Built on Facts

The Theory of Theory

I recently learned about a great blog by S.C. Kavassalis of the University of Toronto called The Language of Bad Physics. She discusses, among other things, the way language is used in physics. She’s got an interesting piece on the use of the word “theory”. This is always a hot area of discussion, but in physics it has particular resonance because so many non-physicists like to come up with their own “theories” about how nature might work.

I put “theory” in scare quotes not because amateurs can’t make contributions to physics – they can and do – but because there’s a heck of a lot of cranks out there with theories that aren’t actually theories. In physics, if you want to come up with a theory at minimum it has to:

1. Generate numbers.
2. Match those numbers consistently with observation.

This is a guideline rather than a formal definition and there’s a little semantic wiggle room that I don’t pretend to have fully captured. But the idea is that for a theory to be worth anything it has got to accurately describe what nature does. If you’ve decided that, I dunno, “the proton mass and the quark mass originate from a gaseous cloud of micro-particles“, then that’s lovely but how exactly do you propose to tell if the theory is right? Unless there’s something measurable it describes (and describes to greater accuracy than current theory, if applicable), you haven’t accomplished anything. Let me give an example of how a person – in this case a fictionalized Isaac Newton – might have an idea and then test it numerically.

Newton had the idea that everything with mass is attracted to everything else with mass. That’s nice – it might even be true – but in and of itself that idea isn’t worth much because it doesn’t predict anything. So Newton of course didn’t just say that masses attracted each other, he expanded on his insight mathematically and guessed that they did so with a force in proportion to the product of their masses divided by the square of the distance between them.

i-d4bb9fe09d6b78eb832985821d8a307f-1.png

Where M is the mass of one object, m is the mass of the other, G is the gravitational constant, and r is the distance between them. (This is specific to point masses, but Newton showed that spherically symmetric objects obey this equation exactly if you take r to be the distance between their centers of mass . Other objects can be treated as a collection of many tiny point masses and their gravitational influences added up via calculus.)

So what does this predict? Knowing that a force F on an object with mass m produces an acceleration by F = ma,* Newton could say that an object on the surface of the earth would experience an acceleration equal to

i-88516ca505d84f969b7ab15a965c3fb3-2.png

Where M is the mass of the earth and r is its radius. Now we know by experiment that the acceleration at the earth’s surface is 9.8 m/s^2. Newton knew this, but he had no way of knowing G or M. Still, he did know r (about 6400 km) and so he could at least solve for the product GM. If you do this, you’ll find GM = 3.99 x 10^14 m^3/s^2, which is some wacky units but that’s ok.

But so far Newton hasn’t really tested his theory. He has calculated what GM must be for his theory to work for objects on earth, but there’s no reason to believe it’s actually a description of physical reality since you can fit pretty much any screwball idea to one data point. He needed to take his theory and see if it worked in other contexts. So that’s what he did. Newton knew that the acceleration required to keep an object moving in uniform circular motion is equal to

i-d18063683dcc0d42b9be45451a84d1e3-3.png

We won’t pause to prove it – the curious can Google “uniform circular motion” – but it can be mathematically proved in a straightforward way. Therefore if Newton’s idea about gravity could also work to describe things in a circular orbit, he could equate the two above equations to find the velocity of an object in orbit about the earth with an orbital radius r:

i-8d7070ce28f0af28047c7a5fb8246d53-4.png

Newton wanted to see if this was right for the Moon. Knowing that velocity is distance divided by time, it’s easy to see that the Moon’s velocity v = 2*pi*r/T, where 2*pi*r is the circular distance it covers in one orbit and where T is the time of one orbit. Solving that for T, we get:

i-bb5c2c6b0452df43a61e3974bd9b473f-5.png

So we can plug in Newton’s previously obtained GM, and the known orbital distance of the Moon (about 384,000 km). That distance, by the way, had been measured with surprisingly good accuracy as far back as the ancient Greeks. Plugging in, we get

T = 27.4 days.

The Moon’s actual orbital period? The well known 27.3 days. In my simplified version of the story I’ve neglected the fact that the Moon’s orbit isn’t actually quite circular and I’ve neglected the effect of the Moon on the earth. Newton neglected neither, of course.

So Newton showed that if his theory described the gravity of the earth on you and me, then the moon’s orbital period would have to be a certain value. If it had been anything else, his theory would have had to be scrapped. If, for instance, his idea had involved a GMm/r^4 force then the two values would have been wildly different.

This is in spirit the way every theory should be developed and checked. The theory has got to generate testable numbers, and those numbers have to pass the test of matching with observation. Indeed this was only the first rather than the last test of Newton’s idea, with people like Cavendish testing it on laboratory-scale masses and so on. It passed every test until eventually Einstein predicted some slight deviations under certain circumstances, and of course Einstein’s theory then had to be tested to see if it matched observations. So far it has every time, though it may be that a yet more precise theory will be developed someday.

So keeping this in mind, theorize away! But do it with math, and check it against measurement.

*In this context this is a definition of force rather than an independent physical law.

Comments

  1. #1 CCPhysicist
    May 7, 2010

    Excellent example, but you dodged the real question. Cranks might have a legitimate reason to think they are doing physics.

    Let’s rewrite something from your article:
    If you’ve decided that, I dunno, “particle properties arise from multi-dimensional strings”, then that’s lovely but how exactly do you propose to tell if the theory is right?

    Your opinion as an experimentalist?

  2. #2 Matt Springer
    May 7, 2010

    I figured someone was bound to ask that!

    String theory ought to be called string conjecture. But I’m not quite going to put my foot down and denounce it for two main reasons:

    1) Experimental test is very tough because adequate particle accelerators are so expensive.
    2) Many of the alternative ideas are testable, and have been found not to work. (random example: Loop Quantum Gravity models with variations in c above observed limits)

    So it’s either string theory or have fundamental physicists twiddle their thumbs until one of them comes up with something entirely new and brilliant. Until that happens, might as well keep working on the main currently available idea that at least might eventually get figured out enough to be testable.

  3. #3 Sam K.
    May 7, 2010

    Since we’re on the topic, how do you think this applies to other fields, e.g. climate science?

  4. #4 Matt Springer
    May 7, 2010

    Wow, the comment section is like Jesus and the Pharisees!

    The short answer is that while I’m completely on board with the idea of reducing human environmental impact and CO2 emissions, the science of climate modeling has not exactly covered itself in glory over the last few years.

  5. #5 CCPhysicist
    May 7, 2010

    I like your analogy!

    I’d be happy if the people involved admitted that it was pure conjecture and that their challenge was to find a way to make it a theory. I question your two excuses because

    1) This statement only applies if there is a theory that says a specific phenomenon will appear at a specific energy that we can’t yet reach. I am unaware of a claim from “string theory” that is on the same level as saying what energy is needed to make the Z, or even what other measurement would tell us what that energy might be. “Something has to happen” is not much different than simply looking at unitarity as was done in the 50s.

    2) It is totally specious to assert your theory is right because some other theory is wrong. That is the same “logic” used by creationists to argue that any evidence against a specific evolutionary model is evidence for their non-existent model.

    The difference between string theory and atmospheric modeling is that people know how to model fluids and can use that model to design spectacularly fast cars, high performance wings, and predict the weather. They also know how the limitations on the initial values, boundary values, and current values that must be used in such models affect those predictions and thus limit predictions of where leaking oil will go next or what the climate did in places or times where we don’t have data.

  6. #6 Uncle Al
    May 8, 2010

    The Moon’s orbit has a 29.53059 day synodic period.

    Thirty years of string theory and its 10^1000 consistent metastable vacua (the “landscape”) are egregious. Peter Woit and Lee Smolin don’t like it,

    Not even wrong: The failure of string theory and the search for unity in physical law; Basic Books: New York, 2006; p. 241; The trouble with physics: the rise of string theory, the fall of a science, and what comes next; Houghton Mifflin Co.: Boston, 2006; p. 158.

    But wait! What does Lenny Suskind say?

    arxiv:hep-th/0302219

    “It is much more likely that the number of discrete vacua is astronomical, measured not in the millions or billions but in googles or googleplexes” [sic].”

    Looks to Uncle Al that Lenny also says it’s crap – and he should know.

  7. #7 Coturnix
    May 8, 2010

    I am glad you like The Language of Bad Physics. Not being a physicist I can barely understand it, but what I understand is great.

  8. #8 Nathan Myers
    May 8, 2010

    So, Strings merits special pleading? Is this a social matter, because piling on would make dinners awkward? Or is this that common psychological failing among students of science, where not to know is so painful that you prefer to pretend something is true when you have no reason to think so, or even when you have reasons to think otherwise?

    Each generation brings us a few real scientists, and a whole crop of believers who just happen to believe what actual scientists of the previous generation said. Under slightly different circumstances the latter would happily believe any old thing they were taught.

  9. #9 Matt Springer
    May 9, 2010

    Don’t be so grim, Nathan! All I’m saying is that I’m not willing to declare it worthless, and that only because of the scarcity of data and alternatives and the fact that it’s interesting as pure math. And I completely agree with CC that lack of alternatives doesn’t indicate string theory is any more likely to be correct.

    I am more than willing to declare it wildly speculative, a thus far evidence-free conjecture that deserves no consideration as anything more than that. You may also be pleased to know that at least anecdotally I’ve observed many physicists who aren’t working in string theory regard the whole project with amusement, as something akin to the scholastics arguing about angels dancing on pins.

  10. #10 ppnl
    May 10, 2010

    I have read “The trouble with physics” and I think Smolin’s point isn’t that string theory is wrong or that it isn’t science. He just argues that physicists may be over investing in it. He argues for diversity.

    He may be right. However without a doubt the mathematical tools developed will be useful even if string theory is wrong. For example many string theorists eventually move on into condensed matter physics where the tool kit has many unexpected applications. Thats kinda strange and may be a clue that even if string theory is substantially correct it cannot be a fundamental theory. It may simply be a window into a whole new realm of more fundamental physics. After all atoms were once viewed as fundamental.

    Maybe it really is turtles all the way down.

  11. #11 Uncle Al
    May 10, 2010

    Contemporary physical theory is obsessed with fundamental, intrinsic, intensive properties of highest initial symmetry. Gauge/gravity duality – proposed equivalence between various Yang-Mills and string theories – is only true for highly supersymmetric idealizations of quantum chromodynamics (a stacked deck).

    Reality is symmetry-broken massed fermions that choke gravitation theories and the standard model. Reality is parity-odd. Differential vacuum interaction toward mass requires metaphoric opposite shoes not socks. Five such tests arise from extrinsic, extensive, emergent-scale properties that physics disdains without proof:

    1) Parity Eotvos experiment: Do chemically and macroscopically identical, opposite geometric parity atomic mass distributions violate the Equivalence Principle?

    http://www.mazepath.com/uncleal/erotor1.jpg

    2) Parity calorimetry experiment. Do opposite parity test masses that melt to a common achiral (not racemic) fluid have different enthalpies of fusion vs. time of day?

    http://www.mazepath.com/uncleal/lajos.htm#a2

    3) Parity gyroball experiment. Two small solid single crystal quartz balls, enantiomorphic space groups P3(1)21 and P3(2)21 plus an amorphous fused silica ball, are plated with superconductor, cooled in hard vacuum and Meissner-effect levitated. Versus time of day, do the crystal balls spontaneously counter-rotate while the amorphous ball is irrotational? That detects all interactive vacuum backgrounds.

    4) Parity molecular rotor experiment. The rotors are racemic twistane or 2-twistylidene dimer right-right, left-right, left-left.

    http://www.mazepath.com/uncleal/twisten2.png

    Supersonic expansion of seeded inert gas into vacuum obtains a 1 kelvin rotational temp molecular beam. Pulse that into an FT microwave vacuum cavity vs. time of day. Do rotational populations diurnally diverge?

    Eotvos experiments sense 5×10^(-14) difference/average mass/mass. E=mc^2 that is 4.49 J/g. Go Boltzmann for the dimer rotors. 145 times initial absolute temp is not a subtle thing.

    [(4.49 J/g)(268.436 g/mol)]/[6.022x10^23 /mol)(1.3807x10^(-23) J/K)] = 145 K

    5) Parity vacuum free fall. A rocket shoots 1000 miles up. Test masses and their sensor payload then vacuum free fall straight down for 15 minutes. Beautiful!

    Class. Quantum Grav. 27 095005 (2010)

    The proposal is aluminum vs. lead. Composition dipoles are nulled by 1.74 solar-mass 465.14 Hz pulsar PSR J1903+0327 (superconducting, supermagnetized, supergravitationally bound, relativistically spinning neutronium) and its 1.05 solar-mass star (proton electron plasma) binary. Orbit, orbital precession, and orbital decay validate the EP.

    Somebody should run a massed parity experiment. The worst it can do is succeed (killing string theory wherein BRST invariance unites the effects of a massed body and an accelerated inertial frame).

  12. #12 Nathan Myers
    May 11, 2010

    So, packing physics departments with spiritualists is harmless because after nobody can prove there aren’t fairies?

    It really might be harmless but for all the real physicists off valuing credit-default swaps because all the physics appointments were taken by stringualists.

  13. #13 Bear Giles
    May 11, 2010

    See Karl Popper and Philosophy of Science. The concepts are simple although you’ll have to explain them to most people.

    Foremost is probably ‘falsifiability’ — what you spent most of your blog entry demonstrating! You can’t prove something is true if there’s no way to prove it’s false.

    Underlying that is ‘measurability’. That usually means that you can put numbers on it but not always. Sometimes the simple fact that something occurred is all you need.

    Finally(?) there’s ‘repeatability’, especially under controlled circumstances. In physics that’s usually the lab but in a lot of scientific fields you have to take what you have. E.g., nobody can set up different stellar circumstances and see which go supernova and which don’t!

    There’s still a lot of room for misunderstanding. Watch Mythbusters – I’ve seen a few things that really surprised me and could easily be misunderstood by somebody with only HS physics (e.g., levitating a wire via electron flow.) But it goes a long way.

    BTW my favorite false theory is that things drop to the floor when you drop them. Obvious, right? Only it’s not – ‘drop’ a helium balloon or a live bird.

  14. #14 Nathan Myers
    May 11, 2010

    Falsifiability? What of Big Bang? Can there be any new evidence that cannot be folded into it by inventing some magickal new process, thitherto unimagined? Can there be any such process that cosmologists would shrink from?

  15. #15 ball valves
    March 27, 2011

    The solid truth about this blog post is, that it spoke to me greatly. Thank you for sharing your thoughts and concerns.

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