Revoke Shaquille’s Doctorate in Education… he doesn’t deserve it.

We are in a world where truth doesn’t matter.

Read this and weep. These men are apparently the authorities of truth in our world.

Everywhere you look, truth itself is under assault. It doesn’t really matter whether you believe, it really doesn’t matter what you want it to say. Truth is not beholden to human whims. We can’t ultimately change it by manipulating it with cellphone apps. We can’t reinterpret it if we wanted to. One of these days, in however great of importance we hold ourselves, the truth will catch up. And we will deserve what happens to us after that point in time.

“It’s true. The Earth is flat. The Earth is flat. Yes, it is. Listen, there are three ways to manipulate the mind — what you read, what you see and what you hear. In school, first thing they teach us is, ‘Oh, Columbus discovered America,’ but when he got there, there were some fair-skinned people with the long hair smoking on the peace pipes. So, what does that tell you? Columbus didn’t discover America. So, listen, I drive from coast to coast, and this s*** is flat to me. I’m just saying. I drive from Florida to California all the time, and it’s flat to me. I do not go up and down at a 360-degree angle, and all that stuff about gravity, have you looked outside Atlanta lately and seen all these buildings? You mean to tell me that China is under us? China is under us? It’s not. The world is flat.”

This spoken by a man with a public platform and a Doctorate in Education. This is the paragon of teachers!

{Edit: 3-20-17 since I’m thinking better about this now, I will rebut his meaningless points.

First, arguments about whether or not Columbus discovered America are a non-sequitur as to whether or not the Earth is round.

Second, driving coast to coast can tell you very little about the overall roundness of the Earth, especially if you aren’t paying attention to the things that do. The curvature of the earth is extremely small: only about 8 inches per mile. This means that on the scale of feet, the curvature is in thousandths of an inch, so that you can’t measure it to not be flat at the dimensions that a human being can meaningfully experience standing directly on the surface. Can you see the couple feet of curvature at a distance of fifty miles looking off a sky scraper in the middle of Atlanta, or distinguish the deviation from the same direction of ‘up’ of two sky scrapers separated by ten miles? You can’t resolve tens of feet with your eyes at a distance of miles. That said, you actually can see Pikes Peak emerge over the horizon as you come out of Kansas into Colorado, but I suppose you would explain that away by some sort of giant conspiracy theory elevator device. To actually start to directly see the curvature at a meaningful degree with your eyes, you need to be at an altitude of hundreds of thousands of feet above the surface… which you could actually do as somebody with ridiculous wealth.

Third, how would you know that China is not ‘under?’ How would you know where China isn’t when you wouldn’t be able to see that distance along a flat surface no matter which direction you look? Can you explain the phase factor that you pick up to your day that causes your damn jet lag every time your wealthy, ignorant ass travels to places like China? By your logic, you should be able to use your colossal wealth to travel to where the globe of the sun pops out of the plane of the Earth in the east every morning. Hasn’t it once occurred to you that if you’re truly right, you should test a hypothesis first before making an assertion that can be easily shown to be wrong?}

You made a mint of money on the backs of a lot of people who made it possible for you to be internationally known, all because of the truth that they determined for you! You do not respect them, you do not understand the depth of their efforts, you do not know how hard they worked. You do not deserve the soapbox they built for you.

For everyone who values the truth, take a moment to share a little about it. Read other things in my blog to see what else I have to say. I have very little I can say right this second; I’m aghast and I feel the need to cry. My hard work is rendered essentially meaningless by morons like Shaquille O’Neal… men of no particular intellect or real skill dictating what reality ‘actually is’ while having no particular capacity to judge it for themselves.

From a time before cellphone apps and computer graphics manipulation, I leave you with one of the greatest pinnacles of truth ever to be achieved by the human species:


Like it or not, that’s Earth.

If you care to, I ask you to go and hug the scientist or engineer in your life. Tell them that you care about what they do and that you value their hard work. The flame of enlightenment kindled in our world is precious and at dire risk of guttering out.


An open letter to the Shaq:

Dear Shaquille O’Neal,

I’m incredibly dismayed by your use of your public personae to endorse an intellectually bankrupt idea like flat earth conspiracy theories particularly in light of your Doctorate Degree in Education. If you are truly educated, and value truth, you should know that holding this stance devalues the hard work of generations of physicists and engineers and jeopardizes the standing of actual scientific truth in the public arena. The purpose of an educator is to educate, not to misinform… the difference is in whether you spread the truth or not.

There is so much evidence of the round earth available in the world around us without appeal to digital media, the cycle of the seasons, scheduled passages of the moon and the planets, observations of Coriolis forces in the weather patterns and simple ballistics, the capacity to jump in an airplane heading west and continue to head west until you get back to where you started, the passage of satellites and spacecraft visible from the surface of the Earth over our heads, the very existence of GPS available on your goddamn smart phone, to the common shapes of objects like the moon and planets visible through telescopes in the night skies around us, that appeals to flat earth conspiracies show a breathtaking lack of capacity to understand how the world fits together. That it comes from a figure who is ostensibly a force of truth –an educator– is truly deeply hurtful to those of us who developed that truth… modern scientists and engineers.

Since you are so profoundly wealthy, you among all people are singularly in a position to prove to yourself the roundness of our world. I bet you 50 million dollars that I don’t even have and will spend my entire life trying to repay, that you can rent an airliner with an honest pilot of your choice and fly west along a route also of your choice, and come back to the airport you originally departed from without any significant eastward travel. Heck, you can do the same exercise heading north or south if you want. And, if that experiment isn’t enough, use your celebrity to talk to Elon Musk: I hear he’s selling tickets now to rich people for flights around the moon. I bet he would build you a specially-sized two-person-converted-to-one berth in his Dragon capsule to give you a ride high enough to take a look for yourself at the shape of the world, if your eyes are the only thing you’ll believe. If you lose, you pay a 49 million dollar endowment to the University of Colorado Department of Physics for the support of Physics Education –and a million to me for the heartache you caused making a mockery of my education and profession by use of your ill-gotten public soapbox and mindlessly open mouth. Moreover, if you lose, you relinquish your Doctorate and make a public apology for standing for exactly the opposite of what that degree means.


Foolish Physicist
of Poetry in Physics

Edit 4-5-17:

So, Shaq walked back his comments.

O’Neal: “The first part of the theory is, I’m joking, you idiots. That’s the first part of the theory. The second part is, I said jokingly that when I’m in my bus and I drive from Florida to California, which I do every summer, it seems to be flat. When I’m in my plane, and we’re getting ready to land, and I open up the window, and I’m looking at all the land that we’re flying over, it seems to be flat.”

“This world we live in, people take things too seriously, but I’m going to give the people answers to my test,” he said. “Knowing that I’m a funny guy, if something seems controversial or boom, boom, boom, you’ve got to have my funny points on, right? So now, once you have my funny points on, that should eradicate and get rid of all your negative thoughts, right? That’s what you should do when you hear a Shaquille O’Neal statement, OK? You should know that he has funny points right over here, and what did he say? Boom, boom, boom, add the funny points. You either laugh or you don’t laugh, but don’t take me seriously. When I want you to take me seriously, you will know by the tone of my voice that I’m being serious.”

“No, I don’t think that,” O’Neal told Harbinger of a flat Earth. “It was a joke, OK? So know that when Shaquille O’Neal says something, 80 percent of the time I’m being humorous, and it is a joke. And 20 percent of the time, I’m being serious, but when I’m being serious, you’ll know. You want to see me, seriously? See me and Charles Barkley going back and forth on TNT. That’s when I’m mad and when I’m serious. Other than that, you’re not going to get that out of me, so I was just joking people. The Earth is not round, it’s flat. I mean, the Earth is not flat, it’s round.”

One thing that should be added to these statements is this: there are people who are actively spreading misinformation about the state of the world, for instance that the earth is flat. The internet, Youtube, blogs, you name it, has given these people a soapbox that they would not otherwise have. Given that there is a blatant antiscientific thread in the United States which is attacking accepted, settled science as a big cover-up designed to destroy the rights of the everyday man, it is the duty of scientists and educators to take the truth seriously. In a world where Theory of Evolution, Climatology and Vaccine science are all actively politicized, we have to stand up for the truth.

Where real scientists are about studying and doing our work, the antiscientific activists are solely about spreading their belief… they don’t study, they don’t question, they spend their time actively lobbying the government and appealing to legislators, running for and getting onto school boards where they have an opportunity to pick which books are presented to school districts and various places where they can actively undercut what students are told about the truth of the world. They aren’t spending their energy studying, they are spending their energy solely on tinkering with the social mechanisms which provide our society with the next generation of scientists. As such, their efforts are more directed at undercutting the mechanisms that preserve the truth rather than on evaluating the truth… as scientists do. These people can do huge damage to us all. Every screwball coming out of a diploma mill “Quantum University” with a useless, unaccredited ‘PhD’… who goes off to promote woo-bong herbalist healthcare as an alternative to science based medicine, does damage to us all by undercutting what it means to get healthcare and by putting crankery and quackery in all seriousness at the same level as scientific truth when there should be no comparison.

If everybody understood that there is no ‘alternative’ to the truth, joking about what is true would mean something totally different to me. But, we live in a world where ‘alternative facts’ are a real thing and where everyone with a soapbox can say whatever they wish without fear of reprisal. Lying is a protected right! But someone has to stand up for truth. That someone should be scientists and educators. That should include an ‘education doctorate’ like the Shaq. If he were an NBA numbskull without the doctorate, I would care less: Kyrie Irving is a joke. But he isn’t; he’s got a doctorate and he has a responsibility to uphold what that degree means! The only reason humor in irony can work is if it can be clear that one is being ironic instead of serious… and that is never completely clear in this world.

Nuclear Toxins

A physicist from Lawrence Livermore Labs has been restoring old nuclear bomb detonation footage. This seems to me to be an incredibly valuable task because all of the original footage was shot on film, which is currently in the process of decaying and falling apart. There have been no open air nuclear bomb detonations on planet Earth since probably the 1960s, which is good… except that people are in the process of forgetting exactly how bad a nuclear weapon is. The effort of saving this footage makes it possible for people to know something about this world-changing technology that wasn’t previously declassified. Nukes are sort of mythical to a body like me who wasn’t even born until about the time that testing went underground: to everybody younger than me, I suspect that nukes are an old-people thing, a less important weapon than computers. That Lawrence Livermore Labs has posted this footage to Youtube is an amazing public service, I think.

As I was reading an article on Gizmodo about this piece of news, I happened to wander into the comment threads to see what the echo chamber had to say about all this. I should know better. Admittedly, I actually didn’t post any comments castigating anyone, but there was a particular comment that got me thinking… and calculating.

Here is the comment:

Nuclear explosions produce radioactive substances that are rare in nature — like carbon-14, a radioactive form of the carbon atom that forms the chemical basis of all life on earth.

Once released into the atmosphere, carbon-14 enters the food chain and gets bound up in the cells of most living things. There’s still enough floating around for researchers to detect in the DNA of humans born in 2016. If you’re reading this, it’s inside you.

This is fear mongering. If you’ve never seen fear mongering before, this is what it looks like. The comment is intended to deliberately inspire fear not just in nuclear weapons, but in the prospect of radionuclides present in the environment. The last sentence is pure body terror. Dear godz, the radionuclides, they’re inside me and there’s no way to clean them out! I thought for a time about responding to this comment. I decided not to because there is enough truth here that anyone should probably stop and think about it.

For anyone curious, the wikipedia article on the subject has some nice details and seems thorough.

It is true the C-14 is fairly rare in nature. The natural abundance is 1 part per trillion of carbon. It is also true that the atmospheric test detonations of nuclear bombs created a spike in the C-14 present in the environment. And, while it’s true that C-14 is rare, it is actually not technically unnatural since it is formed by cosmic rays impinging on the upper atmosphere. For the astute reader, C-14 produced by cosmic rays forms the basis of radiocarbon dating since C-14 is present at a particular known, constant proportion in living things right up until you die and stop uptaking it from the environment –a scientist can then determine the date when living matter died based on the radioactive decay curve for C-14.

Since it’s not unnatural, the real question here is whether the spike of radionuclides created by nuclear testing significantly increases the health hazard posed by excess C-14 above and beyond what it would normally be. You have it in your body anyway, is there greater hazard due to the extra amount released? This puzzle is actually a somewhat intriguing one to me because I worked for a time with radionuclides and it is kind of chilling all the protective equipment that you need to use and all the safety measures that are required. The risk is a non-trivial one.

But, what is the real risk? Does having a detectable amount of radionuclide in your body that can be ascribed to atomic air tests constitute an increased health threat?

To begin with, what is the health threat? For the particular case of C-14, one of a handful of radionuclides that can be incorporated into your normal body structures, the health threat would obviously come from the radioactivity of the atom. In this particular case, C-14 is a beta-emitter. This means that C-14 radiates electrons; specifically, one of the neutrons in the atom’s nucleus converts into a proton by giving off an electron and a neutrino, resulting in the carbon turning into nitrogen. The neutrino basically doesn’t interact with anything, but the radiated electron can travel with energies of 156 keV (or about 2.4×10^-14 Joules). This will do damage to the human body in two routes, either by direct collision of the radiated electron with the body, or by a structurally important carbon atom converting into a nitrogen atom during the decay process if the C-14 was part of your body already. Obviously, if a carbon atom turns suddenly into nitrogen, that’s conducive to organic chemistry occurring since nitrogen can’t maintain the same number of valence interactions as carbon without taking on a charge. So, energy deposition by particle collision, or spontaneous chemistry is the potential cause of the health threat.

In normal terms, the carbon-nitrogen chemistry routes for damage are not accounted for in radiation damage health effects simply because of how radiation is usually encountered: you need a lot of radiation in order to have a health effect, and this is usually from an exogenous source, that is, provided by a radiation source that is outside the body rather than incorporated with it, like endogenous C-14. This would be radiation much like the UV radiation which causes a sunburn. Heath effects due to radiation exposure are measured on a scale by a dose unit called a ‘rem.’ A rem expresses an amount of radiation energy deposited into body mass, where 1 rem is equal to 1.0×10^-5 Joules of radiation energy deposited into 1 gram of body mass. Here is a table giving the general scale of rem doses which causes health effects. People who work around radiation as part of their job are limited to a full-body yearly dose of 5 rem, while the general public is limited to 0.1 rem per year. Everybody is expected to have an environmental radiation dose exposure of about 0.3 rem per year and there’s an allowance of 0.05 rem per year for medical x-rays. It’s noteworthy that not all radiation doses are created equal and that the target body tissue matters; this is manifest by different radiation doses being allowed to occur to the eyes (15 rem) or the extremities, like the skin (50 rem). A sunburn would be like a dose of 100 to 600 rem to the skin.

What part of an organism must the damage affect in order to cause a health problem? Really, only one is truly significant, and that’s your DNA. Easy to guess. Pretty much everything else is replaceable to the extent that even a single cell dying from critical damage is totally expendable in the context of an organism built of a trillion cells. The problem of C-14 being located in your DNA directly is numerically a rather minor problem: DNA actually only accounts for about 3% of the dry mass of your cells, meaning that only about 3% of the C-14 incorporated into your body is directly incorporated into your DNA, so that most of the damage to your DNA is due to C-14 not directly incorporated in that molecule. This is not to say that chemistry doesn’t cause the damage, merely that most of the chemical damage is probably due to energy deposition in molecules around the DNA which then react with the DNA, say by generation of superoxides or similar paths. This may surprise you, but DNA damage isn’t always a complete all-or-nothing proposition either: to an extent, the cell has machinery which is able to repair damaged DNA… the bacterium Dienococcus radiodurans is able to repair its DNA so efficiently that it’s able to subsist indefinitely inside a nuclear reactor. Humans have some repair mechanisms as well.

Cells handling radiation damage in humans have about two levels of response. For minor damage, the cell repairs its DNA. If the DNA damage is too great to fix, a mechanism triggers in the cell to cause it to commit suicide. You can see the effect of this in a sunburn: critically radiation damaged skin cells commit suicide en mass in the substratum of your skin, ultimately sacrificing the structural integrity of your skin, causing the external layer to sough off. This is why your skin peels due to a sunburn. If the damage is somewhere in between, matters are a little murkier… your immune system has a way of tracking down damaged cells and destroying them, but those screwed up cells sometimes slip through the cracks to cause serious disease. Inevitably cancer. Affects like these emerge for ~20 rem full body doses. People love to worry about superpowers and three-arm, three-eye type heritable mutations due to radiation exposure, but congenital mutations are a less frequent outcome simply because your gonads are such a small proportion of your body; you’re more likely to have other things screwed up first.

One important trick in all of this to notice is that to start having serious health effects that can be clearly ascribed to radiation damage, you must absorb a dose of greater than about 5 rem.

Now, what kind of a radiation dose do you acquire on a yearly basis from body-incorporated C-14 and how much did that dose change in people due to atmospheric nuclear testing?

I did my calculations on the supposition of a 70 kg person (which is 154 lbs). I also adjusted rem into a more easily used physical quantity of Joules/gram (1 rem = 1×10^-5 J/g, see above.)  One rem of exposure for a 70 kg person works out to an absorbed dose of 0.7 J/year. An exposure sufficient to hit 5 rems is 3.5 J/year while 20 rem is 14 J/year. Beta-electrons from c-14 maximally hit with 2.4×10^-14 J/strike (150 keV) with about 0.8×10^-14 J/hit on average (50 keV).

In the following part of the calculation, I use radioactive decay and half-life in order to determine the rate of energy transference to the human body on the assumption that all the beta-electron energy emitted by radiation is absorbed by the human body. Radiation rates are a purely probabilistic event where the likelihood of seeing a radiated electron is proportional to the size of the radioactive atom population. The differential equation is a simple one and looks like this:

decay rate differential equation

This just means that the rate of decay (and therefore electron production rate) is proportional to the size of the decaying population where the k variable is a rate constant that can be determined from the half-life. The decay differential equation is solved by the following function:

exponential decay

This is just a simple exponential decay which takes an initial population of some number of objects and reduces it over time. You can solve for the decay constant by plugging the half-life into the time and simply asserting that you have 1/2 of your original quantity of objects at that time. The above exponential rearranges to find the decay constant:

decay constant

Here, Tau is the half-life in seconds (I could have used my time as years, but I’m pretty thoroughly trained to stick with SI units) and I’ve already substituted 1/2 for the population change. With k from half-life, I just need the population of radiation emitters present in the body in order to know the rate given in the first equation above… where I would simply multiply k by N.

To do this calculation, the half-life of C-14 is known to be 5730 years, which I then converted into seconds (ick; if I only care about years, next time I only calculate in years). This gives a decay constant of 3.836×10^-12 emissions/sec. In order to get the decay rate, I also need the population of C-14 emitters present in the human body. We know that C-14 has a natural prevalence of 1 per trillion and also that a 70 kg human body is 16 kg carbon after a little google searching, which gives me 1.6×10^-8 g of C-14. With C-14’s mass of 14 g/mole and Avagadro’s number, this gives about 6.88×10^14 C-14 atoms present in a 154 lb person. This population together with the rate constant gives me the decay rate by the first equation above, which is 2.639×10^3 decays per second. Energy per beta-electron absorbed times the decay rate gives the rate of energy deposited into the body per second on the assumption that all beta-decay energy is absorbed by the target: 2.639×10^3 decays/sec * 2.4×10^-14 Joules/decay = 6.33 x 10^-11 J/s. For the course of an entire year, the amount of energy works out to about 0.002 Joules/year.

This gets me to a place where I can start making comparisons. The exposure limit for any old member of the general public to ‘artificial’ radiation is 0.1 rem, or 0.07 J/year. The maximum… maximum… contribution due to endogenous C-14 is 35 times smaller than the allowed public exposure limits (for mean energy, it’s more like 100 times smaller). On average, endogenous C-14 gives 1/100th of the allowed permitted artificial radiation dose.

But, I’ve actually fudged here. Note that I said above that humans normally get a yearly environmental radiation dose of about 0.3 rem (0.21 J/year)… meaning that endogenous C-14 only provides about 1/300th of your natural dose. Other radiation sources that you encounter on a daily basis provide radiation exposure that is 300 times stronger than C-14 directly incorporated into the structure of your body. And, keep in mind that this is way lower than the 5 rem where health effects due to radiation exposure begin to emerge.

How does C-14 produced by atmospheric nuclear testing figure into all of this?

The wikipedia article I cited above has a nice histogram of detected changes in the environmental C-14 levels due to atmospheric nuclear testing. At the time of such testing, C-14 prevalence spiked in the environment by about 2 fold and has decayed over the intervening years to be less than 1.1-fold. This has an effect on C-14 exposure specifically of changing it from 1/300th of your natural dose to 1/150th, or about 0.5%, which then tapers to less than a tenth of a percent above natural prevalence in less than fifty years. Detectable, yes. Significant? No. Responsible for health effects…… not above the noise!

This is not to say that a nuclear war wouldn’t be bad. It would be very bad. But, don’t exaggerate environmental toxins. We have radionuclides present in our bodies no matter what and the ones put there by 1950s nuclear testing are only a negligible part, even at the time –what’s 100% next to 100.5%? A big nuclear war might be much worse than this, but this is basically a forgettable amount of radiation.

For anybody who is worried about environmental radiation, I draw your attention back to a really simple fact:


The woman depicted in the picture above has received a 100 to 600 rem dose of very (very very) soft X-rays by deliberately sitting out in front of a nuclear furnace. You can even see the nuclear shadow on her back left by her scant clothing. Do you think I’m kidding? UV light, which is lower energy than x-rays, but not by that much… about 3 eV versus maybe 500 eV, is ionizing radiation which is absorbed directly by skin DNA to produce real radiation damage, which your body treats indistinguishably from how it treats damage from particle radiation of radionuclides or X-rays or gamma-rays. The dose which produced this affect is something like two to twelve times higher than the federally permitted dose that radiation workers are allowed to receive in their skin over the course of an entire year… and she did it to herself deliberately in a matter hours!

Here’s a hint, don’t worry about the boogieman under the bed when what you just happily did to yourself over the weekend among friends is much much worse.

What is a qubit?

I was trolling around in the comments of a news article presented on Yahoo the other day. What I saw there has sort of stuck with me and I’ve decided I should write about it. The article in question, which may have been by an outfit other than Yahoo itself, was about the recent decision by IBM to direct a division of people toward the task of learning how to program a quantum computer.

Using the word ‘quantum’ in the title of a news article is a sure fire way to incite click-bait. People flock in awe to quantum-ness even if they don’t understand what the hell they’re reading. This article was a prime example. All the article really talked about was that IBM has decided that quantum computers are now a promising enough technology that they’re going to start devoting themselves to the task of figuring out how to compute with them. Note, the article spent a lot of time kind of masturbating over how marvelous quantum computers will be, but it really actually didn’t say anything new. Another tech company deciding to pretend to be in quantum computing by figuring out how to program an imaginary computer is not an advance in our technology… digital quantum computers are generally agreed to be at least a few years off yet and they’ve been a few years off for a while now. There’s no guarantee that the technology will suddenly emerge into the mainstream –and I’m neglecting the DSpace quantum computer because it is generally agreed among experts that DSpace hasn’t even managed to prove that their qubits remain coherent through a calculation to actually be a useful quantum computer, let alone that they achieved anything at all by scaling it up.

The title of this article was a prime example of media quantum click-bait. The title boldly declared that “IBM is planning to build a quantum computer millions of times faster than a normal computer.” Now, that title was based on an extrapolation in the midst of the article where a quantum computer containing a mere 1000 qubits suddenly becomes the fastest computing machine imaginable. We’re very used to computers that contain gigabytes of RAM now, which is actually several billion on-off switches on the chip, so a mere 1,000 qubits seems like a really tiny number. This should be underwritten with the general concerns of the physics community that an array of 100 entangled qubits may exceed what’s physically possible… and it neglects that the difficulty of dealing with entangled systems increases exponentially with the number of qubits to be entangled. Scaling up normal bits doesn’t bump into the same difficulty. I don’t know if it’s physically possible or not, but I am aware that IBM’s declaration isn’t a major break-through so much as splashing around a bit of tech gism to keep the stockholders happy. All the article really said was that IBM has happily decided to hop on the quantum train because that seems to be the thing to do right now.

I really should understand that trolling around in the comments on such articles is a lost cause. There are so many misconceptions about quantum mechanics running around in popular culture that there’s almost no hope of finding the truth in such threads.

All this background gets us to what I was hoping to talk about. One big misconception that seemed to be somewhat common among commenters on this article is that two identical things in two places actually constitute only one thing magically in two places. This may stem from a conflation of what a wave function is versus what a qubit is and it may also be a big misunderstanding of the information that can be encoded in a qubit.

In a normal computer we all know that pretty much every calculation is built around representing numbers using binary. As everybody knows, a digital computer switch has two positions: we say that one position is 0 and the other is 1. An array of two digital on-off switches then can produce four distinct states: in binary, to represent the on-off settings of these states, we have 00, 01, 10 and 11. You could easily map those four settings to mean 1, 2, 3 and 4.

Suppose we switch now to talk about a quantum computer where the array is not bits anymore, but qubits. A very common qubit to talk about is the spin of an atom or an electron. This atom can be in two spin states: spin-up and spin-down. We could easily map the state spin-up to be 1, and call it ‘on,’ while spin-down is 0, or ‘off.’ For two qubits, we then get the states 00, 01, 10 and 11 that we had before, where we know about what states the bits are in, but we also can turn around and invoke entanglement. Entanglement is a situation where we create a wave function that contains multiple distinct particles at the same time such that the states those particles are in are interdependent on one another based upon what we can’t know about the system as a whole. Note, these two particles are separate objects, but they are both present in the wave function as separate objects. For two spin-up/spin-down type particles, this can give access to the so-called singlet and triplet states in addition to the normal binary states that the usual digital register can explore.

The quantum mechanics works like this. For the system of spin-up and spin-down, the usual way to look at this is in increments of spinning angular momentum: spin-up is a 1/2 unit of angular momentum pointed up while spin-down is -1/2 unit of angular moment, but pointed the opposite direction because of the negative sign. For the entangled system of two such particles, you can get three different values of entangled angular momentum: 1, 0 and -1. Spin 1 has both spins pointing up, but not ‘observed,’ meaning that it is completely degenerate with the 11 state of the digital register since it can’t fall into anything but 11 when the wave function collapses. Spin -1 is the same way: both spins are down, meaning that they have 100% probability of dropping into 00. The spin 0 state, on the other hand, is kind of screwy, and this is where the extra information encoding space of quantum computing emerges. The 0 states could be the symmetric combination of spin-up with spin-down or the anti-symmetric combination of the same thing. Now, these are distinct states, meaning that the size of your register just expanded from (00, 01, 10 and 11) to (00, 01, 10, 11 plus anti-symmetric 10-01 and symmetric 10+01). So, the two qubit register can encode 6 possible values instead of just 4. I’m still trying to decide if the spin 1 and -1 states could be considered different from 11 and 00, but I don’t think they can since they lack the indeterminacy present in the different spin 0 states. I’m also somewhat uncertain whether you have two extra states to give a capacity in the register of 6 or just 5 since I’m not certain what the field has to say about the practicality of determining the phase constant between the two mixed spin-up/spin-down eigenstates, since this is the only way to determine the difference between the symmetric and anti-symmetric combinations of spin.

As I was writing here, I realized also that I made a mistake myself in the interpretation of the qubit as I was writing my comment last night. At the very unentangled minimum, an array of two qubits contains the same number of states as an array of two normal bits. If I consider only the states possible by entangled qubits, without considering the phasing constant between 10+01 and 10-01, this gives only three states, or at most four states with the phase constant. I wrote my comment without including the four purely unentangled cases, giving fewer total states accessible to the device, or at most the same number.

Now, the thing that makes this incredibly special is that the number of extra states available to a register of qubits grows exponentially with the number of qubits present in the register. This means that a register of 10 qubits can encode many more numbers than a register of ten bits! Further, this means that fewer bits can be used to make much bigger calculations, which ultimately translates to a much faster computer if the speed of turning over the register is comparable to that of a more conventional computer –which is actually somewhat doubtful since a quantum computer would need to repeat calculations potentially many times in order to build up quantum statistics.

One of the big things that is limiting the size of quantum computers at this point is maintaining coherence. Maintaining coherence is very difficult and proving that the computer maintains all the entanglements that you create 100% of the time is exceptionally non-trivial. This comes back to the old cat-in-the-box difficulty of truly isolating the quantum system from the rest of the universe. And, it becomes more non-trivial the more qubits you include. I saw a seminar recently where the presenting professor was expressing optimism about creating a register of 100 Josephson junction type qubits, but was forced to admit that he didn’t know for sure whether it would work because of the difficulties that emerge in trying to maintain coherence across a register of that size.

I personally think it likely that we’ll have real digital quantum computers in the relatively near future, but I think the jury is still out as to exactly how powerful they’ll be when compared to conventional computers. There are simply too many variables yet which could influence the power and speed of a quantum computer in meaningful ways.

Coming back to my outrage at reading comments in that thread, I’m still at ‘dear god.’ Quantum computers do not work by teleportation: they do not have any way of magically putting a single object in multiple places. The structure of a wave function is defined simply by what you consider to be a collection of objects that are simultaneously isolated from the rest of the universe at a given time. A wave function quite easily spans many objects all at once since it is merely a statistical description of the disposition of that system as seen from the outside, and nothing more. It is not exactly a ‘thing’ in and of itself insomuch as collections of indescribably simple objects tend to behave in absolutely consistent ways among themselves. Where it becomes wave-like and weird is that we have definable limits to how precisely we can understand what’s going on at this basic level and that our inability to directly ‘interact’ with that level more or less assures that we can’t ever know everything about that level or how it behaves. Quantum mechanics follows from there. It really is all about what’s knowable; building a situation where certain things are selectively knowable is what it means to build a quantum computer.

That’s admittedly pretty weird if you stop and think about it, but not crazy or magical in that wide-eyed new agey smack-babbling way.