Has the sun gone under the horizon?

"What a beautiful sun set!"
"It's as if prepared for us, isn't it?"
Alice and Bob came in Sounion during their honeymoon. Sounion, 70 km west from Athens, is said to be one of the best places to watch the setting sun in the world. They were staring the sun set with a dreamy eye over the Aegean Sea under the Greek remains. The golden sun is just landing on the water. The lapping of waves merely seems to dramatize their sweet time.

"Actually, however, the sun is already below the horizon. The sun we are watching is the one 8 minutes and 19 seconds ago."
Stupid Bob! It is not necessary to say such a scientific thing in the middle of honeymoon. But, it is true that the distance between the sun and the earth is 150 million km, which takes 8 minutes and 19 seconds for light to travel, and the optic angle change of the sun just corresponds to its diameter during that period. Bob's saying seems to be correct...?

"No! The sun has not gone under the sea!" shouted Alice.
Did Bob's thoughtless words completely upset her?

It seems not. She continued.
"You are right if the sun is moving around the earth. But actually the sun is staying, and it looks as if the sun is moving because we are on the rotating earth. Therefore, the direction of the sun is nothing but the direction we are watching, although the light we are watching was emitted 8 minutes and 19 seconds before."

This is easily understood by the following figure.





"The correct is the Copernican theory. The Ptolemaic theory is completely wrong," said Alice.
"Oh yeah. You are right."
Bob admitted his defeat. He felt a little bit ashamed that he has not completely swept the Ptolemaic theory away.

After a while, however, he said,
"Isn't it a little bit overstating that the Ptolemaic theory is completely wrong?"
"What?"
"You can describe everything choosing a coordinate system in which the earth is not moving or even rotating. Of course, in that case, the system will not be an inertial reference frame. You need to take centrifugal force, Coriolis force, and other things into account. But still you can."

A short seconds of silence passed.

"OK, but it is not a natural way of description. There is no reason to choose such a complicated coordinate. The truth should be simple, isn't it?"

A careful conversation continued.

"Not desirable, I agree. But it is not wrong in the sense that the theory can predict everything correctly."

"Oh, wait a minute. I remember similar arguments in quantum mechanics. There are several interpretations such as Copenhagen, Everett, and Bohm interpretations. They are equivalent in the sense that any of them predicts things correctly. Which is close to the truth depends on the taste of physicists..."

I plan to refer to this QM issue in another essay some time. Anyway, it seems that Alice and Bob really like technical discussions, which seem to have made their honeymoon more blessed and worthwhile one.

[Written in Japanese on 10, May 1998, translated in English on 6, Jan. 2010]


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