Okay. 
So we found some, at the, at the cost of 
a lot of time. 
We found some nice property of Newtonian 
mechanics. 
Well, invariant, under these 
transformations of Galilean relativity, 
as observed by one observer and as 
observed by another observer, moving 
relative to the first with a constant 
velocity. 
Physics is the same. 
What makes that a principle is what you 
do when it doesn't work. 
And when it doesn't work is when we 
introduce Maxwell's equations. 
Electrodynamics causes a problem. 
Remember, Maxwell wrote down his 
equations as a description of the 
interactions of electric currents and 
electric charges, and magnetic fields and 
so on. And he found when he wrote the 
right equations, that his equations had 
emitted wave solutions, and he computed 
from known measured quantities the speed 
of those waves, and discovered that it 
agreed with the measured speed of light, 
and therefore, had discovered that light 
was an electromagnetic phenomenon. 
But he measured the speed of light, 
and 
what that means is, now that you remember 
our velocity edition formula, was that 
the speed of light as measured by the 
black observer, or the speed of light as 
measured by the blue observer, they 
should get different results depending 
upon which way they're moving. If they 
both time the motion of a pulse of light, 
they should obtain different results. 
So Maxwell's equations can at most hold 
for one of those observers and the other 
observer must detect different electric 
and magnetic phenomena so that when they 
compute the speed of light they will get 
an answer consistent with their 
measurements. 
A technical way of saying this is that 
the electromagnetism, the equations, 
Maxwell's equations are not invariant, do 
not retain their form when you do the 
change of variables that we call Galilean 
relativity transformations, what we 
computed in the previous clip. 
So there are two possible solutions to 
this. 
I mean look, Newton, albeit with some 
error, computed the speed of sound 
already and sound moves with a speed that 
you can compute and it moves with that 
speed through air, and if you are moving 
through the air or if there is a brisk 
wind blowing, then of course sound will 
move at two different speeds, upwind and 
downwind, because it moves at a constant 
speed through the air and then in 
addition is carried on by the air's 
motion. 
So, the solution that Maxwell, in fact, 
adopt, suggested, 
is that there is something called, he, he 
called the luminiferous ether, 
some medium through which light 
propagates. 
And it's the properties of this, this 
ether that cause light to propagate at 
speed c, much as it is the properties of 
air that cause sound to propagate at the 
speed at which it propagates. 
And Maxwell's equations would then be 
valid for observers at rest relative to 
this ether. 
Just like the speed of sound would be 
measured correctly for an observer. 
If someone is, there is a brisk wind 
blowing, you would measure different 
properties of air, compared to what you 
would measure in a, 
steady, stationary air, and when you are 
moving relative to the ether, the 
velocity edition formula will tell you, 
you will measure a different speed of 
propagation of light. 
The other, much more radical solution, 
which will turn out to be experimentally, 
verifiably correct in fact, is that light 
propagates with a uniform speed C through 
space. 
there is no real ether, no material 
implementation of what the medium through 
which light propagates. 
The medium if you want is space. 
Maxwell's equations, in fact, hold for 
all inertial observers whatever their 
constant velocity. 
Remember an inertial observer is one for 
who Newton's first law holds. 
That means that all inertial observers 
relative to each other, are moving at 
constant velocities. 
We don't know who the rest observer is, 
but we know what the collection of all 
inertial observers are all those for whom 
Newton's First Law works. 
If Newton's First Law works in your, 
measurements. 
Then, when you measure the properties of 
electricity and magnetism, 
you will find that they obey Maxwell's 
equations, 
and therefore if you measured the motion 
of the path of light, you would find that 
it moves at the speed c, and the speed c 
will not depend on your velocity relative 
to another observer. 
This contradicts common sense, so let's 
see why it is that we believe it. 
Indeed the initial idea was that Maxel 
was right. 
There is an ether through which light 
propagates at speed C, and then your task 
is to measure your velocity relative to 
the ether. 
And you can do that by measuring the 
properties of light. 
And you do this with the following 
experimental apparatus. in Einsteinian 
terms it's called a light clock, in 
others an interferometer. 
What you're doing is you will set up two 
mirrors separated by distance L, as drawn 
over here on the right. 
And you will set up a beam of light to 
bounce between them. 
We know how to do this, this is 
technology that was well developed in the 
nineteenth century. 
And you can imagine that over here on the 
mirror on the right there is a counter 
that ticks over. 
We have a pulse of light bouncing back 
and forth, every time the pulse of light 
hits the mirror on the right, counter 
ticks over. 
You now have a clock and it's a good 
clock because the speed of light being a 
constant. 
The time that it takes light to bounce 
back and forth through this 
interferometer is twice the length 
divided by C because that is how far 
light has to travel. 
So this is true if light moves at a speed 
C, in other words, if you're at rest with 
respect to the ether. 
What happens if you take this whole clock 
and, assuming that the transparency is 
addressed with respect to the ether, you 
set this whole clock moving at a speed V 
to the right. 
Well, what that means is that when the 
light beam starts out here and is moving 
to the left, the mirror on the left is 
itself moving to the right, towards the 
light beam. 
The relative velocity between, the pulse 
with which the pulse of light is 
approaching the mirror is, of course, C 
plus V, when moving in this direction. 
Let me use red pen to indicate the motion 
of light relative to this moving, 
interferometer. 
The speed of light in this direction 
would be c plus v. 
This is exactly the addition, velocity 
addition formula we computed. 
On the other hand, when light is moving 
from the left mirror back towards the 
right mirror, then the right mirror is 
receding from it, and the light pulse 
will be closing on the mirror at a speed 
C minus V. 
And so, it'll take a shorter time for 
light to move from here to there than it 
does for light to move from here to 
there, but you can add the two. 
And you can obtain the, time that it will 
take light to move to the left and then 
back to the right by taking the time it 
takes to move to the right. 
plus the time it took to move to the 
left. 
And doing some algebra, you can write it 
this way. 
You see that the faster. 
The clock is moving at the end of the 
day, the longer it will take for a light 
pulse to move back and forth. 
if you think about it that's because it 
spends more time moving at the slower 
velocity because this is a larger number 
with a smaller denominator. 
Okay so moving the clock should slow it 
down so you can measure. 
yeah, but how do you know what the speed 
of the clock is when it's addressed, if 
you don't know what addressed is? 
Remember, it's hard to detect when you're 
addressed. 
well the trick is, that was what the 
clock will measure when it's moving along 
its axis. 
What happens if it moves perpendicular to 
its axis? 
So now we're taking the same light clock, 
except now the motion is with a speed v 
in the up direction. 
So we have those two mirrors and they're 
moving up. 
Of course, now if a light pulse bounces 
off the right mirror and moves directly 
to the left, it'll just go off into space 
because the left hand mirror will have 
moved up in the time that it took the 
light to transverse the, to traverse the 
clock. And so the light beam that we're 
interested in is a light beam that 
bounces back and forth between the moving 
mirrors. So it bounced off the red mirror 
here, hit the mirror on the left here, 
will bounce off and hit the right mirror 
back there, when the right mirror has 
moved up to this position. 
Right? 
So, 
and what we want to know is how long it 
takes light to transverse, traverse the 
clock, when the clock is moving in this 
direction. 
This is a geometric calculation. 
We're going to assume that despite the 
fact that there is a small motion 
relative to the, ether of the light beam, 
that this angle is small enough, or V is 
small compared to C, and to leading 
order, we're going to assume that light 
actually moves with a speed C. 
What that tells us is that if little T is 
the time it takes a light pulse to go 
from here to here, and by symmetry little 
T is also the time it takes it to get 
back so bit T's going to be just little T 
here is half the period of this light 
clock. 
Well we can do a calculation over the 
time little t. 
the light beam has traversed the distance 
ct. 
times t, in the same time the clock has 
moved up by a distance vt, times t. 
So that's this vertical blue segment over 
here. 
The distance between the mirrors is L. 
The, an application of the Pythagorean 
theorem shows us that l squared plus v 
squared t squared is the length square, 
of the length of a hypotenuse. 
We can solve this for t, and we find that 
t is given by this. 
Remember that the period of the clock is 
twice t so we write it down, and we see 
that moving gensferously also slows down 
the clock, but by a different factor. 
Notice the square root here. 
So the light clock slows down by one 
factor when its moving longitudinally by 
another factor when its moving 
transversely. 
If we spin the light clock around and 
assume that the Earth is not at rest with 
respect to the either we should find that 
we measure one 
That we measure a periodic change in the 
period of a light clock as its relative 
motion with respect to the either changes 
in its direction. 
And this measurement was essentially to a 
very high precision by Michaelson and 
Morely in 1887 and their result is that 
there is no change. 
There is no periodic change in the period 
of a light clock and so there are various 
theories advanced how to understand this 
perhaps just as if you measure the speed 
of sound on average north south and east 
west you get the same answer, despite the 
fact that the Earth is rotated to the 
east perhaps the either is being dragged 
along by the Earth. 
Lots of complicated ideas. 
the simplifying Gordian knot resolving 
solution of Einstein proposed in 1905 
because there is no such things as, as 
the ether. 
Maxwell's equations hold at any inertial 
frame. 
Consequences that you have to change your 
rules for velocity addition. 
Galilean relativity needs modification. 
Deep changes in what we think of as the 
obvious properties of space and time are 
necessary, but remember, Newtonian 
physics needs to still be valid, and 
hence, Galilean relativity, in some 
appropriate limit. 
So we're going to take Einstein's idea 
and see what it tells us, and then show 
why we believe it.