Why Noether Was the Most Important Female Mathematician (According to Einstein)
Вставка
- Опубліковано 27 чер 2024
- Offset your carbon footprint on Wren: www.wren.co/start/parthg1m
The first 100 to sign up will get their first month of the subscription covered by Wren for free!
Emmy Noether was a brilliant mathematician, who was described by Einstein as "the most significant creative mathematical genius thus far produced since the higher education of women began". In fact, she may have been one of the most important mathematicians of all time when it comes to changing physics forever. She discovered a theorem that links together seemingly unrelated concepts that are very fundamental to our understanding of physics.
Noether's theorem, (technically Noether's first theorem) states that there is an inherent link between certain kinds of symmetry within the universe, and conservation laws (such as conservation of momentum, energy, and angular momentum). If one exists, then so must the other.
In this video, we start by understanding what we mean by a symmetry. Specifically, this refers to unchanging behaviours of any system that we study even when a specific variable is changed. For example, if we move a ball to a different position in space, its behaviour does not suddenly change. This is "translational symmetry". We also look at "temporal symmetry" (symmetry over time) and "rotational symmetry" (symmetry over angular displacement). Basically, a system's behaviours do not inherently change, and these symmetries exist, because the laws of physics stay the same regardless of position, time, or angle!
Noether's theorem states that if such a symmetry exists, then there HAS to be a conservation law that corresponds to it. Conservation of momentum comes about because of translational symmetry. Conservation of energy comes about because of temporal symmetry. And conservation of angular momentum comes about because of rotational symmetry. So this possibly gives us a reason as to WHY these conservation laws exist in the first place. But how do we know that symmetries must have an associated conservation law?
To understand this, we take a look at the Euler-Lagrange equation. This allows us to use some basic Lagrangian mechanics to understand how a system changes over time. One special case of the Euler-Lagrange equation can be shown to be equivalent to Newton's Second Law of Motion - the force on the system being equal to its rate of change of momentum. So if the force exerted on the overall system is zero, then its momentum is constant (or conserved)! This also applies to other types of symmetry and conservation law through the use of the Euler-Lagrange equations.
Thanks for watching, please do check out my links:
MERCH - parth-gs-merch-stand.creator-...
INSTAGRAM - @parthvlogs
PATREON - patreon.com/parthg
MUSIC CHANNEL - Parth G's Shenanigans
Here are some affiliate links for things I use!
Quantum Physics Book I Enjoy: amzn.to/3sxLlgL
My Camera: amzn.to/2SjZzWq
ND Filter: amzn.to/3qoGwHk
Timestamps:
0:00 - Emmy Noether
0:40 - Noether's Theorem: Symmetries
3:33 - Check out Wren to Calculate Your Carbon Footprint!
5:10 - Symmetries and Conservation Laws
6:28 - Lagrangian Mechanics
7:28 - The Euler-Lagrange Equation
(My video on Lagrangian Mechanics and the Euler-Lagrange Equation: • Why Lagrangian Mechani... )
#physics #scientist #mathematics
#ad this video was sponsored by Wren!
Hi friends, huge thanks for watching! I'd like to thank Wren for sponsoring this video - Offset your carbon footprint here: www.wren.co/start/parthg1m
The first 100 to sign up will get their first month of the subscription covered by Wren for free!
And as always, let me know what other topics you'd like me to cover in future videos :)
Could you explain differential equations, both PDE & ODE.
I think your title should have been "Uncovering The Important Woman in Physics". Her Noether's Theorem is the foundation for many of today's Quantum Mechanics predictions and discoveries. What makes it even more impressive is that this theorem is purely a mathematical prove without having requiring any experiments to substantiate this proof. I do think she was highly underrated for over a century. Even though technically she is a mathematician, her contribute to science to far greater. To me, her theorem is no less significant or impressive than Einstein's General Relativity. People should talk more about her and her theorem should be more covered by college and university physics courses.
She is my favorite mathematician-physicist and has been since Autumn 2011.
I think your channel is my favourite thing on yt :) Getting the core idea out like that is good, because this way it enters my every day life & I think about it more calmly than when I'm "cramming for an exam"
Amazing video Parth! Happy to see you are still crushing it :D
Thanks for watching buddy! Hope you're keeping well, let's catch up some time :D
@@ParthGChannel I would love that
Great video dude very well explained! Would definitely love to see that follow up video in the future!
hi! I love the simplified version of the topic and i'd highly appriciate the deatiled video on noethers theorem, i was just reading this yesterday!
This video is just amazing. Thank you for making so good content.
Hey Parth! I've recently heard about amplituhedrons. This concept seems to have excited particle physicists. Any chance you could make a vid about this, along with scattering probabilities?
This was really good. Could you please make more videos on the intuition behind the Euler-Lagrange equation and how it is derived from variational calculus?
Can you explain differential equations both PDE and ODE?
Just when i was trying to understand what the heck this meant , my brother in science you delivered......thank you
I know that she was a mathematician but she discovered arguably the most fundamental law of physics, explaining where the conservation laws come from. This is the cornerstone of modern physics and I were to write a textbook for Physics 101, I would start with the Noether's theorem.
Excellent. Thank you.
Good on you for bigging up that lady's work. Emmy Noether has been long ignored. I think someone down-thread said she might pop up in a maths course, but rarely in physics. That fits my recollection.
This is Excellent 😊
This really should have gotten her a Nobel Prize.
It absolutely should. I she were male, I think she would get the Nobel Prize in Physics.
Excellent. Thank you!
I'd long forgotten Noether's Theorem. We never came across it in Physics. We came across it in Applied Maths, Theoretical Mechanics and only in our third year. I remember at the time understanding it, seeing the beauty and wondering if I could have come up with such a theorem.
What I find very interesting is that the most incredible theorems and theories in physics anyone could come up with on their own. Nonetheless, it only remains availiable to those who are patient and willing to take their time looking at the consequences of our current understanding.
Great vid! Can't wait to watch it!
I really am interested in going deeper into the stuff. For instance, I never quite understood how to figure out the "recipe" for the Lagrangian.
Plz make video series on qft concepts...
I have long wanted to understand the intuitive explanation behind Noether’s theorem and Lagrangian mechanics and until today been unsatisfied. Partha G you have achieved what no video I have seen ever did… I now feel I have that intuitive grasp. Could you make another video showing the intuition behind how Noether’s theorem predicts conservation of energy? Would q simply be t in that context? And what does the dot above the q mean?
So, in a way, the First Law of Thermodynamics is a statement about time (and symmetry). And the Second Law too is a statement about time (and asymmetry). Is there some way of understanding the Third Law of Thermodynamics also as a statement about time?
Aside from first law of thermodynamics that is founded on conservation principle, others, 2nd, and 3rd are not
@@charlesgodswill6161 Well, no. Of course not. That wasn’t my question.
@@ailblentyn ok
I'm glad someone just said the KE - PE doesn't mean anything physical. Been racking my brains for a physical intuition. It just happens to work as part of the description for the EOM. Otherwise, a nice intuition oriented explanation for the equation, in the rest of the video.
It seems as though the theorem has limited applicability because of the premise that it is limited to systems that will behave in the same way even if we change something about the system. Given our limited understanding of the breadth of systems from the smallest to largest physical systems across the universe, wouldn't you say that it is possible or even likely that the physics of systems may change either geographically or over time (including allowance for disparate time dilation effects among segments of the universe around the edge) and therefore the symmetries and related conservation concepts may only hold for a segment of the universe at a particular time (especially with say MOND? Excellent video and I'm a great fan of your efforts.
9:15 _"If our system has some sort of symmetery in 1 coordinate like: x then we can think of this as the Lagrangian not depending on x"_
I'm finding it hard to understand what this means & i wish there was an example of "some sort of symmetery in 1 coordinate like: x"
but I think at 6:02 there is actually an example of "some sort of symmetery in 1 coordinate like: x"
Translational
x₁ x₂
this |¯¯¯¯¯| |¯¯¯¯¯|
is a | |---------------------->| | Conservation of linear momentum
circle |_____| |_____|
i think what this diagram means is that an object moving sideways has a type of symmetery called 'translational' symmetery
which is a bit different from the symmetery of a mirror.
With a mirror you have 2 versions of e.g. your face = 1) your actual face 2) the reflection of your face
& there is a slight difference between the 2 versions = the reflection has left & right switched around, (so if you hold some writing to a mirror it is back-to-front.)
So let's suggest a general rule that every symmetery = 2 versions of an object + 1 slight difference
& with Parth's diagram at 6:02
we have the circle at x₁
& we have the circle a little bit later on in time once it's reached x₂
So we have 2 versions of the same object! (& a slight difference = they are at a different location in space = they have a different x coordinate)
Parth says at 6:42 the Lagrangian, L = kinetic energy, T - potential energy, V
If the object is moving at 300 metres per sec to the right & it's in a vacuum, then when it reaches x₂ it will *still* be moving at 300 msᐨ¹ to the right => there's no change in velocity
Kinetic energy = ½mv² but this object has same velocity throughout => the kinetic energy at x₁ = the kinetic energy at x₂
=> there's no change in kinetic energy
& there's no potential energy in the system
(If it was e.g. a bouncing ball then the PE would turn into KE would turn into PE would turn into KE etc. but our system is simpler than that - we just have 1 object moving sideways in a vacuum)
=> as the object moves along the x coordinate, the Lagrangian, L doesn't change
At 9:43 Parth says
̲ ∂̲L ̲
∂ x measures how L changes depending on x
so as the object moves from x1 to x2
̲ ∂̲L ̲ = 0
∂ x
Ok i feel like I'm making progress in understanding this!
Your description of a symmetry is very on point, with the subtle distinction being that instead of 2 versions you have a "continuum" of versions all the same but different in one way. With your mirror symmetry, everything the same except "handedness" which can only be left or right. With translational symmetry, everything is the same except position, which can be any coordinate in space.
The only thing you said which could be a little misleading is that it seems like you might be implying that the translational symmetry only applies in the direction of motion of the object, which isn't the case (but it is related to the conservation of momentum *in* a given direction)
Yeah looking forward to temporal symmetry and energy conservation intertwinement
I liked this link between symmetries and conservation laws
Please make more videos bout Noether's theorem. I also do think it's the most important theorem in physics. Without it physics would be loss, but please talk about it's relevance to all of physics as a whole.
Incredible😮
But what is the reason we use the Lagrangian here to help understand laws of conservation and not the Hamiltonian? Can the Hamiltonian not be broken up into different coordinate equations like the Lagrangian can?
I heard her about yesterday in one of your vedio now I am also a big fanboy
Can you solve the jee advanced
A question: is energy really conserved, like on cosmic scales...?
We don't have reason to believe so. The math which gives us conservation of energy only holds in a space that is not changing size/shape with time. From experiment, it appears as though the space between galaxies is expanding, so we cannot apply this result at intergalactic scales.
However, "locally" (within our galaxy) we cannot detect this expansion, so, locally, it is conserved.
My role-model, superwoman and math goddess.
there's No-ether in space was a great discovery. What a coincidence.
Such women are real influencers!!
lmao one in 100 billion yea
Like, thanks to Emmy we have quantum with non local stuff covered by her theorem 🤓🖖
🤔😫🤯🤯
Well. It's cool.
Oh the lagrangian already? It's like the difference between the kinetic and potential energy and it conserves. 🥺 Poor L =T-U
And H conserves and it's very linear, always the total energy, I used it for a n bodies program I wrote for solar system but using energy equations instead of standard Newton's. And the checksum was H
And you didn't speak about the generalised coordinates that seem pretty specific because we change coordinates system according to the scenario we are working on 🤓🖖 😲😳🤯😅🤓🖖
Yep I'd need a lot of psychedelics to have an idea like Noether's theorem😋
Then take some
Psychedelics and math don't go well together
Usually when you add a qualifier it downgrade the importance. She is the most important Mathematician to modern physics. No need to add female and Einstein. You can have a view, can't you?
Source?
Yeah, but, what is momentum ?? ...
Skin Aperture Theory - The Higgs Inertia/Kinetic/Gravity mechanisms
Assume the particle/atomic aperture is circular if stationary.
1. Forward movement through space distorts the symmetry in such away that the incoming spacial dowel pressure is higher on the side equivalent to the velocity vector. (Frame grabbing WISC distorts atomic aperture)
Generating an imbalance in spacial flow resulting in permanent velocity along the same vector line.
2. The same WISC affect of Gravity distorts the "tail" of the particle increasing curvature distance and therefore decreasing G "flow" pressure opposite the larger mass' gravity flow causing the particle to accelerate along the Gravity vector recursing on 1.
Note: There is an implication that the interface angle between our visible space and the BB space is always 90º regardless of Visible space vector direction!
M.B.Eringa 2022
Why curved space ?
Orbital mechanics has proven the orbital mass of an object = M+(M*V)
As opposed to a collision mass of M*V^2
Which means an object orbiting another object is in a continuous "Stable" vector, not a constantly changing vector as most descriptions would imply, i.e. Gravity should have a V^2 energy if it's constantly "pulling" on the object to change its' directional vector.
(C) 1985 M.B.Eringa, S.Hawking
So Gravity is causing a partial spin of the orbital mass' atoms! , changing the momentum vector without any apparent external force!
The objects in TENET would be the contrary? I know, it is a fiction.
Such women are true feminists
Total Agreement, full support
can you elaborate on that statement?
Bro what so only Einstein is a true man?
@Chamo feminism is a philosophy not a gender. Even men can be feminists.
What does this even mean?
First
Did someone say woman? 👀
Sp0ns0rBlock
"Why Noether Was the Most Important -Female- Mathematician"
You don't need the word "female" here. Either she is the best woman can offer and the worst male mathematician can destroy her in math, or the male mathematician is worse than her. This inclusion of the word "female" makes the sentence meaningless.
it can mean:
This is as good as woman get, and it pales in comparison to men, or
This is very good math, equal to men, and we just wanted to let you know for no reason that the mathematician happens to be female, or
She is the best mathematician and she happens to be female, or
Women are better than men at math and she is the best of the females.
I cringe when people use the pseudo-verb "orientated". The correct verb is "oriented." This verb is turned into the noun "orientation" by adding "ation", not just "ion."
I cringed when reading this
@@dylanjones7472 you're probably among those who like the word "proactive" to mean the opposite of "reactive" when the proper opposite of "reactive" is "active."
@@laurendoe168 - perhaps you're using an American version of English? I'm English & I think "orientated" is fine
Collins dictionary website says:
orientate in British English
(ˈɔːrɪənˌteɪt IPA Pronunciation Guide )
verb
a variant of orient
I'll watch the whole video later, but I'm just here to comment a thing. Here we see women who changed physics (hence the world in a way) and then today we have women who well, can't do anything, kudos to the women who are able to do something actually meaningful with logic in this shit era too.
Back in the day women were just as stupid don't worry bro
Women were already stupid and mediocre back in the day bro
Like there aren't men what can't do shit either
Your idea that "women today can't do anything" is exactly the sort of BS idea that Noether had to deal with back in her day.
You need to reject the primitive centuries-old ideas such as "women today can't do anything" & embrace the more advanced concepts such as:
̲∂̲L ̲ = 0 => momentum is conserved
∂ x
@@alwaysdisputin9930 nah women are useless