Mathematician Emmy Noether in 1918 published a fundamental pillar of modern theoretical physics that bridges the gap between symmetry and conservation laws.
It establishes that every continuous symmetry of a physical system corresponds to a conserved quantity, and vice versa.
> If a system remains unchanged (invariant) under a continuous transformation, a corresponding quantity remains constant over time (conserved).
> These are transformations that can be applied in small, gradual steps, such as rotating an object or moving it through space, which do not change the underlying physical laws.
>The theorem is usually expressed using Lagrangian mechanics, specifically looking at the action integral of a physical system
These Red sprites are bursts of lights in the upper atmosphere resembling gigantic jellyfish
Its a type of Transient Luminous Event that appear as bright, reddish-orange flashes or tendrils above thunderstorms.
They are triggered by positive lightning discharges within thunderstorms, occurring in mesosphere (~60km above), and are incredibly fast,lasting only a millisecond or two
Most of them are difficult to observe from Earth, especially during the day, and they are often best seen from space.
One unusual feature of sprites is that they are relatively cold. They operate more like long fluorescent light tubes than hot compact light bulbs.
Einstein believed quantum mechanics was incomplete, as per him if two particles were entangled, they must carry a hidden variables which is pre-determined instruction sets that tell them how to behave when measured.
Coming to 1964, John Bell devised a mathematical way to test this. He showed that if Einstein were right (if local hidden variables existed), there would be a strict limit on how correlated the measurements of two distant particles could be. This limit is known as Bell’s inequality.
Quantum mechanics predicted that entangled particles would be more strongly correlated than any local theory could allow, thus violating Bell’s inequality.
Starting with John Clauser in 1972 and followed by Alain Aspect in 1982, experiments have consistently shown that nature violates Bell’s inequality.
This experimental confirmation led to the 2022 Nobel Prize in Physics for Alain Aspect, John Clauser, and Anton Zeilinger.
A breakthrough has been achieved when Scientist, for the first time, have recorded the moment when both Hydrogen and Oxygen atoms combine at nanoscale to form water molecules
Einstein believed quantum mechanics was incomplete, as per him if two particles were entangled, they must carry a hidden variables which is pre-determined instruction sets that tell them how to behave when measured.
Coming to 1964, John Bell devised a mathematical way to test this. He showed that if Einstein were right (if local hidden variables existed), there would be a strict limit on how correlated the measurements of two distant particles could be. This limit is known as Bell’s inequality.
Quantum mechanics predicted that entangled particles would be more strongly correlated than any local theory could allow, thus violating Bell’s inequality.
Starting with John Clauser in 1972 and followed by Alain Aspect in 1982, experiments have consistently shown that nature violates Bell’s inequality.
This experimental confirmation led to the 2022 Nobel Prize in Physics for Alain Aspect, John Clauser, and Anton Zeilinger.
The Einstein Field Equations, composed by Albert Einstein's theory of general relativity in 1915,
A set of ten non-linear partial differential equations that describe how matter and energy influence the curvature of spacetime.
Galileo Galilei's middle finger is preserved at the Museo Galileo in Florence, Italy. It was removed after his death and is now displayed in a glass egg.
It became part of the ceremony when his remains were moved in 1737. It is a piece of his legacy—and for those who punished him.
Why does the bell curve show up everywhere? Whether in heights, test scores, stock returns, and measurement errors?
If you Roll a single die. You get 1 through 6 with equal probability.
That's a flat, uniform distribution — nothing special.
Now roll two dice and add them. Suddenly 7 is more likely than 2 or 12, because there are more ways to make 7. The distribution starts forming a triangle shape.
Roll 5 dice and add them. It starts looking like a hill.
Roll 10 dice and add them. It looks almost exactly like a bell curve.
You never changed the die. Each die is still perfectly uniform. But something remarkable happened when you started adding them together.
This is the Central Limit Theorem.
It says - take any random variable — it doesn't matter what distribution it follows and add together a large number of independent samples from it. The distribution of that sum will always approach a normal distribution.
Always. Regardless of the original shape.
Whenever a quantity is the result of many small independent effects piling on top of each other, the CLT kicks in and forces a normal distribution to emerge.
CLT is one of the most beautiful results in all of mathematics. And it's hiding behind almost everything.