all of it intuitively. So if you're ready for this, let's begin. We have
theories for why things fall down for
thousands of years. For example,
Aristotle believed everything naturally
tends to move towards the center of the
universe, which is obviously the earth.
Meanwhile, Brahmagupta in ancient India
used the term guruta,
a Sanskrit word meaning attraction due
to heaviness. That's pretty cool if you
ask me. So these ideas were pretty
impressive for their time, but they were
still pretty vague and local. For a long
time, we believed the laws of the earth
were completely separate from those that
govern the heavens. But starting in the
1500s, all of that changed very quickly.
Copernicus helped replace the earth with
the sun at the center. Galileo made
breakthroughs in inertia and motion, and
Kepler uncovered stunningly accurate
features of planetary orbits. for
example, that they were ellipses, not
perfect circles. At the time, these were
all disconnected thoughts. They had no
broader significance. That is until a
young man stuck at home because of a
plague, decided to do something about
it.
In 1665, one of the deadliest plagues
swept through London, killing up to a
100,000 people, nearly 15 to 20% of the
city's population. As a precaution,
Cambridge decided to shut down, sending
students home and halting their studies.
One of those students was a young man
named Isaac. Isaac Newton. For the next
couple of years, Newton was pretty much
stuck at home. But free from exams and
lectures, he could pursue whatever he
wanted. And so he did. And what followed
is arguably one of the most creative
bursts in scientific history. Historians
call it Newton's Anos Morabilus. his
years of wonder. During this time, he
laid the foundations of calculus, showed
that white light was made of rainbow,
and most importantly for our story, he
began connecting Galileo's earthly
insights with Kepler's heavenly ones.
Years later, this would lead to his
universal theory of gravity published in
the legendary Principia.
And here's that book, Principia. Okay,
actually it's a copy of it translated in
English. But if we go to volume three
here, you can see that he proposes that
the planets experience a force towards
the sun that drops as 1 / r². I find it
fascinating because this is the copy of
the original text that for the very
first time wrote it down in the history.
Oh my god, that's amazing, right?
Anyways, and over here you can see he
proposes that that force must be
proportional to their masses. In other
words, the law of gravity we all learned
in school. And this was radical because
for the very first time, we had a single
unified rule, a rule that can be applied
both to the Earth and the heavens.
It didn't just explain orbits or how
things fell, but also the tides
predicted the return of Haley's comet
and a couple of centuries later even
helped discover a brand new planet,
Neptune, purely from the math.
But it didn't stop there. As our
instruments got sharper and sharper, our
cosmic reach got deeper and deeper. And
Newton's laws passed every single test.
from binary stars to galaxies
themselves. Every observation just kept
confirming Newton's law of gravity. That
is until a young man who had already
shattered the old ideas of space and
time started doing some experiments in
his head.
That man was Albert Einstein. At first,
he found some cracks in the universal
law. But as he went deeper, the whole
framework shattered. But Einstein, why?
What made you look at one of the most
successful unified model of the universe
with so much observational evidence and
then say, "Nope, Newton must be wrong.
Gravity is not really a force. It's just
it's just a manifestation of
four-dimensional space-time curvature."
I mean, that's inconceivable.
And Ein says, "Mah, it's kind of like
solving a puzzle one piece at a time
25% off on your first payment. Okay, happy coding. Back to the video. In
1905, Einstein published a series of
papers that would redefine physics
forever. It was Einstein's anis
Morabilus. One of those led to special
relativity. It replaced Newton's old
ideas of space and time and predicted
that mass is just confined energy which
led the groundwork for particle
accelerators helped understand how stars
shine and helped humanity harness
nuclear power.
But there was a problem. Special
relativity and Newton's law of gravity
were incompatible.
But why? Well, Einstein says according
to special relativity, no information
can travel faster than light. But
Newton's gravity is instantaneous. So if
the sun were to disappear, then the
gravitational force on Earth would
instantly be zero and it would
immediately feel the change. This
violates special relativity. Okay,
Einstein, but can't we just modify
Newton's laws to fit special relativity?
And Ein says he thought that too until
he had the happiest thought of his life.
Imagining a man falling to his death.
Why Einstein? Why is that the happiest
thought of your life? And Einstein says,
"Mes consider this. When you're in an
airplane and that airplane is taking
off, it accelerates forward. You feel
pressed backwards." Right? Similarly,
when you're in a car taking a turn, you
accelerate inwards, but you get thrown
outwards, which means every time you
accelerate in a particular direction,
you feel a jolt in the opposite
direction, right? And I'm like, yeah,
that makes sense. Okay. Now, he asks,
Mah, but what about when you're falling?
Because when you're falling, according
to Newton, you are accelerating down at
9.8 m/s squared. But Mahesh, do you feel
it? Like in the other cases, even here,
do you feel a jolt in the opposite
direction?
I remember skydiving a few years ago in
Switzerland. It was honestly pretty
amazing experience.
But when I jumped, the moment I jumped
from the plane, I felt nothing. No
jolts. Totally weightless for a few
seconds until the air started pushing.
And by the way, this is also the reason
why I puke later on because of the
zerog. But the point is, no, Einstein, I
didn't feel a jolt. So I don't think you
feel a jolt when you're falling. And
Einstein asks, why not? I mean, you are
accelerating down. So why don't you feel
an opposite jolt like we feel in the
other cases? And I'm like, wait, I know
the answer to this. If you go back to
the airplane for example, the seat
pushes and accelerates my body first,
but my head wants to stay in place due
to inertia. Remember, a head at rest
tends to stay at rest until my neck
pulls it along. So, there is a lag and
that's why I feel a backward jolt. And
the same thing happens with a car. When
I take a turn, the friction between my
butt and the seat pulls my lower body
first towards the center. But my head
tends to move in the straight line
because of its inertia until my neck
starts pulling along with it. And that's
why again because of that lag, I feel an
outward push, an outward jolt. And fun
fact, this is the reason why F1 drivers
have enormous neck muscles. They need it
to withstand huge turning forces. But
coming back to the point Einstein,
gravity is different.
While I'm falling, if I were to drop an
apple, that apple would fall along with
me because gravity accelerates every
single thing at the same rate regardless
of its mass. Close to Earth, that is
about 9.8 m/s squared. So when I'm
falling, every single part of my body is
accelerated at the exact same time and
the same rate, 9.8 m/s squared. That's
why there is no lag, Einstein. And
that's why I don't feel an opposite
jolt. And that's why I feel weightless,
but the acceleration is there. Come on,
Einstein. This is high school stuff. But
then Einstein asks Mo, why does the
force of gravity accelerate everything
at the same rate regardless of its mass
or material or anything? And I'm like,
because of Newton's second law.
The net force acting on my body while
I'm falling is the force of gravity. And
that equals according to Newton's second
law mass times my acceleration. So look
my mass cancels out and as a result the
acceleration due to gravity is
independent of the mass of the falling
body. And Ein says this is the crux of
the problem. Mahes this mass let's call
it your gravitational charge because it
decides how much gravity you feel. And
this mass, let's call it your inertial
mass because it decides how much inertia
you have, how much you resist
acceleration. These two are completely
independent and different quantities
altogether. And yet for some reason they
happen to be the same. Why? That's not
how other forces work. For example, how
much electric force you feel depends
upon how much charge you have, which is
very different from your inertia. How
much magnetic force you feel depends on
something called your spin. Again, very
different from inertia. And that's how
you know all other forces are. For every
other force, there's a different kind of
charge that decides how much force you
feel. And yet, for gravity, that charge,
gravitational charge, just happens to be
your inertial mass.
Why? Isn't that a little suspicious?
And I'm like, wow, Einstein. They say
that science is about asking the right
questions. And this is at its best. And
this is why I love to understand the
thinking process rather than the facts
themselves. So this is amazing. Anyways,
Einstein is still waiting for an answer.
And so I'm like, maybe that's just how
it is. Maybe there is no deeper
explanation for that. And Einstein says,
Mahesh, let's find a deeper explanation
for that. Okay, what do we know so far?
When you're falling, you don't feel your
acceleration. In fact, if you were to
close your eyes, you wouldn't know if
you're falling on Earth or you are in
some deep intergalactic space just
floating over there. And if you had an
accelerometer with you, it wouldn't even
detect any acceleration. Okay? Now,
instead of coming up with some
convoluted explanation like your
gravitational charge just happens to be
the same as inertial mass and that's why
you don't feel it but it's there, why
don't we come up with the most
straightforward answer? If you don't
feel your acceleration and you can't
detect it, maybe it's not there. Which
means maybe when you're falling, you're
not accelerating at all. And I'm like,
uh, hello. There's gravitational force
pulling on me. And Einstein said, okay,
maybe there is no force of gravity. And
I'm like, wait, there is no force of
gravity acting on me. I'm just floating
there. Then why do I hit the ground? And
Ein's like, maybe you don't hit the
ground. Maybe it's the ground that's
accelerating up at 9.8 m/s squared and
it hits you. At first, I'm like, come
on, Einstein. That's crazy. And Ein says
maybe so, but it answers a nagging
question because it's the ground that's
really accelerating up at 9.8 m/s
squared. From the point of view of the
ground, someone standing on the ground,
it gives you the illusion that gravity
accelerates everything down at 9.8 m/s
squared. Isn't that a much simpler
explanation, Mahes?
So, this is where the whole gravity must
be an illusion, you know, perspective
comes from. And this reminds me of
something called the Akams razor which
says often when you're trying to solve a
problem the simplest explanation is the
best. And again you can see that's what
Einstein's that's what Einstein is doing
over here. But wait a second Einstein if
there is no such thing as gravity it's
all an illusion. Why am I feeling my
weight right now? Because Mahesh the
ground and the chair that you're sitting
on right now that's accelerating you up
at 9.8 8 m/s squared. And just like in
the airplane when you were accelerated
forward, you felt an opposite jolt due
to the lag and inertia. Right now,
because you're being accelerated up, due
to your inertia, you're feeling a
downward jolt. And that downward jolt is
what makes you feel like you have
weight.
There is no real force of gravity. What
you feel as gravity is just inertia. And
this is why the gravitational charge in
the Newton's formula of gravity just
happens to be your inertial mass because
there was no gravity. What you've been
feeling all along is just your inertia.
It's no different than the opposite jolt
you feel when your airplane is taking
off. It's the same thing. It's just that
the jolt is downwards and that makes you
feel like you have weight.
That is insane. That is crazy. So, just
to be clear, Newton says the ground is
inertial, not accelerating, and it's the
falling things that are accelerating.
But Einstein says, "Nope, it's the
falling things that are inertial, not
accelerating. It's the ground that's
accelerating upwards, making everything
stick to the ground." But wait a second,
both models seem plausible. How do we
know who's right?
Well, we need an experiment to tell them
apart and there isn't any. So, both
points of view are equally valid and
therefore Einstein calls it the
equivalence principle. So, his big claim
is that being in an accelerated frame is
indistinguishable from being in a
gravitational field. This seems to be an
extension to Galileo's relativity.
Gallio figured out that rest and
constant velocity motions are the same
thing. Look from different points of
view. Now Einstein takes it to the next
step and says maybe acceleration and
gravity are also the same thing just two
different points of view. So he's trying
to generalize things. But hang on
Einstein your equivalence principle has
a big problem. First of all earth is
round. So if uh the the ground is
accelerating up in all the directions,
shouldn't the earth be expanding?
But there's another issue. Falling
things also stretch and squeeze. It's
just that for small things, we don't
notice it. But if there was something
huge like an asteroid hurling towards
the earth, it would stretch
significantly. Sometimes it can even
tear the asteroid apart. And it's not
just the asteroids. Even the Earth and
Moon fall towards each other and they're
pretty big. So they too significantly
stretch. and squeeze and on earth this
effect is what gives rise to tides.
That's why we call this effect the tidal
effect.
Newton's model where you consider
gravity as a physical force can explain
this beautifully. Gravity gets stronger
closer to the earth. So if you've got a
big object like an asteroid, this part
feels slightly stronger pull compared to
this one. So this part accelerates more
than the part behind. And look, that's
what stretches the asteroid. And the
math works out and it nails the
explanation for tides. But Einstein, you
say there is no such thing as
gravitational force. According to you,
this asteroid is just floating.
Absolutely no forces acting on any parts
of it. No accelerations at all. So how
do you explain the stretching? You can't
explain the title forces, buddy. Your
equivalence principle breaks. What you
got to say about that? And Ein says,
"Yeah, you're right. This means that the
equivalence principle is only valid
locally in small regions where gravity
can be assumed to be uniform. But in
large regions where the gravitational
field varies, it cannot explain the
title effects. And so I struggled with
this problem for nearly 5 years. But
then I had a breakthrough. I found a way
to explain how an asteroid can stretch
even without any forces acting on it.
How how is that even possible? Einstein
and Ein says, "Maysh, first let's bring
this problem into my territory. Let's
draw a space-time diagram for that."
Now, a quick refresher. If a small rock
is at rest in space, it's still moving
in time. So, its graph is straight and
vertical. We call this the rock's world
line. If the rock's moving at a constant
velocity,
it's still straight but tilted. So look,
inertial motion always give you straight
world lines. But if the rock
accelerates, that world line curves.
More the acceleration, more curved the
world lines. So remember in spacetime
straight world lines are inertial non-
accelerating. And curved world lines are
accelerating.
Okay. Now according to Newton, we can
consider the ground to be inertial.
Let's assume it to be at rest. and the
falling person is accelerating towards
the ground. So their world line curves
but in Einstein's model the falling
person is inertial say at rest. So their
world line is straight and it's the
ground that's accelerating up. So far so
good. But what if a big asteroid is
falling? In Newton's model, the front of
the asteroid being closer feels stronger
gravity. So its world line curves more
than the back. That's why it stretches.
This is the tidal force. And we know
this is a fact. So the same thing must
happen in Einstein's model as well.
Somehow these points on the asteroid
must also move further apart. But wait
Einstein according to you that asteroid
is inertial. There are no forces acting
on it. Which means I can assume that all
the parts of that asteroid are at rest.
So the world lines of these two points
should be vertical and parallel. There
should be no curves, no acceleration.
And yet somehow the asteroid should
stretch. Meaning the distance between
these vertical parallel lines should
increase.
How can the distance between parallel
lines, straight lines increase without
curving? That's impossible. Einstein
and Einstein says, "Mahes, that's not
the attitude we have over here. Don't
say it's impossible. If you want to have
breakthroughs, instead ask, how can I
make this possible?"
And I'm like, "Okay,
how can we make parallel straight lines
move farther apart without curving them?
How is that how can we make that
possible?" And Einstein says, "What if
we drew them on a globe? Imagine
two people walking north from the
equator along the lines of longitude.
They start off parallel and they are
walking as straight as possible. No
turning, no curving. And yet they slowly
move closer together. Why? Because the
surface itself is curved. On curved
surfaces, look, straight pots can come
closer. Now if the surface was like a
saddle then the straight parallel paths
could also drift apart and I'm like wait
wait wait these are not straight lines
Einstein these are curves I mean the
line of longitude is a part of a circle
so isn't this doesn't apply over here
right and Einstein asks mish what's your
definition of a straight line and I'm
like well it's the shortest path between
two points and says well a line of
longitude is a shortest path between say
the two poles of the Earth. So it fits
the definition of straight line. Now to
avoid this confusion with this whole
straight terminology, the shortest path
between any two points is in general
called a geodisic. Okay. So long story
short, on a flat piece of paper, if you
draw two parallel geodisics, they will
have to stay equidistant.
But on a curved surface, parallel
geodysics can converge or diverge or do
whatever they want.
So coming back every tiny part of this
asteroid including these front and back
pieces are inertial. Right? If we assume
it to be at rest then their paths
through spaceime must be straight
geodiesic and parallel. Right? Now we
know the asteroid stretches. So I want
these parts to move away but still stay
a geodeic.
There is only one way that can happen.
If the underlying spacetime itself is
curved then like on a saddle parallel
geodysics can diverge.
This is how we can explain the asteroid
stretching. Even though there are no
external forces acting on it, it
stretches because even though there are
no forces, these inertial world lines
are on a curved spaceime drifting apart
making the asteroid stretch. This is how
Einstein concludes by analyzing the
tidal forces that our spacetime must be
curved. Isn't that amazing? I mean, oh
my god, this is how it happens.
Einstein, this is amazing. But I still
want to circle back to the question that
I asked earlier. If the ground is
accelerating up, shouldn't the Earth
expand over time? And Ein says, "All
right, let's draw a spaceime diagram one
more time. Without any mass, spacetime
is flat. That means two parallel
geodisics like the world lines of these
two apples at rest for example will stay
parallel. So the distance between them
stays constant. What happens when we add
the earth? Now in Newton's model,
spacetime still stays flat. The earth
pulls on the apples curving their world
lines inward. So look, the apples
deviate from their straight inertial
paths. they accelerate. That's gravity
as a force. But in Einstein's model,
there is no force. Instead, the Earth
curves spacetime itself. So these
parallel geodysics don't stay parallel.
They converge. The apples are now just
following their inertial paths, straight
lines in curved spacetime. On the
diagram, those paths look curved, but
they're not accelerating. That curvature
is just what straight looks like in
curved spacetime. Now zoom out and look
at the opposite ends of the earth
mahesh. Their geodisics should also
curve inwards curve because spacetime is
curved. So if these two pieces of earth
were inertial they too would move
towards the center but they can't
because the earth's matter below resists
it. So it constantly pushes them
outwards accelerating them away from
their inertial geodic.
So on the diagram these world lines look
straight but they're accelerating.
That straight line is just what an
accelerated path looks like again when
the spacetime itself is curved. So look
Mah in curved spacetime earth's surface
must be in a constant outward
acceleration just to maintain its shape
otherwise it would collapse inwards. By
the way it's similar on the globe. If
these two now want to maintain a
constant distance between them they have
to move away from their geodics. So look
they have to keep moving away from each
other just to maintain their distance.
And this kind of makes sense right
because the curvature naturally tends to
bring them closer. So if they don't want
to come closer, they have to move away
from each other. Similarly, the ends of
the earth have to be accelerating away
from each other outwards just to
maintain the shape in the curved
spaceime. And because of that outward
acceleration, people on the earth feel
their weight due to their inertia.
So can we now summarize Einstein's
thinking process that led him to this
whole idea of curved spacetime? First,
freely falling objects all accelerate at
the same rate regardless of their mass.
He finds that very suspicious. He
doesn't accept the whole gravitational
charge must just happens to be the same
as inertial mass. He says, "Let's keep
it simple since falling folks don't feel
or measure any acceleration." He claims
that falling can be treated to be
inertial and gravity is just equivalent
to acceleration. And as a result, he
concludes that gravity must not be a
real force. It's just an illusion. But
that doesn't explain why falling objects
get stretched. So the next crucial step
is he rephrases that problem using
geometry. He realizes that asking how
can a floating object with no forces on
them stretch is the same as asking how
can parallel straight lines move away
without curving. I find that a stroke of
genius because that he rephrased the
problem um you know in in in terms of
geometry a physical problem in terms of
geometry and that's amazing if you ask
me and finally he connects all the dots
and realizes on curved surfaces parallel
lines can drift apart without curving
themselves and so the same thing must be
happening over here and that's how he
explains the title forces by saying
spaceime itself must be curved we just
rediscovered the step-bystep thinking
process that planted the seeds for
general relativity. But this is just the
tip of the iceberg. I mean, Einstein got
stuck again.
So, let me know if you want to dig
deeper. There is so much more to
rediscover over here. Stay tuned.