Thought Experiment: Standard Meter

    Extraterrestrials from a far distant planet visit Earth. They are given a standard length to take back to their home. After examination, they claim the length is the distance light travels in a vacuum in 1/120,000,000 drekts with time measured by a cesium-133 atomic clock. They say it is 1 standard retkt long. A retkt is associated with a rational number. They had to leave in a hurry so they weren’t given the complete story.
    Meanwhile on Earth the setup was this:
The legs of a right triangle are both 1 standard meter long. 1 stand meter is the distance light travels in a vacuum in 1/299,792,458 seconds with time measured by a cesium-133 atomic clock. The Extraterrestrials in their rush to attend to urgent business, escaped planet Earth with a sample length derived from the hypotenuse. They assumed the length given was an isolated straight line used as a standard measurement unit like the retkt.

On Earth the length of the hypotenuse is √2 meters which can not be calculated exactly. If you could count the number of wavelengths then it would not be an irrational number.

The E.T.’s have shown that the hypotenuse that they unknowingly measured by mistake is given by a rational number. They are able to calculate its distance.

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