What is Weak: Definition and 503 Discussions

In mathematics, weak topology is an alternative term for certain initial topologies, often on topological vector spaces or spaces of linear operators, for instance on a Hilbert space. The term is most commonly used for the initial topology of a topological vector space (such as a normed vector space) with respect to its continuous dual. The remainder of this article will deal with this case, which is one of the concepts of functional analysis.
One may call subsets of a topological vector space weakly closed (respectively, weakly compact, etc.) if they are closed (respectively, compact, etc.) with respect to the weak topology. Likewise, functions are sometimes called weakly continuous (respectively, weakly differentiable, weakly analytic, etc.) if they are continuous (respectively, differentiable, analytic, etc.) with respect to the weak topology.

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  1. marce

    I Neutrinos and theoretical necessity

    - One of the most fascinating particles for me , have always been neutrino's because of them balancing between mass and massless properties. So the question 'why was this needed' in the context of the weak force has led me to the question : as with attempts to explain 3 generations of particles...
  2. nafisanazlee

    Chemistry A confusion about conductance of weak electrolytes

    My attempt is the handwritten one. But my reference book solved it in a different way, they left a note saying at infinite dilution α = 1(100%). (the attached picture) Which one is the correct approach?
  3. E

    Admissions Applying for PhD despite very weak undergraduate GPA

    Hi everyone, I'll keep it short and to the point. Just as the title say, I'm looking for advice on my situation. I'm very passionate about physics and want nothing more than a career in academia. I went to NYU and graduated with a bachelor's in physics in 2019. Due to various health issues...
  4. H

    I Gravitational Field Existence in Void: Philosophical Inquiry

    This is of a more philosophical inquiry. If two particles are in a void and moving apart, if they are sufficiently far apart, like say the distance between two galaxy cluster walls, does the gravitational field between them still fundamentally exist? I'm trying to understand if gravity will...
  5. S

    B The green comet is just a weak smudge now

    I think I has observed it a few weeks ago (maybe it was something else), and it was long & bright, but now it's barely visible . (I'm using a 12X, 60mm binocular.)
  6. A

    What does weak chemisorption mean?

    I am reading a research paper that says weak chemisorption of silver with olefins basically means more effective olefin/paraffin separation. If silver weakly binds to olefins, wouldn't that make a lousy separator?
  7. abdulbadii

    Failed function within SMPS giving weak current

    What is the very common culprit component and what is its function within SMPS having weak current, far weaker than its rating while its voltage is always perfect?
  8. fluidistic

    I Finding the weak form of an eq. with DG elements (finite elements)

    My goal is to numerically solve (finite elements using FEniCSx software) Ohm's law ##\vec J = \sigma \vec E##, where ##\vec E = -\nabla V##, ##\vec J## is given (the current density is given on some boundaries), and ##\sigma## is algo given (the electrical conductivity). The problem is solved...
  9. S

    B Graphical representation of the weak mixing angle

    The graphical pattern of particles in the weak hypercharge and weak isospin plane, visible in this wiki page, shows the mixing angle between the Yw and Q axes. Actually , from the weak hypercharge (-2) of a right-handed electron and its electric charge (-1), one obtains an angle Pi/3, not the...
  10. livio

    Estimates of voltage drop with distance in weak electric field

    If I resolve the equation in 0, imposing a voltage value of 5 mV, it gives a non real solution, therefore I cannot resolve it for R=1 because I do not know which voltage value to impose. I am sure this is simpler than I am putting it :) thanks for any advice!
  11. G

    I Geodesic in Weak Field Limit: Introducing Einstein's Relativity

    I'm reading《Introducing Einstein's Relativity_ A Deeper Understanding Ed 2》on page 180,it says: since we are interested in the Newtonian limit,we restrict our attention to the spatial part of the geodesic equation,i.e.when a=##\alpha####\quad ##,and we obtain,by using...
  12. Filip Larsen

    B Weak Equivalence Principle Confirmed by MICROSCOPE Satellite to 10^-15

    https://arstechnica.com/science/2022/09/einstein-wins-again-space-satellite-confirms-weak-equivalence-principle/ See also http://dx.doi.org/10.1103/PhysRevLett.129.121102 (limited access)
  13. O

    I Why are the spectral lines weak in my hydrogen Geissler tube?

    Using a hand spectroscope, I looked at the spectrum of two geissler tubes, helium and hydrogen. The helium spectrum is what I expected, dominated by five distinct lines. The hydrogen spectrum, however, is somewhat disappointing. It is dominated by an almost continuous spectrum, it is not evident...
  14. atyy

    I Relativistic Bohmian trajectories of photons via weak measurements

    I found out about this interesting paper through a Tweet by Steven Thomson. https://arxiv.org/abs/2108.05169 https://www.nature.com/articles/s41467-022-31608-6 Relativistic Bohmian trajectories of photons via weak measurements Joshua Foo, Estelle Asmodelle, Austin P. Lund, Timothy C. Ralph...
  15. H

    A Is the weak interaction asymptotically free?

    Is the ##SU(2)_L## part of the SM asymptotically free like a typical non-Abelian gauge theory? I've been made to understand that confinement does not occur for ##SU(2)_L## because the spontaneous symmetry breaking scale is above the confinement scale, however I can't find any information on...
  16. qnt200

    I Weak principle of equivalence (Galileo, Newton)

    Many tutorials that explain the weak principle of equivalence (Galileo, Newton) do not clearly state whether the body is affected by the force of inertia during free fall as a result of the gravitational acceleration of the body. In other words, the question is whether, during the free fall of a...
  17. Rub3y

    Do oxides react react with a weak acid like phosphoric acid?

    I have an ash which is a mix of oxides (Cr2O3, CuO, ZnO, PbO, CdO, NiO, SiO2, MgO, CaO). I am adding phosphoric acid. But as a weak acid, will it react with oxides? If so, are these conversions 100% or more of a equillibrium (partial conversion). I you need more information, be sure to ask.
  18. tworitdash

    A Quantum weak measurement parameter estimation vs Classical Estimation

    I am not an expert in quantum theory. I want to carry out some parameter estimation on a set of data I have. I have a model for the data with the parameter(s) of interest as variable(s). The data available is sporadic, meaning non-statistical or techniques involving no prior knowledge on the...
  19. angweieng

    A Definition of finite size, radiative and weak magnetism corrections

    Hi all, I would like to understand the definition of finite size correction, radiative correction and weak magnetism correction, with their impacts on the beta spectrum. I'm not a physics student, thus I would like to seek for a help about the simple explanation that can be understand by...
  20. A

    B Is the weak nuclear force attractive or repulsive or both?

    Hi Of the 4 fundamental forces, I did not understand the weak nuclear force. Is the weak nuclear force attractive or repulsive or both? It works between two particles, that is, it is the interaction of two particles?
  21. tworitdash

    A Applications of weak measurement of quantum mechanics in other domains

    This is a surface level question and I don't want to go into detail. Imagine an algorithm which when used with a sensor output gives the statistical moments of a variable in nature (for example mean and standard deviation of a variable). The sensor measures this once in a while (like once in a...
  22. only1god

    B The Mini Rocket Experiment: A Test of Einstein's Equivalence Principle?

    Alright, this is my idea of an experiment that could distinguish between the examples of the EP. Now, obviously I'm wrong (I don't say this because of your acceptance, i say this because I've tried with other ideas but they were wrong). The thing here is that i don't see where I'm wrong, and i...
  23. F

    Weak solutions under finite elements

    Finite elements give weak solutions, that is, the solutions to a PDE are only correct in its integral form. Is it possible that in finite element software, the solution differs a lot from the analytic one locally while it's exact in its integral form (globally)?
  24. Killtech

    I Weak measurement and the measurement problem

    When I think about it my biggest issue with the interpretation of QT can be boiled down to this question. There are the axioms of measurement in QT, which have their limiting nature and claim to be the only way to extract information from a quantum system - but that is just a claim with enough...
  25. SilverSoldier

    Approximations in Chemical Equilibrium (add a weak acid HA into pure water)

    Suppose we add a weak acid HA into pure water, so that upon addition its initial concentration is c. The following equilibria should establish in the system. $$\text{HA}+\text{H}_2\text{O}\rightleftharpoons\text{H}_3\text{O}^++\text{A}^-$$...
  26. A

    COVID Weak or non immunity after virus or vaccine

    How can it be that some people develop next to no immunity , cell memory after a Covid infection or vaccination? Immunity develops after the body sees and fights off foreign protein aka virus presenting within the body, so whichever has gotten infected with the virus has to undergo these steps...
  27. mcas

    Finding Energy in FCC Lattice Using Weak Potential Method

    I have a problem with finding the energy of an electron in an FCC lattice using the weak potential method. We did that for a one-dimensional lattice during class, and I know that there was a double degeneration at the boundaries of the first Brillouin Zone. However, I'm not sure what...
  28. Haorong Wu

    I Weak Gravitational Field & Wave Eq. - Analyzing Effects on Massless Scalar Field

    A massless scalar field in a curved spacetime propagates as $$(-g)^{-1/2}\partial_\mu(-g)^{1/2}g^{\mu\nu}\partial_\nu \psi=0 .$$ Suppose the gravitational field is weak, and ##g_{\mu\nu}=\eta_{\mu\nu}+\epsilon \gamma_{\mu\nu}## where ##\epsilon## is the perturbation parameter. And let the field...
  29. I

    Chemistry PKb of weak base titrated with strong acid

    What is true about the pK of the analyte? a) pKa = 9.2 b) pKb = 9.2 c) pKb = 4.8 d) pKa = 11.7 The halfway point is at point 4, at approximately pH=9.2. Therefore, the pOH = pKb = 4.8, and I think the answer is c). The solution says b) is the correct answer. Could anyone explain why, or whether...
  30. M

    Studying How do you deal with weak background at the start of PhD?

    Hi all, I just started in a PhD in a General Relativity related problem. Although the problems that I am going to work with are purely classical (in the sense of no QM required), I feel bad about my lack of proficiency in QFT. I had to follow a course in some advanced topics (such as String...
  31. SamRoss

    I How is the weak force related to a change in velocity?

    Hi everyone, The four fundamental forces are gravity (I understand that G.R. does not look upon gravity as a force but I'm not worried about that here), the Lorentz force, the weak force, and the strong force. I'm familiar with the inverse square law for gravitation and the Lorentz force...
  32. C

    Solubility of weak acid salts of aluminum and silver

    I'm curious what weak acids will form soluble salts with aluminum, but not silver. From a solubility chart (https://www.flinnsci.com/globalassets/flinn-scientific/all-product-images-rgb-jpegs/ap6901etc.jpg?v=cc7f986a028e4adf833ea6341200add2), HCl, HBr, and HI will form soluble aluminum salts...
  33. LuisBabboni

    I Why is the weak force a force?

    Hi! I could understand gravitational force as a force that move mass. I could understand electromagnetic force as a force that moves chaerged particles. I even could understand strong force as a force that atrack protons I could not understand the moment of what weak force changes. The moment...
  34. Nick tringali

    How to turn a weak acid into a strong acid

    so my question is how do I turn .1M HCL into a super strong acid like 10M or higher HCL. What is the highest M ever recorded for HCL? At what Molarity do I have to wear gloves and avoid skin contact?
  35. Lucasterre

    Weak Force Weapon Effects on Wall Elements

    Hello, I am a creative scifi writer and i only have basic quantum physics knowledge, if someone could answer my question please. I was wondering some type of weapon that uses weak force, therefore it would promote distorcions at weaf force field causing interaction with atoms My question is, if...
  36. S

    I Conductors and weak interaction

    Are there any plausible semiconducting or superconducting devices which would show clear parity violation? Electrons in matter are governed overwhelmingly by electromagnetic interactions. Electron-electron, and electron-nuclei. However, there is in principle some weak interaction. Elastic weak...
  37. jaumzaum

    I Strong and Weak Nuclear forces at long ranges

    A lot of articles I already read says the Strong and Weak Nuclear interactions have a very short range, the first one being ##10^{-15}m## and the second ##10^{-18}m##. My first question is how is this calculated? This leads me to 2 possibilities:$ 1. Both forces actually act with an infinite...
  38. Marilyn67

    A R. Mallett's Device: Exploring Weak Energy Possibilities

    Hello, I am sorry to raise this old subject concerning the device of R. Mallett, in particular, one is right to quote has violation of the condition on the weak energy which is not respected. Okay, let's give up this violation of the weak energy condition for now. In my opinion, the big...
  39. J

    MHB Weak Convergence to Normal Distribution

    Problem: Let $X_n$ be independent random variables such that $X_1 = 1$, and for $n \geq 2$, $P(X_n=n)=n^{-2}$ and $P(X_n=1)=P(X_n=0)=\frac{1}{2}(1-n^{-2})$. Show $(1/\sqrt{n})(\sum_{m=1}^{n}X_n-n/2)$ converges weakly to a normal distribution as $n \rightarrow \infty$.Thoughts: My professor...
  40. H

    Comparing a hydronium with a hydroxide in a weak acid solution (0.1M)

    This question says: An HA weak acid solution with a molarity of 0.1M is dissolved in water. In the new solution, is the molarity of OH- greater than the H3O+ molarity, or the opposite? Or are they equal? I came up with two possible answers: 1. [H3O+]>[OH-] because there are no hydroxides...
  41. S

    I When is weak interaction a force?

    When is weak interaction actually a force, rather than merely cause of some process? Not in beta decay - it is process. There are simpler weak interaction processes around: elastic scatterings that change only momentum but not taste. But those are still processes and are over as the particles...
  42. DaTario

    I On the weak force and beta decay

    Hi All We know that beta decay is and ejection of an electron from nucleus, making a proton turn into a neutron (and a neutrino). Is it correct to say that is the weak force responsible for the increasing in the distance between electron and proton during this process (since the feel atracked...
  43. Mr-Thirty

    Concentrations at equilibrium (strong base weak acid)

    So my professor covered acids and bases recently, and this is how he presented the method (please see attached word document). I believe its the same as the I.C.E method, though I am not sure. Anyways my problem is perhaps conceptual, but I don't understand why the concentrations at equilibrium...
  44. A

    Allowed or forbidden reactions

    Hello everybody! I have a doubt about a reaction. $$ p + n \rightarrow \Lambda + \Sigma^+ $$ I have to establish if it is allowed or not. Charge is conserved (1 -> 1) Baryon number is conserved (2 -> 2) Strangeness is not conserved (0 -> -2) Third component of the isospin is not conserved (0...
  45. K

    What is the equation for calculating [H3O+] in a salt of weak acid and base?

    Because of character limit I have exposed my question in the attached pdf
  46. Futurestar33

    Shelf in a box, treating the shelf as a weak perturbation

    In this problem I am supposed to treat the shelf as a weak perturbation. However it doesn't give us what the perturbed state H' is. At the step V(x) = Vo, but that is all that is given and isn't needed to determine H'. This isn't in a weak magnetic field so I wouldn't you use H'=qEx and then...
  47. DHO232

    I Does a photon experience time while interacting with the weak force?

    Long time reader, first time posting here in physics forums. I know that according to relativity photons have no proper time. I also know that a photon of sufficient energy can interact with a nucleus's nuclear force via the weak interaction resulting in pair production. I was looking at a...
  48. T

    Weak Induction implies Strong Induction

    Homework Statement [/B] Weak Induction: If (i) ##S(1)## holds, and (ii) for every ##k \geq 1(S(k) \Rightarrow S(k+1)##. Then ##\forall n \geq 1##, ##S(n)## holds. Strong Induction: If (i) ##S(k)## is true and (ii) ##\forall m\geq k [S(k) \land \cdots \land S(m)]\Rightarrow S(m+1)##. Then for...
  49. P

    I Weak interaction between electrons

    The two electrons will be repelled by electrostatic force, but they interact with weak force, means that in addition to the electrostatic force between the electrons there will be weak force?
  50. M

    A Reference for the A field of the Weak Force

    A reference please to a review paper, textbook, or website for an expression, or development of an expression for the field in Electro weak, similar to the A field in EM.