Gravitational Anomaly.

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.

Inherent ability = difficulty * accomplishment.

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.

Aberrations; a lecture in Optics.

Optical systems are studied under two assumptions

object point does not lie far away from the axis of the optical system.

rays taking part in image formation make a small angle with the axis of the optical system.

The domain of optics where above two assumptions are valid is called as Paraxial optics. Paraxial systems are highly idealized and in reality do not perfectly represent the situation. The consequential errors in image reconstruction are known as aberrations.
The paraxial assumption can be represented by truncating at the first term of the polynomial expansion of the sin function by the Maclaurin series.

A c++ code for calculating pi value.

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.

OUTPUT
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.

#include
#include
#include
#include
//#include
using namespace std;

double pi_estimate(const unsigned long points)

There is only one physical favor the Universe did on life.

But all of them are not stable. We have made great strides in understanding them collectively called as standard model of particle physics which involves electroweak and strong interactions. Its a weird mess of beautiful list of particles and their behavior toward each other. Sometimes there is symmetry breaking sometimes there is symmetry and sometimes there is confinement.

What such an astounding theory backed by the most swashbuckling experimental measurements have meant is there are only countable number of stable particles.

Let’s begin counting out of 100s electron, proton, photon and neutrinos … That’s it. End counting.

It explains almost everything we see around us. The matter. If we are to see dark matter we would be explaining that as well. But hold your breath we haven’t seen that so far.

Since almost everything we have seen are so unstable we wouldn’t be created.

But the very few stable particles made atoms possible and the atoms made life possible.

Here is how the atom is possible.

The neutron guy is not very happy as its not stable. It met proton on a blind date and they got

1 2 3 35