What Do You Mean, Time Slows Down? 61
minagi observes light in
his clock move directly
upwards and downwards,
but minagi observes the
light in my clock procd
at a longer path, at an
angle.
Let's consider
this using the
Pythagorean
Theorem.
Pythagorean
Theorem
The Pythagorean Theorem
states that "the square
of the length of the
hypotenuse is equal to the
sum of the squares of the
other two sides"...that is...
It's the theorem that
says for this right
triangle ABC, the
relationship c
2
= a
2
+ b
2
holds, right?
RELATIVITY_03.indb 61 3/15/2011 3:26:38 PM
62 Chapter 2
If we aly the Pythagorean
Theorem to the observations
of the light clocks, we find
that the light moving along the
hypoteneuse travels a longer
distance than the height of the
light clock, right?
Yeah, that's
right!
If we consider the principle that
the spd of light is constant
here, which states that "the spd
of light is constant regardle
of who is making
the observation,"
Light is emied
simultaneously!
Even when Minagi observes the
light clock on the space station
and determines that 1
ns has
elapsed, the light sti wi not
have reached the top in the light
clock on the rocket.
Huh?
The light sti
hasn't reached
the top for the
light clock on
the rocket?!
Ping!
We can iustrate
it like this.
does this
reay work?!
Distance
rocket's light
traveled
After 1
ns
Distance space
station's light
traveled
Sti
has not
aived
Even though
it has already
reached it here!
Distance Mi Uraga traveled
RELATIVITY_03.indb 62 3/15/2011 3:26:39 PM
What Do You Mean, Time Slows Down? 63
when the light in the
rocket's clock is observed
by minagi to have returned
to the boom, more than
2ns wi have elapsed on
minagi'sclock.
In other words, time
advances slower
for the rocket I'm
riding on.
Although this sti
sounds strange,
it's what actuay
haens.
When a 3:4:5 right
triangle is used
as an example
Time elapsed (and light
movement) observed from
Minagi on the space station
Light on the
space station
(observed by
Minagi)
The path of
light inside
the rocket,
as observed
by the space
station
The path of light inside the
space station, as observed
by the space station
Light on the rocket
(observed by Minagi)
RELATIVITY_03.indb 63 3/15/2011 3:26:41 PM

Get The Manga Guide to Relativity now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.