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.
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.
The beauty of Maxwell’s equations can be seen in how it helps us understand nature as well as instruments, at the same time. Medical devices are simply an advanced understanding that began with understanding electromagnetic waves through Maxwell’s equations.
Each of the following 4 equations has a different name, by which we call’em, but together they are called as the Maxwell’s equations. Together they constitute what I am inspired to say; the golden equations of Physics. If we do some easy tricks they will be converted into whats called as the Wave Equations (of motion) ! Yes, they describe the wave behavior “fully”.
— By that I don’t mean sound waves, but any sort of waves that move at the speed of light. Sound waves are ordinary pressure oscillations, that travel much slower than even rockets.
The 4 equations therefore describe how electromagnetic waves are created and broadcast. Hence TV radio and satellite communication were understood because these 4 equations were understood.
First two are time-independent or static equations.
The first equation is known as Gauss’s law of electrostatics and says “Electric fields (E), are a result of sources of electrostatic charge”.
The 2nd equation is analogous and called as Gauss’s law of static magnetic field. But it says “apparently there are no sources of magneto-static charge or single magnetic pole from which the magnetic field B is created”.
Then how are magnetic fields created? We needed to know further to find the answer. Lets look at the 3rd and 4th equations.
Based on real incident, perhaps in 2006, published on this website, Feb, 2011.
I hate proselytizers. I miss my bus because of them and I can’t sleep because they knock on my doors .
This really happened.
P: Hi bro
P: You heard Beethoven?
(I am thinking one part of that no is, yes)
P: He played Piano long long ago
(No wonder, I didn’t hear him)