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.
Demons and Doubling
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
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.
Demons and Doubling
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
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