Inspire kids to become scientists by saying that…..…………………………………………
Einstein’s general relativity best describes how gravity operates.

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I wonder if energy is a condensed form of spacetime and matter is a condensed form of energy!

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I wonder if condensed spacetime, in the form of matter or energy, pushes aside open spacetime causing  curvatures manifested to us as gravitation!

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Matter or energy is identical to  space-time distortion!

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Gravity is distorted space-time!

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I wonder if matter is a consequence of the ripples of space-time exposed to quantum fluctuations identical to Heisenberg’s uncertainty principle!

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Everything is embedded in time! I wonder if physical universe is just a sort of  time’s unfurling into expanse!

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Though we are immersed in the infinite  spectrum of reality, only a tiny part of it is evolutionarily significant and accessible to our senses!

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Earth  floats in solar system, solar system in galaxy, Galaxy in Super galaxy, Super Galaxy in Universe, Universe in Multiverse, etc etc. Such systems within systems are defined by some holomorphic (locally uncomparable)  contours!

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In Einstein’s special relativity (relative simultaneity),  the motion of bodies in space over time are  too complicated to visualize since the same event might look  evenly spaced in time in one frame of reference while ‘staggered’ in another!

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If we use Minkowski’s space-time geometry to visualize Einstein’s special relativity (relative simultaneity), we need to play out no movie in our head!
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Minkowski’s space-time geometry helps us visualize the motion by  disentangling relativistic effects!

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Stacking up snapshots of two-dimensional spaces at all successive instants of time amounts to a three-dimensional view of Minkowski’s four-dimensional geometry!

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On two-dimensional paper or screen we feel the three-dimensional view of Minkowski’s four-dimensional geometry!

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A small body at rest intersects each instantaneous space at the same spot. In Minkowski’s four-dimensional space-time geometry, a vertical line represents such a small body at rest!

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If a small body is moving, it will intersect each instantaneous space at a different spot. In Minkowski’s four-dimensional space-time geometry, a  line at an angle to the vertical represents such a small body at motion!

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Minkowski’s four-dimensional  geometry has stunningly turned modern physics into geometry!

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‘The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.’

-Minkowski

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‘The validity without exception of the world postulate [i.e., the relativity postulate], I like to think, is the true nucleus of an electromagnetic image of the world, which, discovered by Lorentz, and further revealed by Einstein, now lies open in the full light of day’.

-Minkowski

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Minkowski’s spacetime has been the greatest discovery in physics of all times!

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Minkowski’s discovery of spacetime  paved the way for Einstein’s general relativity ( that gravity is not a force but curvature of spacetime)!

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“The generalization of the theory of relativity has been facilitated considerably by Minkowski, a mathematician who was the first one to recognize the formal equivalence of space coordinates and the time coordinate, and utilize this in the construction of the theory.”

-Einstein (1916 paper on general relativity)

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Minkowski’s space-time hypothesis was  a geometric avatar of Einstein’s special relativity before its expansion into general relativity!

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Even in special relativity, natural phenomena were thought to occur in an Euclidean space of three dimensions and to flow through time!

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Minkowski first hypothesized that time itself is a dimension, like length, breadth, and height!

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Minkowski first hypothesized a four-dimensional Euclidean space-time continuum of length, breadth, height and time!

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Einstein’s general relativity was nothing but turning Minkowski’s  Euclidean space-time into a non-Euclidean one in an attempt to explain ‘free fall’!

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Minkowski’s intuition about physical reality (space-time as a whole) helped Einstein formulate his     general relativity(gravity as a spacetime curvature)!
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Minkowski’s ‘space-time diagrams’ helped Stephen Hawking and Roger Penrose further develop Einstein’s  general relativity!

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Einstein’s special relativity (that energy and mass are interchangeable and that nothing can travel faster than light!) is just a logical extension of  the notion that the speed of light in space  is always the same wherever it is measured from, and however fast and in whatever direction the observer is moving!

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Einstein’s relativity became popular soon after Minkowski had  expressed its  algebraic equations in terms of geometry!

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Though Einstein discovered special relativity  via equations and thought experiments involving trains, Minkowski’s Euclidean geometry now  helps us easily visualize it !

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The rules of special relativity emerge organically from Minkowski’s Euclidean geometry interlinking space and time into a single whole!

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Einstein relativized space and time, not existence itself!

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Simultaneity is relative! Observers in relative motion have different spaces

and times!

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Simultaneous events (i.e.

the spaces) of observers in relative motion are “cross sections” of an absolute four-dimensional world!

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The relativity of simultaneity (the existence of many spaces) led Einstein and Minkowski to the idea of spacetime!

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The faster through space, the slower through time! It’s Einstein’s relativity in a single line.

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“Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.”
-Hermann Minkowski
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In Minkowskian(3+1)D  universe, an event is a  point with a position in Euclidean 3D space and a position in 1D time!
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Minkowskian(3+1)D geometry doesn’t allow more than one event at a particular spatial point!
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One event, one place! It’s Minkowski space!

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Only one event is allowed in a particular Minkowski space!

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Events happen one after another only  at different Minkowski places!
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A cup and a ring  are topologically equivalent since they both have a single hole and can be deformed from one into another without tearing or gluing!

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The shape that remains unchanged after  an object’s stretching or deformation is a topological shape!

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A manifold is a topological space that is locally Euclidean but globally non-Euclidean!

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A homeomorphism is a map between spaces that preserves all topological properties!

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Each point of an n-dimensional manifold has a neighborhood that is homeomorphic to the Euclidean space of n-dimensions!

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The surface of the Earth is a manifold since it is locally  flat but globally( actually ) spherical!

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In general relativity, space-time is a 4 dimensional manifold since it is locally flat (Euclidean) but globally curved ( non-Euclidean)!

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In general relativity, our universe is four-dimensional! 3 space dimensions and 1 time dimension! On two-dimensional paper, vertically both time and one space dimension are assumed! One space dimension is assumed to extend horizontally! The rest space dimension is excluded! This method simplifies our intuition about dimensions!

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The very existence of the universe excludes ‘zero-gravity’. Like an apple, moon and space-stations fall towards earth. Just right amount of sideways momentum helps them constantly miss the earth! 

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Even a single electron’s  gravity has infinite reach! If the earth was the only massive object in the universe, all smaller objects will  fall on earth! When a constant free-fall speed is cancelled by a slightly more sideway momentum, an object gets a stable orbit around a massive gravity source!

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Things fall slower at first due to the

inverse square law of gravitational attraction.

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Astronauts on the International Space Station are not in a zero-gravity environment. They are surrounded by the earth’s and the sun’s immense gravity. Since both the space station and the astronauts inside it are all

constantly ‘free-fall’ing together  towards the earth only to miss it, they enjoy weightlessness!

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Heavenly orbits are just objects falling but traveling sideways fast enough to miss the source of the gravity!

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The sun curves away faster than the earth can fall towards it. As a result, the earth continually falls and misses and ends up circling the sun!

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Since the equal speed of  all falling bodies (whether heavy or light) baffled Galileo, we can now enjoy  general relativity ( the cerebral celebration of curved space-time)!

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According to the latest CMB data, our universe isn’t flat but  curved!
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In a curved four-dimensional universe, no matter which direction we go to, we end up at the starting point – just like Magellan’s ship around the spherical earth!

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In Newtonian physics, ‘free fall’ or  ‘weightlessness’  arises from the uniform (due to the absence of any other forces) gravitational field accelerating each part of an attracted  body (roughly) equally!

It is the (same) sensation of weightlessness in the absence of any gravity!

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We feel ‘free fall’ when gravity is the only acceleration acting upon us!

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In general relativity, we feel no force in ‘free fall’  since even gravity is not a force but space-time curvature!

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A gravitationally attracted body itself always feels like a fall, even when goes upward or sideward in the eyes of a distant observer!

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In Einstein’s  general relativity, space and time are merged together into a unified framework (space-time). This space-time isn’t a  fixed stage-like background. It is dynamic enough to bend and stretch in response to the presence of matter and energy.
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In Einstein’s  general relativity, the  bending, warping and flexing of space-time force light and matter  to follow curved trajectories — like following the peaks and valleys of the topography while trying to cross a mountain in a straight line.
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Warping of space-time manifests itself as gravitational field. Mandetorily following (by an object ) the  undulations of space-time takes on gravitational pull.

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Like a flexible trampoline, space-time is stretchable.

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You can bend the trampoline down just by standing on it. Whenever anyone goes past you, they feel your “gravity” i.e.  follow a slightly curved path. But far enough away from you, the path is smooth and so without ‘gravity’.

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Like a flexible trampoline, space-time vibrates. When shaken, spacetime sends waves and tremors through the whole thing.
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Such gravitational waves transmit energy through  the fabric of space-time.

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Gravitational ripples originate from just about every kind of motion possible, but only the most energetic movements create instrumentally detectable ripples.

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On earth, gravitational waves move things around  less than the width of an atom.

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Even we are being constantly  squeezed and stretched by gravitational waves created billions of light-years away.

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Gravitational waves become a source of new gravitational waves, similarly ad infinitum. Such a permanent distortion of space-time is called a space-time “memory”.

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“Work in silence and let your success make noise.”

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Whenever an electrical charge accelerates, an electromagnetic disturbance spreads as a spherical wave in space at the speed of light. It is an experimental fact.

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Since the speed of a wave on water is the sum of the speed of the wave  and the speed of the flowing water, physicists mistakenly (but reasonably enough) tried to detect the draft of an imaginary ether as the medium of electromagnetic waves like light. Empty-handed they imagined  that an object traveling through the ether contracts and its time slows down. None could explain the physical implications of such mathematical tricks. Unlike Newton, Einstein dared to say that space,time , motion,  rest, mass and energy are just mutually adjustable properties of a physical universe with an absolute speed of light. 

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Einstein’s relativity not only explains the behavior of objects in space and time but also predicts everything from the existence of black holes, to light bending due to gravity, to the behavior of the planet Mercury in its orbit.

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Though there is no “absolute” frame of reference, nothing can beat  the absolutely constant speed of light, rather spacetime/energy adjusts itself to it.This ‘special’ theory of relativity becomes ‘general’ when it it describes gravity as the spacetime curvature due to the presence of mass.

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Since the speed of light is always the same, time slows down( to an external observer only ) for an astronaut (to whom, however,  time flows normally) going very fast relative to the Earth. It is the only way to make light’s speed constant( to that external observer  ) even with the spacecraft’s added velocity!

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One earth-year might equal  one spaceship-minute ( to an external observer only )!

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Fot someone travelling at c,  time freezes to an external observer. The traveler experiences nothing amiss rather sees  the whole 4th dimension at a glance.

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‘Free fall’ as force
‘Free fall’ as four-dimensional curvature

Momentum is made up of two components: mass and velocity. Experimental evidence shows massless  photons have momentum. In Einstein’s special relativity, the kinetic energy of a photon is equivalent to a quantity of ‘spookily acquired’ mass associated with  the momentum.

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Since kinetic energy is equivalent to a quantity of ‘spookily acquired’ mass, even if a mass is observed macroscopically to be at rest, it contains  energy that can be extracted by decreasing the rest-mass amount as per the mass-energy equivalence equation.

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Einstein’s mass-energy equivalence has not yet been observed for chemical reactions because the amount of mass liberated is very little.

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Einstein’s mass-energy equivalence has  been observed in nuclear reactions.

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