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And see where that leads us in terms of what it tells us about how one

person may observe time passing versus another person observing time passing.

So here is the idea of a light clock.

Let's look at, we've got two clocks here, Alice and Bob.

Both identical and let's see what the idea here is of this light clock.

So two mirrors set up and,

we won't go into all the details of how we might actually implement this.

But the basic idea is we have a light beam that travels up.

We insert that, it hits the top mirror, travels back down again.

And obviously then would keep back and forth between the various mirrors.

And we'll say of this light clock, this apparatus,

that one tick of the clock represents one round trip of the light beam.

So, it goes up, bounces off the upper mirror, comes back down,

and when it hits over here, a tick.

So, it's just tick tick or tick tock,

if you wanted to do the tick tock noise there.

So, that's the idea of a light clock, essentially just a light beam bouncing

back and forth Between two mirrors it'll be traveling at speed c, of course.

And if the mirrors are far apart, close together, doesn't really matter.

We just assume we have the necessary technology to actually record the ticks

as the light beam bounces up and down.

And Bob's clock, the same thing.

So it has a light beam going up Same light beam bounces back down to speed C.

This distance between the mirrors is exactly the same.

We know what that is in theory, or

in terms of just the principle of the light clock.

And therefore,

we can find out more details about it as we go along here as we shall see.

So that's the basic idea of the light clock.

Now what we want to do is set Alice's clock into motion, so

we'll put it on her spaceship.

She'll then be traveling at some velocity v.

Bob will be observing in this case.

And so, this is our second situation in here.

Here's Bob's clock, as Bob sees it.

Again, no difference from over here, he's going to see the light Travel

up and down at speed c, so he's not seeing any difference.

But now, let's think about how Bob sees Alice's clock in motion.

And three step process here, so, say at time t equals zero,

when the light beam is just leaving the bottom here of Alice versus

a little bit later on, the top mirror is going to be over here, to the right.

On other words clearly the light clock is moving this way,

to the right, as the light bean leaves here.

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The top mirror is not going to be here anymore,

is actually going to travel to the right and hit the mirror there, because that is

where the position of the mirror on that point as Bob is observing it.

And then the bottom mirror will be here by the time it gets back down again.

Long story short is the path of the light beam as Bob observes is because

we know it has to hit the top mirror and takes awhile to get up there.

If it missed the top mirror, then we'd have two different situations here and

something would be wrong.

We'd have a contradiction so we know it Alice was observing her clock like this.

As far as she's concerned, she's not in motion.

So she just sees the light beam bounding up and down like this.

We know it hits the top mirror.

Therefore, Bob also has to observe it hitting the top mirror.

Otherwise, there'd be a contradiction, you can't have hitting the top mirror for

Alice and not hitting the top mirror for Bob.

And so therefore we know that, since the top mirror is now over here

a certain time later because Alice is moving with velocity v,

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So qualitatively can you see what's going on here?

We know that and here's the key point, just like we saw

When we are looking at the relativity of simultaneity and synchronized clocks.

The key point was that the speed of light always travels at speed C.

It doesn't have speed subtracted or added to it,

no matter what kind of motion is going on.

So in this case, Bob see the light beam, Alice's light beam,

travel diagonally up and then diagonally down.

But he also sees it traveling at speed C.

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Light always travels at speed C for

any observer not matter what direction you're going.

And therefore, just right off the bar we can say that that's a longer path for

Alice is light beam to get from here up to there and down again.

And then, the tick occur that's a longer path at the same speed

as compared to Bob's clock here, his light is just going up and down, up and down.

Alice's takes longer to get there and longer to get back down again.

What we are seeing here is that from Bob's perspective is

that Alice's clock is running more slowly than his clock.

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And this goes by a famous thing, we are going to investigate this more obviously

as I just mention, just to give you the name of this effect that you may

have heard about time dilation.

And another way to say this is moving clocks

run slow compared to an identical clock that is not moving.

So again, we have Bob's clock and Alice's clock.

Identical clocks When they're at rest they're synchronized so

they run just fine.

But Alice's clock in motion though and Bob's clock here ticks away nicely.

Alice's clock from Bob's perspective is ticking more slowly than his now.

Her moving clock runs slow compared to his clock.

That's known as time dilation.

Now there is a flip side of it as well, you could say well, but

from Alice's perspective Bob's clock is running slow.

Right? Because from Alice's perspective,

she is stationary, it is Bob who is moving this way and

she could do this exact same analysis that we just did.

For her clock from Bob's perspective, she could do the same from her perspective on

Bob's clock, and she would conclude that his clock runs slow.

So this is one of the paradoxes when you say, well, wait a minute.

How can they both conclude the same thing?

There seemed to be a contradiction there.

Yet as we investigate this more, we have to hold that contradiction intention,

that seeming contradiction because actually.

It really goes back to the whole idea of you can't define an absolute time

[INAUDIBLE] as relative, clock synchronization is relative as well.

To give you a very rough analogy because to try to get our minds around a little

bit, think about everyday experience if I see somebody far away.

They look shorter than they actually or

if they're standing right next to me, if they're the same height as I am.

They travel 100 meters away something like that, they look short, okay.

I could measure them in some perspective, they look about 6 inches high or

something like that and yet they observing me,

my friend observing me Which see me as short.

You say, well, that's not a contraction.

Of course, it's just how perspective works a little bit of the same idea here.

It's actually not a contradiction.

It's just how the perspective works in terms of Alice observing a clock,

Bob's clock, and Bob observing Alice's clock.

So again not an exact analogy, but

in common every day life are common sense perspectives.

We understand, the idea of perspective,

something farther where it's going to look shorter.

because we're just used to it, we see it all the time.

This we don't see in real life because we're

usually not going that fast enough to see a difference between two clocks,

because the actual fact, this light beam going up and down.

By the time we got to position three,

the light beam in terms of getting up and down.

It would not have move very far, this tiny fraction of the medium and

send in the [INAUDIBLE] for the meter is what would going to happen.

By the way something will probably mention later as well.

Speed of light, may have already mentioned it.

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Recall from last week about waves.

But when we talk about the speed of light, easy way to remember or

one easy to remember it is it's about one foot per nanosecond.

If a foot being one third of a meter, roughly one third of a meter,

one third of a yard.

So one foot per nanosecond.

One foot per billionth of a second.

So, if our meters here are one foot apart, it

takes one billionth of a second to go up and one billionth of a second to go down.

About two billionths of a second And so, Alice's clock

even if it was moving very fast from our perspective, maybe even supersonic speed.

The time it took to take the light beam to go up and back down again the mirror

would have actually move slightly but not so much that we would really notice it.

So that's why we don't notice these effects

In our normal every day experience.

Okay, so that's introduction to the light clock and the idea.

This is a qualitative analysis of it now.

In our next video click we'll go do a quantitative analysis of it.

But again, the idea is that two identical clocks, they both took

the same way and you put one in motion and Bob's observation of Alice's clock.

In this case he's going to say, hey Alice, your clock is running slow now.

And she'd say the same thing about his clock as well.

Now, I can guess some of you are probably thinking now this light clock thing and

this idea of time dilation, this is a very special clock Right?

Real clocks probably don't work that way.

Well, later on, we'll have an argument showing that if a light clock works

this way, then any clock has to work this way.

Otherwise, we'll get a violation in the principle of relativity.

So, if the principle of relativity is true we'll see that give this behaviour of this

somehow special light clock setup then any clock no matter whether it's watches.