Nuclear Chicanery in ‘Batman Vs. Superman’

What a headache. I watched “Batman vs. Superman” last night and it was kind of painful.

I will admit right out that I liked some parts of that movie, but quite a lot of it I did not. If you haven’t seen the movie, beware, there will be some *SPOILERS* here.

The reason I’m bringing this up on a physics blog is because I’m getting sort of tired of seeing nuclear weapons misused in popular media. I think people just don’t understand how they work.

At a critical juncture near the end of ‘Batman vs. Superman,’ it suddenly became a good idea for the U.S. government to just shoot a nuclear missile at everybody and sweep the entire Superman vs. DoomsDay incident under the rug. This may have met a pass with me under other circumstances since it is a comic book movie and can’t be expected to comprehend the direction to reality even if given a compass and a map, but I have spent some time learning about how ballistic missiles, nuclear weapons and EMPs all work.

To begin with, the fact of the matter is that you don’t just shoot off a nuclear tipped ballistic missile as if it were an antiaircraft missile. With the antiaircraft mission, there is an entire collection of detection and targeting functionalities associated with the weapon. If the weapon is radar guided, a radio frequency pulse must be sent out by a convenient radar to illuminate the target and the missile must have radio detection equipment on-board in order to receive that pulse. If the weapon is heat guided, it must have some kind of infrared eye sensor. These weapons implicitly contain some expectation that the target is moving during the flight and that the weapon must be steered in order to score a hit, necessitating guidance fins and machineries with which to steer. Further, the weapon typically has some way of telling that it’s close enough to the target in order to go off and do damage. Here is a heat seeking missile:

DF-ST-82-10199It has a sensor at the front and steering surfaces all over it.

Here is Standard Missile 3:


Standard Missile 3 is a weapon with an antiballistic missile mission, meaning that it’s fired to kill a ballistic missile. Again, note that it has sensors on it and steering surfaces all over it. You could launch one of these and nail a superhero flying around in the upper atmosphere… never mind that Superman has the old “I’m rubber, you’re glue” infantile adjustment of being basically impervious to everything.

Here is a submarine launched ballistic missile:


This is a Trident missile. In contrast to the previous weapons, I draw your attention to the outside of this vehicle. Note the smooth lines. It has essentially no steering surfaces at all. During launch, it is steered by reaction wheels and (maybe) exhaust gimbaling. That is not super agile steering. I also checked on the guidance package: it uses star sighting and inertial guidance. It’s a ‘ballistic’ missile, meaning that it follows a basically preset parabolic flight path and uses no specific guidance to adjust its flight, much like a bullet. What this means is that the ballistic missile steers while it’s falling out of the sky, not really while on the way up. Further, star sighting is a system where the missile takes a look at the stars in the sky around it and uses that to judge its orientation… it contains no mechanism for telling how near it is to a target that might be encountered in space. The Trident is a rather typical ballistic missile, which is intended to deliver these things:


The thing with all the cones on it is a MIRV, a rather vicious sounding acronym that means “Multiple Independently targeted Reentry Vehicles.” This is the part of a ballistic missile that really maneuvers in order to aim the weapons. During the coast phase of the flight, the platform carrying the warheads (the cones) uses small jets to adjust its trajectory and then it kicks off warhead after warhead, which reenter the atmosphere unguided and strike their intended target. Keep in mind that targeting doesn’t have to be tremendous accurate with a nuclear warhead; off by a mile or two is ‘good enough.’

In the movie, the nuclear missile is more or less just a symbolic gesture of ‘the biggest thing humans can do’ when faced with this fight. Is there anything people can do? Not really, just throw a nuclear missile over that way and hope for the best. This is one of the things I like least about superhero movies: the 7 billion members of the human species are sort of reduced to this gaggle of chickens running around with their heads cut off, except this one guy, who just has to step in to save everyone. Who can do anything about it? Nobody but Bruce Wayne! The best anybody else will manage is an explosive stuffed in a wheelchair or maybe an insane ramble followed by some tinkering with a very user friendly piece of superpowerful, supersmart alien technology that is apparently too stupid to know that it’s talking to a person. Can humans do anything? No way; they mostly just run in circles screaming. All rambling aside, the real point is that a nuclear missile is actually a very honed, complicated system with an extremely specific task: none of the nuclear missiles currently plugged into silos here in the continental U.S. would be capable of beaning an incoming meteorite let alone a wayward man of steel.

The weapon needed to shoot at Superman and Doomsday would be more like the SM-3 than the Trident and, I expect, it would be specifically designed to tackle the mission at hand. I would suggest that some very motivated defense contractors could produce such a weapon in 18 months and probably would have after the previous Krytonian invasion. The technology is basically all there and little new engineering is need. The Pentagon is constantly reevaluating their fighting capabilities and probably wouldn’t be running around like a decapitated chicken, contrary to Hollywood fantasy.

Despite what it looked like, we could suppose that the weapon deployed against Supes and Baddie was some sort of nuclear tipped SM-3 variant. So, suppose that Superman does what he did and they all end up climbing up out of the atmosphere, whereupon the nuclear weapon is detonated.

Clearly the resulting explosion seriously hurt Superman. I’ll live with that, okay. There are some thermodynamic issues with Doomsday “Getting stronger as he absorbs Energy,” but there are also issues with Superman flying, so I guess I can’t be too picky: it is a comic book movie. I can even accept that maybe Supes could die on Doomsday’s spike because he was weakened by Kryptonite when a nuclear explosion was not otherwise enough to kill him. The lack of coherent sense in it all just is since nothing happening in these movies is confined by what can actually happen.

Ahead of all these other things, I will focus for the sake of the blog on the poor depiction of what happens with a nuclear explosion in low earth orbit. A nuke detonated on Hiroshima is a totally different animal from a nuke detonated above the atmosphere. A different weapon even. Something very special happens when you set a nuclear weapon off high in the stratosphere.

A nuclear weapon goes off by a critical mass nuclear chain reaction. The weapon core is imploded by a series of conventional explosives, crushing the core down so that the radioactive atoms of the weapon are in closer proximity to one another. These atoms, usually Uranium or Plutonium, are unstable nuclei which fall apart at some slow rate by a fission reaction, where the Uranium or Plutonium nucleus splits into parts and expels neutrons. If such nuclei are pushed very close together, the neutrons from one splitting event flying around crashing into surrounding nuclei and cause those nuclei to fall apart also, shooting out more neutrons. The act of splitting gives up a tiny bit of mass into energy as high energy light in the form of gamma rays. The initial rate of the explosion is very fast, something approaching the speed of light across the width of the weapon: nanoseconds as the gamma-rays emerge and less than milliseconds for the whole explosion to take place and the mass of the weapon to be consumed by it. The gamma ray pulse standing right in front of the weapon would be so powerful that it would turn all normal matter right there into an ionized gas of nuclei stripped of their electrons –the quantum transition for a electron absorbing a gamma ray is for the electron to simply jump out of orbit around whatever nucleus was holding it and fly away at some velocity close to the speed of light. For the most part, the energy of the explosion is initially stored in this powerful wave of gamma-rays, which you can’t directly ‘see’ per se since the chemical reaction which allows for sight is not compatible with the energy of gamma-rays.

If the bomb is exploded on the ground, a large amount of the gamma-radiation slams into nearby matter, converting those gamma-rays into kinetic energy in electrons and atomic nuclei, which in turn broadcast that energy into whatever they interact with, downgrading gamma-rays into smaller quanta of thermal energy or lower energy light, which in turn get subdivided further, more or less making a lot of heat and a lot of visible light and certainly a lot of moving material with significant amounts of kinetic energy. This translates into a blinding blast wave of sound and heat which moves as a powerful concussion.

If the bomb is detonated high in the atmosphere or in space, the energy of the gamma-rays produced by the explosion is deposited into matter in a different way. It mostly hits the atmosphere in a place where the atoms of the atmospheric gases do not interact with each other as frequently as they do near the surface, which allows the energy being conveyed from the bomb to be diverted into fewer extraneous paths. Electrons knocked from the atoms of atmospheric gases fly through the atmosphere at relativistic speeds without interacting with anything except the Earth’s magnetic field, producing a powerful electrical current that generates a huge electric field, reaching its peak strength in 5 nanoseconds and persisting about a microsecond. It’s a huge, coherent pulse! The resulting field hits the ground with a strength of roughly 50,000 volts per square meter (edit: the units here are actually volts per meter), sensitive to the geometry of the Earth’s magnetic field as the electrons spiral along the magnetic lines. The conveyed power is of an intensity of 6.6 megawatts per square meter (for comparison, sun light at Earth is only 1.3 kilowatts per square meter, or 5000 times weaker). In a way, the electrons stripped from the atmospheric gases convert the gamma-rays into a very powerful radiowave/microwave pulse. At the surface, this huge voltage causes motion of electrons in every conductor absorbing the pulse, mostly at above the breakdown voltage, killing everything electronic that you care about capable of providing Facebook or Snapchat. This is called the E1 pulse of the nuclear EMP and the strength of the pulse increases with increasing altitude of the nuclear detonation.

The E2 pulse takes place a moment later, about a microsecond to a second after the explosion. This is an incoherent pulse of radiofrequency noise as the remaining scattered gamma-rays knock loose other electrons. It’s much like the spark of noise caused by a lightning bolt.

There is also an E3 pulse of low energy radiowaves as the Earth’s magnetic field sloshes around due to the explosion, causing spikes of power to be deposited in long conductors, like power lines, which may knock out electrical power.

Now then, why do I care about this? Because the conventional crappy comic book cliche of towing the nuclear bomb out of the atmosphere to prevent it from causing harm to innocent civilians below is just that, a crappy, poorly considered cliche. Would real life military risk hamstringing themselves by just randomly lobbing a nuke into an uncertain situation over a big, populated city of people that they are supposed to be defending? Gotham and Metropolis would both have been subject to a massive power outage, at the very least, which would have knocked out anybody’s ability to use radar to track Superman or Doomsday –especially since an EMP renders radar useless for a moment, never mind the big booming visible electrical current arcs that Doomsday keeps sending out, which are actually lower energy than a nuke anyway since you can see them (yes, you can see a nuke, just keep in mind that the parts which don’t burn your eyes out are not necessarily the most powerful parts.)

So then, the symbol of a nuclear weapon really should be respected. I feel that a movie with heroes is much more believable if the power of such a weapon isn’t simply used as a blind analogy to show just how powerful a superhero is. It’s like a Chuck Norris joke. Using a nuclear weapon on superman just to show that he can walk away from it is just stupid: there is no ‘stuff’ in our comprehensible physical universe that can remain intact from this sort of treatment at point-blank range. I mean, really, is Supes made of neutronium? If you say ‘yes,’ you really don’t know how ridiculous that sounds. Neutronium powered by sunlight, huh? What story would you ever be able to tell where the jeopardy to normal people is believable and the hero remains relatable? A story working around the actual power of a nuclear weapon would be more interesting to me. I truly hated “Watchmen,” but there is something to be said for the character of Dr. Manhattan. So you upped the ante to nuclear weapons already, where do you go in the next story? Freeza?

(Small edit a long time after the fact: 10-13-16)

Suppose conservation of energy. A nuclear bomb of 1 Megaton strength releases 4.2 x 10^15 Joules in ~1 microsecond. 1 Watt/m^2 of light intensity is 1 Joule/(1 sec*m^2). The intensity of sunlight is about 1.3 kW/m^2. Superman is standing point blank in the blast of a nuclear explosion. The shot is very close and superman occludes 1% of the solid angle where the energy from the bomb is emitted uniformly across a sphere, and he absorbs that 1% completely. Suppose now that superman’s healing quantum yield is about one to one, meaning that he can resist one quantum of energetic damage absorbed by exerting an equivalent amount of energy –this is a generous estimate; few processes in nature have a perfect quantum yield. It’s like postulating that superman is better than a perfect refrigerator, which is appropriate, since he’s a superhero! How long would superman need to rest in the sun in order to recover the amount of energy he exerted to resist the nuclear explosion?

Laying in the sun, Superman would need ~3.2 x 10^10 seconds to recover his energy. That is 1024 years!

Really sets the scale, doesn’t it?


Schwinging the Pendulum

Masses on springs get a lot of use in physics; you see them early in that first year of introductory classical mechanics with Hooke’s law and they come back over and over again after that. Physicists are fond of saying that basically everything in reality reduces to a mass on a spring if you squint at it the right way. I chose the tortured title for this post thinking about how a pendulum bob can be described as a mass on a spring at small angles of deflection and that Schwinger’s method, which is important to the Quantum mechanics problem I’m covering, is almost like a pendulum swinging in an ellipse at a small angle.

If you haven’t guessed, this post is back to Sakurai problem 3.19, finally –of which I’ve spoken previously. What dalliance in quantum mechanics would be complete without spending time on Schwinger’s angular momentum method? Julian Schwinger should be familiar to anyone with a background in 20th century physics since he won the Nobel Prize at the same time as Richard Feynman. His wikipedia entry shows how his approaches contrasted with those of Feynman, but he was certainly no less brilliant.

As a quick refresher, the problem is asking about two of Schwinger’s operators, K+ and K-. “What do these two operators do?”

The quantum mechanical version of a mass on a spring is the ‘quantum simple harmonic oscillator.’ This system differs from the basic ‘mass on a spring’ model in that you really can’t think about it as something moving ‘back and forth’ the way a pendulum bob can. In the quantum version, it would be most accurate to say that the bob tends to be distributed along the range of its swing and that it is more likely to be found highly compressed and highly extended, at the extreme positions of its swing, the greater the energy it contains. In this, the swinging of the pendulum bob can be broken down into a spectrum of energy eigenstates where you can describe the motion as some combination of these states. Eigenstates are, of course, the bread and butter of quantum mechanics and correspond to stationary probability waves which are not overall that different from vibrations in a guitar string –even though it would be very very wrong to draw too close of an analogy here in absence of the math. A probability wave is literally existential, not ‘vibrational’ like a sound wave.

An important structure in this version of the quantum mass-on-a-spring is the existence of the so-called ‘creation’ and ‘annihilation’ operators (a† and a), which are very central to Schwinger’s method. These operators work together in a set where one undoes the action of the other. Together, these operators allow the skilled technician to transit the eigenstate energy spectrum of the mass-on-a-spring, using the creation operator to step from one state to the next higher energy state and the annihilation operator doing the opposite, stepping down in energy between successive states. These operators work sort of like moving your finger on the frets of a guitar string, the annihilator moving toward the tuning pegs and the creator moving down the neck toward the body of the instrument. If you get too close to the tuning pegs, the annihilator can actually cause you to fall off the end of the instrument. Not kidding, really: that’s part of why it earned the name ‘annihilator.’ The creation operator, on the other hand, can get arbitrarily close to the bottom of the string and still find notes, provided you continue to have some way of plucking the string.

Now then, Schwinger’s method takes this collection of ideas and turns it on its head to produce what can only be described as a stroke of genius. This idea follows from the basic observation that if you have an object moving at a constant speed around a circular track, that you can parameterize it using two mass-spring systems at right angles to each other in the plane of the track and have a complete description of the circular motion. Literally, if you’re moving in a circle in the x-y plane, the equation describing the x-position is a harmonic oscillator, as is the one describing the y-position. Schwinger’s brilliance was simply to say, “So, why don’t we do this in quantum mechanics?”

Schwinger’s angular momentum method applies to quantum mechanical rotation: the spinning top. As a physical parameter, angular momentum tends to describe what might be thought of as the ‘strength of a rotation.’ Having more angular momentum tends to correspond to greater speed in rotation, but in quantum mechanics, it also tends to strongly influence how ‘spinning’ objects are distributed within whatever volumes they occupy by giving them distinct ‘orientations.’

Coming back to the Sakurai problem, which I’ve been orbiting at quite a distance, the operators K+ and K- manipulate a state of rotation. K+ is two creation operators and K- is two annihilation operators. Mathematically, K+ increases the binary harmonic oscillator state by one unit of total angular momentum, while K- does the opposite. If you actually consider K+ to be two creation operators (a†a†) you can see it directly in the description of the general two-oscillator eigenstate:
Schwinger rotation 1Here, n+ and n- are just the two numbers needed to find the address of any one eigenstate among an infinite number where one mass-on-a-spring is labeled as ‘+’ while the one perpendicular to it is labeled as ‘-‘. The ket (state) on the right |0,0> is just the ground state where some number ‘n’ applications of a† elevates you to any eigenstate in spectrum. The equation, as written, simply tells you where you put your finger on the guitar string(s) to produce any note you want. The Schwinger method is actually where to put your finger on two strings in order to produce a particular kind of rotation in 2 dimensions. Do you see K+ in this equation? If n+ and n- are equal, K+ is just the thing right in the middle!

So, if you read my previous post (and survived far enough to read this), you’ll know that the Sakurai 3.19 problem was asking about matrix elements. Since ‘operators’ in quantum mechanics take states and convert them into other states, the structure of an operator is in a matrix where each element tells how one eigenstate is referenced to another during whatever transformation that operator is supposed to mediate. You could write K+ and K- in such a way that you can tell how any one state is converted to any other state by action of the operator.

This will almost certainly lose readers, but if you don’t actually like physics, you probably won’t like this blog anyway. As I worked problem 3.19, here are the forms I found for the matrix elements of the K+ and K- operators acting on the space of all harmonic oscillator eigenstates.



Solving the matrix element problem is actually quite simple and, as I worked the problem, I delayed executing this step until I had slogged exhaustively through the Schwinger method and was certain I knew what was up. To get the answer listed here, you just take the form for K+ or K- as presented in the previous blog post and act them on a particular ket |n’+,n’->, then sandwich with a particular bra <n+,n-|. This is like looking for the expectation value, but for only one element out of an entire matrix. The primed value of each ‘n’ is understood to be a different number from the unprimed form. Talk of Bra and Ket will sound weird to anyone who has never encountered the Dirac ‘bracket’ notation, which denotes eigenstates as ‘bra’-‘ket’ where the ‘bra’ is the conjugate transpose of the ‘ket’ and the ‘ket’ is a representation-free form of a particular quantum mechanical eigenstate. A matrix element is just a ‘bra’ sandwiched with a ‘ket’ and after the kets and bras are all gone, what’s left are Kroenecker deltas that describe where a particular element is located in a matrix since you only get non-zero elements where the indices of the ‘delta’s are equal. This form can be a very handy alternative to the two dimensional lists that every linear algebra student has learned to hate… in this case, the matrices are infinitely large in their two dimensions and you could never actually write them. With the delta notation, you only need to say which matrix elements are non-zero, thus reducing a matrix which can’t fit on this Earth into a single line expression. What’s written above are both two-matrix things where each matrix acts on one of two ket-spaces and each ket space is the series of eigenstates for one of the harmonic oscillators that Schwinger used in his description of angular momentum.

It certainly may not look it and it definitely doesn’t sound like it, but this does all come down to rotational quantum mechanics.

Post script:

As an apology to any reader who may stray here, I’m still deciding exactly what the voice of this blog will be. My initial vision was to be as broadly friendly as possible, but I’ve ping-ponged back and forth on this. I expect that there will be articles involving the far more crowd-friendly subject of ‘physics and/or science in popular culture,’ but I also had a desire to create a space where I could store my practicing. A formal truth about education in general is that you don’t keep what you make no effort to keep, which means that if you don’t actively practice, things you care about can disappear out of your life forever… particularly in a subject as hard as physics. I think we live in a world where it seems like everybody wants to believe they have a high level understanding of everything without having actually invested sufficient effort to attain even a basic level understanding of anything. One thing I want here is to serve as an example of what it takes to maintain skill and maybe make people think twice about what’s needed to be good at an intellectual pursuit. I have a desire to one day read an article quoting someone like Jaden Smith or Terrence Howard where they say “I was in this class at school learning how to do physics and it was so cool; I finally understood this and I wish everybody did!” but I fear that this will never happen. I have notebooks that are literally crammed with my physics practicing and I wish I could open them to the world and convince people to stop being afraid of playing at math. In some ways, it’s like working a crossword puzzle and I think anybody who has invested deeply probably can do as well as me. I’m no genius, I’m just a walking testament to hard work and due diligence.

The Question of How You Build a Black Hole

‘If Ant-man can’t do it, how does it happen?’ After I finished working on that post yesterday, I was left with this question.

It’s kind of a squirrelly question if you stop and think about it. I made an argument by Uncertainty Principle that particles can’t be compressed into such a tiny space in order to be trapped within the black hole formed by the mass of a single human man, and yet individual particles of matter must be compressed to this degree in order to make a real astrophysical black hole. How does that actually happen?

For one thing, the matter forming Black Holes has a very specific hysteresis to it. In real terms, you can’t just jump to a black hole, you have to take a huge mass and basically work through the life cycle of a star. At the end of that, you end up going through a series of states where pressure of material on the outside is pushing down on material in the inside and there are no physical forces that are able to resist the drive toward compression. As such, there is definitely communication going on between many particles and the state of the matter as a whole will end up being a particular statistical mechanical construct based upon some quantum mechanical allowances. What those are, nobody exactly knows yet! Presumably, this is some sort of many-body coherent state, some kind of mega-boson where all the constituent matter is allowed to reside in the same quantum mechanical ground state, which is utterly different from the postulate of the man trying to crush an electron with his gravity.

One of the pivotal difficulties with addressing questions surrounding this state of matter is that Quantum Mechanics is difficult to reconcile with General Relativity. The Uncertainty Principle as I used it yesterday does not take into account relativistic effects. In fact, basic level Quantum Mechanics, like the Schrodinger Equation, are actually classical with how they look at energy. Schrodinger’s Equation is composed of direct kinetic and potential energy terms which only match to first order with the relativistic expression for energy, which is essentially like saying that Schrodinger’s Equation contains no allowances for the travel-time of information from one point to another –which is why you have to be careful about simultaneity on a global level when considering quantum mechanics. In the drive toward including Relativity in Quantum Mechanics, you end up in the territory of the Klein-Gordon and Dirac Equations, both of which expand on Schrodinger’s Equation to bring special relativity into quantum mechanics, much the way Schrodinger’s Equation brings Quantum Mechanics to Classical physics; within appropriate scales, both descriptions work. Schrodinger’s equation is not simply wrong, it just has a limit. The modern Quantum Field Theories that brought us the Standard Model of particle physics, producing things like the Higg’s Boson along the way, all are symmetric in such a way that they allow for Special Relativity.

General Relativity is much harder. There have not yet been any successful theories that completely meld gravity with quantum mechanics. I wish you could find such a thing on this blog, but I’m not that smart.

What a Black Hole ‘is’ internally is still very much a cryptic thing. We can look at them externally, but information only flows into them and doesn’t come back out. Hawking radiation allows a way that energy can leak out, but a Black Hole does not really communicate its structure into this radiation.

Supposing you can’t just build a Black Hole by waiting for a star to collapse, are there other ways one might be produced? One potential candidate is particle accelerators, like the LHC. The reason this could work is actually fairly superficial. When you’re accelerating particles, Special Relativity comes into play. From the laboratory looking at accelerated particles zipping by, because of Special Relativity, a scientist would think the particles are flattened along their direction of travel. This is because of the phenomenon of length contraction, which is where a particle traveling at nearly the speed of light appears to be foreshortened because measurements of length within the frame of reference of the particle do not match with those of the lab. If you accelerated that particle to a high enough speed, the Uncertainty Principle as worked from the lab frame would claim that the particle fits within the length of a Schwarzchild radius for some tiny mass of black hole and, if it were to have a collision with another such particle, they could stick together as a black hole. A secondary feature of this is mass-energy: at a high speed, 4-momentum makes the particle have much greater mass than it would have at rest, presumably increasing the gravity and therefore also increasing the Schwarzchild radius. I don’t know the balance of these effects mathematically (having not actually worked through them and having only trivial skill with the Einstein Equations), but one additional consideration here is that the distance contraction foreshortening is only along the direction of travel, meaning that the spacetime metric surrounding the collision of two such particles is not of Schwarzchild geometry (the metric that produces the black hole hypothesis in General Relativity) and it seems unlikely to me that such a collision can be anything but just a collision as a result. What I mean is that even though they are foreshortened in one length, their distributions are normal in other directions and they may ‘leak’ out of the collision without being compressed into a black hole.

From the basic structure of quantum mechanics, it would also be possible to make the argument that every particle is itself already a black hole. All particles intrinsically have particle-wave duality and the quantum mechanical wave function tells only of ‘likelihood with which you might find said particle at this or that location.’ Beyond the envelope which describes where you may find it in a given circumstance, an electron is itself is a featureless, dimensionless point mass and we can’t be certain if that ‘point’ is smaller than the Schwarzchild radius necessary for it to be a black hole. If there were a way to randomly reach out and ‘find’ it in a location smaller than it’s own Schwarzchild radius, it would be a black hole by definition if only for that moment –never mind that localized to so tiny a volume, the light a charge like an electron can radiate would have a ridiculously small wavelength. Again, we don’t know if there’s something special about the material inside a black hole and our only real definition is that a black hole be of such density that it’s irradiated light can’t escape it’s gravity well.

It’s a very complicated series of questions that have been the subject of a lot of careers in physics. Discarding the complexity or making blanket statements like ‘science supports this’ are massively oversimplifying the whole field. In reality, science is still deciding exactly what it supports.

Hank Pym is not the deadliest Marvel Superhero ‘Because Blackholes’

I was reading blog articles as I was wont to do and I stumbled over a blog entry on ScreenRant about the deadliest Marvel superheroes. Most of the article is very tongue and cheek and can be taken with a grain of salt. I felt no alarm until I read the #1 entry placing Hank Pym (Scott Lang) as the deadliest Marvel superhero.

Why do I mention this on a physics blog? Well, when somebody uses the words, “It’s thanks to actual science,” they have essentially just shot themselves in the head and invited me to take pictures of the mess. I have a definite love-hate relationship with superheroes to begin with…

Here’s how the article begins:

It seems only fitting that the superhero who seems the most out of his depth, and literally the smallest would pose the biggest threat, but he does – and it’s thanks to actual science. The movie, like the comics, tries to base Scott Lang’s powers and the Ant-Man suit in actual quantum and atomic science. They explain that the suit doesn’t shrink the wearer, exactly, but uses Pym Particles to shrink the distance between the wearer’s atoms. In other words, an object’s mass stays the same, but is just compacted by removing some of the negative space between the molecules it’s made up of.

I can live with how this starts out. Sure thing, the suit shrinks the dead space in atoms, which is definitely quite a lot of volume since atomic radii are around half an angstrom (10^-10 meters) while nucleii are about five orders of magnitude smaller (10^-15 meters). Never mind that there’s not really any quantum mechanics in this statement, it is livable if fantastical territory. ‘Tries to base’ is a fair statement in so much as a squirrel can try to build a skyscraper out of acorns.

As any comic book fan knows, Ant-man gets his power by retaining his man-sized strength when shrinking down to microscopic size. Yeah, fine, okay, that follows. I even sat still through the laymen’s description of microscopic black holes formed by the large hadron collider and the horrific name dropping of ‘Stephen Hawking,’ as if using his name instantly grants legitimacy. Where I cracked loose was in the following paragraph.

By shrinking to a size smaller than any observable particle, but doing it with all of his mass, Scott would, according to actual science, have created a black hole with a ton more mass than would actually be needed to keep it stable. Stable long enough to start pulling in the matter around it – which happens to be Earth, and everyone on it. He might escape and save the day, but according to the science that the movie lays out itself, Ant-Man wouldn’t just be the greatest killer in the history of the planet… he’d be the last.

Um no. Just, no.

You need to chase around these damn journalists with a rolled up newspaper to keep them from shitting all over the science they are claiming to quote. Just no. Not even…

I wanted to grab him by the lapels and shake him really hard. Did you bother to learn anything about what the science actually says before you wrote word one of that paragraph above?

Just because you have a black hole doesn’t mean that it’s necessarily a threat to the existence of the Earth. Black holes do what they do usually because they have a lot of mass, but mass conservation is actually a real thing. Without actually eating anything, any particular stellar scale black hole has no greater mass than the star that formed it and therefore no greater gravity than that star. If our sun were replaced miraculously right at this second with a black hole of equal mass to our sun, the Earth would continue to orbit as it always has and would do so until the end of time. Gravity is proportional to mass, even in general relativity (where you start thinking about mass-energy, but the energy part is usually very small). You don’t notice the peculiarities associated with black holes until you get very very close to them. In the case of a black hole the mass of our sun (1.99×10^30 kg), the event horizon, the place where light can’t escape, is only 2967 meters in radius (roughly 30 football fields, about the distance of a 3k run). That is in comparison to a radius of the sun of 696 Million meters. That’s 234,000 times smaller. To see the general relativistic effects to any significant degree, you have to be a distance of thousands of meters from the event horizon because the gravity force tends to fall off approximately as 1/radius^2. Once you get out to the radius of Earth’s orbit, Newtonian physics rules and none of the crazy space-time stuff applies to a significant enough degree to screw up most of your calculations. This is all relative to a mass the size of the sun.

Consider now a mass the size of a typical man, say 70 kg. How small would he have to get in order to have an event horizon? Easy, you work the Schwarzchild radius equation. For a 70 kg man, that radius would be about 1×10^-25 m. How small is that? That is 10 billion times smaller than the scale radius of the nucleus of an atom (10^-15 m). For a sense of the size difference here, the distribution of the nucleus of an atom would be on roughly the same scale (10 million to several billion kilometers) as the solar system would be around the sun-sized black hole. Parking our man-sized black hole at the center of an atomic nucleus, most of the nuclear volume would be at Newtonian physics scale distances from this tiny black hole. That’s the nucleus, I’m not even talking about the radius of an orbiting electron.

Now then, since the original author invoked the Q-word without adequately thinking anything through, let’s see what quantum mechanics has to say about any of this. In order for a mass as tiny as an electron to be trapped within the event horizon of the Pym black hole, it must be located within the distance of the event horizon, a radius of 1×10^-25 m. Here we just turn around and use the Heisenberg Uncertainty Principle, which tells how tightly a particle can be localized. In this, for an electron-sized mass to be confined within the event horizon at 100% certainty, that electron would also end up with a momentum distribution of 1.01×10^-9 kg*(m/s)… if you divide out the mass of the electron, this requires the electron to be moving at an aphysically high velocity of 1.12×10^21 m/s. Wickedly pathological because it’s breaking the speed of light by roughly twelve orders of magnitude. The chances of finding even an electron within the Pym event horizon are catastrophically nil. Confining something like a proton would have a slightly less aphysical result, but still quantum mechanically impossible.

One can even ask the question: does Scott Lang/Hank Pym have enough gravity to hold onto a single electron the way a proton can hold down an electron by electrical forces? In this case, the force factor for the electrical charges is about 10^11 bigger than the gravity force, meaning that a stable ground level eigenstate for Pym holding a single electron gives an orbital radius of probably meters… meaning that the rest of the universe would strip that electron free by normal processes. As such, Pym can’t even fake being his own atom.

My conclusion: Hank Pym/Scott Lang can’t make a black hole strong enough by human mass alone to effect the rest of the universe anytime in the age of the universe, let alone eat the earth or deflect the course of any wayward positrons without making a deliberate effort to be in the way. My other conclusion: blog authors say lot’s of shit without firing a single neuron to see if what they’re saying is anything but nonsense.

Angular momentum by harmonic oscillator

I’ve been thinking about Sakurai problem 3.19 for the past few days.

The problem reads:

19.) What is the physical significance of the operators

K+ ≡ a+†a†        and       K ≡ a+a

in Schwinger’s Scheme for angular momentum? Give nonvanishing matrix elements of K±

I’m not sure I completely understand this problem yet. The ‘a’ operators are the creation (daggered operator) and annihilation operators (undaggered operator) for the simple Harmonic oscillator. Applying these operators to simple harmonic oscillator eigenstates increase or decrease, respectively, the energy quantum number of the state, allowing you to move up or down the energy spectrum. In Schwinger’s scheme, two harmonic oscillators are put together  to create an angular momentum eigenstate (thus proving that you really can create everything out of harmonic oscillators). These oscillators are represented by the ‘+’ and ‘-‘ subs on the ‘a’ operators. K+ and K- are almost but not quite the same as the ladder operators, defined in Schwinger’s Scheme as a+†a and a+a† which is definitely subtly different. In Schwinger’s scheme, the two harmonic oscillators are independent eigenspaces that are coupled together and applying a+†a increases the ‘+’ state while decreasing the ‘-‘ state. Eventually, the ‘-‘ state hits its ground state and a further application gives a zero. Going the other way with the second operator does the same thing, decreasing the ‘+’ state while increasing the ‘-‘ state until you hit the bottom of the ‘+’ state spectrum and annihilate the combination with a zero. The affect is like the Ladder operators walking across the ladder, either up or down ‘m’ values until you hit the end and kill the last state.

My conclusion about the K± operators is that they will essentially increment or decrement the total angular momentum (l-value) of the coupled state, which is actually really kind of wicked. I haven’t worked the math yet, but I think this is cool. This problem is also interesting to me because it gives a basic hit with a way that QFT deals with photon formalism. Photons are loaded into eigenstates using operators like these.

I’ve decided that Julian Schwinger was a very smart guy.

How Quantum Mysticism Slips Free of the Math

(Subtitle: How I’m still seething after reading about Quantum University and seeing a bunch of boobs calling themselves ‘quantum physicists.’)

After finishing that previous post, I realized that I still have more to say about the topic. I’ve actually read quite a bit from quantum cranks before and the topic never fails to inflame me. To see a group of people calling themselves ‘quantum physicists’ when they have exactly no background in actual quantum physics is disturbing.

The freedom of speech, a civil right we consider mightily to be a foundation of our culture, brings with it a grave penalty. People cannot be persecuted by any authority for what they say. This means that lying, in some ways, is a protected right. As far as I can tell, as a scientist with no expertise in legal doctrine, there are three forms of speech that can be litigated in court: Libel, Slander and Plagiarism. The first two are ‘defamation.’ Is harassment a kind of speech that can be litigated? As far as I know, even hate speech is protected by freedom of speech if the person using it is not actually acting on their hatred. Libel, Slander and Plagiarism are all things that you can be sued for because they actively incur damage to the victim, either by harming someone’s reputation or by stealing somebody’s property. People who parade around with diploma-mill degrees claiming to be ‘quantum physicists’ never mind that they know neither quantum nor physics nor likely any kind of deeper math, are permitted to do this as long as they are not victimizing anyone else in the process. If they tried to show up at the APS march meeting or DAMOP, they would be laughed out the door, but that doesn’t stop them from making the claim. Deepak Chopra and Lionel Milgrom and the Amit Goswami can all say basically whatever they want, twist Quantum Mechanics, slander and libel it, plagiarize and skew its theses to say whatever they want it to say without breaking their freedom of speech all because Quantum Mechanics is not a person. No court in the land will prosecute ‘harm to a concept.’ The grave penalty of the freedom of speech is that it means that no authority can be appointed to preserve Truth. Defamation of the Truth?

Quantum Mechanics is a broad area of study that spans clear from organic chemistry all the way through nuclear physics clear over to string theory. That is so many paths of study that nobody can claim to be a master of all of it. As a biophysicist, it helps that I know about it, but I can’t claim that I directly study it. Most of my work with quantum is in my spare time because I loved what I learned and don’t want to forget it. But, that also doesn’t mean that I know nothing about it. I have taken literally years of quantum. “What do you know?” a crank would say, “You’re not a quantum physicist!”

That’s true: I’m not an authority figure on quantum mechanics. I cannot level any arguments by authority. But, I am a physicist and I can argue the logic of the physics.

Quantum physics walks a precarious line to the laymen. Fact is, if you don’t know how to do the math, the only way you can know anything about quantum is by the metaphors that have been invented to analogize the subject into our common vernacular. ‘Particle-wave duality’ and ‘Uncertainty principle’ are sets of words that have been parked atop a mathematical concept in order to convey an image that roughly describes what the concept means. There is nothing in our common experience that operates the way quantum mechanics does and we struggle to find ways to convey the discovery. At this point, it is one of the most soundly confirmed scientific principles that has ever been explored. People do not miss that fact, nor do they miss the spooky sounding language that inundates the popular representations of the field. “Uncertainty Principle” sounds like physics has this place where it comes completely unhinged and where magical possibilities peak through the seams!

I don’t argue that. The spooky parts of quantum mechanics are real things. I would encourage anybody to spend time learning about them because they are flamboyantly bizarre.

The problems with quantum begin because people don’t look more carefully at the math and get stuck on the metaphors and anecdotes. The metaphor of Schrodinger’s Cat can quite easily be confused in its purpose. For anybody who doesn’t know, (and surely your numbers must be countable on one hand) the Cat metaphor is that a cat is sealed in a box with a beaker of acid connected to a radioactive sample with a Geiger counter: if the counter registers a strike from a radioactive decay event, the device tips the acid onto the cat, killing the cat. The idea here is that an event like a radioactive decay completely isolated from outside intervention (and I mean isolated _completely_ from outside intervention) will remain in a superposition of possible quantum mechanical outcomes until the box is opened to find whether the decay occurred. Since the cat’s life is intertwined with the uncertain outcome of radioactive decay, the cat is neither dead nor alive until the box is opened and the result of the experiment is determined. This thought experiment was originally postulated by Schrodinger as a way to connect a quantum event, like a radioactive decay, to a macroscopic phenomenon like the life of a cat. The science of the field still argues about the existence of so-called ‘cat states’ due to entanglement, but you have to understand the limits.

From the way that this anecdote is worded, it would appear that the physical act of a person opening a box to look inside –the conscious presence of a person performing a willful act— ties human agency to the outcome. As if the observer as a person is the deciding factor as to whether or not one quantum outcome is observed over another. Observation here is opening the eyes and thinking about the result. I think that cranks love this interpretation because it seems to hint at magical connections between the human observer and the world around them.

In reality, the original purpose of Schrodinger’s Cat was as a reductio ad absurdum to point out how we don’t understand the way fundamental physics builds up to give rise to the classical world that we see around us every day.

When Erwin Schrodinger means ‘inside a box,’ he’s talking about a situation that is absolutely and utterly isolated from the rest of the physical universe. No information in the box can leak out, heat, light or any other physical coupling, and no information from the rest of the universe can leak in. ‘Looking’ in the sense of a quantum mechanical thing is the physical act of bouncing a probe off the specimen in question. You cannot ‘see’ a thing unless information about the location or state of an object reaches your sensory apparatus. For that to happen, a physical interaction must occur between the observer and the specimen being observed. This does mean that the observer becomes entangled with the specimen in a quantum mechanical sense, but it also means that the observer can confound the state of the specimen by forming entanglement. Further, it means that entanglement may result without you knowing that it did since as much as a photon interacting with the system creates a connection between the contents of the box and everything outside… this is called decoherence, when the isolated state loses quantum mechanical coherence by becoming coupled to the surroundings. And, this comes back to my argument of scale in the post I wrote yesterday responding to what I saw in the ‘Respectful Insolence’ article since an ‘observation’ in a physical sense is not really a ‘thoughtful’ event like opening the box and peeking with your eyes, but a mere physical interaction between sensor and specimen. Such an interaction can be mediated whether a person is thinking about it or not, which completely removes consciousness as any required influence on quantum behavior. That’s why an MRI machine can work even if you don’t have a person sitting there witnessing it.

Secondarily, the idea of reducing a cat to a superposition of ‘alive’ and ‘dead’ eigenstates is massively oversimplifying. I worded the anecdote to eliminate a typical preference toward describing alive or dead as eigenstates partly because an ‘eigenstate’ is such a foreign concept from our usual realm of experience. While eigenstates are by definition the most simple, clear-cut things imaginable, ‘Alive’ and ‘Dead’ are both extremely complex statistical mechanical states of being with a surprising amount of overlap –alive and dead are not orthogonal in the manner of eigenstates. Life and Death are so complicated in the quantum mechanical sense that they are probably not calculable and you would never know if you had collapsed into any particular state in an entire spectrum that must include a rather infinite palette of maiming for our poor cat. Then, does ‘observation’ of this system still count if you can’t know how it lost coherence or if it was ever coherent to begin with? If spilling the acid is inevitable, is the cat being ‘alive’ or ‘dead’ a quantum mechanical observation, or merely a classical one? Our classical universe is quantum mechanical, after all, and quantum mechanics itself makes classical outcomes inevitable at the scale where human beings live.

The anecdote of Schrodinger’s Cat has power because it conveys behavior associated with Quantum Mechanics in such a way that an audience can understand basically what Erwin Schrodinger means without actually knowing as much math as Schrodinger needed to originate the concept. In a grain, it is the truth. Even as interpreted by people who coopt quantum legitimacy in order to prop up whatever garbage they favor, that grain of truth remains. In order to understand how far the anecdote is valid, one must look at the layer beneath the words. Within the physics, math becomes essential because it can convey scale and regularity. Words in an anecdote or metaphor contain only as much regularity as the imagination of a listener finds in them. A ‘wave equation’ can easily become ‘spirit’ or ‘entanglement’ can become ‘psychic connection.’ This is especially bad in our world because quantum mechanics has no manifestation that human beings can easily refer to in order to make certain that they understand a concept for themselves. The only way to know that such interpretations are invalid is if they are left in context of the math that produced them. Math in the hands of two different people yields a consistent result (unless you’re Lionel Milgrom) whereas a linguistic sentence interpreted by two different people can have totally different meaning. In this, a linguistic metaphor can lift a concept out of the math, but it does not pick up the entire substance conveyed by that math.

When you use Quantum metaphors bereft of math, no structure remains to control the scope of the meaning in the words. No boundary conditions hold those meanings to what they’re supposed to describe. The words may fit together however they’re being used, but the context where they occur may be completely invalid. Without the math, this is hard to know. To quote something I remember from Deepak Chopra, “In the absence of a conscious entity the moon remains a radically ambiguous and ceaselessly flowing quantum soup.” This has a cat-in-the-box spooky quantum feel to it and the meaning sort of resembles what actual quantum things do, but the context of this metaphor makes it completely dishonest, no matter the poetry or aesthetic appeal. Without the math and the context which formed the math, this metaphor doesn’t stand up. It’s just a lie. Just as homeopathy is killed by the size of Avagadro’s number, quantum mysticism is killed by the miniscule size of Planck’s constant.

It’s an inevitable result: if you leave the scale of Planck’s constant, quantum mechanics tends to become classical. That’s not a lie, it’s simply built into the way quantum-ness works, which isn’t captured by the metaphors.

As an example of this effect, here is one of the most fundamental quantum mechanical equations. This is called the DeBroglie relation:


This simple relation lets one determine the quantum mechanical wavelength of an object given the mass and velocity of that object (the Greek letter lambda refers to wavelength in meters). If you want, you can calculate your own wavelength while you walk, which is a fun exercise. Just set ‘h’ to 6.63×10^-34, ‘m’ to your own weight in kilograms and ‘v’ to your walking speed in meters/sec and you too can find your wavelength. I bet you never believed that a person exhibits particle-wave duality! Or, maybe you did believe it, but thought I was going to be all closed-minded and disagree with you. Note, in order to actually see the wave-like behavior, the wavelength has to be roughly equal to the size scale where you observe the object. For comparison, I would urge plugging in the mass of an electron moving at your walking speed (electron mass is 9.11×10^-31 kg).

There is a quirk to this equation that needs to be explained: if you’re sitting still, where velocity approaches zero, your wavelength becomes big. The uncertainty principle is actually at the heart of this, but for an object like a person, you must always keep in mind that you are moving about at an appreciable speed (micrometers/second) no matter how macroscopically still you try to sit. No matter what, your speed will always be big enough that your wavelength will remain small. (Ask yourself how small that wavelength is and keep in mind that the size of an atom is considered to be 10^-10 meters and the size of an atomic nucleus is 10^-15 meters.)

I do understand how people manage to wedge quantum mechanics into homeopathy, or acupuncture or ayurveda. They look at the metaphors and reinterpret scope and massage what the words mean. The problem is that using such words are no longer a truth. Uncertainty Principle didn’t suddenly facilitate Reiki. I also know that practitioners of these sorts of magic will accuse me of being closed-minded and of using quantum mechanics the ‘wrong way.’ Do you know if you’re using it the ‘right way?’ In this case, there damn well is a right way! How do you know that leading ‘quantum theorists’ support whatever gobbledigook you’ve crammed into it? How do you know? Do you consider ‘leading’ to be a guy who has never actually published as a quantum physicist? If you say I can’t be ‘correct’ because I’m ‘mainstream,’ ask yourself if you would have any quantum metaphors to quote if the mainstream hadn’t ultimately invented them for you? Your only reason for touting quantum mechanics is because you think it somehow adds legitimacy to whatever you’re talking about. Are you truly sure that it does or are you only quoting platitudes you’ve heard from someone else? How in the world do you know that they’re true?

Freedom of Speech has a horrible price. There are no penalties for screwing up and being wrong except for the existential continuity of Truth itself. I’ve come to think that practically nobody in the country cares about the truth anymore, if you look at our presidential candidates. So, the internet has no error check mechanism and no real warning bell to tell you that whatever webpage you’re reading is loaded down with lies. Heck, somebody dead set on Homeopathy is going to accuse what I’ve written here as being some sort of lie. Honestly, I don’t care a whit about homeopathy; I care about people distorting a beautiful physics in order to support something that is not related to it at all. It’s about borrowing legitimacy. Since quantum can’t fight back and most people don’t know enough about it to be certain of lies, I guess people like me are the only champions to protect it. The people who lie are free to keep on lying and they sometimes believe that they are the ones curating the Truth. Are you sure you’re telling a truth? How do you know? If you are, then prove it. In this case, it had better not just be by pulling out some integrative medicine paper; you’d better actually know the physics.

Grade A crankery at Quantum University

It would be accurate to call me a skeptic. There’s no intention in me to use this blog to debunk the overwhelming quantity of crap floating around the internet, but sometimes, I just need to open my mouth. Such an inspiration hit me while reading Respectful Insolence. In that post, Orac is talking about a reddit thread where a woman with an entrenched antivaccine view tries to drum up support for her unyielding stance of not vaccinating her unborn child, despite the father’s desire to vaccinate. While I have done my time in microbiology and immunology courses, I am certainly not a leading expert in medicine. For a medical professional’s opinion of vaccination, you’re not about to find it here. I am unquestionably pro-vaccine, but my interest in the blog post appears about midway through. The woman is trying to bolster her bonafides by outlining her education.

I am still finishing it up but it is a bachelors in holistic health sciences from the International Quantum University of Integrative Medicine ( They are a relatively young establishment so not well known, but many of the faculty members are leading experts in quantum physics and many other areas (the school’s focus is a new perspective on medicine as based on modern quantum physics findings). It’s so fascinating whether you are interested in natural medicine or physics or both!

The word driving my interest should be clear. It’s the only word with a ‘Q’ in that entire paragraph.

You can’t just throw that word anywhere and expect it to mean what it means in its natural context. From what she has said here, I find it highly unlikely that she’s ever touched a Hamiltonian or worked a probability.

In curiosity, I went to the Quantum University website just to see what the education there entails. Is there even the vaguest possibility that the graduates learn any real quantum mechanics? I ended up centering on a blog post there titled “Quantum Physics: A New Scientific Foundation for Integrative Medicine” in some hopes that they would boil their teaching philosophy down to a bite-sized snippet. I was looking for some sign of physics provenance that might be traced to something real in their philosophy and I found the following.

A leading quantum physicist, Amit Goswami, PhD., has already laid the foundation for this in his book, The Quantum Doctor, a physicist’s guide to health and healing.

Apparently they attribute their ‘quantum physics’ to a guy named Amit Goswami. It isn’t hard to noticed that everybody on this website wears a PhD or a Doctorate behind their name and you have to wonder where these degrees came from–I don’t yet have a PhD and I am in a physics graduate program. Going for a PhD in physics was the hardest thing I’ve done in my life and it has given me real gray hair. I looked for publications by Amit Goswami on Web of Science and hoped for a list of ‘Physical Review Letters’ citations. Did I find them? Nope. But, he does have a couple citations in an Integrative Medicine journal. I’m trying to decide how this guy can be a leading quantum physicist when he has apparently never published under his name in a physics journal. Poor antivax lady, strike one for your capacity to discover the reality of anything. I am more broadly published in the primary literature than this guy and I don’t even have my PhD yet. I have no idea who Amit Goswami is beyond that, but I bet he’s making more money than me…

He is after all using quantum physics to justifying some pretty remarkable stuff:

Through the principles of quantum physics we can explain how ancient traditions of healing such as Oriental Medicine and Acupuncture, Ayurvedic Medicine, and modalities such as Homeopathy and Naturopathy, work with the body’s subtle energy systems such as ch’i, prana, and vital force energy.

The post really doesn’t say a huge amount more, but I saw absolutely no quantum mechanics. As I drifted down through the comments I eventually hit a guy making some statements that seems to be what I’m looking for.

Aiding us in our questioning, the tool of Quantum Physics provides much hope. Quantum theory holds the promise of helping us escape the ontological prison imposed by classical physics in which we objectify our observation experiences as events in a real world. In quantum theory, a single superposition state can give rise to multiple observation experiences, thereby, opening the door to confounding the classically determinate states that obtain in the world prior to and independent of our acts of observation.

Now, some of this sounds like stuff that might come out of a layman’s description of QM, but you’ve got to remember that whenever this guy says ‘observation’ he means ‘what a person sees in the world around them.’ Yes, indeed, a single state function can be a superposition of a number of eigenstates and an ‘observation’ can cause the superposition to collapse into a particular eigenstate. But, when a physicist uses the word ‘observation,’ he/she doesn’t literally mean ‘to look at with eyes.’ The world of the quantum is unfortunately divided from our world by a factor of Planck’s constant. This constant is in units of joule*seconds and has the value of 6.63×10^-34. This constant effectively puts a wall between classical reality and quantum reality so high that you can’t hope to cross it in your everyday life. Here’s why: quantization of state energies is discretized by increments of Planck’s constant, which is to say that this constant sets the energy difference between two eigenstates. That number is tiny –Homeopathy is often listed as aphysical because of a lack of comprehension of Avagadro’s number, here’s a number that’s even further out! For an object to behave in a quantum fashion, the energy of the difference between successive states in an energy spectrum must be about the same size as, or greater than, the ambient thermal energy (KbT, boltzman constant times the temperature). On the scale of human experience, the difference between two eigenstates is so tiny that you could not ever realize that there were different states, even if you witnessed a collapse. From our perspective, the discrete look continuous. This is why classical physics works at all: quantum physics reduces to classical physics when you start asking for observations on a level observable by human beings.

Consider yellow light, something we can witness in everyday life. Yellow light has a wavelength of approximately 550 nm. A back of the envelope calculation tells us that the frequency of this light is approximately 5.4×10^14 Hz. A quantum mechanical energy transition (the passage between two successive eigenstates) that produces yellow light is 3.6×10^-19 Joules. That’s the amount of energy contained in a single yellow light photon, a photon being the quantum scale package of light energy. To be quantum mechanical here, you have to be distinguishing on the scale of photons. Consider now the heat capacity of water (you are made mostly of water): it takes 4.2 joules of heat to raise one gram of water one degree Celsius in temperature. It would take 1.17×10^19 approximately yellow photons to raise one gram of water by a single degree. By physiological means alone, a human being cannot detect being hit by a single photon –can you tell the change in temperature by 1 part in 10^19th of a degree? That’s not one part per million, not one part per billion, not even one part per trillion… there are still seven zeroes to go to get to 1 in 10^19!

The back of your eye produces images from physiologic scales of yellow light interacting with cis-trans retinal in the Rhodopsin ion channels of cone cells in your retina (of which there are ~6 million). Rhodopsin is expressed en mass in these cells and they need bright light to operate, so you can figure some large number of Rhodopsin per cell, probably on the order of thousands, of which many need to fire simultaneously in order to cause the cell to transmit a signal to your brain. The color images you see are being produced by conservatively billions of interactions with light. Can you distinguish one strike? The limits of a human being work in a very obvious fashion: for something you see, perception transitions from discrete to continuous at about the frame rate of a TV, 32 frames per second, or 0.03 Hz, roughly 10^12 times slower than the frequency of yellow light and we need huge numbers of photons to build any visual images and billions and billions of photons to tell even the best we can for changes of temperature on our skin. The physiological human being is not fast enough or sensitive enough to witness ‘quantum events’ and understand them as ‘quantum.’ This is why Classical Physics is good enough to describe basically everything you encounter and observe in your day-to-day life. Ontological prison or not, we simply can’t see ‘quantum-ness’ directly.

Real physicists get around these huge gulfs of performance by conceding that a human being can’t witness a quantum thing directly. Doing experiments in quantum physics requires machines to intercede between human perception and quantum phenomena. One example is the MRI machine. To build an image by MRI, this huge machine is performing an experiment that causes the collapse of a quantum spin state ‘by observation.’ The MRI operator fires up a program in a computer that does the entire observation on the instrument whether the operator is standing there witnessing it or not. A computer is mediating the interaction. The person doing ‘the observing’ is not cognitively present for the quantum observation in question because the machine literally runs the state collapse experiment dozens to hundreds of times before spitting out a single result that the self-aware human mind begins to interact with. Everything quantum mechanical has been long since resolved when the human mind finally enters into the loop. Worse, in MRI, you basically don’t see the data about the quantum states; the computer performs a major mathematical operation in a split second to reconstruct where the signals of the quantum events are located into a tomogram that contains only the information about ‘density of signal.’ The person does not once directly interact with anything quantum… the keyboard, mouse and screen are all classically describable.

*sigh* Quantum theory is amazing. It is truly amazing. The math is neat and the results are mind bending. However, if there is no big machine between the thing being observed and the person doing the observing, what you’re talking about is probably not quantum mechanical. Empathy and emotional connection is a helpful thing in healthcare, frame of mind certainly helps to buoy distress, but none of these things is quantum mechanical in a way that human beings can directly understand, manipulate or control. Shoving the word ‘quantum’ into sympathetic magic and calling yourself a ‘quantum physicist’ insults generations of honest physicists who actually worked really hard to give us powerful medical tools like MRI, which don’t require an intimate understanding of their quantum mechanical underpinnings in order to operate. In that quote above, the speaker has stripped all the actual quantum mechanics out of the words and reduced them to a feel-good metaphor that has no more relation to quantum mechanics than a glass cuvette has to an elephant. I don’t care how well you articulate the words ‘ontological prison,’ if you can’t work a Hamiltonian or operate within the constraints of Planck’s constant, you’re not a quantum physicist and the place where you’re learning this metaphorical garbage is a diploma mill. The only ontological prison you’re interacting with is the one you set up for yourself when you started believing these comfort-food lies about quantum physics. That poor antivax woman in the reddit thread kind of deserves the bashing she received: she’s eroding the credibility of a real science.

Edit 8-10-17:

There is a disingenuous quality to my argument here which has always bothered me. I hesitate in bringing it up because I think that without really understanding the physics the argument will seem to give credence to the cranks. There is some difficulty here in defining what an observation even means in terms of quantum mechanics and what physical interaction is required for the observation to occur.

I specified “observation” in the main body of the blog to be due to interactions between the human biological sensory apparatus and light. Our organism is limited to interacting with quantum mechanical phenomena by means of light. Question comes down to what quantum thing we’re observing.

If we’re looking for quantum mechanical behavior of the material universe around us, what we’re interested in is particle/wave duality of objects with mass, like the electrons and atoms that build up into the molecules and larger continuum of matter that composes our world. We can directly observe the outcome of quantum mechanics involving our material world in the light that comes to us from pretty much any source: you take a prism made of glass or plastic (or some material which has dispersity) and hold it into a beam of broad spectrum light from basically any source and that light can be split into its constituent colors. If you examine this sort of color spectrum, you’ll notice that it contains gaps. These gaps turn out to be a direct quantum mechanical phenomenon that you can see with your own eyes, but good luck describing how these gaps got there without actually invoking what quantum mechanics really says. Notice that even here, there is a tool being used to render the quantum mechanical behavior discernible. Without the prism, you can’t see this very well. By noticing that the light from an incandescent bulb is different from sunlight which is different from fluorescent light, you are directly seeing a quantum mechanical effect, but that you are unable to decompose the observation with precision to note exactly what it is that you’re seeing. What do the differences in color mean? Fact remains that most lightbulbs can be confirmed to be turned on whether you’re looking at them or not in the non-trivial effect they have on your power bill and that consciousness is not required for them to generate light (do you have to understand why the switch on the electrical generator must be flipped in order for it to make a bulb light up? Not really: you only need to know that it does.)

A second facet of this conversation is in the light itself. Because light has no mass, particle/wave duality permits it to be very wavelike. In fact, it is so wavelike that it was not initially understood to have particle-like properties. My arguments in the main body of this blog post center around the fact that the human apparatus is almost completely incapable of distinguishing the particle-ness of photons unaided. But, you can witness the wavelike properties directly: this is the reason shadows are always fuzzy along the edge (well, spot size is finite anyway… quite a bit of the shadow fuzziness arises from the light source being a particular size and shape). This is the reason images bend through water so that swimming fish appear to be in a different spot from where they actually are when viewed through the surface of a lake. This is the reason prisms split white light into all its colors. All of that is wavelike. It does not reduce to the ocean wave picture most people have in their heads of “waves” or the tangible vibrating guitar string, but all of that is wavelike. Further, it is all completely describable by classical electromagnetism, a form of classical physics. You really don’t need quantum mechanics to describe how waves of light work. In fact, EM is computationally easier to deal with, so it’s preferred wherever necessary because the quantum is much more difficult to manage. It is really quite stunning that classical models of light behavior lend themselves very readily to quantum mechanical models and it is no accident that you need to have a fairly good understanding of EM in order to really be able to manage quantum.

One thing that quantum does for physics is that it wraps distinct behaviors into the same explanation. Wavelike behaviors seen with material objects like electrons and atoms are the same sort of wavelike behaviors seen with light because of quantum mechanics. Particle-like behaviors of light are similar to those of material objects also because of quantum mechanics. Many people become fruity talking about quantum because they don’t even know what it’s intended to describe. Ayurveda? Prana Energy? How in the hell are these things even relevant to the discussion? People fixate on the indecisive language that is intrinsic to quantum mechanics –“Uncertainty,” “Wavelike,” “indeterminacy”– and they assume that this means there’s an open gap of nonspecific meaning where garbage can be crammed. If you note the “Ontological prison” quote I included above, this is exactly what the original author is intending with his comment; “because quantum supercedes classical physics and because quantum uses wiggedy language, I can use quantum to validate whatever I feel like validating despite the fact that classical physics would seem to claim that such things are impossible.”

I could go on like this all day, but it really doesn’t illuminate the conversation.