The Hole In Relativity Einstein Didn't Predict [27:39]

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· What is symmetry?
0:00 · - Imagine you are an astronaut out drifting in deep space
0:03 · when you throw a rock as hard as you can.
0:07 · What's gonna happen to that rock?
0:09 · Well, you would think that it would continue
0:11 · with constant velocity in a straight line.
0:13 · That's just Newton's first law.
0:15 · But what actually happens is it eventually slows down
0:20 · and stops.
0:22 · So why does this happen?
0:24 · Where did all the rock's energy go?
0:26 · (pensive orchestral music)
0:27 · At the turn of the 20th century,
0:29 · the problem of energy conservation
0:31 · baffled some of the greatest minds,
0:33 · including Albert Einstein.
0:35 · Einstein came up with a possible solution,
0:39 · but then a little-known unpaid mathematician
0:42 · named Emmy Noether proved he was wrong.
0:45 · And in doing so,
0:46 · she created a whole new paradigm for physics,
0:48 · one that underlies all of particle physics
0:51 · and explains why anything is conserved.
0:55 · (gentle inquisitive music)
0:57 · It all started in 1915 at the University of Gottingen,
1:01 · where Einstein was giving six lectures
1:03 · on his new theory of gravity.
1:05 · What would become the general theory of relativity.
1:09 · The lectures were well received,
1:11 · but Einstein hadn't yet settled on the final form
1:14 · of the field equations.
1:15 · One problem he was facing
1:17 · was how to show that total energy was conserved
1:20 · in his new theory.
1:21 · - And this is the whole beginning of this story, right?
1:23 · Classically, they thought they had this understanding
1:25 · of what the energy of the gravitational field was.
1:28 · All of a sudden with these new equations,
1:29 · they go, "Where is it?
1:31 · You know, is it in the curvature?
1:33 · You know, is it in the stress-energy tensor?
1:35 · Where's the term that we're looking for?"
1:38 · - [Derek] Einstein suggested that the principle
1:40 · of conservation of energy,
1:41 · long established as a bedrock of physics,
1:43 · might hold the key to working out
1:45 · the correct field equations.
1:47 · In the audience, legendary mathematician
1:49 · David Hilbert was intrigued.
1:51 · So he started to look for the energy conservation equations
1:54 · in Einstein's new theory, but the best he could find
1:57 · was a set of equations known as the Bianchi identities.
2:01 · They showed that energy was conserved,
2:03 · but only in a completely empty universe.
2:06 · So for one like ours filled with stuff, they seemed useless.
2:11 · Hilbert was stumped.
2:14 · - Fortunately, he knew just the person for the job.
2:17 · His new assistant, Emmy Noether.
2:20 · (light thoughtful music)
2:21 · - [Derek] From an early age, Noether had dreamed
2:23 · of following the footsteps of her father,
2:25 · a mathematics professor at the University of Erlangen.
2:28 · She got special permission
2:29 · to attend lectures at the university,
2:31 · but they refused to admit her as an official student.
2:35 · The Erlangen Academic Senate
2:36 · held that the admission of women
2:38 · "would overthrow all academic order."
2:41 · (lively orchestral music)
2:42 · So in 1903, she spent a semester at Gottingen instead.
2:46 · There she learned about a new way to approach geometry
2:50 · using symmetry.
2:51 · (gentle thoughtful music)
2:54 · Symmetry is one of those ideas that's easy to recognize
2:57 · but harder to describe.
2:59 · - If I align a mirror on this triangle like so,
3:02 · then it looks the same as without the mirror,
3:05 · and that's because this is an axis of symmetry.
3:08 · The reflections about this axis
3:10 · leave the triangle unchanged.
3:12 · And the same thing happens if I put the mirror like this
3:14 · or if I orient the mirror like this.
3:17 · So this triangle has three axes of symmetry.
3:22 · Now, mathematicians generalize the idea of symmetry further
3:25 · to be any action you can take
3:27 · that leaves an object unchanged.
3:29 · So something else I could do is I could rotate this triangle
3:32 · by 120 degrees or by 240 degrees
3:37 · or by 360 degrees.
3:39 · Together, these six actions
3:41 · capture all the symmetries of the equilateral triangle.
3:45 · - [Derek] But you can also have more abstract symmetries,
3:48 · for example, with a mathematical function.
3:50 · If I shift this function up or down by some constant amount,
3:54 · call it a, then all of its y values will change.
3:59 · But if I differentiate that function, I get the slope,
4:02 · and that remains unchanged
4:04 · regardless of whatever constant is added.
4:07 · So you can add any constant to this function,
4:10 · and its derivative always stays the same.
4:13 · So there is a kind of translation symmetry.
4:16 · And unlike the symmetries of the triangle,
4:18 · this is a continuous symmetry,
4:20 · meaning you can shift it by any amount you like.
· Emmy Noether and Einstein
4:25 · Over the next 12 years,
4:27 · Noether became a leading expert on symmetry.
4:30 · She became only the second woman in Germany
4:32 · to earn a PhD in mathematics,
4:34 · and she used this expertise to help Hilbert
4:37 · and Einstein with their problem of energy conservation.
4:41 · The issue had bothered Einstein so much
4:43 · that he proposed a new conservation equation.
4:47 · It said that if we add together the energy of matter
4:50 · and the energy of the gravitational field,
4:52 · then that total remains constant.
4:54 · Its change over time and space is zero.
4:59 · But when Noether saw this,
5:00 · she was convinced Einstein had made a fundamental mistake
5:04 · because this equation disregards the foundational principle
5:07 · that general relativity is built on.
5:09 · (light pensive music)
5:11 · 10 years earlier, in 1905,
5:13 · Einstein had introduced his special theory of relativity,
5:16 · and it was built on the idea that the laws of physics
5:19 · were independent of your frame of reference.
5:22 · But so far Einstein had only applied this principle
5:25 · to inertial frames of reference.
5:27 · Those are frames that move at a constant speed.
5:30 · - He began wondering
5:31 · what would it take to generalize that,
5:33 · to consider more general states of motion.
5:35 · After all, trains on the platform; he loved trains.
5:38 · Trains would speed up or slow down.
5:40 · People, you know, moving around the world
5:42 · don't only move at a single constant speed forever.
5:45 · - In 1907, he wrote,
5:47 · "Is it conceivable that the principle of relativity
5:49 · also applies to systems that are accelerated
5:52 · relative to each other?"
5:53 · This made him wonder;
5:55 · perhaps his principle could also be applied to accelerating
5:58 · and rotating frames, frames that move in any way in general.
6:02 · That's the "general" in general relativity.
6:05 · So Einstein got to work
6:06 · on this largely intellectual pursuit.
6:10 · - But then, as he was daydreaming in the patent office,
6:13 · he had what he called the happiest thought of his life.
6:18 · - [Derek] He imagined the window cleaner
6:20 · at the top of the opposite building falling off.
6:22 · (window cleaner screams)
6:25 · And Einstein realized that while the man was falling,
6:28 · he wouldn't feel his own weight.
6:30 · He would be weightless,
6:32 · and anything he dropped on his way down
6:33 · would remain stationary relative to him.
6:37 · It would be just as if he was floating in outer space.
6:41 · - It's ironic, we would've said,
6:42 · "Oh, he's being pulled down to the ground
6:43 · because the gravity of the Earth is exerting a force.
6:47 · But Einstein said, while that person is in motion,
6:50 · what we call free fall motion,
6:52 · they would actually feel no gravity at all.
6:54 · There must be some equivalence between accelerated motion
6:58 · and the action of gravity.
7:00 · So Einstein arrived
7:01 · at what he called the equivalence principle.
7:04 · - [Derek] If you were stuck in a rocket in outer space
7:06 · accelerating at 9.8 meters per second squared,
7:09 · then it would be the exact same
7:11 · as if you were standing on the surface of Earth.
7:14 · - And this was huge
7:16 · because it meant that if Einstein could figure out
7:18 · how to understand accelerating frames,
7:20 · then he didn't just get a more general theory;
7:23 · he would also have a new theory of gravity.
7:26 · - But to achieve this,
7:27 · Einstein needed to make sure the laws of gravity
7:29 · had the same form in every frame of reference.
7:32 · (train whooshing)
· General Covariance
7:34 · This is the idea of general covariance,
7:37 · and it's one of the core tenets of general relativity.
7:40 · To satisfy it, Einstein knew he had to use
7:43 · special mathematical objects called tensors.
7:46 · A simple kind of tensor is a vector.
7:48 · You can write a vector as a set of components
7:50 · multiplied by their basis vectors.
7:53 · For example, this vector can be written as
7:55 · 3x hat plus 2y hat.
7:57 · But I can also write this
7:59 · using a different coordinate system.
8:01 · And with these new basis vectors,
8:03 · the original vector is now written as 2a plus 1b.
8:07 · So the components, the numbers in this list, changed,
8:11 · but the vector didn't.
8:12 · It stayed the same.
8:14 · And that's because when the basis vectors change,
8:16 · the components adjust in a complementary way
8:19 · to keep the vector the same.
8:21 · The vector itself is independent
8:23 · of which coordinate system you use.
8:26 · And the same is true for tensors,
8:28 · only now instead of having just two components,
8:30 · a general tensor can have any number of them
8:32 · in the form of a matrix.
8:34 · And just like with vectors, you can change a tensor
8:37 · from one coordinate system to another,
8:39 · and the tensor stays the same.
8:41 · So that's why Einstein had to use them
8:43 · to build his new theory.
8:46 · - And that was exactly the problem that Noether found
8:48 · because when she looked
8:50 · at Einstein's proposed energy conservation equation,
8:52 · it contained a pseudotensor.
8:54 · And as the name implies, that isn't quite a tensor.
8:58 · When you try to transform it
8:59 · from one frame of reference to another,
9:01 · it doesn't remain the same quantity in different frames.
9:04 · The gravitational energy you might observe in one frame
9:08 · completely disappears in another.
9:10 · - And Einstein, you know,
9:11 · he had some strange thoughts about this.
9:13 · I mean, people were trying to stamp conservation of energy
9:17 · into relativity by bending the rules
9:22 · of mathematics.
9:24 · - So, Noether knew that Einstein's proposed solution
9:27 · couldn't be the answer, and that made her think,
9:31 · "What if general covariance
9:32 · and energy conservation are simply incompatible?
9:36 · And if that's the case, then why?"
9:39 · General covariance says that laws of physics
9:42 · must stay the same when you change reference frames.
9:45 · So that is a kind of symmetry,
9:48 · exactly what Noether had spent her career studying.
9:51 · So she started thinking
9:52 · about the symmetries of the universe,
9:55 · beginning with the simplest possible case,
9:58 · an empty static universe.
10:00 · (light contemplative music)
10:02 · Imagine you are an astronaut in this universe.
10:05 · Since it's empty, there is nothing special
10:07 · about any particular point.
10:09 · I mean, it doesn't matter if you're over here or over there;
10:13 · the universe is completely symmetric
10:15 · under translations in space.
10:18 · So suppose you throw a ball;
10:20 · well, it'll travel at a given speed,
10:22 · and after a short amount of time,
10:24 · it will have traveled some distance.
10:26 · But since the laws of physics are the same here
10:28 · as just before, we can shift the whole universe,
10:31 · and we're back to the situation we started with.
10:34 · And we can keep doing this over and over,
10:37 · and this shows us that the object will continue
10:40 · with that same speed indefinitely.
10:43 · So what we've discovered
10:44 · is that the principle of conservation of momentum
10:47 · is a direct result
10:48 · of the fact that there's a translation symmetry
10:51 · in the universe, that an experiment done in one spot
10:54 · will give identical results
10:55 · to that same experiment done somewhere else.
10:59 · You could move everything from one place to another,
11:01 · and the physics won't change.
11:03 · Similarly, the laws of physics don't depend
11:05 · on whether you perform an experiment like this
11:07 · or rotate everything by 90 degrees.
11:10 · This universe is symmetric under rotations.
11:14 · So imagine we take a metal rod and spin it.
11:17 · If we let it rotate for a minute,
11:19 · then it will have moved through a small angle,
11:21 · but we can rotate the whole universe back
11:23 · by that same angle
11:25 · and now we're at the starting position again.
11:27 · And we can keep doing this
11:28 · so that each instant looks exactly the same
11:31 · as the one before, which means the object
11:34 · will keep rotating this way indefinitely.
11:37 · So the law of conservation of angular momentum
11:40 · comes from the rotational symmetry of the universe.
11:44 · Now, another important symmetry of this universe
11:46 · is time symmetry.
11:48 · The laws of physics don't change over time;
11:51 · if you do an experiment today or tomorrow,
11:53 · you will get the same result.
11:55 · So what does this symmetry lead to?
· The Principle of Least Action
11:59 · Well, to understand this, we're gonna dig into some math
12:02 · and a different way of doing mechanics
12:04 · using the principle of least action.
12:07 · Previously on Veritasium,
12:08 · we learned that everything always follows the path
12:11 · that minimizes a quantity known as the action.
12:13 · This is equivalent to the integral
12:15 · of the Lagrangian L over time.
12:18 · In the simplest case,
12:19 · that's just the kinetic minus potential energy.
12:22 · Euler and Lagrange found
12:23 · that the principle of least action is obeyed,
12:25 · so long as this set of differential equations is satisfied.
12:29 · So Noether used action to see how physics
12:32 · was affected by different symmetries.
12:35 · - So suppose we do an experiment
12:37 · where the result is the same now
12:38 · as some tiny time interval epsilon later,
12:41 · then how does this affect the action?
12:44 · Well, the time is going to change from just t
12:47 · to t plus epsilon,
12:50 · and as a result, the Lagrangian is also going to change.
12:53 · So the new Lagrangian will be L prime,
12:56 · which is equal to the old Lagrangian,
12:58 · plus how much the Lagrangian changes over time,
13:02 · that's just dL by dt,
13:03 · multiplied by how long that change lasts,
13:06 · so multiplied by epsilon.
13:09 · But now also remember that the result
13:11 · is gonna be the exact same now as a little while later,
13:14 · which means that whatever this term is,
13:17 · the dL over dt, doesn't affect the equations of motion,
13:21 · and it's from this symmetry in the action
13:24 · that we're gonna be able to find the conserved quantity.
13:27 · So let's take dL/dt and rewrite it using the chain rule.
13:31 · That gives us the partial derivative of L with respect to X
13:35 · times dx over dt,
13:36 · plus the partial derivative of L with respect to v
13:39 · times dv over dt.
13:41 · But we can sub in the partial derivative of L
13:44 · with respect to x
13:45 · with this term from the Euler-Lagrange equation.
13:48 · And we can simplify this further
13:49 · by writing dx over dt as v,
13:51 · and that gives us this expression.
13:54 · And now notice what we've got right here.
13:56 · We've got the time derivative of some function, dL over dv,
14:00 · times another function, plus that first function
14:04 · times the time derivative of the second function.
14:06 · So we can use the reverse of the product rule
14:09 · to simplify this to the time derivative of dL over dv
14:13 · times v.
14:15 · Then as a final step, we can bring dL over dt to the right.
14:19 · So what we found is that
14:20 · if you take the time derivative of this quantity,
14:23 · it's equal to zero,
14:24 · which means that whatever this is has to be a constant.
14:28 · So what is it?
14:30 · Well, remember that in the simplest case, the Lagrangian
14:34 · is just equal to the kinetic minus potential energy,
14:36 · which we can write as 1/2 mv squared minus v.
14:42 · So if we take the partial derivative of the Lagrangian
14:46 · with respect to v, we're just gonna get d over dt,
14:50 · m times v multiplied by v,
14:53 · so this is gonna become mv squared.
14:55 · And then we can sub in the Lagrangian.
14:56 · So this becomes minus 1/2 mv squared minus v,
15:03 · but also minus here.
15:04 · So this becomes plus v, and all of that's equal to zero,
15:08 · which we can simplify to just 1/2 mv squared
15:13 · plus v is equal to zero.
15:17 · But wait a second because this is just the total energy.
15:21 · So what we've discovered is that time translation symmetry
15:24 · is equivalent to saying that energy is conserved.
15:27 · (dramatic orchestral music)
· Noether's First Theorem
15:29 · - The principle of conservation of energy
15:31 · is a direct consequence of time translation symmetry.
15:37 · In a theorem, Noether proved
15:38 · that all of these examples are no coincidence.
15:42 · For centuries, people had no idea
15:44 · where conservation laws came from.
15:46 · But now Noether had discovered the origin of all of them.
15:50 · She proved that anytime you have a continuous symmetry,
15:53 · you get a corresponding conservation law.
15:56 · Translational symmetry gives you conservation of momentum,
15:59 · rotational symmetry gives you
16:00 · conservation of angular momentum,
16:02 · and time translation symmetry
16:04 · gives you conservation of energy.
16:08 · But these are all symmetries of a static empty universe.
16:13 · The universe we live in is very different.
16:16 · In the 1920s, astronomers measured the velocities
16:19 · of distant galaxies,
16:21 · and they realized all of them are moving away from us.
16:24 · The farther away they are, the faster they're moving.
16:28 · The implication was clear.
16:30 · In the distant past,
16:31 · everything must have been much closer together.
16:34 · In the 1990s, precise measurements of supernovae
16:37 · revealed that not only was the universe expanding,
16:40 · but that expansion was speeding up.
16:44 · This means over large timescales,
16:46 · our universe is not symmetric in time.
16:48 · It was very different 13 billion years ago,
16:51 · and it'll be different billions of years from now.
16:55 · Since we don't have time symmetry,
16:57 · that also means energy, as we usually think of it,
17:00 · isn't conserved.
17:02 · - There's no reason for energy to be conserved anymore
17:04 · 'cause you don't have that symmetry.
17:07 · - [Derek] Think about a photon of visible light
17:08 · emitted 380,000 years after the Big Bang,
17:12 · it travels through the universe unimpeded
17:14 · to arrive at our telescopes,
17:16 · not as visible light but as a microwave.
17:19 · It has lost 99.9% of its energy.
17:23 · - Where did the energy go?
17:25 · Doesn't go anywhere.
17:27 · Energy's not conserved.
17:30 · - [Derek] And this is exactly
17:31 · what's happening to the rock as well.
17:33 · It starts off with energy,
17:35 · but as it travels through the expanding universe,
17:37 · it slows down and stops.
17:39 · (gentle thoughtful music)
17:40 · The energy doesn't really go anywhere; it just disappears.
17:45 · - It ends up coming to rest
17:48 · with regard to the other particles in the universe.
17:52 · - This doesn't violate any laws of physics
17:54 · because energy and momentum aren't conserved
17:56 · if there is no time or spatial symmetry.
17:59 · - So once you know that
18:00 · symmetries give you conservation laws,
18:02 · and so once those symmetries are gone,
18:05 · you don't have to worry about
18:06 · those conservation laws anymore,
18:08 · then you can start dropping these concepts
18:10 · of trying to force something
18:12 · that you want to say is fundamental into the theory,
18:15 · and you just deal with what the theory gives you.
18:18 · - But if energy isn't conserved in our universe,
18:21 · then why does it usually seem like it is?
18:23 · (light mysterious music)
· The Continuity Equation
18:25 · That's because when you're looking at the short timescales
18:27 · that we're used to,
18:28 · time translation symmetry pretty much holds;
18:31 · an experiment done today will give the same results
18:33 · as the same experiment done tomorrow.
18:35 · So that means for all intents and purposes,
18:38 · energy is conserved.
18:40 · But over large timescales on the order of millions of years,
18:43 · well, then the expansion of the universe can't be neglected,
18:46 · and the symmetry is broken.
18:48 · So only when you look at timescales that big
18:51 · do you notice that energy isn't conserved.
18:55 · Noether's first theorem explains why a rock
18:58 · or a photon loses energy,
19:00 · but it didn't fully solve the problem
19:02 · of energy conservation in general relativity.
19:05 · See, so far, Noether had only dealt with an empty universe
19:08 · where you could shift the whole universe
19:09 · and the laws of physics would stay the same.
19:12 · But this doesn't work in general relativity,
19:14 · where the curvature can change from one point to another.
19:17 · Now if you shift the whole universe,
19:19 · rotate it, or let it evolve in time,
19:22 · things don't stay exactly the same.
19:24 · So you no longer have these global symmetries,
19:27 · but Noether realized there are still other symmetries left.
19:31 · See, no matter how you're moving,
19:33 · the laws of physics always look the same.
19:36 · That's general covariance,
19:37 · and it is a kind of symmetry that holds everywhere.
19:40 · It means that in any small region,
19:42 · we can always change our frame of reference.
19:45 · We can transform the points of space around
19:48 · as much as we like.
19:49 · And since these transformations aren't global but local,
19:52 · these are called local symmetries.
19:55 · In a second theorem,
19:56 · Noether proved that for these local symmetries,
19:59 · you no longer get proper conservation laws
20:01 · like we're used to in classical physics.
20:04 · Instead, you get something that only works locally:
20:06 · a continuity equation.
20:08 · One example of a continuity equation
20:10 · describes the flow of water through a pipe.
20:13 · This first term tells you how the amount of water changes
20:17 · in a section of the pipe,
20:18 · and the second tells you the difference
20:20 · between how much water is flowing out
20:22 · and how much is flowing in.
20:24 · In this case, the first term is positive
20:26 · because the water level in this pipe section is increasing,
20:30 · and the second term will be negative
20:31 · because less water is flowing out of the section than in.
20:36 · Together, the two terms cancel to give zero,
20:38 · which guarantees that no water is created or destroyed.
20:42 · If the total amount of water changes in a section,
20:44 · there must either be excess water flowing in or out.
20:48 · - In the case of general relativity,
20:50 · Noether found a similar continuity equation,
20:52 · but with an important difference.
20:54 · Imagine that now our pipes are little patches of space-time,
20:57 · and the water is energy flowing from one patch to another.
21:02 · In any individual section,
21:03 · the continuity equation looks exactly the same as before,
21:06 · so that in any small region of space-time,
21:09 · energy is conserved.
21:10 · But when we link these sections together,
21:13 · we need to take into account the curvature of space-time.
21:16 · And this changes the equation.
21:18 · Now, it's as if there are little cracks appearing
21:20 · between different sections of pipe,
21:23 · between the local patches of space-time,
21:25 · and through those cracks, energy can leak out.
21:29 · - In special activity, the pipe is imperturbable
21:32 · because the pipe is fixed.
21:34 · And in general activity, you know,
21:36 · we have to account for the energy
21:38 · that goes into other kinds of change over time,
21:41 · and that gets correspondingly more tricky.
21:44 · - [Derek] Now that we have this new equation,
21:45 · we can see how it works
21:46 · by expanding it as a sum of different terms.
21:49 · This first term is analogous
21:51 · to the continuity equation from before,
21:53 · the one which conserves energy
21:55 · within a local patch of space-time.
21:57 · But now we have all these extra terms.
22:00 · These describe the curvature of space-time.
22:02 · So as energy decreases in the first term,
22:05 · these curvature terms increase.
22:07 · - The energy that you lose from the system you're tracking,
22:11 · we now start attributing it to things like
22:12 · the gravitational field,
22:14 · which has changed 'cause the whole universe is stretched.
22:16 · We have to account for the energy
22:17 · that we attribute to the action
22:18 · of the gravitational field as well
22:21 · because space and time themselves aren't sitting still.
22:24 · - And all of this can be described
22:26 · by the continuity equation Noether had found.
22:28 · But when she looked at it, she realized something.
22:32 · It was exactly equivalent to the Bianchi identities,
22:35 · the half-solution Hilbert had found.
22:37 · He had dismissed it because it only gave you
22:39 · proper energy conservation in an empty universe.
22:42 · But now Noether proved that it was the best you could do
22:46 · in general relativity.
22:50 · With one paper, she had uncovered the source
22:52 · of all conservation laws, and she had solved the problem
22:56 · in general relativity that eluded Hilbert and Einstein.
22:59 · - She was so amazing.
23:01 · I mean, I would go out on a limb,
23:02 · and I would say these two theorems are probably
23:04 · the most important theorems for physics of the 20th century.
23:07 · - [Derek] In the following years,
23:08 · the University of Gottingen
23:09 · took steps to make Noether's position more official,
23:12 · allowing her to do what she loved most: to teach.
23:15 · They made her a professor,
23:16 · and she even got a small salary starting in 1923.
· Escape from Germany
23:21 · But all of that changed on the 30th of January, 1933,
23:25 · when Hitler became chancellor of Germany.
23:28 · The Nazis banned Jewish people from working at universities,
23:32 · and almost immediately, one of her former students
23:35 · told the authorities of her Jewish heritage,
23:37 · and she was suspended.
23:40 · Despite this dismissal,
23:41 · she continued teaching in the kitchen of her home.
23:45 · Then one day, one of her old students knocked on her door.
23:48 · (hand knocking on door)
23:49 · Clothed in the brown shirt of the Nazi stormtroopers,
23:52 · Noether let him in.
23:55 · He had come to learn math,
23:57 · and Noether was happy to teach him.
23:59 · - I love what this sort of shows about Noether.
24:01 · You know, she truly, deeply cared about math,
24:05 · and she wouldn't discriminate.
24:06 · Whether someone was wearing a Nazi shirt or not;
24:10 · she taught all.
24:12 · - [Derek] But staying in Germany became untenable.
24:15 · Fortunately, with the help of other academics,
24:17 · she managed to obtain a teaching position at Bryn Mawr,
24:20 · a woman's college in America,
24:22 · where she would teach until her death.
24:25 · In an obituary for the New York Times,
24:27 · Einstein wrote that "Fraulein Noether
24:29 · was the most significant creative mathematical genius
24:32 · thus far produced
24:33 · since the higher education of women began."
24:37 · - The reason that Noether's theorem is so important
24:41 · is that everybody just changed their state of mind.
24:44 · All of a sudden, the physicists were thinking about physics
24:47 · in terms of these symmetries.
· The Standard Model - Higgs and Quarks
24:49 · - Physicists started applying these ideas
24:51 · to the quantum world too, realizing that charged particles
24:55 · like electrons also have symmetries.
24:57 · Electrons have a phase, which you can think of
25:00 · as an arrow pointing in some direction,
25:03 · but you can offset this phase by any arbitrary amount
25:07 · so long as you do it simultaneously for all electrons.
25:11 · And that doesn't change anything physically,
25:14 · so there's another symmetry.
25:16 · So what does this offset or gauge symmetry lead to?
25:21 · Well, it leads to the conservation of electric charge.
25:25 · In the 1960s and '70s,
25:27 · Noether's insights led directly to the discovery
25:29 · of new fundamental particles
25:31 · like quarks and the Higgs boson.
25:33 · It taught us where the forces of nature come from,
25:36 · and it even helped to explain the origin of all mass
25:39 · in the universe.
25:40 · Noether's two theorems, although little known,
25:43 · are what has gotten us the closest we've ever come
25:45 · to a theory of everything.
25:48 · But all of this and much more
25:49 · will be covered in a second video.
25:51 · So make sure you're subscribed
25:53 · to get notified when that video comes out.
25:58 · (radio waves whizzing)
26:02 · When Emmy Noether set out to study mathematics,
26:04 · she was following in her father's footsteps,
26:07 · but from there she forged her own path.
26:09 · And before long, she was coming up with a whole theory
26:11 · that reshaped our understanding of the universe.
26:14 · That is the great thing about learning.
26:16 · You start by following instructions,
26:18 · building on what others have done before you.
26:20 · But then at some point, you start asking your own questions;
26:23 · you start experimenting and making discoveries.
26:26 · I've loved watching my own kids start this journey,
26:29 · and my longtime sponsor, KiwiCo, has been a big part of it.
26:33 · This month they sent me their
26:34 · Rapid-Fire Disc Launcher crate,
26:36 · and at first, we followed the instructions carefully,
26:38 · putting it together step by step.
26:40 · But as soon as it was built,
26:41 · my kids immediately started experimenting.
26:44 · - [Child] Can I launch it?
26:45 · - Testing different launch techniques
26:47 · to better hit the target, changing the launch angles,
26:49 · and figuring out what would make the discs fly farther.
26:52 · Without even realizing it,
26:54 · they were engaging with the same questioning mindset
26:56 · that drives real scientific discoveries.
26:59 · So who knows, maybe a simple disc launcher
27:01 · will inspire a young scientist
27:03 · who will go on to make the next great breakthrough
27:05 · in science or engineering.
27:07 · KiwiCo makes this easy
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27:31 · and I wanna thank you for watching.

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