Symmetry : what you need to know about

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Symmetry : what you need to know about

Postby hyksos on January 7th, 2020, 4:32 am 

The periodic table of elements is a scheme of types of atomic elements.

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This scheme with its rows and columns is explained by the number of protons residing in its nucleus, paired with the number of electrons that stack up in shells. The number and position of the electrons in shells determines the chemistry of the elements. Done and done.

This is the table of fundamental particles which are elementary.
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Very much like the Periodic Table above, we may ask : What is the scheme that underlies this table?

It's just that straightforward. This isn't philosophy or speculation about the metaphysics of reality. Just a simple question: What is Nature's scheme that underlies this table?

We do know that there must be a scheme because (just like atomic elements above) many particles in this diagram decay into each other. A photon when colliding with one of the hadrons, will split into an electron/positron pair in a process called pair production. When antimatter collides with 'regular' matter, their energy is converted back into a photon of equivalent energy to their mass. Electron anti-neutrinos turn up in many nuclear decays.


To first approximation, human civilization in 2020 AD does not know the scheme.

Of course, shelves-worth of books have been written, and rivers of ink have been spilt in regards to highly-educated hypothesese about Nature's Scheme for the Standard Model. Having agreed that humanity does not understand everything, one might be seduced into believing we therefore understand nothing. Fortunately that's not true.

Deeper approximations to this issue follow. In quiet nights in the professor's office, when nobody is around, in quiet conversations one-on-one going up the elevator ... in those situations one could claim (quietly) that science already knows Nature's Scheme. Whereas the principle that underlies the Periodic Table of Elements is the number of protons in the nucleus, the principle that underlies the Standard Model is Symmetry.
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Re: Symmetry : what you need to know about

Postby hyksos on January 7th, 2020, 4:53 am 

Symmetry.

Symmetry preliminaries and prerequisite videos.











Diagram showing how finite simple sporadic groups are often contained in each other.

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Articles to nose around

https://en.wikipedia.org/wiki/Classific ... ple_groups


https://en.wikipedia.org/wiki/Monster_group

https://en.wikipedia.org/wiki/Monstrous_moonshine

https://sitp.stanford.edu/news/superstr ... -moonshine
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Re: Symmetry : what you need to know about

Postby hyksos on January 7th, 2020, 5:19 am 

After you have familiarized with the materials in the preceding post, you may feel ready to stretch your legs -- to go out and apply one's newfound wisdom-- to find a use for the new intellectual tools in one's toolbox.

To do so, clickity-click on over the lead article on wikipedia on String Theory. Then take a glance at the sidebar frame that contains a glossary of article links.

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Whoever edits string theory articles on wikipedia, felt that Monstrous Moonshine was important enough to include it in the frame of all string-theory-related articles on wikipedia, which could be more than 50.

Click through where your heart leads you. E8xE8, mirror symmetry, wherever you like. Notice now (perhaps to your astonishment) that you can actually read what the articles are saying.

When meeting a professor late at night in the teacher's lounge.. you can carry a conversation about unification and the Standard Model. There must be a scheme to Nature, and whatever that scheme ends up being in the end, it must necessarily be something about symmetry. Even if String THeory turns out to be a terrible wrong description of our universe, the central catalyzing idea -- that nature's scheme involves symmetry -- the idea is not going away anytime soon.


The adventurous (or masochistic, be that as it may) can continue this line-of-thinking to even further. Those deeper waters are found here https://en.wikipedia.org/wiki/Supersymmetry_algebra
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Re: Symmetry : what you need to know about

Postby socrat44 on February 24th, 2020, 6:19 am 

@hyksos
---
1 - SU(1)
2 - The SU(3), SU(2) and U(1) symmetries of the standard model.
3 - Different kind of symmetry, the so‐called flavor symmetry,
which turns out to be only approximate. Flavor symmetry is not
associated with the forces of the standard model; instead it
pertains to the particles, especially the quarks, between which
the forces act.
4 - "SU(5)" For the specific grand unification theory,
5 - supersymmetry (without experimental evidence)
6 - . . .
---
Every symmetry needs force.
To create a new symmetry is needed a new force.
Many symmetries - many forces.
One more symmetry and Pegasus will fly.
#
Every symmetry couldn't exist for ever,
sooner or later it will become asymmetric.
===
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