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The Science Of Being Wrong

December 4th, 2003

A layman would be forgiven for thinking that the answers scientists strive to obtain are the correct ones. It would be silly, the layman would elaborate were he feeling particularly verbose that day, to strive to obtain wrong answers. Far easier, suggests he, to invent a number and declare it The Wrong Answer. This is how laymen are different to physicists.

In physics it is totally unnecessary to find the correct answer. A wrong answer is perfectly acceptable as long as you have some idea just how wrong it is. In carbon-dating, for example, every single measurement ever taken is wrong because when physicists discovered they’d been using the wrong number all this time they decided to stick with it anyway and call it a convention. A convention is something which is wrong but people do anyway because its easier than what’s right, for example, electric current is (for all intents and purposes) defined to go backwards because someone made a wrong guess before electrons were discovered and it would be too much work to change it all now. Worse still, according to my friends who have dropped off the astrophysics course, in astrophysics pi is frequently approximated to one when it suits them. If pressed to explain why they do this, they will wave their hands about and talk about ‘orders of magnitude’ until they forget where they’d got to in the lecture. In fact, a “hand-waving argument” is now accepted to mean one which gets the point across but neatly ignores any of the difficult bits. (When there are outsiders around the word ‘qualitative’ is used to mean the same thing but sound cleverer.)

You probably think quantum mechanics is difficult. And it is, if you want to do it right, but doing things right is too hard for physicists, which is why ‘approximations’ were invented. Entire branches of mathematics have been invented to define exactly which bits of physics can be safely ignored to get answers which are sort-of near the right ones. The approximations, though, usually only work properly for a narrow band of inputs, for example all pendulums are assumed to swing by no more than 10�, and if they swing by any more than this, then the accepted physics governing their motion gets too wrong and stops working. It’s slightly wrong anyway, but not enough to matter very much unless you live in Switzerland and make clocks. Physicists get round this problem by ignoring it. They continue to use approximations that don’t really work at all because it’s easier than working out the correct answer.

The most complicated mathematics we had to do in the first year lab was not working out answers at all but, in fact, working out how wrong our answers were. This involved lots of calculus, a few tiresome rules, and a lot of calculator work. (Eventually they told us that none of this had been shown to be the ‘correct’ way to work out how wrong we were and someone had, in fact, just made it up and it had become convention. Are you spotting a pattern here?) Frequently, our error margins would come out to be rather larger than the actual result, which meant firstly that we could have just said “the answer is zero” and have been closer, and secondly that we had spent four hours experimenting and failed entirely to prove, for example, that gravity does not point up.

In strict fact, of course, pretty much all accepted science you know is wrong. Thanks to relativity and quantum theory we now think we know less about the universe than we thought we knew a hundred years ago. If you have never done degree level science, you probably think that most of the following statements are true:

No matter how long you travel in a straight line, you will never get back to where you started.

An object can only be in one place at one time.
You can stand still.

Your office layout does not affect your lifespan.

You can touch things.

If you rotate any object by 360� it won’t make any difference.

In fact none of those things are true. I will go through each one and leave out important bits of science and get things wrong. But that’s okay, as I think I’ve mentioned.

No matter how long you travel in a straight line, you will never get back to where you started.

This is a common misconception, because it is based on common sense. If you keep going in a straight line, you will arrive back where you started, because space is “finite but unbounded,” “cyclic,” or, to the non-scientists, wraps around like an old one-screen Spectrum game when you get to the end.

An object can only be in one place at one time.

According to quantum theory, a small enough object, say an electron, can be shown to exist in several places at once, until you actually go to the bother of looking at it, when it instantaneously plumps for one place or another and stays there until you start applying forces.

You can stand still.

According to relativity, absolute motion is undetectable (and therefore basically doesn’t exist). If you think about it, you stand on the Earth. the Earth orbits the Sun, which spins around the Milky Way, which is in a moving cluster of galaxies. There is no way to tell, though, if the cluster is moving or not. (We assume it is because its the only assumption that makes sense.) If two objects pass in space, it makes no difference if you say one stays still and the other drifts past. And this is the easy part of relativity. When one of the objects is a beam of light, it doesn’t matter how fast you are moving, you still see it move past you at the same speed.

Your office layout does not affect your lifespan.

This is an interesting one. Relativity says that an object moving quickly experiences time dilation. The very top floor of a tall building is far enough off the ground (and therefore spinning fast enough) that over an average lifespan time dilation effects add up to an extra day. Unfortunately, this has the effect of taking a day from your retirement and distributing it in tiny pieces throughout your office hours. To the ground-level observer, you live a day shorter and seem infinitessimally more tired after a day’s work. You also weigh a little more and are a little thinner, but these effects aren’t culminative so don’t matter so much. Besides, the gravity is lower up there so you probably weigh a little less. I can’t be bothered going through the maths to work it all out.

You can touch things.

Wrong. You can get about a tenth of a micrometre from something. At this point, the electrostatic force between electrons in your skin and electrons in the object is strong enough to move the object and create the illusion of touching it. You only think you touch things for the same reason that balloons are slightly inclinded to stick to walls. It’s probably best not to think about this while kissing. It can only put you off.

If you rotate any object by 360� it won�t make any difference.

I don’t quite understand why, but apparently if you do this to a hydrogen atom, then quantum physics says you have to rotate it another 360� to get it back where it started. That’s crazy to me, but I’m about prepared to believe it since I have accepted that everything else in the list is wrong it seems only rational to question this assumption.

Now that I have shattered your view of the world, I’m going to leave you to go slightly mad on your own. This is why physicist use approximations — the truth is far, far too complicated to be any use to anyone.You can tell if a scientist is lying to you, because they will use one of the following phrases: qualititavely, classically, approximately, to the first approximation, in first order terms, to an order of magnitude, or I’ll have it done by tommorow morning.

The lies are useful even to scientists though. For example, people who have done some science but not that much tend to think the following statements are true:

Nothing can go faster than the speed of light.

Objects cannot spontaneously move of their own volition.

Electrons orbit the nucleus of an atom.

Again, I will explain them all in a quick and oversimplified manner.

Nothing can go faster than the speed of light.

In practice, several things (but mostly light) have been moved faster than lightspeed, and Bell’s Theorem suggests instant effects over almost infinite distances which messes up the whole thing. In fact, no information can travel faster than light, but objects or waves can under the right circumstances.

Objects cannot spontaneously move of their own volition.

It seems logical that things don’t move unless you make them. In fact, Newton declared it a law and if they do the Physics Police come round and arrest them. The interesting thing about quantum theory (well, one of them) is that it says, in effect, “Idunno. You tell me,” and shrugs. In more detail, it says that you can’t predict what any particular particle will do. All you can calculate is how likely different responses are. Then we rely on statistics to do the rest. All science says is that objects are very unlikely to spontaneously move of their own volition, but in theory a very small chance exists that all the particles could simultaneously decide to go the wrong way.

Electrons orbit the nucleus of an atom.

If this were true, the electron would emit radiation and lose all its energy doing so. Then it would spiral into the nucleus and probably combine with protons and the universe would end up as little more than lots of very hot neutrons. In fact, electrons tend to exist as a kind of fuzzy cloud around the nucleus.

I hope I have shown you that almost all science you are taught until you are about nineteen is a lie. Please don’t mention any of this in GCSE lessons. It won’t help matters.

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