(Swans - November 29, 2010) What are scientific world pictures, the Big Bang for example? It is not, of course, a static picture, but something like an imaginary movie, a movie that requires extensive explanation. We imagine time going backwards and all the stars and galaxies gathering together until they finally disappear in a point. Then we run the picture forwards and see a huge explosion out of nothing that creates a dust cloud that gradually congeals into everything we know. Now this is supposed to be a scientific picture. What makes it scientific? Well, as usual with theories, it all comes down to experiments.
But before turning to experiments I want to note that a picture in imagination is really grammatical. It is evoked in the above paragraph written in ordinary English. No drawing could adequately describe it. Animated movie depictions must come with commentary that reveals just what in the picture is important, what is merely factitious. Such pictures are always in danger of becoming grammatically incoherent, for words have several different meanings and it is easy to think that moving between them is a logical step. For example, it is said that the Big Bang did not occur in space, but that space was actually created with the Big Bang. Now space, empty space, is another word for "nothing." Does it make sense to say that "nothing" was created out of nothing and before that there was no "nothing?" In order to solve this problem scientists have re-imagined space as, not nothing, but as a kind of stretchable rubber that is still called space. It is a three dimensional "analog" of a two dimensional rubber sheet. Since space, imagined in this way, is no longer merely nothing, but a whole new kind of "nothing," we can imagine it as being created out of nothing. Is this a legitimate move? No, for by giving "space" a new identity we allow ourselves to slip unnoticeably from "a rubber sheet" to "nothing." The new "nothing" must have all the characteristics of what we used to call space (or just nothing), but when we are in danger of seeing the absurdity of the creation of nothing out of nothing, it becomes a rubber sheet. By giving this imaginary sheet of rubber the name "space" we have allowed a grammatical incoherence to slip through. For we now think of this rubber as having all the characteristics of space only where this incoherence does not come into view, namely, where it is suddenly created out of nothing, a nothing identical to what we used to call space. There it is, a piece of rubber, easily imagined to burst into existence out of nothing. Once out of this context it can return to its usual condition as just nothing. Along similar lines I have had a physicist tell me that "time changes at very small sizes." Now scientific time as we know it is a rhythmic counting, it has no spatial size. Counting has no size, obviously. But by making time into "the fourth dimension" we imagine it as something like space. Then, when we imagine space as some kind of stretchable rubber it is easy to imagine time, like space, having spatial texture that might look different when viewed under a microscope. By using words in this way we allow incoherent formulations to slip by.
How, you might ask, do such things slip by so many people? Here is a video of a lecture about the expanding universe given by Dr. Leonard Suskind, a Stanford professor and one of the world's most illustrious physicists. Early on, before Dr. Suskind gets into his equations, a student asks the crucial question. The student asks (at 4:00) if the measuring rods don't expand too. It is obviously a crucial question, for if the measuring rods and everything else did expand then everything would, as Suskind says, fly apart. All the planets and suns would have long ago dissolved into subatomic dust. And that, obviously, hasn't happened. Of course, if they didn't fly apart but just got bigger at the same rate as "space" got bigger, why then the size change would be undetectable. So, what gives?
Dr. Suskind quickly answers the student with the necessary assurance that the meter sticks are not expanding because the forces, gravity in particular, but also electromagnetic and strong forces, are much stronger than the force expanding the universe and those forces hold the meter sticks together. Dr. Suskind then draws a picture of a spring connected to the wall and points out that a small force directed away from the wall would only expand the spring a little bit before it reached an equilibrium position again. The student, or perhaps another one, senses that something is wrong and tries to respond to Suskind. Dr. Suskind seems confused by the student's response, though it seems quite clear to me. Instead of trying to answer he says that "they will come to it," and drops the subject.
If we look closely we can see that the student is quite right to be uneasy, though his response might not be the best one. The forces Dr. Suskind counts on to keep the meter stick from expanding along with the rest of the universe vary inversely with the square of the distance between masses. Gravity becomes weaker as things get further apart. But the supposed force that is expanding the universe is constant throughout. It doesn't get weaker with the distance between bodies but in fact is unaffected by neighboring bodies. Thus the spring he draws is the wrong picture. The spring is supposed to correspond to gravity, but the force the spring exerts, unlike that of gravity, increases as the spring stretches, that is, as the two masses get further apart.
Gravity wouldn't do this. If a force, no matter how small, were exerted continuously on a planet in orbit around a sun, or on an atom held close to another through gravity or any other force that weakened with distance, they would, once they separated even a little, continue to separate at an ever increasing speed. If there was a space ship equivalent of a rowboat and it were tied to the earth and could budge the earth even a little away from the sun, it could row the damn thing out into darkest space. To picture a force pulling against gravity Suskind might better have used a disk of metal precariously floating between two magnets. That would show that the slightest increase in the force of the upper magnet (corresponding to the small distance away from the sun it moves) would set in motion an ever greater acceleration away from the bottom magnet. That is what would actually happen, not the equilibrium the spring promises.
We should note Dr. Suskind's slight mystification at the student's question. For this is the technique for gliding over difficulties. It is not physics that mystifies Dr. Suskind, but the workings of the student's mind. Physics students are terrified of looking stupid. Dr. Suskind's gesture is a relatively kind one, but I have seen others look out at a questioning student with scorn, or even better, with a futile attempt to repress scorn. Physics students, perhaps more than any others, will avoid the danger of revealing themselves as stupid at all costs, and will therefore repress such misgivings as these, sliding over and burying them -- forever.
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About the Author
Michael Doliner studied with Hannah Arendt at the University of Chicago (1964-1970) and has taught at Valparaiso University and Ithaca College. He lives with his family in Ithaca, N.Y. (back)