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Facts
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1. If gravity was slightly more powerful the universe would collapse into a ball or if gravity was slightly less powerful the universe would fly apart and their would be no stars or planets. It means that the gravity is just as strong as it needs to be. Also if the ratio of the electromagnetic force to the strong force wasn't 1% the life wouldn't exist.
Explanation
The strength of gravity and the ratio of the fundamental forces in the universe are finely tuned to allow for the formation and existence of stars, planets, and life as we know it. The gravitational force, which is responsible for holding celestial bodies together and keeping them in orbit, is balanced against the expansion of the universe. A slight increase in the strength of gravity would cause the universe to collapse, while a slight decrease would cause it to fly apart.
The ratio of the electromagnetic force to the strong force, which is responsible for holding atoms together, is also finely tuned. The electromagnetic force is about 10^36 times stronger than the strong force, which is the force that holds the protons and neutrons in the nucleus of an atom together. If this ratio were slightly different, atoms would not be able to form and the building blocks of matter would not exist.
This fine-tuning of the fundamental constants of the universe is one of the mysteries of physics and cosmology, and it's an open question in science how these constants came to have the values they do. Some scientists have proposed the idea of a multiverse, where there are an infinite number of universes with different constants and laws, but this idea is still purely speculative.
2. EUMETSAT
The European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT) is dedicated to monitoring weather and climate from space -- 24 hours a day, 365 days a year.
EUMETSAT is an international organisation,
founded in 1986. shows how polar orbiting satellites build up a picture of the Earth from consecutive passes, known as 'swaths', as the Earth rotates. The example is based on Metop satellites, which fly with an inclination of 98.7° to the equator:
Watch the video to understand
3. Enistin had strong misgivings about black hole. He concluded in a 1939 paper in the Annals of Mathematics that the idea was “not convincing” and the phenomena did not exist “in the real world.”
4. De Broglie's hypothesis states that matter has wave-like properties. The de Broglie‐Bohr model of the hydrogen atom states that the electron is a particle on a ring with wave‐like properties.
5. Giant dying star collapses straight into black hole, The left image shows the star as it appeared in 2007, The right image shows the same region in 2015, with the star missing.
(for more visit Wikipedia)
6. The James Webb Space Telescope has taken a picture of Earendel - the most distant star we've ever seen. Normally, only galaxies can be seen that far away but a cosmic coincidence made it possible to take the image. (For more visit New scientist)
7. A quantum computer speaks in bits but unlike a conventional bit which can be either O OR 1 at any moment. Just as Schrödinger's cat the cat in the box can be dead and alive at the same time. A quantum bit also called qubit can be 0 &1 at the same time. Hence, they are great at multitasking. Also quantum computers are so powerful that it could do a task in four minutes which would take a supercomputer (till date) 10,000 years to accomplish.
8. Researches found that black holes have same Quantum property, dead and alive at the same time. A new study reveals that cosmic objects can be small and big, heavy and light, dead and alive at the same time just like Schrödinger's cat. The team developed a mathematical framework that placed a simulated quantum particle just outside a giant simulated black hole. The simulation revealed that the black hole showed signs of quantum superposition, the ability to exist in multiple states at once. In this case, both massive and not massive at the same time. If you want to know more about Schrödinger's cat experiment, quantum superposition, how teleportation is possible using quantum mechanics and more. You can visit :- Basics Of Quantum Mechanics. |Teleportation Explained
9. Protons has 2 up quark and 1 down quark and a neutron has 2 down quark and 1 up quark. When we put protons and neutrons together we have a nucleus and add electrons to it, then we get an atom and when we put atoms together we get matter (us).
Explanation
Protons and neutrons are made up of smaller particles called quarks. Protons are made up of two "up" quarks and one "down" quark, while neutrons are made up of two "down" quarks and one "up" quark. Together, protons and neutrons make up the nucleus of an atom.
Electrons, which are negatively charged particles, orbit the nucleus. The number of protons in the nucleus determines the atomic number of an element and thus its chemical properties. The number of neutrons in the nucleus can vary, leading to isotopes of an element.
When atoms come together, they can form molecules, which are the building blocks of matter. The chemical properties of an element are determined by the number of protons in its nucleus, while the number of neutrons can affect the physical properties such as the stability and the radioactivity of the atom.
The properties and behavior of matter at the atomic and subatomic level are described by the field of physics known as quantum mechanics. It is a complex and fascinating subject that has led to many technological advancements and a deeper understanding of the nature of our universe.
10. One of the most famous equations in black hole physics is the Schwarzschild metric, which describes the spacetime around a non-rotating, uncharged black hole. The equation is:
ds^2 = (1 - (2GM/c^2)r)c^2dt^2 - (1/(1 - (2GM/c^2)r))dr^2 - r^2(dθ^2 + sin^2θdφ^2)
Where:
ds is the interval of spacetime (a measure of the distance between two events)
G is the gravitational constant
M is the mass of the black hole
c is the speed of light
r is the radial coordinate (the distance from the black hole's center)
t is time
θ and φ are the angular coordinates on a sphere.
This equation describes the geometry of spacetime around a non-rotating, uncharged black hole. It predicts that there is a singularity at the center of the black hole, where the curvature of spacetime becomes infinite, and it also predicts that there is an event horizon at the Schwarzschild radius, where the escape velocity exceeds the speed of light. Beyond the event horizon, nothing can escape from the black hole.
Questions
1. What is galactic year? And How long is a galactic year?
Ans:- The galactic year, also known as a cosmic year, is a unit of time that is used to describe the duration of time required for the Sun and the Solar System to complete one orbit around the center of the Milky Way Galaxy. The Milky Way is a spiral galaxy, and the Solar System is located in one of its spiral arms, about 25,000 light-years from the center. The orbit of the Solar System around the center of the galaxy is not a perfect circle, but rather an elongated ellipse, and it takes the Solar System about 225 to 250 million terrestrial years to complete one orbit.
The galactic year is a very long time, much longer than the age of the Solar System, which is estimated to be about 4.6 billion years. This means that the Solar System has not yet completed a full orbit around the center of the galaxy. Scientists use the galactic year as a reference to describe the long-term evolution of the Milky Way and its structure, as well as the processes that shape it.
It's worth noting that the Milky Way is not the only galaxy in the universe, and different galaxies have different orbits, velocities, and sizes, thus the galactic year for other galaxies would be different from the Milky Way.
2. What are some misconception regarding black holes?
Ans:- 1. black holes suck everything in.
2. All stars become black holes.
3. event horizons cause spaghettification.
4. The Large Hadron Collider will create black holes that destroy us all. (More)
3. How would you determine the ground state of a quantum system with no exact solution?
Ans:- By attempting to approximate the wave-function and adjusting its parameters until the lowest energy solution is achieved.
Detailed explanation:-
There are a few ways to approximate the ground state of a quantum system for which there is no exact solution. One of the most commonly used methods is the variational method, in which a trial wave function is chosen and the expectation value of the Hamiltonian is calculated for that wave function. The trial wave function is then modified until the expectation value is minimized, at which point the wave function is considered to be an approximation of the ground state. Another method that can be used is the Monte Carlo method, in which the wave function is randomly sampled to find the lowest energy state.
Another method that can be used is the density functional theory, which is a computational method based on the electron density rather than the wave function. It can also be used to find approximate solutions to the ground state of a quantum system.
It should be noted that these methods, while useful, only provide approximate solutions and the results may not be highly accurate.
Another way is known as the variational method, which involves making an educated guess for the wave function, and then optimizing its parameters to minimize the energy of the system. This method can be computationally efficient, but it is not guaranteed to give the exact ground state wave function. Other methods such as numerical diagonalization or quantum Monte Carlo can also be used to find the ground state of a quantum system.
4. What is Brachistochrone problem? And how it relates to the calculus of variations?
Ans:- The Brachistochrone problem involves determining the quickest route for a point-like object to travel between two points under the influence of gravity. Through mathematical analysis, it has been shown that the optimal path is not the shortest one, but rather an inverted cycloid curve. This concept is be visualized with the help of GIF below. Essentially, while the shortest path between two points is a straight line, the fastest path is an inverted cycloid.
The Brachistochrone problem, also known as the "shortest time" problem, is a classic problem in physics and mathematics that was first posed by the Swiss mathematician Johann Bernoulli in 1696. The problem is to determine the shape of the curve that a particle will follow in order to travel between two points in the shortest amount of time, assuming that the particle is subject to a uniform gravitational field.
The solution to the Brachistochrone problem is not a straight line, but rather an inverted cycloid. A cycloid is the path traced by a point on the circumference of a rolling wheel. An inverted cycloid is the path traced by a point on the inside of a wheel as it rolls along a flat surface.
The reason why an inverted cycloid is the fastest path is due to the fact that it takes advantage of the principle of conservation of energy. As a particle moves along the inverted cycloid, it loses potential energy due to the gravitational field and converts it into kinetic energy. Since the gravitational force is constant, the rate at which the particle loses potential energy is also constant, and the particle will move faster where it has the most kinetic energy.
The Brachistochrone problem was one of the first problems to be solved using the calculus of variations, which is a branch of mathematics that deals with finding the solution to problems that involve finding the maximum or minimum value of a function. This problem has been studied and generalized by many mathematicians and scientists over the years, and it still remains an important problem in physics and mathematics today.
5. How to integrate X squared times e to the minus X, without looking it up?
Ans:- Feynman's trick is a method for evaluating definite integrals using the idea of differentiating under the integral sign. The trick is based on the fact that the derivative of an integral is the integral of the derivative, and it can be used to simplify the process of evaluating certain types of definite integrals.
To use Feynman's trick to integrate x^2 * e^(-x), we can start by taking the derivative of e^(-x) with respect to x, which is -e^(-x). We can then multiply this by x^2, which gives us -x^2 * e^(-x). Next, we can integrate this expression with respect to x, which gives us -(x^3/3) * e^(-x) + constant.
Now we have to integrate the original function with respect to x, x^2 * e^(-x). We can use the result we got above and multiply it with -1 to get (x^3/3) * e^(-x) + constant.
Alternatively, you can use the integration by parts method, with u = x^2 and dv/dx = e^(-x), and get the same result.
6. What is the correct interpretation of quantum mechanics?
Ans:- Since every interpretation gives exactly the same answer to every measurement, they are all equally correct.
Detailed explanation:-
The Many Worlds Interpretation (MWI) of quantum mechanics is a popular interpretation that tries to explain the behavior of quantum systems. It suggests that every time a quantum system interacts with the macroscopic world, the universe splits into multiple branches, each corresponding to a different outcome of the measurement.
According to MWI, all possible outcomes of a quantum measurement happen simultaneously in different parallel universes. This means that there is a vast number of parallel universes, each with its own set of physical laws, and each corresponding to a different outcome of every quantum measurement.
MWI is one of several interpretations of quantum mechanics, and while it is not universally accepted, it has been gaining popularity in recent years. It offers a way to resolve some of the paradoxes and inconsistencies of other interpretations, such as the Schrödinger's cat paradox, but it also raises new questions and challenges, such as the problem of probability, the problem of the emergence of classicality, and the problem of the interpretation of the wave function.
It is a fascinating concept but still not a scientific theory that has been experimentally verified or disproven.
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