I managed to trash yet another laptop - the city commute through the subways seems to be pretty hard on computers! - so while I'm sitting and slowly restoring my backups, I was looking through the folder where I keep links to crankpots that I'd like to mock someday. I noticed one that I found quite a long time ago - and to my surprise, I realized that I never wrote about it! And given that I've been mocking relativity-haters lately, it's particularly appropriate to cover it now.
The site is called "The Nasty Little Truth About Spacetime Physics". It takes quite a different approach to criticizing relativity. As we've seen in past posts, most anti-relativity rants dislike relativity because it implies that there is no fixed reference frame - that there's no such thing as an absolute velocity, no distinguished point at the unmoving center of the universe. That's not this guys tack; no, he's much smarter than that. His argument is that if you accept the idea of spacetime as defined by relativity, that
it logically implies that motion is impossible - and since we can clearly move, than means
that relativity is wrong!
Some of the most famous physicists in the world are not telling the truth about one of the most taken for granted concepts in scientific history. They are not telling us how they can come up with their fanciful time travel theories (wormholes, advanced and retarded waves traveling in spacetime, etc...) using a model of the universe that precludes the possibility of motion. Nothing can move in spacetime or in a time dimension-axis by definition. This is because motion in time is self-referential. It is for this reason that Sir Karl Popper compared Einstein's spacetime to Parmenide's unchanging block universe[*], in which nothing ever happens.
Before I continue, less I be immediately branded as an anti-relativity crank, let me make it perfectly clear that I agree with the mathematical and predictive correctness of both the Special and the General Theory of Relativity.
Now that is some primo crackpottery! You've got to love it when the crackpot starts off his argument by both denying that he's a crackpot, and refuting his own argument!
After that, he goes into a long rant in which he insults every physicist or mathematician who's ever said anything nice about relativity. As a computer scientist who (like many CS people) is deeply fascinated by Gödel, I've got to quote his attack on Gödel:
Kurt Gödel (how did I forget him?) is one of the gods of the voodoo science pantheon. Gödel is
probably one of the most often quoted inconsequential mathematicians of the world. He is known
for his incompleteness theorem, the most obfuscated, non-scientific, chicken feather voodoo
nonsense ever penned by a member of the human species. In 1949, Gödel announced that
Einstein's General Theory of Relativity allows time travel to the past via "closed time-like
curves." The only thing Gödel proved, in my opinion, was the incompleteness of his frontal
That's pretty typical of his mode of attack: it's all personal insults about how stupid and obnoxious all of these people are, without ever being able to address anything that any of them said.
But on to his main point. Why does relativity imply that motion is impossible?
Well, you see, relativity says that time is a dimension. And that means that,
by definition, you can't move. How does that work? Well, let's look at his explanation.
Why is motion in spacetime impossible? It has to do with the definitions of space and time and the equation of velocity v = dx/dt. What the equation is saying is that, if an object moves over any distance x, there is an elapsed time t. Since time is defined in physics as a parameter for denoting change (evolution), the equation for velocity along the time axis must be given as v = dt/dt which is self-referential. The self-reference comes from having to divide dt by itself. dt/dt always equals 1 because the units cancel out. This is of course meaningless as far as velocity is concerned.
To emphasize, it is logically impossible for the t coordinate of an object to change because such a change is self-referential. Et voilà! It is that simple. No time travel, no motion in spacetime, no spacetime and no time dimension. They are all abstract mathematical constructs without any counterpart in nature.
So, if you define a "velocity" of motion in the time dimension as distance in the time dimension per distance in the time dimension, then you've got something self-referential, which doesn't make any sense. Since you can't have a meaningless measure of "velocity" in the time dimension using motion/time, that means that motion in the time dimension is impossible. And if motion in time is impossible, then since motion in space is defined by "distance traversed in space per unit time", that means that you can't move in space, either.
This is, of course, rubbish.
First - let me refresh your memory about what a dimension is. The easiest (although not
necessarily completely accurate) definition of a dimension is an independent direction. So,
for example, if you take a plane, and you put two points on it, you can draw a line between
them, which describes the distance between the two points. With one line which you use for
measurement, that's all you can do - just distance between them. You've only got one dimension
that you can use for measurement. If you have a third point, and it's not on the same line as
the other two points, then you can't really describe its position relative to the two points:
you can move back and forth along your line, but you'll never reach the third point: it's not
on the line. To get to the third point, you need something else: you need to be able to move
in another direction. So you add a perpendicular line - now you've got two
dimensions, and you can describe the position of the third point, in two steps: "You
move left three steps, and north two". You can't describe the position of all three relative to one another without invoking two different directions, where moving in one of them - say north/south - doesn't change your position in the other - east/west. You can add a third dimension: add another point, not on the same plane as the first three. Now to be able to describe its position, you'll need to use east/west, north/south, and up/down.
When we say time is a dimension, that's roughly what we mean. It's another direction, or axis of change, which is completely independent of the other directions that we call space. When we define a velocity as Δx/Δt, what we really mean is that every time we move "Δt" units in time, we move Δx units in space.
Think of simple line drawn on graph paper: y=3x+2. Can we ask how fast y changes relative to x? According to the argument of our crackpot, the answer is no. Because how can we define motion in x? The line is already drawn on the page. x doesn't move. Any motion in x must be defined in one of three ways. It could be motion in x relative to something outside of the system that we're measuring, but that doesn't make sense: we're talking about measurement inside the system - we can't define that in terms of something that has nothing to do with the system we're looking at. We could define motion in x in terms of motion in y - but since motion in y is defined in terms of motion in x, that's circular - and that's clearly no good. And finally, we could define motion in x in terms of motion in x. But that's circular. So you can't look at the rate of change along that line, because "change" is meaningless on the line - any definition of it is nonsensical.
That's exactly the game that he's playing. What he's really doing is invoking a sort of meta-time, and then saying that it's really the same thing as the time dimension. So to move along the time dimension, you need to move through meta-time; and since he defines meta-time as being the same thing as time, that means that motion through time makes no sense.
Now you can start to see why it is that I quoted his critique of Gödel. He's created a self-reference loop - exactly the kind of thing that Gödel studied. But his self-reference loop isn't nearly as interesting as the ones that Gödel studied. It's more along the lines of Russell's paradox: an artifact of a poorly designed model. He's building his argument on unstated axioms which aren't valid - and as a result, he's able to create non-sensical statements derived from them.
You can't introduce "meta-time" into a discussion of relativity, without somehow defining what meta-time is. You most certainly can't require the existence of this meta-time thing, and then implicitly assert that it's the same thing as (non-meta) time. Since that's what he did, his whole argument collapses, and reveals itself as a giant heap of foolish nonsense.
For all the scorn that he heaps on every major 20th century physicist or mathematician that he can think of, he's the one who's actually the idiot: he can't understand the simple concept of "dimension".