(This post was generated in response to a Quantum University Crank over the last month and tacked at the end of my Quantum University post. I left it there for the Quantum U jackasses to come and gawk and pretend their pseudoscience will give them some supernatural powers, but I also post it here because I wish for it to stand on its own.)
The very notion of Quantum University sets my heart on fire. I want to take away that funhouse mirror they use to admire themselves and put them in front of a real mirror so that they understand why people with actual comprehension laugh at them (or should be given the opportunity to laugh and point and maybe throw some rotten cabbage).
Still, the reality is that you can’t fix a believer. The one great problem with cranks of this sort is that a lot of them genuinely believe they’re onto something. Never really quite occurs to them that basically everything they ever do never achieves anything and that any achievements they come across only come from fellow travelers who also believe. A believer can only butt their uncomprehending head against the granite block that is reality and stop to wonder why there’s blood. They do not actually achieve, ever, they waste time running in circles doing everything they can to collect testimonials from dupes to mark their “achievements.” Oh, and utter curses about the vast conspiracies being leveled to keep what they believe down. Still, if they can get people to believe them, they can do one achievement that is meaningful in society: they can make money.
The fellow in the comments honestly believes that there’s a “brand” of quantum physics out there that doesn’t require you to know how to use calculus.
The profession of physics has a very distinct and simple structure. The entire purpose of a physicist is to translate a series of real world observations into numerical representations and then fit those values onto mathematical formulae. If the fitting is sufficiently good, the process can be reversed: the mathematical formulae discovered in the fitting process can be used to predict what real world conditions are required to reproduce certain observational outcomes. Note, this is flat-out crystal ball stuff; physicists predict what will happen observationally if conditions for a given formula are met and to what precision that outcome can be expected. I’m not saying “some brand of physicist” or “sometimes this is one thing we do”… this is what physicists do, end of story. If you cannot carry out this function, you are by definition not a physicist. Physics is completely inseparable from the math, so much so that the profession is divided down the middle into two classes: the people who wrangle the math, called the “Theorists,” and the people who wrangle the observations to plug into the math, called the “Experimentalists.” Theorists and Experimentalists work together to get physics to operate.
Any jackass bleating, “Well, you don’t know the Real(tm) science because you haven’t gotten around your evil, malicious logical right brain and circumvented the math to find the Real Reality,” has essentially shoved his own hand down the garbage disposal. By dumping the math, that person has admitted to not being a physicist –despite his/her claims to the contrary– without math, there is no physics. Period. End of story. This is totally non-negotiable. You cannot redefine reality and expect the rest of the universe to suddenly adhere to your declaration.
Since understanding this subtlety is a real challenge for those of Quantum University, I’m going to make an example here of just what it is that a physicist does and why physicists are deserving of the street cred that they’ve earned. These Quantum U jackasses crave the legitimacy of that word: “Physicist.” There is no other reason why anyone would accuse an actual physicist of being uncomprehending of the nature of physics. From what I intend to add here, anybody reading this blog post will be able to make an assessment of themselves as to whether they could ever be qualified to call themselves a physicist.
Quantum Physicist Self-Evaluation Quiz:
What I’m going to add is a quiz containing a series of questions that a genuine quantum physicist would have no difficulty at least attempting to answer –some will be very easy, but some may require more than transient thought. If you have any hope of completing it, you will have to do some math. I will write the problems in order of increasing difficulty, then detail what each problem gives to the overall puzzle of exploring quantum physics and try to add a real life outcome from the given type of calculation to show why physicists have credibility in society in the first place. Credibility is the point here; this is why Quantum U craves the word “Physicist” and is willing to rewrite reality for it. My point is that if you jettison the part of physics that allows it to attain credibility, you lose the right to claim credibility by association.
Problem 1) You suspend a 5 kg bowling ball on a 2 meter cable from the ceiling. With the cable taut, you pull the ball aside until the cable is at an angle 30 degrees from vertical. You release the ball and allow it to swing. What is the maximum speed of the ball as it swings and where is it achieved?
Why does this matter to Quantum Physics? This is a very basic classical physics problem that would be encountered midway through your first semester in introductory physics. The Quantum U jackass would immediately scoff, “Well, this is classical, quantum allows us to escape that!” Well, no, actually it doesn’t. This problem is the root from which quantum physics grows. This is one of the simplest Conservation of Energy problems imaginable and the layout of the calculation sets the root of Hamiltonian formalism, meaning that it is almost exactly the same as the layout of the time-independent Schrodinger equation. If you lose the Schrodinger equation, you’d better have something impressive ready to replace it because you can’t do quantum without this.
Why is this important to Physicist cred? Most introductory physics does not seem like it should be all that important. If you can solve this problem, does it mean you can load heavy things into your car without straining your back? Maybe, maybe not. This problem is important to society because it involves exchange of potential and kinetic energy in a conservative situation. With a tiny bit of tweaking, this particular problem can be rewritten to estimate how much hydroelectric power can be generated from a particular design of hydroelectric dam. What? You mean to say physics has real world implications? That sound you just heard was me driving a nail into the third eye of a quantum U jackass.
In this picture is an electronic circuit. I’ve labeled all the components. The switch connects the unlabeled wire to either wire 1) or wire 2). It starts connected at position 1). What happens when you turn it to position 2)… in other words, what’s the time varying behavior after the connection is closed? That’s the easy part of the question; to be a physicist, you have to answer this: what values of ‘L’ and ‘C’ could you pick to get a period of 2 milliseconds?
Why does this matter to Quantum Physics? I debated for a long time what sort of basic electromagnetism problems to add. I thought originally to keep it to one, but I decided instead on two because you really can never get away from electromagnetism while you’re doing quantum physics. There are four known fundamental forces and this is one; electromagnetism crops up in everything. This particular problem involves an oscillator and is therefore a forerunner to wave behavior. If you can’t do oscillators, you can’t do probability waves. If you know a thing about physics, this problem is actually extremely easy and is typically encountered in second semester basic electromagnetism and in whatever electronics classes you’re forced to take. The chemists, who do quantum physics of one sort, may have some difficulty with this problem, but the physicists really shouldn’t. If you call yourself a physicist, this should be as easy as wiping your ass.
Why is this important to Physicist cred? You have an evolved, heavily engineered offspring of this little doodad in every connected device carried on your person at this moment. The oscillators have all changed faces and the components to achieve them are probably almost unrecognizable at this point, but the physics is not. The thing in the picture above could be converted into the tank circuit of a radio. This was a gift to the 20th century by the hard work of 19th century physicists. Radio, electric power and the associated ability to instantaneously communicate long distances has built our world. If you stop to realize that William Thomson, the Lord Kelvin, made a mint off laying a telegraph cable across the Atlantic to connect England and North America for communications purposes, you will understand the power that all the offshoots of this technology had. The circuit above is two-fold; it relies on the electric conduction physics upon which Thomson’s telegraph infrastructure depended and also could be used to facilitate the generation of electromagnetic waves that could be transmitted through the air, as performed by Marconi (and Tesla… the real one, not the car maker). If you know what you’re doing, you can turn this device into a small EMP generator… you’re welcome. (As an aside, I always feel a little sorry for William Thomson: modern people mostly only ever call him Lord Kelvin and forget his actual name… the title of Lord Kelvin was created for him because of his success as a physicist, and so, his success deprived history of his actual name!)
Problem 3) You’re stranded on a deserted island. You go and hunt for food along the flood plain around the island when the tide comes in. You see a fish swimming along the sand beneath the flat surface of unperturbed water, by eye 60 degrees below the horizon line of the ocean. You stand 1.8 m tall and you have a 1.5 m spear. Measuring with your spear, you know the depth of the water is 2/3 the length of your spear. The index of refraction of water is about 1.333. You have a calculator for a brain. If you thrust the spear from your shoulder, what angle must you launch it at in order to hit the fish.
Why does this matter to Quantum Physics? Good question. This is the second EM question that I will add and it’s added because it deals directly with the physics of light. Snell’s law is a product of electromagnetism and it emerges from applying Maxwell’s equations to a boundary situation much like I’ve detailed in the problem above. Index of refraction is a direct ratio of speed of light in a vacuum over speed of that same light in a substance (like water). The phenomenon of light bending its path as it passes through the boundary between two translucent substances is a direct consequence of the wave-like properties of light. I have no doubt that the Quantum U jackasses love waves and vibrations. Can they handle this one? As I chose to add a problem about electromagnetic force, I needed to add a problem about the basics of light, which is directly connected to the EM force. Light is very pivotal to Quantum physics because most every observation people ever make involves some measurement of light.
Why is this important to Physicist cred? The lens maker equation is expanded from this foundation. Without this, there would be no glasses, no contact lenses and no corrective laser eye surgery. The work of physicists actually corrects vision in the two eyes that matter.
Problem 4) The half life of a muon is 2.2 microseconds. If it’s a cosmic ray traveling at 99.999% of the speed of light, on average how long does that muon appear to last if you happen to see it fly by while you’re standing on Earth?
Why does this matter to Quantum Physics? This is a token special relativity problem. A large portion of Quantum physics does not require relativity, but an equal amount does. As such, you can’t get away from relativity. You need to know at least some to be a quantum physicist. Quantum U jackasses clearly want to marginalize all those “particles and math-ematical equations” and beg that something exists beyond that, never mind that by removing the math, they have zero chance of ever defining what… I say fine, remove what you like, I’ll steamroll you flat anyway. I could as easily have said “You will live 79 years and 10 seconds, how long does that appear to be to somebody watching you run past at human foot speed for your entire life?” The relativity will probably say 79 years and 10.000001 seconds or something (I didn’t calculate it), but at least this is better than begging the limits of human potential and claiming the person ran by at 99.999% the speed of light. Somebody has to realistic about human potential. Relativity is pretty important because it’s the first time humans changed Newtonian physics. That precedent is important to understand in light of quantum physics (which was about the third time humans changed Newtonian physics, General Relativity being the second). Quantum physics didn’t emerge by immaculate conception… there was a huge background of math that lead to it. Discard it at your risk.
Why is this important to Physicist cred? Congratulations, you can now perform one of the clock calculations needed to make the Global Positioning System (GPS) work. You’re welcome; physicists just saved you from getting lost… again. Note, we’re also responsible for the military ability to drop a bomb down your chimney from a flying aircraft. I’d love to see you astral project out of that.
Problem 5) What do the ‘A’ and ‘B’ constants refer to in Einstein’s stimulated emission equations?
Problem context: To detail the situation for the mathematically illiterate, who are none-the-less following along because they are genuinely interested, Einstein’s set-up is a Bohr atom… a nucleus with electrons orbiting it at levels; he postulated that a passing electromagnetic wave causes a lower energy electron to hop up to a higher energy level orbit if the wave matches the energy difference between the two levels (absorbing a photon). The electron in this now excited state can either spontaneously hop back down to the lower state, giving off a photon, or it can be ‘jarred’ to give off the photon and hop back down to the lower state by being subjected to an electromagnetic wave that happens to match the energy difference between the two states –called stimulated emission.
Why does this matter to Quantum Physics? Einstein’s work on stimulated emission occurred in 1917, in the framework of what’s called the “Old Quantum.” This is my first genuine quantum physics question for you. Oh goody, right? Tired of the equations yet? Sorry, but if you can’t handle equations, you’re not a physicist. This work is the front runner of the Fermi Golden Rule. I’m skipping most of the other Old Quantum because it was still too incomplete.
Why is this important to Physicist cred? Without us, no lasers bio-tch! And, in the interest of full disclosure, the laser is one example of short-sightedness in physicists. Einstein had this realization in 1917, but failed to see the significance himself. Physicists then hurried on and found their focus on other shiny things while nobody thought more carefully about it. It took some 40 years until Maiman, Gould, Townes and Schawlow (physicists whose names you may not know, though Maiman was also an engineer) had the critical insights to finally make it work. I ended up including this problem on a lark mainly because it also helps to put guided missiles through windows militarily. Gotta put the p’chank of fear into somebody’s chakra. How many CD players do you suppose were built because of us?
Problem 6) A drunken hobo, who weighs 70 kg including his tattered blanket and a full bottle of peach schnapps, shambles along at about 0.5 m/s. If he were to stumble through a two-slit apparatus, how far apart would the slits need to be spaced for him to exhibit quantum mechanical interference? Can this setup be built?
Why does this matter to Quantum Physics? This question involves the de Broglie equation, the beating heart of modern quantum physics. This equation is one of several reasons why Quantum University craves the word “Quantum.” For those less versed, the de Broglie relation is the first equation written that explores the ‘wave’-ness of physical objects and is the source of particle-wave duality in matter waves. With the way that most quantum mechanical wave equations are written, the de Broglie relation is always hidden somewhere inside the argument (particularly in time-independent cases). In essence, because they do no math, quantum U gets it wrong because they fail to include Planck’s constant. Ask yourself what came first, an “institution” calling itself “Quantum U” or Planck’s constant?
Why is this important to Physicist cred? Do I really need to say it?
Problem 7) The hobo from the previous problem shambles along for a moment, then stumbles to a stop. He stands there wavering about, struggling to keep his balance, foot speed now reduced to 0 m/s. Because of the alcohol induced gaps in his memory, he may certainly think that this happens, but why doesn’t he ever just suddenly *pop* into existence in front of the hardware store or soup kitchen? Careful examination of the previous problem would suggest that if he stops moving, maybe he can!
Why does this matter to Quantum Physics? Are you kidding? This is the weird-ass core of quantum physics! I never did claim that weird stuff doesn’t happen. What I claimed was that there are specific expectations for how the weirdness can emerge. What is written in this problem should be analyzed with the Heisenberg Uncertainty Principle. The cranks typically use the Uncertainty principle as a get out of jail free card, “Well, there is uncertainty, so anything is possible, right?” The actuality is that the Uncertainty Principle acts like a governor, telling how much weird is possible depending on the set-up of a given situation. How exactly stopped must the bum be for his position to grow so uncertain that he can teleport around town? Note, the argument here would actually also work if he’s still walking, despite the hole in de Broglie’s relation, but his speed must be very perfectly uniform… the uncertainty of his momentum must be nil.
Why is this important to Physicist cred? This stuff is one of the fundamental reasons why quantum U jackasses covet the word “physicist.” Did the uncertainty principle come first, or the slack-jaws desperate to misunderstand it in order to promote their woo?
Problem 8) A lightning bolt strikes for about 30 microseconds, creating a radio frequency EMP. What is the frequency spread of the interference it causes in radio/microwave transmissions occurring around it?
Why does this matter to Quantum Physics? This is a second application of the Uncertainty Principle. In this form, it addresses a different pair of uncertainties, but it’s the same principle. I’ve included this problem to show the stark quantitative nature of the equation. There is nothing at all qualitative or indecisive about the Heisenberg Principle. It says something extremely specific and if you lose the math, it becomes a lie, period.
Why is this important to Physicist cred? We invented the Uncertainty Principle and we damn well have a say in how it works.
Problem 9) A tiny, effectively featureless quantum mechanical tiger of mass ‘m’ is caught in a prison of only one dimension. He runs back and forth trying to get out, but the walls on either end are infinitely high. The prison is large compared to the actual physical shape of the tiger and this tiger lives by feeding on heat energy. Further, the prison is sized so that it’s on about the same size-scale as the tiger’s de Broglie wavelength for the low temperature where this tiger lives –and in fact keeps the tiger alive under those circumstances where he’s starving. The zoo keeper must fire photons into the tiger’s cell one at a time to try to hit the tiger and see where he is. The frequency of the photon is very high and the zoo keeper can tell exactly where the photon went in and will be able to tell exactly where the photon comes back out, thus giving him an accurate understanding of the location of whatever the photon bounces off of. The photon will interact elastically with the tiger and the interaction is independent of the photon’s frequency. If the tiger has been allowed to starve and has the smallest energy a tiger of this impossible sort can, what is the probability of finding him at any particular place in this prison with a photon? After you hit him that first time with a photon, finding exactly where he is, how many of the prison’s eigenstates are needed to describe his location thereafter?
Why does this matter to Quantum Physics? This is the most basic Schrodinger equation problem, the particle-in-the-box. You should substitute ‘electron’ for ‘tiger’ in the interests of reality, but I can choose how I write the problem. A part of why I wrote this problem the way I did is to give a little bit of a feeling for what the quantum mechanics is like and how it works. In this kind of problem, you are outside the system looking in and the system is completely dark, you cannot see what’s going on. You could be a zoo keeper facing an angry tiger in a sealed crate; your only way to find this tiger is shove a prod through a breathing hole and see if you bump something. If he’s sleeping, you may discover a mass distributed somewhere in the middle of the crate. If he’s lunging back and forth, the prod may bounce off of something now and then, but it appears as if the tiger is distributed everywhere in the box. I added an embellishment too. In my version of the problem, I’ve included a prepared state and then a state collapse: I would recommend asking yourself what the difference is between the Hilbert space associated with the photon probe (designed around a position space representation) and the Hilbert space of the box (which would be the eigenspace solving the Hamiltonian of the tiger trapped in the box).
Why is this important to Physicist cred? The particle-in-the-box problem has actual physical applications. The 1D version can be used to approximate the absorbance spectra of aliphatic molecules containing stretches of conjugated bond. A 3D version of this problem can be invoked to describe the light absorption characteristics of quantum dots. Ever seen one of those beautiful Samsung quantum dot TVs? You’re welcome.
Problem 10) Suppose you did hit that tiger in the previous problem with a photon, momentarily finding his exact location in the box. What happens to the probability of finding him again at that location over time afterward?
Why does this matter to Quantum Physics? This is a time-dependent Schrodinger equation question. If you can’t understand why this is important to quantum mechanics, I feel truly sorry for you.
Why is this important to Physicist cred? The sort of logic in this problem is used in pump-probe experiments to see how excited states evolve, for instance. This is a real life example of Deepak Chopra’s “ceaselessly flowing quantum soup,” and I mean it in the sense that this is how it would actually be employed in reality by physicists that actually do quantum physics. In one sense only, Chopra is not wrong: the physics can be weird. But, for it to work in weird ways, you must match the circumstances where the effect is seen… the confinement must be on the size-scale of the matter wave. When you fail to invoke the appropriate scale, involving Planck’s constant and the size of the confinement relative to the size of matter wave of the object being considered, is where it becomes a lie. That’s why math is needed… it saves the reality from flowing over into becoming a lie.
Problem 11) In order to make a point about the nature of quantum mechanical tunneling, a physics professor lecturing a group of graduate students turns and runs across the classroom and crashes face-first into a wall. He has just insisted that one day he knows he’ll tunnel through and reach the other side. For a 0.25 m thick wall and a 70 kg physics professor, estimate the ratio of probability amplitude for the professor’s wave function on either side of the wall (or better, estimate the probability flux). Assume that the actual potential of the wall is constant over its width and can be approximated from the knowledge that the wall is just a little stronger than the normal force required to decelerate a 70 kg physics professor from human foot speed to stopped in a tenth of a second over the space of a hundredth of an inch. How many times would the professor need to try this experiment in order to achieve his dream of tunneling through?
Why does this matter to Quantum Physics? Quantum mechanical tunneling is a real thing. This is the effect where a physical object pops through a barrier, unimpeded. Think Kitty Pryde. To perform this, you need to do the particle in the box problem, but backward (a real physicist will understand my recommendation). This is prime weirdness, exactly why the cranks love quantum. I would recommend trying the same problem with an object the mass of an electron where the thickness of the barrier in question is about the same as the object’s de Broglie wavelength. This problem is based in part on a real-life anecdote, where the experiment in question was initiated by a real physics professor. When asked why he wouldn’t try it again since he knows that the probability is small and a large numbers of trials would improve his chances of success, he answered that the university only pays him enough to perform the experiment once a semester.
Why is this important to Physicist cred? Tunneling is responsible for radioactive decay –indeed, we just gave you nuclear power. Also, some of the best microscopes ever built, scanning tunneling microscopes (STM), rely on this physics.
Problem 12) You have a cubic (or rhombohedral) crystal of Ammonium Dihydrogen Phosphate whose optic axis is 52.4 degrees from normal to the crystal faces. You shine a 325 nm He-Cad laser through this crystal at some known angle to the optic axis. If the laser output is reduced so that you’re at the shot noise limit, hitting the crystal with one photon at a time, every so often, you see two photons coming out of the crystal. Many measurements show that the output photons lie in the same plane as the input photon, where both out-bound photons possess ordinary polarization and the same wavelength as each other and that they depart from the crystal along beam paths on the surface of a cone away from the incident beam –in other words, they leave at the same angle in opposite directions. Why are these new photons produced and what’s special about them? Suppose I tell you the output angle is 50 mradian, use physics to tell me the wavelengths of the output photons. Supposing the two photons are detected by detectors positioned equal distances from the crystal, what’s the time delay between detections?
Why does this matter to Quantum Physics? I spent some significant time thinking about this problem –this addresses a piece of quantum physics badly abused by everyone and their brother, but most intensely by the cranks. What’s written above is in basic structure an actual experiment dating from 1970. I avoided writing about this experiment in the typical pop-culture manner so that you can see what the reality actually looks like. I won’t name the quantum mechanical phenomenon that this demonstrates, but I will refer you to a paper by Einstein, Podolsky and Rosen from 1935. I’m hoping that it looks superficially boring because people want to see something really crazy here without thinking about what they’re actually seeing.
Why is this important to Physicist cred? I won’t be snarky this time. I want people to genuinely think about what’s written here for themselves. Preferably, you read the papers and really try to process it. Can you separate even the initial idea from the math? Believe me, it’s there in all its blazing, bizarre glory. What’s the point of this observation? Asking this question is the core of an education that is devoid of indoctrination. Don’t take my word for it, damn well do the work for yourself!
Problem 13) You have a proton and an electron interacting by electromagnetic force. Find the eigenstates of the electron. Impress me by finding the unbounded eigenstates of the electron (for electron energies greater than zero).
Why does this matter to Quantum Physics? This is at its heart a very basic problem that every physicist sees. If you haven’t seen it and you’re calling yourself a quantum physicist, you’re not from a place where they teach quantum physics and, no, you are not a quantum physicist. Tired of the math yet? Sorry, but you can’t be a physicist if you’re afraid of math. In all honesty, I’ve met physicists who claim to be afraid of the math, but these are people who do derivatives as well as they breathe and then get scared of what mathematicians do.
Why is this important to Physicist cred? The periodic table of the elements is largely understood based on the bound states found in this problem. The unbounded states are important for understanding how atoms collide in a low energy, non-relativistic collider. We’ll get to the relativistic ones soon enough…
Problem 14) You have a 4 Tesla magnet. You stick your hand into the bore and somebody across the room fires up a computer program to shoot radiowaves into the cavity of the magnet. What frequency and pulse duration must you fire into your arm in order to set your protons to clamoring most noisily? To what radio frequency must you listen to pick up that clamor? Should the input be polarized? Are you able to feel or hear this clamor? Why or why not?
Why does this matter to Quantum Physics? If you read my blog, you know that this problem can be approached in part classically. If you want to impress me as a quantum physicist, I expect the quantum version. This problem involves spin.
Why is this important to Physicist cred? This problem is about MRI. Yes, we’re responsible for MRI too. If I microwave somebody’s chi long enough, does a mystical turkey timer pop out to tell me it’s metaphysically done? I suggest we do an experiment and see; we can jam the safety on the door of a microwave oven and stick somebody’s face in there… any takers? (Oh, right, physicists also gave us microwave ovens and invented the safety screen in the window. Was it a mechanical engineer who suggested the door latch with the safety interlink? Actually, that was probably us too; we’ve been shooting holes through our own heads at particle accelerators for years.)
Problem 15) If I say a certain perturbative interaction involves spin-orbit coupling, write the term which would go into the Hamiltonian. From the symmetry of the term, are there any forbidden matrix elements? Use the eigenstates found in problem 13 to calculate the first order perturbation between the ground state and the first excited state.
Why does this matter to Quantum Physics? I am gradually turning up the heat here. State of the art modern quantum physics is still way up somewhere ahead. This problem is about a component of Fine structure.
Why is this important to Physicist cred? Fine structure and Hyperfine structure are basics necessary to explain spectroscopy. This tool is one of many that people use to engineer materials from medications to coatings for prescription glasses to the plastics used to built the chair you’re sitting in. Spectroscopy is how we know about the atmospheres of planets orbiting nearby stars (yes, this is a measurement that has been made in a few cases).
Problem 16) A certain transition involves the quadrupole moment operator. Determine selection rules for the operator and estimate the transition rate between levels connected by this operator. If you want to use the eigenstates from problem 13, go for it.
Why does this matter to Quantum Physics? I have a lot of these mechanistic problems floating around. These are middling level quantum physics. Wigner-Eckart theorem and Fermi Golden rule are both essentials; if you haven’t even heard of them, shame on you.
Why is this important to Physicist cred? These things are needed for modern laser engineering and are the product of physicists. I’m sorry, but this is what physicists do.
Problem 17) What is the set of matrices that can be used to represent the group of all proper rotations?
Why does this matter to Quantum Physics? I’ve asked a couple questions here that involve rotation in some form or another. Truth is that I just like this problem and have been thinking about adding it since I started writing these. This is hitting higher level quantum physics and it is actually peripherally a math problem rather than a physics problem.
Why is this important to Physicist cred? If you aren’t a physicist, you won’t understand why group theory is interesting. Your reaction to this problem should tell you something very strong about whether you should use the word “physicist” to describe yourself or not. Sorry, I can’t change the reality of what we are.
Problem 18) Write the character table for translational symmetry (Correction: discrete translations on a 1D lattice). Propose a viable candidate for the 1D representation and explain the associated eigenstates.
Why does this matter to Quantum Physics? Can’t mention group symmetry without spending a moment talking about Bloch theory. This is like taking the particle-in-a-box problem and putting it between mirrors.
Why is this important to Physicist cred? If you truly understand this, you can go tell Intel how to dope their semi-conductors. Yes, I just gave you microchips; without us, you wouldn’t be poring over this screed on your smartphone.
Problem 19) Is a Cooper pair a majorana fermion? How is the Fermi temperature associated with the disappearance of electrical resistivity in a cold solid?
Why does this matter to Quantum Physics? Can’t mention semi-conductors without going whole hog and mentioning superconductors. Majorana fermions are a concept that is still argued in many domains of quantum physics. This question is actually fairly qualitative… if you want to go the physicist route, I would suggest using the eigenstates from the particle-in-a-box problem and describing a fermion next to a boson. If you really want to impress me, pull a page out of a Feynman book and derive the partition function for fermions.
Why is this important to Physicist cred? Remember that 4 Tesla magnet in problem 14? Probably can’t build that without the super-conductivity mentioned here (full disclosure, we can do rare earth magnets that are that strength too, but again, real physicists are responsible for this). Maybe someday superconductors will give us floating trains.
Problem 20) Use the Roothaan equations to do a restricted self-consistent field calculation in order to determine what the ground state energy of propane is.
Why does this matter to Quantum Physics? I’ve recently done a version of this problem from scratch on my own time and I couldn’t rightly produce this quiz without adding it. This is starting to push against the limits of quantum physics. This problem matters because it is one of the few ways that we can determine wave functions of real systems more complicated than problem 13. If you legitimately try to do this problem from scratch by hand, you will discover that it is one of the most frighteningly difficult things you’ve ever done. As a supplement to this problem, when do relativistic corrections become necessary? What’s the Hartree-Fock limit and what do people do to try to get around it?
Why is this important to Physicist cred? This is one of the chief tools by which we understand the structure of atoms heavier than hydrogen. A Nobel prize was awarded for work automating the solution to this problem. For full disclosure, this prize was awarded in chemistry, but keep in mind that it is pure physics in the sense that modern chemistry is almost totally dependent on quantum physics. The automation for solving this problem is broadly disseminated in the hands of normal chemists so that they can design molecules without having to trudge through the nightmare of this physics problem for themselves.
Problem 21) Why does the Klein-Gordon equation imply antimatter?
Problem context: Buckle up sports fans, the ride gets bumpy from here. For mathematical context, Klein-Gordon equation is a low level relativistic analog to Schrodinger equation.
Why does this matter to Quantum Physics? Schrodinger equation is actually a manifestly classical construction. I’m sure this probably throws a wrench at the Quantum U worldview with me just somehow colliding the words “classical” and “quantum,” since Schrodinger’s equation is fundamentally the backbone of quantum physics as far as most people understand it. But, it’s actually true; Schrodinger’s equation has a pseudoclassical limit in that it assumes that information travels between particles without a speed limit –you derive Schrodinger’s equation by putting non-commuting operators into the equation I initially introduced you to all the way back in problem 1. Klein-Gordon is derived the same way, but from putting the non-commuting operators into the relativistic energy-momentum relation. In this sense, Schrodinger’s equation is a form of classical (in the sense of being non-relativistic) physics. One upshot from this is that you must be very careful about claims of simultaneity that hinge on non-relativistic quantum physics; like say, collapse of entanglement (you cannot tell the other guy that he should look at his particle, or what you saw when you looked at your particle at faster than the speed of light). Klein-Gordon implies antimatter, but this is actually understood in retrospect; Paul Dirac (another luminary you may not have heard of) suggested it from the Dirac equation, which is a fermionic analog to the bosonic Klein-Gordon. Disturbed by all this reference to math? Don’t be; this is what physicists do… they look at math used to represent reality and then make claims about reality based on that math. For the tenth time, a “physicist” who does no math is not a physicist.
Why is this important to Physicist cred? Physicists suggested antimatter to the world. Antimatter isn’t exactly sitting on every table or in every gas tank, but it does have at least one practical application. Have you ever gone to the hospital to get a PET scan? That’s positron emission tomography, which uses antimatter to make tomographic images of the human body. What, another real medical application that actually is known to work. Don’t believe me? That’s fine, go back to tending your cupping bruises and hope that nobody screwed up.
Problem 22) Show that non-relativistic path integral formalism is equivalent to Schrodinger’s equation.
Problem context: Yes, integrating along a path is mathematical. No, you can’t escape math if you’re in physics.
Why does this matter to Quantum Physics? Path integral formalism is a big part of everything that is used in high energy physics. Path integrals are introduced early in your quantum physics education, but they don’t become really important until gauge symmetry is introduced and you start working with functionals on fields. That’s right, no quantum field theory without path integrals. A more basic demonstration of path integral formalism is to show that in non-relativistic terms, it’s equal to the more basic Schrodinger’s equation. It’s a tricky conceptual proof that shows you really understand your quantum physics. And, no, I won’t do it for you.
Why is this important to Physicist cred? You want modern quantum physics, this is one route to it.
Problem 23) Two uncharged thin metal plates are placed in a vacuum such that they lie with surfaces parallel to one another. Explain why they spontaneously exert force on one another. How much force do they exert and how does it vary with distance between the plates?
Why does this matter to Quantum Physics? This is the set-up for Casimir effect. Welcome to the bizarre world of zero-point energy and vacuum fluctuations. Yes, this is a real thing.
Why is this important to Physicist cred? Someday, maybe this will form the basis of a science fictional star drive which requires no exhaust. Until then, it’s pretty curious and kind of cool. One thing to remember about the bleeding edge of physics is that many things we learn about do not always find technological application. Sometimes, the insight which leads to an application is years away. But, it requires having the real basis and not just the ability to spout nonsense technobabble. If you can apply Casimir effect to build something useful, be my guest… my hat will be off to you if you can actually prove you’re doing it.
Taken from INSPIRE high energy physics, these are Feyman diagrams for production of the Higgs Boson. Use these diagrams to write the Lagrangian for coupling to the Higgs field.
Why does this matter to Quantum Physics? Several somebodies won a Nobel prize for this. If you don’t get why and are claiming to be a physicist, shame on you.
Why is this important to Physicist cred? Good question. You tell me. Why?
This quiz could go on a long way. I have to tie it off because I only know so much myself (words of wisdom: know thy limits!). There is so much real physics in quantum mechanics that specialists in the various subfields could add questions forever beyond my single class in QFT and nearly non-existent solid state. Why does renormalization work? What is a topological insulator? Why do people try to build computers using atomic spins for bits? How is it that Chinese scientists are passing undecryptable messages to themselves? Why why why? A thousand questions with a thousand real answers. Anybody wasting time pretending they are learning anything about reality at Quantum University will never be able to answer any of them. They will continue to putz around and make believe that they know more than everybody else, calling themselves physicists, even though they do no math and therefore no physics.
I know there’s a huge number of physics cranks out there and I know that attacking one or ten or fifty will probably not make a scratch in the surface. I started writing this in a fit of rage, if you couldn’t tell in my response in the original version of this post. These people utterly piss me off. They think very highly of their own essentially non-existent attainment and pretty much can’t be convinced of their own self-deficit. Writing this, I feel a bit like Don Quixote, astride my horse, charging as fast as I can at that windmill blade on the downswing. It’s a fool’s errand; Quantum University still stands and it still pulls in chumps paying money, no matter what I write.
One thing that angered me most was the insinuation that people essentially throw out their ability to be creative when they strive to accomplish in real physical sciences, that somehow the “Left brain” atrophies and becomes a ghost of itself under the weight of the cold, calculating “Right brain” and that the higher reaches of my soul are made off-limits because of reductionism. This is the view of somebody who knows no scientists. The reality is very much more nuanced and complicated. I’ve met so many scientists with acid wit and magnificent creative bents that I can’t stand the thought of just lumping them all into some big pail of monolithic monotony. Science itself is an act of enormous creativity in designing and executing the right experiment. Almost none of it is reached solely on cold calculation. The people who inhabit the discipline are a broad cross-section of humanity, possessing all the faults and strengths that that implies, but also there are some amazing geniuses the like of which pretty much no other walk in life can claim. Faking genius is what Quantum U wants to package.
My rage is spent. I have little else to say right now.
There was a discouraged comment provoked by this post that I would like to try to respond to.
The comment was that this quiz was very good, but that it showed the speaker that he/she should leave physics to the professionals (essentially). This is paraphrasing.
Professional physicists have to deal with the feelings that have apparently been elicited by this quiz. Physics scales in difficulty to match your capacity for understanding it –it literally gets harder and harder until you can’t go any further. As a discipline, it was created by a collaborative effort among some of the smartest people who have ever lived. The physics written in books is one big act of genius, the sum total of all the eureka moments of these smartest people. It is every life’s work and piercing insight all at once! Nobody measures up to that. Nobody understands it all. Of physics as a whole, quantum physics is one of the hardest parts.
This is maybe one of the most difficult things that human beings have ever learned in the history of the world.
If it feels daunting to you, that’s the way the truth works. Coming to grips with that is necessary in order to move forward. Nobody understands it all. At the oceanside, it’s easy to walk on the beach and visit the shallows. But, if you swim out into it, at some point it gets deeper than you can handle. Not even Michael Phelps can swim from San Francisco to Tokyo.
There is a reward for coming to grips with that. Physics is built on the genius moments of some of the greatest geniuses that there ever was. If you study what they did and come to understand what their work actually means, you can have that spark of insight that the very best of us have had. If you want to understand what Einstein’s genius was, for instance, studying his work directly is a way to commune with him. Working really hard and finally breaking through and really seeing it is like nothing else.
Nobody gets it all, but most of us come to grips with the fact that nobody has to. See what you can see and enjoy the trip. There are gems even in the shallows.