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In 1928, a young man shuffled onto a stage in Germany to present a lecture on his recent work.

He had a slightly unusual presentation style.

Physicist Eugene Wigner described the lecture as detached, almost like a recitation of a technical text.

He said the man spoke without giving any sign of enjoying his own lecture.

But the work this strange, unassuming man presented was about to send some of the most famous quantum physicists of the 20th century spiraling.

After the lecture, Werner Heisenberg described the man's theory as the saddest chapter in modern physics.

Heisenberg also wrote to Niels Bohr and said, I find the present situation quite absurd, and on that account, almost out of despair,

I have taken up another field.

Legend has it that Wolfgang Pauli even announced that he was abandoning quantum physics, and then he started writing a utopian novel.

What had the young man said to disrupt the world of quantum mechanics so profoundly?

Well, he had been working on a problem that physicists are still tackling today.

The unification of Einstein's relativity and quantum mechanics.

And his work had revealed something troubling.

A particle unlike any seen in the world.

A particle with negative energy.

In 1905, Albert Einstein published his special theory of relativity.

It was based on the simple idea that for anyone moving with constant speed, the laws of physics should be the same.

And this includes any measurement of the speed of light.

So it doesn't matter how you're moving relative to a beam of light, you should measure its speed to be 300 million meters per second.

This means that things that we ordinarily think of as fixed,

like time and space, have to transform so that the speed of light is always measured to have the same value.

In making this discovery, Einstein realized that space

and time are not really separate dimensions at all they're linked in a four -dimensional fabric called spacetime

when Einstein applied this idea to an object emitting light he found something peculiar

when an object loses energy by emitting photons its mass must also decrease

and the change in the objects mass is equal to the

energy of the photons emitted divided by the speed of light squared in other words he found

that energy must be equal to mc squared.

E equals mc squared.

Mass and energy are for different manifestations of the same thing.

So a particle's total energy comes from its momentum and its rest mass, giving a new relationship between energy and momentum.

Now if we take the square root of both sides,

we get an expression for the energy of a particle in terms of its mass and momentum.

And if we plot energy versus momentum in a single dimension, we get this curve, where mc squared, the rest mass energy of the object,

is the lowest possible value for energy.

But really, when we took the square root, we should have put a plus minus out front, which would give us two curves,

one for positive energies and another for negative energies.

But we don't observe things that have energy less than zero.

I mean, what would that even mean?

So in classical physics, the solution is simple.

You just ignore the negative energy solutions.

They can't physically represent anything, right, Casper?

Well, sure, that sounds right.

But around the same time that Einstein was coming up with his special theory of relativity,

physicists began observing some strange phenomena in atomic physics that were overthrowing all of these classical assumptions.

First of all, they noticed that when looking at the energy levels of subatomic particles like electrons, they weren't continuous at all.

They were discrete.

And they also didn't just behave as particles, but as waves.

So if you would take electrons

and fire them through two narrow slits

then they would create interference patterns just like light does what they were discovering was the new field of quantum mechanics

and in 1926 erwin schrodinger formalized this field by coming up with his now famous wave equation

which describes how quantum mechanical systems evolve over time this was the most radical new theory of the 20th century,

and would remain so.

This is not a bit like

Newton or a bit like Maxwell.

This was radically new.

The equation solution, called the wave function, psi, does not describe a particle with a precise position and momentum, as classical laws would.

But instead, the modulus squared can give us the probability of finding the particle in a specific location at a specific time.

Deriving the Schrodinger equation is actually surprisingly simple.

Just start by writing down the total energy, which for a free particle is just its kinetic energy, half mv squared.

And we can rewrite it in terms of momentum, mass times velocity.

So kinetic energy is just momentum squared divided by 2m.

Now we're going to make this quantum.

And to do that, we need two things.

The first is the wave function, psi, which describes how particles act as waves at quantum scales and the second is something called a quantum operator.

This is just a mathematical tool that extracts information from the wave function to reveal a specific property of the particle,

like its position, energy, or momentum.

The operators for energy and momentum look like this.

By inputting these operators, we can make each side of the equation act on the wave function.

And that gives us the Schrodinger equation for a free particle.

For particles that aren't free, like electrons and atoms, you need to factor in potential energy too, which gives you the full Schrodinger equation.

but there are some places where it doesn't produce the right

prediction for example take the element gold the schrodinger equation suggests

that it should be a silver gray color just like all the other metals

but it's not i mean it's gold and for mercury the schrodinger equation predicts

that it should be a solid at room temperature

but it's a liquid so what is wrong well i'll give you a hint

because both gold and mercury are heavy elements they have a high number of protons in their nuclei

which attract orbiting electrons more strongly so

if you're thinking in a classical sense the electrons would be bound tighter in

and they'd be whizzing around at higher speeds than in other elements

and for electrons in some orbits those speeds start to get a little too close to the speed of light

so let's go back to the schrodinger equation there we had the kinetic energy was p squared over 2m

but for particles moving at relativistic speeds close to the speed of light

that equation isn't the right one the correct equation is the

energy momentum relation from special relativity Schrodinger's equation is not consistent with the theory of relativity

so it's technically it's not right

so the solution seems simple enough just start with the relativistic energy momentum relation and use

that to derive a new wave equation well this is exactly what a physicist named oscar klein did in 1926 he

He subbed in the same energy and momentum operators that Schrodinger used and found this equation.

Klein's work was pretty well received by a number of his colleagues.

In fact, it turned out the two other physicists, Walter Gordon and Vladimir Falk, had independently arrived at the same equation in that same year.

It became known as the Klein -Gordon equation, which was a bit of a burn for Falk.

But that's often how it goes.

You do all the hard work and then no one notices.

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I wanna thank Hostinger for sponsoring this part of the video and now back to Klein, Gordon and Falk.

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The Klein, Gordon, Falk equation even made its way over to one of the fathers of quantum physics,

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Niels Bohr, who must've been impressed because at the 1927 Solvay Conference, Bohr was chatting to a promising young physicist about what he was working on.

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The young man said, I'm trying to get a relativistic theory of the electron.

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Bohr replied, but Klein has already solved this problem.

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The young man disagreed.

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So who was this bold 25 -year -old?

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He was Paul Dirac, a man who Bohr would later give the nickname the strangest man

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because he was truly one of a kind.

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The first time I went to Princeton, I met a couple who invited Dirac and his wife, and Dirac for the whole meal,

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which lasted three hours, didn't say a single word.

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Not one word.

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He wasn't sulking.

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He wasn't angry.

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He just saw no reason to speak.

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That's crazy.

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Dirac was a man of so few words that his colleagues invented a special unit, a dirac, equivalent to speaking one word per hour.

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Legend also has it that he liked to relax by climbing trees in three -piece suits.

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And that wasn't his only strange hobby.

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As a student, Dirac had attended seminars on Einstein's theory of relativity, and he'd kind of fallen in love with it.

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He was impressed by the elegance and beauty of its mathematics.

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To Dirac, this got to the core of what a good theory must do.

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He once said, It is more important to have beauty in one's equations than to have them fit experiment.

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Do you know why Dirac was so drawn to relativity?

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Einstein went in there and did it all, not all, but almost all by deductive reasoning.

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That made a huge impression on Dirac.

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He realized that it was advanced mathematics was really important to understanding the way that nature works.

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So Dirac found a new hobby, obsessively updating classical equations with Einstein's theory of relativity,

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so that they would now work for relativistic scenarios as well that are those approaching the speed of light.

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He later said this was like a game for him.

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And so it's maybe not too much of a surprise then

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that he was one of the people trying to unite quantum physics and relativity.

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Because a theory that would cover both of these would be truly beautiful in his eyes.

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Dirac didn't see the beauty in Klein, Gordon, and Fox's relativistic update of the Schrodinger equation.

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And he wasn't alone.

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Fellow physicist Wolfgang Pauli, after reading Klein's paper, wrote him a letter wishing his physics a speedy recovery.

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Pauli was known for being pretty savage, and actually the Klein -Gordon equation is useful in some cases.

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But he and Dirac were both concerned with one particular feature of the equation.

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And that's because the Klein -Gordon equation contains this term.

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That's a second -order time derivative, so the wave function is being differentiated twice with respect to time.

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Now, remember, the Schrodinger equation also contains a second -order derivative, but that's with space, not with time.

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Time is just first order.

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So why is this such a problem?

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Well, think of a very simple second -order time derivative.

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Something like d squared y over dt squared is equal to 3.

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Now, to figure out what y is, the function that satisfies this equation, we just have to integrate it twice.

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But notice, to find the solution, we now have two integration constants, c and d.

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And the problem is that we can only find that if we know both y at a given time,

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and if we know the first derivative of y at a given time.

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This makes sense physically if you think about, say, throwing a ball in the air.

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If you want to predict the ball's future motion, well, then you need to know where you threw it from,

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that's its position, and how hard you threw it, that's its velocity.

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Or in other words, you need to know both the position and the first derivative of the position.

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Similarly, to predict a quantum system's future state using the Klein -Gordon equation,

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you'd need the initial wave function and the initial first derivative of the wave function.

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Now, the beauty of the Schrodinger equation was that

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if you knew only the wave function of a system at a given time,

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you could use it to determine all the future states of that system.

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But in the Klein -Gordon equation, the wave function no longer told the whole story.

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And this introduced a further problem.

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The probability of finding a particle in a given area could

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no longer be simply described by the modulus of the wave function, as it was for the Schrodinger equation.

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For the Klein -Gordon equation, a new equation was needed to describe the probability using the wave function, which takes a while to derive,

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so we won't get into that here, but it looks like this.

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And the problem with that equation is that, unlike the simple modulus of the wave function, it can have negative solutions, negative probabilities.

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How can the chance of something happening be less than zero?

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As Dirac put it, that, of course, is physically nonsense.

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So Dirac did what Dirac does best, and he set out to find his own solution that contained no second -order time derivatives.

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First, he rewrote the relativistic energy -momentum relationship like this, which is a linear equation, so no squaring E, that is, no squaring the energy operator,

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which is what gave rise to that second -order time derivative in the Klein -Gordon equation.

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Now, he just had to solve this equation and find the coefficients alpha x, alpha y, alpha z, and beta, and he would have a solution.

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To do this, we can start by squaring both sides of the equation.

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Next, we can expand the momentum on the left -hand side into its three dimensions,

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and then expand the right -hand side to end up with this long equation.

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It might look pretty complicated, but there is a trick we can use.

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Notice that all these terms on the right -hand side are multiplied by pmc cubed, but on the left -hand side,

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there are no terms containing pmc cubed.

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So that tells us that when you multiply these coefficients together, like alpha times beta and beta times alphas, all of that must be zero.

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And similarly, notice that these terms are multiplied by two different momenta, like px and py times c squared,

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which also don't have a counterpart on the left -hand side.

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So these alpha times alpha terms must also be equal to zero.

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And that just leaves this top row.

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These terms do match on both sides, which tells us that alpha x squared must be equal to 1, and so must alpha y squared,

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alpha z squared, and beta squared.

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So Dirac now had a set of simultaneous equations for alpha x, alpha y, alpha z, and beta that he just needed to solve.

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That sounds easy, right?

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But it's not that straightforward.

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To see why, let's do some examples.

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So say alpha x is 1 and beta equals minus 1.

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Well, then we get 1 squared, which is 1, equals minus 1 squared, which is also 1.

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So that satisfies the top equation.

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But if we fill it in here, we get 1 times minus 1, which is just minus 1, plus minus 1 times 1,

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which is again minus 1, for a total of minus 2.

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So that doesn't work.

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So let's try another number.

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Say alpha x is 1, and now it's alpha z that is minus 1.

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Well, in that case, we get 1 times minus 1, so again we get minus 1, plus minus 1 times 1,

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again minus 1, so we again get minus 2.

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And in fact, if you look at this top equation, the only numbers that satisfy this relation is 1 and minus 1.

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So all these coefficients have to be either 1 or minus 1.

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But if you fill that in, then the only two possible answers you're going to get in these equations is minus 2 or positive 2.

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Now, the two equations that are giving problems are these two.

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And that's because alpha times beta is the same as beta times alpha.

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So you're always going to get minus 2 or 2.

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So the only way to get out of this is to somehow make the order of multiplication matter.

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But where do you find something like that?

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Let's think about a really simple vector, say 1 in the x -direction and 2 in the y -direction.

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If I reflect this vector along the line y equals x, and then reflect it about the x -axis, I get this.

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But if I start again and instead reflect it first about the x -axis, and then along y equals x,

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I get this, which is totally different.

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So the order matters.

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How do we express this mathematically?

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Mathematically, we need some way to represent transformations like reflections as a single coefficient, which means we need matrices.

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Matrices are arrays of numbers which encapsulate these transformations, telling us how to reflect, rotate, stretch, or squish across each dimension.

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Mathematically, the order we multiply them matters, since we multiply the rows of the first matrix by the columns of the second.

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A matrix that reflects along y equals x looks like this, and a matrix that reflects about the x -axis looks like this.

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And if I apply them to that original vector one by one, you can see how we end up with different results.

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And actually, using matrices in quantum mechanics was not completely out there.

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Dirac had already seen it done by Werner Heisenberg, his new, if unlikely, friend.

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Dirac and Heisenberg were very different characters.

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Heisenberg was charming and outgoing.

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Dirac hated socializing and small talk.

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Once, the two were on a cruise ship to a conference together, and Heisenberg spent a lot of time dancing with women on board.

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So Dirac asked him, why do you dance?

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Heisenberg replied, when there are nice girls, it is a pleasure.

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Dirac thought about this for a bit before saying, how do you know beforehand that the girls are nice?

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So they were pretty different guys, but Heisenberg had a profound impact on Dirac.

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Do you know what drew him to quantum mechanics initially?

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He always said that Heisenberg gave him his start.

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He always said that.

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In later life, he used to begin lectures when he was 70, even 80 years old with the following words.

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Quantum mechanics was discovered by Heisenberg in 1925.

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As a PhD student, Dirac had closely followed Heisenberg's work.

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And a few years earlier, Heisenberg had found that for certain properties, like position and momentum, the order of multiplication matters,

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so x times p is not the same as p times x.

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This was actually the beginning of Heisenberg's famous uncertainty principle,

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which says that there's a limit to how precisely we can know certain pairs of physical properties in quantum systems.

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It turns out that if the order of multiplication matters for two properties,

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like position and momentum, then that means there's an inherent uncertainty in their combined measurements.

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The order we measure them in will change the outcome.

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Heisenberg's mentor, Max Born, suggested that he could represent this mathematically by using matrices, because there the order of multiplication also matters.

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This led Heisenberg to a new form of quantum mechanics, which was mathematically equivalent to Schrodinger's equation, but it was based on matrix algebra.

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Dirac recognized something similar in his coefficients, where the order of multiplication clearly mattered.

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So he thought matrices might be the solution.

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For his coefficients, he tried two -by -two matrices, since they're the smallest, simplest matrices that could make the order of multiplication matter.

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He found that some worked with the equations.

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In fact, those reflection matrices we tried earlier worked well.

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But he just couldn't find solutions for all four coefficients that all work together.

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This is not simple.

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You're directly one of the smartest people of the 20th century in physics, right?

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But it was not easy.

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You don't have just to twiddle with bits of the Schrodinger equation.

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You have to do something completely radical.

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His working is in there and you could see him really struggling.

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Then Dirac had a stroke of genius.

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He said, I suddenly realized that there was no need to stick to quantities

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which can be represented by matrices with just two rows and columns.

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Why not go to four rows and columns?

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With these four 4x4 matrices, Dirac got these solutions to his simultaneous equations.

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A matrix with 1s on the diagonal is mathematically equivalent to a 1, and a whole array of 0s is the same thing as 0.

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So all of the equations were satisfied.

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Dirac had found coefficients that worked.

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Now, we can substitute those matrices back into Dirac's linear equation, then rewrite the 3 -momenta and alpha coefficients as vectors,

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and, just as we did with the Schrodinger and Klein -Gordon equations,

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we can use the energy and momentum operators to make both sides act on the wave function.

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If we substitute those operators in, we get Dirac's final equation for the relativistic free electron.

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The young man who spent his life looking for mathematical beauty had found, perhaps, his most beautiful equation of all.

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People were expecting the solution to be horrible, and it turned out to be a thing of beauty, right?

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It was something you look at and you think, that is absolutely amazing.

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It's a pattern that Dirac had found deep in nature.

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Nothing like that had been seen in physics at that time.

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To see some of that beauty, you only have to compare it to the Schrodinger equation, which you can see right here.

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Now, the two look very similar, but there is a lot hidden in the Dirac equation.

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First of all, it's relativistic, so it works at really, really high speeds because it uses Einstein's energy -momentum relationship.

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Unlike the Schrodinger equation, which breaks down there.

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But what's even more beautiful is that if you look at this, the Ruggs equation isn't just first order in time derivatives,

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it's also first order in spatial derivatives.

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Whereas the Schrodinger equation was second order in spatial derivatives.

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So you might wonder, well, why does that matter?

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Well, because not only does going first order in all derivatives solve the second order time derivative problem of the Klein -Gordon equation,

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it now also treats time and space symmetrically.

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And it becomes really important if you start thinking about relativity, where time and space are not separate dimensions.

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They're intertwined in a four -dimensional space -time.

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And while the Schrodinger equation had just a single component wave function, to make the wave function work with these four -by -four matrices,

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in the Ruck's case, you actually need a wave function that has four components.

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So it will look something like this.

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Psi 1, Psi 2, Psi 3, and Psi 4.

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The four -component wave function means that the Dirac equation describes four possible states for any quantum system,

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which reveals something Schrodinger's single wave function didn't.

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An electron at a given energy level actually has two possible states due to different orientations of its intrinsic angular momentum, spin up and spin down.

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This spin creates a tiny magnetic field, so these two states are like tiny magnets pointing in opposite directions.

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And that has an interesting implication.

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Take hydrogen, which has one proton and one electron.

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Classically, the electron whizzes around the proton.

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But if you switch to the perspective of the electron, well, now it's the proton that's moving.

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And since it's positively charged, that moving charge creates a magnetic field in the electron's frame of reference.

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So now you've got this electron, which has its own mini magnetic field, interacting with a larger magnetic field,

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and that interaction will be slightly different for a spin -up and a spin -down electron.

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And as a result, some energy levels of the electron split into two closely -spaced energy levels.

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And you can actually see this if you zoom into the emission spectrum for a hydrogen atom.

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Schrodinger's equation didn't predict that splitting, since it just had one solution for each energy level.

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But with Dirac's four -component solution, the top two wave functions now described two different spin states with two slightly different energies.

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Dirac admitted himself that he had never set out to capture spin in his equation.

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I started out this work without any intention at all of bringing in the spin of the electron.

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But hold on, because if an electron at a given energy level only has two possible spin states,

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then why do we have a four -component wave function?

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Why are there four states and not just two?

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Well, that's what brings us back to that 1928 lecture at the start,

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the one that seemed to drive even the most well -established quantum physicist mad, because that strange man presenting his work was actually Paul Dirac.

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Sharing his new equation with the world it was Dirac's beautiful equation that Heisenberg called the saddest chapter in modern physics

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To understand why all those physicists were losing their minds

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We only have to look at the simple case when a particle is at rest

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This term right here describes the momentum

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So when the particle doesn't move this becomes zero and it drops out which gives us this

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next we can sub in the energy for this quantum operator to get this

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so now we know that beta times mc squared must be equal to the particle's energy

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and if we write out beta

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and multiplied by mc squared then we find two positive solutions

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and two negative solutions for the energy

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so negative energy solutions are baked right into the rock equation this idea

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that a free electron could have negative energy was impossible for any of these physicists to accept

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because think about it if electrons can have a negative energy then

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that means that they could continually radiate positive energy

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that is emit photons and drop into lower

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and lower negative energy states there would be no limit to how far

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they could fall into the negative energy of this it looked like to many very smart people

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and dirac was smart enough to know they had a point

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that this equation it got the mass

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and the magnetic moment of the electron yes

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but on the other hand it predicts this ridiculous situation where they have negative energy values right that's nonsense

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so heisenberg said i give up this is just this is just ridiculous

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so dirac he had in some very clear sense had to

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rescue his equation dirac spent three years sticking to his guns

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he tried all sorts of ways to interpret his new equation to explain where the negative energy was coming from.

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Then, in 1931, he proposed something radical to explain the negative energy solutions.

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A new kind of particle, unknown to experimental physics, having the same mass and opposite charge to an electron.

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We may call such a particle an anti -electron.

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We should not expect to find any of them in nature on account of their rapid rate of recombination with electrons.

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So Dirac was proposing that those four states described in his four -component wave function are a spin -up electron,

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a spin -down electron, a spin -up anti -electron, and a spin -down anti -electron.

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When Dirac said that, people didn't stop running around saying where's this anti -electron, they just ignored it.

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Cut to the laboratory at Caltech. In 1932,

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a Caltech postdoc named Carl Anderson was working on a project trying to identify the charge particles produced by cosmic rays.

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He photographed the tracks these particles left in a cloud chamber containing a uniform magnetic field.

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Anderson noticed several instances of a similar track.

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It looked a lot like the tracks he'd seen left by electrons, only it curved in the opposite direction in the magnetic field,

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kind of like the tracks of positively charged protons.

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But there was no way it could be a proton based on the length of the track.

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It had traveled farther in air and therefore it had to be much lighter.

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It had to be something with around the same mass as an electron, but opposite charge.

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A positive electron, or as he named it, a positron.

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He actually also tried to rebrand electrons as negatrons, but that one didn't quite stick.

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Just one year after Dirac proposed the anti -electron, Carl Anderson found it, entirely by accident.

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But this alone doesn't get rid of the negative energy problem.

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Remember what we said earlier, if any particles, like these positrons,

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can have negative energy, then they could continually radiate energy and drop into lower and lower negative energy states.

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Fortunately, Dirac proposed a solution to this problem as well, although it was a little crazy.

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He theorized something called the Dirac Sea, describing a vacuum as an infinite sea of electrons occupying all available negative energy states.

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And since no two electrons can occupy the same state, this prevents observable positive energy electrons from falling into the negative energy states.

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A hole or vacancy in this sea then becomes a positron.

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When an electron and a positron meet and annihilate, well that's just an electron falling back into the sea and filling that hole.

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The theory is mathematically sound, of course it's Dirac we're talking about, but if you feel like it's hard to come to terms with the idea

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that we're floating on an infinite sea of electrons, well, you wouldn't be alone.

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It's not even that crazy if, I don't know, several decades later people find that exact model in a physical system.

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In condensed matter physics you see an exact analogy of also having electrons in the conduction

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Band and Save Phelan's Band.

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Yes, that's true.

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That's true.

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But Dirac really was, you know, out there.

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You see what I mean?

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Maybe it was people like, you know, really senior people saying, this is nonsense.

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But it was a way of Dirac's rectilinear thinking, thinking, well, maybe this one.

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And then it drove him to antimatter.

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Thankfully, in 1941, a Swiss physicist named Ernst Stuckelberg had a clever idea.

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The wave function contains a term that looks like this, where energy is multiplied by time.

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So we can see that if we just change the sign of time when the energy is negative, then we get the same result,

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because a negative multiplied by a negative gives us a positive.

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Stuckelberg took this, and he suggested that negative energy electrons traveling backwards in time are mathematically equivalent to positive energy anti -electrons,

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that is positrons, traveling forwards in time.

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A few years later, around 1948, Richard Feynman took this idea and used it in one of the most powerful tools in modern physics,

391

the Feynman diagrams.

392

In his sketches of particle interactions, he showed antiparticles traveling the opposite way to particles, backwards in time.

393

It was a brilliant trick.

394

Negative energy solutions no longer had to mean there was negative energy or a Dirac -C.

395

They simply indicated the presence of an antiparticle.

396

We now know that there's a corresponding antiparticle for every subatomic particle, with the same mass but opposite charge.

397

So the proton has the antiproton, the neutrino has the antineutrino, and so on.

398

According to his friend Heisenberg, that was the biggest leap in 20th century physics,

399

to say there's a whole slew of antiparticles corresponding to particles.

400

And Dirac got that through this crazy model.

401

But all is not solved.

402

This new anti -world introduces some big questions about the very nature of our universe.

403

Because particles and their antiparticles are equal and opposite,

404

when they come together, they annihilate and produce two photons with energy equivalent to their mass and kinetic energy.

405

And this process is reversible.

406

Two photons with the right energies can produce a matter and antimatter pair.

407

This is called bright wheeler pair production.

408

During the first moments after the big bang, the universe was hot, dense, and full of these pairs popping into and out of existence.

409

If an equal number of matter and antimatter particles were created, you would expect them to all annihilate each other in this dense environment,

410

leaving behind only energy.

411

But that didn't happen.

412

We ended up with a universe full of matter.

413

If we work backwards from how much matter and antimatter is in the universe today,

414

it's actually estimated that only one particle per billion of matter needed to survive this hot, dense era and not get annihilated.

415

That tiny difference would give us the makeup of our universe today, where matter dominates.

416

so what allowed that one particle per billion to escape annihilation why did matter win out over anti -matter

417

well that's a pretty big question with some not so simple answers

418

so we're doing an entire second video where we have some pretty spectacular stuff happening

419

we're getting into the beast it's absolutely insane i feel like i should not be in here

420

So you're making anti -atoms?

421

Yes.

422

It's so cool.

423

Dirac is probably less well -known than people like Heisenberg or Schrodinger, but his contribution to quantum physics was immense, and he was recognized for it.

424

He shared the 1933

425

Nobel Prize with Schrodinger for the discovery of new productive forms of atomic theory.

426

And perhaps this gave strange, quiet Dirac some newfound confidence, because that physicist in the audience of his 1928 lecture at the start,

427

Eugene Wigner, actually became a reasonable friend of Dirac's and in 1934 introduced Dirac to his sister,

428

Majit Wigner, a woman who would change Dirac's life perhaps more than any equation or Nobel Prize.

429

They were antiparticles, right?

430

They had completely different personalities.

431

He had almost no empathy right

432

and he knew it she had buckets of it he hardly talked

433

she couldn't stop talking you could just go on like they are completely different people

434

but the marriage did work my great friend Lillia Harris Chandra who knew them

435

she came out with a great line great line

436

which is he gave her status she gave him a life

437

so I guess there is one particle antiparticle pair that that never annihilated.

438

and it's the perfect way to challenge your friends.

439

Every time we play it at Veritasium, things get a little bit heated and that is so much fun.

440

If you want to go check it out, then head over to our Kickstarter where you can pre -order your own version.

441

And right now we've enabled global shipping, so no matter where you are in the world, you can get your own version.

442

We're coming close to the final few days of the Kickstarter campaign,

443

so this is your last chance to get your hands on the exclusive launch edition.

444

So if you want to support us, head over to Kickstarter by clicking the link in the description or scanning this QR code.

445

I want to thank you for all your support and most of all, thank you for watching.

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Từ vựng và ghi chú luyện nói cho bài học này

Bài luyện nói này dựa trên video “Why is there antimatter?”. Những từ được nhắc lại nhiều nhất trong bài: equation, energy, dirac, electron, particle. Video này có 445 câu và 6013 từ để luyện shadowing. Phần lời nói dài 35:22. Người nói nói với tốc độ tự nhiên, khoảng 170 từ mỗi phút, gần với hội thoại hằng ngày. Chỉ 77% số từ nằm trong 3.000 từ tiếng Anh thông dụng nhất, nên từ vựng khá khó.

Từ vựng quan trọng trong video

15 từ đáng học trong video, kèm phiên âm và nghĩa:

Từ	Phiên âm	Nghĩa
equation danh từ	/ɪˈkweɪ.ʒən/	phương trình
particle danh từ	/ˈpɑɹtək(ə)l/	hạt
electron danh từ	/ɪˈlɛk.tɹɑn/	ê-léc-trông, điện tử
momentum danh từ	/ˌmə(ʊ)ˈmɛntəm/	động lượng
quantum danh từ	/ˈkwɑntəm/	số lượng, lượng
minus	/ˈmaɪ.nəs/	trừ
physics danh từ	/ˈfɪz.ɪks/	vật lý học
spin động từ	/spɪn/	quay
derivative danh từ	/dɪˈɹɪvətɪv/	đạo hàm
beta danh từ	/ˈbeɪtə/	bêta
operator danh từ	/ˈɑpəˌɹeɪtɚ/	toán tử
mechanic danh từ	/mɪˈkænɪk/	thợ máy
reflect động từ	/ɹɪˈflɛkt/	phản chiếu
component danh từ	/kəmˈpoʊ.nənt/	bộ phận
lecture danh từ	/ˈlɛk.t͡ʃə/	bài giảng

Cụm động từ bạn sẽ nghe

Từ	Nghĩa
break down động từ	hỏng, hỏng hóc
check out động từ	tính tiền, trả phòng
give up động từ	đầu hàng
write down động từ	viết ra, ghi xuống

Những câu đáng luyện lại

Các câu ngắn, trọn ý trong video mà bạn có thể dùng lại khi giao tiếp hằng ngày:

I mean, what would that even mean?
To see why, let's do some examples.
How do we express this mathematically?
Do you know what drew him to quantum mechanics initially?
You see what I mean?

Ngữ pháp trong video

Những cấu trúc người nói dùng nhiều nhất, kèm đúng cụm từ trong video:

Cấu trúc	Trong video
Câu bị động be + quá khứ phân từ — nhấn vào việc xảy ra, không phải người làm	was based · is always measured · would be bound
Mệnh đề quan hệ who / which + mệnh đề — thêm thông tin về người hoặc vật	equation, which was · man who Bohr · this, which is
Thì hiện tại hoàn thành have/has + quá khứ phân từ — việc đã xảy ra nhưng còn liên quan đến hiện tại	have taken · have changed · has already solved

Phát âm cần chú ý

Người nói dùng 57 dạng rút gọn, ví dụ didn't, you're, we're. Hãy nói theo dạng ngắn đúng như bạn nghe.

Âm “th”: mathematics /mæθ(.ə)ˈmæt.ɪks/, mathematical /ˌmæθ(.ə)ˈmæt.ɪ.kəl/
Âm “sh” và “zh”: equation /ɪˈkweɪ.ʒən/, dimension /daɪˈmɛn.ʃən/, relation /ɹɪˈleɪʃ(ə)n/, transformation /ˌtɹæns.fɔɹˈmeɪ.ʃən/, dimensional /daɪˈmɛn.ʃə.nəl/
Từ dài — đặt trọng âm cho đúng: momentum /ˌmə(ʊ)ˈmɛntəm/, derivative /dɪˈɹɪvətɪv/, operator /ˈɑpəˌɹeɪtɚ/, probability /ˌpɹɑ.bəˈbɪl.ə.ti/, ridiculous /ɹɪˈdɪk.jə.ləs/

Những âm người Việt thường gặp khó:

Cụm phụ âm cuối — đọc đủ từng âm, đừng nuốt âm cuối: matrix /ˈmeɪ.tɹɪks/, physics /ˈfɪz.ɪks/, reflect /ɹɪˈflɛkt/, component /kəmˈpoʊ.nənt/, solve /sɒlv/
Âm /tʃ/, /dʒ/ và /ʒ/ — tiếng Việt không có, đừng đọc thành “ch” hay “gi”: equation /ɪˈkweɪ.ʒən/, lecture /ˈlɛk.t͡ʃə/, legend /ˈlɛd͡ʒ.ənd/, substitute /ˈsʌb.stɪ.tʃuːt/, hydrogen /ˈhaɪdɹəd͡ʒ(ə)n/
Âm /æ/ — mở miệng rộng hơn âm “e”: alpha /ˈæl.fə/, magnetic /mæɡˈnɛtɪk/, mechanic /mɪˈkænɪk/, classical /ˈklæs.ɪ.k(ə)l/, radical /ˈɹædɪkəl/

Cách luyện với video này

Nghe hết video một lần, chưa cần nói, và ghi lại những từ bạn chưa biết.
Bắt đầu ở tốc độ 0,75×, nói đuổi từng câu, rồi quay lại tốc độ bình thường khi đã quen.
Ghi âm giọng mình rồi so với bản gốc, chú ý các từ như equation, particle, electron.

Phương Pháp Shadowing Là Gì?

Shadowing là kỹ thuật học ngôn ngữ có cơ sở khoa học, ban đầu được phát triển cho chương trình đào tạo phiên dịch viên chuyên nghiệp và được phổ biến rộng rãi bởi nhà đa ngôn ngữ học Dr. Alexander Arguelles. Nguyên lý cốt lõi đơn giản nhưng cực kỳ hiệu quả: bạn nghe tiếng Anh của người bản xứ và lặp lại to ngay lập tức — như một "cái bóng" (shadow) đuổi theo người nói với độ trễ chỉ 1–2 giây. Khác với luyện ngữ pháp hay học từ vựng bị động, Shadowing buộc não bộ và cơ miệng phải đồng thời xử lý và tái tạo ngôn ngữ thực tế. Các nghiên cứu khoa học xác nhận phương pháp này cải thiện đáng kể phát âm, ngữ điệu, nhịp điệu, nối âm, kỹ năng nghe và độ lưu loát khi nói — đặc biệt hiệu quả cho người luyện IELTS Speaking và muốn giao tiếp tiếng Anh tự nhiên như người bản ngữ.

Phương pháp shadowing: đọc hướng dẫn từng bước đầy đủ →

Luyện nói tiếng Anh bằng Shadowing qua video: Why is there antimatter?

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Từ vựng và ghi chú luyện nói cho bài học này

Từ vựng quan trọng trong video

Cụm động từ bạn sẽ nghe

Những câu đáng luyện lại

Ngữ pháp trong video

Phát âm cần chú ý

Cách luyện với video này

Phương Pháp Shadowing Là Gì?