رونوشت 🔗
WEBVTT
00:00:00.000 --> 00:00:04.959
When the electron became a wave, the Schrdinger bohrer and the music inside the atom.
00:00:06.320 --> 00:00:14.640
Welcome back to Quantum on the Treadmill, where I use my time on the treadmill to explore the people, ideas, and strange turns that created quantum mechanics.
00:00:14.880 --> 00:00:21.760
In our journey so far, we have seen physicists slowly dismantle the comfortable mechanical universe inherited from Newton.
00:00:22.000 --> 00:00:25.519
Planck discovered that energy seemed to come in discrete packets.
00:00:25.760 --> 00:00:28.879
Einstein proposed that light itself could behave as particles.
00:00:29.199 --> 00:00:37.119
Bohr then placed those ideas inside the atom, arguing that electrons could occupy only certain energy levels and could jump from one level to another.
00:00:37.359 --> 00:00:42.560
Bohr's model worked surprisingly well, but it left behind an enormous unanswered question.
00:00:42.799 --> 00:00:43.119
Why?
00:00:43.280 --> 00:00:47.759
Why could an electron occupy one energy level but not the space between levels?
00:00:47.920 --> 00:00:50.320
Why were only certain orbits permitted?
00:00:50.479 --> 00:00:55.280
And what exactly happened when an electron performed one of Bohr's mysterious quantum jumps?
00:00:55.439 --> 00:01:00.320
Bohr had discovered an astonishing rule about nature, but he had not really explained where the rule came from.
00:01:00.560 --> 00:01:04.640
Then Erwin Schrödinger entered the story and proposed something even stranger.
00:01:04.799 --> 00:01:09.280
What if the electron was not best understood as a tiny object traveling around the nucleus?
00:01:09.439 --> 00:01:12.000
What if it had to be understood as a wave?
00:01:12.319 --> 00:01:14.400
The problem with Bohr's atom.
00:01:15.359 --> 00:01:17.120
Bohr's atom is easy to picture.
00:01:17.200 --> 00:01:19.040
It resembles a miniature solar system.
00:01:19.200 --> 00:01:24.480
The nucleus sits in the center like the sun, while electrons travel around it in permitted orbits.
00:01:24.560 --> 00:01:26.719
But Bohr's orbits were not ordinary orbits.
00:01:26.879 --> 00:01:35.200
A planet can circle the Sun at many different distances, move it slightly closer or farther away, and it simply settles into a different orbit.
00:01:35.439 --> 00:01:37.680
Bohr said electrons could not do that.
00:01:37.920 --> 00:01:40.400
They could exist only at particular energy levels.
00:01:40.560 --> 00:01:45.200
An electron could occupy one level or another, but it could not settle halfway between them.
00:01:45.439 --> 00:01:52.319
When an electron moved from a higher energy level to a lower one, the atom released the difference as a specific packet of light.
00:01:52.480 --> 00:02:01.040
That helped explain why atoms produced distinctive lines of color rather than a continuous rainbow, but Bohr had essentially declared that only certain orbits were allowed.
00:02:01.200 --> 00:02:05.280
His model did not explain
Load full transcript
why nature selected those particular orbits.
00:02:05.439 --> 00:02:07.840
It is also worth clearing up a common confusion.
00:02:08.000 --> 00:02:11.120
Bohr's model was about electrons orbiting the nucleus.
00:02:11.199 --> 00:02:13.039
It was not about electron spin.
00:02:13.199 --> 00:02:16.639
Spin is a separate quantum property that entered the story later.
00:02:16.800 --> 00:02:22.000
Although we use the word spin, an electron is not simply a tiny ball rotating like Earth.
00:02:22.240 --> 00:02:25.919
Bohr was still trying to preserve part of the old mechanical picture.
00:02:26.080 --> 00:02:29.039
The electron remained a particle traveling along an orbit.
00:02:29.199 --> 00:02:33.919
Schrödinger would eventually replace that picture with something much less familiar.
00:02:34.400 --> 00:02:36.240
A wave before Schrdinger.
00:02:37.199 --> 00:02:39.599
The idea did not begin entirely with Schrdinger.
00:02:39.919 --> 00:02:46.960
A few years earlier a young French physicist named Louis de Broly had noticed a strange imbalance in quantum physics.
00:02:47.199 --> 00:02:53.919
Einstein had shown that light, which had long been understood as a wave, could also behave like a collection of particles.
00:02:54.080 --> 00:02:56.560
De Broly asked a wonderfully simple question.
00:02:56.800 --> 00:03:00.240
If a wave can behave like a particle, could a particle behave like a wave?
00:03:00.400 --> 00:03:05.120
He proposed that material objects, including electrons, have a wavelength associated with them.
00:03:05.280 --> 00:03:08.080
An electron with greater momentum would have a shorter wavelength.
00:03:08.240 --> 00:03:15.919
An electron with less momentum would have a longer wavelength, and this sounded radical, but it gave Schrödinger a clue about Bohr's permitted orbits.
00:03:16.159 --> 00:03:18.560
Imagine a wave traveling around a circle.
00:03:18.800 --> 00:03:21.840
After completing one trip, the wave has to meet itself again.
00:03:22.000 --> 00:03:28.000
If the crest of the returning wave meets another crest and the trough meets another trough, the wave reinforces itself.
00:03:28.159 --> 00:03:29.599
It creates a stable pattern.
00:03:29.759 --> 00:03:34.080
But if a crest returns and meets a trough, the wave begins to cancel itself out.
00:03:34.240 --> 00:03:36.080
That pattern cannot remain stable.
00:03:36.240 --> 00:03:38.479
This is similar to what happens on a guitar string.
00:03:38.639 --> 00:03:41.280
A string cannot produce just any stable vibration.
00:03:41.599 --> 00:03:43.280
The wave must fit the length of the string.
00:03:43.439 --> 00:03:45.680
Some patterns fit perfectly and produce clear notes.
00:03:45.840 --> 00:03:48.400
Other patterns interfere with themselves and quickly disappear.
00:03:48.560 --> 00:03:52.080
Schrdinger began to see the electron around the nucleus in a similar way.
00:03:52.319 --> 00:03:57.759
Perhaps Bohr's permitted energies existed because only certain electron waves could form stable patterns.
00:03:57.919 --> 00:04:02.719
The forbidden spaces between Bohr's levels were not being prohibited by an arbitrary rule.
00:04:02.960 --> 00:04:05.039
They were patterns that simply could not fit.
00:04:05.199 --> 00:04:07.120
Bohr had identified the permitted notes.
00:04:07.280 --> 00:04:10.080
Schrdinger was beginning to discover the instrument.
00:04:10.400 --> 00:04:12.560
What did Schrdinger mean by a wave?
00:04:13.680 --> 00:04:21.439
When we hear the word wave, we usually imagine water rising and falling, a sound moving through the air, or a guitar string vibrating back and forth.
00:04:21.680 --> 00:04:24.240
In each case, something appears to be waving.
00:04:24.399 --> 00:04:28.720
Water waves involve moving water, sound waves involve changing pressure in the air.
00:04:28.879 --> 00:04:31.439
A guitar string physically changes position.
00:04:31.600 --> 00:04:33.600
So what was waving in Schrdinger's theory?
00:04:33.759 --> 00:04:36.399
That became one of the deepest questions in quantum mechanics.
00:04:36.639 --> 00:04:44.720
Schrdinger initially hoped that an electron might literally be a physical wave, perhaps a distribution of electrical charge spread through space.
00:04:44.879 --> 00:04:46.959
But this interpretation created problems.
00:04:47.120 --> 00:04:52.959
When physicists detect an electron, they do not normally find fragments of it scattered throughout the laboratory.
00:04:53.120 --> 00:04:56.160
They detect a complete electron in a particular place.
00:04:56.319 --> 00:05:01.199
The physicist Max Born offered the interpretation that eventually became standard.
00:05:01.439 --> 00:05:07.120
Schrödinger's wave does not describe a material substance spread through space in the ordinary sense.
00:05:07.279 --> 00:05:09.839
It describes the possibilities for what we might observe.
00:05:10.000 --> 00:05:13.120
The wave is represented by something called the wave function.
00:05:13.279 --> 00:05:17.600
The wave function contains information about the electron's quantum state.
00:05:17.839 --> 00:05:24.879
When physicists mathematically square its magnitude, they obtain the probability of detecting the electron in different places.
00:05:25.120 --> 00:05:29.040
Where the wave function is strong, the electron is more likely to be detected.
00:05:29.199 --> 00:05:32.560
Where it is weak, the electron is less likely to be detected.
00:05:32.720 --> 00:05:36.000
Where it falls to zero, the electron will not be detected.
00:05:36.160 --> 00:05:42.720
This is not merely a statement that the electron occupies a definite position, and we happen not to know where it is.
00:05:42.959 --> 00:05:48.079
Before measurement, quantum mechanics describes the electron through a spread of possible outcomes.
00:05:48.319 --> 00:05:51.279
That is one of the most difficult shifts in the quantum story.
00:05:51.519 --> 00:05:57.279
The wave is not necessarily a wave of physical stuff, it is a structured wave of possibility.
00:05:58.000 --> 00:06:00.480
How Schrodinger found his equation.
00:06:01.439 --> 00:06:04.160
Schrodinger now needed more than an interesting picture.
00:06:04.319 --> 00:06:07.680
He needed an equation that could describe how these matter waves behaved.
00:06:07.920 --> 00:06:09.759
He drew together several different clues.
00:06:09.920 --> 00:06:14.160
The first was de Broly's connection between a particle's motion and its wavelength.
00:06:14.240 --> 00:06:17.360
The second came from the traditional mathematics of waves.
00:06:17.600 --> 00:06:23.199
Physicists already had equations describing how waves change through space and time.
00:06:23.439 --> 00:06:30.639
The third clue came from classical mechanics, particularly the work of the 19th-century mathematician William Rowan Hamilton.
00:06:30.800 --> 00:06:35.040
Hamilton had developed an elegant way to describe the motion and energy of physical systems.
00:06:35.199 --> 00:06:43.279
Schrdinger noticed that parts of Hamilton's mechanics looked remarkably similar to the mathematics used to describe the movement of waves and light.
00:06:43.439 --> 00:06:47.519
This suggested that classical particles might be only part of a larger picture.
00:06:47.759 --> 00:06:54.480
A ray of light looks as though it follows a precise path, but underneath that path is a spreading electromagnetic wave.
00:06:54.639 --> 00:07:00.160
Perhaps the paths of classical particles were also approximations of some deeper wave behavior.
00:07:00.319 --> 00:07:08.480
Schrdinger looked for an equation that combined the electron's total energy, its motion, the forces acting upon it, and its wave-like nature.
00:07:08.639 --> 00:07:18.480
In plain language, the equation asks something like this: given the energy of a quantum system and the forces acting within it, what wave patterns are possible and how will those patterns change over time?
00:07:18.720 --> 00:07:22.879
For an electron bound to a nucleus, Schrdinger searched for stable wave patterns.
00:07:22.959 --> 00:07:28.319
He effectively treated the atom like a three-dimensional musical instrument and asked which notes it could play.
00:07:28.560 --> 00:07:32.160
When he solved the equation for hydrogen, something extraordinary happened.
00:07:32.319 --> 00:07:33.920
Only particular solutions worked.
00:07:34.079 --> 00:07:36.959
Each acceptable wave pattern came with a particular energy.
00:07:37.199 --> 00:07:43.360
Those energies matched the levels Bohr had already proposed and the spectral lines scientists had observed in experiments.
00:07:43.519 --> 00:07:49.519
But Schrdinger had not placed Bohr's energy levels into the theory as special rules.
00:07:49.759 --> 00:07:52.639
The energy levels emerged naturally from the equation.
00:07:52.879 --> 00:07:53.839
That was the breakthrough.
00:07:54.000 --> 00:07:57.519
Bohr said the electron was permitted to occupy only certain energies.
00:07:57.680 --> 00:08:04.800
Schrdinger showed that only certain wave patterns could exist as stable states from orbits to orbitals.
00:08:05.439 --> 00:08:08.639
Schrödinger's work also changed the picture of the atom.
00:08:08.879 --> 00:08:13.040
In Bohr's model, electrons traveled along defined orbits.
00:08:13.199 --> 00:08:16.639
In Schrdinger's quantum mechanics, electrons occupied orbitals.
00:08:16.720 --> 00:08:19.519
The words sound similar, but they describe very different ideas.
00:08:19.680 --> 00:08:20.959
An orbit is a path.
00:08:21.120 --> 00:08:26.000
An orbital is a three-dimensional probability pattern produced by the wave function.
00:08:26.160 --> 00:08:29.279
The simplest orbital around a nucleus is spherical.
00:08:29.519 --> 00:08:35.679
Other orbitals form shapes that resemble dumbbells, rings, or more complicated arrangements of lobes.
00:08:35.840 --> 00:08:39.440
These shapes do not represent solid containers holding the electron.
00:08:39.519 --> 00:08:42.720
They show where the electron is more or less likely to be detected.
00:08:42.960 --> 00:08:48.240
The shapes arise for the same basic reason that different musical notes have different vibration patterns.
00:08:48.320 --> 00:08:50.720
They are the permitted standing waves of the atom.
00:08:51.200 --> 00:08:55.919
This also helps explain why electrons do not simply fall into the nucleus.
00:08:56.080 --> 00:09:01.279
An electron in an atom is not a tiny planet gradually losing energy and spiraling inward.
00:09:01.440 --> 00:09:04.000
It occupies a stable quantum state.
00:09:04.159 --> 00:09:09.200
The lowest energy state is the lowest permitted note of the atomic instrument.
00:09:09.360 --> 00:09:13.840
There is no lower stable wave pattern into which it can continuously collapse.
00:09:14.080 --> 00:09:16.480
That's why Schrodinger's equation matters.
00:09:17.679 --> 00:09:24.960
Schrodinger's equation became one of the foundations of modern physics because it did far more than improve Bohr's model of hydrogen.
00:09:25.120 --> 00:09:28.559
It helped explain the structure of more complicated atoms.
00:09:28.799 --> 00:09:36.799
Those atomic structures helped explain chemical bonds, the organization of the periodic table, and why different elements behave differently.
00:09:37.039 --> 00:09:45.200
Chemistry became understandable at a deeper level because the ways atoms combine are largely determined by the quantum states of their electrons.
00:09:45.360 --> 00:09:54.799
The same framework eventually helped us understand solids, semiconductors, lasers, superconductors, molecular biology, and much of modern material science.
00:09:55.039 --> 00:10:02.000
The computers and phones we use today depend on technologies built from our ability to understand and manipulate electron states.
00:10:02.159 --> 00:10:09.360
Schrdinger's equation plays a role in quantum mechanics similar to the role Newton's laws play in classical mechanics.
00:10:09.519 --> 00:10:18.879
If we know the initial quantum state and the forces acting on the system, the equation tells us how the wave function develops over time, but it comes with an important mystery.
00:10:19.039 --> 00:10:23.679
The Schrdinger equation describes the wave function changing smoothly and predictably.
00:10:23.840 --> 00:10:26.559
Measurement, however, gives us one definite outcome.
00:10:26.639 --> 00:10:30.159
We do not observe a blurred mixture of possible electron locations.
00:10:30.320 --> 00:10:41.440
We detect the electron in one place, and the equation tells us how the field of possibilities evolves, but it does not by itself completely explain why one particular possibility becomes the result we experience.
00:10:41.600 --> 00:10:52.480
That gap would produce some of the greatest arguments in twentieth century physics, including debates between Einstein and Bohr and Schrdinger's own famous story about a cat that appears to be both alive and dead.
00:10:53.279 --> 00:10:54.879
The bigger shifts.
00:10:55.519 --> 00:11:01.200
The real importance of Schrdinger's work was not merely that he found a better way to calculate atomic energies.
00:11:01.360 --> 00:11:05.200
He changed what physicists thought a physical explanation could look like.
00:11:05.519 --> 00:11:08.559
Bohr still gave us something resembling a mechanical model.
00:11:08.720 --> 00:11:12.320
There was a nucleus, an electron, and a collection of permitted orbits.
00:11:12.480 --> 00:11:16.639
Schrdinger replaced those orbits with mathematical waves of possibility.
00:11:16.879 --> 00:11:21.360
The electron did not simply have a hidden path waiting for us to discover it.
00:11:21.519 --> 00:11:25.519
Its quantum state was spread across a range of possible observations.
00:11:25.679 --> 00:11:31.440
The stable structures inside the atom were not miniature planetary systems, they were standing wave patterns.
00:11:31.600 --> 00:11:33.919
This is the transition I find most helpful.
00:11:34.159 --> 00:11:36.799
Bohr discovered that the atom played only certain notes.
00:11:37.039 --> 00:11:40.559
De Broly suggested that matter itself might have a wavelength.
00:11:40.799 --> 00:11:46.159
Schrdinger built the equation that revealed the instrument and explained why only those notes were possible.
00:11:46.399 --> 00:11:52.879
Born then told us that the music was not describing where the electron definitely was, it was describing where the electron might be found.
00:11:53.039 --> 00:11:56.159
Schrdinger therefore solved one mystery while opening another.
00:11:56.320 --> 00:12:00.399
He showed how the strange jumps in Bohr's atom could emerge from stable waves.
00:12:00.559 --> 00:12:03.840
But he also forced physics to confront a more unsettling question.
00:12:04.000 --> 00:12:10.720
If the quantum wave describes many possibilities, how does the world we observe end up giving us only one reality?
00:12:10.960 --> 00:12:14.159
And that is where our walk through quantum history becomes even stranger.