Page 151 - The Perpetrations of Captain Kaga

Breaking the Grapefruit Connection
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“I can’t tell you the name of the planet we’re on, but I expect this
building belongs to the Freight Group, whatever that is. I can also tell
you what time it is back on Radnelac III if my watch isn’t broken. We
haven’t lost any time, you see.”
“What?”
“Our friend Pamplemousse has discovered a very interesting
means of transportation. Fortunately I was able to figure it out, too,
and construct a device for sending myself here. I would have brought
you back instead of sending myself if I’d been certain it would work,
but if it hadn’t you might be in a worse situation now.”
“If that is possible,” said Lugo bitterly.
“Anyway, apart from your personal predicament, we may an
opportunity to test a well-known cosmological hypothesis.”
“Really!” said Lugo indignantly. “This is hardly the time or place
to—”
“But it is! This time and place, or specific point in spacetime,
could be located somewhere very interesting. Do you remember
anything about the geometry of spacetime from those elementary
relativity physics courses we took at the PKU Academy years and
years ago? I didn’t think so. I’ll make a drawing for you. Look: any
finite path through spacetime (a person’s life, for instance) can
represented as a line segment on a Minkowski diagram. The three
dimensions of space are compressed into one, the horizontal axis; the
fourth dimension, time, is represented by the vertical axis. It makes it
tidy if we scale equal sections of one second and 186,000 miles on the
time and space axes, respectively.”
“Why?” asked Lugo.
“Well, that way light, or electromagnetic radiation, which always
travels at 186,000 miles per second, can be drawn as a path through
spacetime at forty-five degrees to the axes. Now, since the speed of
light is the maximum velocity possible, we can use it to cut spacetime
into three areas relative to any point in it. There. Now you will be able
to see the limitation on access to spacetime for any given path. This
lower area is the possible past for the point: light waves converging
upon it circumscribe its origins. The upper area likewise defines the
future accessible to a given present point; it cannot take any path
beyond the spacetime bounded by light waves emanating from it.”

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