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\f0\fs28 \cf0 Imagine learning for the first eighteen years of your life that the earth
is flat. All through elementary school and high school you grow up hearing about the
flat earth we live on and doing boring flat-earth physics homework and then (if you're lucky
enough) you get to college and PSYCH! \f1 for the first time they show you a globe
and say "sorry for lying, the earth is actually round".\
\ Well, this is, unfortunately, exactly what
we do with\ \
1) Gravity\ You probably learned that objects attract
each other based on their mass so you probably grew up thinking that light can't possibly
be affected by gravity because light is massless. I know I did. Well guess what? The source
of gravity is not mass - it's energy and momentum, which light certainly has (of course, regular
matter does too). So not only does light get bent passing by a star or planet or black
hole, but light attracts the planet or star or black hole in return (to be sure, it's
only a very very small amount. But a small amount is not zero). Anyway, the point is
that Newton's law of gravitation is just an approximation - good enough to get us to the
moon, but not perfect. General relativity is better.\
\ 2) Special Relativity\
Speaking of the moon, you probably also learned that if a sheep is moving 2 mph relative to
a train and that train is moving 2 mph in the same direction relative to the ground,
then the sheep is moving four mph relative to the ground. 2mph+2mph=4mph, right? FALSE.
Experiments in special relativity have confirmed that velocities don't simply add together
and so the sheep will in fact be moving very very ever-so-slightly slower than four mph
relative to the ground. And the formula that correctly predicts this deviation from just
adding the velocities is (v1+v2)/(1+v1*v2/c^2). It's not a very big effect, but then again,
the earth looks pretty flat, doesn't it?\ \
But the earth isn't flat: if I walk 10,000km away from my cat, and you continue on walking
10,000km more, you're NOT 20,000km away from my cat. You're just 12,750km away\'85 in fact,
the farthest on earth you can get from ANYTHING on earth is 12,750km. It's the "earthly distance-limit",
though we normally call it the diameter of the earth. And similarly, when you try to
add two velocities together, there's a "cosmic speed limit" of 300,000,000m/s - that is,
the speed of light.\ \
So, just because to our eyes the earth looks flat, velocities look like they simply add
together, and light looks like it doesn't attract gravitationally, is that an excuse
to mislead ourselves and our children about the true nature of things?\}