Theorem Definition and 1000 Threads

In https://arxiv.org/ftp/arxiv/papers/1409/1409.5158.pdf, the author (Donald A. Graft) concludes that Bell tests cannot refute local realism, because they employ a wrong analysis. He says: "The quantum joint prediction cannot be recovered in an experiment with separated (marginal) measurements...

Homework Statement A man owns two old cars, A and B, and has trouble starting them on cold mornings. The probability both will start is 0.1; the probability B starts and A does not is 0.1; the probability that neither starts is 0.4 a) Find the probability that car A will start. b) Find the...

I'm reading through Crooks's paper: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.60.2721 as well as a review paper by Mansour et al.: https://aip.scitation.org/doi/10.1063/1.4986600 trying to figure out their derivation of the fluctuation theorem (section II of both papers). I had a...

I just read about Carnot theorem (the highest efficiency is the one of reversible machines and all reversible machines working between two given temperatures have the same efficiency). Then I found a problem where I have a reversible cycle made of an isochoric, adiabatic and isotherm. I report...

Homework Statement [/B] A 4 kg mass slides 2 m over a horizontal surface with force of kinetic friction of 2N, initial velocity is 5 m/s. Find it's final velocity. My problem... we've been asked to solve this problem using the Work-Energy theorem, and we've been given it in the form of: W =...

This theorem is summarized here: https://en.wikipedia.org/wiki/Coleman%E2%80%93Mandula_theorem I sort of understand the mathematical content of the theorem, that But what I don't understand is, intuitively, what sort of possibilities are ruled out. I've heard it said that flavor conservation...

Having come experimentally to an interesting electrostatic effect, I have returned, aged 47, to my old books in physics. It turns out that my books delight in using Gauss theorem etc. in rather ideal geometrical surface charge distribution, but never gave me the tools to answer to this simple...

Homework Statement FIGURE 1 shows a 50 Ω load being fed from two voltage sources via their associated reactances. Determine the current i flowing in the load by: (a) applying Thévenin’s theorem (b) applying the superposition theorem (c) by transforming the two voltage sources and their...

A large portion of physicists thinks that Bell's theorem shows that reality does not exist. Another large portion of physicists thinks that reality is not an assumption of Bell's theorem, so that Bell's theorem just proves nonlocality, period. A third large portion of physicists thinks that both...

Hi, in this link https://math.stackexchange.com/questions/2605752/proof-log-convex-implies-convexity , there is a theorem that labelled with yellow. I do not know the name of theorem and would like to know it's derivation. Could you please help me?

Recently I started looking back at some basic mathematical principles, and I started thinking about the theorem of corresponding angles. It's such a basic idea that it seems obvious on an intuitive level, but despite that (or possibly because of that) I can't think of a good way to formally...

Hello! Einstein's theorem is in the last sentence of the following quote (bold) [1]: "If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its...

I was looking at the following proof of Louviles theorem : we define a velocity field as V=(dpi/dt, dqi/dt). using Hamilton equations we find that div(V)=0. using continuity equation we find that the volume doesn't change. I couldn't figure out the following : 1- the whole point was to show...

In this video (the link should take you 23 minutes in, where) Professor Susskind writes a theorem. (He says E and S are functions of T and V.) I am just wondering if what he writes is an abuse of notation? And if so, how would you write it? (Susskind gives his own proof from 26:30 to 36:00...

Hello, A generic force ##F##, which may be conservative or not, performs mechanical work which is always equal to $$W=\Delta KE=KE_{final}-KE{initial}$$ i.e. produce a change in the object's kinetic energy ##KE##. Work is essentially a way to inject or subtract kinetic energy from a system. If...

i read that question and Weinberg book (A,B)-Representation of Lorentz Group: Coefficient functions of fields why u(a,b)=Cab/sqrt(2m) ? where Cab is Clebsch-Gordan coefficients, and m is mass of particle

Hi, I have been studying thermodynamics from Herbert Callen's "Thermodynamics : an introduction to the physical theories of equilibrium thermostatics and irreversible thermodynamics" In Chapter 4, Section 4.4, he writes : " all processes occurring between a given initial and a given final state...

Homework Statement Assume we have two thin bars of length L and mass M. The moment of inertia of one bar with respect to axis through center of gravity of said bar is ##I=\frac {mL^2}{12}##. The two bars stick together at their ends, forming a right angle. What's the moment of inertia of the...

Homework Statement Let ##G## be a group. Let ##H \triangleleft G## and ##K \leq G## such that ##H\subseteq K##. a) Show that ##K\triangleleft G## iff ##K/H \triangleleft G/H## b) Suppose that ##K/H \triangleleft G/H##. Show that ##(G/H)/(K/H) \simeq G/K## Homework Equations The three...

In my textbook there is the following paragraph: "The usual application of the Baire category theorem is to show that a point ##x## of a complete metric space exists with a particular property ##P##. A typical argument runs as follows. Let ##X = \{x\in M \mid x \text{ does not have property }...

I am new here, so hi for all ^-^ I have a problem in the Clapeyron theorem, the work of a force by definition is equal to the force multiplied by the displacement, and in this theorem it says that the work = (1/2) * force * displacement. why there is 1/2 ? I also saw Maxwell-Betti's theorem...

I was planning to do an essay exploring Morley's Trisector Theorem, but I was having trouble finding and real life applications of it? It states that "in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle". I thought it was pretty...

What is an example of an experiment that if you were to simulate using hidden variables would violate the PBR theorem's conclusion? If you were able to simulate the EPR experiment using photons, one entangled photon pair at a time, and get results that are indistinguishable from experimental...

I am reading Loring W.Tu's book: "An Introduction to Manifolds" (Second Edition) ... I need help in order to fully understand Theorem 2.2 and the remarks after the theorem ...Theorem 2.2 and the remarks after the theorem read as follows: My questions on the above text from Tu are as follows...

There are two recent threads about the subject, however I want to ask a different question. What does the wavefunction is "real" imply or what such "clarification" actually mean to the deeper understanding of QM. The theory is purported to be revolutionary and important breakthrough, yet it...

This thread is inspired by PeterDonis' thread about "hidden" assumptions in the PBR Theorem. He referenced Matt Leifer's in depth article on PBR (original referenced). And Demystifier has provided an excellent summary of PBR as a PDF file, which I have attached. Leifer's "Is The Quantum State...

I am reading Loring W.Tu's book: "An Introduction to Manifolds" (Second Edition) ... I need help in order to fully understand the proof of Tu's Lemma 1.4: Taylor's Theorem with Remainder ... Lemma 1.4 reads as follows: My questions are as follows:Question 1 In the above text from Tu we read...

I've a general question. I'm self-studying classical mechanics using various means one of which is Leonard Susskind's Theoretical Minimum lecture series. I'm on Lecture 7 and we are doing Liouville's Theorem. My understanding of it so far is that in phase space as something expands in, say, the...

Homework Statement I'm asked to find the thevenin equivalent circuit, the load being ##R_1## ##e(t)=E_0\cos{(\omega t)}## ##R_1=1k\Omega \ R_2=R_3=1k\Omega## ##C=220nF \ f = 250Hz \ E_0=10V## Homework EquationsThe Attempt at a Solution ##Z_{th} = Z_{R_2}//(Z_c+Z_{R_3}) =...

Lusin's Theorem: Let $f$ be a real-valued measurable function on $E$. Then for each $\epsilon > 0$, there is a continuous function $g$ on $R$ and a closed set $F$ contained in $E$ for which $f=g$ on $F$ and $m(E - F)<\epsilon$. I'm going through exercises in the book... almost finals time. The...

I have been reading up on the PBR theorem, and it seems to me that there might be an additional assumption that is not discussed in the treatments I have read. The most comprehensive treatment of the general subject of theorems of which PBR is an example (theorems which attempt to show that the...

Hi everyone! I recently came across the Lyusternik-Fet theorem concerning closed geodesics on a compact manifold. For simplicity of description, take the 2-torus, and imagine it represents the configuration space of a double pendulum. For every pair of integers m, n (where m represents the...

Homework Statement Question from Fundamentals of Physics (Halliday, Resnick, Walker) This figure below shows a cord attached to a cart that can slide along a frictionless horizontal rail aligned along an x axis. The left end of the cord is pulled over a pulley, of negligible mass and friction...

I am reading Stephen Abbott's book: "Understanding Analysis" (Second Edition) ... I am focused on Chapter 6: Sequences and Series of Functions ... and in particular on power series ... I need some help to understand Theorem 6.5.1 ... specifically, some remarks that Abbott makes after the proof...

Problem: Let $f : \mathbb{R} \rightarrow \mathbb{R}$ be measurable. Then there exists a sequence of continuous functions $(g_n)$ such that $limg_n(x)$ exists for all $x \in \mathbb{R}$ and $limg_n(x) = f(x)$ a.e. x. Is this like Lusin's Theorem? Lusin's theorem for the real numbers? If so, how...

Greg Bernhardt submitted a new blog post A Numerical Insight for the Fundamental Theorem of Calculus Continue reading the Original Blog Post.

In many texts I have seen, Gauss theorem has the form of$$\frac{q}{\epsilon_0}=\oint\vec{E}d\vec{A}$$ Why a line integral symbol was used for this surface integral everywhere? The more I see it the more I believe there is something wrong with my understanding about this. I didn't think too much...

So the question is: express (sqrt(2)/2 + sqrt(2)/2 i)^8 in a+bi form I know r=1 and tangent=pi/4 Using the theorem i get 1(cos (2pi) +i*sin (2pi)) which becomes 1(1*i)=1*i however WebAssign says this is incorrect. I've also tried "0+1i" and just "i" What am I doing wrong?

Dear How to solve the CRT for cryptography as below - (1) Find x such that x = 2(mod3) x = 5(mod9) x = 7(mod11) (2) Find x such that x = 2(mod3) x = 4(mod7) x = 5(mod11) (3) Find x such that x^2 = 26(mod77) (4) Find x such that x^2 = 38(mod77) Please help me by provide your advice and...

https://xkcd.com/2059 A new interesting self-referential theorem that "self-corrects" for the theorem's own probability of correctness. ?? Hold your pointer still in the middle if the cartoon for a few seconds to get P(C).

I am reading Tom M Apostol's book "Mathematical Analysis" (Second Edition) ...I am focuses on Chapter 3: Elements of Point Set Topology ... I need help regarding a remark of Apostol's made after Definition 3.2 and Theorem 3.3 ...Definition 3.2 and Theorem 3.3 read as follows: In a note at the...

Hi, I have done up the proof for the question below. Please correct me if I have done wrong for the proof. Thanks in advanced!Question: Prove that if ab < 0 then the equation ax^3 + bx + c = 0 has at most three real roots.Proof: Let f(x) = ax^3 + bx + c. Assume that f(x) has 4 distinct...

Homework Statement C is the directed curve forming the triangle (0, 0, 0) to (0, 1, 1) to (1, 1, 1) to (0, 0, 0). Let F=(x,xy,xz) Find ∫F·ds. Homework EquationsThe Attempt at a Solution My intial instinct was to check if it was conservative. Upon calculating: ∇xF=(0,-z,y) I concluded that...

I have deduce a proof as stated below and am not sure if it is correct, therefore need some advice. Question: Prove that if ab > 0 then the equation ax^3 + bx + c = 0 has exactly one root by rolle's theoremProof: Let f(x) = ax^3+bx+c = 0. f(x) is continuous and differentiable since it is a...

Homework Statement I have a general question how I calculate the expectation value of V (potential energy) with Ehrenfest’s theorem. Do I have to integrate d<p>/dt with respect to d<x>. Also if the potential is symmetric (even) would that mean the expectation value of the potential is 0...

I am seeking advice on how to effectively and efficiently learn mathematics textbooks. Currently, I adopt the style of trying to prove theorems in the book before reading the provided proof. I have had good success in this; I noticed a considerable gap in experience between me and my peers in...

I am reading Micheal Searcoid's book: "Elements of Abstract Analysis" ... ... I am currently focused on understanding Chapter 1: Sets ... and in particular Section 1.4 Ordinals ... I need some help in fully understanding Theorem 1.4.6 ... Theorem 1.4.6 reads as follows: My question...

Homework Statement Let ##S = \{(x_1, \dots, x_p) \mid x_i \in G, x_1 x_2 \cdots x_p = e\}##. Let ##C_p## denote cyclic subgroup of ##S_p## of order ##p## generated by the ##p##-cycle, ##\sigma = (1 \, 2 \, \cdots \, p)##. Show that the following rule gives an action of ##C_p## on ##S## $$...

I am reading Micheal Searcoid's book: "Elements of Abstract Analysis" ... ... I am currently focused on understanding Chapter 1: Sets ... and in particular Section 1.4 Ordinals ... I have another question regarding the proof of Theorem 1.4.4 ... Theorem 1.4.4 reads as follows: In the above...

I am reading Micheal Searcoid's book: "Elements of Abstract Analysis" ... ... I am currently focused on understanding Chapter 1: Sets ... and in particular Section 1.4 Ordinals ... I need some help in fully understanding Theorem 1.4.4 ... Theorem 1.4.4 reads as follows: In the above proof...