Okay, according to her clocks,

it's going to be 1.77 years because he's got his clock right there.

It's ticking away nicely.

When the star reaches him, yes, they take the photograph it's at 1.77 years.

But the clock's at 5.3 years, but we're not going to worry about that for

the moment.

She thinks it's correct, he has other ideas about that.

But what is the elapsed time from Earth to the star, or

really the star getting to Bob here that Bob sees on Alice's clocks?

And it's 1.77 because that's the time on his clock.

So it's 1.77 years divided by the gamma factor.

It's always 1/gamma here in this case, when we're going in that direction.

So that's divided by gamma which is 3.

And the answer you get if you do that is, I think,

0.59 years.

And now you really go right?

How can this make sense?

Now we can sort of see yeah, okay I get time dilation.

Alice will observe Bob's clocks running more slowly and so

instead of 5.3 years gets 1.77 years.

And sort of get Bob over here, the rocket observer.

The distance is contracted, right, and therefore shorter distance.

And therefore his clock will run for 1.77 years, okay, that.

But then Bob looking at Alice's clocks running slowly,

just as Alice sees Bob's clocks running slowly.

Bob is seeing Alice's clocks running slowly by the factor of gamma.

You get his elapsed time divided by gamma is 0.59 years.

How in the world, you've got 5.3 years,

isn't that the elapsed time on Alice's clocks?

That's the elapsed time she's getting.

How is Bob getting a value of 0.59 years for the elapsed time on Alice's clocks?

And to understand this quantitatively,

we're going to have to do some work this week.

We're going to develop something called the Lorentz transformation because that's

going to help us understand this, among many other things.

It's useful for much more than just that.

So it's going to help us understand this but I'll give you a hint on it.

And that is when you think about the special theory of relativity,

you can't just focus on time dilation.

As we've seen here, time dilation and length contraction go together in

the analysis, often from different frames of reference.

In one case you're using time dilation.

From the other perspective it's length contraction that is the issue.

But there's a third thing here too, that we cannot forget.

And that is the relativity of simultaneity.

That clocks synchronized in one system frame of reference

are not synchronized in the other frame of reference, moving at a velocity v,

an inertial frame of reference.

And that is the key to understanding this.

And earlier on in the course,

qualitatively we talked about how leading clocks lag.

That if you have two clocks, they are a series of clocks moving past you at,

obviously, for this to really be observed it has to be a pretty high velocity.

But in principle, it's for any velocity.

As it's moving past you, if you're observing those clocks go by,

the clock in front is going to lag the clock behind.

The clock behind will be ahead of, time-wise, the clock in front.

And that is the key to understanding this discrepancy here.

And we want to be able to understand it quantitatively.

We want to be able to show that add the numbers together in some way and yes,

you actually do get the 5.3 years back in.

So to do that, we have some work to do this week.

But this is again, exploring time dilation and length contraction.

Originally, I thought I would do this in a couple a weeks,

when we talk about the twin paradox.

But I decided it was good to introduce it this week

to try to mull over a little bit how time dilation and length contraction works and

also the relativity of simultaneity.

So that's where we're heading over the next few video lectures,

to do the Lorentz contraction.

And then do leading clocks lag in a quantitative sense,

as well as looking at some aspects of velocity, and so on and so forth.