Imagine trying to put Sheldon Flash Cooper in cage? While in the frame of the cage, Sheldon gets contracted and fits in the cage, we seem to have to conclude the exact opposite from Sheldon’s frame. In this episode, we solve this apparent paradox using Minkowski’s diagrams.

### Video Archives

# What does E=mc² really mean? Relativity 22

E=mc² is probably the most beautiful equation of physics. Yet, its deep and subtle meaning is often misappropriated! In this video, I work out Einstein’s original thoughts to better understand the message he intended to convey.

# The Poincaré conjecture | Relativité 21

Could a universe without border, not go on and on forever?

Poincaré not only gave an answer, he also proposed a fundamental conjecture…

# Albert Einstein, the iconic figure of science | Genius 2

Will there ever even be another Einstein? Doubtful. Einstein not only is a great genius, he’s also and most importantly the iconic figure of science, in its purest and greatest form.

# Twin & Grandfather Paradox | Science4All 20

Leave your twin on Earth while you travel across the universe. When you come back, will you be younger or older than your twin? The answer lies in (gravitational) time dilation

# Can’t you “see” the Big Bang? Relativity 19

One of the most amazing thing about our universe is that we can see its baby picture by just looking up there. What’s equally surprising is that it’s only 50 years ago that we have seen this baby picture! Before that, Big Bang theories sounded ridiculous, especially because of Hubble… The key to understand it all is the cosmological microwave background (CMB) and the Doppler effect!

# Einstein’s biggest blunder | Relativity 18

Because the young Einstein couldn’t accept the possibility of a universe with an end of time, he made obscure modifications to his equations… He would later call this the biggest blunder of his life! Yet, these days, these obscure modifications may somehow shed some light on an even darker secret of our universe…

# Einstein’s heart palpitations | Relativity 17

This video retraces Einstein’s footsteps towards worldwide celebrity. From his first steps into a theory of spacetime curvature to his epic dual with the greatest mathematician of that time and to the eventual confirmation of his theory through eclipse observation. At last, Einstein had triumphed!

# Is gravity acceleration or curvature? Relativity 16

Not many general relativity popularizations distinguish acceleration and curvature, and even suggest that gravity is… both. I know I did. Yet, these are mathematically very, very distinct. So, allow me to clarify myself by drawing the line between what gravity is, and what it is not!

# General relativity explained! Relativity 15

Last time, we saw that Einstein explains the falling of the apple by the upwards acceleration of the ground. This is Einstein’s happiest thought. But wouldn’t this imply that the surface of the Earth is expanding outwards? Well, no. Why? Because of spacetime curvature! At last, this video explains how Einstein’s gravity really works.

# Einstein’s happiest thought | Relativity 14

In 1907, Einstein had the happiest thought of his life, the one that would initiate an 8-year-old seemingly impossible quest for a theory of gravity. While the theory is awfully complex, the thought that led Einstein therefore is wonderfully simple… and has to do with astronauts’ weightlessness.

# How did Newton figure out gravity? Relativity 13

The theory of gravity did not fall from trees. It took a giant, standing on the shoulders of other giants. Building upon Descartes’ algebraic geometry, Galileo’s law of falling objects and Kepler’s law of planetary orbits, Newton would mark History, as he would infer the fundamental laws of motion and gravity.

# Don’t heavier objects fall faster? Relativity 12

It’s often said that Galileo proved by experiment that objects all fall at the same rate. But that can’t be true, as everyday experience shows that heavier objects do fall faster. So, why did nevertheless he claim that all objects fall at the same rate?

# Hyperbolic Geometry | Relativity 11

Believe it or not, my underpants contradict 2000 years of mathematical certainty! It’s only in the 19th Century that Gauss, Lobachevsky and, Bolyai would get a grasp on the hidden geometry underlying my underpants — the so-called hyperbolic geometry… which would lead to new fundamental insights into the nature of geometry itself!

Can you glue opposite edges of a square? Nash’s embedding | Science4All 7

What’s wrong with that map? Spherical Geometry | Science4All 9

What’s a straight line? Curved-space geometry | Science4All 10

What’s Einstein’s gravity? General relativity explained! Science4All 15

What’s the destiny of the universe? Einstein’s biggest blunder | Science4All 18

# Curved-space geometry | Relativity 10

There’s a fine line between straight and curved lines… Or is there not? What’s a straight line (in a curved space)?

What’s wrong with that map? Spherical Geometry | Science4All 9

What’s the geometry of my underpants? Hyperbolic Geometry | Science4All 11

What’s Einstein’s gravity? General relativity explained! Science4All 15

Is gravity acceleration or curvature? Follow-up clarifications | Science4All 16

What proved general relativity? Einstein’s heart palpitations | Science4All 17

What’s the destiny of the universe? Einstein’s biggest blunder | Science4All 18

# What’s wrong with that map? Relativity 9

Maps are wonderful to picture our planet Earth! But they are also deeply misleading… All of them. And there’s a fundamental theorem behind this!

Can you glue opposite edges of a square? Relativity 7

Why do soccer balls have the shape they have? Relativity 8

What’s a straight line? Curved-space geometry | Science4All 10

What’s the geometry of my underpants? Hyperbolic Geometry | Science4All 11

Could space be finite? Poincare conjecture | Science4All 21

# The shapes of soccer balls | Relativity 8

Soccer balls are iconically made of hexagons and pentagons. But why? Why did Adidas choose this beautifully symmetric shape? The answers lie in the geometry of Platonic solids, and, in particular, of the truncated icosahedron. But there’s more. In recent years, Adidas’s balls were actually designed based on the tetrahedron and the cube…

The Cubic Ball of the 2014 World Cup | Science4All Article

Can you glue opposite edges of a square? Relativity 7

# John Nash, a Beautiful Mind | Genius 1

Nobel prize winner John Nash passed away on May 23rd, 2015. He was 86. He had lived an amazing and difficult life. Early on, he was a mathematical prodigy who faced and solved several of the toughest problems of his time. However, at the top of his mathematical genius, he fell into paranoid schizophrenia. After 30 years of struggle with this terrible disease, he miraculously recovered and tamed his demons. Allow me to pay tribute to this beautiful mind.

# Can you glue opposite edges of a square? Relativity 7

This is a conundrum that many of the greatest mathematicians couldn’t figure out. While John Nash did answer yes – by proving the wonderful Nash isometric embedding theorems – he couldn’t say how. After 160 years of research, the Hévéa project finally did it! And it is spectacularly beautiful!

The shapes of soccer balls | Relativity 8

General relativity explained! Relativity 15

The Poincaré conjecture | Relativity 21

# Space contraction and time dilation | Relativity 6

What if space and time were relative? This was Einstein’s insight that led him to a revolutionary understanding of our universe. But this insight was not based on the idea of relativity…

Einstein’s happiest thought | Relativity 14

General relativity explained! Relativity 15

Is gravity acceleration or curvature? Relativity 16

Twin & Grandfather paradox | Relativity 20