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!).
Ethereal solutions
Loading...
Do curso por Stanford University
Understanding Einstein: The Special Theory of Relativity
1035 ratings
Na lição
Ethereal Problems and Solutions
Week 3: Ethereal Problems and Solutions
Conheça os instrutores
Larry Randles LagerstromAcademic Director
So we have this puzzle or physicists had this puzzle in the 1890s,
what to do with something like the Michelson-Morley result, the null result.
That showed that emotion through the ether could not be
detected even though it should be detectable especially when you compare
to the results of things like stellar aberration.
Where it said clearly it either cannot be dragged.
Which was one possible solution that the Michelson-Morley experiment said.
We're not detecting the motion of the Earth,
through the ether as the earth revolves around the sun.
Maybe it's because the ether in the vicinity of the earth gets bright along
and therefore, we don't feel that ether wind or ether breeze as it were.
Our experiments do not detect it, yet
other results like stellar aberrations said, no the ether can't be right along
by the earth if you're going to get the correct result for things like that.
So it was real puzzle but there were some solutions that were proffered for it.
A British physicist, G F Fitzgerald, really just came up with an idea that,
in the Michelson-Morley experiment, you have light travelling one way,
sort of the headwind-tailwind with either wind supposedly.
And then are going perpendicular where either wind would be crosswind to it.
And there should be a time difference between them because
the headwind tailwind case should take a little bit longer than the crosswind case.
So what he hypothesized was he just had the sort of idea that we're
dealing the ether, the luminiferous ether,
clearly there's some electromagnetic effects perhaps going on.
Matter itself was thought to be composed of perhaps electrical particles
that the electron hadn't actually quite been discovered at this point.
But the idea was in the air that soon the electromagnetic
quantities could explain perhaps the very essence the constitution of matter.
So, if matter itself was electromagnetic in nature that the atoms involved and
so on and so forth.
Perhaps there was an effect as matter,
in this case the Michelson-Morley apparatus traveled through
the ether against it and then it got compressed a little bit.
Just that the very nature sort of drag a fact in the sense that
not they ether drag and we talked about before but
just the compression affect if it's going straight to the ether.
And going cross ways you wouldn't have that compression affect.
So one leg of the Michelson-Morley
apparatus would get compressed just slightly.
And the other leg wouldn't and it'd be just enough to make up that time
difference so that the light beam going this way with the headwind-tailwind case
would actually have slightly less distance to travel than you would expect,
compared to the crosswind case.
And that slight difference in the distance travel would make up for
the fact that it's actually a little bit slower.
So even though that, yes it is slower but the time
travel distance is the same because the distance gets compressed a little bit.
And this was actually became known as the Lorentz contraction because
Fitzgerald published it in the American Journal of Science.
He sent a letter off actually, it wasn't a full publication.
Sent a letter off to the American Journal of Science,
which was very new at the time and hardly anyone ever read.
He wasn't even sure it had been published, really he was on to other things.
A few years after this in the mid 1890s, Lorentz who we've mentioned before,
was developing a full-fledged theory and extending Maxwell's theory and
really puzzling over the Michelson-Morley result, and had a similar idea.
Then he mathematized it and introduced it into his theory.
He later found out that Fitzgerald had actually had this idea a few years before
and had sort of published it.
Lorentz being the kind of person he was gave credit to Fitzgerald and
therefor became known often as the Lorentz-Fitzgerald contraction.
So we're talking about the Lorentz Fitzgerald contraction.
And again the idea here is that if you have any material object going against
the ether.
Just traveling through the ether in a longitudinal direction and
the direction of travel here, it decompress slightly.
So if it's a spherical object, it becomes sort of slight a lip soy, not, so
actually you could really notice it unless you're doing very precise experiments,
that's exactly what Michelson-Morley was.
It's a very precise experiment and therefore the idea was that this effect
would show up in the Michelson-Morley experiment.
Shorten the distance slightly so
that even though the travel time should be longer that way.
The distance was shortened a bit and so the travel time
equals out whichever way you're going on the Michelson-Morley apparatus and
therefore you get this null effect.
You don't see any effect of the ether wind.
So that is, ether the wind is actually there but
we don't notice it because of this contraction effect.
That was the idea of the Lorentz-Fitzgerald contraction.
Henri Poincaré also took some of Lorentz's ideas 1895 and
falling over the next ten years and they both developed them.
Further, both of them also played with ideas that time itself might be elastic.
Sort of like length is a little bit elastic here it can change a little bit.
The physical length of something.
If it's moving against the ether can change.
They have the idea that maybe time is involved as well because to make things
work out in the full context of the theory.
If length is changing a little bit, then there seem to be some need for
time to change.
Now the ideas they have are more mathematical constructs within the theory.
They weren't necessarily saying these are actual physical changes in time.
Time they would say is absolute, it still goes along for everybody the same way.
But there were hints of perhaps a change in how we view time,
and that maybe time was not as absolute as everybody thought it was.
In the work of Lorenz and Poincare.
And so that's where Einstein enters the scene and
comes at it from a very different perspective.
All of Lorentz, Poincare, Fitzgerald,
they were working in the context of how do you construct a model of the ether.
How do you explain these experimental results, the null result of
Michelson-Morley, the result from stellar aberration, other things like that.
Einstein really came at it from a more theoretical perspective.
In fact there is a debate,
was a debate really, about was there any effect
of the Michelson-Morley experiment on Einstein's thinking at this point in time.
And were not sure and
later year's about 15, 20 years later he actually mention the Michelson-Morley
experiment that it did have influence on dis thinking of the null result but
at the time when his actual paper he doesn't cited specifically.
He clearly was aware of it and a number of other experiments like it in terms
of investigating a properties of the ether because we know he read an article about
1899 or so where it was mentioned among the number other of this experiments.
But the evidence that it really had a decisive influence at the time is lacking.
He seemed to be bothered more by as we mentioned previously these theoretical
asymmetries in electromagnetic theory versus the principle of relativity.
So it's really a question that we can't quite answer but
the evidence seems to be pointing to the fact that that Michelson-Morley experiment
even though many others were very worried about it didn't bother Einstein
as much as that point.
And this actually is important in terms of sometimes people the point
to how should we do science is there the one correct way to do science?
And the example the Michelson-Morley experiments sometimes is pointed to
say you should do experiments first see what results are and then build theories
from that and they would then point see that's exactly what Einstein did.
That he took the Michelson-Morley result, built his theory on that.
When in actual fact he almost did the opposite.
We talked about the two postulates.
He really took results from electromagnetic theory and
the principle of relativity from physical theory.
And built this theory on those two postulates and
then later on compared it to experiment.
So philosopher for science and others argue about these things.
But the evidence, the store of evidence seems to say that Einstein did not, we
should say the Michelson-Morley experiment didn't have a decisive influence on
Einstein in terms of his June 1905 paper on the special theory of relativity.
Well, what was Einstein's etherial solution?
So the solutions of Fitzgerald, Lorentz,
Poincare are still working within the context of the ether.
Figuring that maybe matter itself is modified as it travels through the ether
and maybe even time, the nature of time itself,
is modified at least in a mathematical sense in terms of the theory.
What did Einstein come up with while we talked about
his two principles or two postulates.
So let's go back to them now another way we have a better understanding especially
of how our ways working, how light works hopefully.
And let's think about the principle of light constancy.
One of the two postulates the other of course being the principle of relatively.
And we want to look at three cases here.
because what Einstein, his great insight was to say yes,
the principle of light constancy.
That's true, good evidence for it.
Both from theory and then actually from experiment as well.
We'll remind ourselves about that in a second.
The principle of relativity, that's true also.
They seem to be in conflict but actually we'll take them both as true and
then see what the implications are and the results we get.
And so what are those results?
Well the principle of light constancy, remember it essentially says that if light
is a wave, an electromagnetic wave and if you have a moving source of a wave.
In our example we used water waves in a paddle device.
If that paddle device that's generating those waves,
the source of the waves is moving through the medium, moving through the water.
It does not change the velocity of the waves coming off that pedal device, okay?
The velocity of the waves depends on the medium in this case.
It will still flow away with whatever velocity,
whether the source is stationary or not.
And so let's imagine, let's go back to Alice here.
Let's say here's Alice.
And we're going to put the ether in here at first.
So we'll imagine something roughly like this, okay?
For the background of the ether there so she's sort of standing on it,
imagine a floor, something like that or just the context are the ether around her,
that's why I was trying to draw here to indicate that.
And over here, we have a light source.
Now let's get the, so it's generating a light beam that
is going to travel past Alice there, or Bob, whoever we want observing it there.
So if everything is stationary here, Alice would just measure this as velocity c.
All right, nothing too
strange about that it's just the velocity of light going by, nothing in motion.
Okay, so that's our first case.
Now, let's say though, what happens if we put our light source in motion.
Okay, so this is again like our paddle device,
this is the source of the waves were going to put it in motion,
we're assuming the ether exists that's our median.
So if we do that if we say, this is moving now with velocity v,
Alice is still standing over there,
has a device that can measure the velocity of light going by,
Based on the principle of light constancy, or really it's a wave
constancy that the speed of the wave in this case is not affected.
Moving source does not affect the speed of the wave.
In other words if I move my light source of
just a fancy flashlight here that's shedding the light beam going by.
If that's moving at some velocity v, the velocity that Alice sees for
the light wave will not be c plus v it will still just be c.
The velocity of light again presumed moving through the ether, okay?
So that's that case.
Again, it's standard, nothing strange there.
But now what Einstein essentially said is
Let's apply the principle of relativity to this case.
because we're assuming this is true, perfectly fine here, but
we're also assuming the principle of relativity is true.
So what the principle of relativity would say is that
this case here where the light source is in motion towards Alice
is the same thing as, I'm just going to let's just put an x through here for
me to remind ourselves that was there a minute ago.
What if we put Alice in motion this way?
Okay, for the light source so now the light source is stationary,
Alice if the ether exist is moving through the ether toward the light source.
And essentially at that case, well,
first we'll note that these two cases should be equivalent, okay?
That if the principle of relativity is true,
we shouldn't be able tell the two cases from each other.
That whether Alice is moving toward the light source or
the light source is moving toward Alice, it should be the same thing.
We can't tell the difference if it goes back to the coil and magnet that
the Einstein used at the beginning if his paper on his special theory of relativity.
They should be equivalent situations
then let's think about this minute in the context of the ether
that would say then that now Alice is moving through the ether.
So from her perspective there's a moving medium involved.
Remember we talked about with waves when you move the actual medium itself and
you have a wave going through it then that speeds things up.
That the speed of the wave to an outside observer will seem to be going faster
because the medium is moving.
And then the wave itself through the medium is moving so
it carries it all along.
You get an increase in speed.
But what Einstein is saying is if the principle of relativity is true here,
both these cases should be equivalent.
That if the light source is moving toward Alice and
Alice is stationary, by the principle of light constancy,
the velocity of light is still c, nothing changes.
But if we switch it and have Alice moving toward the light source.
It should be in equivalent situation.
The normal theory of waves which say, no now we add some velocity to this light.
Einstein says, now we're going to take the principle of relativity as true.
There's a good reasons, theoretically and experimental to accept that.
And so even though it seems like there's a contradiction here,
we will assume there isn't.
And therefore, this situation, Alice will still see the speed of light to be c.
And in fact, the general conclusion is no matter how an observer's moving with
respect to a light source or a lightning going by therefore, it will always be c.
It will never be c plus v in any given situation because the principle of
light constancy is true.
If the light source is moving that way at c,
therefore by the principle of relativity, if you have Alice, this stationary,
Alice moving this way, which is equivalent.
If the principle of relativity is true,
you can't tell the difference between those two situations.
And therefore in that case too, Alice will still see it be c not c plus v.
And what this means is Einstein's conclusion
was that the ether was superfluous.
And if you looked at his paper, he states it almost right at the very beginning.
First page or two of the paper he say's results of this paper work that effect
will show that the constant of the ether is fair for us and then you develop
some the implications to that which we will be looking at starting next week.
But it's almost a throw away line there.
Well this just shows the ether is superfluous.
And the response of anything would be going what are you talking about.
We need the ether, how do you explain how light waves work without the ether.
People like Lorentz and Poincare have been working for years on this and
developed very sophisticated theories.
And you just want to throw all that out, this 26 year old Einstein.
And yet by going back to the basic foundations of physics,
how we thing about length and time based on these two postulates,
Einstein gradually won people over.
Later in the course, we'll talk about sort of what happened after 1905.
because it wasn't an immediate acceptance of the theory but it did take a while.
But eventually,
people were won over to sort of the Einsteinian point of view in this.
So again, principle of light constancy plus the principle of relativity.
The conclusion Einstein drew is that c,
the velocity of light is a constant no matter how you moving, whether you're
moving toward the beam or away from the beam or sideways of the beam or
how will the beam is moving you will always measure the speed of light as c.
And again that's going to have some very interesting and
strange consequences which we'll get into starting next week.
Explore nosso catálogo
Registre-se gratuitamente e obtenha recomendações, atualizações e ofertas personalizadas.
O Coursera proporciona acesso universal à melhor educação do mundo fazendo parcerias com as melhores universidades e organizações para oferecer cursos on-line.
© 2018 Coursera Inc. Todos os direitos reservados.
