Emmy Noether
The symmetry theorem created by Emmy Noether still today boosts new discoveries in particle physics and quantum computing.
Emmy Noether (1882-1935) was one of the first German women to be able to study at the university.
Thanks to your Symmetry Theorem It was acclaimed as a “genius of mathematics” while still living (which tends to be rare).
It was precisely its focus on mathematical problems that caught the attention of Albert Einstein.
As it counts, when the theory of general relativity of Einstein scholars such as David Hilbert and Felix Klein noted that theory could violate the law of energy conservation. The way Einstein had presented his equations included an expression that could be interpreted as implying energy conservation; But which, according to Hilbert and Klein, was equivalent to saying xx = 0: though true, nothing tells us about x.
It was noether that proved that energy must be preserved – In any theory – if the laws of physics remain the same regardless of time – in other words, if they are invariant in time.
It was here that Einstein wrote to Hilbert: “Yesterday I received from Mrs. Noether a very interesting article about invariant forms. I am impressed by the fact that these issues can be understood from such a general point of view, ”says New Scientist.
But Noether didn’t stay here
This temporal invariance is a form of mathematical symmetrybecause the rules are the same wherever we are in time. There are, in fact, two types of symmetry, which we can understand by observing simple geometry.
The two types of symmetry
If we take a square and run 90 degrees, it is the same as a look. This is a type of symmetry. But if we run the square 45 degrees, it looks different, like a diamond. This is called a discreet symmetrybecause you need to take discontinuous steps to recover the original look.
On the other hand, if we have a circle, we can run it at any angle that continues to have the same aspect. This is called a continuous symmetry.
What became known as the teorema de Noether proof that, in nature, the existence of any continuous symmetry is always associated with a law of conservation.
On the one hand, it can use symmetry to calculate the conservation law; On the other hand, it can use the Conservation Law to reveal the underlying symmetry.
The fact that it provides a mathematical basis for understanding the functioning of the daily world has made Noether a reputation.
Revolutionized science – to this day
The best theories make predictions about the behavior of things that were not previously understood, and Noether’s theorem also passed this test with distinction.
As New Scientist writes, what is intriguing is that these equations have continuous continuous symmetries.
According to Noether’s theorem, the presence of these mathematical symmetries implies existence of corresponding conservation laws.
Such laws are linked to real physical phenomenajust as the existence of rotational symmetry requires the conservation of the angular momentum.
It turns out that this connection continues to today and moving with physics, and can be applied in the investigation of particles and fields quantum level.
When physicists find particles that behave according to a given symmetry, they can then use this symmetry to predict the existence of other particles of the same family. This is one of the tools used by theorists to predict the existence of particle families.
However, this is not the only way for Noether’s work to contribute to modern particle physics; also made great contributions to the study of what mathematicians call “Rings”.
The “rings” are the sets of things that can be added or multiplied by each other to form other members of the ring. The classic example is the set of integers 1, 2, 3, 4 and so on. It turns out that more complicated mathematical rings are associated with the behavior of quantum entities, such as quantum computers.
The great conclusion is that One hundred years after Emmy Noether have published your work, this continues to be at the forefront of theoretical physics.
As they highlight, cited by New Scientist, Leon Lederman e Christopher Hilltwo major physicists of the 21st century, Noether’s theorem is “one of the most important mathematical theorems ever proven to guide the development of modern physics, possibly along with the Pythagoras theorem.”
