So that is our time relation equation and

it going to shows the moving clock runs slow.

Now it have to be precise about this.

In fact awhile back, I got an inquiry from a television game show

about a question they wanted to ask their contestants.

Or they were thinking about asking their contestants, and, essentially,

without going into all the details.

They wanted a question along the lines of,

if you could travel near the speed of light Would time slow down?

Or time would slow down.

Would it slow down or speed up or go to infinity or go to zero?

There are a number of different choices.

The answer they thought was correct was time would slow down, okay.

And you can look at our elapsed time equation and

the moving clock time slows down.

Yeah, that makes sense.

Think about it carefully however.

Because this is Bob observing the moving clock.

Alice, sitting on her spaceship say as she's traveling along there

at some high velocity v, her clock is just running normally.

She does not perceive any difference in time at all.

For her, time does not slow down, so that's often when we say things like that,

if you could travel near the speed of light,

the special theory of relativity says, Einstein says that time would slow down.

Not for the person who's actually traveling at that speed, it's the person

outside Observing the clock that's moving past that sees time slowing down.

And does to some things that we'll talk about a little later on in the course

especially, the so called twin paradox of two people actually age differently and

so on and so forth.

But, we're not there yet but, that would be coming up in a In a few weeks here.

So time dilation equations.

Delta t, elapsed time on a moving clock, from an observer watching it go by,

is one over gamma delta t on a clock at rest next to them, okay.

So again, time dilation, we could write it in different form,

we could say delta t rest equals gamma delta t moving.

But usually it's best to pick one form,

this is the form that I think shows the time dilation affect most effectively.

Because the gamma is always greater than or equal to one, so this will

be a fraction like one third, if we did a guess of three or something like that.

So the moving clock left time less than the rest time on identical rest clock.

Okay, so that's time dilation and again just to

emphasize this does not mean time slows down for the person on their spaceship.

Alice in this case it means the person deserving them sees their clock

running more slowly than the identical clock that they have next to them.

And of course, you can actually reverse analysis and have Alice look at Bob,

and to Alice, Bob is moving away from her.

She will also see her clock running normally and

Bob's clock ticking more slowly.

And that's where you get into some of these paradoxes in terms of the twin

paradox, which we'll consider later on, figure out how that works.

One more thing to do here though for time dilation, and that is might say,

well this is all very nice and I sort of see where it comes from.

But these light clocks they're a little weird, they're strange.

How do we know regular clocks work like that?

Maybe this is just a special case with these light clocks.

And this could also go back to one, further point where these all coming from.

Remember, it's because Einstein's Led to the fact

that the speed of light is the same for all observers no matter how you're moving.

And therefore, for Bob here with his clock at rest,

he just sees the speed of light going up and down at c.

He sees the light on Alice's clock go taking a diagonal path, also at c.

It's clearly a longer path, therefore it takes longer to get up and down.

And our three snapshots here,

remember these are the snapshots, one, two, and three as we watched the light.

As Bob watches Alice's light go up and down.

Therefore, it ticks more slowly.

But, is this just a special case.

Well, let's consider that a minute and earlier in one of the videos.

I promised that we would make a little argument here to say no,

if a light clock acts like this.

All clocks must act like this If the special, if,

not the special theory of relativity.

It's true, but if the principle of relativity is true.

So let's consider that here.