Labyrinths of Reason (11 page)

A big part of philosophy is deciding which questions about the world are meaningful. Antirealism is the dogma that only those questions that may be settled on the basis of observation or experiment have meaning. It resists assuming anything about the unobserved and unobservable. Antirealism sees the world as something like a movie set where the buildings are just façades. It resists the temptation to fill out the buildings behind the façades.

The difference between what is unknown and unknowable may be subtle. No one knows Charles Dickens’s blood type. The ABO blood types were not discovered until a generation after Dickens’s death (by Austrian biologist Karl Lansteiner in 1900), and thus Dickens’s blood type was never determined. Though the Dickens’s blood type may remain forever unknown, most would feel that that doesn’t change the fact that Dickens had
some
blood type.

In contrast, everyone recognizes as meaningless a question like “What was David Copperfield’s blood type?” It is meaningless because the fictional character exists only insofar as Dickens imagined him, and Dickens did not give this information in the story. It is not merely that we are ignorant of Copperfield’s blood type. There is nothing to be ignorant of.

Antirealism speaks of questions that are undecidable in principle, like nocturnal doubling. In its most radical form, antirealism is the belief that the unknowables of the external world are just as meaningless as questions about a fictional character’s blood type. There is nothing to be ignorant of.

Were that all there was to it, the question of realism vs. antirealism would be purely a matter of philosophical preference. Actually, there are many open questions of physics, cognitive science, and other fields where the relationship between what is unknowable and
what is meaningful blurs. This chapter will examine several of these variations on the unheard tree.

There is more to the nocturnal-doubling debate. For one thing, not everyone agrees that a nighttime doubling would be undetectable. One of the best cases for detectability has been put forward by philosophers Brian Ellis and George Schlesinger.

In 1962 and 1964 papers, Ellis and Schlesinger claimed that the doubling would have a large number of physically measurable effects. Their conclusions depend on how you interpret the thought experiment, but they are worth considering.

For instance, Schlesinger claimed that gravity would be only one-fourth as strong because the earth’s radius would have doubled while its mass remained the same. Newtonian theory says that gravitational force is proportional to the
square
of the distance between objects (in this case the center of the earth and falling objects at its surface). Doubling the radius without increasing the mass causes a fourfold reduction of gravity.

Some of the more direct ways of measuring this change in gravitational pull would fail. It wouldn’t do to measure the weights of objects in a balance. The balance can only compare the lessened gravitational pull on objects against the equally lessened pull on standard pound or kilogram weights. Schlesinger argued, however, that the weakened gravity could be measured by the height of the mercury column in old-fashioned barometers. The height of the mercury depends on three factors: the air pressure, the density of mercury, and the strength of gravity. Under normal circumstances, only air pressure changes very much.

The air pressure would be eight times less after the doubling, for all volumes would be increased 2
³
times, or eightfold. (You wouldn’t get the bends, though, because your blood pressure would also be eight times less.) The density of mercury would also be eight times less; these two effects would cancel out, leaving the weakened gravity as the measurable change. Since gravity is four times weaker, the mercury should rise four times higher—which will be measured as
two
times higher with the doubled yardsticks. That, then, is a measurable difference.

Schlesinger applied the doubling to some other standard physical laws and further claimed:

You can quibble with some of Schlesinger’s work. Schlesinger uses a pendulum clock as the unit of time. This clock is much slower because gravity is weaker and the length of the pendulum is doubled. Other types of clocks would not share this slowing. You can argue on the basis of Hooke’s law (which governs the resistance of springs) that an ordinary watch with a mainspring would run at exactly the same rate after the doubling.

There is also the question of whether the usual conservation laws apply during the expansion. Schlesinger supposes that the angular momentum of the earth must remain constant (as it normally would in any possible interaction), even during the doubling. If the earth’s angular momentum is to remain constant, then the rotation of the earth must slow.

There would be other consequences of conservation laws. The universe is mostly hydrogen, which is an electron orbiting a proton. There is electrical attraction between the two particles. To double the size of all atoms is to move all the electrons “uphill,” twice as far away from the protons. This would require a stupendous output of energy. If the law of conservation of mass-energy holds during the doubling, this energy has to come from somewhere. Most plausibly, it would come from a universal lowering of the temperature. Everything would get colder, which would be another consequence of the doubling.

The thrust of Schlesinger’s argument is this: Suppose we got up one morning and found that every mercury barometer in the world had shattered. Investigating further, we find that mercury now rises to about 60 inches rather than 30. (The barometers shattered because no one made the glass columns that long.) Pendulum clocks and spring-wound clocks now keep different time. The velocity of light, when measured by a pendulum clock, is 41.4 percent greater. The length of the year has changed. There are thousands of changes; it is as if all the laws of physics went haywire.

Then someone suggests that what’s happened is that all lengths have doubled. This hypothesis accounts for all the observed changes, and makes many predictions about other changes. Upon
hearing of the nocturnal-doubling hypothesis, specialists in the most recondite subfields of physics can say, “Now wait a minute, so-and-so’s law, which talks about distances, would cause such and such to happen if it was true that all lengths have doubled.” Every time such a consequence is checked, it is found to be accurate. The doubling theory would quickly be confirmed and established as scientific fact. Not only that—it would bid fair to be a paradigm of confirmation. It is hard to imagine any theory that would have so many independently checkable consequences.

Now for the nub of the issue. Since there is a conceivable state of affairs in which we would be forced to conclude that all lengths have doubled, and since that state of affairs does not currently obtain, we are correct in saying that everything
didn’t
double last night.

Schlesinger’s point is well taken. It delimits rather than demolishes the intent of the original thought experiment. There are really two conceivable versions of Poincaré’s thought experiment. You may find it helpful to think about it this way:

Imagine that the laws of physics are implemented by a demon who runs around the universe making sure that everything squares with said laws. The demon works like a cop on the beat, going from place to place and making sure that laws are observed.

The instant after the doubling, the demon is making a routine check of Newton’s law of universal gravitation. This law says that the force
(F)
between any two objects equals the gravitational constant
(G)
times the product of their masses
(m
₁
and m
₂
), divided by the distance between them
(r)
squared:

The demon is making sure that the earth and the moon obey this law. He measures the mass of the earth, the mass of the moon, and the distance between them. He looks up the value of the gravitational constant in his handbook. He punches these numbers into his calculator and gets the correct value for the gravitational force between the earth and the moon. Then he turns a dial on a control panel and sets the momentary strength of the gravitational force between the earth and the moon.

The question is: How does the demon measure distances? Does he just “know” them, and thus is magically aware of the doubling? Or is he in the same boat with us, and has to measure distances by comparing them with other distances?

If the demon knows about the doubling (“if the laws of physics recognize the doubling”), then we have Schlesinger’s version of the thought experiment. That kind of doubling would be detectable, and since we have not detected it, we are justified in saying that a nocturnal doubling
visible to the laws of physics
has not occurred. If, on the other hand, the expansion is invisible even to natural laws, then there is no way of detecting the expansion. I think there is no question but that Poincaré would say he meant a doubling that was invisible to the laws of physics.

For the record, universal changes are not the sole province of philosophers. Physicist Robert Dicke has proposed a theory of gravity in which the gravitational constant changes slowly with time. It is clear from Poincaré’s example that any useful hypothesis must have measurable consequences. Dicke’s theory does. The gravitational constant measures the universal strength of gravity. If it doubled one night, you’d know it. The bathroom scales would tell you you weighed twice as much the next morning. Birds would have trouble flying; yo-yo’s wouldn’t work; in a myriad ways, the world would be a very different place. In fact, it’s doubtful anyone could survive a doubling of the gravitational constant. The intensified gravity would compress the earth in a series of unfathomable earthquakes and tidal waves. The sun would shrink too, and burn hotter, searing the earth.

Dicke’s theory suggests that the gravitational constant is decreasing, not increasing. A halving of the gravitational constant would have the opposite effects but probably would be as deadly: you’d weigh less; birds would soar higher than ever before; the sun would cool off as it bloated, and we’d freeze to death. Of course, in Dicke’s theory the decrease is imperceptibly slow: maybe as much as a 1 percent decrease in a billion years. Even that slight change might be detectable in highly precise measurements of planetary motion and perhaps in geophysical effects. Attempts to find evidence of a change in the gravitational constant have so far failed.

Poincaré’s thought experiment, which helped pave the way for the acceptance of Einstein’s relativity, illustrates one of the most
palatable forms of antirealism. Many variations on Poincaré’s fantasy are possible. Obviously, a nocturnal shrinking of the universe would be equally undetectable. Would there be any way of telling if:

Most would say that all these scenarios would be equally undetectable and meaningless. The last two questions in the list deserve comment.

You could never know it if time stopped. You
can
know that it didn’t stop last night or three seconds ago when you read the word “NOW!” (I speak of time stopping “forever,” and not just stopping for a “while” and then starting back up again. A temporary suspension of time would be undetectable.) Whether this very moment is the moment in which time stops is something you cannot know until after the fact.

If you are sure that time is
not
running backward, ask yourself how you know this. You probably cite your memories of the past. It is now 1988. You have memories of experiences in 1987, 1986, 1985, etc.; you do not have memories of 1989, 1990, etc. But you would, for the moment, have the memories you do whether time was going forward or backward from 1988. The question is whether the moving finger of time adds to or deletes from this stock of memories. There is no way of telling!

The best-known thought experiment about time was devised by Bertrand Russell in 1921 (or was it?). Suppose that the world was created five minutes ago. All memories and other traces of “prior” events were likewise created five minutes ago as a private joke on
the Creator’s part. How do you prove otherwise? You can’t, Russell insisted.