Quantum Theory Made Easy [1]

the year was 1919 zuv solving a problem that had haunted him for the better part of a decade what was the relationship between the intensity of a blackbody like the Sun and the frequency of the light that it emitted though he had at last arrived at an answer Planck was dissatisfied his solution utilized the ideas of Ludwig Boltzmann ideas so outrageous that almost nobody accepted them but because no conventional attempt at a solution was forthcoming Planck employed these highly unorthodox ideas out of desperation little did he know that in doing so he had plunged headfirst into realms of physics have their two unknown and untested what he discovered would fundamentally change our understanding of nature forever in order to begin to understand what motivated the development of quantum theory one must first understand the status of physics at the end of the 19th century at the time there were three main branches of physics first there was mechanics which was designed to predict the motions of masses things that were influenced by gravity then there was thermodynamics which was concerned with the relation of heat and temperature to energy and forces finally there was a lecture magnetism which dealt with interactions between charged particles it is within the realm of electromagnetism that the story of quantum mechanics begins in the early 1860s James Clerk Maxwell had produced a set of equations that summarized electromagnetism before Maxwell electricity and magnetism were considered two separate forces but as the 19th century progressed it steadily became more and more clear that these two interactions were fundamentally related as it turned out they were both the product of charge charge is an analogue of mass like mass charges an inherent property of matter that is associated with the fundamental interaction mass produces gravitational fields and these fields cause masses to attract to one another similarly charge produces electric fields which interact with other charges by causing them to either attract or repel the concept of fields can be somewhat counterintuitive so it might be helpful to think of them as odors the closer you are to the source of an odor the more strongly you'll feel its effects if you dislike the odor you'll tend to move away from the source but if you find the odor attractive you'll tend to come in closer electric fields work analogously opposite charges will be pulled toward each other because their fields or odors attract one another like charges will move away from each other because their fields repel them when these charges begin to move they generate magnetic fields which further effect the motions of other charges additionally it was discovered that not only to changing the leg trick fields generate magnetic fields but changing magnetic fields will also produce changing electric fields moving a charged particle will produce magnetic effects moving a magnet will generate electric voltage taken together what this all suggests is that electricity and magnetism are different aspects of the same force the theory of electromagnetism involved many difficult derivations and meticulous experiments but when the dust finally settled it became clear to all that not only are electric and magnetic phenomena fundamentally the same force but that electric and magnetic fields could together produce a wave a wave is a disturbance that travels through some material called a medium when this string experiences an impulse a disturbance passes through it the same general principle applies to sound waves which in the common case are a disturbance passing through air molecules waves at the beach are also based on the same concept disturbances passed through the water manifesting themselves in these familiar forms what's crucial to recognize is that in each case the medium itself the string the air molecules the water is not moving from one end to the other they are simply being displaced by the energy that's passing through so what happens when you take an electric charge and start to shake it back and forth analogously to the way this boy is shaking the string the electric field surrounding the charge will start to oscillate as a result of this change in the electric field an oscillating magnetic field will be generated which in turn will create an oscillating electric field and on and on it will go the result is an electromagnetic wave according to Maxwell's equations the speed with which an electromagnetic wave travels is equal to the speed of light this led him to conclude that light is a type of electromagnetic wave as it turns out there are many different types of electromagnetic waves while they all fundamentally have the same structure they differ in their wavelengths and frequencies wavelength is defined as the distance between successive crests in a wave frequency is defined as the number of complete wave sets to pass through a point per unit time generally we measure frequencies in hertz which is defined as the number of waves passing through a point per second since frequency and wavelength are inversely related electromagnetic waves with higher frequencies like x-rays and gamma-rays will have shorter wavelengths the contrapositive holds true as well longer wavelengths like those of radio waves and microwaves have lower frequencies so at the end of the day it was determined that light is just a disturbance of electric fields and magnetic fields the wave picture of light was fully developed and experiments had vindicated the notion that light was a wave interference diffraction dispersion these behaviors are characteristic of waves and waves alone and light exhibited each of them light was a wave and that was the end of the story then Along Came Max Planck in the final years of the 19th century Planck was experimenting with blackbody radiation all black bodies which are objects that perfectly emit and absorb electromagnetic radiation release energy in the form of heat and light actually most of the energy released by a blackbody takes the form of heat and it was Planck's hoped that by understanding the fundamental relationship between the intensities and the frequencies of the light that black bodies emit he would be able to develop a more efficient light bulb when that maximized light output and minimized heat output but there was a problem the classical theory predicted that as higher frequencies of the emitted electromagnetic waves are considered their intensities approach infinity and the universe should be burning in an inconceivable blaze of blackbody radiation this evidently wasn't happening so obviously there was a problem a problem that came to be known as the ultraviolet catastrophe though it was not Planck's mission to tackle this problem he did end up resolving it by introducing an assumption that at the time seemed outrageous in a private correspondence with his friend Planck referred to the implementation of his assumption as an act of despair and that he was willing to forego all of his previous conceptions about physics if it meant arriving at a curette solution the assumption that Max Planck made was that energy rather than coming in a continuous mesh of smooth values came in discrete granular packets which came to be known as quanta formally the assumption that he made can be expressed with this equation e equals n HF energy equals some integer times some constant that would later come to be named after plunk times the frequency of one of the standing electromagnetic waves inside of the black body cavity a standing wave is what you get when two waves traveling in opposite directions interfere with one another and form a single wave whose Peaks appear to move up and down so what Planck specifically ended up assuming was that the energy spectrum of standing waves within a black body cavity was not continuous as the classical way of thinking posited rather there were specific values that the energies could take and that any other values including values between the allowed ones were impossible put simply here's what happened classical physics tells us that energy is like a ramp to get from one end of the slope to the other you can step on pretty much any part of the ramp there are an infinite number of places you could occupy between the top and the bottom and these points are all separated by infinitely small distances what Planck assumed was that energy is like a staircase you can stand here here here here and here but you cannot stand here or here and the distance that separates each of these allowed energy levels is scaled by some factor of Planck's constant the general principle that Planck had assumed and applied to energy is called quantization one Splunk had made his assumption he was able to derive an equation that accurately modeled the distribution of blackbody radiation intensity as a function of temperature and frequency heat at long last found a solution to the problem that he labored over and he eventually got a Nobel Prize for doing so Planck then proceeded to measure his constant which would go on to become the most important number in all of quantum physics and found that I had dimensions of energy times time today the accepted value for Planck's constant and standard international units is about six point six to six times 10 to the negative 34 joule-seconds were equivalently four point 136 times 10 to the negative 15 electron volt seconds it is an incredibly tiny number and it appears in almost every equation in quantum mechanics often with two pi and the denominator this expression is so common in fact that a new letter was invented to represent it H bar which denotes Planck's reduced constant H bar equals H divided by 2 pi because this number is so small we don't notice the effects of quantization in our everyday lives when you zoom out and look at the staircase from the perspective of a human being who regularly deals with ranges of energy considerably larger than the ones dealt with in quantum physics the staircase looks like a ramp this is what gives rise to the classical way of thinking it's a situation akin to looking at a piece of paper and considering it flat but then placing it under a microscope and seeing that it is anything but such as nature Planck's assumption seems to suggest but Planck didn't really like this the assumption of quantization was simply at odds with everything that was known about physics at the time to understand why consider a standing wave like the ones inside of the cavity of a blackbody and suppose that this particular light wave is a bluish violet light which is a frequency of about seven hundred and twenty five trillion Hertz multiplying by Planck's constant we find that the energy content of this light is some integer multiplied by three electron volts this means that the wave can have an energy of three electron volts six electron volts nine electron volts and so on but it can never contain one two four or any number of electron volts that is not an integer multiple of three this is a strange result because it's analogous to saying that you can push someone on a swing by one foot or four feet but by no amount in between and again the explanation for why such strange consequences didn't seem to take place in people's every lives is because Planck's constant which dictates the scale of quantization is such an incredibly tiny number still the wisdom of the day was that such a preposterous picture of reality couldn't possibly be right Planck had arrived at a solution to the ultraviolet catastrophe that actually worked but doing so required him to make an assumption that didn't seem to have any basis in reality there didn't seem to be any good reason for why the energy of an electromagnetic wave should be quantized more importantly it seemed to contradict the well-established picture that light was a wave waves are not granular they do not contain distinct constituents disturbances passing through media simply don't have discrete elements perhaps the medium itself may have individual components but the wave passing through it ridiculous waves are not reducible to tiny pieces and both the maths and the experiments seem to confirm this therefore Planck and the scientific community as a whole regarded the assumption of quantization as a mere mathematical trick nobody actually believed that the quantum picture of light had any basis in reality so nobody paid much attention to it nobody except for a nameless and faceless clerk working in a Swiss Patent Office in 1905 this clerk published an analysis of Brownian motion which made predictions that ultimately led to the confirmation of the existence of atoms he established that the universe has a speed limit and that space and time are relative he constructed the most famous equation in physics and he showed beyond a shadow of a doubt that Planck's mathematical trick manifested itself in a very real way the year in which Einstein did all this became known as the annus mirabilis a year of miracles when Einstein was still a child the physicist Heinrich Hertz whose claim to fame was his experimental vindication of electromagnetic waves and after whom the unit of frequency was named discovered an anomalous phenomenon that later became known as the photoelectric effect it works like this when light is shined onto a metal surface the energy from the incoming electromagnetic waves gets transferred to the electrons in the metal the electrons are initially bound to the metal but the sudden kick and energy that they receive causes some of them to escape we called these escaped electrons photoelectrons the manner in which light behaved in the photoelectric effect was anomalous it didn't seem to do what electromagnetic waves were expected to do this experimental setup of the photoelectric effect involves a white light which is composed of all frequencies of light shining onto a metal who's outgoing photo electrons have their energies measured and displayed on the right first a red filter is placed in front of the light which means that only red light is hitting the metal the needles position is at zero which means that no electrons are being kicked out of the metal the process is repeated first with a yellow filter then with a green one and finally with a blue filter notice that in each case the needle immediately jumps to a specific position on the energy measuring device and that it stays there the entire time the filter is in place this means that photo electrons are immediately being kicked out of the metal the moment they get struck by the light and that the energy with which they're escaping is not changing also notice that the energy increases as the filters admit electromagnetic waves with higher frequencies this suggests that the energy of photoelectrons and by extension the energy of the light waves that are knocking them out of the metal is related to the frequencies of the incident light to a physicist in the early 20th century these results were a complete enigma according to the wave picture of light the photoelectric effect should occur at any frequency but should rise with intensity yet experiments showed that the intensity of the incident light was irrelevant to how energetic the outgoing photo electrons were it doesn't matter how much red light you shine onto a metal the photoelectric effect simply won't occur on the other hand you could shine a far less intense beam of ultraviolet light onto the metal and the energies of the photo electrons will be off the charts this shows that the photoelectric effect is a sort of all-or-nothing process either light is energetic enough to kick the electron out of the metal or it isn't there's a quota of energy the threshold energy that simply isn't being met when red light is shining onto a metal none of this was consistent with the behavior of waves according to the wave picture of light as more of these monochromatic electromagnetic waves were fired at the metal the amount of energy that they released should have steadily increased as the incoming light rays combined their energies yet we clearly saw that the energies of the photoelectrons for each separate frequency remained constant this characteristic is more akin to that of a stream of particles where each individual piece of the light beam contains the same amount of energy and thus releases the same amount of energy as every other piece of light preceding and succeeding it so if light is just a stream of particles it follows that monochromatic light having a narrow range of frequencies and thus a narrow range of energies should yield a constant energy output which is exactly what we observed finally the wave picture of light predicts that there should be a buildup of energy prior to there being a photoelectric effect due to the existence of the work function the work function whose empirically determined value varies with the type of material being considered is the amount of energy needed by an electromagnetic wave to free an electron from the metallic surface basically it's the threshold energy according to the wave picture of light if a light wave has low enough intensity then the energy of incoming light beams should gradually build up energy until the energy of the light overcomes the work function at which point the photoelectric effect may occur yet we observed that the photoelectric effect took place immediately there was no need for a buildup of wave energy because once again individual pieces of light either were capable of knocking out electrons or weren't and this capability was determined immediately you can have a beam of red light shining from a spotlight and it will never release a single electron from the metal no matter how long you shine it on there then you could have a beam of violet light shining out of a little laser pointer and the metal will immediately start shooting out electrons from all this information Einstein found that the maximum kinetic energy of each photo electron que max equals HF minus Phee where k max is the maximum energy of an outgoing photoelectron h is planck's constant-- F is the frequency of the light beam and fee is the work function which again depends on the material being illuminated now think again about what's happening during the photoelectric effect light which has a certain amount of energy is hitting an electron that has zero kinetic energy since the electron is stationary if it transfers all of its energy into the electron then the kinetic energy of the outgoing photo electron is equal to the lights energy minus whatever energy was needed to free the electron and this is exactly what the equation is saying this term is the kinetic energy of the outgoing photo electron and this term is the energy needed to free it so this term must be equal to the energy that the incoming light contained since the experiments seem to indicate that individual packets of light were responsible for the photoelectric effect as opposed to entire beams of light waves this expression refers to the energy of a single particle of light a quantum of light a photon the energy of a photon is Planck's constant times the photons frequency this formula is called the Planck Einstein relation it was Einsteins analysis of the photoelectric effect the first solid bit of evidence of the granular nature of light that would eventually win him his first and only Nobel Prize in Physics but it would still be a while before Einsteins photon model of light would gain widespread acceptance within academia though his model showed that light can behave like a particle when being absorbed there was no indication that light could behave like a particle when being emitted or in the intervening time between emission and absorption one decade before Einstein published his groundbreaking analysis on the photoelectric effect an experiment opposite to the previous one had been performed by another german physicist named Wilhelm roentgen who produced the first x-rays he did this by firing high-energy electrons at a piece of metal which yielded electromagnetic radiation that was almost entirely in the x-ray region of the electromagnetic spectrum the phenomenon was called bremsstrahlung according to the wave picture of what should have happened was that when the incident electron struck the atoms in the metal sheet there should have been a shower of electromagnetic radiation in every frequency this is analogous to striking a symbol which will produce sound waves that cover an entire portion of the audio spectrum this is not what happened though the resulting electromagnetic waves were x-rays they didn't include all x-ray frequencies in fact what did happen was the reverse of the photoelectric effect the greater the kinetic energy of the incoming electron the higher the frequency and thus energy of the outgoing Photon the wave theory broke down once again but with Einsteins photon theory of light the results made perfect sense the frequencies of the outgoing photons were dependent upon how much energy the electrons transferred to the atoms that they struck which suggests that the nature of this interaction is discrete rather than continuous and again this makes no sense under the wave paradigm of light such results only make sense within the context of light acting like a particle the equation for bremsstrahlung is K equals H times F max where K is the kinetic energy of the incoming electron F max is the maximum frequency of light emitted and H as the usual is Planck's constant notice that this equation is almost identical to that of the photoelectric effect this makes perfect sense since it's the same process just in Reverse you may also notice that in the case of bremsstrahlung there's no work function that's because the value for it is so small compared to the energies being dealt with that it can be neglected altogether but in principle these equations which represent the absorption and emission of light are both based on the underlying principle that light behaves like a particle so thus far it's been established that light behaves like a particle when it's emitted and behaves like a particle again when it's absorbed what about the time in between enter Arthur Compton in 1922 who fired x-ray beams at blocks of carbon and measured the wavelengths of the outgoing electromagnetic radiation the phenomenon that he was experimenting with is called scattering which can basically be summarized as one thing hitting a thing unlike the previous experiments what Compton was explicitly measuring was the wavelengths which again is defined as the distance between two successive peaks of a wave according to the wave picture of light when an electromagnetic wave strikes an electron in the carbon the electron should absorb some of the x-rays energy and start oscillating in response this in turn should cause the electron to reradiating in a variety of directions in the form of scattered electromagnetic waves the key point is that the wavelengths of the light beams that come in and the light beams that get reradiating should stay the same lambda denotes the wavelengths of the incoming light lambda prime denotes the wavelengths of the outgoing light according to the wave theory of light these two values should be equal throughout the scattering process but they weren't after the experiment was performed Compton found that this relationship held instead the wavelength of scattered light minus the initial wave length of the light equals Planck's constant divided by the product of the speed of light and the mass of whatever the light was striking which in this case was an electron times 1 minus cosine of fie where fie is the angle at which the light was deflected obviously the incoming and outgoing wavelengths are not equal if they were their difference would be zero instead this equation implies that the wavelengths of scattered light are larger than the wavelengths of the incoming light and once again we have this mysterious factor of H in the equation so what's going on here the situation is analogous to what happens in a game of pool when a billiard ball strikes the side of a pool table it transfers some of its energy to the wall causing it to recoil while the billiard ball rolls off in some direction similarly when light scatters off of an electron it strikes it with a certain amount of energy which causes the electron to recoil and the light then bounces away somewhere else with less energy since it already transferred some to the electron now this is all well and good but Compton's equation doesn't tell us anything about the energies of the light beams well actually it does if you accept the particle picture of light which ties everything together quite nicely the wavelength of electromagnetic wave is proportional to its frequency if we accept that this light is comprised of photons then using the Planck Einstein relation we can show that since the change in wavelength corresponds to a change in frequency and since a change in frequency corresponds to a change in energy then a change in wavelength must correspond to a change in energy why does that matter because Compton's equation tells us something very important about how the motion of a photon corresponds to how much its energy changes if we're dealing with a situation where photons are just hitting electrons what you have here are a bunch of constant terms multiplied by this parameter which is what determines how much a photons wavelength and by extension how much are photons energy changes when it scatters what we find is that the change in energy depends on the angle at which the photon scatters if the angle is zero that is if the photon just passes through without scattering off of anything then the change in the photons wavelength is zero which seems pretty reasonable if it doesn't scatter off of anything its energy is not going to change so the wavelengths not going to change if the photon scatters off of an electron at an angle of 90 degrees however the change in its wavelength will be equal to these constant terms times 1 and if the photon scatters off of an electron at an angle of 180 degrees that is it hits the electron directly and moves back exactly the way it came then the change in wavelength will be twice as high in other words the more direct the hit the greater the change in wavelength and by extension the greater the change in energy from the stand point of particles like billiard balls this makes perfect sense a head-on collision is going to transfer more energy than a glancing blow from all of this Compton was able to show that light must behave like a particle in order for these results to make sense by painting such a beautiful picture of how the photon theory of light must be correct Compton had confirmed Einstein's theory beyond any reasonable doubt and he got a Nobel Prize for it so at last we have this picture of light where it can behave like a particle when it's submitted it can behave like a particle when it bounces off of things and it behaves like a particle when it gets absorbed but physicists were not very happy this since there was equally overwhelming evidence that light was a wave interference diffraction and dispersion were indisputable but these properties are exclusively wave like particles simply don't have any properties that would allow them to do these things waves and particles are incompatible their properties are mutually contradictory and completely irreconcilable and yet light could behave like a wave or a particle in different situations both pictures work without the wave picture of light we wouldn't be able to make infer a meter we wouldn't be able to make microscopes we wouldn't be able to make cameras and yet without the photoelectric effect we wouldn't be able to make night-vision devices without brimstar loom we wouldn't be able to use medical x-rays without compton scattering there would be no MRI ultrasound or any other type of radiation therapy so how does one get around this contradiction the answer which will be explored in a future video is actually a principle that encompasses all of quantum theory and as certain philosophical ramifications that should not be considered until after the theory of quantum mechanics is developed before one asks what quantum physics means one must first understand what quantum physics says for now suffice it to say that light exhibits wave particle duality sometimes it's a wave sometimes it's a particle but never both at the same time in situations where the results seem to correspond to wave behavior light is a wave in situations where the results seem to correspond to particle behavior light as a particle but what's essential is that it can never be both at the same time light can behave as a wave or a particle but light cannot behave as a wave and a particle a lot of physicists were very puzzled by this and the duality of light became a subject of much heated debate maybe there was some mathematical means of reconciling particles and waves that they hadn't figured out yet maybe there was some external factor that was influencing the results of contradictory experiments maybe their understanding of light was simply incomplete and that future experiments would tie together the contradictory ones physicists speculated endlessly about the possible and then one of them had a crazy idea lights seem to be characterized by duality but why stop there why stop with electromagnetic radiation why should light be the only thing that exhibits wave particle duality waves behaving like particles that was only the beginning

Channel: King Crocoduck

Views: 1,754,763

Rating: 4.8692665 out of 5

Keywords: quantum mechanics, quantum physics, quantum theory made easy, king crocoduck, wave particle duality, photon, max planck, blackbody, radiation, bresstrauhlung, photoelectric effect, compton scattering, faraday, ampere, maxwell, hertz, rontgen, einstein, compton, physics, documentary

Id: e5_V78SWGF0

Length: 31min 9sec (1869 seconds)

Published: Fri Jul 17 2015

Reddit Comments

[u/Vash_the_Stampede987]

I knew it was Crocoduck!

[u/Charzarn]

At the end he says light can only be particle or a wave but never both but we have evidence now that says that that is not the case. I wonder if he knows or if he is just saving it for later or I'm completely wrong ha.

[u/kingphysics]

I loved the suspense he left off at the end!

[u/redhousebythebog]

Next video atomic orbitals?

[u/Rideron150]

Okay hold on. He says that because the speed of the electromagnetic wave is equal to the speed of light, that light must be a type of EM wave. If I run at a speed equivalent to light, that doesn't make me an EM wave, so how does that make light an EM wave?