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PROFESSOR: So I'm going to come to 8.20--
Special Relativity.
It's a great pleasure to introduce David Kaiser.
David is a faculty in the physics department.
He's also a historian of science.
So he's in a super great position
to talk about Einstein and special relativity
and give kind of the frame for this class.
So please welcome David.
And take it along.
DAVID KAISER: Great.
Well, hello, everyone.
Happy New Year.
Welcome back at least virtually to MIT.
It's really a great pleasure to talk with you today
about this material.
I love this material.
So hopefully you can all see that first slide--
smiling Einstein on the bicycle.
OK.
So I want to talk about three main parts today
for the material.
And we'll talk about how all of the most
accomplished physicists were thinking about motion of bodies
through space and time during the middle, late years
of the 19th century, roughly, say, 100 to 150 years ago,
give or take, because that really sets up
a pretty sharp contrast with how at the time
a rather young and very little known
person named Albert Einstein began asking similar questions
but often in very different ways.
So we'll start with some of this context of what
was happening before Einstein even came on the scene
to help us better make sense of why his approach seemed
really so unfamiliar and so surprising at the time.
And then for the last part--
I find it really fascinating, drawing on work
from some of my friends and colleagues, other historians--
we'll try to ask, what was going on with Einstein?
Why was Einstein's approach so different?
And can we make sense of it since it wasn't just
the ordinary routine that we might have otherwise expected?
That's that last part about coordinating clocks.
Well, let's jump right in.
Let's start not with Albert Einstein
but with another very familiar name, James Clerk Maxwell.
I thought about growing a beard like that during COVID.
I haven't made much progress.
But that's a typical 19th century, fine Cambridge beard--
Cambridge, England.
So we all know Maxwell's name.
Many of you probably own a t-shirt
with Maxwell's equations on it.
If you do, I'm very jealous.
I don't have one anymore.
Anyway, so we still use his approach
to electromagnetism, as of course you all know very well.
And we've been able to boil it down
to basically a tweet or a single t-shirt.
It turns out, as you may know, what
we now call Maxwell's equations were hammered out by Maxwell
and actually some other colleagues
during the 1860s and early 1870s,
so approximately 150 years ago.
And in fact when he first wrote them down,
they weren't in such a nice, compact form.
It was in a 900-page, two-volume treatise that was first
published in 1873--
two volumes, a total of 900 pages.
It was a weapon.
You could hurt someone with these books,
it was so fat, even though now we can boil it down
to a simple t-shirt.
And so what's even more interesting to me
is that even though we still use Maxwell's equations, what
we think they say about the world
is really, really different than what
Maxwell and his immediate circle thought.
And the biggest difference of all
is that for Maxwell and really for all of his contemporaries
and his students, the equations of electricity and magnetism,
as far as they were concerned, had everything
to do with some physical substance,
a medium that they called the ether that they assumed
must be spread evenly throughout the entire universe,
filling every nook and cranny of space.
So all of the phenomena that we would associate
with electricity or magnetism, the flow of currents,
the splaying of iron filings around a bar magnet,
and even much more complicated things,
to Maxwell and his group, these were all just
evidence of the state of stress of this underlying
physical medium.
It was like a springy, substantial, resistive medium
that they called the ether.
And he says that in the opening pages, for example,
of his now very famous treatise and throughout,
that the whole point of studying this field, as far as he
was concerned, was to study the behavior of the distribution
of stress in this medium extending continuously
throughout the universe, the ether.
It wasn't just Maxwell.
His a little bit more senior colleague, William Thomson,
who went on to be known as Lord Kelvin, like the Kelvin
temperature scale and many things
we still use from Thomson's work,
he wanted to give a sense to non-scientists
a few years later in a popular lecture what
all the excitement was about.
He said, here's what we're doing.
We want you to get a sense for what we're doing.
We're studying the physics of this elastic, physical medium
called the ether.
And he instructed his very elite, very fancy audience
who went to one of these popular lectures,
stick your hand in a bowl of jelly, he tells them.
And see how it wiggles and vibrates
as you move your hand around.
That's the highest of high-end physics in the 1860s and '70s.
It was all about understanding the behavior
of this elastic medium called the ether.
And that had very specific follow-on implications
for this group.
So one of the first things that you all know already,
one of the most exciting features of Maxwell's work
that really got himself excited and solidified his reputation
was this unexpected unification that he put together
in the 1860s.
Not only was there a deep relationship
between electricity and magnetism.
That had been wondered about but never really formalized.
But even more surprising, that these two areas,
electricity and magnetism, were also
deeply associated with optics, with the propagation of light.
So it was Maxwell, as I'm sure you know and probably
have already done this on problem sets
by now yourselves--
using Maxwell's equations, you can
derive the quantitative behavior of light
as it travels through space.
Light, as Maxwell intuited, was nothing
but a certain pattern of propagating
electric and magnetic fields.
Again, to Maxwell, these were propagating in this material,
physical ether.
They were disturbances propagating,
skittering through this physical stuff that filled all of space.
And in fact, by trying to calculate the speed
with which disturbances would travel through space based
on other properties of the ether that he
and his colleagues had already measured,
basically sets up like spring constants,
he found that the speed of propagation
would be equal to the value that had already
been calculated many years before for the speed with which
light travels.
And he says in his own words, in this lovely old-fashioned
phrasing, "The velocity of transverse undulations"--
a certain kind of wave--
"in our hypothetical medium agrees so exactly
with the velocity of light calculated
from optical experiments"-- mostly astronomy at the time--
"that we can scarcely avoid the inference
that light consists of the transverse undulations
of the same medium which is the cause
of electric and magnetic phenomena."
That's why his book was 900 pages, right?
Today we can put in on a t-shirt.
He was really just walking through this very old fashioned
language to come to the point saying
light was nothing but a certain kind of pattern in the ether.
And so in fact they often called this not just the ether
but an even fancier name.
They called it the luminiferous ether.
And from the Latin, it means "light bearing"
or "light carrying."
So "lumin", like "lumos" for you Harry Potter fans, that part
you probably recognize.
And the "ferous" is like a Ferris wheel.
That means, like, to carry or to move through space.
So this was the light-bearing or light-carrying ether.
And that's what Maxwell and really all
of his contemporaries were convinced
was most exciting about Maxwell's work,
that this was a way of characterizing
the state of the ether including these optical phenomena.
OK, so that's where things stood in the 1860s and 1870s.
But that led to a whole new set of questions.
And the next generation quite understandably
wanted to kind of follow up on that
and ask ways to generalize that framework.
Maxwell's work had really assumed
that there was no relative motion between either
the source of light or the receiver of light,
that everything was analyzed in what we would now
call the same rest frame, or frame of reference,
as the ether itself.
But of course that wasn't the most general situation,
as Maxwell's own contemporaries or the next younger generation
began to wonder about.
One of the most influential of that next wave
is this gentleman shown here, Hendrik Lorentz
from the Netherlands, from Leiden.
So Lorentz wanted to ask about the electrodynamics of moving
bodies.
What if either the emitter of light or the receiver or both
were moving with respect to this all-pervasive medium?
And so Lorentz, as we'll see, had
really two distinct motivations in mind
when he tried to think about the electrodynamics of moving
bodies, or let's say optics for moving sources or receivers.
He had a kind of mathematical set of quandaries.
And we'll talk about those first.
But he also had a series of very puzzling experimental results.
So he had an empirical set of ideas
that we'll come to in a moment and also these more
formal or mathematical.
We'll start with the math.
Lorentz was really one of the best-trained, leading
mathematical physicists of his age.
So he knew very well how to handle relative motion.
Galileo had derived that in the 1610s.
That was hardly news in the 1890s.
We would do what we still call the Galileo-Newton
transformation.
For example, Galileo wrote very famously
in his charming dialogues in the 17th century,
if you watch your friend float down a river on a boat that
moves at a constant speed, neither speeding up nor slowing
down, then you know very well how
to compare the coordinates between you, sitting
at rest on the bank of that river,
and your friend as she floats down on her boat,
that what you call the origin, the spatial origin,
of your coordinate system, you can fix at, say, x equals 0.
But your friend could call the center of her boat
the origin for her coordinate system.
And then you can see how her system coordinates will
move with respect to yours.
If the boat moves at a constant speed,
little v, then you just have to calculate
the offset between where the origin, the center of her boat,
is as it floats further and further down the river.
So what she calls the origin of her spatial coordinates
will be offset from yours because this relative motion,
this relative drift.
Meanwhile, as Newton himself famously said
in the beginning of his Principia
where we learn about Newton's laws of mechanics,
that time is time is time.
There's some absolute time.
He actually referred it to the sensorium of God.
He thought there was only one possible time to consider.
And so formally there'd be no change
to the rate at which your clock ticked
versus the rate at which your friend's clock ticked
on her boat.
This is called the Galileo-Newton transformation.
I made a big deal out of it.
You probably would have done this in your sleep.
Lorentz did this in his sleep.
However, it drove him to nightmares
because when he then applied this
to Maxwell's really beautiful and much newer
set of equations for things like optics
or the propagation of electric and magnetic disturbances
in the ether, he found that in that
transformed reference frame if you
take into account that relative motion between either emitter
or receiver of light, then Maxwell's beautiful description
of light, his quantitative description, looked very ugly.
And in particular, it would no longer
suggest that light should behave as oscillating
sines and cosines.
It worked beautifully with Maxwell's equations
if you look only at both sources and receivers of light that
are fixed in place and not moving with respect
to the ether.
Once you apply the very, very well-known transformation
to take into account relative motion,
then your description of light gets all literally out
of whack.
And this was a mathematical conundrum for Lorentz.
It didn't seem to make any sense because on the Earth,
on the moving Earth presumably moving through the ether,
he and his colleagues could measure
light to behave like beautiful sines and cosines all the time.
So we have an empirical reminder that Maxwell's description
seems really, really accurate for describing optics
even on our own moving ship of the Earth.
So this is a real conundrum for him.
He was a very, very clever, mathematically
gifted physicist.
So he introduced a mathematical clue.
He introduced a mathematical stopgap to address this.
He called it local time.
And he was actually very clear in his writings.
He said it was a mathematical fiction--
his word.
It was literally just a mathematical trick.
If he introduced a new transformation
for the time variable, so when you compare your coordinates
with those of your friend on the boat,
what if you actually did make a transformation of t prime,
not just of x prime?
And the transformation he kind of worked out,
he reverse engineered the form it
would need to have so that Maxwell's description
of light waves would be restored to the very simple form
that Maxwell himself had written down a few years earlier.
So this is where we still call this the Lorentz
transformation.
Many of you might have seen it.
If not, you'll have plenty of time to learn about it
and practice it during IAP.
We call it Lorentz, not Einstein,
because Lorentz derived these equations first in a series
of papers in the 1890s.
And he was responding to this question of the electrodynamics
of moving bodies.
How do you preserve this beautiful description of light
from Maxwell even if there's relative motion with respect
to the ether?
He said it was a trick.
It was merely mathematics.
But it would at least get the right form back.
So that was the mathematical motivation.
Lorentz, as we know, was also concerned
about an empirical or experimental curiosity.
He was following very closely the work
of a US-based physicist named Albert Michelson.
Michelson's story is really fascinating.
I won't take too much time now, but super interesting.
He was actually an immigrant from what's now Germany,
was often part of Poland, central Europe.
He moved to the US when he was about two years old, very
young, and was raised right around the time
of the gold rush in California.
And before I get carried away, I'll
stop talking about Michelson, although he's
super interesting.
So what Michelson wound up doing was
he was fascinated by this question of Maxwell waves,
of waves of electricity and magnetism in the ether.
And he was convinced that if we are on this moving
ship of the Earth moving through the ether,
that should have a measurable impact on the light waves
that we can produce and measure here on Earth.
So he set really his life's goal starting from very,
very early trying to build devices,
extremely sensitive instruments with which
he could measure the fact that the Earth was
moving through this ether.
Like all his contemporaries, Michelson
believed without any hesitation that there must
exist the material, the ether.
What else could light waves be but disturbances in the ether?
And then he figured that much like
if a bicyclist going for a bike ride,
we should be able to tell that we're
moving through that medium.
So before I describe his device called the interferometer,
let me just give a little more of an analogy for why Michelson
was so convinced there should be a measurable effect.
If we walk outside our houses, which is now a luxury--
we can still do it with masks on--
walk outside on a still day when there's no wind or no breeze,
we won't feel any particular wind on our face
if we're standing still.
So we're outside in a physical medium.
There's a physical atmosphere.
But if we're at rest with respect to that atmosphere,
if there's no wind, we don't feel it on our face.
On the other hand, if it's still a still day,
there's no breeze, when we get on our bicycle
and pedal really quickly, we'll now feel a breeze on our face
because we're moving through that physical medium.
We're moving through the Earth's atmosphere.
Even if the atmosphere seems to be perfectly
at rest, no strong breeze, no hurricane,
whatever, if we're going quickly enough through it,
we'll feel a breeze on our face.
And Michelson thought the same thing
should be happening for light waves
as they are carried by the Earth through this medium, not
the Earth's atmosphere but this all-pervasive, light-bearing
ether.
So he really thought it would be like the bicyclist.
Now, his real genius was devising this device,
we now call it the interferometer,
with which he could try to measure
the impact of that motion of the Earth, the entire Earth,
through the medium.
So he took a source of light.
Today we use lasers because they're awesome
and they're also monochromatic.
Their light shines basically at one frequency, or very
dominantly one frequency.
Lasers of course weren't available to Michelson.
So he used very bright sodium arc lamps.
Sodium lamps will shine mostly at one dominant color,
not nearly so monochromatic as modern lasers.
But they were the industry standard at the time.
So he basically took sodium lamps
that mostly shine a particular yellow color, shined them
at what we now call a beam splitter.
It was a half-silvered mirror, as its name implies,
that would let half the light through.
It would act like a window roughly half the time.
But it would act like a mirror the other half of the time.
So half of this incident beam will go right through this
as if it were just a plate of glass.
It would be transmitted.
It will then make its way to a fully reflecting mirror--
sorry-- a fully reflecting mirror at the end of the path.
It'll be reflected and come back.
And then, again, half of that return light
will be reflected by the mirror and come out to a screen.
Meanwhile, you can run the same kind of story
for light that gets deflected towards path 2.
From that same, single incident source,
half of the incident beam will be
reflected by that beam splitter, that half-silvered mirror.
It'll travel a path down to a fully reflecting mirror, come
back.
And then half of that returning light will be transmitted.
So you have light coming together on some detector
screen, that it started out as a single light wave
from a single, nearly monochromatic source.
But you split it into two beams so the beams
travel different paths.
And now the light starts out fully in phase with itself.
It's one light beam.
So crests are with crests and troughs with troughs.
And the idea was that you then split
it to set up a race to see if there
was any difference in the travel for light
that traveled through path 1 and out
to the screen versus light that traveled
path 2 and back to the screen.
All the light starts as a single light wave in sync or in phase
with itself.
If there was any difference in the travels
of that light between path 1 and path 2,
you should see a shift in the interference pattern.
Crests should no longer arrive lining up with crests
or troughs with troughs.
You should see a very characteristic set
of interference fringes.
What is called an interferometer,
extremely sensitive.
Now, his idea was if, like the bicyclist,
we're on the moving Earth, then the path is heading directly
into the ether.
That is, say, the path that's along the Earth's motion
through the ether should be just like the bicyclists feeling
the direct headwind of that breeze directly
on her or his face.
That means the effective speed--
let's say this is the direction of the Earth's motion.
The effective speed with which this light beam
could travel toward its mirror should
be experiencing a direct headwind for its upward path
and a direct tailwind for its downward path.
It should have a different speed than the light that
follows the more orthogonal path so that even the light starts
out perfectly in phase, you should find
a shift in the interference fringes
because the light's effective speed through the medium
is different for path 1 than path 2--
again, an analogy to the ether wind of a bicyclist
through the atmosphere.
Not only that-- a little foreshadowing
for what's to come later--
this device is so sensitive, it's
sensitive to second order in a very small quantity.
So it could measure differences to the second order
in the relative speed of, say, the Earth through the ether
compared to the speed of light.
So that's called a second order because it goes
this small quantity squared.
That's how sensitive this really ingenious device was.
And as many of you might know, we
use interferometers all the time now in all kinds
of industrial applications.
Even more, my favorite example is
from our friends who detect gravitational waves with LIGO.
That's essentially a super-sized interferometer
with very, very similar principles of design.
So Michelson was doing this really cool work.
It was among the earliest work that any
of the super fancy, elite European scientists
paid any attention to coming out of the US.
Michelson was among the first who
made even the people like Hendrik Lorentz sit up and pay
attention at a time when the US was still otherwise pretty much
a scientific backwater.
So it's a really cool idea.
It's a remarkably clever design for a device.
Michelson built a small prototype.
Then he super sized it with his colleague Edward Morley.
They built a device 11 meters long
for each arm, so roughly 33 or 34 feet long--
huge, huge for its day, very long arms.
They floated the whole thing in a vat of mercury,
which I don't recommend.
But they were trying to tamp down any vibrations
from nearby cable cars.
They wanted to have a clean laboratory environment.
Then they did this for years and years
and years, months and months and years and years
because, of course, you never know
what the ether's actual rest frame is.
Who's to say that at this moment,
this is the direction of the Earth's
motion through the ether?
Maybe it's this direction or some other angle in between.
They would look for day to night variations.
They would look for annual variations
as the Earth went around its orbit around the sun.
They would try to find any time, day or night, winter
versus spring, year after year when
they could measure some measurable offset or change
in those interference fringes because at some point,
this direction should have lined up
with the Earth's direction of motion,
even it wouldn't be every time.
That's why they kept doing this over and over and over again.
And as you might know, they found nothing.
So after years of painstaking data collection,
they found no compelling empirical evidence
of the Earth's motion through the ether.
Michelson won the Nobel Prize for this and related work.
He was an astoundingly accomplished experimentalist.
He was the first US-based physicist
to win the Nobel Prize.
He lived 20 more years after that
and died considering himself a failure.
So I hope you all win the Nobel Prize.
And I hope you think better of yourselves
and give yourselves more credit.
Michelson knew for certain the ether must exist.
And yet he had failed to find it.
So Lorentz was following this back in Europe.
And this was really his second main motivation
to think about these funny ways of handling
coordinates in what we now call the Lorentz transformation.
So I mentioned his mathematical concerns
about the transformation properties
of Maxwell's equations.
He was also following the Michelson-Morley work
with great interest and citing it.
And we know he was really following each update.
So he was concerned about this failure
to measure a shift in the interference fringes.
But Lorentz said, oh, but actually
maybe there's a physical reason to account for that.
If there really is, as he knew there must be,
this physical, resistive medium, kind of elastic medium
through which the Earth and everything else is moving,
then there must be a force exerted by that viscous medium
on every single atom and molecule
making up all the stuff in Michelson's device
as well as in everything else.
And so it would be like picturing a beach ball.
If you try to drag a beach ball underwater,
in a resistive medium, the shape will be deformed
along the direction of motion.
If you drag that beach ball fast enough underwater,
it will shrink in the direction of motion.
It will be deformed like this picture here.
And so Lorentz said that must be happening
for every bit of matter in the arm of Michelson's
interferometer that's most subject to that resistive force
of the ether.
There should be a contraction along the direction of motion.
So then, again because he's a very
gifted mathematical physicist, he
calculated exactly how much shift must there
be for the resultant path to be shortened just enough to make
it a tie race after all.
So the arm of the interferometer that's
experiencing this shrinking, this extra force
due to the resistive medium, would
have to shrink by a specific calculable amount.
We now use the Greek letter gamma.
If you haven't seen that already,
you'll see it throughout IAP and the rest of your life.
It takes this somewhat simple-looking form--
1 over the square root of 1 minus v over c squared.
If you plot it, you can see it diverges.
When the relative speed gets close to the speed of light,
you have 1 minus 1 in the denominator.
You divide by 0.
Your eyes bug out.
And cats and dogs live together.
Everything goes crazy.
So it diverges at v equals c.
On the other hand, for small speeds,
small compared to the speed of light,
this factor is indistinguishable from 1.
So here's a quick plot.
For ordinary speeds that we encounter on the highway,
let alone on a bicycle, our speed
compared to the speed of light is vanishingly small.
So this factor gamma is very, very close to 1.
Only when you get to speeds approaching the speed of light
would you expect to measure any shift from that.
Nonetheless, Lorentz said in principle this
happens at any speed.
And the shrink, the amount of contraction,
is governed by that relative speed
given by this Greek letter gamma.
So gamma is always greater than or equal to 1.
That means 1 over gamma must be smaller than 1.
And that's saying that the contracted length of one
of those arms of the interferometer
got shorter by a certain amount depending
on the relative speed.
That would be enough to account for this null result,
Lorentz argued.
It turned out that exact form of gamma
was the same form he'd found for his mathematical local time
manipulations.
So here's how we can live in a physical ether
even though we don't measure its effects.
OK.
Let me now shift to how a different person began
thinking about very familiar questions by that point
but coming at them quite differently.
That's young Albert Einstein.
So Einstein was born in the midst of all this.
He was born in 1879 in kind of rural,
roughly speaking, nowheresville Germany,
not near any of the big cities.
So Lorentz was already a practicing physicist
when Einstein was born.
He was much younger.
Einstein's main ambition was actually
to become an electrical engineer at a time
when that term itself was actually brand new.
Einstein's father and uncle had gone into business
together in this really brand new field
of electrical engineering.
This was the age of electrification.
Think about extended street lighting,
trolley cars with the shared electric lines above.
This was transforming the face of everyday life
in cities and eventually even in more rural areas.
And Einstein's father and uncle were in on that.
They were early professionals in this new field
of electrical engineering.
And Einstein loved it.
He loved to tinker with electrotechnical gadgets.
He had many strong feelings about many things.
Among them, he hated what he considered
the overly militaristic German high school that he attended.
He would argue and insult his teachers.
They didn't like him any better.
They were delighted when he dropped out,
so they didn't have to kick him out.
He was really very obnoxious, it turns out.
So he was a high-school dropout.
He dreamed of entering the Swiss Federal Technical Institute.
It was kind of like the MIT of Switzerland.
Except to be more proper, MIT is the Massachusetts version
of their school.
Zurich's was founded first.
It's often called the ETH, or the Eidgenossische Technische
Hochschule.
It was really a very elite technical university
in Zurich, Switzerland.
Einstein, by this point, had renounced
his German citizenship.
He dropped out of high school.
And one of the best things about this technical university
in Zurich was that you didn't have
to have a high school diploma.
He said, perfect.
That's the place for me.
So they had an entrance exam, which he very dutifully studied
for and then failed because, after all, he
ignored the topics that weren't of interest to him.
He did well enough on the physics and math
portions of the overall exam that a kindly physics professor
took him aside and said, you know,
if you go to basically a kind of regional, something
almost like a community college, go
to a local, regional school for a year,
study up, retake the exam, you might do better.
And that's what Einstein did.
So he went to a little regional school
in, again, in rural Switzerland for a year,
took the exam again, and passed.
So now he's able to enter his dream
school, the ETH in Zurich.
Once he then worked so hard to get in,
he proceeded to cut classes.
This guy was a horrible student.
Whatever you do, don't be like Albert Einstein,
at least while you're in university.
He worked so hard to get in.
And then he, again, would insult his professors
as much as he'd insulted his high school teachers.
He thought everything they did was boring.
They didn't know what was really interesting.
So he would cut classes and read on his own
and then borrow notes from his girlfriend,
his long, suffering, very patient girlfriend, Mileva
Maric, who was doing very well in her own physics and math
courses.
And likewise, he borrowed notes from another friend
of his, Marcel Grossmann.
So he'd just cram and scrape through for the exams.
Not an ideal student.
For some reason that Einstein couldn't possibly fathom,
because he actually was a dolt frankly,
he impressed none of his professors.
So when it came time to graduate, none of them
would write him a strong letter of recommendation.
Again, his life bears many important lessons for us today.
Attend class.
And be slightly less obnoxious to your instructors.
And maybe things will turn out better.
So none of his teachers would basically
support him because he had middling grades
and he was rude to them.
So he couldn't get a job after graduation.
So finally one of his close friends,
Marcel Grossmann, one of the folks
from whom he'd borrowed notes, his father had connections.
And so basically through connections,
he was able to get Einstein an entry-level civil service
job at the patent office in Bern, Switzerland.
So still in Switzerland.
He was a patent officer, third class.
As I'm always fond of saying, there was no fourth class.
You were the lowest entry-level gig.
So even for young Einstein, it wasn't what you know.
It was who you know.
What he then proceeded to do was he
had a day job at what they called
the electrotechnical desk, much like what his father and uncle
were doing.
He was a patent examiner for a lot
of these cool, new electrical gadgets.
And then he would go hang out with a bunch
of friends and drink beer a lot at the pubs.
So they formed what they called the Olympia Academy.
And this was very ironic.
They gave themselves the most elite
sounding name because they're basically
three semi-bums hanging out, reading,
and blowing off their families.
So they gave themselves a very, very prestigious name,
even though it was literally three recent college
graduates hanging out.
It was Maurice Solovine, Conrad Habicht,
and young Albert Einstein.
And they would go and sometimes drink coffee, often drink beer,
and talk about stuff they'd read.
And they would read a lot of physics
and read a lot of philosophy and talk about it.
And one of the books that we know from their correspondence
at the time that they were really interested in
was this fascinating book by an Austrian polymath
named Ernst Mach.
Here's the book translated into English, known
as The Science of Mechanics.
It had come out in the 1880s.
Mach was really remarkable.
He was both a mathematical physicist
and experimental physicist.
You might know the terminology for Mach number,
like speed of sound, Mach 1, Mach 2, Mach 3-- same Mach.
He did a lot of studies of acoustics and optics
but also of what we would now call psychology,
like sensory experiments and so on, and eventually
medical surgery.
And then at the end of his career,
he was a professor of the history and philosophy
of science.
This guy did it all.
He wrote these very, very dense, conceptual critiques
of Newtonian physics, among other things.
And Mach was convinced that Newton was really
getting himself into a horrible muddle
because he had not paid sufficient attention
philosophically.
And this is what the young members of the Olympia Academy
got really excited about.
We know from their letters and their notes at the time.
Mach was advocating a position that
came to be known as positivism.
According to Ernst Mach, unlike Isaac Newton,
or for that matter even some folks like Maxwell, Mach
argued that only quantities that could become objects
of positive experience, that is to say things we
could actively measure or sense or feel or touch,
only those things belonged in our scientific theories.
Anything else was just like mere speculation,
like counting the number of angels that could
dance on the head of a pin.
He was scathingly critical of Newton.
And in particular, Mach wrote in detail
that Newton's notions of absolute space
and absolute time had no meaning because how could you
ever measure absolute time?
Show me the clock that could measure absolute time.
That was the kind of classic Machian response.
I can measure the passage of time by using a clock.
But who says that's what Newton wrote absolute time was?
This had an amazing impact, as we know, on the young Einstein.
So he's in this milieu.
He's now not in a university setting.
He scraped through his undergraduate studies.
He has a nice day job.
But he's not doing particularly well professionally.
He's hanging out with his buddies
and reading some interesting and hard, obscure philosophy
science in the evenings.
Well, he has what's now commonly called his miraculous year,
his annus mirabilis, in 1905.
In fact, he only took about six months.
It was, like, half a year, during which he submitted
four really astonishing, original papers to the leading
journal of physics, the Annalen der
Physik in Germany at the time.
They've since been published and translated.
There's a particularly nice edition
you can find edited by John Stachel with very nice essays
to accompany them.
You can find them online.
So for IAP and for the rest of today
and even throughout the month, we're
really interested in what was the third of these articles
that he submitted.
He submitted it to the journal in June of 1905.
It's on what we would now call special relativity.
Its title, as you can see up top,
was actually, in translation, "On the Electrodynamics
of Moving Bodies," a thoroughly familiar title, exactly what
Lorentz and all of Lorentz's colleagues
have been talking about for decades by that point.
So the title of Einstein's paper in 1905
was not surprising, even though, as we'll see,
his approach was quite distinct.
He begins this now very well done paper not by saying,
I found an error in Lorentz's calculation.
There was a missing factor of 2 pi or whatever.
He doesn't say, I conducted my own measurements.
And I found these results with an experimental error.
He starts out by saying there's an asymmetry
in the explanation which is not present in the phenomena.
It sounds very philosophical.
He goes on in his very opening paragraph
to say that when we use Maxwell's equations,
we come up with very different kinds of accounts for what
should be the same phenomenon.
Very simple.
Nothing super fancy like an interferometer.
Just take a bar magnet and a coil through which current
could flow.
And make sure you have a current meter, an ammeter attached
to the coil.
So if electric current flows through the coil,
it will be measured.
The ammeter needle will be deflected.
And we are free to move either the magnet or the coil.
In his opening paragraph, Einstein says, physicists
had treated this situation completely orthogonally even
though, as far as Einstein was concerned,
there's only one explanation needed.
And so with case 1, if you assume
the bar magnet is moving, you're shaking the magnet
back and forth and keeping the coil fixed in location,
then you would appeal to one set of Maxwell's equations.
And again, on the t-shirt it would be this one.
You have a time-varying magnetic field
which will induce a spatially varying electric field.
And that will exert a push, a force on the little ions,
the little electric charges within that coil.
They'll feel a push.
They'll move along the coil.
Electric current, as Maxwell himself had argued,
was nothing but the motion of these electric-charge bearers.
So because you have a time-varying magnetic field,
the little bits of matter in the coil will be pushed along.
You'll induce a current.
That's case 1-- moving magnets, stationary coil.
But if you want to analyze the other situation,
to hold the magnet rigidly fixed in place
and shift the coil back and forth,
then physicists would give an entirely separate explanation.
They would appeal to a different one of Maxwell's equations.
Now they'd say that there's a static magnetic field that
varied in space.
It's spatial gradients were non-vanishing.
And that would exert a force, like a kind of Lorentz force
law, on those charges.
So they have some velocity in a magnetic field.
They'll be pushed along the wire.
And you'll measure a current.
Einstein said that's one explanation too many.
All that we could ever measure--
again, you can almost hear the kind of Mach coming through--
all we can ever see as an element of positive experience
is some relative motion between the magnet and the coil
which induces an electric current.
Who's to say one was actually still
while the other was moving?
So Einstein begins this paper by saying
that there's something wrong with the stories
we tell about the equations.
He doesn't argue about the equations.
He argues about our interpretation
of the equations.
Very striking.
He then goes on, just in, like, paragraph 3-- still
very early in the introduction-- to posit two postulates.
He doesn't prove them.
He doesn't derive them.
He doesn't say, I have demonstrated these
by doing experiments.
He says, let me hypothesize these and see what follows.
And these are the two in rough paraphrase.
The first one was actually already called
the principle of relativity, or sometimes simply called
Galilean relativity, going back again to the 17th century.
Galileo had argued by thinking about that boat
floating down the river, that to a person on the boat, as long
as the boat is moving at a constant speed,
neither speeding up nor slowing down,
that all the laws of mechanics should work perfectly well
for that observer the same as they would
for us at rest on the shore.
If you toss a ball, it'll land back in your hand
as you expect.
Even though to us, we see the ball trace
a complicated parabola, to the person on the boat,
she's perfectly entitled to say, I'm sitting at rest.
The ball went straight up and landed straight
back in my hand.
All the laws of mechanics should work equally well
in any reference frame that's moving at a constant speed.
Einstein just takes that existing principle
of relativity from mechanics and just assumes,
just hypothesizes that that should
apply not only to mechanics but to every physical phenomenon--
electricity, magnetism, optics, thermodynamics.
And that's just a leap.
He just says, what if?
What if this applies to any kind of physical phenomenon, not
just mechanics?
And then he introduces the second postulate
which seems actually to be in tension a bit with the first.
His second postulate is, the speed of light
is a constant independent of the motion of the source.
What?
That doesn't sound right.
If you go back to Galileo and watching his friend
on the boat, if she fires a cannon,
the speed with which we measure the cannonball
is different than the speed she measures it, right?
If you watch her lobbing a tennis ball,
our measurement of the speed of an object in her reference
frame is not the same as ours.
And Einstein here is saying light
is special, that unlike tennis balls, ping pong balls,
cannonballs, or trains, or anything else,
the speed of light, as a postulate,
will be constant for any observer
as long as they're in an inertial frame of reference.
And here's an excerpt from the English translation.
I won't read all this out.
But he says, what follows from these postulates
is that the luminiferous ether will prove to be superfluous--
[GERMAN]
He doesn't say, I've disproven it, ether.
He says it's just irrelevant.
50 years' worth, by that point 100 years' worth of study
by all of Europe's most prestigious physicists was
irrelevant.
That's probably why he didn't have many friends in physics
at the time.
So he doesn't disprove the ether.
He says we just won't even need to refer to it anymore.
It makes the entire set of questions
that had driven people like Lorentz
really kind of fall away, at least as far as Einstein
himself is concerned.
So why does Einstein introduce that second postulate?
And again, historians and physicists and philosophers
have studied this question a lot.
And we have some good documentary evidence
because Einstein was writing letters and diaries
and stuff all the time.
And a lot of those have survived.
So we have some contemporaneous documentation as well as
his own later recollections and so on.
We know that actually 10 years before this paper, back
when Einstein was a mere teenager,
he'd like to pose these kind of thought experiments
or questions to himself.
And one of the questions he would return
to really over the course of a full decade
was, what would it look like, what would you experience,
if you could catch up to a light wave?
And he reasoned it would be like a surfer riding along an ocean
wave, that to us on the shore, we'd
see both these things moving.
We would see a dynamical wave moving over time,
not just a frozen waveform in space.
But to the surfer, if she's really
moving at the same speed as the wave,
then she would see the wave frozen in time.
It would be a crest here, a trough there.
At least for some extended period of time,
the surfer would see the wave frozen,
not dynamical-- a frozen waveform varying in space
but frozen in time.
So Einstein said that doesn't make any sense if we think
about Maxwell's equations.
When he got a little more sophisticated
and learned more about Maxwell, he
said there's no solution to Maxwell's equations.
If you're in a source-free region,
if there's no clump of electric charge around,
no electric currents around, if both rho and J vanish,
then there's no way to have spatially varying
electric and magnetic fields that
are nonetheless static, right?
That seems to be a contradiction.
So how do you get out of this contradiction
of thinking you would have a static waveform of light
if you could catch up and move at the same speed
as that light wave?
How do you avoid that?
You just make sure you can never catch up to the wave.
How can you never ever catch up to the wave
if the wave is always traveling at the speed c
even if you're traveling on a very fast train or now
a hypersonic jet or a spaceship of your imagination?
That second postulate for Einstein we now know
was really the endpoint of a 10-year series of thought
experiments about, what would it look
like to catch up with a light wave?
And he said that would make so many other things mutually
inconsistent.
Let's make sure no one could ever catch a light wave.
And that's what starts driving much
of the rest of his thinking, not worrying about interferometers
and all the rest.
So what he does, unlike Lorentz and really all the masters
in the field at the time, Einstein
begins with kinematics, with the force-free motion
of bodies through space and time,
which is a very Machian thing to do.
What can we see?
We measure objects moving through space and time.
Whereas people like Lorentz, and Maxwell for that matter,
have been starting with forces, with dynamics.
Remember, Lorentz has this great idea
that there's a force from the ether on the matter.
And in Michelson's instrument, it's
all about dynamics, forces.
Einstein inverts that order.
He says forces will be important.
But first let's make sure we understand force-free motion
kinematics first.
After all, that's what could become
objects of positive experience.
And so he has these wonderful quotations.
It's now from the introduction of the paper.
It's on the bottom of page 2.
He's really redescribing how to lay out coordinates.
It sounds childish.
It sounds thoroughly unprofessional to the folks
of the time.
Hendrik Lorentz says don't bother with 'what do we mean
by coordinates?'
But Einstein was convinced we have
to think through how do we describe motion
through space and time first.
And I won't bother reading it out.
I'll share this slide.
And you can see it.
But that's really what he's doing in the very opening
paragraphs of this paper.
And that leads him to other follow-up conclusions,
one of which very famously becomes
known as the relativity of simultaneity.
And you might have heard of that before.
You'll spend more time with this in IAP, I'm sure.
If there's no such thing as absolute time,
if time is what we measure with time-measuring devices
like clocks, if that's all time is,
is what can be measured by an actual instrument like a clock,
then how can we compare the times in different places?
After all, I'm sitting here with my clock.
Well, he says one thing we could do
is trade light signals because, at least according
to his postulate number 2, light is special.
If I throw ping pong balls, that's not so special
because we will disagree on the speed with which
those ping pong balls travel.
If I send a light wave, then we had better
agree on the speed with which that light moved from point A
to point B because of postulate 2.
So he starts thinking about one of his favorite things
in the universe, trains.
He loved trains.
It came up all the time.
So he imagines a train moving along a platform
at a constant speed, a nice, inertial frame of reference.
Einstein is standing here on the embankment, the train platform.
He has two friends.
We can call them Alice and Bob, A and B. Einstein
has marked himself out to be in the perfect midpoint of where
Alice and Bob are standing.
So they mark this all out ahead of time.
He marks himself perfectly in the middle.
Alice and Bob are each equipped with a lantern and a watch.
And by prior arrangement, they say
at 12:00 noon on the dot, turn on your lanterns.
So the light will travel from both A and B
toward the midpoint.
Point your lanterns toward Einstein
at point M. Turn them on at the same time.
Meanwhile on this zooming train, there's
another friend of Einstein's sitting
at the midpoint of the train.
At the point, this is Marge, M prime here.
She knows that she's in the exact midpoint of the train.
She knows by prior arrangement that Alice and Bob
are standing one train length apart from each other.
And again, she's expecting that they will turn their lanterns
on at the same time.
So how do these different folks describe this series
of events that follow?
Let's focus first on what Einstein
sees when he's standing still on the train
platform, the embankment, watching the train go by.
The observer who's standing still
on the platform at point M was, by prior arrangement,
at equal distance from Alice and Bob.
I guess I changed it.
Now it's a she.
So Mileva, his wife, is standing there.
Maybe M stands for Mileva.
So she receives the light waves from points A and B
at the same time.
So she can conclude that the light flashes were emitted
at the same time, that the event of person A and person
B shining the lights, those events were simultaneous.
How do you know?
Because the light had equal distances to travel.
And the light could only travel at but one speed.
And they arrived at the same time.
They must have started the journeys at the same time.
The act of shining those lanterns
must have been simultaneous.
But what about the person who's on the moving train?
She sees the following as she is zooming along at point M prime.
She sees the light from point B arrive at her location first.
Now, Mileva or Einstein would say, oh,
that's because you're racing toward it.
She says, not so fast.
I'm in a perfectly self-consistent
mechanical system.
All the laws of physics work as well for me as for you.
And the light couldn't have sped up
or slowed down by your own postulate,
she would say-- she would be entitled to say.
So if she's equal distant between points A and B
and she receives the light from B first,
the only possible explanation is that the lights were not
shown simultaneously, that A and B did not turn the lanterns
on at the same time.
So the person on the train platform and the person
on the moving train disagree about what
happens simultaneously.
This becomes known as the relativity of simultaneity.
So who's correct?
I've already said, according to Einstein, no one or both
of them because of postulate 1.
They're both entitled to work out
a perfectly self-consistent set of laws
involving electromagnetism, optics, and mechanics.
They agree they were at the midpoint.
They agree that light didn't speed up or slow down.
So they are both right, which is to say
there is no right answer to the question, what
was really simultaneous?
Simultaneity becomes relative to one's frame of reference.
That's a pretty deep change from the Newtonian system.
And as Einstein says-- again, it's bottom of page 2,
very early in the paper--
"we see that we can attribute no absolute meaning
to the concept of simultaneity, but that two events which
examined from a coordinate system
are simultaneous"-- like him on the embankment--
"can no longer be interpreted as simultaneous events when
examined from a system which is in motion
relative to that system."
OK, that's about kinematics.
It's not about forces or resistive medium or dynamics.
So now he goes on-- again, very early on in the paper--
once you get to the relativity of simultaneity-- again,
as you'll have a chance to unpack with more patience
in the coming days and weeks--
other strange phenomena seem to follow from that,
argues Einstein.
One of the first he talks about is length contraction.
So this had been found and published by Lorentz.
Einstein is about to give an entirely different derivation,
even though quantitatively it's the same form of the equation.
For Einstein, it has nothing to do with forces.
It's all about kinematics.
In general, like a good Machian, he asks,
how do we measure the length of an object?
How do we make length an object of positive experience?
Well, at the same time measure the location
of the front of the object and the back of the object
and take the difference.
So if you want to measure the length of the train,
that's fine.
Just measure where the front is and the back
is at the same time, and then mark off
the difference between those two locations in space.
Our friends Alice and Bob can do that with the train.
And they find the answer capital L. The train is length L long.
Meanwhile, Alice and Bob--
and I should say that's when the train is at rest.
When they do this with a moving train,
Alice and Bob measure the length of a moving train,
they measure some length shorter than what
the person on the train was expecting.
The person on the train expected the full length L. The person
who's moving with the object, either at rest with it
or moving together with it, says the train is L units long.
But when Alice and Bob measure the train
by measuring the front and back at the same time,
they find a shorter answer.
They found it shrunk along the direction of motion
by some specific amount.
Now, how could that be?
Remember, we disagree about "at the same time."
So if we disagree about simultaneity,
we will-- perforce, we must start
to disagree about lengths.
So the person on the train says, you did your measurement wrong.
You measured the front of the train first.
We know that event B happened first, she says,
because we got the light from event B first.
So you measured the front of the train
and then waited while the train slid and then later measured
the position of the rear of the train.
So of course you have a shorter distance
because you performed a bad measurement,
because you didn't measure the front
and back at the same time.
We say, don't be silly.
They were at the same time.
We checked by trading light beams.
We know they were simultaneous.
And we got the answer L prime.
Your train is short.
Who's right?
Sort of both and neither, that because we disagree
on simultaneity, we disagree on the outcomes
of simultaneous events like measurements of length.
And so he goes on with just a few lines of algebra
to find the exact form of what was already
known as the Lorentz contraction, that same factor
gamma that you'll be using all IAP,
that the measurement of an object in motion
shrinks along the direction of motion.
Whereas if we were at rest with that object,
we'd find a longer length.
And the amount it shrinks depends on that relative speed
v over c.
It depends, in particular, on this form gamma.
This has nothing, for Einstein, to do with forces or dynamics.
It's a totally different derivation than Lorentz's.
It's simply a consequence of kinematics and, in particular,
about simultaneity.
It's a very simple exercise.
You'll probably wind up doing it very soon
to find a similar consequence for the rate at which clocks
will tick.
This has now became known as time dilation.
Imagine a very simple kind of clock, the simplest one--
two highly polished mirrors with a light beam
that just bounces straight back and forth between them.
If the clock is at rest with respect to us,
we hold the clock perfectly still at a fixed height,
then the time it takes for that light
to travel from the bottom mirror to the top mirror
will count as one tick of our clock.
[SNAPPING]
And we know that light can only travel at a fixed speed.
So it's a really great, uniform clock.
As long as we can hold that height really fixed,
this is a great way of defining a unit of time and therefore
our clock rate.
What happens if our friend has an identical clock,
same mirrors, held equally rigidly at the same height
apart but zooming past us on that moving train?
Then we watch the light have to travel this longer
path because after the light beam leaves the bottom mirror,
in order to reach the top mirror,
the whole assembly has moved with the train to the right,
some distance v times t in the time during which
that light beam was in transit.
So it has to travel the hypotenuse
of this right triangle.
Instead of just this simple up and down,
it travels perforce a longer distance
and likewise back down.
So our observation of the moving clock
is that it takes longer between ticks.
That becomes known as time dilation.
The time between ticks has stretched,
which is to say the clock is running slowly as we measure.
We measure the moving clock to run slowly
by that same factor gamma.
The time between ticks gets stretched.
Remember, gamma is greater than 1.
So the time between ticks gets stretched.
And that's the same with the clock is running slowly.
Meanwhile, the person on the train says, you're ridiculous.
I had the clock with me the whole time.
It kept perfect time.
But your clock ran slowly.
I watched as I ran by the station.
Perfectly symmetrical conclusions.
So Einstein was working all this out, very much inspired
by Ernst Mach, by this notion of positivism, of what can we
hope to measure, not starting with forces
but with the force-free motion of objects
through space and time, and really trying to bring it back
to, what would be measurable?
What would I see if I were in this situation?
One of his teachers at the ETH, a mathematician
named Hermann Minkowski, had formed a deservedly low opinion
of student Einstein.
Einstein used to cut class, was very rude.
But one of their mutual friends, after Einstein's paper
came out, sent the paper to Minkowski saying, you know,
it's actually kind of interesting.
Take a look, to paraphrase.
And Minkowski said, well, despite the fact
that I knew Einstein was never going to amount to anything,
I read the paper.
And I was right, Minkowski says.
He really made a mess of this, as well.
So Minkowski's just interested enough
to redo Einstein's work in a form that
made much more sense to Minkowski,
who was, after all, a professional geometer.
He wasn't just a mathematician.
He loved geometry most of all.
So Minkowski, not Einstein, is the one
who actually brings these pieces together
a few years later in-- it was published
in 1908 instead of 1905.
And he says, all this talk about moving trains
and polished mirrors, all of that's just a distraction.
To a properly trained mathematician,
which Einstein was not, all we're doing
is performing rotations or projections
in a certain kind of space, in this case
a spacetime in which there's, say, one direction of space
running along the horizontal axis
and one dimension of time running up the page.
We now call these Minkowski diagrams
in his honor, or simply spacetime diagrams.
None of this appears in Einstein's early work.
This was done by his former teacher in response
to what Minkowski considered to be Einstein's continuing
confusion and sloppiness.
And there's a benefit from doing that, Minkowski finds.
He agrees with Einstein that we will disagree
on certain kinds of measurements,
for example lengths and durations of time,
because we disagree on simultaneity.
But Minkowski finds something that had not been
so clear to Einstein himself.
There are combinations of those kinds of intervals
on which we will all agree.
This is what we would now call a spacetime invariant.
Put together, a combination of the time interval
minus the space interval, a relative minus sign and each
of those quantities squared, that combination
we will all agree on as long as we're
each in states of non-accelerating motion
even though we disagree separately
on the duration between two events, delta t, or the lengths
between them, delta x.
And that, from Minkowski, is what any geometer should do.
Some relationships remain invariant
even under changes of coordinates.
And for Minkowski, that was what any undergraduate geometry
student should know to do first.
So we actually have this notion of one kind
of thing called spacetime coming from Minkowski kind of redoing
Einstein's work.
And as Minkowski famously writes in his own article--
it was published posthumously; he died quite young.
And he gave a lecture.
And it was published soon after he died.
And he wrote upon introducing this new work,
"Henceforth space by itself and time
by itself are doomed to fade away into mere shadows
and only a kind of union of the two
will preserve independence."
And by shadows, he really meant projections, just
drop perpendicular to the appropriate axis
and then think about coordinate transformations
in that spacetime of x and t.
So that's, again, something you'll
get much more practice with if you haven't seen it already.
But that's a preview.
That comes in response to Einstein's work.
It wasn't an Einstein's own original.
Although, just to jump ahead very briefly,
Einstein first thought that was horrible
because he didn't like Minkowski.
But then over the next several years,
the better part of a decade, Einstein
himself became more impressed by that way of thinking
and really adopted it for his own later work
on what became known as the general theory of relativity.
That's for later.
OK, very briefly here's the third part
of the material I wanted to share with you.
And then hopefully there'll be some time for discussion,
as well.
So this last part is much more brief.
But it's, how do we make sense of this?
Why was Einstein doing all this seemingly unusual,
maybe even crazy stuff, certainly
out of step with Lorentz, with his own teachers
like Minkowski?
How can we account for Einstein's quite idiosyncratic
approach to what was otherwise a common set of questions
about the electrodynamics of moving bodies?
Now, here's some of my favorite work by other colleagues,
by other historians and physicists who really
looked at this in great detail.
So for a long, long time, I mean literally
for the better part of 100 years,
since people began taking relativity seriously,
which is a long time by now, it had become very common to say,
well, Einstein must have been motivated
much like Hendrik Lorentz was, really like that
much of that generation was.
Einstein must have been responding
to the null result from Michelson and Morley
and their interferometer, that Einstein
must have been trying to explain why they couldn't measure
our motion through the ether much as Lorentz, we know,
very explicitly was trying to do.
And there's a fascinating-- one of the first really careful
examinations of that claim was by Gerald Holton, who's
a real kind of hero of mine.
Holton did his first PhD in physics,
low-temperature physics, and then retooled many years later
in the history of science.
And he wrote a series of really remarkable essays
about Einstein once a lot of Einstein's papers and letters
and notes became available.
Holton was among the first to really dig
through these with great care and almost
like a detective going through the evidence.
And what Holton concluded was it's
not clear that Einstein even knew
about the Michelson-Morley interferometer.
Lorentz knew about it and followed it carefully.
There's very little trace that Einstein paid it any attention
at all.
If he did know about it, it was kind of in passing.
It was certainly not front of mind in the months and years
leading up to the 1905 paper.
He might have known about it secondhand
from reading through all the footnotes of Lorentz.
But it's not something he seems to have been paying
much attention to at all.
And so there's nice textual evidence
even in Einstein's paper, that 1905 paper
that I keep showing some brief excerpts from.
Again, this is on the first or second page.
When he's trying to reason why we should think about maybe
giving up on the ether, he mentions--
without citing any of them-- he mentions
several unsuccessful attempts to discover
any motion of the Earth relative to the light medium, the ether.
He doesn't say which ones he means.
But he actually then goes on to say in the same paragraph,
none of these have found any deviation to first order in v
over c.
And what's so striking, as Holton reminds us,
is Michelson-Morley was actually second order.
Einstein seems to be talking about a whole different class
of earlier experiments even before Michelson
got in the game.
He's certainly not obsessing over
the Michelson-Morley interferometer the way
other people were.
And so some people then read Holton's analysis
to say a kind of overcorrection.
Does that mean Einstein didn't care
about any kinds of experiments at all?
If he wasn't trying to respond directly
to the Michelson-Morley experiment,
was he just off in a kind of philosophical dream world?
And that's where I think we again
can now say quite firmly no.
In fact, it makes sense to go back
to Einstein's own early years, his early fascination
with electrotechnical gadgets, and remind ourselves
what his day job was in the early 1900s, including 1905.
Put him back in the patent office in Central Europe
at this very specific moment.
So let's think about Einstein's favorite technology, trains.
Trains and railroads themselves were actually
fairly new in the 19th century.
They were introduced to widespread commercial usage
for commercial transportation really only
in the 1830s and '40s.
Remember, Einstein was born in 1879.
They were relatively new even in his childhood.
During this whole time until very late in the 19th century,
there were no coordinated time zones.
There was nothing like Eastern Standard Time or Pacific
Time or Central European Time.
Each town set its own local time.
And all the residents could coordinate
by agreeing that we'll use that clock tower, either
some municipal building or often a tall church in the town
square, say that's our local time.
We'll set our local watches to when
that clock chimes 12:00 noon.
So each town kept its own local time.
And before railway, who would ever need anything else?
Because one was rarely encountering more than one
town in a given day.
After the advent of railroads, you still have this local time.
But that became more and more of a problem.
It was true in North America as in Europe
and other parts of the world, as well.
So here, closer to Boston, passengers
riding on the train between Boston and New York
during this time would have to change their watches
by an average of 37 minutes.
Today we're all in the same time zone.
But that's how different the local variations
tended to be just up and down the US
portion of the mid-Atlantic seacoast
and likewise throughout Europe.
That was becoming more and more of a problem
when you have to coordinate lots of trains traveling
across large distances.
It wasn't only a problem for commercial railway
or for shipping.
It became a very potent, added challenge in Germany
during Einstein's youth.
So again, as many of you may know,
there only became one single country
of Germany, a unified Germany, in 1871 following
yet another war with France.
That was basically the story of the previous 500 years,
German-speaking lands fighting with French-speaking ones.
There was another one, the Franco-Prussian war,
throughout 1870.
The German-speaking folks prevailed.
And it was at that moment, in the wake of that war,
that there was then a first unification
of a country of Germany, now a much larger expanse of what
had otherwise been independent German-speaking territories.
So now there's an added reason to worry
about trains that have to be coordinated across distances.
There's now a new country's worth
that has to defend its borders all the way from basically
Poland or Russia on the East and France on the West.
And there's a famous quotation from a leading German general,
Count von Moltke, who in the 1890s, 20
years into German unification, is basically saying,
we have a problem on our hands.
We have to coordinate trains for military purposes
as well as commercial, passenger rail, and merchant shipping.
We have a problem with the fact that we
don't have unified time zones.
This is all happening in Einstein's childhood.
Remember, Einstein was born in 1879,
very early in this period of unified Germany
and a new focus on coordinating clocks at a distance.
So one of the main ideas that many clever people, inventors,
came up with throughout Europe and other parts of the world,
as well, was to try to coordinate clocks
and therefore help coordinate train stations
in these different cities.
Now, much of continental Europe was now
being connected by rail.
If the major hubs, if the major train stations
could agree on the time, then you could set your watch then.
And the trains could be better coordinated throughout even
into the hinterlands.
And the main idea that many inventors and entrepreneurs
kind of zeroed in on was to install these so-called
[GERMAN] clocks, mother clocks, central clocks
that you would say were the standard ones.
And then connect those by electromagnetic signal,
either telegraph or, increasingly, radio waves,
literally traveling electromagnetic waves
in the ether.
Some of you might know that the Eiffel Tower, which
is under construction in just this period,
was originally built to aid radio communication.
It was a radio beacon before it was a reason for all of us
to go visit Paris.
There were other reasons before that.
The Eiffel Tower was built really
in this period in large part to become a radio
beacon to broadcast standardized time signals.
And then the idea was you would know
how far you were from Paris.
You know there'd be some delay of when you'd expect
to receive the radio beacon.
If it's 12:00 noon in Paris when that beam was sent,
you have an offset based on how far away you are
and the speed of light that it would take to get there.
So then these very clever folks who
make all these gadgets to both receive
the time, either telegraph or radio wave,
and then implement the offset and then reset
the clock in your next train station clock
and down the line.
So imagine these coordinated sets of coordinates
where you have local clocks at every important location that
are sending and receiving electromagnetic signals
to coordinate the local time.
That's exactly the scenario that Einstein
mentions in the abstract in the opening
pages of his 1905 paper.
He doesn't talk about these patent applications
or about trains in this more practical way.
But it turns out, as my friend Peter Galison shows
in this beautiful book Einstein's Clocks,
Poincare's Maps, this is the subject
of an enormous tech spree.
This was the tech challenge of the day for all these
very smart, young electrical engineers
to build up and patent every bit, every switch and gear,
for this way of coordinating clocks at a distance often
using electromagnetic signals.
Not only that, Einstein was at the electrotechnical part
of the Bern patent office, where a lot of these
were flowing through.
So he was an examiner on many of the little widgets
and gadgets as part of this clock-coordination sequence.
Even better, my favorite part of Peter's otherwise quite
fascinating book, was that Peter and his research assistants
pieced together the walk that Einstein
used to take from his apartment to the office--
he had a lovely stroll through Bern
during this time of his life--
and then finding out when each of the clocks along his route
were wired up to this now coordinated system.
So literally the clocks that Einstein
would walk past between his apartment
and his office were in this exact moment being wired up
in this new, explicit, electrotechnical clock
coordination system, not just across distant train stations
but soon even across the semi-urban regions
where he lived.
It was literally his day job and the path
that he walked to get to work.
So this notion of using electromagnetic signals
to coordinate clocks in a measurable, repeatable way
was of philosophical interest.
It was certainly inspired in part
by the writing of Ernst Mach.
But Einstein was also immersed in a different set of realities
than someone like Hendrik Lorentz
or the other Maxwellians.
And so when he comes to the question of electrodynamics
of moving bodies, Einstein's immersed
in different conversations and day-to-day questions
compared to those of the physics elite of his day.
So we come back to this very iconic but kind of unusual
paper from 1905, "On the Electrodynamics
of Moving Bodies."
I think we can make a bit more sense of it, informed by work
by people like Peter Galison.
Einstein's paper has almost no references.
Much like many patent applications,
you want to emphasize priority and downplay precedence.
Einstein focuses on the operational details.
How would you actually perform these measurements
and compare the answers at some distance?
It starts to look sort of like a patent application,
not like a fancy exercise in mathematical physics.
So we can come back to this question of,
why was Einstein doing things differently?
And what was he up to?
And we see him really enmeshed in just a different set
of ideas, of philosophical conversations,
of mathematical techniques, and also of actual gadgets
compared to some of the other experts of his day.