Beautiful Equations

[Tweety.Abd]

Equations are beautiful. Within a few symbols, equations can capture far reaching aspects of the physical universe. Here are 3 of my favorites.

1. The General theory of Relativity, Albert Einstein.

2. The Dirac Equation, Paul Dirac

3. The Uncertainty Principle, Werner Heisenberg.

[tezza]

:hehe:

[Airstream_Bill]

Boy I WISH I understood that. 2 X 3 = 6 Now you know where I am . Somebody needs to know that math. :rolleyes:

[rudrax]

@Tweety.abd, can you explain them in words?

[Tweety.Abd]

@Tweety.abd, can you explain them in words?

Einstein's equation of General Relativity simply says the following: the Ricci curvature tensor minus one half the Contracted curvature tensor (Scalar curvature) times the Metric tensor is proportional to the Stress-Energy tensor. (Left out the cosmological constant since it was removed by Einstein once the universe was proved to be expanding). All this says that if you start with a star, a planet, a galaxy or even a universe (right hand side of the equation), that determines the curvature that surrounds that concentration of matter and energy (given by the left hand side of the equation). In other words

"Spacetime tells matter how to move; matter tells spacetime how to curve" - John Wheeler

General Relativity is basically a theory of gravitation. It forms the basis of our understanding about gravity being the simplest and most elegant theory in all of science. The reason for its simplicity is because it has only two free parameters: cosmological constant and Newton's gravitational constant. This is one of the prime reasons physicists prefer GR over other competing theories (Brans-Dicke theory, etc.) Also one of its key features is that its 'background independent'.

Some of the predictions of General Relativity:

- The gravitational redshift (also called 'Einstein shift', result of gravitational time-dilation)

- The gravitational wave (unconfirmed, indirect evidence Hulse–Taylor binary pulsar 1974)

- Precession of the perihelion of Mercury's orbit. (Albert Einstein 1915)

- The bending of light (Arthur Eddington, 1919 - 1922)

- Back holes (Schwarzschild solution 1916)

- The 'Big Bang' (Friedmann 1922, Lemaitre 1927)

- Expansion of the universe (Friedmann 1922, Lemaitre 1927, confirmed by Hubble 1929)

- Acceleration of the expansion [Possible explanation by 'Cosmological constant'] (Saul Perlmutter, Brian Schmidt, and Adam Riess 1998)

- General relativity is necessary for GPS!

The mathematics of General Relativity still presents physicists with a formidable challenge. Unlike most of the other fundamental physical theories, GR is a highly non-linear. Some of the difficulties:

- Difficult (or impossible without mathematics) to visualize 4 dimensional curved space-time.

- Non-Euclidean nature

- Solving for 'co-ordinate system' or the metric tensor. (Major difficulty in GR)

According to Einstein, General Relativity made Special Relativity look like 'child's play'.

In short, General Relativity describes the entire arena on which physics takes place.

[Tweety.Abd]

:hehe:

The guy in the picture looks like Ed Witten :think:

[Tweety.Abd]

@Tweety.abd, can you explain them in words?

I don't know much about Dirac equation, but I'll try my best. I'll write about the uncertainty principle soon.

[rudrax]

@Tweety.abd, can you explain them in words?

I don't know much about Dirac equation, but I'll try my best. I'll write about the uncertainty principle soon.

I'm waiting for that. And do state what the respective symbols in the equations designates. This is important because without designation of the symbols (the respective elements), a equation is meaningless.