07 Oct-2021
YT: General Relativity Explained in 7 Levels of Difficulty
A) Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric, i.e. with an inner product on the tangent space at each point that varies smoothly from point to point.
B) Lorentzian geometry is a vivid field of mathematical research that can be seen as part of differential geometry as well as mathematical physics. It represents the mathematical foundation of the general theory of relativity - which is probably one of the most successful and beautiful theories of physics.
C) A geodesic is a locally length-minimizing curve. Equivalently, it is a path that a particle which is not accelerating would follow. In the plane, the geodesics are straight lines. On the sphere, the geodesics are great circles (like the equator).
D) In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it.
E) Aphelion is the point of the Earth's orbit that is farthest away from the Sun. · Perihelion is the point of the Earth's orbit that is nearest to the Sun.
F) The dark matter of gravitational lensing
G) Two Kinds Of Gravitational Lenses Both Reveal Dark Matter
H) Dark matter is a hypothetical form of matter thought to account for approximately 85% of the matter in the universe.
I) New gravitational-lensing study hints at problems for dark matter models
J) Smaller objects, like individual stars, can also act as gravitational lenses when they pass in front of more distant stars. For a few days or weeks, light from the more distant star temporarily appears brighter because it is magnified by the gravity of the closer object. This effect is known as gravitational microlensing.
K) Optical Clocks and Relativity
L) Over a century ago, Einstein presented the theory of relativity—where space and time are no longer fixed concepts, but are relative to an observer and their frame of reference. Tests of relativity have usually been confined to space-based measurements and/or with objects with velocities approaching the speed of light. Time-dilation and length-contraction have been confirmed and are used in satellite communication and global positioning systems.
M) We can now also detect time dilation due to a change in height near Earth’s surface of less than 1 meter.
N) Albert Einstein’s theory of relativity forced us to alter our concepts of reality. One of the more startling outcomes of the theory is that we have to give up our notions of simultaneity. This is manifest in the so-called twin paradox
O) Another consequence of Einstein’s theory is that clocks run more slowly near massive objects.
P) In the range of speeds and length scales encountered in our daily life, relativistic effects are extremely small. For example, if two identical clocks are separated vertically by 1 km near the surface of Earth, the higher clock emits about three more second-ticks than the lower one in a million years.
Q) Atom interferometry is the technique that underlies most of our precision measurements. We exploit the fact that matter, like light, exhibits wave-like properties. Atoms, unlike light, are massive and bear gravitational signals in their interference patterns.
R) Mössbauer spectroscopy is a spectroscopic technique based on the Mössbauer effect. This effect, discovered by Rudolf Mössbauer (sometimes written "Moessbauer", German: "Mößbauer") in 1958, consists of the nearly recoil-free emission and absorption of nuclear gamma rays in solids.
S) The geodetic effect (also known as geodetic precession, de Sitter precession or de Sitter effect) represents the effect of the curvature of spacetime, predicted by general relativity, on a vector carried along with an orbiting body.
T) Evidence Supports Einstein's Geodetic Effect > Mass warps space and time, just as Albert Einstein said it would, confirms data from a NASA satellite launched to test two of the great physicist’s predictions. One of these effects is called the geodetic effect, the other is called frame dragging. .... Satellite data confirmed the geodetic effect, but it will take scientists another eight months to analyze the frame dragging data, even though Superman proved it was true nearly 30 years ago.
U) The cosmic microwave background (CMB, CMBR), in Big Bang cosmology, is electromagnetic radiation which is a remnant from an early stage of the universe, also known as "relic radiation".
http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch7/ie_ea.html
https://www.britannica.com/science/ionization-energy
Alternatively, lattice energy can be thought of as the energy required to separate a mole of an ionic solid into the gaseous form of its ions (that is, the reverse of the reaction shown above).
11 Dec-2021
A light wave that is vibrating in more than one plane is referred to as unpolarized light. Light emitted by the sun, by a lamp in the classroom, or by a candle flame is unpolarized light.
Most light sources emit unpolarized light, but there are several ways light can be polarized. One way to polarize light is by reflection. Light reflecting off a surface will tend to be polarized, with the direction of polarization (the way the electric field vectors point) being parallel to the plane of the interface.
The most common source of polarized light is a laser.
The concept that matter behaves like a wave was proposed by French physicist Louis de Broglie (/dəˈbrɔɪ/) in 1924. It is also referred to as the de Broglie hypothesis.[1] Matter waves are referred to as de Broglie waves. // https://en.wikipedia.org/wiki/Matter_wave
The de Broglie wavelength is the wavelength, λ, associated with a massive particle (i.e., a particle with mass, as opposed to a massless particle) and is related to its momentum, p, through the Planck constant, h:
Mathematics and life.
This image is circulating widely on the Web. What caption would you give it? What lesson is there to learn? How does it relate to our lives?
Teachers, stimulate your students with "The Universe of Numbers." Which class of numbers are new to you? (P.S. "Nimbers" is not a misspelling.)
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