THE FOUR FUNDAMENTAL FORCES OF NATURE

The concept of the four fundamental forces of nature is a crucial aspect in physics. While frictional force, tension force, normal reaction, and fluid resistance are some of the common forces we have all learned about in lower grade physics, none of them is classified as fundamental forces. Instead, these forces belong to one of the four distinct classes of the fundamental forces. Two of these forces are well-known, while the other two are impossible to perceive with our senses alone.

The first of these forces is the gravitational force, which is the force between any objects with mass. It is the force that governs the movement of planets in orbit, and even the internal structure of massive celestial objects such as stars, planets, and galaxies is a result of the gravitational force. Because of this force, most planets are almost spherical, while asteroids with less mass have irregular shapes.

The second fundamental force is the electromagnetic force, which is a combination of electric and magnetic forces. Collectively, these forces form the electromagnetic force. At one time, scientists believed they were separate types of forces, but Faraday's work unified them into one. This force is responsible for the formation of molecules. Atoms possess a positive, negative, or zero charge, which means they can exert a force on each other if they are brought near to each other. This force turns into intermolecular force once they combine as one: it is the second strongest force out of the four.

#Theforces #part1
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Loop Quantum Gravity (LQG) is a theory of quantum gravity, which aims to merge quantum mechanics and general relativity, incorporating matter of the Standard Model into the framework established for the pure quantum gravity case. It is an attempt to develop a quantum theory of gravity based directly on Einstein's geometric formulation rather than the treatment of gravity as a force.

As a theory LQG postulates that the structure of space and time is composed of finite loops woven into an extremely fine fabric or network. These networks of loops are called spin networks. The evolution of a spin network, or spin foam, has a scale above the order of a Planck length, approximately 10⁻³⁵ meters, and smaller scales are meaningless. Consequently, not just matter, but space itself, prefers an atomic structure. ✨

Physicists Conduct The Most Massive Test Ever of The Einstein-Podolsky-Rosen Paradox using two entangled Bose-Einstein condensates, each consisting of 700 atoms. They show that the conflict between quantum mechanics and local realism does not disappear as the system size increases to more than a thousand massive particles.

Local realism also states that for an object or energy to affect another, the two have to interact. The EPR paradox, therefore, is complex. When you measure one particle in an entangled system, that measurement somehow influences the other particle, even though the measurement isn't taking place locally. EPR suggests that quantum mechanical theory is incomplete.

Bose-Einstein condensates, a state of matter created by cooling a cloud of bosons to just a fraction above absolute zero. At such low temperatures, the atoms sink to their lowest possible energy state without stopping completely. When they reach these low energies, the particle's quantum properties can no longer interfere with each other ; they move close enough to each other to sort of overlap, resulting in a high-density cloud of atoms that behaves like one 'super atom' or matter wave.

Colciaghi, Li, and their physicist colleagues generated 2 BEC using two clouds, separated these condensates spatially by up to 100 micrometers and measured the properties. They measured the quantum property pseudospins & found that the two condensate's properties seemed to be correlated in a way that could not be attributed to random chance, demonstrating the EPR paradox holding firm at a much larger scale.

DOI : doi.org/10.1103/PhysRevX.13.021031

For those who don't know about topics of calculus 1, 2 and 3, here is explanation

Calculus 1:
• Limits
• Continuity
• Differentiation
• Applications of differentiation

Calculus 2:
• Integration
• Application of integration
• Sequences and Series
• Taylor Polynomials and Series
• Differential Equations (overview)

Calculus 3:
• Vector algebra and Geometry
• Vector functions (space curves)
• Functions of several variables (partial derivatives)
• Double and triple integrals
• Vector calculus (grad, div and curl operators)

Note that I haven't mentioned the sub-topics of each topics.

Credit: @CUAVU

What do you need to know before studying calculus?

Before studying calculus you must know elementary algebra, coordinate geometry, trigonometry, concept of function and concept of slope.

I have already covered the topics that comes under calculus 1, 2 & 3 (here). Now in this section, I will share the resources from where you can learn them.

Study material for calculus 1 & 2:

YouTube playlists:

• Don't memorize's playlist
• Essence of calculus by 3Blue1Brown
• MIT playlist by David Jersion
• MIT playlist by Herbert Gross
• Professor Leonard's playlist
• Khan academy's playlist

Book recommendation:

• Calculus: Early Transcendentals by James Stewart
Soft Copy (PDF) | Hard Copy

Study material for calculus 3:

YouTube playlists:

• MIT playlist by Denis Auroux
• MIT playlist by Herbert Gross
• 3Blue1Brown's playlist on Khan Academy
• Professor Leonard's playlist
• Multivariable calculus by Dr. Trefor Bazett
• Multivariable calculus by Diana Davis

Book recommendation:

• Calculus: Early Transcendentals by James Stewart
Soft Copy (PDF) | Hard Copy

Note that: I will add more books when I come across them.

Credit: @CUAVU

THE FORCES

The strong nuclear force is one of the four fundamental forces of nature, along with gravity, electromagnetism, and the weak nuclear force. It is the strongest of all the fundamental forces and is responsible for holding the nucleus of an atom together. Without the strong nuclear force, atoms would not exist as we know them today.
The strong nuclear force is mediated by particles called gluons, which are constantly exchanged between quarks, the building blocks of protons and neutrons. This force only operates over very short distances, within the nucleus of an atom.
On the other hand, the weak nuclear force is responsible for radioactive decay. It is much weaker than the strong nuclear force and is mediated by particles called W and Z bosons. The weak nuclear force is responsible for beta decay, where a neutron in an atomic nucleus changes into a proton, emitting an electron and an antineutrino in the process.
Gravity is the weakest of all the fundamental forces, but it plays a crucial role in keeping planets in orbit around stars and in holding galaxies together. Electromagnetism is responsible for the behavior of electrically charged particles and is responsible for phenomena such as magnetism and light.
In summary, the four fundamental forces of nature are gravity, electromagnetism, strong nuclear force, and weak nuclear force. While each of these forces plays a unique role in shaping our universe, it is the strong nuclear force that holds the key to understanding the structure of matter at its most fundamental level.

#Theforces #Part2

Darwin on Natural selection.

Poisson's equation relates "the Laplacian of the potential to the local charge density." If a potential function obeys Poisson’s equation and satisfies the known boundary conditions it is the only solution to a problem : uniqueness theorem.

Poisson's equation is an elliptic partial differential equation. Solving Poisson's equation for the "potential" requires knowing the charge density distribution. If the charge density is zero, then Laplace's equation results. If the charge density follows a Boltzmann distribution, then the Poisson–Boltzmann equation results. Some technique for guessing (and then verifying) the solution to Poisson’s equation are The Method of Images, Separation of variables & Green's function.

In layman's terms, we can use Poisson's equation to describe the static electricity of an object. The entire subject of electrostatics from a mathematical point of view, is merely a study of the solutions of the Poisson's equation. ✨

Bound & free at the same time - Asymptotic freedom !

David Gross, David Politzer and Frank Wilczek shared the Nobel prize in 2004 for the discovery of asymptotic freedom in the theory of the strong interaction.