Is Symmetry Fundamental to Reality? Gauge Theory has an Answer

If you found yourself lost in this video or if you want to brush up on some of the background information, here are some videos I made that will help: An overview of how All Fundamental Forces work: https://www.youtube.com/watch?v=xZqID1zSm0k All Fundamental Particles and Forces Visualized: https://www.youtube.com/watch?v=TDYex6VSd7o Maxwell's Equations: https://www.youtube.com/watch?v=FSEJ4YLXtt8 Quantum Electrodynamics (QED): https://www.youtube.com/watch?v=PutOOpAkjQ4 Quantum Chromodynamics (QCD): https://www.youtube.com/watch?v=KnbrRhkJCRk

The U(1)×SU(2) group actually combine into a single group called the electroweak symmetry. This symmetry is broken by the higgs field, creating a completely different U(1) group for electromagnetism, sometimes denoted U_em(1) to differentiate it. The weak force remaims completely broken and doesn't actually have a symmetry group.

I have no knowledge of these complex maths. But I still like listening to your explanations. Sometimes I get some vague idea and sometimes clear. I learn something new. I wish I knew math well.

This is a great video to get started on how Symmetry leads to the Standard Model. It provides a learning path, tells you what you have to go away and study more deeply elsewhere if you are going to get to the bottom of this subject. We learn that symmetries lead to conserved quantities, Noether's theorem, generators, Euler's number, then rotation in a complex plane, the symmetry groups U(1), SU(2), SU(3). Most other videos assume that you already know stuff. This is the very best "beginning "video that I've found. I feel orientated.

Amazing video, as always. Also, thank you for including some governing equations. Many authors/creators/producers avoid including any mathematical equations because they fear it would intimidate their audience. So, it is refreshing to see some maths equations not only being included, but also being clearly explained. Thank you for respecting our intelligence enough to include some maths. Excellent work. I'm looking forward to your next video

Howdy Arwin! Here again from Perú. Just watched your video. I had to watch it three times to repeat the dopamine rush! Thank you so much for your wonderful CLARITY. There is so much BEAUTY in it! Thank you.

Look how much effort it takes to mathematically explain ONE PARTICLE or Three, moving around in space and time and accounting for any surrounding forces acting upon them. Its just mind boggling something as complex and diverse and intricate. So massive and also consisting of such vastly small aspects to itself is just mind bending and awe inspiring and fills me with intense drive to explore. I am so curious about all the forms of matter and densities, mineralization, geological, magnetic fields, etc etc etc. The natural world is awesome!

Thank you so much for the wonderful video as usual. 🤩 Next, please tell us about SU(5) symmetry, SO(10) symmetry, E6 symmetry,,, 🥺

Wow, this video was stunning. I did not expect this to be described this well. Your best video I’ve seen by far.

Your CG and visualization work has gotten a lot better!

Every process in the universe favors the formation of high symmetry objects. I believe the reason is to use the less possible energy and to use less information to increase the entropy. I have seen these patterns while working on my research project and by studying Claude Shannon's information theory.

I looks to me that symmetrical objects are more "stable" than irregular ones. A force acting on an irregular object tends to reduce those irregularities. Round pebbles in a stream are a good example.

this video honestly blew my mind, i feel like i am a step closer to understanding where all of the terms and theories come from, i like actually showing the equations much more than straying away from them, because they’re scary to the general public

I love your videos, in my mind you cant be lazy if you're learning, so when im at my boring job at the front desk of a multiplex i just put your videos on for my entire shift and i really learn a lot Thank you

None of this would have been possible without Emmy Noether, she truly deserves much more recognition.

That was very informative, thanks to you and your team for creating and uploading this!

I cannot take this off of my WATCH LATER list after watching it, as I need to watch it again (...and again). Thanks for presenting some really deep stuff as simply as possible.

Thank you so much for this. I've struggled so much with these concepts and bought a lot of books from physicists probably much more well-known than you, but this is the clearest, most logical explanation I've come across and you explained everything so well. Amazing work!

This video is incredibly well put together and beautiful. My thanks to dear Mr. Ash! Another masterpiece!

Thank you for simplifying the most complex nature's laws to us and everyone. This is like translating other languages to a more comprehensible every day englisch language. I think this is the way we may or should teach the next generation all over the world in the schools at least theoretically. That is, instead of wasting a lot of energy and time on teaching other complex lengthy mathematical logical relationships used usually to prove principles, which i like petsonally but i aknowledge its complexity. Maybe we should start from the top to the bottom in teaching science by teaching such profound and clear meaning of nature's laws to everyone who is eager to learn and then giving the opportunity of specialization to those who like to learn how to prove them. This way everyone may understand the laws of nature. I agree that symmetry when exists and is not broken may facilitate the process of discovering and understanding the laws of nature. Personnally, beauty and symmetry helped me a lot to understand mathematics and statistics in my field of study and work. However, i agree with you and others that there is no obligation to the nature to be always symmetric or beatifull in all the connections and details in its laws. This is my humble opinion as a fan of physics and maths and as an outsider of the field. Please could you present in another field of science like statistical analyses in other less solid sciences (although these fields have also some solid evidence) like in social and health sciences. In these last fields the literature is usually highly based on a conventional but rather arbitrary threshold of significance like p-value of 0.05 (i.e., p-value and null hypothesis testing were first proposed in the early 20th century i think). These last statistical techniques might to be biased to some levels if not other methods of appreciating the overall evidence levels are taken into consideration, like considering the effect size and/ or the bayesian methods of comparing alternative tested hypotheses or other methods i might have missed to mention. There are indeed many sources of biases and heterogeneities of study designs in such fields (e.g., studies are varying from observational to randomized blinded controlled trials with varied variables definitions), with varied tools of measurements showing varied psychometric properties (e.g., having different levels of validity, fidelity and sensitivity to change) as well as the use of varied methods of statistical analyses (e.g., stepwise analyses and its potential biasing effect on p-value, or using statistical tevhnique without respecting the underlying postulates. etc.) or using statistical adjustment for co-variables which may all very easily bias the usually reported marginally significant p-value. The last is frequently used as a lone measure of significance level with or without confidence intervals; and this can also bias the reported evidence level on the tested hypotheses. I think that also in physics, there is some problems of non replicability of some new discoveries like in astrophysics and where you use a more strict criterion like having something equal or greater than 5 sigmas, i think. The problem in social science that if we want to decrease the threshold of significance to more than two standard deviation from the hypothetical mean, as using a threshold of statistical significance of 0.01or even 0.001, we should increase the sample size which is usually impossible for practical and economical issues; otherwise, we will lose the statistical power and testing would be meaningless. I think that the use of significance level of 5% may be a good practical and conventional way of deciding in these fields, even though the philosophical meaning of using null htpothesis might be questionable to some extent. Man can argue that thete is rarely a difference which is exactly equal 0, and this is may be reflected in the fact that the more we increase the sample size the more the statistical tests would be sensitive to discover more and more smaller differences or even any random fluctuation in the sample which usually lack practical or clinical meaning. What i like in physics, is that scientists suggest some new hypotheses and then they try to refute it, and which is also used in social and health sciences but the process might be sometimes less robust considering all what is mentioned above. In fact, in social or health science like psychology, some authors found some increased p-value frequency just below the threshold of significance (0.05), which may indicate biased results with publication bias for example, others reported up to 50 % percentage of studies failing to replicate previous results (example. in the psychology field). The more one can study the literature in human sciences-based research, the more one may opt for a post-postpositivistic way of thinking where the real world associations in these fields might not be completely or precisely reachable using the actual scientific methods and techiques, at least nowadays, and which might improve in the future gradually to some extent, i hope. I think therefore that having an opinion of you as an expert in another scientific field might help to shade light on such a problem and what might others have missed in tackling this problems of results replicabilities. Sorry for my lengthy comments that i just wanted to share as a fan of your presentations🙏 and as a lifelong learner with some background in research 😊. Thanks again, i always enjoy your presentations and videos and i think that a lot of people share the same opinion with me. Please keep with this amazing pace. All the best. H.B.