I was reading an article on Slashdot the other day about a recent discovery of what might be a MECO. A [MECO][wiki-meco] is a “magnetospheric eternally collapsing object”; if this were true, it would be a big deal because according to relativity, either black holes exist and MECOs don’t, or MECOs exist and black holes don’t.

I have no intention of getting into the MECO vs. black hole argument. But a commenter there put down a link to something that he seemed to think was a [reasonable argument against relativity][nastytruth]. I took a look, and it’s just *hysterically* funny. The author of the site is a total crackpot; not only does he propose a way of totally redefining physics, but he also proposes an explanation for everything that’s wrong with modern software, and exactly how to build a real, proper AI.

One of my mantras for dealing with crackpots is: “The very worst math is no math”. This guy does a spectacular job of demonstrating that.

Just for fun, I’ve got to quote the beginning of his diatribe. There’s nothing more fun than watching a crackpot rant about how it’s the *rest* of the world that are crackpots.

>The Crackpottery

>

>We have all been taught that there is no such thing as absolute motion or

>position or that every motion and position in the universe is relative. This

>unsubstantiated belief, which I have named exclusive relativity, has been

>around for centuries, even before the advent of Albert Einstein and the theory

>of relativity. It was not until early in the twentieth century, however, that

>exclusive relativity became in vogue. Nowadays most physicists consider the

>concept of absolute motion to be no more credible than the flat earth.

>Simple Proof #1 That Exclusive Relativity Is Bogus

>If all positions are relative, then we have a self-referential system in which

>every position is ultimately relative to itself. For example, suppose we have a

>two-body universe. Body A’s position is relative to body B’s position and vice

>versa. Since both positions are relative to the other and there are no other

>bodies, each body’s position is ultimately relative to itself. Of course, it

>does not matter whether there are only two bodies or a billion.

>

>Exclusive relativity amounts to saying things like, “you are as tall as you

>are” or “this sound is as loud as itself” or “pick yourself up by your own

>bootstraps.” Of course this is silly but this is the sort of silliness we have

>to believe in if we accept exclusive relativity.

Nope.

If you have two particles and nothing else, you can define their *positions* relative to each other in terms of their *distance* from each other. It’s not circular. Distance is the important fact. In a relativistic universe, there is no special *distinguished* reference point where the “real” position of objects is defined relative to that reference. Everything is described relative to *a* reference; but that reference can be pretty much any location you choose.

This doesn’t mean that measurements or positions are meaningless. It just means that they’re *relative*.

There’s actually a whole field of mathematics that studies things like this: it’s called metric topology. Speaking *very* loosely, metric topology looks at what kinds of *shapes* a continuous surface can take, and how to measure distance in those different kinds of spaces.

For example, if we lived in a two dimensional world, we could imagine that the world was a flat plane. In that case, the distance between two points is defined in one way. And it doesn’t matter *where* you put your reference point on the plane; the distance between two objects on that surface will be the same. We could also imagine a two dimensional world that was the surface of a torus. The distance between objects would be rather different there; but still, you could measure the distance between two objects on the surface of the torus. And no matter what point of reference you choose, the torus looks the same.

But if you’re a clueless twit who doesn’t understand what “relative position” means, then you can end up with the argument that this guy just presented.

>Simple Proof #2 That Exclusive Relativity Is Bogus

>

>Suppose there is a force acting on a particle so as to accelerate it. The

>particle has as many relative velocities as there are possible frames of

>reference, an infinite number in fact. Which of the myriads of relative

>velocities does the force change? How does the accelerating agent know about

>them so as to change them all? Answer, it does not. Only one velocity is

>changed by the force because it has no access to the others. The others are

>abstract, i.e., non-physical.

Once again, nope.

One of the things that’s beautiful about relativity is that it provides a set of equations that make this all work. From one point of reference, it may appear that an object is accelerating at rate X; from another point of view, it may appear that it’s accelerating at rate Y; work out the relativity equations, and they’re *both* right. Time dilation and relativistic mass shift makes it all work. (If fact, if you were around to read [my series on group theory][groups], you can see [where Blake Stacey explained in a comment][relativity] how relativity describes a lot of things as groups that are symmetric over the kinds of transformations that we’re discussing.)

The problem with the author of this piece is that *he’s not doing math*. Relativity isn’t just a theory with a bunch of words that say “position is relative”, etc. It’s a set of mathematical equations that define in a very precise way what that means, and how it works. Like I said: the worst math is no math. If he’d tried to understand the math, he’d know that there’s no problem here.

>Simple Proof #3 That Exclusive Relativity Is Bogus

>

>Let’s consider the motion of a particle. How does a particle “know” about its

>motion or rest relative to extrinsic frames of references so as to move or be

>at rest relative to them? Are particles psychic? I think not. No particle in

>the universe can make use of the relative because it has no access to it. It

>follows that the universe does not use the relative. The only properties that

>it can use are absolute ones.

Same exact problem as his “simple proof #2″. He didn’t do the math, and so he drew a really stupid invalid conclusion. The math of relativity explains how this works: the apparent velocity and acceleration of a particle in all frames of reference are equally valid; and the reason that they’re equally valid is because if you do the math for shifting the reference frame, you find that the different apparent values are really just different views of the same thing.

[nastytruth]: http://pages.sbcglobal.net/louis.savain/Crackpots/nasty.htm

[groups]: http://goodmath.blogspot.com/2006/06/group-theory-index.html

[relativity]: http://goodmath.blogspot.com/2006/04/some-applications-of-group-theory.html

[wiki-meco]: http://en.wikipedia.org/wiki/Magnetospheric_eternally_collapsing_object

[slashdot-meco]: http://science.slashdot.org/article.pl?sid=06/07/28/0543250