps, but need a more philosophical type of breakdown. Also can't the random movement and diffusion law movement of the particles be just as well explained by fluctuations of pressure and density of continuous matter?
Is it correct to say: for any family of bounded operators (proper subset of B(H)) acting on a non-separable Hilbert space there is a non-trivial subspace of the Hilbert space that reduces the family? I know that this is true for any operator on the space so, I assume that it holds also for the von Neumann algebra generated by this operator. Can we generalize to non-commutative families? If the answers is positive (or positive with certain restriction imposed on the family) how can we show it? Is there any reference?
If you were to measure a regular hexagon, is there a way to rotate the hexagon so that if there were two lines bisecting the center of the hexagon, both lines would be the same length? Can we then use the lengths of those lines to determine the area of the hexagon? Edit: To clarify, I mean that I intend for the lines to be perpendicular.
There are four concepts which are studied in Calculus and Analysis: Convergence, Continuity, Differentiability and Integrability. In Calculus, you can define the latter three in terms of the first, but also you can define integrability without convergence using Darboux approach. In topology, you can define convergence and continuity in terms of neighborhoods, and in measure theory you can define integrability in terms of measurable functions. I wonder if there is a definition of differentiability without making any reference to the concept of limit or convergence, thank you so much by your help.
Consider the following diagram Here, the diode is in forward bias, and allows current to flow. However, I am slightly confused why this is the case. A diode is defined to only allow current to flow from the anode ( Positive ) to the cathode ( Negative ). When drawing a diode, the cathode is the line and the anode the base of the triangle. Conventional current flows from the positive terminal to negative terminal, but in reality the electrons flow vice versa. Hence, considering the above diagram, shouldn't the electrons not be able to flow through the diode? The only way I can see around this, is that diodes are also drawn, considering conventional current. Is this correct?
In the derivation of Torriceli's law it is assumed that the pressure at the tank hole is equal to atmospheric pressure. I believe this is true when the water starts flowing through the hole but I do not understand why this should hold during the whole purge procedure. Do you have ideas about the explanation? CFD calculations showing this behavior would be great. Many thanks.
The second law of thermodynamics states, that entropy (of the universe) always increases. Entropy can, however, be (locally) reduced when energy is provided. At the phase transition from a relatively unordered to a more ordered state (e.g. condensation of vapor to a liquid), the entropy is lowered. At the same time, energy is released from the system (thanks to the enthalpy of condensation). Naively, I would expect that I need to provide energy (instead of gaining some) to the system to lower the entropy. Why does this not contradict the second law of thermodynamics?
I know that the Heisenberg Uncertainty principle states that the position of an electron is uncertain, however, if an electron is created due to beta decay, then at what location is it more likely to begin its movement? Is it right inside the proton? Is it the outer edge of the proton? Is it adjacent to the proton? Is it near the proton? I mean is there a possibility of a beta particle from a nuclear decay to come into existence at the far end of the galaxy for example? What is the limiting condition for its position?
According to Fermat's principle, light should take the least time between two points. Therefore, is it correct to say that the angle of refraction is solely dependent on the difference between speed of light in two mediums? Surely the the position of the observer is a key factor too, given the findings of the double-slit experiment that show a photon is only actualised on measurement/observation. Does this not imply the necessity of an observer for the existence of an angle of refraction?
I've been reading more category theory as a prerequisite to understanding some more complicated theorems, and for the first time I'm running into arrows that are distinctly colored. Examples include these diagrams from Wikipedia for natural transformations and universal morphisms: The Wikipedia articles do not readily show me a link to where the coloring for these diagrams is explained, and I have not seen these colored diagrams in the textbook I have been reading for Category theory. Why are these arrows (and objects) colored blue and red? Better yet, (if possible) can someone give me a link/source/textbook that explains this coloring procedure? Thanks in advance.
I understand that the word spook is a racial slur that rose in usage during WWII; I also know Germans called black gunners Spookwaffe. What I don't understand is why. Spook seems to also mean 'ghost' in German. Did the Americans call them spooks because the Germans did? If so, why did the Germans call them that? Or, if the Germans called them that because Americans called them spooks, then why did the Americans call them that? And how did Americans know the Germans had a nickname for black gunners?
When researching the reflexive, symmetric, transitive, addition, subtraction, multiplication, division, and substitution properties of equality, the sources I found said they were true "for all real numbers". Are any or all of them not true for complex numbers? i.e., is the "for all real numbers" a necessary caveat, or should it say "for all numbers"? Also, I know the reflexive property applies to mathematical objects as well (any mathematical object is congruent to itself). Do the other properties of equality apply to all mathematical objects as well?
I am trying to calculate the determinant of the following matrix. I literally have no idea if there's a general approach for solving such strange looking determinants, but I decided to subtract the first row from each row after the second. I don't know what to do next... May you show me what we're supposed to do and how do we find the determinant? Thanks!
Assume a Gaussian surface in a non-uniform electric field that is directed along X-axis. Say the field is getting weaker as we go along positive X direction and it's constant along Y and Z directions. Then, if the Gaussian surface is a cube and charge enclosed is zero, the electric flux coming into the surface is more than that flowing out. So, shouldn't the net electric flux be non-zero contradicting Gauss's law? Does it mean such an electric field is impossible without a charge being distributed along the path?
The usual semantics of first-order theories involves models who have a structure-set. Hence it is required to use some sort of set theory as the metatheory. However it is also widely known that one can do logic with a minimal metatheory, say a fragment of Peano. If we are using such a metatheory, what will the semantics become ? What will replace the notion of "set-model" ?
Here is the problem, I thought it the I've been thinking for a long time, but I still don't have any ideas. Problem: Let A(S) be the group of all bijective functions on S with composition as its binary operation. then A(S) is finitely generated if and only if S is finite set. I know that proving from the right to the left is relatively easier, but when it comes to proving from the left to the right, I really don't have any ideas. I hope someone can help.
I am typesetting my thesis in latex overleaf. I am struggling with one issue. I want to highlight my section with blue rectangular background with white color for heading as can be seen in picture. For subsection I don't want a background rectangle I simply want subsection of a blue color as can be seen in attached picture. I will really appreciate it if someone help me regarding this. Thanks.
I was given an honors project to solve for the equations of motions of a pendulum with an oscillating fulcrum. I (somewhat) understand the procedure on how to solve it with lagrangian mechanics and the Euler-Lagrange equation, but I am stuck at a question. How do we know this cannot be solved with Newtonian mechanics? I tried to look up the answer on Google and even tried to solve for it myself but I obtained an equation with theta, acceleration in the x and y direction so Im not sure what to make of it. Does anyone know? Or are there any resources to understand the precise limitations of Newtonian mechanics? I am a physics undergrad who just finished electromagnetism and linear algebra, thank you!
I am having trouble understanding why is temperature coefficient for avalanche breakdown is positive? The explanation I found online says as the temperature increase the mean free path decreases making collision and generation of carrier pair easier. But the electric field require to accelerate charge carriers to point of collision remains constant . So why does avalanche breakdown voltage increases with temperature if the electric field remains same? Doesn't increase in voltage indicate it is slightly harder to obtain avalanche breakdown? If the mean free path is decreasing and charge carrier generation is getting easier shouldn't occur at same voltage and not increase further
The Coriolis force predicts that winds in the northern hemisphere should be deflected in a clockwise pattern and winds in the southern hemisphere should be deflected in an anti-clockwise pattern. Why is it that in the case of cyclones however, the cyclones spin anti-clockwise in the northern hemisphere and clockwise in the southern hemisphere? If it's indeed true then what is clockwise and anti-clockwise direction?!