In this course we will seek to “understand Einstein,” especially focusing on the special theory of relativity that Albert Einstein, as a twenty-six year old patent clerk, introduced in his “miracle year” of 1905. Our goal will be to go behind the myth-making and beyond the popularized presentations of relativity in order to gain a deeper understanding of both Einstein the person and the concepts, predictions, and strange paradoxes of his theory. Some of the questions we will address include: How did Einstein come up with his ideas? What was the nature of his genius? What is the meaning of relativity? What’s “special” about the special theory of relativity? Why did the theory initially seem to be dead on arrival? What does it mean to say that time is the “fourth dimension”? Can time actually run more slowly for one person than another, and the size of things change depending on their velocity? Is time travel possible, and if so, how? Why can’t things travel faster than the speed of light? Is it possible to travel to the center of the galaxy and return in one lifetime? Is there any evidence that definitively confirms the theory, or is it mainly speculation? Why didn’t Einstein win the Nobel Prize for the theory of relativity? About the instructor: Dr. Larry Lagerstrom is the Director of Academic Programs at Stanford University’s Center for Professional Development, which offers graduate certificates in subjects such as artificial intelligence, cyber security, data mining, nanotechnology, innovation, and management science. He holds degrees in physics, mathematics, and the history of science, has published a book and a TED Ed video on "Young Einstein: From the Doxerl Affair to the Miracle Year," and has had over 30,000 students worldwide enroll in his online course on the special theory of relativity (this course!).
Events, clocks, and observers (part 2)
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来自 Stanford University 的课程
Understanding Einstein: The Special Theory of Relativity
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从本节课中
Events, Clocks, and Reference Frames
Week 2: Events, Clocks, and Reference Frames
与讲师见面
Larry Randles LagerstromAcademic Director
All right, we ended the last video clip which was on part 1 of events,
clocks and observers, we are talking about lattice or
grid of clocks that we're going to use to specify when something happens.
Actually, not only when but where, so we'll have clock at
every location in space, say three dimensions.
And then, using a photo device, whenever an event occurs
at that location, photo will be taken that records not only the location of the event
in xyz coordinates, but also the time on the clock at that location.
But it raises the question of how do we synchronize the clocks?
How do we make sure they're synchronized?
And so that's what we're going to work on in this part, this video clip.
We've reduced it just to one dimension now, as I mentioned last time.
We did three dimensions last time just to get the general concept.
From now on we'll be working in one dimension.
So we just have the x axis here.
So anything that occurs can only occur along the x axis,
along this line any event that occurs in a flash of light.
And so here is an example of a lattice or a grid of clocks in or
along the x axis, so that each point along the x axis I have a clock.
Clearly if I want to specify like halves and tenths and things like that,
I just imagine I have them a clock at every given tick mark say on our x axis.
Here's the origin, here is the observer.
We'll just imagine it's us standing there.
We're going to be observing things and so here's our grid of clocks.
I also mentioned in the last video clip that,
there are two different ways of doing this and
actually we didn't quite get to those two different ways in the last video clip, and
in this video clip we will talk about those two different ways, so
if you're wondering what happened to that, this is what's coming up here.
So, challenge is how to synchronize those clocks.
Here we are, we're the observer, we have a whole bunch of clocks and
we need to get them at each point along our x-axis.
And we need to make sure they're synchronized.
So first we'll assume we have a master clock.
And by the way, hopefully you did the thought experiment, sort of
priming the brain experiment it terms of thinking about how you might do this.
Because actually you might think again this seems sort of trivial.
This is one of the fundamental insights of Einstein that led him to the special
theory of relativity that there were challenges with synchronizing clock and
that wasn't quite as obvious and straightforward as one might seem.
And in fact, this is a case where
this was not just some esoteric thought experiment Einstein was doing.
These were problems that came out of the electro-technological context of the day.
That it was very important as railroads expanded,
as railroad expanded, you need to have good time keeping systems.
So that every city had more or less the same time.
And you had to make sure your clocks were synchronized between various stations,
and so on and so forth.
And there were a lot of patents and inventions,
I should say a lot of inventions that then people submitted patents for
at places like the Swiss patent office where Einstein was working.
So he clearly was getting a lot of this.
Not only just from sort of thinking about esoteric abstract matters of how do you
synchronize clocks, but from the technology of the day it was a key
issue that people were trying to solve in various ways.
So the whole idea of how do we synchronize these clocks?
One way perhaps could be we'll have a master clock, say here, that the observer
has and the observer will bring all the clocks together in one place and
set them according to the master clock.
So everything is running just fine, they're all identical clocks and
then move them out along the x-axis at that point.
And so that when something occurs,
a flash of light occurs over here and it records it in a photograph,
then the observer can be confident that it was the correct time and
this clock is synchronized to the master clock here at the origin.
What Einstein came to realize, though, and again, later on in the course we'll
get into few more details of this, is that when you actually move a clock,
you can't be guaranteed it remains in sync with the original clock.
And so, even though that method seems like it should work just fine, bring them all
together to one master clock, they're all identical, they're all running properly.
Synchronize them all and then move them out along to wherever they need to be.
In actual fact, it has some potential problems with that where things will get
unsynchronized as soon as you start moving them.
Now what you could say is that We will move them as slowly as we want such
that if there is any unsynchronization, desynchronization that occurs.
It's going to be small enough that we won't care about it.
So there are ways to get around this, but we're going to use a different method.
So this is the first method that In principle, could work,
if you're really careful about it, but we're going to use a different method.
And this method is, I guess we're going to use a different method in principle here,
this method is put all the clocks out there, but we won't have them running yet.
Okay, we'll just have our master clock here, put all the clocks along, and
the idea is that at time t = 0,
we'll have a light pulse be sent along in both directions.
So we'll just say, we'll use orange here for a light pulse again,
so, We used green last time, so we use orange this time.
So here's the light pulse
sent out from the master clock position at t = 0.
And then as the light pulse goes along my line of clocks here,
when a given clock receives that light pulse or when the light pulse goes by and
that given clock, it's triggered by the light pulse, it will start running.
But then you say, well, if this starts at zero and sends a light pulse out and
then this one starts running when it receives the light pulse,
it's going to be behind this clock clearly.
So we're going to get around that.
We're going to say okay, if this clock here is four units away,
whatever units we happen to be using, miles, kilometers, meters, Whatever.
We know how long it takes light to get there so we'll say okay clock number
four here, clock at position four, we're going to set it ahead just
the amount of time we know that the light pulse takes to get from zero to four.
Now let's just imagine it's three seconds, okay.
So it's pretty far away here obviously at the speed of light.
But we'll say, okay, we know that the light pulse,
we know what this distance is, we know how fast the light will travel, and
we know that it will take three seconds to get to that position there.
And so we will set this clock three seconds ahead.
So that the light pulse goes off here is zero, t = 0.
It's going along here.
When it reaches this clock, three seconds have elapsed.
And if we set this clock three seconds ahead, it's not running at this point.
When the light pulse reaches it, it will trigger the clock to run and
it will start running at three seconds.
And then maybe this clock here is up here,
let's see if that's it'd actually be eight here, six seconds ahead.
So when the light pulse reached here it would have taken six seconds from
the origin to get there from our master clock.
And therefore, it would be set six seconds ahead.
And when the light pulse reached it, it would trigger it and start running.
And then everything,
assuming we did that with all the clocks, everything will be synchronized.
You don't have to worry about any problems with moving the clocks around,
all we have to note is what the speed of light is and
then how far away each clock is from my master clock.
So that's the idea of how we could synchronize our clocks in theory.
Obviously, we're just doing all this as thought experiments.
But that's a method we can use to make sure all our clocks are synchronized.
And so that for the observer here, once they have their lattice of clocks,
they can be assured that in the event that occurs, we'll use green this time.
So say some event occurs right here.
Flash of green light and so we know the position along the x-axis is that x = 7.
The clock will record the time of the flash and
then the observer later on can go out and look at that clock and
say okay, look at the photograph there and say it was,
the flash was recorded at x = 7 at t = 3.8 seconds or something like that.
And, so again, that's the idea of events, clocks and observers, and
how they all fit together.
And what it means to make an observation.
So from now on, when we say, somebody observes something,
observed an event to occur, what we mean is, if we're using just the x axis here,
it's the x location of it and
the time recorded on that photo that is taken at that instant in time.
So again, the photo clock principle, or
the clock principle, is what we're basing this on.
And we're assuming we can synchronize all the clocks by sending out the pulse of
light, as long as in advance of that we have set each clock ahead just the proper
amount so when the pulse of light reaches it and
it starts running then they're all synchronized with each other that way.
Okay, so events, clocks and observers and
in the next video clip, what we're going to do is look at a different
way to visualize how events occur and
something called space time diagrams which we'll find will be very useful for
visualizing some of the concepts in the special theory of relativity.
