Posts

Messi won his sixth Ballon D’or yesterday 2019-12-02. I used to fancy this award and used to put a lot of value to this award a few years ago but lately I do not regard them to the same standard I used to. What is fundamentally wrong with this award in particular is that they say it reconiges the best player over the last season but the ones who vote put different constraint on it. So what ends up happening is that the person winning this award is hailed as media as the best player in the last season when clearly the “best player” is qualified further more. ...

The first time I had a real encounter with an insane person and I gave a good thought about it was when I was in high school. Everyday at 8:30 I used to go to school to attend the morning assembly at 9:15. I didn’t usually see him when I reached the school but almost everyday when we returned back from school to catch bus home, I saw him doing some usual things by the passenger waiting area. He would do things that were not considered normal by the usual standard of the society and the kind of things people would do in that context. ...

Introduction So, free will right? We know that it doesn’t exist. I mean, how can it exist if we belive in rule of law and nobody can gen the law or act otherwise in any way? So, once the initial condition was set (somehow, we won’t get into the detail of it) we are merely just flowing here and floating. I cound’t have done anything different from what I am doing now. I can’t blame myself, or anyone else for that matter, for anything wrong that I think happened to me. Expecting for us to have free will is like watching a already made movie and expect the character to act differently from the last time we watched the same movie. They ain’t gonna act differently because the theater is just playing a recorded cassette. Case of free will is almost similar but a little different in a sense that the movie is read from the stored media but is being created in real time with the existing metadata for the movie. ...

डिजिटल माध्यम सामान्यतः डिजिटल उपकरणहरूको केन्द्रमा अत्ति नै सुक्ष्म उपकरणको सङ्गालो हुन्छ, यस्ता सुक्ष्म उपकरणलाई हामी ट्रान्जिस्टर भन्छौँ। यसलाई हामी दैनिक जिवनमा प्रयोग गर्ने बत्तीको स्वीचजस्तो मान्न सक्छौँ। यस्तो एउटा स्वीचको अवस्थालाई बिट पनि भनिन्छ। समान्यतः कुनै पनि स्वीच कि खुला हुन्छ कि बन्द हुन्छ। जस्तो कि हामीले दुईवटा स्वीच/वत्ती लियौ भने त्यसलाई चारवटा अवस्थामा राख्न सकिन्छ। दुबै निभेको, पहिलो बलेको दोस्रो निभेको, दोस्रो बलेको पहिलो निभेको र दुबै बलेको। यस्तो चारवटा अवस्था हामीले कुनै पनि माध्यमबाट सुरक्षित गर्न सक्यौँ भने, भविष्यमा त्यसलाई कुनै उपयोगी जानकारीको रूपमा लिन सकिन्छ। कम्प्यूटरम वा कुनै डिजिटल माध्यममा केही कुरा सञ्चय गर्नु भनेको, यस्ता स्वीचहरूलाई कुनै निश्चित तरिकाले खुला वा बन्द राख्नु हो। एउटा बत्ति मात्र लिँदा कि खुला वा कि बन्द‌ गरी दुईवटा मात्र सम्भावना भए जस्तै दुईवटाको बत्तिको क्रम लिँदा चारवटा अवस्थाको सम्भावना हुन्छ। यस्ता खुला र बन्द स्वीचहरूको क्रमलाई सजिलोका लागि कुनैपनि सङ्ख्याले चिन्न सकिन्छ। जस्तो कि हाम्रो उदाहरणको दुईवटा बत्ती बन्द भएकोलाई ०, पहिलो बन्द र दोस्रो खुला भएकोलाई १, पहिलो खुला दोस्रो बन्द भएकोलाई २ र दुबैवटा खुला भएकोलाई ३ भनेर मान्यौँ भने, कुनै निश्चित अवस्थाका खुला र बन्द वत्तीहरूलाई सङ्ख्याले चिन्न सकिन्छ। यस्तो अनुक्रमलाई सङ्ख्याले पनि चिनिने भएकैले तिनलाई डिजिटल (साङ्ख्यिक) माध्यम भनिएको हो। ...

Klein Gordan Equation We have seen in this post that Klein-Gordan equation describes a spinless particle with mass $m$. The Klein-Gordan equation formally is $$ \begin{align*} \left( \square + m^{2} \right) \psi = 0 \end{align*} $$Unlike Schrödinger’s equation, this equation doesn’t treat time differently from space derivatives. It can be shown that this in indeed Lorentz invariant. However, the problem with Klein-Gordan equation is that it violates the conservation of probability, which is a serious problem. We need a first order differential equation which would indeed conserve the probability. ...

Schrödinger’s Equation Two of the greatest triumphs in Physics in the first three decades of 20th century are, i) Einstein’s Theory of Relativity", both special and general, and ii) Quantum Mechanics. While both of them are very successful, there is still some friction between them. Special Theory of Relativity taught us that space and time (which we thought were independent), in fact, were just components of more fundamental 4-dimensional spacetime. There are various ways we can formulate quantum mechanics, in any case, Schrödinger’s equation can be thought of as of central importance to the theory. The Schrödinger’s equation is ...

Einstein’s Field Equations $$ \begin{equation} G_{\mu \nu} + \Lambda g_{\mu \nu} = 8\pi T_{\mu \nu} \end{equation} $$This innocent looking equation packs one of the most startling concepts of all of nature. This is a stub article, I will update it gradually.

Classical Electrodynamics In the early days of the encounter with Electricity and magnetism, these were studied seperately as independent phenomenon in nature. With more studies, it was evident that Electricity and magnetism were intimately related. Maxwell painstakingly combined the known laws of electricity and magnetism into a set of four beautiful first order differential equations and showed the intimate connection. $$ \begin{align*} \nabla \cdot \vec{B} &= 0 \end{align*} $$$$ \begin{align*} \nabla \cdot \vec{E} &= \frac{\rho}{\epsilon_0} \end{align*} $$$$ \begin{align*} \nabla \times \vec{E} - \frac{\partial \vec{B}}{ \partial t} &= 0 \end{align*} $$$$ \begin{align*} \nabla \times \vec{B} - \frac{\partial \vec{E}}{\partial t} &= \vec{J} \end{align*} $$$$ \begin{align*} \vec{F} = q(\vec{v}\times \vec{B} + \vec{E}) \end{align*} $$In classical electrodynamics the four maxwells’ equation together with the Lorentz force law form the complete set of equation required to understand all electromagnetic phenomenon. ...

कायरताको इतिहास प्रमाणित भयो आज मैले इतिहास रचेको मेरा नामको मानवताको इतिहासमा यस्तो इतिहास कहिल्यै रचिएको भए अभिलेख छैन यसको कुनै किनकी इतिहास बहादुरीको लेखिन्छ कायरताको होइन त्यो इतिहसस अभिलेखको लायक छैन मेरो शरीरको कुनै कुना वा अनकन्टार इन्टरनेटका साङ्ख्यिक मानकबाहेक यसको अस्तित्वको मानक कसैले राख्नु उपुक्त हुने छैन यो कायरताको इतिहास भविष्यमा पढिइने छैन चर्चा यसको कदापी कसैगरी हुने छैन किनकी, इतिहास इतिहासै हो तर कायरका लागि इतिहासमा ठाउँ हुँदैन बहादुर कर्मको इतिहास जसले भावी पुस्तालाई हौस्याउँछ चन्द्र छुने, तिलस्मी कर्म गर्ने प्रेरणा दिन्छ फगत कायर कथा सुनेर समय वर्बाद गर्ने चेष्टा कसैले गर्नेछैन ...

Setup first lets setup up some imports import numpy as np import sympy as smp import matplotlib.pyplot as plt plt.rcParams['figure.figsize'] = (16.0, 6.0) smp.init_printing() from sympy.physics import mechanics as mcx #mcx.init_vprinting() mcx.mechanics_printing() #smp.init_printing() Goldstein 1.19 Solve spherical pendulum by lagrangian. t = smp.Symbol('t') g = smp.symbols('g',constant=True); #accleration due to gravity m = smp.symbols('m',real=True,positive=True,constant=True) theta,phi= mcx.dynamicsymbols('theta,phi'); r = smp.symbols('r',constant=True) rdt = smp.diff(r); thd = smp.diff(theta); phd = smp.diff(phi) x = r*smp.sin(theta)*smp.cos(phi); xdt = smp.diff(x,t) y = r*smp.sin(theta)*smp.sin(phi); ydt = smp.diff(y,t) z = r*smp.cos(theta); zdt = smp.diff(z,t); ydt $$r \operatorname{sin}\left(\phi\right) \operatorname{cos}\left(\theta\right) \dot{\theta} + r \operatorname{sin}\left(\theta\right) \operatorname{cos}\left(\phi\right) \dot{\phi}$$V = m*g*r*smp.cos(phi) T = smp.Rational(1,2)*m*(xdt**2+ydt**2+zdt**2); T; smp.simplify(T) $$\frac{m r^{2}}{2} \left(\operatorname{sin}^{2}\left(\theta\right) \dot{\phi}^{2} + \dot{\theta}^{2}\right)$$So the total kinetic energy of the spherical pendulum is ...