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# Understanding the concept of symmetry using Neuter's theorem and the bird that didn't get electrocuted!

If you go back to the 1920s in Gttingen, Germany, on a hot
summer evening you might hear the buzz of conversation coming from
an apartment in Friedlander. With a glance through the room's
window, you can see a gathering of students talking about the day's
math problems. With more eavesdropping, you might finally hear the
laughter of the woman who is hosting the party, and she is none
other than Emmy Noether, the genius mathematician who gave
Noether's **theorem** to the world of science!

**that**changed the way physicists study the world.

- Amy Nutter, the woman who changed the face of physics!li>
- Noether's theorem, laws of constancy and symmetries
- gender view in science; From Marie Curie to Amy Noether
- Symmetries are more important than you think!
- General relativity and Noether's theorem
- An overview of Amy Noether's life
- li>
- Scalar symmetries and Noether's theorem
- Summary

## Amy Noether, the woman who changed the face of physics!

About a century has passed since the day on July 23, 1918, when
the famous Noether **theorem** was introduced to the world of
science, with This has not diminished its importance one bit. In
fact, this case was and is like a guiding star for the physicists
of the 20th and 21st centuries. Noether was a leading mathematician
of his time, and in addition to his famous theorem, which is now
called "Noether's theorem", he also launched a branch of
mathematics called abstract algebra.

Noether's **theorem** at its peak shows **that** any
**symmetry** can represent a certain quantity keep More
precisely, for each **symmetry** in the system (the existence of
a symmetric and differentiable function), there is a physical
quantity **that** is intractable. The above equation expresses
the **concept** **that** the quantity in parentheses does not
change over time.

But Noether's professional life did not go so well despite such
genius. After getting his doctorate, he had to work for years
without pay. Although she began working at the University of
Gttingen in 1915, she was initially only allowed to teach as an
assistant to her male colleague and received no salary until 1923.
Ten years later, when the Nazis came to power, Notter was forced to
leave his job by the government because he was not only Jewish but
also suspected of having left-wing political views. "Bryn Mawr" in
Pennsylvania left for the United States of America; But less than
two years later, he died at the age of 52 due to complications from
surgery! While the importance of his case was not fully known!
Although most people have never heard of Amy Notter, physicists
always praise her. In this regard, Ruth Gregory, a theoretical
physicist at Durham University in England, admits **that**
Noether's **theorem** is current in everything **that**
physicists do.

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## Noether's Theorem, conservation laws and symmetries

Noether specified the connection between two important concepts
in physics, i.e. conservation laws and symmetries. In general,
conservation laws, such as conservation of energy, state
**that** a certain quantity such as energy is neither created
nor destroyed, but is always constant. The same certainty in the
conservation of energy helps physicists to solve many problems,
from calculating the speed of a ball rolling down a hill to
**Understanding** the processes of nuclear fusion. , indicates
the stability of a physical quantity related to a specific system
during the evolution of **that** system. **symmetry** in
physics includes physical or mathematical properties **that**
remain unchanged under certain transformations (such as
rotation).

On the other hand, symmetries describe changes **that** can
be made without changing the appearance or function of an object.
For example, a sphere is perfectly symmetrical, because if you
rotate it in any direction, it still looks like the original shape.
The same description includes the **symmetry** of the laws of
physics. This means **that** the equations do not change at
different times or places.

A picture of Amy Noether, whose Noether's **theorem** became
one of the most important theories of modern physics in 1918!

Now, according to the explanation of these two important
principles in physics, you should know **that** Noether's
**theorem** admits **that** every A **symmetry** has an
associated conservation law and vice versa (for every conservation
law, there is an associated symmetry!).

Noether's **theorem** states **that** every
**symmetry** has an associated conservation law and every The
law of conservation is associated with a related symmetry!

Simply put, the law of conservation of energy states **that**
the physical laws **that** govern today are the same as they
were yesterday. Likewise, conservation of momentum is related to
the fact **that** physics in this part of the world is similar
to anywhere else in the world. This connection between
**symmetry** and survival reveals the existence of a reason
behind the characteristics of the universe, which seemed to be
random before **that** relationship was known! And it became the
basis of the standard model of particle physics. The Standard Model
of particle physics examines the universe from a subatomic
perspective and is the same model **that** predicted the
existence of the Higgs boson, a particle **that** was discovered
with much fanfare in 2012.

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## gender view in science; From Marie Curie to Amy Noether

When Amy Noether died, Albert Einstein wrote in the New York Times Amy Nutter was the most creative genius mathematician there has been since the beginning of higher education among women. Although this is an intimate compliment on Einstein's part, Einstein's praise referred to Amy's gender rather than her scientific prominence among her male colleagues!

Similarly, several other mathematicians who praised Amy They had brought, along with those compliments, they commented on her appearance, and even in one of these cases, comments were made about Amy's sex life! So as you can see, even those who admired Noether judged him by different standards than men.

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## Symmetries from They are more important than you think!

In general, the discussion of **symmetry** is one of the
fascinating topics from the past. so far For example, some studies
report **that** people with more symmetrical faces are more
beautiful than asymmetrical faces. This means **that** the two
halves of these people's faces are almost mirror images of each
other (mirror symmetry). On the other hand, in most cases, art
displays symmetry, you can understand this well by looking at
Iranian designs and tiles. In addition to these things, nature also
likes symmetry; Because when you rotate the snowflake by 60
degrees, it looks the same. Besides that, petals, flowers, spider
webs and many other things are formed with the principles of
symmetry.

But at the same time, you should know **that** Noether's
**theorem** does not directly apply to these familiar examples;
This is because the symmetries we see around us are discrete,
meaning they only apply to certain values. For example, a rotation
of exactly 60 degrees for a snowflake is discrete. In general, the
symmetries related to Noether's **theorem** are continuous,
which means **that** no matter how much you move in space or
time, continuous symmetries are always preserved and do not depend
on specific values.

The symmetries related to Noether's **theorem** They are of a
continuous type and are not considered discrete like the
**symmetry** of a snowflake with a 60-degree rotation.

Among these, one of the types of continuous symmetry, which is
known as translation symmetry, implies this principle. It says
**that** the laws of physics do not change with movement in the
universe and remain the same.

Consistency laws are among the basic tools in physics. In
physics classes, students are taught the principle **that**
energy is always constant. Because when the first billiard ball
hits other balls, the energy of the first ball's motion is divided
during the collision. Part of the energy makes other balls move,
part produces sound or heat, and some energy remains in the first
ball. In such a case, no matter what happens, the total amount of
energy always remains the same. This is also true of momentum.

Generally these laws are taught to students as undisputed and
unequivocal truths, but you need to know **that** there is a
mathematical reason behind all of them. According to Noether, the
conservation of energy is due to transitive **symmetry** in
time. Similarly, the principle of conservation of momentum is also
in space due to translational symmetry. Angular momentum
conservation is a feature **that** allows skaters to increase
their spin speed by hugging their arms. This fast rotation comes
from rotational **symmetry** and it means **that** by
rotating in space, everything will be in the same original
shape.

In Einstein's theory of general relativity, there is no absolute
sense of time or space. It doesn't exist, so it's harder to
understand the consistency laws, so as we said at the beginning of
the article, this is where Noder's **theorem** comes in and
overcomes the leading challenges.

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## General relativity and Noether's theorem

Although general relativity was introduced to the world as a new
and fascinating theory in 1915, the situation was such **that**
David Hilbert and Felix Klein, the German mathematicians, were
overwhelmed by the ambiguities of this new view. In this regard,
Hilbert in order The mathematical development of the theory, which
described gravity as the result of the curvature of matter in
spacetime, was in competition with Einstein.

It was in this atmosphere **that** Hilbert and Klein stumbled
upon a new challenge. The problem ahead was **that** trying to
write an equation for the conservation of energy in the framework
of general relativity would lead to tautology! In other words, like
writing the expression "0 equals 0", the equation of conservation
of energy in the framework of general relativity had no physical
significance. This was surprising, because no accepted theory had
such energy conservation laws. So these two mathematicians hired
Amy Notter, who had special expertise in various fields of
mathematics, to join them in Gttingen and help solve the puzzle
ahead. It belongs to a special class of theories **that** are
generally called covariant. In such theories, the equations related
to the theory, whether you are moving continuously and without
acceleration or with acceleration; Remains constant. Because during
movement, both sides of the theoretical equation change together.
As a result, covariant theories, including general relativity, are
always associated with these unusual conservation laws; This
discovery is known as Noether's second theorem. On the way to
proving the second theorem, Notter proved his first **theorem**
on the connection between symmetries and conservation laws, and
published both results on July 23, 1918, in an article called
"Gttinger Nachrichten".

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## A review of Amy Noether's life

Amy Noether was born in 1882 and was the daughter of two
mathematicians Max Noether and Ida Amalia Noether was "Ida Amalia
Noether". Growing up with her three brothers in Erlangen, Germany,
young Amy's mathematical talent was not obvious as a child.
However, he was known for solving puzzles **that** baffled other
children. At the University of Erlangen, where her father taught,
women were not officially allowed to teach, although they could
attend classes on an exceptional basis with the professor's
permission. When this rule changed in 1904, Amy Nutter quickly took
advantage of it and earned her doctorate in 1907. An academic
position with stipend was sought. Although the University of
Gttingen finally began paying Notter a salary in 1923, it never
recognized him as a full-fledged professor! However, Noter soon
became everyone's favorite with his warm and kind personality. He
used to take long walks in the countryside with his students and
colleagues and hold long and stimulating debates on mathematical
topics. Noter even sometimes took his students to his apartment and
the conversation continued until the remains of the dessert dried
on the dishes. According to these interpretations, his death, less
than two years after his entry into the academic community in 1935,
saddened everyone.

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In the world of particle physics, hidden symmetries called scale
symmetries There are gauge symmetries **that** appear in the
electromagnetic world **that** lead to the conservation of
electric charge. In general, scale **symmetry** appears in the
definition of electric voltage in such a way **that** the
voltage (for example, between the two ends of the battery) is the
result of the electric potential difference. In fact, the amount of
electric potential is not important in itself, but it is the
potential difference **that** is important.

This explanation shows the **symmetry** in electric
potential, because the overall amount of electric potential without
affecting the voltage difference (electrical potential difference)
can be changed In fact, this is the same problem **that**
explains why a **bird** can sit on an electric wire without
getting electrocuted, but if it touches two wires with different
electrical potentials at the same time, it must say goodbye to the
world!

In the 1960s And in the 1970s, physicists expanded on this idea
and found other hidden symmetries associated with the conservation
laws to develop the Standard Model of particle physics. Therefore,
it can be said **that** paying attention to the laws of
stability and its connection with symmetries in physics, scientists
are like those who have a hammer in their hands and are looking for
a nail. Because wherever physicists find the conservation law, they
are looking for **symmetry** and vice versa.

It is also necessary to know **that** the development of the
standard model also owes to Noder and his important theorem. The
standard model is a theory proposed by Wilczek to explain a large
number of particles and the interactions between them, and he won
the Nobel Prize in 2004 for his role in developing this model. The
Standard Model is currently considered by many physicists as one of
the most successful scientific theories due to its ability to
accurately predict the results of experiments.

In the same vein, the Large Hadron Collider is looking for new
particles predicted **using** Noether's insight and Noether's
theorem, because a hypothesized hidden symmetry, Called
supersymmetry, it suggests a heavier sister to every known particle
in the universe. Of course, despite the great hopes to identify
these particles, so far no such particles have been found with the
descriptions proposed in the theory of supersymmetry!

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## Summary

The physics we deal with every day relies on Noether's theorem;
Because the laws of stability **that** we mentioned many times
in this article help to explain systems such as waves on the
surface of the oceans and air flow on the wings of an airplane. In
fact, simulating such systems helps physicists to make predictions
about weather patterns, bridge vibrations, or the effects of
nuclear explosions.

Besides the importance of Noether and her **theorem** in
physics, this woman's ideas are also somewhat important in
mathematics. It is notable **that** his name is placed as an
adjective behind many elements of mathematics (such as Notherian
rings, Notherian groups, and Notherian modules). Finally, it should
be noted **that** although women in science today still face
challenges, no one has to fight to **get** paid for their
scientific work. This is Amy Nutter's social legacy **that** she
gave us with her efforts.

- The story of Einstein's brain
**that**was stolen and had nothing special!

**Original sources:**

R. Gregory and P. Olver. Emmy Noether: Her life, work, and influence. Convergence, Perimeter Institute for Theoretical Physics, Waterloo, Canada, June 22, 2015.

Y. Kosmann-Schwarzbach. The Noether Theorems: Invariance and Conservation Laws in the Twentieth Century. Translated by Bertram E. Schwarzbach, Springer, 2011.

K. Brading. A Note on General Relativity, Energy Conservation, and Noether's Theorems. In: The Universe of General Relativity. Birkhuser, 2005.

K.A. Brading Which symmetry? Noether, Weyl, and conservation of electric charge. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics. Vol. 33, March 1 2002, p. 3. doi: 10.1016/S1355-2198(01)00033-8.

N. Byers. The Life and Times of Emmy Noether: Contributions of E. Noether to particle physics. arXiv:hep-th/9411110. Posted November 15, 1994.

N. Byers. E. Noether's Discovery of the Deep Connection Between Symmetries and Conservation Laws. arXiv: physics/9807044 Posted July 23, 1998.

A. Dick. Emmy Noether 1882-1935. Translated by H.I. Blocher. Birkhuser, 1981.

K. Brading and H.R. Brown. Noether's Theorems and Gauge Symmetries. arXiv:hep-the/0009058. Posted September 8, 2000

Source: ScienceNews