*The Life of the Cosmos*, by physicist Lee Smolin (New York: Oxford University Press, 1997). He articulates some of these things (though you will run into them in just about any substantial book on modern physics or theoretical physics).

Here is a quotation from Smolin's description of the development of a theory called "string theory" (p. 64):

What was even more significant is that in the cases where the program worked, physicists--beginning with Yochiro Nambu, Holgar Nielsen and Leonard Susskind--realized that the solutions they found did not correspond to the traditional conception that a fundamental particle is a point that has no extension or dimension. Rather than behaving like mathematical points, they behaved more like stretched, one dimensional objects, something like rubber bands.

This led to the idea that perhaps atomism is right, because there are fundamental things in the world. Only these things are not to be visualized as point particles; they are instead one-dimensional. These fundamental one dimensional objects are what we call now strings. Just as a point has no size, these also take up no space, as their diameters are zero. But they do have length.

OK, let's analyze this for a moment. What it sounds like Smolin is saying is that there were two ideas of what the world is fundamentally made of being discussed. One idea was that the world is made up of point particles which take up no space and have no size, which have no length, height, or depth. The other idea was that the world is made up not of point particles but of one-dimensional strings. These strings take up no space, being one-dimensional, but they do have length.

Here's the problem: Taken at face value, both of these ideas are meaningless nonsense. In case you haven't noticed, material objects take up space. They have size. They have dimensions--height, width, length. So how could they be made up of particles which have no size and take up no space? And what even

*is*a "particle" which has no size or dimensions and takes up no space? It is exactly equivalent to "nothing." Material objects, by definition, have size and dimension and take up space. That's just what "matter" is. If you remove size and space from a material object, you remove its very essence, its very substance. So why in the world are we talking about material particles which have no size and take up no space?!

The idea of "strings" is even better. They, too, take up no space. They have only one dimension (length, I guess), but no height or width. But this concept, too, makes absolutely no sense taken at face value. What in the world is an object that has length but no height or width? If a supposed "material object" has no width, it has no substance at all. But these amazing objects, which have no material substance at all and take up no space, yet are of definite length. "Nothing" now has a definite length, and is the fundamental building block of all material objects!

What in the world is going on here? I think we're still in the world of serious scientists. I don't think these ideas are intended as an elaborate practical joke. But, taken at face value, they are meaningless gibberish, utter nonsense. Yet these scientists talk about them as if they make perfect sense, and they claim that the ideas make predictions that can be tested, etc. One possibility to explain this bizarre situation is that the physicists have developed mathematical formulas that work to describe in mathematical form the sorts of observations they are making. Perhaps the whole thing makes sense as math, and they are simply using extremely odd and misleading ways of communicating these math concepts as descriptions of objects and functions in the real world. Perhaps they have failed to distinguish between mathematical ideas that work in mathematics and descriptions of physical reality. For example, 2-4=-2 works just fine in math. It is a very useful idea. But as soon as you start to think that the formula is describing an actual material state of affairs ("I had two apples on the table, and I took four away, so now I have negative two apples on the table."), you run into serious trouble. Not all mathematics describes material objects and functions. Sometimes mathematics works at a purely logical and theoretical level--which is very useful, but not to be confused with one-to-one descriptions of what can exist or go on in the physical universe. In the case of some of these ideas in modern physics, I really don't know what is going on. My guess is that there is something of value here in terms of mathematics, and that either the scientists are using language I simply do not understand or they are using the wrong language (either because they are simply misusing language or because they truly are confused about the distinction between mathematical formulas and descriptions of physical reality).

Here's another example of the same sort of thing, from the same Lee Smolin book. This time, we are talking about the odd characteristic of string theory to require more than three dimensions to exist in the universe. If this seems like a problematic situation to you, welcome to my club. But, have no fear, string theorists think they can solve this problem (p. 67):

The idea is to postulate that our world does have nine dimensions, but that six of them are rolled up, so that the diameter of the universe in these directions is not much more than a Planck length. There would then be no way for any of the elementary particles, such as the protons--which are twenty orders of magnitude larger than the diameter of these curled up dimensions--to know about anything other than the three remaining dimensions.

Feel better? I hope not. If I'm understanding correctly, what I just heard was this: "String theory has the unfortunate characteristic of adding six dimensions to the universe in addition to our usual three, which seems to be a problem. But not to worry! The other six dimensions are all rolled up into tiny little balls, so they don't get in the way."

It will be helpful here to remember what a "dimension" is. The three dimensions are height, width, and length. They are nothing other than directions in space. There are three fundamental directions you can go (or grow) in space. Imagine yourself standing in the middle of a room. You can go 1. forwards and backwards, 2. left and right, 3. up or down, or 4. a combination of these. Those are the only possibilities in the physical universe. There just aren't any other directions to go, if you think about it. But string theory is telling us that there are six other directions things can go (or grow) in. Perhaps you are wondering why you haven't noticed them? Well, it's because they're itty-bitty and rolled up into little balls. What?! We're talking about directions, right? What in the world does it mean to say that there are six directions that are rolled up into tiny little balls?! Directions are not material objects. I can roll playdough up into little balls. I can roll paper up into little balls. These are physical objects or substances. But directions aren't that sort of thing. You can't pick up a direction, put it in your pocket, drop it on the floor, put it in some water to see if it floats or not ("Look, dad, I just put 'up' into a glass of water, and it floats!" "That's really neat, son!").

Again, I don't think I'm the victim of an elaborate practical joke. These PhD scientists seem to really mean what they're saying. But how can they? How can anyone with the smallest modicum of an ability to think in a logical and intelligent manner speak seriously this kind of complete nonsense? Again, I suspect that there is some mathematical truth at the heart of these things, and that something is going seriously wrong in communication or translation. But I wish I could figure out what it is, because they're driving me nuts!

I'm sure I'll be writing more on this in days to come, and it will end up under the label "Modern Physics". So stay tuned.

## 6 comments:

I'm a first year physics graduate student; I am very, very busy but I can offer some brief, drive-by comments that might also be helpful. I think you're correct there is something being lost in translation, although I don't want to pretend that all physicists are philosophically aware of their statements. For those who are (as some of my professors), I think one way to understand their statements on the connection of math to reality is that the real objects behave to some approximation as the math dictates. Thus for point particles, the real particles behave like mathematical point particles (to some approximation). Point particles have long been known to be problematic even mathematically though (look into the self-energy of an electron). This point of view might be held for strings too, but I don't know enough about string theory to safely say.

This point of view on point particles (and strings) seems to be within Smolin's quotation itself: "Rather than behaving like mathematical points, they behaved more like stretched, one dimensional objects, something like rubber bands."

It is common for even physicists who are philosophically aware to move smoothly and without warning between the mathematical model and the actual objects, so that literal reality is attributed to the mathematical objects. This can be confusing at times, even for physicists. I myself sometimes forget that the particles we are dealing with are not literally mathematical points (thanks for the reminder in this blog post!). Such is one of the limitations of the scientific method, I guess, in which we can only go by how the objects seem to behave as determined by empirical observation.

As for curled up dimensions, I don't know string theory so I can't say for sure, but just going by the quotation, it seems to me the dimensions are not literally "curled." Rather, it seems they mean that the universe in the directions of those dimensions is extremely small: "the diameter of the universe in these directions is not much more than a Planck length." I don't know why they call it "curled" though; it is perhaps an artifact of the mathematical process that has the end result of making the equations describe a universe that is small in those directions. Perhaps the "curled" or "rolled" up means the universe "folds" in on itself in those directions so that its diameter is extremely tiny in those directions. But again, I don't know enough string theory.

Hi Raymond. Thanks for your very helpful comments. I think what I hear you saying, at least with regard to "point particles" and possibly the nature of the "strings" of string theory, is that physicists use mathematically over-precise (for lack of a better word) descriptions of physical realities, and sometimes forget that the mathematical description is an approximation. For example, it is convenient in math to think of a particle as a point, even though a point cannot literally exist in the world, but physicists sometimes keep talking about particles as points even when they move into descriptions of the physical world. If I've understood you correctly, I think that makes a lot of sense. I can see how that kind of thing could easily happen.

With regard to "curled up" dimensions, even if we say that the language of being "curled up" is not literal, we still have to deal with the idea of there being nine dimensions and six of them being "very small." Dimensions are nothing but spatial directions, and directions cannot be large or small. They are not physical objects. It is like saying that "up" is very little, or very big. This makes as much sense as saying that pi is bouncy, or that 2+2=4 sounds scratchy. It's blatant category confusion.

But, I suspect that there are valid mathematical formulations underlying this language that work mathematically, and for some reason physicists have taken to using the language of "dimensions" to talk about them, even though they are not really a description of more than three literal dimensions in the physical world. Speaking literally, there cannot be more than three dimensions, because there simply aren't any other directions in space besides the three (and mixings of the three). This is evident from observation. But probably there are aspects of reality that can be mapped mathematically that are behind that language, and it is simply the language itself that is confusing in that it uses terms that originally meant something else and gives them a specialized meaning that is not adequately explained.

Special relativity has some interesting concepts too. A meter stick traveling near the speed of light is a meter long from the meter stick's perspective, but it's less than a meter long from the perspective of a stationary observer. Both are literally true at the same time, not optical illusions. Although simultaneity is also relative...

And according to general relativity, light moving in a straight line past a massive object travels farther than light moving in a straight line without the massive object.

"A meter stick traveling near the speed of light is a meter long from the meter stick's perspective, but it's less than a meter long from the perspective of a stationary observer. Both are literally true at the same time, not optical illusions."

I'm not sure what this means as a description of physical reality. I need to give it some more thought before saying anything.

"And according to general relativity, light moving in a straight line past a massive object travels farther than light moving in a straight line without the massive object."

Taken straightforwardly, in terms of what the words seem to mean, this sounds problematic. If light is traveling in a straight line, in a literal sense, it has to go a certain distance, and if it goes that distance, it goes that distance. If light travels one mile, then it travels one mile. It cannot travel one mile and 1/2 mile at the same time, for then it would end up in two different places at once. If I walk a mile in a straight line, it cannot also be true that I've walked only a half mile in a straight line, for a half-mile away and a mile away are two different locations. We would have to say that I ended up a half a mile away from myself, which makes no sense. I suppose the same issue would apply to the meter stick as well. It must be a certain length, because one end must be a certain distance from the other end. If it is a meter and also only half a meter, one end of it would be in two different places at the same time.

But certainly distances can appear differently to different observers in various ways, so perhaps there is a sensible understanding of this phenomenon. I'm not sure. What do you think?

I'm not really sure what the math behind these theories could mean aside from what physicists say it means, but I'd be really interested to hear what philosophers say it means. The theoretical math fits the experimental data very precisely, and modern technology such as the GPS wouldn't work without it.

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