Is Symmetry Fundamental to Reality? Gauge Theory has an Answer
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- Опубліковано 5 чер 2024
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BACKGROUND VIDEOS:
How All Fundamental Forces work: • Why & How do the 4 fun...
All Fundamental Particles visualized: • All Fundamental Forces...
Maxwell's Equations: • Why is the speed of li...
Quantum Electrodynamics (QED): • How QED Unites Relativ...
Quantum Chromodynamics (QCD): • QCD: Visualizing the S...
CHAPTERS:
00:00 Symmetry - root of physics
01:31 What is symmetry?
03:24 Intro to Group Theory
06:04 Noether's Theorem
07:17 U(1) symmetry simplified
09:43 Dirac equation transformation
11:10 How QED comes from U(1) symmetry
12:47 U(1) SU(2) SU(3) explained simply
15:32 Symmetry is the foundation of the universe
15:54 Further study on Wondrium
SUMMARY:
If you ask a physicist, what is at the core of physics, you will hear symmetry. What is symmetry? Gauge theory explained simply.
Symmetry is about actions that don't change anything. If we take an equilateral triangle, and put a mirror from one corner to the middle of the opposite side, we will see that the whole triangle. This is a symmetry of the equilateral triangle. Similarly we can rotate the triangle by 120 degrees, and it will look identical to what it was before.
What we just did is a simple example of something more complex - group theory. Group theory is the math behind the symmetries.The mathematics behind the symmetries of the equilateral triangle is called the dihedral GROUP of degree 3, where 3 refers to the triangle having three corners. We can change the elements, or permutations, using two different operations, rotation, and reflection. These two operations are called generators. The result of applying a generator doesn’t change anything visible. This is symmetry.
Symmetries give us rules for how to transform something while conserving a quantity. For the triangle, that conserved quantity is its shape, and the generators are rotation and reflection.
This leads us to Noether’s theorem which states that “For every symmetry there is a corresponding conservation law.” This directly connects symmetries with conserved quantities.
What happens if we take the limit of a polygon with an infinite number of edges? We get a circle. A circle of some radius, r, can be described on a 2D plane using polar coordinates by two equations. If we use complex numbers to represent the circle, we can write it with just ONE equation. This allows us to write one complex equation that achieves the same mathematically as two real equations.
It turns out that there’s also a symmetry group associated with this circle of complex numbers with a radius or magnitude of 1. It is called the U(1) group. The elements of the group are all the infinite possible angles phi around the circle.
Quantum mechanics is built on complex numbers. We can apply the symmetry with the simple transformation of moving around the circle. Do described the movement of fermions, we can use the Dirac equation. It describes any matter particle, like an electron, with some mass m moving in space. It does not describe any forces.
If U(1) symmetry exists, it would mean that if we applied our transformation, the Lagrangian would not change. The problem is that the Lagrangian DOES change when we apply this transformation, so this tells us that no U(1) symmetry exists.
However, if we modify the equation, by adding a new quantum field to the theory, a gauge field, we can get a symmetry. Another name for a gauge field is a force. Our theory works, and obeys U(1) symmetry transformations if we add some new terms to the equation. It turns out that this new term describes the electromagnetic force. The entire theory of Quantum Electrodynamics can be derived by the new transformed equation.
So by taking a theory for fermions (Dirac equation) and demanding a U(1) transformation we got the theory of electromagnetism. Similarly, the standard model is constructed to respect three symmetries or special unitary groups. And each group leads to a symmetry resulting in a conservation law and a fundamental force.
The U(1) group gives us conservation of electric charge, and is associated with the electromagnetic force. The SU(2) group gives us conservation of weak isospin, or weak charge, and is associated with the weak force. The SU(3) group leads to conservation of color charge and is associated with the strong force. It leads to the theory of quantum chromodynamics.
In addition, the number of generators corresponds to the number of bosons involved with each force. U(1) has one generator and one photon. SU(2) has 3 generators and 3 W+, W-, and Z. SU(3) has 8 generators and 8 different gluons.
#gaugesymmetry
#grouptheory
#noetherstheorem
Symmetries seem to be the foundation of the laws of physics. Why this is the case is something no one knows. - Наука та технологія
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: ua-cam.com/video/xZqID1zSm0k/v-deo.html
All Fundamental Particles and Forces Visualized: ua-cam.com/video/TDYex6VSd7o/v-deo.html
Maxwell's Equations: ua-cam.com/video/FSEJ4YLXtt8/v-deo.html
Quantum Electrodynamics (QED): ua-cam.com/video/PutOOpAkjQ4/v-deo.html
Quantum Chromodynamics (QCD): ua-cam.com/video/KnbrRhkJCRk/v-deo.html
In a article on UA-cam giving proofs of existance of god one proof is symmetry. After watching Arvin Ash although not fully understood it can be said symmetry is in physics and so is god
@@sabbirpachorawala8797 its really how you choose to percieve it. To some its "awareness", to others "conciousness", "god" and yet to others its "symmetry." One way or another they all get there in the end but to focus on one and deny the others is only self limiting.
I have a feeling you are one of the greatest bullshiters in the world right now.
I have a question, ahora sí, I saw the entire vídeo.
When it say SU3 theory, for the quantum chromodinamics, have 8 Gell-man matrixes of 3x3 of the SU3, it says that need 8 dimensions, ¿that dimensions are abstract and complex or 8 extra spacial dimensions?
If I want to do a theory like kaluza klein and parametrize the shape of the universe, the SU3, ¿can be necesarialy a hyperspherical space surface of eight dimensions (8D sphere with a surface of 7 variables)?
And this is a hypercylinder when the SU3 is a base and the heigh or hyper line is the 4D spacial dimensions.
Grewtings from Chile🇨🇱🇨🇱👋👋
1D-9D (easy mode):
1D, 2D, 3D are spatial
4D, 5D, 6D are temporal
7D, 8D, 9D are spectral
1D, 4D, 7D line/length/continuous
2D, 5D, 8D width/breadth/emission
3D, 6D, 9D height/depth/absorption
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.
you will be what you want in the End
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.
Lucky you. I'm lost. 🙄
@@wecas9596 Maybe you are looking for information that isn't here. This is just an introduction. We learn the idea that every continuous symmetry leads to a conservation law, but this doesn't go into enough detail to explain why. For that you need something like the book "Emmy Noether's Wonderful Theorem" by Dwight E. Neuenschwander. I've got as far as page 6 in that book and I'm struggling a bit already. I'd like to understand why Time Translation Symmetry leads to Conservation of ENERGY and Spatial Translation Symmetry leads to conservation of Momentum and not vice versa. After all the formulae for these two conserved quantities are very similar both involving just mass and velocity.
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.
Glad you enjoyed it!
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
The equations here were, IMO, *not* clearly explained, even just to the degree that would be relevant to the point being made.
(Like, I’m not saying that he should have said “this upper index mu here and this lower index mu here is an example of einstein summation notation, where we sum up the versions of it where mu ranges among the t,x,y,z coordinates. These gamma symbols are blah blah and obey these commutation relations, and this partial here is partial derivative along the axis labeled by mu”
I’m saying that he acted like he had demonstrated how something would be not symmetric under some particular transformation, but had not demonstrated that. I don’t even mean that he didn’t prove it. I mean he didn’t seem to showcase it.)
None of this would have been possible without Emmy Noether, she truly deserves much more recognition.
More recognition than she gets in every university level physics course? :-)
@@schmetterling4477 of course , same recognition as einstein gets, because her theorems form the foundations of modern physics and mathematical physics. And also, she revolutionized maths too, with her pioneering work in abstract algebra and topology.
@@devamjani8041 Physics is not saint veneration, kid. You are talking about people because you can't talk about nature.
@@schmetterling4477 and who are you to talk about nature kid 😂, you haven't produced any work in physics yet, so come back when you actually contribute something to physics or any subject for that matter.
@@devamjani8041 Who am I? I am a physics PhD who deigned the core component of one of the world's largest high energy physics detectors. What did you do, except for sex and drugs and Rock'n Roll? ;-)
Wow, this video was stunning. I did not expect this to be described this well. Your best video I’ve seen by far.
Glad you enjoyed it!
My channel name is ARYABHAT CENTER FOR THEORETICAL PHYSICS.
Can you review the quality of this channel ?
Your CG and visualization work has gotten a lot better!
Thank you so much for the wonderful video as usual. 🤩
Next, please tell us about SU(5) symmetry, SO(10) symmetry, E6 symmetry,,, 🥺
Symmetry is a mathematical illusion based on neurotic idealism
It's simple really... it is just that it appears complex.
@@waldwassermann This is true of all of Physics - the least complex of all the scientific disciplines. (and the highest reliance on spherical cows and idealistic stochastic convenient nonsense.
@@PetraKann Yes. It almost feels that some in the field of science including but not limited to cosmology purposely circumnavigate the truth to safeguard their paycheck.
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.
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!
ya"He's hooked
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.
It's not so much that they're stable, it's that round shapes have more entropy than irregular shaped pebbles. Why? Because there are far more ways for that pebble to become rounded.
Irregular shapes have less entropy because they are essentially all unique. How many ways can you get this pebble to have this exact shape? Not as many. So they have low entropy.
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
15:23 Curiously, I've also come across the sequence 1, 3, 8 in Ramanujan's continued fractions related to the three symmetries of the Platonic solids. Note that the ONLY integers n > 1 such that 24/(n^2-1) is also an integer are 5, 3, 2, yielding the aforementioned 1, 3, 8. The integer n=5, of course, figures prominently in the Rogers-Ramanujan continued fraction and icosahedral symmetry. There are analogous continued fractions involving n=3 (for tetrahedral symmetry) and n=2 (for octahedral symmetry.) Hmm, I wonder if there is a connection?
Hi, is 24 chosen artificially or is there something there? Because I guess for any triplet you can generate another triplet by engineering a function such as 24/(n^2-1). Or you mean they are the same symmetry groups and that's the number of generators?
@@summerQuanta No, the integer 24 is not chosen artificially. It arises naturally in a lot of number theoretic contexts such as the Dedekind eta function which has the factor q^(1/24), or the 24-dimensional Leech lattice, etc, etc. For some reason, the Dedekind eta function can express those 3 Ramanujan-type continued fractions, and for some reason those 3 cfracs are connected to the 3 Platonic symmetry groups. Now it turns out the sequence 1, 3, 8 is the number of bosons of 3 fundamental forces. I don't know if it is just coincidence, but Felix Klein and Ramanujan, wherever they are now, would have known more.
Interesting insights.
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.
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
That was very informative, thanks to you and your team for creating and uploading this!
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!
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.
What a picture on group theory.
I have always thought of this Field of maths to be mysterious and elusive, but with videos like this one, I feel like a maths genius already. Thanks for the good works
This video is incredibly well put together and beautiful. My thanks to dear Mr. Ash! Another masterpiece!
That was an awesome presentation. Cool to see that symmetry is built on the work of Emmy Noether.
Everytime I move up the "understanding physics" ladder, you somehow always post a video that explains my next question.
Excelent video, well explained. Can someone solve a question that I have? why does we ask the Lagrangian to fulfill for instance the U(1) symmetry a priori, without knowing that this Will give us the EM interaction? thanks
I started my self-study of Lagrangian mechanics yesterday, then I find this video that presents an application. Exciting!
This was fantastic! Now, how about a video about broken symmetries?
Years. YEARS! I have been trying to understand symmetry and Noether's Theorem and SU(3) and forces and the Stardard Model for YEARS. Now I get it. Thank you.
ua-cam.com/video/lxMwQqrfe9k/v-deo.html
This was so awesome! Very clearly explained. And the end blew my mind 😀
This is one of those videos I'll have to watch more than once... great job, as always! Thanks, Arv!
The dawn has already broken out and the day is getting brighter.
👍 after watching your videos, which r really simple n sensible 👍, I go through your answers to queries, which is equally 🌹 BEST 🌹PART 🌹. Thanks Sir.
Is symmetry similar to entropy in that the universe seems to want to find an equilibrium of all its constituent parts? Could ' reverse engineering ' the math behind symmetry and entropy lead us to answers, ie..a true understanding of gravity?
Hey Arvin - mind if I make a quick observation and unsolicited suggestion?
I'm a long-time viewer and I've noticed that your videos are much louder than other videos. I hope I'm not overstepping here, but might I suggest having your audio normalized with a peak of -3dB? I know there's no industry standard or anything, but I'm pretty sure that spoken word is typically normalized to a -3dB peak.
Otherwise - excellent job :) Symmetry is utterly fascinating to me - great video!
Thanks for that. The audio in this video was suboptimal. We are working on getting it right for future videos.
Huge science/math hobbyist here. LOVE Arvin's videos and channel. This one just made my head hurt though. 😳😳😳
In order to understand the meaning of any phenomenon, it is necessary to have a detached point of view that gives the observer a standard as a cumulative criterion for the congruent characteristics of observation - the nature of the force hidden in the neurodynamics of consciousness. At the same time, the physics of awareness is provided by the symmetry of the configuration of splitting the informational stimulus into symmetrical parts of the symmetrical redistribution of the energy of the internal and external response of the human body, reflecting the implementation of the genetic code of the fertilized egg in the dynamics of embryological transformations and the consonant specialization of body functions as it moves along the evolutionary chain of metamorphoses from fertilization to death, life.
Fantastic video my friend! Could we include Mandelbrot sets in the symmetry theory to test the systems of the universe? Even if we don’t get accurate answers, we could get the direction towards which a particular system is headed?
Hope I am not too abstract?!
I’m not exactly sure what you mean, but the Mandelbrot set isn’t really a symmetry group. Though it does show the complexity of the relationship between the translational symmetry and the rotational symmetry of the complex numbers under addition and multiplication respectively which are symmetry groups.
@@ryanlangman4266 Could the Mandelbrot have a form of scale symmetry?
So humour me here Arvin. Please. So H bar is a symmetry you say. This nice visualisation you guys did here clicks with me because from watching random stuff with Sean Carroll, Susskind and Brian Greene. I heard the H bar before and it was like something over 2 pi. Maybe?
Again, humour me.
I really liked this post because I sort of get it now. It’s all about the polar coordinates. The spin. The circle. The way to just describe it. That mention that you can reduce the description to on lesser description just twigged with me. Bit like when I realised what exponent differential equations or calculus really was just about.
One of the best videos ever! Deep, so deep.
And gravity breaks symmetry, apparently. Only over totality of universe is it symmetric
Great explanation. Although please correct me if I am wrong, but I think the most general definition of a Lagrangian is "any mathematical expression that generates the equations of motion when Euler-Lagrange equations are applied ( the action is minimized) ". It turns out that when the forces are conservative that the Lagrangian is the Kinetic - Potential energies, if in fact you are able to write out the Kinetic and/or Potential energies, as sometimes it is difficult or impossible to do.
Yes, I am talking about it in simple terms, just so people can get a gist of the concept. For the context of this video, there's no need to get bogged down with the Lagrangian. My description is not incorrect.
@@ArvinAsh Yes I realize that. It would have added undue complexity to your video. Your video is perfect. I just wanted to mention it for people who want a deeper understanding. That was me a while back and I was confused about it so I am helping out some other people. I am not an expert but trying to understand at deeper level.
@@DrDeuteron First of all when I first started exploring the subject it was very confusing because nobody really explains what a Lagrangian actually is. Trust me when I say it took me a lot of in-depth research to find out the facts. His video and content is pretty exceptional in terms of bringing complicated subjects down to a level so people can understand them, however it frustrated me immensely when I first started exploring the subject that almost nobody, and I really mean that nobody, explained exactly what the Lagrangian is or the details about it. So I wanted to spare somebody else that frustration. People will use his videos as a stepping off point to study the subject on a deeper level. I think it’s extremely important to know this actual fact about what a good Lagrange is.Second of all, your comment about densities is not pertinent to the discussion. He did not mention field theory or densities, but he did mention what a Lagrangian is in terms of kinetic and potential energies.
@@waynelast1685 In QED, the Lagrangian formulation for the Dirac equation requires a Lagrangian-density of the electron/positron field
@@DrDeuteron good to know
That part near the end (numbers of gauge bosons) was fascinating.
I'm not sure if this is generally true, but in the triangle example, reflection is the same as a 180 degree rotation around the axis in the third dimension--a "flip" if you will. If the example had used an "R" instead of "A" it could have used "flipping" to show the symmetries. I like this idea because it suggests a "hands-on" approach that only involves the object being rotated and not an interaction with a second object (the mirror). Also, it unifies the action for the symmetry being one of rotation and the parameters of that action. Anyway, thank you for this video. I love this topic!
There is no third dimension in which to do the flip, on a 2D triangle.
@@ArvinAsh How does the 2d mirror work?
Hi Arvin! I wonder how gravity would stick to these symetries? What might be the symetry that corresponds to a gravitational force? Or is there any symetry for it? Alessandro Roussel (I guess you watch his UA-cam channel with wonderfull explanations and animations) shows us the gravitational force as a form of "moving" reference frame inside the matter. This gives me an idea: may be there is no such thing as gravitation but rather the space stratches and sinked into the matter at the same time? Think about the Coriolis force: if you are in the rotation frame, you see that objects are deflected due to the new "force" but in reality these object just converve the energy and move straight in their non rotating frame. In case of gravity: all objects are moving straight in their non distorted spacial frame, but from our earth-like frame of referrence we see that the object is falling due to "gravity" like with the coriolis force.
In regards to gravity it is indeed a bit unique and in the context of general relativity it is a fictitious force related to the rotation of a 4 momentum vector linked to the path of a geodesic for some inertial frame of reference in warped space associated with the energy contained within a region of space. The UA-cam channel Science Clic English which it appears is the channel you are referring to so I now know who made it has not just one but a number of good insightful videos explaining this in much more detail both a more general discussion of the topic and an 8 part video series on the math of GR. This picture in terms of inertial frame of reference in curved spacetime is an important concept to have in place to explain gravitational redshift with a number of implications on what a free falling observer would see. Namely the hawking radiation if conserved between frames of reference would require that due to curvature it would be both gravitationally blueshifted and more luminous as the inertial frame of reference is bent into more rays of radiation and lengths become contracted meaning the local metric length elements get smaller and smaller causing the horizon to appear further away. It has weird implications but from a practical perspective this should largely eliminate the concerns of information loss for an infalling observer.
But if you aren't adverse to reading more things can get much more interesting if we consider the implications of the "No big crunch theorem" which shows that within the general unconstrained inhomogeneous and anisotropic limit (Matthew Kleban and Leonardo Senatore JCAP10(2016)022) any nontrivial flat or open geometry universe that namely we can prove by self contradiction that within any given slice of time in spacetime there can't exist a maximum spatial volume for any initially expanding universe. In essence an expanding universe must expand forever and any local attraction of matter due to overdensities will always be compensated for by creating underdensities which accelerate the rate of expansion ensuring the volume of spacetime always increases forwards in time. Any other possible metric within this domain of expanding nontrivial flat or open universes which doesn't have this explicit property is always going to be logically invalid as a solution to the Einstein field equations. The off diagonal elements will never perfectly cancel out and thus the off diagonal terms of the metric tensor of the Einstein field equations can't be simplified i.e. the forward arrow of time the loss of symmetry within the metric due to expansion is an irreversible phase transition within the metric itself.
There are a number of profound implications from this mathematical proof the most natural is that there is a thermodynamics like irreversible directionality caused by the breaking of symmetry itself. In this context gravity can be thought of in terms of inhomogeneities and anisotropy as in a fully symmetric universe there effectively is no gravity. In this context it is the symmetry breaking due to expansion which drives inhomogeneities and the apparent force of gravity but also provides the driver of the observed acceleration of the expansion of the universe without requiring any mysterious dark energy.
You see in cosmology generally the Friedmann Lemaitre Robertson Walker(FLRW) metric is used because it was proven to be an exact solution to the Einstein field equations so it made a nice mathematical simplification from which cosmology has assumed you can approximate the universe by viewing any deviations as small such that off diagonal metric tensor elements cancel.
However as the "No big crunch theorem" proves this assumption can never be valid because the metric tensor off diagonal so such approximations while they have worked well for us at small scales must break down at cosmological scales meaning that the existence of any scale at which spacetime becomes homogenous actually is logically invalid. In this respect the behavior of the volume of space within any timeslice of spacetime likely provides a crucial clue as this property behaves suspiciously similar to entropy from information theory especially as the number of configurations which a universe can evolve is countably finite in principal it suggests we have a direct link between the volume of space and an associated Shannon entropy. This can be understood within the context of the recently identified gravitational path integral as being a slice through time within the set of all possible (and impossible) paths for which information from the universes initial conditions at can propagate outwards.
With this insight and applying something analogous to the principal of stokes theorem(though both appear within an integral over the temporal dimension) this effectively gives us the entropy of the associated cosmological event horizon for each given initial frame of reference and thus assuming I didn't screw up somewhere indirectly giving at least a limited case for black hole thermodynamics purely from within the framework of GR with the only modification being ensuring that all solutions remain logical continuity for all possible arbitrary initial conditions.
This in essence means this condition of logical continuity is equivalent to the conservation of information and thus because approximate metrics like Schwarzschild or Kerr metrics are themselves in violation with the conservation of information and thus efforts to integrate them in the quantum regime become doomed to failure under these limits.
This also seems to hint that modified gravity with some form of nonlocality is necessary in some aspect in order for information to be conserved but doesn't constrain what exact form that would take beyond that. Though if causality still applies then quantization seems a good bet as this takes on the form expected from a nonlocal hidden variable theory where the hidden variable is the associated entropy of the universe linked to the universes information content meaning it passes bells inequality making the wormhole to entanglement leap direct without need for any kind of supersymmetry.
this may be a really weird question, but physics is weird, so right up your alley! I remember a part of string theory, called M-theory, which your friend Dr. Sabine Hossenfelder used to describe dimensions. 1 dimension for the electromagnetic force, 2 dimensions for the weak force, 4 dimensions for the strong force, and the rest of course 1 temporal dimension for time and 3 spatial dimension for gravity. Now when I think about that, and I look at those forces neatly next to each other on your video, I can't help looking at a pattern, from 1 to 2 from 2 to 4, it doubles with each change to a higher group. As a physicist you can't really look at a combination of particles to for example build a proton as glueing a bunch of balls together and pipes to represent the gluons, because QFT tells us that all fundamental particles are nothing but fields of energy with a particular amount of energy in that field or a multiple of that amount. they have no shape, size or structure. But, if we do imagine how those particles all fit well together to make a proton, would a certain angle for gluons make a difference in QCD? I mean, there are 8 gluons, and if you cut a sphere in 4 equal parts, by cutting it at 120° angles, you get 8 possible angles on that sphere. Why this particular way? Well, if you stack equally sized balls like a tetrahedron, the lowest amount of balls to fully surround any other ball, you get 8 inwardly curved tetrahedrons that completely wrap 1 ball. This would fit for a gluon I thought to myself. What if QCD is nothing but certain angles a ball can have? Quarks have 3, gluons have 8, and so on, and so forth? Or is this a bad way of thinking?
QCD is not described by some kind of “how many connections can each of these have”.
The computations are very complicated, and if it could be described more easily and as correctly in terms like that, it would be.
It is related iirc to the representation theory of SU(3)
And...
Hm.
Ok, I don’t know QCD, but, still
Great video, I have one remark, isn't r^2 = x^2 + y^2 also one equation describing a circle?
This video has Science and Art combined.
Excellent subject and video!
Technically, the group described here for the triangle would be C3v, not D3h (dihedral), since the C2 rotations normal to the principal axis of rotation, the sigma-h reflection in the plane of the triangle, and the S3 improper rotation symmetry wasn't included.
Regardless, great video!
Simply amazing..Thanks Arvin
3:09 - Fascinating! #Triangles
Along with symmetries, there are also pseudo-symmetries which can cause much confusion. The classical example is in the FOUR non-relativistic Maxwell equations and are equivalent to the equations shown in the video at 12:04. The equations are almost the same pairwise except for a couple of extra terms. If terms are added to the non-symmetric equations to symmetrize them, they led to the notion of the magnetic monopole. This however, is a pseudo-symmetry without physical content and results from the use of non-invariant operators such as the cross-product. Many barrels of ink have been spilled on the non-existent monopoles which VANISH when the relativistic equations are used instead. The relativist equations make if completely clear that the magnetic field arises SOLELY from the application of the Lorentz transformation caused by moving charges.
And how do you know that the equations without magnetic monopoles are the correct ones? You are basically hammering away at the tautology that there are no monopoles if we don't put them into the equations. ;-)
I've got a postgraduate degree in maths and I feel sorry for anyone less mathematically educated trying to follow the math 🤣. Thanks for this so much Arvin Ash, I love the mathematical detail you go into, personally.
I feel lost. Could you please tell me where to start? I understood only up to Noether's theorem.
One might start with learning how to solve some simple differentiatial equations because the operators used in the shrodinger equation build on this more simple idea
Bruh I'm literally sweating rn trying to understand the maths
Very nice. Super complicated topic. Nice.
Brilliant explanation. This is how kids should see how cool Physics is. Cheers !!!
Cool subject! These kind of things triggers my interest, questions like: "What's at the heart of it all?"
Fascinating and very informative. How does this symmetry conservation apply within an expanding universe? Does conservation still apply? Thank you and best wishes.
It is not clear. Conservation of energy probably still applies.
@@ArvinAsh Hi Arvin, Thank you for the reply. Best wishes.
Incredible video sir! Will have to watch this one again as my brain kept running off with the ideas and I'd miss a bunch
You really did make it comprehensible to me, even if my mathematical understanding is limited to just simple metrics. Also, you amazes me with an enlightening simplicity and clarity! Congratulations, this video is a masterpiece!
Wow. What a great explanation. Thanks.
What would be the benefit if there were a 2-D visualization of a higher dimensional space? 3-D on 2-D still maintains vector transformation and you have the dot and cross product etc but what would be the theoretical application of having a simple 2-D visualization of all 3 unitary groups?
THANK YOU DR. ARVIN ASH ...!!!
I am learning from DR.SEAN CARROLL TOO ...!!! HE TOO A GREAT TEACHER...!!!
THANKS AGAIN...!!!
Why do I feel that I am in a 'matrix'?
Is Reality too hard???
I want to stop thinking,
Hahaha Hahaha. Love your work.
Actually many people are in stressful situations and just need a fantasy story to get them through the day.
Now I really digress.
This is where the bad people, dictators, corrupt politicians, corrupt powerful step in.
Arvin thank you another mind challenging video, please may I ask you a couple of questions, firstly given that symmetry is a fundamental of our universe, did it sort itself out to conform in this way or did it form this way because all the correct elements were in place to allow it to happen. could the universe have been formed in any other way. apologies in advance if these are dumb questions
We only know how the universe works. Why it happened this way, or how did the universe we have come to be, are questions we can't answer.
@@ArvinAsh thank you Arvin I'm never sure if I should be asking questions but its so gratifying to receive a reply please keep putting out the videos they are outstanding.
The more you know, the more you don't know. In Indian sloka it is said, "dharamsya tattyang nihitang guhayang" in Sanskrit , that means the Gyan or knowledge is a Mistry .
Gyan and Mithya Gyan go side by side.
One more thing physical objects or within 4th dimension is rule based by laws.
In higher dimension in non physical state no physical laws applied.
Omkar connects between physical and concious ( subtle higher dimension) world.
Also you know everything inside out through meditation, not outside in, it is said what is outside, everything is inside.
Sir, you are extremely knowledgeable and talented person probe into Sanatan ( classical ) spiritual world
Loved it !❤️
At 10:30 - why n=1 for antimatter and -1 for matter?
fascinating! great video!
Great video!
I don't know, maybe im just lucky but they video topics match my progression in learning about fundamental physics. I've been yearning to understand symmetry.
Now it makes sense of group theory completely
awesome as always, greetings from Brazil 🇧🇷🇧🇷
Can you please do a video on the physics behind replacing a sledgehammer handle? Thank you.
Tank you for this nice vulgarisation. At least it gives me where I can start to deepen my understanding....
So, what is the symmetry field for quantum chronodynamics? I get a 27-dimensional manifold in 28-space as a first working, but I don't recall seeing 27 flavors of gravitons. And how does that correspond to the galactic black hole collision recently reported? Seems improbable that we'll be able to do an experiment on that scale to test the math vs. observations any time soon.
Emmy Noether was a cool mathematician during an extended scientific revolution entangled with uncool political times.
Are energy and entropy really conserved in our expanding, increasingly accelerating universe over time?
The electroweak or to simplify weak force points to an asymmetric chirality, from madame Wu's experimental work?
Is the universe flat, it can be curved but its longer period and wavelength larger-set Hamiltonian transforms the curvature into linear & rectangular components on the fly if it's self compensating?
There's something interesting about, about quarks and gluons, neutrinos, electrons and protons, and space-time curvature, particle spin, charge and the flow of time itself, or the time gradient, down at the boundary horizon of protons and neutrons; their tensor surfaces are obviously there being older than the CMB by about 380,000 years, but these indeterminate, randomly fluctuating jiggly gluon and quark encapsulating event horizon shells do likely appear, to be photon spheres entangled with acceleraton spheres, creating resonating time-crystals of a sort? A proton is an example of a Wilczekian time crystal perpetuating the periodic table along with neutrons and electrons into the future one step ahead of the first light of the CMB? There's a spectrum of resonating & self-compensating sets of nested or entangled electromagnetic and spacetime acceleration Hamiltonians, all the way up and down?
Let us indulge in another cup of that high altitude Ecuadorean java & the jittery energy it creates! Cheerio & adios for this weekend!
Hemlooo arvin sir,, do u know any channel Or website or platform where I can get rigorous maths and physics being taught, for college student
When n in Dirac's equations as operators got the value +1&-1 symmetry is broken On adding a force term by hand broken symmetry became continuous i.e oparator is infinite hence smooth.
Angel is also infinity , is geometry response by this continuous symmetry is the basic force ?
Role of force in Dirac's relativistic modified equations is doubtful
How does the 8d sphere for SU(3) symmetry relate to the extra dimensions needed in string theory?
There is no connection (as far as I know). The extra dimensions in String Theory are required to get rid of something called symmetry anomalies.
Also, the SU(3) space is actually not quite an 8d sphere. It's more like a 5d sphere with 3d spheres attached at all points.
Good video here. Good detail, not too generic that it doesn't make sense.
i see what you did there!! you doubled the views by providing a deep and *very* interesting video which have to be viewed twice to fully appreciate!!
*e x c e l l e n t* job!!
12:08 Does this mean that there are no magnetic monopoles? I recognize the mu-J term which is the term that's asymmetrical in Maxwell's equations.
It is a part of Maxwell's equations, but their existence in the early universe can't be ruled out.
6:42 Doesn't Dark Energy violate what is said at this point in the video?
Space Translation Symetry that the laws of physics are same everywhere in the universe to paraphrase .... Yet as space expands it is expanding faster and faster. It isn't the same everywhere now is it?
and....thus momentum and energy aren't conserved on cosmological scales..e.g., the CMB is cooling.
One might ask how it is that symmetry comes about in the first place. I would suggest that if everything comes from nothing, that breaking down nothing forces a symmetry. One easy way to see this is (-1) + (1) = 0 . The total to nothing is conserved and implies a symmetry.
Great video! The hypothesized graviton is only one particle. Would that imply gravity also being a U(1) symmetry?
Don't know. No quantum theory of gravity exists. It is not a force according to General Relativity.
But it is a kinde of force, how may look its symmetry?
Thank you for the excellent content!
Could the relatively newly discovered time symmetry inherent in "time crystals" help us understand the "force" of gravity? Time and gravity are so intrinsically tied together.
I think that's unlikely. Gravity isn't actually a force like the others, it's a natural consequence of spacetime and relativity. I doubt there's a graviton, or that time crystals will be useful for understanding it.
@@Tanath No one knows what causes gravity so you're wrong to say it's consequence of XYZ.
Let's say you make the objection: "it's curved spacetime that causes gravity; near Earth spacetime is curved so objects fall towards earth"
If this is true then the thing that caused the spacetime to curve is the thing that causes gravity. But physicists don't know why spacetime's curved around Earth. It could've been Merlin the Lord Buddha for all physicsts know. It could've been time crystals.
@@alwaysdisputin9930 you're still operating under the assumption that gravity is "caused" by something as if it's a force, when in reality it's an illusion. When I say it's a natural consequence of the curvature of spacetime, I mean that's sufficient to explain gravity in general. It's actually well understood by physicists. The thing that's not understood is how it works with quantum mechanics. See here for instance: ua-cam.com/video/qyxx7hzmwj0/v-deo.html as well as ua-cam.com/video/XRr1kaXKBsU/v-deo.html
@@Tanath Either 1) spacetime curved for no reason whatsoever or 2) it curved because something caused it to curve. There's no other possibility. Therefore I'm just relying on logic not "assumption". Physicsts don't know what 2) could possibly be & you're completely wrong to say they do - they often lie that they know but it's just complete bullshit & all your links are total BS & all your explanations of what causes gravity will also be total BS regardless of whether or not you dress it up as "natural consequence of XYZ" you're still asserting gravity is caused & you don't know what caused it.
@@alwaysdisputin9930 you seem to be getting worked up over what I'm confident is a miscommunication. I assumed you knew (that physicists know) gravity (curvature) is caused by mass. My links were not "BS", they're good sources and help clarify & support what I'm trying to say.
Thanks Arvin!
why isn't rotation through other axes (e.g. flipping from heads to tails) part of the group for a circle? or for that matter, the triangle with "A" written on it? if that's a different group, what conservation law does it relate to?
Outstanding explanation; the math was brilliantly presented and explained as well.
Thank you so much sir, it will be a great help .
What about gravity? How do you describe it with symmetry or group theory?
Oooowee, this explanation is friggin paramount!! 👑
One of his best.
This was a great video, I feel like I just sat through a punchier and better produced physics lecture
what about central symettry through the midpoints of each side of the equilateral triangle?
Best video on physics that I have ever seen! Keep them coming. Add more math details, history, and suggested books for further study. Thanks!
Thanks! Glad you enjoyed it.
I understood everything 100% because I did particle physics. Honestly it was a nightmare the first time I learnt this but each time I see your videos they cement and further my understanding of things I already did in my degree.
What do you do now?
Love your stuff
Excellent video.