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 procd

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 aly 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 spd of light is constant

here, which states that "the spd

of light is constant regardle

of who is making

the observation,"

Light is emied

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 iustrate

it like this.

does this

reay work?!

Distance

rocket's light

traveled

After 1

ns

Distance space

station's light

traveled

Sti

has not

aived

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 boom, more than

2ns wi have elapsed on

minagi'sclock.

In other words, time

advances slower

for the rocket I'm

riding on.

Although this sti

sounds strange,

it's what actuay

haens.

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

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