This lecture note will make your life ten-fold easier in the scope of the problems it addresses. Consider it a talisman. I discovered this a couple of weeks ago when I was solving these problems for my own conceptual understanding. So I waited till I can completely enunciate the big picture. When I confirmed that its valid for all the following problems I made this note and sharing with you.
According to classical mechanics — from 400 year old knowledge of physics, space and time have been considered to be separate entities but not fundamental. Space and time were not considered fundamental quantities as these parameters did not have the mandate to change physical laws of nature. They were merely the tools of the mind or the more aptly the conscious mind. They help us visualize but not dictate what ought to happen.
Gravitational Anomaly: (asked by a student for very simple explanation)
Basically it means the new laws of physics known as Quantum Mechanics invalidates the sanctity of nature’s principles or laws (that is QM brings exceptions to the validity of the physical laws of nature itself)
Let us discuss this in simpler ideas from the basics only.
Remember the most basic physics, that of principle of conservation of energy and the principle of conservation of (linear) momentum.
In the more rigorous formalism of physics these two principles emanate (that is derivable) from two ideas of symmetry. In-fact every conservation principle of physics are manifestations of a corresponding principle of symmetry and vice-a-versa (also every symmetry must correspond to a conservation law). This general idea of connection between conservation laws and symmetry is collectively known as Noether’s theorem and is a central underpinning in all of today’s conceptual physics.
All of Physics is this “Inherent ability = difficulty * accomplishment”. Thats just intuitive but can easily be seen to correspond mathematically with the Principle of least action.
First the edifice: whats the problem? The problem is given you move in straight line when every direction is same around you, which direction will you chose? While you are waiting for a good answer from astrologers intelligent people already give a good hint. Think you have some inherent ability which is fixed.
fixed: which changes only if estimated wrong.
That inherent ability is actually action. Accomplishments are adjusted for difficulties, you waded through a swamp 5 meters you would have accomplished in sand 8 meters with that given inherent ability called action. Because action is abstract we have been sticking to time and path-length, but they are not as fundamental, they are merely specifics.
Finally I am successful in calculating pi value — less than 0.3% error, by using random number generation. Although my computer needs some fixation on its compiler or path definition etc, there are very good online compilers which helps in testing and running c++ codes: try the given link.
Computing the value of pi using std::rand()
Enter number of trials: 10000
Enter number of random (x,y) points per trial: 10
pi = 3.14376 +- 0.00519107
average – exact = 0.00216735
CPU time = 0.004027 secs
Here is the code I found by searching a good deal on the web. Yes I did tinker around but only because my own compiler (Turbo C++ on windows 10, 64 bits) was throwing some exceptions on the included headers.
using namespace std;
double pi_estimate(const unsigned long points)
A long and technical discourse on Quantum Wave Function. A 64 slide presentation styled discourse on the Quantum Wave Function. It consists of detailed solution