## Richard Feynman: Science and Chess

By Shamus
on Dec 5, 2010
Filed under:
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Richard Feynman describes scientific inquiry as someone observing a game of chess.

Years ago I was reading A Brief History of Time and I came up with a very similar analogy where I was likening the study of quantum physics to observing a game of billiards. For example, perhaps you can only observe the table between turns, when everything is still. Eventually we’ve come up with a list of rules and observations:

1) Probability of any given ball being on the table, or vanishing from the table.
2) Probably that a given ball will move between the observations, noting that this is 100% for the cue ball, but lower for other balls.
3) Observations noting how balls tend to move less the closer they are to the corners, and more likely to move greater distances when in the middle of the table.
4) The most likely outcome is that a single ball will vanish. The next most likely outcome is that none vanish, followed by two, three, and on down in sharply declining probability.
5) The cue ball is the only ball that re-appears after disappearing from the table.

We could have hundreds of observations like this. Charts, equations, theories… and still have no idea what the rules of the game are or how it’s played. This is where I think we are with quantum mechanics.

I had the same problem back in seventh grade (1984-1985) when we were taught the system of fixed obits on atoms. I’m not talking about current wave-based atomic orbital theory, I’m talking about the older one, which I can’t even find on Wikipedia, perhaps because I can no longer remember the proper name for it. In that old system there were a lot of seemingly arbitrary rules for electrons orbiting a nucleus. There were fixed orbital distances and odd rules about how many electrons could share a given orbit. I thought it was a bunch of nonsense. It lacked the elegance and the usefulness of gravitational theory. Oh, I’m sure the math worked out, but like seeing a game of billiards in terms of probabilities, it felt like we were describing without discovering.

I felt somewhat vindicated a few years ago when I learned they no longer taught that stuff. (Although don’t give me too much credit here. I haven’t gone out and learned the current theory or anything.) I don’t have a scientific background. Heck, I don’t even have enough mathematics to noodle around with the simple stuff they give to first-year students. But I enjoy watching from the sidelines, and am really hoping someone does for Quantum Physics what Einstein did for gravitational physics a hundred years ago. Because our lack of an elegant theory is really starting to bug me.

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1. Soylent Dave says:

You may have been looking for the Rutherford Model of the atom, or the Bohr Model of electron energy levels (which is based on Rutherford’s.

They’re both a bit dependent on arbitariness – electrons repel each other all the time, except when they don’t, and you can only have so many electrons in each energy orbital but some of them have more than others (even though they’re all the same in the model)… and so on.

They’re still sort of useful as a shorthand, and they’re good for teaching kids in a “by the way, all this stuff we’re teaching you is wrong but it’ll enable you to understand the other stuff we’re going to teach you later. Which is also probably wrong (but less wrong)” way.

• Veloxyll says:

They’re also handy for understanding the chemistry of atoms since they’re enough of an approximation for what chemists need to know, at least at high school levels. No idea what model(s) people who actually work with chemistry use

• Nick Bell says:

When I was in high school chemistry, I learned the Bohr model of electron energy levels. I had all sorts of questions to understand how it worked, since its inner workings were not the least bit apparent to me. My teacher refused, literally REFUSED to answer my questions and demanded that I stop asking them because “the answers would confuse the rest of the students.”

I am still angry about it, all these years later. What a shitty response to a student who simply wanted to know more about the subject you are teaching. As a capable person, I went out and taught myself instead. But how many other kids have their education stifled like that and never recover, instead simply accepting everything they are taught without critical thought?

• eri says:

I think you must have had my high school science teacher. I damn near failed it in grade ten because the teacher nor the textbook took any effort to explain what was going on or why – it just “was”. I think that’s also the reason why I ended up failing math in grade eleven as well – rather than provide actual reasons as to why we were solving problems in X ways, they simply said I was doing it wrong and told me to keep practicing. I guess I’m just not the type of person who can understand or even accept things if I don’t have any idea of the logic and reasoning behind it.

Incidentally, my failure at math and science also coincided with my excelling at English, history and sociology, where some semblance of real critical analysis was actually performed. Funny how that works out.

• I fell into the same boat. My grades were always low (even coming from a straight “A” family) and my dad was kind enough to try to tutor me in math. Each night at the dinner table he’d sit down and work the problems with me and he noticed something. I was learning these formulas by memorization and not REALLY understanding why they worked, and it was he lack of understanding that was my core problem. I could tell you HOW to solve the problem but not WHY that solution was right, i just took it on as doing what my teachers were showing.
My other courses never suffered as bad as my math (art, biology, and history were usually my best) cause I was able to at least draw my own conclusions. As an adult, I consider myself fairly knowledgeable in those areas but when it comes to leaving a tip I have to pull out my phone and calculate 15%…
People learn in different ways, and I was lucky enough to have someone who cared about my education enough to give me the support I needed.

P.S. Amusingly when I took the SAT I scored better then my siblings in everything except the math part (HAH!)

• Aldowyn says:

This has always been my key to success in Math and Science: Learn why the formulas are the way they are, and the formulas will come naturally. I don’t do memorization, pretty much ever, I just learn the concepts, and the formulas and stuff come naturally after that.

• Volatar says:

Ditto.

• glassdirigible says:

This is why I usually like to see the proof. If you don’t see the proof it can be a lot harder to see why something makes sense.

Plus, proofs are sometimes many times easier to remember than the theorem they produce. If you forget how to do a problem you can sometimes redo the proof and see how to do the problem. This stops working as the tests get longer though.

• Jeff says:

I have a math degree. Pretty much 95% if not more of post-secondary math courses are proofs.

• Zak McKracken says:

Yeah, it’s horrible how much memorization is being encouraged, even at universities. I know engineers who give you completely arcane ideas about physics when asked why this or that equation is valid (which actually is valid, but for different reasons).

• Miral says:

I recall a case when our maths teacher had just taught us the formula for calculating the volume of a cube and pyramid. I asked how to calculate the volume of other regular shapes (specifically, the remaining Platonic solids — having been exposed to D&D and its dice at a young age), and the reply was along the lines of “I don’t think it’s possible”.

I took that as a challenge, and in the next day or two I presented them a formula that worked for all Platonic solids (and why). (This was before the days of the Internet, so I had worked it out myself from principles.) The teacher was amazed.

But I don’t think the teacher was dumb, or particularly ignorant, or anything. It’s just that they’re teaching material at a particular level, over and over again; in that situation it’s not hard to get a bit of tunnel vision and focus on the material without looking deeper (or higher).

• Heron says:

“I could tell you HOW to solve the problem but not WHY that solution was right”

It always bothered me when high school and college math/physics/chemistry tests would prohibit using a calculator. The implication was that memorizing the equation or the steps for solving the problem are more important than learning when and why various equations should be used. Tests can be designed to determine whether you’ve learned the why rather than the how; I had some teachers do just that.

I use calculators for simple math most of the time, too, unless I’m just working with multiples of two or five or ten… I can handle those.

• Freeze_L says:

Taking no calculator timed tests is evil for me, i have a type of dyslexia. Until i learned how to cope with it i would never have been able to handle a timed test with no calculator. Its funny because i am very good at math and grasp it easily in part because of my dyslexics, it screwed with me when i learned easy things but helps me on more advanced topics. funny how that works.

• Slothful says:

I used to never use calculators unless I was seriously bored and needed something to fiddle with. No sense letting some stupid machine with clumsy buttons get in the way between me and my numbers.

Then along came Sines and Cosines and Tangents and all sorts of other things that the teachers wouldn’t explain, and I had to beseech the almighty calculator god to deliver the answer unto me, without telling me what the hell it meant.

And then my math grades went down the toilet.

• MrWhales says:

I also must use a calculator for simple math, while being able to do complex math in my head. “How did i forget what 4×8 is?” or something similar. And the no calculator rule is beyond dumb. I had a teacher in High school who stressed the importance of what we were doing, then DEMANDED that we only do it with the calculator and refused to show us by hand. Although she wasnt a very good teacher in the first place…..

• Zak McKracken says:

Thats strange, for me it was just the other way round.
I failed English (as a foreign language) because I started reading Dickens in 9th grade and from then on, my style became somewhat more complex than was expected of us which in turn lead to bad bad marks … history and sociology were all about learning and repeating facts and nothing about arguing pros and cons (except if you were in complete agreement with the teacher but then there’s no need to argue…), so I stuck with natural sciences and for much of the time after school I did not even think of history and sociology as being sciences at all. Which I had to correct later. A bit :) I still think that if you have no clue at all it’s easier to pass as a serious scientist in sociology than in natural sciences. Although that is also relative, as I’ve had to realize …

• LassLisa says:

Same here. I had a couple of decent history/lit classes but for the most part was driven away from it by memorization (I was good at it, but it’s not any fun). Whereas science and math were just applied problem-solving, which I loved.

• Slothful says:

My writing style became pretty complex early on too, only then I think it just scared off the teachers so they’d say “Well, it’s above and beyond the level he’s supposed to be at, just let it slide.”

I only got a teacher who tried to explain the high-level errors to me in my last year in high school.

• Mistwraithe says:

This is precisely why I gave up Chemistry. I got sick and tired of them teaching us one thing then next year telling us that most of last year’s stuff was wrong and they were going to teach us the ‘truth’ (which then next year turned out to also be wrong).

In their defence the real truth isn’t known and what we do know about the truth is too complex to comprehend adequately at that level but it is still a crappy way of teaching!

• Soylent Dave says:

Electrons are now particles and waves (or ‘wavicles’ as my lecturer insisted on repeating, over and over and over long after it stopped being even slightly funny)

Particles, in that there is always an integer amount of them wandering about near the nucleus (they aren’t orbiting it any more, oh no, that would be too straightforward. They just sort of amble about near the nucleus a bit).

They jump between orbitals (because they’re still called orbitals, obviously even though they aren’t actually orbiting any more) when they’re poked with sticks and things (or ‘energy’ if you like) – just like you’d expect from something solid.

They’re also waves, in that they don’t actually exist at all, but are a probability instead. So you can’t look at them, or figure out exactly where they are – but they’re probably within the orbital somewhere (or ‘energy shell’). Except sometimes electrons cheat and teleport to places they don’t have enough energy for, the scamps.

So, because they are wavicles (see, I’m doing it now), they can’t be described by location and momentum, because they might not have any. Sometimes.

So you describe them by how far away they are from the nucleus (in energy), by the shape of the area they might be in (what sort of weird shape the not-an-orbital is), how much energy they have within their sub-shell (their ‘quantum state’), and which direction they’re spinning around in.

That’s n, l, m & s.

And no two electrons can have the same 4 numbers, because Pauli said so (that’s a bit like “no two electrons can share the same energy shell, except sometimes they have to” in the old orbital model).

And that is why we still teach kids the old version.

I’ve used ‘probably’ and ‘sometimes’ a lot up there, but it’s actually a lot more useful than the old orbital model (you can use it to predict the exact amount of energy required to bump electrons about – so it works and everything).

It’s still an approximation of what is really happening though.

This is more or less what I was going to say, except I also need to mention The Science of Discworld.

TSoD is a book about real-life science as seen through the eyes of Discworld wizards who are finding out about non-magical physics for the first time. In TSoD, Pratchett comes right out and tells you in practically every chapter “we are lying to you, but we will lie to you less in the next chapter”. It is done for humorous effect, but that makes it no less true.

I wish it was in print in the U.S. (or maybe it is, but not last time I looked)

• Aldowyn says:

My chem book actually says this sort of thing. “Yeah, this is wrong, primarily in X ways, but it works on a basic level. Next section we’ll teach you the more complicated version that fixes these problems, but it has it’s own, more minor ones.”

And, lo and behold, it IS more complicated, and it IS more accurate!

• Background_Noise says:

We tend to use atomic and mollecular orbitals, which can roughly be described as the area of space where finding the electron is >95%.

The “Approximation of Chemistry” is that electrons from different orbitals don’t affect each other. This works well for our needs but is none the less an approximation. The alternative is (as far as i know) totally impossible to form exact wave equations to explain multi electron systems, and so impossible to find their exact energy.

Chemistry is largely concerned with interactions between the HOMO (Highest Occupied Mollecular Orbital) and LUMO (Lowest Unocupied Mollecular Orbital). The relationship between these in terms of space and energy generally dictates chemistry between two species.

(I’m a 2nd year Chemistry undergrad, so please correct if i have miss explained something)

• Soylent Dave says:

Sounds about right, although you can do the wave equation for Hydrogen without using the Born-Oppenheimer approximation.

(and the B-O approximation gets less and less accurate the bigger the molecule is, but OH LOOK OVER THERE)

• Joe says:

Hell, we’re still using the Bohr model in my graduate glass/ceramics engineering course. It works *enough*

• Jakale says:

Haha, “by the way, all this stuff we’re teaching you is wrong but it’ll enable you to understand the other stuff we’re going to teach you later. Which is also probably wrong (but less wrong)” will never stop.

I’m in a one of the last undergraduate college chemistry courses and just this semester we get told “Yeah, that model you’ve been using since your first high school course(Lewis Dot if anyone cares)? Wrong, and here’s the model(MO Theory) and data that proves it. Don’t tell the freshman though, it would just confuse them and we still use it because it’s convenient.”

• Kaeltik says:

I can confirm this through the PhD level, at least for biochemistry and biophysics.

In my final couple of chemistry courses were essentially quantum mechanics as applied to macromolecular systems. The list of assumptions, implicit and explicit, was about a mile long. Now, I don’t know what the next level would look like, or if there is another level, but it felt just like the simplifications from all previous classes. Maybe a proper physicist would have an answer.

2. Murkbeard says:

The way we explain things at a younger age are simplified for the simple reason that we don’t have the language to give a more accurate explanation at the high school level. Specifically, the students don’t have enough mathematical knowledge. In order to be able to work with “real” quantum mechanical problems, you need concepts like complex numbers, probability theory, differential equations and/or linear algebra. These are not currently taught at a young age. I’m not saying they couldn’t be, but they aren’t currently.

As far as your “billiard table analogy” is concerned, it is completely false and not in any way related to the way quantum mechanics work. The reason why it cannot be related is subtle, and it is due to Bell’s theorem. The gist of it is, that if there was some other structure in the world, that is, some variables which track all the positions of the billiard balls when we are not observing them, then we would have to find a certain relation, which we could write as
A < B
where A and B are probabilities of something happening, to be true.

If we actually use quantum mechanics to find those probabilities, we can construct a situation where A=0.7 and B=0.3, which is clearly not consistent. Thus, in quantum mechanics, there is no billiard table.

Of course, we need to resort to experiment to see which is manifest in our world. To a very high degree of accuracy, Bell's inequality is found to be false, and thus there can be no billiard table. The truth is a bit more complicated than this, of course, but the simple picture does not hold water.

Of course, there must be some rules for how to get from situation A to situation B, and we seem to know these rules quite well. The problem is, that these rules do not apply to objects that are anything like the ones we are used to. Instead, they apply to what is called “states”, and they tell us how a state evolves in time. (See below)

If you'd like to see more of Feynman's excellent work on elucidating physics, I can highly recommend a lecture series consisting of 3 videos given in New Zealand in 1979, first video below:

• Soylent Dave says:

It’s worth noting that Bohm formulated* that non local hidden variables can have an impact on quantum mechanics, even where local hidden variables cannot.

I think the reality is that we can’t afford to be too categoric about the way quantum mechanics works, because rather too much of it is based beyond theories that work ‘well enough’.

There’s reason we can’t come up with an elegant theory for QM – and that’s because we’re Doing It Wrong. We’re just (probably) doing it more right than we used to (and we’re definitely doing it well enough to explain loads of awesome things).

It’s also the same reason we can’t marry classical and quantum physics – our understand of one or both is wrong. It doesn’t really make a lot of sense for very small things to behave entirely differently to things that are a bit bigger (but made from those very small things); it makes more sense for us not to understand exactly what is going on yet.

It is fun watching electrons teleport, though.

*I’d say ‘proved’ but we’re talking about quantum mechanics here. He proved it a bit. Some other physicists proved the opposite a bit.

• Murkbeard says:

I tucked the bit about non-local theories into the “slightly more complicated” part, and it is true, that a non-local theory does not need to obey Bell’s inequality. However, non-local theories carry with them an entirely different set of conceptual problems. If you have a non-local hidden variable theory, you also have transmission of information going faster than light. If this can be exploited to actually transmit information, there are multiple paradoxes that open up (Most famously the grandfather paradox).

You talk of quantum theory and classical physics as if they are seperate things. They are not! If you take quantum theory to the limit of large masses (Specifically h -> 0), it reduces perfectly to classical mechanics. Quantum theory still describes our “normal” world, but the weird phenomena it brings with it are so insanely tiny compared to the size of the thing it applies to as to be ignorable.

One quantum effect we could talk about is uncertainty in position. If you have some object, and you know the speed at which it is moving to some degree of accuracy, dP, Quantum mechanics says that you cannot know it’s position more accurately than some value dX, and that dP * dX = h / 2pi. For a baseball a typical value for dX could be a few micrometers. This clearly does not effect your ability to hit the baseball during practice, and the quantum effect is not visible.

• Soylent Dave says:

Sometimes when you apply quantum effects to large things they’re small enough to be ignorable. But we can very often describe those same effects using classical physics and get a precise result.

(or a much more precise result, anyway)

The quantum effects aren’t being so much being hidden as they’re being rounded off.

Obviously classical physics doesn’t really work at all for little stuff, but if quantum mechanics only ‘sort of’ works for the big stuff – that still means we’re only in ‘good enough’ territory.

And it doesn’t even ‘sort of’ work for all the big stuff, either…

(not that this is a particularly bad thing – it’s pretty much the way humans go about figuring stuff out. I just think it’s too easy to turn ‘physics’ into ‘faith’, so it’s worth remembering that we’re figuring it all out as we go along – and getting nearly there isn’t quite the same as ‘there’)

• Murkbeard says:

But that’s the thing: Quantum Mechanics does not only “sort of work” for large things, it works at all scales. Any result you get from a classical calculation in a domain where quantum effects are very small, you can get just as well with a quantum mechanical calculation.

To be more precise: In a quantum theory you calculate probabilities for different values of some number A. If you were to take the (quantum mechanical) average value for A, you would find that it behaves _exactly_ as what you would expect from a classical calculation, provided the scale compared to the quantum fluctuations is small. In this sense, you get the same answer as a classical calculation, and the quantum theory is _at least_ as good as the classical one.

I suspect the “not working for big stuff” you are referring to is gravitationally bound systems. It is true that we don’t have a full quantum understanding of gravitation, but if we can just assume the usual gravitational force law, it all still fits. We can see that this should give quantum effects with gravity, but because they are so very small, we can’t see them yet. We simply can’t distinguish between a quantum and a classical (I should say relativistic) treatment yet.

The important thing is, that for all regular, everyday phenomena, the usual uncertainty (say, from measuring with a ruler) is so much larger than the quantum uncertainty, that the latter can be safely ignored. Note that it’s still there, and if we could measure well enough we could still find it. But if we can’t see it, there’s no reason to worry about it. This is why we can use classical calculations very well for most problems.

• Soylent Dave says:

I very much agree with your last paragraph.

But that’s really what I’m using as my proof that ‘none of our physics is good enough’, too.

That’s not a criticism – it’s pretty much the entire point of science. We put all those qualifiers there, and ultimately try to remove them (but while we’re using ‘most’, let’s see what else we can get away with)

• Murkbeard says:

I feel I should be a bit more moderate in the above statement;

The analogy to a game that Feynman gives in the video in the post should be taken as just that; an analogy. It makes the quantum mechanical variables (The positions on the board) much too concrete, and incites an image in the viewer that is not favourable to actually “get” the fundamental properties of the theory.

What he is talking about is the process of scientific discovery, and how science finds out about nature.

3. DancePuppets says:

That’s a really interesting way of putting it across, although the major difference between the billiards game and the world in which we live is that in billiards there are what we call “hidden variables” (ie. the players), whereas in the Universe (when quantum mechanics applies, at least) current evidence (both theoretical and empirical) would appear to point away from “hidden variables”, suggesting that the Universe is by it’s very nature, probabilistic. Quantum mechanics appears to defy common sense which argues that everything should be deterministic, but, as far as evidence suggests this is not the case, so something that hasn’t been observed (or interacted with something else) is made up of a probability distribution of all possible states, it is only on interaction that it takes a defined state.

4. DancePuppets says:

I apologise for the rambleyness of the above post, but I’m an astronomer not a quantum theorist so I’m not all that good at explaining quantum mechanics (granted, neither are many of them).

• Soylent Dave says:

I used to be a chemist, so my primary contact with quantum mechanics was to go “ARGH! Get your stupid arbitrary physics out of my lab!”

… then they’d show me something cool you can do with it (like ‘move atoms around with a little atomic crane’ and I’d get all interested, until they started doing maths at me again)

• mac says:

Soylent Dave, that is the funnest description I ever heard for AFM. :)

• Soylent Dave says:

Hee.

I remember getting pretty excited by the atomic spectroscopy lab, especially the bit where I got to make some Tungsten wire that was atomically sharp (with corrosion), and definitely didn’t contemplate stabbing anyone with it to see what would happen (the wire would get blunt and someone would say “ow” is what would happen, but don’t shatter the dream).

Then someone pointed out that you get atomic sharpness about 60% of the time when you cut Tungsten with snips. That’s just annoying. It should be difficult.

5. Drexer says:

Besides the various stuff that Murkbeard already said and that perfectly ilustrates the fact that Quantum Mechanics in and out of itself is quite elegant(reduction to classical mechanics for large wavelenghts objects and such); I’m gonna pick also on that small bit about Quantum Mechanics needing some kind of re-organization or such to be more ‘real’.

Although there still are quite a bit of weird stuff on quantum mechanics which need better explanations, in general it is quite elegant, the only problem is that this elegant behaviour can only be seen when looking at the equations; usually trying to explain this to people who lack the proper background is nigh-impossible.

• DancePuppets says:

And trying to model anything larger than a hydrogen atom requires either (a) a bodge job, perturbation theory or (b) GIANT COMPUTERS!

6. chuko says:

A lot of what you’re talking about here is sometimes called the old quantum theory, the set of observations, approximate calculations, and rules of thumb developed in the teens and 20’s. But in the late 20’s and the 30’s, Dirac and von Neumann and others, made a unified mathematical theory of quantum mechanics. It’s axiomatic, simple in the way other fundamental theories are, complete for non-relativistic particles, and based on some beautiful math.

I wonder if this is the theory you’re looking for. Maybe the fault lies more in popular explanations, which don’t seem to emphasize this point of view, probably because they’re trying so hard to get across the idea that all of this is based on experiment. Maybe this is a better link than the wikipedia page.

• AR says:

I felt somewhat vindicated a few years ago when I learned they no longer taught that stuff.

You may be interested to know that they actually do still teach that at the college physics level, since quantum mechanics and relativity are taught, to some extent, chronologically, in order to imbue a historic understanding of where modern theories came from.

The way its taught to some school children and much of the general public, you’d think the Bohr model was just some guy tripping out and thinking, “Dude, what if, like, electrons orbited the nucleus. Whoah.” But in fact there is a lot impressive physical reasoning that went into these models and which did turn out to give good results. When tests got more accurate and revealed errors, further physical reasoning revealed a model that accounted for such things, until better models came up. The problem is that the physical reasoning can’t be or just isn’t taught in high school, making the theory look a lot less elegant than it was.

Though, in any case, one must still be prepared to accept that the universe is just not obligated to your aesthetic sense of elegance. One would not want to be like the Pythagoreans, who could not accept the existence of irrational numbers.

• AR says:

Opps, didn’t mean for this to be a reply. I’ll just… hey, what happened to that awesome feature that let you edit your own posts for a little while?

Edit: Nevermind, just didn’t have the right scripts enabled. Still can’t delete, though, so oh well.

7. o.O *glazed over stare*

8. Josh R says:

Everyone knows the world is just a disc on top of four elephants riding a giant turtle anyway

• Nick Pitino says:

It’s turtles all the way down baby!

• Mari says:

ARGH! Stupid turtles. Why is it always turtles? The turtle mythology makes my brain all melty and stuff! The giant tree with a snake makes more sense than TURTLES. Not that it makes a great deal of sense, just more than the turtle thing. And now I’m going to spend all night trying to remember the title of that anime that was basically non-moody “Dark City” except the world was on a giant space turtle.

• Keeshhound says:

If you’re really wondering where all the turtle mythology comes from, I can point you in two directions; a certain British satire author, and less facetiously: turtles are generally perceived as beings of almost divine wisdom and longevity due to their wrinkled and “aged” appearance, as well as a general perception that their slow, methodical movements denote a predisposition to caution and stability.

Also, they’re damn delicious, and their shells can be used to predict the future.

• Soylent Dave says:

I think you’ll find the universe was sneezed out of the Great Green Arkleseizure, actually.

9. Samkathran says:

Mmmmm… quantum mechanics. Yeah, I gave up on trying to understand that stuff a long time ago, right about the same time I figured out that studying engineering wasn’t right for me either. After a while everything goes from “hey, this is interesting” to “okay, that’s getting ridiculous” and finally to “screw you guys, I’m going home”. If electrons, quarks, photons, higgs-bosons, and all that other stuff want to drink the universe juice and go bat-shit crazy, then I’ll just go study something that’s less likely to drive me to the brink of insanity, like /b/ (only slightly less likely to do that).

That’s not to say I don’t appreciate the work they’re doing, though. I just want my time machine soon, dammit!

10. Background_Noise says:

Also, I would argue there are some very elegent theorys.

The one that comes to mind is the Variation Theorum. The idea that an electron will always be in the lowest energy state it can be (for the conditions present). Therefore, if you come up with two allowed wavefunctions to describe the electron you know that the one with lowest energy is more correct.

This will never get you to an exact wavefunction however. As far as i understand it, it could be likened to trying to find the exact value for Pi, we can keep getting closer and closer, but there will always be more.

I just like how something so simple can be so powerfull.

• Simon Buchan says:

Funny thing about Pi: it is *exactly* (in pythonesque) ‘4 * sum((-1)^k / (2k + 1) for k in 0..infinity)’ (There are far better ways to actually calculate it, btw). Don’t confuse the fact that the decimal *representation* (actually any digital representation) requires an infinite number of digits with it not being *exact*. Maths is hard to think about :).

• Background_Noise says:

I always tried to think about Pi as a relationship rather than a number. That about correct?

Yes, yes it is. And I am no mathematician.

And here I thought your line in yesterday’s post about a quantum mechanical theory critique was just a bluff.

• Julia says:

I thought so, as well.

I’m delighted to be mistaken on that!

12. Tizzy says:

You have indeed found the problem: the math seems to work out and all the predictions of quantum mechanics have been borne out, but one of the reasons physicists can’t really say they understand is that no one is really sure what the mathematical objects used *mean*, in the sense of what do they represent from the physical point of view (they are fairly well understood as mathematical entities, which is necessary for computations but that doesn’t do us any bit of good to understand the physical meaning).

Physicists of course are keenly aware of this gap, and they’re working on this when they’re not doing string theory and trying to do the theory of everything (which btw was a terrible choice for a name).

There are *many* possible interpretations, see
en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics
.
My biggest surprise was to discover that not everyone even agrees that wave functions should represent probabilities.

The article also lists quite a few good reasons why giving an interpretation to the math is no cakewalk. I don’t know anything about quantum mechanics, so I find it mind-boggling to even try to imagine how they came up with the mathematical description.

• Drexer says:

To be fair, in physics the ‘need’ for a real-world interpertation is pretty null. Many times, the math suffices for a physicist, and the article itself mentions that mainly ‘philosophers of physics’ are interested in it; not the physicists themselves. As an example, the concept of entropy is very well accepted even though its only proper description is its mathematical formula, and all those descriptions by words are lacking in one way or the other.

Many mathmatical operators when applied in physics are indeed nigh-impossible to understand in plain human language, but I’ve met many of my college teachers who work in such an area and none had any kind of aphreension or need to translate them to such a cumbersome thing when the mathematical interpretation is so plain.

13. Brian York says:

I guess I’m joining the chorus of people saying that there is an elegant theory of quantum mechanics, it just can’t effectively be taught to people until they’ve already learned differential equations, matrix algebra, Hermite polynomials, Hermitian operators, calculus in a variety of forms, complex analysis, Hilbert space, etc. Which more or less means that most people give up on quantum theory before they have the background to learn how it all hangs together. Including me, to an extent (I ended up in astronomy largely because, although I made it up to QM, it was operating right at the edge of the math that I can handle, and often a bit beyond). Still, it is a surprisingly beautiful theory, and it works quite well.

• Sekundaari says:

I agree with this too. At least for me, a large part of QM courses has been teaching the relevant math that we haven’t encountered before, in actual math studies or other physics courses.

Another thing, not in reply: The billiard analogy may be flawed if you try to equate it too straightforwardly to particles in quantum mechanics, but I don’t think this is what Shamus meant by it. It’s just that billiard balls are one of the very common analogies of particles in classical mechanics (definite place, velocity), and thus Shamus’ analogy seems mistaken for someone who has encountered the other billiard analogy, which I don’t think is used in A Brief History of Time.

As for the actual statement in Shamus’ analogy, from my very limited knowledge I’d say we are past that phase. Most (all?) of the different observations have been condensed into a few rules and equations, and the problem is we may need to make more detailed (difficult) experiments to get more of those observations, to compare different interpretations. I think.

The atomic orbital thing sounds pretty much like the thing I’ve been taught in chemistry, and later in physics in university-level studies. Maybe the difference is Shamus wasn’t ever taught the underlying QM equations and fundamental rules, and so the orbital rules seemed arbitrary and inelegant. The elegance is there, but it requires some pretty abstract math to see the bigger picture in physics, and time in schools is limited.

Anyway, the description sounds like electron configuration + the Bohr model for the fixed orbit radii.

• Shamus says:

Right, I wasn’t saying “particles are like billiard balls”, I was saying “we are observing a game without understanding the rules”. I realize that it’s not a very good analogy. In my defense, I came up with it in ~1991.

Comparing the two:

In relativity, we have a beautiful and simple conceptual system, although the math behind it is (reportedly) tricky.

In QM, we have a system with (reportedly, above) elegant math which is (to my mind) unwieldy conceptually.

Now, we can’t be CERTAIN that there is some more elegant conceptual model out there, but I think there’s lots of good historical reasons to hope for one. When Einstein threw away the idea of absolute time, things fell into place. I have this sense that the same ought to be possible for QM.

• Sorry, but you’re just wrong. As Murkbeard explained, there cannot be an underlying theory that explains it all in a conceptually easy way (usually referred to as ‘hidden variables’), because there is an experiment that would have a certain outcome if that were the case, and it doesn’t.

The basic problem is that you think your intuition about physics, which evolved to deal with objects the size of tigers, should explain everything. It doesn’t; deal. Read this, and follow up with the entire sequence, and behold you should be less confused. As the man says, “Just stop thinking in terms of little billiard balls, with or without confused identities. Start thinking in terms of amplitude flows in configuration space. That’s all there ever is.”

• Shamus says:

Your basic problem is that you either ignored my post or the accompanying video. Also, your tone sucks. You seem to be suggesting that no future integration is possible. I’m not as arrogant as you so I won’t presume to say this is wrong, but I will say it sounds extremely unlikely.

And I’m not the one thinking in terms of billiard balls, as I explained above. My analogy was similar to Feynman’s: I could have used any game as an example, because it wasn’t the balls that mattered, but the rules.

• I am sorry if you disliked my tone, but the fact remains that any hidden-variable theory is going to be just as non-intuitive as quantum mechanics, if not more so. There can be a unification of QFT and GR, but there cannot be a unification which restores any sort of classical behaviour. Murkbeard gave an excellent short explanation of why; if you want to Google for more detail, you want “Bell Inequality” and “EPR paradox”.

I would also suggest that maybe reading “A Brief History of Time” is not the best possible foundation for coming up with critiques of modern physics? It seems fairly clear that you do not have much idea where quantum field theory actually stands at the moment or how much it explains; if you did, you would not use such phrases as “we can make hundreds of observations like this and still not know the rules of the game”. QFT predicts the muon magnetic moment to nine significant digits, from first principles. Let’s see GR explain where the basic gravitational constant come from, then we can talk.

• Shamus says:

“but the fact remains that any hidden-variable theory is going to be just as non-intuitive as quantum mechanics, if not more so. ”

I assume you’re talking about the Uncertainty Principle? I actually find it to be rather neat and elegant. Like doing away with time as an absolute, the idea might feel a bit strange at first, but once you accept it things open up and the pieces fall into place.

“I would also suggest that maybe reading “A Brief History of Time” is not the best possible foundation for coming up with critiques of modern physics?”

Perhaps not. But it’s an enjoyable enough conversation to have on this blog, provided the people involved are polite about it. (See, this is key.) I entertain programming conversations on this blog with people who have less of an idea about programming than I do about quantum mechanics, and I find them to be enjoyable. It’s very instructive to see the field from from the “outside”, and helps me have more productive conversations with laypeople. I could just shoot those people down with “You don’t know anything about programming, so stop trying to talk about it.” There’s certainly no shortage of programmers who behave like that.

“QFT predicts the muon magnetic moment to nine significant digits, from first principles. Let’s see GR explain where the basic gravitational constant come from, then we can talk.”

You really have no understanding of a word I’ve said. It really is remarkable. I don’t even know what you think you’re arguing with. At this point I’d usually try an analogy, but I tried one of those in the OP and you whiffed on that.

• I’m beginning to think we’re talking past each other. Let me try again.

We could have hundreds of observations like this. Charts, equations, theories… and still have no idea what the rules of the game are or how it’s played. This is where I think we are with quantum mechanics.

Suppose we did know how the game was played; what would this look like? What would be taught differently, what experiments could we explain that we can’t now, what concepts would we use in place of quantum amplitudes? I’m not asking you to come up with a theory to replace QFT, I’m just asking what the theory would look like. What must a theory do, which QFT doesn’t, so that within your analogy it corresponds to knowing the rules of the game?

Because our lack of an elegant theory is really starting to bug me.

Yes, and the lack of a programming language that isn’t C++ is a major problem of computer science. If only we had some language that didn’t have all that syntax! Oh, woe is us, we must put semicolons everywhere, how ugly! Functions are not first-class objects, but must be wrapped in icky structs; oh, if only someone could invent a language that didn’t make necessary this horrible hack!

Seriously, this is how you come across to a working physicist. Your ignorance of the beauty of quantum field theory does not an inelegance make.

• Shamus says:

“Suppose we did know how the game was played; what would this look like?”

It would not look like this:

An electron shell is the set of allowed states electrons may occupy which share the same principal quantum number, n (the number before the letter in the orbital label). An atom’s nth electron shell can accommodate 2n2 electrons, e.g. the first shell can accommodate 2 electrons, the second shell 8 electrons, and the third shell 18 electrons. The factor of two arises because the allowed states are doubled due to electron spin—each atomic orbital admits up to two otherwise identical electrons with opposite spin, one with a spin +1/2 (usually noted by an up-arrow) and one with a spin -1/2 (with a down-arrow).

18 electrons in the third shell? Oh really?

It is my belief that an elegant theory would not have this many if / then / else statements. Then there are all the classifications of particles and sub-particles, sorting the little buggers into groups. My belief is – and Feynman sort of backs me up here – that often complex systems like this can be simplified when new thinking comes along. I’m proposing that there is some other way to think of particles or waves that doesn’t lead to the seemingly odd contrivances above.

If you were going to compare me to someone who didn’t know about programming, then I’d be the guy saying, “Language X is so cumbersome! There should be a language that is more powerful, is easier to learn, clearer to read, and easier to maintain!”

And maybe he’s a mad fool. Maybe he’s right. I wouldn’t bet against him.

• Soylent Dave says:

As I pointed out up above, David Bohm has formulated that there are hidden variables that do have an impact on quantum mechanical systems.

They just need to be non-local ones. So it’s possible for a different game of Billiards on a different table to affect the one you’ve been observing (if you like that analogy).

(Bohm’s theory isn’t exactly universally accepted, but he wasn’t the sort of physicist you could easily ignore either. It’s worth acknowledging the possibility that he was right…)

• King of Men says:

Sure, ‘non-local’ is what I meant by ‘just as weird as quantum mechanics’. Non-local theories are deeply weird; they have time travel and the accompanying paradoxes, not as special-case exceptions, but as fundamental mechanisms! Non-locality basically means giving up all our intuitive notions of cause and effect. I would much rather deal with causes that have stochastic effects; that’s intuitively accessible to anyone who has played with dice.

• Soylent Dave says:

As much as I love statistics and probability, I think “the entire universe is ultimately a bit on the random side” is still a pretty weird concept, right up there with non-local phenomena.

Call me old-fashioned, but I like my cause to always equal my effect. It’s nice and sensible that way.

(Rather than my probable cause equalling a few possible effects – ‘probably that one’)

…not that I expect the universe to be all boring and sensible. It’d just be a bit less weird if it was.

• decius says:

I have concerns with the entire FTL=time travel system.

Starting with the fact that when I went through the highest-level text I could find, I saw the speed of light being constant described as a postulate. I went through the entire chapter with the postulate that a given artifact would have constant dimensions to all observers, and found that system to be consistent with the result of all actual experiments conducted. Bonus: Time seemed to elapse to the same degree for all accelerating observers who later rejoined.

• TSED says:

As an English Major with wide-reaching interests (which don’t really go into the physics / quantum / engineering / chemistry fields), I’m fascinated at how many different fields use an analogy of “watching a game without knowing the rules.”

Seriously. I’m currently plowing through a lit theory text and watching football and making observations without knowing the rules of football has come up twice so far.

14. Shamus, I love your blog.
It attracts so many AWESOME people with different interests
Games, Coding, Writing, Humor….and now we can add Quantum Physics
Bringing people together dude

*Please ignore any hippie undertones of this post*

15. Jarenth says:

Hey, a critique of quantum mechanical theory just like you promised. I probably should be surprised, but then I’ve been hanging out here for a while now.

One interesting thing about science that both your and Feynman’s analogies demonstrate well is the fact that we have no idea if our current experiments and observations in the relatively unknown fields are even useful at all: they might describe some new fundamental law, they might be emergent behaviour caused by a deeper law, or they might just be clutter. In your analogy, one of the observations you posit is the ‘Probability of any given ball being on the table, or vanishing from the table’. And if you’re just starting out with observations, that might seem like a relevant statistic. But while I’m not sure about billiards, I feel confident in saying that in a game of pool, that particular probability on its own means nothing. The same could be said about the probability for any given chess piece to vanish off the board; could be interesting when combined with higher level rules, but as a singular piece of information it’s really not as useful as one might think.

So I guess what I’m getting at is, not only do we still have enormous gaps in our understanding of quantum physics, we don’t even know if the stuff we dó know is in any way relevant.

• Drexer says:

Well, it allowed us to make huge leaps forward in various situations which before were unexplainable. Heck, if it wasn’t for the current explanation of quantum physics we wouldn’t have discovered the behaviours that allow us to make some of the latest computer components.

There should be no mistake on the fact that it is relevant, seeing as we’ve gleaned so much more knowledge of the natural interactions of the microscopic world from it.

The only problem is that… well, it’s hard to notice those things just like most discoveries from CERN are hard to trace to Nvidia developments, even though they have a reasonable sinergy there.

• Jarenth says:

Yeah, no, I wasn’t out to call these discoveries pointless, or anything. In fact, it continually amuses me that in Science, everything can be useful. The stuff you discover on purpose, the stuff you discover on accident, the stuff you just randomly happen to stumble across, everything.

16. BlackBloc says:

I’ve long made my peace with the idea that at very small scale the universe might just be weird (probabilistic instead of deterministic, discrete instead of continuous). There’s no reasons our brains would have evolved the capacity to ‘get’ the infinitessimately small. There would have been no survival benefit.

We can explain it with the tools at our disposal but we can’t ascribe meaning to it because meaning is a creation of our own minds, and our minds are pretty much out of their depth in this case.

• FatPope says:

Which is why we need to improve our minds. Transhumanism to the rescue!

17. Aquin says:

Unlike some of the people in the comments, I don’t find anything about quantum mechanics conceptually elegant. I’ve always likened recent mathematical models to those of the epicycles from the Ptolemaic model.

Yes yes, it’s a view of the universe that was quite accurate (for it’s time) and all the math “worked.” You know what else? It was entirely too complicated, over-thought, and turns out, with a simple change of perspective, to be easily replaced.

I suppose I shouldn’t be surprised to see history repeat itself. We’re so eager to explore all the possibilities of this given rule-set, we’re now lost in it.

• Drexer says:

“was quite accurate (for it’s time) and all the math “worked.””
Worked? It’s predictive power was practically nill(specially in the case of Mercury but that one was only solved with General Relativity anyway).

Comparing quantum mechanics to the Ptolemaic model is quite an insult I daresay. First because it undervalues the effort from physicists to open their minds to concepts impossible to liken to anything near the human experience, and because you’re comparing a dogma imposed by the clergy which the science had to be adjusted upon(there were tries before Galileu to change the model, but only with too big a proof did the clergy relented their censorship), with a study of physics upon which hundred of people constantly try to break down and evaluate day after day.

Don’t get me wrong, if QM suddenly was shown to be a not so good approximation when compared with another model, any physicist would jump on it. But lets get real, that possibility is very near zero seeing as it has been showing its predictive qualities for years now under the scrutiny of some very hard science.

• Shamus says:

• Aquin says:

Unfortunately, it was the closest analogy I could accept without getting into some serious nitty gritty. The only real point I was trying to make is, despite it’s predictive power, it seems conceptually ‘off’ in places.

A good example of ‘thinking outside the box’ when it comes to quantum physics would be like Palmer’s idea of a fractal invariant set, which is something I’d like to see more as a direction for theoretical physicists, rather than yet another attempt to verify the existence of the Higg’s-boson which doesn’t seem like a wise investment of time by comparison.

Like I said, nitty gritty. Nevermind. -_-

18. General Karthos says:

What I love about quantum mechanics and electrons is that they could technically be anywhere in the universe. Oh, more than a TINY distance from the nucleus of an atom and you approach infinite improbability with astonishing rapidity, but it’s just not quite impossible. Similarly, all the carbon in my desk could suddenly decompose, and release enough energy to kill a lot of people nearby. But the odds of that are also so astonishingly low that I doubt that even given the astonishing size of the universe, no similar event has occurred.

I figure that since I went through all this orbital stuff five years ago, (it had nothing to do with my Poli Sci major, but I wanted to be knowledgeable) and again two years after that, I most likely learned a contemporary theory, though what Shamus describes sounds like what I learned. The various orbitals, and falling from one orbital to another releases energy, (such as the radiation produced by unstable elements) whereas energy input is required to move UP in orbitals, and so forth.

Point being, I love some of the ridiculousness of quantum mechanics, but there’s a lot of hard science behind the ridiculousness, and the nearly infinitely improbable events are possible, but unlikely to ever be observed.

19. simmuskhan says:

I quite love how quantum theory seems to draw so many people to either wanting to understand it or wanting to prove that we can’t understand it.

There are so many aspects of physics (and other sciences) that don’t get the press and treatment that QM gets.

And so you get a ton of people from high school educations to PhDs to (even worse) movie stars all throwing their coins in the fountain.

I’m not complaining! Else I’d be out of work! But it never ceases to amaze me when people come up and share their interpretation of QM, regardless of their background! Or tell me how nobody understands any of it, then talk on their mobile phones (more hidden verification of the usefulness of QM research over the years).

• Shamus says:

I find this curious as well. You don’t seem the same kind of fascination for physics in general, or for biology, or for any number of things that are a lot more obvious and immediate to the average person.

• Heron says:

I think it’s precisely the fact that those things are a lot more obvious and immediate to the average person that causes our fascination to be directed elsewhere. Obvious things are not interesting, but even slight misunderstandings of quantum mechanics can make for a lot of sensational headlines. Remember all those “The LHC will destroy the universe!” news stories?

Offhand I can think of another area of society that seems to get this wacky level of misinformed scrutiny: the personal lives of celebrities.

People are inherently drawn to things that shock them, scare them, amuse them, and so on. It just happens that quantum mechanics research is one of those things :)

• Shamus says:

Interesting point.

Although I’d gladly trade “OMG! Angelina Jolee is teen pregnant at 45 and was caught selling drugs to Lady GaGa!!!!!!!” for more stories like “Could microwave ovens cause the sun to explode?!?! Tune in at 11!”

The former irritates me and the letter amuses me. Although, maybe if I was in show business I’d wish things were the other way. :)

• Hal says:

Oh, please no. There’s already enough horrible “media science” out there, we don’t need to muddy the waters any further.

• Zak McKracken says:

I’m just reading “Bad Science” from Ben Goldacre. About halfway through I stopped perceiving “sciency” shows as mildly annoying and now view them as a serious problem. The reason is that they distract from actual science, they make it look as if science was just for supergeniuses and madmen, either wacky and useless or not understandeable or both at the same time, and the routinely confuse science with something religion-like. Substitute a priest with a guy with a labcoat and a clipboard and there you go. All of that is not good for actual science, and scientists feel the consequences.
I may be exaggerating the consequences, but I still recommend the book. He’s also got a website (www.badscience.net), but I haven’t really looked at it yet. Most of it is focused on Britain, but the underlying principle is mostly universal.

• Mari says:

I think that’s probably true most of the time. Although personally QM fascinates me because if I can make even the tiniest bit of it make sense in my head I feel an amazing sense of accomplishment. The phrase “rocket scientist” used to connote extreme intelligence but the past decade or two has replaced it with “quantum physicist.” So if I can understand even the smallest part of quantum mechanics properly it’s like an instant (imaginary and entirely self-awarded) 50 points tacked onto my IQ.

• Zak McKracken says:

I think you do see that type of fascination with some other fields, if they are somehow connected to that “wow” factor. Like Airplanes and Rockets. And Space flight. Sometimes even Computer stuff.
The problem I see with that is not people being interested but the media delivering tons of dumbed-down content where journalists who haven’t understood it at all act as if they had and give false (sometimes overcomplicated) explanations to dramatic background music, then cut to a “scientist” with lab coat and protective goggles, with blue light and everything. And then lots of viewers think they know something about the topic and want to join the discussion.
No problem if it gets people interested, some problem if you’ll later need to correct all those misconceptions (like “airfoils produce lift becaus the upper side is longer”), and a big problem if these misconceptions smother a topic like any discussion about climate change and global warming. The public’s and decisionmakers’ opinions about this topic are to a large part not formed by well-done and properly backed-up research but result of a political debate that isn’t quite as factual as it should be.
I once had a debate with someone who didn’t “believe” (is it a religion now?) in climate change and after I tried to point out all his fallacies and refute his arguments I realized I’d have to be a climate-researching scientist myself to do that, because all any of us had was quotes from the media. We could throw that at each other for eternity, but unless you actually go out there and read the research papers (or do them yourself), you don’t have any evidence. What we could agree on, though, was that a lot of the public debate was led on a basis of who had the better rethorics, and the real climate researchers are too smart than to throw themselves into this brawl, so let’s just stop it now.

20. Bryan says:

Regarding QM interpretations — I’m rather partial to Consistent Histories, myself. Where the “wave-function collapse” never actually happens in reality; it’s just a byproduct of the physicist changing the basis for the Hilbert-space subspace in question, from a linear combination of kets, over to individual kets.

(Specifically, unitary time evolution of alpha decay yields a linear combination of kets. But unitary time evolution isn’t the only way to model time passing, and the linear combination of states can’t possibly correspond to any physical property. If you take only the latter statement, then the outcome (particle decayed or not) will correspond to some other ket, which the original state will either evolve into, or not — but that’s incompatible with the linear combination of kets that you get from unitary time evolution. In this case, the correct thing to do *seems* to be to stop using unitary time evolution, not assume that something in the physical world happens to “collapse” the linear combination into a single state. Equivalently, wave function collapse happens on the physicist’s notepad, not in the physical world.)

21. James Block says:

A couple comments from an actual particle physicist (though I work on experiments, not theory, so I must confess to never being very good at the difficult calculations):

I must also confess to not having read any of the preceding comments, because a quick search for the words “QFT”, “Field”, and “QED” turned up nothing. There are actually three generations of quantum theory.

The oldest is the “old quantum theory”, stuff like the theory of the Bohr atom and the other outdated stuff you may have learned in high school. While the ideas were important to the progress of quantum theory, they are now regarded as nearly, if not completely, entirely useless.

Quantum mechanics proper, a non-relativistic theory of particle interactions, was developed next. This is the Schr­oedinger equation and the like, along with the beginnings of a relativistic quantum theory in the Dirac equation. This is what people usually think of when they think “quantum mechanics”; it’s an extremely useful theory that has been used to derive all sorts of important results. But it is not currently regarded as the fundamental theory of nature.

That honor goes to quantum field theory (QFT), first usefully formulated by Feynman and others in the form of quantum electrodynamics, a theory of how charged stuff interacts with other charged stuff. QED has been the most successful theory of nature ever formulated, making predictions that have been tested to the twelfth decimal place. The amazing success of QED led to formulations of two of the other three fundamental interactions of nature (the strong force and weak force) as quantum field theories, creating what is now called the Standard Model (SM) of particle physics.

There is a lot to like about the SM: the theory is deeply elegant in many ways that older theories, even Einstein’s theory of gravity, are not. It is also incomplete — it does not predict a lot of important stuff about nature, but neither does any other theory we have now. Most telling, it does not incorporate gravity at all. Gravity is very difficult to write down a quantum theory of for two reasons:

1. It is a very weak force, so probing the details of what it really does is very hard.
2. Its governing equation, in the same basic form as Einstein’s theory of gravity, is extremely nasty to deal with. Gravity doesn’t just respond to its own type of charge, as the other three forces do: it couples to mass… but mass is the same thing as energy. So gravity couples to all types of energy in the universe. This makes it just about impossible to isolate it and deal with it alone, which is how we solved the other three forces. It also leads to gravity being called “non-perturbative”; this is a serious mathematical issue, since all our mathematical techniques for the other theories are perturbative in nature. There’s a region of QCD, the theory of the strong interaction, that is also non-perturbative; this area is one of the least understood parts of the SM. And also one of the most important: it describes the interior of the proton, among other things.

Sorry I’ve had to write this so quickly, I have to leave in just a minute. I can go into more detail later about why I think the SM is an elegant, even beautiful, theory if people are interested. There is also one deeply, extremely ugly thing about QFT, renormalization, that everyone hates; I can mention that a little bit too.

An excellent reference on QED for laypeople is Feynman’s book QED: The Strange Theory of Light and Matter. It’s remarkably easy to understand, and is actually correct!

• Lanthanide says:

Please write more, your description was more useful to me than the other comments on this post.

22. Kdansky says:

What really bothers me though, is when people who are uninformed theorize on stuff that is way more complex than they have any clue of, and then think they know everything, and insist that they are correct and everyone else is wrong.

A friend of mine still insists that imaginary numbers are wrong, that FTL travel is definitely possible at some point, and that “infinite” is a “number”. So in his world, you can’t do electronics (needs complex numbers) and you cannot do crypto (needs graph and number theorems). And annoyingly, you cannot explain things in metaphors either at that point, since you get a blank “no, that’s something different”. Ignorance is the only real sin, everything else is negligible and can be worked around.

• General Karthos says:

I have a friend who says that EVERYTHING is possible “through science”. Temperatures below absolute zero, travel at faster than the speed of light, the production of greater energy from lesser input (thereby violating the laws of thermodynamics).

It’s pointless to argue with her. Oddly, she takes the exact opposite point of view from the conservative Christians who argue that evolution is just a theory. She believes that science and religion cannot co-exist, and she comes down firmly on the side of science. As I fall on the co-existence part of the scale, we clash occasionally.

I am not an expert. But I know enough to know that, much as we might wish it, FTL travel is not a possibility, Fusion power will be 20 years away for the rest of my lifetime, and while we might find proof of sentient extra-terrestrial life before I die, we’ll never be able to communicate with them in my lifetime.

There’s stuff in the universe that science can’t explain. For everything else, there’s Mastercard.

• ulrichomega says:

I’m definitely of the opinion that, given enough time, science will solve all problems (science problems, that is. Social problems are possible, but I’m not holding my breath).

The only problem is that we have to survive for long enough.

• Shamus says:

“Temperatures below absolute zero”

But… you… I mean…

I’d entertain thoughts of FTL travel and perpetual motion before I signed on with sub-absolute-zero temps. That’s like saying there’s a speed slower than stop. What would the particles do? Go backwards? No. That would be heat. I don’t know. I need to go lie down.

• Soylent Dave says:

We have recalculated absolute zero a couple of times.

Lord Kelvin actually made it a bit warmer than it used to be (-3000 degrees C), although we also had -270 C for a bit.

That’s, technically, Science! changing the value of absolute zero. Mainly by being wrong.

• Mari says:

Luckily I was a theater/English dual major instead of a science major like the rest of you geniuses so I come bearing a newsflash: the speed slower than stop is “traveling backward through time” and my daughter approaches it regularly. Man I love not being bound by all those rigorous “rules” and “reality” by which the rest of the world must live.

• Jeff says:

I thought NASA was working on FTL drives by folding space or somesuch. It was in Popular Science at one time.

• Kdansky says:

I am also firmly in the Science! camp, but I accept that some things are impossible (below 0 Kelvin) and some thing are “probably impossible” (such as FTL). Fusion power on the other hand will be possible at some point. After all, the stars burn! And if the sun can do it, there is no reason why we cannot.
I totally believe that there are aliens somewhere (the universe is just way too huge to only have one planet with life on it, when there are brojilliards of planets), but I would be surprised if we ever met or even saw them, because of those same huge distances.

Five hundred years ago, we thought bleeding people made them healthy. Now we have drug stores at every corner, we cut people open and replace their hearts, we shoot radiation at them to kill evil cells (which seems to be a mediocre idea, to be honest, but it seems to do slightly more good than bad) and we are figuring out how to use genetics to our advantage. It is really only a question of time until we understand everything.

There is stuff in the universe that science cannot explain yet.

• Actually, it’s wholly possible that a lot of things might be permanently out of our grasp. After all, five hundred years ago, people couldn’t fly unaided or regenerate wholly from a single cell either, yet we still can’t do those things. It’s possible that, in principle, some things might be totally random, or too chaotic to meaningfully model and understand, or require too much processing power, or….

• Jarenth says:

The fact that we functionally “shoot radiation […] to kill evil cells“, and that it actually makes people healthier, has firmly made me believe that we live in a universe where everything can be made to work if you can word it awesomely enough.

• Soylent Dave says:

And if people believe hard enough that they’re going to get better, a lot of the time they do (or if they believe hard enough they’re going to be ill, they do that as well).

There’s an awful lot of peculiar stuff we don’t understand properly (not that it stops us exploiting it with placebos and suchlike).

… oh and bleeding people sometimes makes them better, too. So we were a bit right a few hundred years ago. See also : maggots and leeches, and how we’ve started using them in hospitals.

We even drill holes in peoples’ heads. Although we don’t do it to let the demons out any more, so that’s progress.

• Jan says:

Risking further confusion, but in order to promote the truth, I’d like to point out, that in a very restricted setting, temperatures below absolute zero are possible. Systems in this condition behave as having a higher temperature then any system having a “normal” (positive) temperature.

See http://en.wikipedia.org/wiki/Negative_absolute_temperature for some examples.

23. It seems there’s a maximum comment-nesting depth, so I’m continuing the discussion down here.

18 electrons in the third shell? Oh really?

Yes, really. It follows from Pauli exclusion plus plain spherical harmonics. I’m sorry you were badly taught, but the high-level fact you quote is not quantum mechanics, it is a consequence of the Schrodinger equation, many inferential steps from the fundamental axioms. You might as well complain that biology contains too many “if-then-else” statements, therefore quantum mechanics must be wrong. And I’d like to point out that there aren’t actually any “if-then-elses” in there, it’s a plain multiplication that would not require any branch instructions in a CPU.

Had you been taught this properly, you would know why there are eighteen third-level orbitals, to wit, it falls right out of solving the three-dimensional Schrodinger equation for a radially symmetric Coulomb potential. This is math you can do with pencil and paper, indeed it’s a commonly assigned undergraduate problem. It’s just spherical harmonics, man.

Now, if you want to complain about the way physics is taught in American schools, I’m all ears.

Then there are all the classifications of particles and sub-particles, sorting the little buggers into groups.

Again this is not quantum mechanics, it is particle physics, but let that pass. There are six quarks; from those quarks you can make up all of hadronic matter. You really can’t deal with six fundamental building-blocks, which in different combinations make up all the complicated hadrons you seem to be complaining about? I’d hate to see what you did with Lego as a kid. Yeah, ok, there’s the leptons and the carrier bosons, but those don’t even combine to make new particles. So you’ve got six building blocks that make combinations, plus ten particles that are just plain particles.

Now, if you want to say that even this is too much and it seems there should be an underlying scheme that explains it, fine. That’s what string theory was invented for, I remind you. Again I point out, however, that this is not quantum mechanics. To return to the computer analogy, you’re like the guy who’s complaining that there are too many different programming languages, they really need to make one that does everything. Why, he’s had to learn to program in Word, Excel, and PowerPoint, and now there’s this Internet Explorer thingie!

• Shamus says:

Fine, then my comments about lack of elegance are aimed at particle physics.

“To return to the computer analogy, you’re like the guy who’s complaining that there are too many different programming languages, they really need to make one that does everything. Why, he’s had to learn to program in Word, Excel, and PowerPoint, and now there’s this Internet Explorer thingie!”

This is the third time you’ve made this personal and the second time you’ve put words in my mouth in a demeaning way. I’ve been very patient with you because of your expertise, but this is your last warning. I don’t care WHAT knowledge you have, if you’re a jerk then you have no place on my site. If you want to call me stupid, feel free to go and do that on your blog. If you want to join us in this conversation, then stop acting like a kid arguing over which console is best.

• I apologise. You called out my entire field, I over-reacted and then I tried to be clever about it. My bad.

That said, I do feel you demonstrated a considerable amount of arrogant ignorance here, and maybe owe some apologies yourself. Confusing particle physics and quantum mechanics is, actually, a really basic error. It completely misled me, hence your reaction “you didn’t read my post” when I started talking about hidden-variable theories. I did in fact read your post, it’s just that you called things by the wrong names and totally confused anyone who actually knew something about it. Notice that Murkbeard made the same mistake, as did James Block.

Then, quite apart from this confusion, your examples are not very good. Just because you were taught the eighteen-electrons thing as a fact to be memorised by rote doesn’t mean there’s no explanation; as I said, deriving it from the underlying equations is a standard undergraduate exercise. Same for “all the classifications”; I say again, six quarks in various combinations make up all the hadrons you’re probably thinking of. Now it could well be that there’s some underlying particle that can vibrate in six different ways to make those six quarks, but really, six building blocks is not a whole lot of complexity. Looks damn elegant to me.

I admit I was a jerk about pointing it out, but I still think you demonstrated a really thorough ignorance of the field you were attacking, based apparently on your memory of what you were taught in high school.

• Soylent Dave says:

Particle physics is the study of sub-atomic particles, which are actually energy waves and particles in a two-in-one special offer.

Quantum mechanics is the study of how energy and matter interact, with particular* attention paid to how subatomic ‘wavicles’ interact.

They’re easily confused because they’re very closely related branches of physics. That cross over a lot.

You can simplify it into ‘QM is the maths bit of particle physics**’ if you like, but it’s not really fair to expect non-physicists to know the difference.

*pun intended
**Because there’s no maths in particle physics, obviously. They just bang things together and make up words.

• Shamus says:

“That said, I do feel you demonstrated a considerable amount of arrogant ignorance here”

I prefer “hubris”. I even admitted that I hadn’t studied the newer theory. I knew a few math types and (if I was lucky) a few physicists would jump in with objections. It’s a bit of fun for them (who doesn’t like talking about their work? I bet botanists would KILL to get the kind of attention physicists do) and some free education for the rest of us, if all goes well. And, as I explain to new people: These weekend movie posts are usually off-topic conversation-fishing. If I actually thought I had anything substantive to say about physics, I wouldn’t put it in a weekend movie post. (Not that I expected you to know this.)

I’m actually surprised as how much debate I got on this post. I “called out” quantum mechanics (but really, intended particle physics) but this hardly a thing of controversy. People are always coming up with absurd pet theories all the time. (Some of them even come from physicists.) And what I was predicting (or hoping) was that there would be some sort of breakthrough or deeper understanding in the future, which is basically a gimmie. I mean, who would bet against such a prediction?

I was riding in on Feynman’s coattails, predicting the same thing he’d already predicted and using a similar (if sloppier) analogy. Then I backed up his assertion with an anecdote and dissed an old, discarded model. Pretty tame stuff.

If I had to do the analogy over again, I would use boxing or line dancing or some other organized activity that doesn’t involve balls or spheres in any way. (It’s actually hard to come up with good examples for that. We use spheres for everything.)

• Sekundaari says:

I hear you don’t use spheres in football over in America. Or feet, at least not very much (except to run). :)

The “18 electrons in the third shell” bit does sound arbitrary when out of context, but sadly teaching it in context is a long task, and it can be useful without it.

But with context… basically each shell means the electrons with the same principal quantum number n (n=1, 2, 3…). They have other quantum numbers, l, m_l and m_s. The first three can be derived straight from the Schrödinger equation for a hydrogen atom. (The Schrödinger equation is an axiom in this.) The fourth one can be derived from the more general Dirac equation (which I haven’t studied).

Anyway, the electron’s energy depends on n and l, at least on the level chemistry is interested about it. But when only discussing shells and not orbitals, we are only interested in electrons with the same n. l can have integer values from 0 to n-1, and m_l integer values from -l to l. (The Schrödinger equation only has solutions within these limits.) m_s can have two different values. So for each l, you have 2l+1 different l values, and from this you can solve that each value of n has n^2 different l, m_l pairs and 2*n^2 different l, m_l, m_s triplets.

Now the important thing is the Pauli exclusion principle (another axiom), which states that no two electrons in an atom can have the exact same values for the four quantum numbers. Thus in a given shell (given n), you can only have 2*n^2 electrons, or 18 for the third shell (n=3).

I apologize for any inaccurate statements in this, I have only studied this on a basic course. But the general principle should be right.

• Mertseger says:

Yes, the Schrödinger equation for a hydrogen atom is one of the most stunningly beautiful results in Physics. We were assigned to derive it in my undergraduate Quantum Physics course, and I did so, and then looked out my dorm window at the trees busily photosynthesizing and thought, “Oh my God, it’s all there.” It’s not just that the number of electrons in each excitation state falls right out, but the associated values of quanta needed to move between the shells falls right out as well. (As does the shape of the shells!) All derived from some appallingly simple assumptions, and an admittedly cumbersome spherical coordinate system which makes the math a bit annoying. Thus, the result is strikingly elegant: it’s really only the coordinate system that obscures the elegance.

Thus, Shamus’ post applies a thoroughly proper bit of reasoning (“Even simple systems can be hard to analyze and understand from limited data.”) to the wrong target (“What’s the deal with the seemingly over-complexitly of atomic electron exitation states?”).

The timing seems a bit strange as well. I took Quantum in 1983, and the Schrödinger equation for a hydrogen atom was (checks wikipedia) already over fifty years old at that point. Have we not figured out a good way to communicate this material in chemistry courses in the last eighty years?

• Zak McKracken says:

The original analogy in that context is probably the one from Plato, where he equates the scientist (phlilosopher, whatever) as someone sitting in a cave looking inwards and only seeing the shadows of what happens in front of the cave, trying to deduce what’s actually happening.

Of course, this also contains a hint towards aforementioned “hidden variables” which have been proven (although trying — and failing — to understand that proof has driven me nuts) to not exist in Quantum mechanics, but that’s beside the point. No matter how well done any experiments are, you can’t actually “see” what’s happening, you only get some abstract (crazy for most people) results from which you’ll need to deduce laws.

http://en.wikipedia.org/wiki/Allegory_of_the_Cave

And yeah, this gives me both respect for anyone involved in actual science (not everything that is called science is actually science. Rocket science isn’t) and some patience and understanding why some scientific “findings” aren’t as definitive as perceived. It’s not religion, after all. It’s also not the opposite of religion, it’s the attempt to find out stuff that can be seen, measured and reasoned about.

24. Falco Rusticula says:

I think that maybe some people thought you were talking about quantum physics directly, whereas it looked to me more like you were talking about the scientific process, and only taking quantum physics as an example.

Yeah, that’s probably because I’m taking ‘Introduction to the History and Philosophy of Science’ as an undergrad right now, but a lot of what was said on the video matches up with what we’ve been told. (E.g. the fact that we have to try and work out the rules from observations, and make theories and predictions which may suddenly be proved wrong.) So it surprised me that people started to insult your lack of knowledge of quantum mechanics, because I thuoght you were talking about something else entirely.

25. Noam Chomsky has often likened science to the drunk sitting under the light looking for his keys which he lost across the street. We look where we can, which may not be where we care about.

The really silly thing about a lot of laymen responding to science proposals is this idea that “Wow, that sounds useless, why are we funding this?” You don’t know until you do the research. In sociology, my field, there’s been all sorts of little pet theories that have had explosive influence. Take the strength of weak ties: That baby is used everywhere now.

Of course, at the same time, this does give us some social risk. Technocrats and privileged scientists love to have endless research grants with no immediate connection to the real world. But resources are finite, and it’s important we have some idea of where things will go.

And then we have to take into account that it’s likely that no computer can model the universe besides the universe, that there’s chaos and randomness lurking around every corner, that a lot of the things that we want to explain (say, social problems) might be in practice or in principle unexplainable or only explainable trivially, that even with Lamarckian omniscience we might not be able to predict everything….

Incidentally, Feynman’s comments really only apply to the physics as regards things getting simpler over time. In sociology and social sciences, we generally see things getting more complex over time, even after controlling for people trying to expand their prestige with silly research…

In my school (and generally in Germany, I think, or at least in Northrhine-Westphalia), younger grades are still taught the old Rutherfordian model. I learned it when I was there (I am 18 now and in 13th grade, the last year), and I found those rules arbitrary, too. Nobody in my class found that odd – there were rules, they obey them. They never questioned them. Just as in any other subject – there are rules in english, german, math, everywhere – and they never questioned them. “Odd” is written with two “d”, you can’t divide by zero and electrons go the Rutherford-way. But we later learned the new model. The old one is only used to make it simpler for the children before they learn the new one – they normally go through chemistry in the way that humanity went through it. But most children already stopped thinking at that moment. They just copy it into their folders. The new model was nothing fascinating for them, they didn’t care about what is wrong with the old one. It’s just more stuff to learn by hard before the next Klausur. That really bothers me.

• Zak McKracken says:

Hmm… we had the Rutherfordian model as a kind of historical detour and preparation for the Bohr model. Before we even started we were told that this is a simplified model and not quite correct and next lesson (not next year) we’ll see how the development continued. Which was pretty good in my view, because it also told us that all this is no static thing, and that there’s no actual definitive model for everything. Most people were ok with not continuing further down the line because their heads were smoking allready. But we still knew there was more, so that’s fine in my book.
Two years later we derived the Schrödinger equations in Physics and solved them for the first orbital, then got shown why we won’t solve them for the other orbitals in school :)
I guess I was really lucky with my school and my teachers. But then, I’m 14 years ahead of you, so probably you had some stuff that I wasn’t taught, too.

27. Jan says:

I am not a physicist (anymore, I’m a mathematician mostly now), but IMO the current basic theories of physics (Quantum Field Theory (QFT), General Relatitivity (GR) and Thermodynamics ( which is really just a collection of theorems of statistics)) is that it cannot be more elegant.
I mean, in formula’s, the defining equations are
G = 8 Pi T
D psi = m psi
where D is an SU(3) x SU(2) x U(1) covariant connection.

It’s just that
1. In order to understand what they mean you need some advanced (but elegant) mathematics. I did not learn this in physics, most of the time they just follow the “shut up and calculate method”. The mathematics needed tot understand these formula’s is advanced undergrad/early graduate stuff. However…
2. In order to really calculate with it, you need some very advanced mathematics. Renormalization, path integrals (the Feynman variety, not the ordinary sort) and so on. This is really hard mathematics, and some of it is only understood on a physical level (that is, nothing is really proven, the calculations just work out in all cases where we tried). I gave up at that point and just went on to do mathematics instead.
3. They don’t really work together well. QFT and GR are known to be incompatible, and most of the theoretical physics work of the past 20 years has been done in an attempt to find an underlying “Theory of Everything”.

This is the mathematics of the theory, there are some components which have to be added by hand. The most important bit (again IMO) is that of every particle of which we consist (electron, up quark and down quark) there exist 2 heavier copy’s. This is extremely ad-hoc, and any satisfactory theoretical explanation of this fact will go on to win a Nobel prize. Other problems include the exact mass of the particles and the relative strengths of the interactions.

Basically the math behind the fundamental theories of natures is extremely elegant, but hard to understand. But I think this is not a problem of the theory. If we look around us, we see a bewildering amount of variety. If this must all follow from some fundamental theory, this theory must be very “rich” in a mathematical sense, i.e. it must be able to describe a lot of phenomena. The ultimate mathematical theory behind it is in a sense geometry, and mathematical research through the centuries has shown that geometry can be used to express a lot of different ideas. In mathematics, topics from number theory to logic have geometric interpretations.

tl;dr: the mathematical theory behind it is very elegant, but very hard.

28. Warstrike says:

And because things are unintuitive, an elegant theory can “feel” very inelegant. Most of the science we are taught meshes very well in our heads with the way we observe the macroscopic world – balls falling, Newton’s laws, etc. This makes sense because science’s basic foundation is observation. I think the biggest problem for “understanding” QM (for me in graduate school as well) is that we don’t have pictures in our heads to explain what is going on. In many ways I like the idea of teaching it somewhat historically, starting from the late 1800s. The idea that between Maxwell’s and Newton’s equations, we felt like we had a really good handle on how things that we could see worked. And then we started looking at smaller scales and larger scales, and making observations that didn’t quite match up. Now what do we do? The answer to that became Quantum Mechanics in all its forms, as illustrated by James Block above. But I think some of the KEY to the feelings we get that QM is non-intuitive comes from the fact that it was INVENTED to explain non-intuitive OBSERVATIONS. If nature does things that don’t make sense to our brain (wired to observe at the macroscopic level), then why would the theory describing it feel intuitive, when translated into language which interacts with concepts derived entirely from our everyday life and observations?

To sum up: I suspect QM would “feel” just fine if we could put 2 doorways next to each other and observe that Shamus traveled through both simultaneously, unless one of the doors was shut. Since we don’t, our brain has no basis for understanding it conceptually, and we are left with an elegant mathematical theory that leaves almost everyone feeling unsatisfied.

29. Mephane says:

Shamus, I love your billiards analogy. It pretty much describes not only the current status quo on quantum physics, but also some other sciences, such as medicine or biology (so much there is just based on experience like “if this substance is applied in this dose there is a 50% chance of that outcome…”).

Also, Feynman is absolutely brilliant.

30. Sarah says:

[insert obligatory account of being smarter than everyone]

Here’s my issue with the billiards analogy – how often do you come back to look at the table? Any length of time presents problems, because the time between shots is not regular. If you watch only one game, you won’t really have enough data to generate probabilities. If you watch more than one game, then the time between games will throw things off – you look at the table again and nothing has changed. You look at it overnight when no one is playing and there are no balls on the table at all (not even the cueball) for long stretches. And nevermind the problem of Who’s Holding the Cue.

The problem with analogies is that they are analogies. They can be useful for changing the way one thinks about something when that is required (we use thought-problems in philosophy all the time for just this reason) but they can’t give you more than that. Analogy can help you think about particle physics (or anything else, really) but cannot impart actual knowledge about how it works. It feels like knowledge, but isn’t (not by itself).

When most people say they would like something Elegant, what they mean is something that makes sense without having to have too much specialized knowledge. I get that, I was a Humanities kid too. The problem is that the more quantum you get, the less intuitive sense any of it makes. I think we may have to accept the idea that the nature of stuff – existence, everything – will not fit comfortably inside a human skull. It fits inside only exceptional skulls now, and I think we are fast approaching the day when it is only “understood” by machines. And the answer will be 42.

31. Jeff says:

“People are always coming up with absurd pet theories all the time.”

I’d like to point out that absurd pet theories (which are wrong) have a tendency to incite those who know why they’re wrong to nerdrage.

I remember a forum thread discussing black holes by some guy who was absolutely convinced he’s a genius and will revolutionize modern physics… yet clearly demonstrated ignorance of the most basic high-school physics.

32. porschecm2 says:

This is slightly tangential to the original subject, but it had enough relevance I thought I’d link it anyway:

http://www.irregularwebcomic.net/2874.html

33. Cuthalion says:

Heck, I don’t even have enough mathematics to noodle around with the simple stuff they give to first-year students.”

I’m curious: since you’re a programmer by trade, would you then say that it’s not necessary to learn calculus and other advanced math to program well? I ask because it seems every college program in computer science or programming requires a lot of math. Personally, I never needed it when I coded it, but then I haven’t done anything in 3d or in realistic simulations.