thank you brilliant for sponsoring this
video a few years ago while I was still
teaching in the classroom one of my
students asked me this question why is
the speed of light in vacuum this
particular number
299792458
m/s and my instinctive answer to that
was well because it has to be some value
right we just happen to live in a
universe where the speed of light
happens to have that particular value in
vacuum and that's that but for
fortunately that question was stuck with
me and therefore I did a lot of research
and boy my mind was blown because what I
eventually realized is that this number
is not random at all in fact what I
realized is that this number is directly
connected to the Earth's size I kid you
not if the Earth was slightly bigger
than it is right now then the value of
the speed of light in vacuum would have
been smaller and if the Earth was
smaller than as how big as it is right
now
then the value of the speed of light
would have been bigger which means the
reason why speed of light in vacuum has
this specific number is because Earth
has this specific size and I know it
sounds Preposterous as to why the value
of a fundamental constant in the
universe has anything to do with the
size of the Earth well you don't have to
take my word for it by the end of this
video we would have arrived at this
conclusion I would actually walk you
through the series of questions that I
thought about and make my thinking
process clear and then you conclude and
you tell me whether the conclusion makes
sense or not all right so if you're
excited about this let's begin okay so
where do we start well we start by
looking at the fact that the speed of
light value in vacuum this number is an
exact value here's what I mean if you
were to look at the measured value of
some constants like say the
gravitational constant then you would
notice that you probably know about this
number right then you would notice that
the value is not exact there's always
some uncertainty uncertainty over there
it's usually not mentioned but there's
there which means the last few numbers
we are not very certain about it and we
don't know about the numbers that come
after this and that's the case for
anything that you measure whatever
you're measuring there'll always be some
uncertainty at least because your
measuring devices have a limit for
example if you're measuring something in
centimeter using a centimeter scale you
will have uncertainty at a millimeter
range if you're using a millimeter scale
you'll have uncertainty in a micrometer
range and so on and so forth so always
all all measurements will have some or
the other kind of uncertainties but the
speed of light this has no uncertainty
why because this is not a measured value
this value was fixed by Humanity here's
what I mean if you shoot a beam of light
and just wait for exactly 1 second the
distance that the light travels in 1
second is fixed as this number we say
that whatever this distance is we have
called it to be 299792458
M it's not a measurement we have
accepted that this is the number we're
going to call that distance why do we do
that because this is how we Define a
meter you see in our daily life you
don't think about it but if you to ask
me mahes how big is actually a meter I
might say it's about yay big but how big
is this what's the precise definition of
how big a meter is this way a precise
way of thinking about what a meter is is
that we would say that hey if you wait
for 1 second whatever distance light
travels by definition it is 299792458
M which means you take that distance
divide into so many parts and then each
part is exactly exactly one meter that's
the current definition of the meter that
is the system international definition
of the meter today so since the meter is
defined using the speed of light the
speed of light is exact but why why are
we using speed of light to Define our
meter well because speed of light in
vacuum is a fundamental constant speed
of light in vacuum does not depend upon
any reference frames which is awesome
which means anybody who does this
experiment will always get the same
value and therefore tomorrow if we lost
our meter sticks anyone can refine
recreate our meter stick by using this
definition of the meter but now we can
come back to the original question that
my student asked her question was why
did we fix this number to be this much I
mean we could have fixed the number to
be anything that we want but why this
ugly looking number I mean at the least
we could have rounded it off to a very
nice number like 300 million which we
often you know approximated to then why
did we do this ah the thing is this
definition of the meter happened very
recently about 40 years ago somewhere in
1980s we defined the meter this way
before this we had a different
definition of the meter and to
understand why we fix this we have to go
back in time and look at what that
definition was if you go back about 140
years ago the definition of the meter
that we had just built was this we made
a meter bar like a sacred meter bar we
kept it in France and we said you know
what the length of that meter bar we
called it 1 meter exactly not the entire
length the length from the marking so
here so that you know even if the ends
get damaged it's fine but anyways about
140 years ago this is how we had defined
what a meter was that the length of that
particular bar which is kept in France
that's a meter and since we wanted to
make sure that other countries would
also have access to this we made copies
of this we made replicas of this and we
distributed to many countries including
the United States by the way they agreed
to use the metric systems 140 years ago
just saying just saying but anyways
that's how we use the that's how we
Define the meter for a long time but you
can see the problem with this right
first of all if you're making replicas
of this you can always have errors
regardless of how careful you are the
copies will not be ever perfect which
means different countries have slightly
different definition of meters but also
the length of an object depends on the
temperature so even if you keep it in a
wall with com Perfect Temperature
Control whatever it is there will be
minor fluctuations in the temperatures
and because of these fluctu and
temperatures the length of the meters
would keep changing now again this is an
exaggeration but you get the point right
having a physical object is really bad
but guess what we were able to pull it
off for about 100 years right because we
did a really good job at it and this is
exaggerated first of all we made sure
that the temperature variation did not
happen because we made it out of a
particular alloy a platinum iridium
alloy which had really good resistance
to you know thermal changes resistance
for the length changes due to
temperature and you can look at the
shape of this it was engineered in a way
that you know the shape is in such a way
that it can really resist twisting and
bending and all of that but at the end
of the day it is still uh physical
object so if it gets destroyed it can
get destroyed then we would have we will
no longer have a meter and that's the
reason why we had to change it but
anyways you know when we had used this
as a definition of the meter okay
according to this definition of the
meter the speed of light the most
precise measurement of the speed of
light happened to be 299
792 4
56.2 with some uncertainty m/ second
second and then once we had the
technology to measure the speed of light
so precisely we said hey you know what
it's time to get rid of this prototype
it's time to get rid of this thing and
instead of defining meter this way and
measuring the speed of light this way
let's fix a speed of light to some
particular number very close to this and
then redefine meter and that's why we
fix the speed of light to a number close
to this so close to this and that's why
we have 458
I know you may be wondering why is it
4558 and not 457 I don't know about that
if anybody knows about that please let
me know so putting it together why did
we fix the speed of light to this
particular ugly number because we wanted
to make sure that it's as close as
possible to the measured value based on
the previous definition of the meter
this way the new definition of the meter
becomes as close as possible to the
previous definition of the meter but now
comes the most important question of
this video the highlight of this video
who decided how big this meter should be
how do we decide how big this Platinum
idium alloy should be to answer that
question we need a revolution what am I
talking about well a revolution that'll
actually allow you to dig deeper into
any subject by asking questions like
this using brilliant.org the sponsor of
annual subscription so do check it out and now back to the video so how did we
decide how big this meter should be what
was it based on well it was based on the
size of our planet if you go back even
more 100 years about 230 years ago the
French Revolution happened they were
tired of so many things but one of the
things that they were tired of was
people using their own units some people
were using foot to measure the length
some people were using somebody's waist
size which you call the yard by the way
to measure the to measure the length of
things so everybody had their own units
and people were so tired of it they were
like okay I we want a single unit in
fact they were so ambitious they said
that we want a unit that can be globally
used by everyone and therefore they came
up with a new unit for length the meter
the meter was invented and the word by
the way meter comes from the Greek which
means to measure so in some sense they
chose the most pure word that they could
think of for this particular unit but if
we wanted this to be a global unit like
everybody would accept then it had to be
based on some standards that everyone
would accept what could it be what
reference could we use to define the
meter well let's use the globe they said
let's use the size of the Earth itself
to Define what the meter is because
everybody lives on earth right so we
said let's call the distance from the
equator to the North Pole through Paris
it has to be via Paris but let's call
that distance to be exactly 10 million M
or exactly
10,000 kilm this was the very first
definition of the meter but before we go
forward you may be curious about why we
decide to call this distance to be 10
million M why not 1 million or why not
in something else at this particular
point we're going so back into time that
I don't even know if we really have
records that rationalize and give us
reasons for why we did this but I did
find something very funny okay so
apparently we were so the Frenchmen were
so so tired of the old system they
thought that they're going to go change
everything to metric system in fact they
thought that you know what even a day
should not have 24 hours it should have
10 hours and one hour should not have 60
Minutes it should have 100 minutes
completely metric even if you take the
right angle which is 90° they thought no
no no let's call it 100 100° and each
degree is a 60 Minutes well they said no
no no let's say each degree has 100
minutes and this is where it gets
interesting if each degree has 100
minutes then the total number of minutes
in the right angle would be 100 * 100
10,000 Minutes right and so since a
right angle has 10,000 Minutes that's
where they probably decided let's say
that each minute will subtend an arc of
1 kilm so this whole right angle will
subtend an arc of 10,000 kilm and that's
probably the reason why they decided it
to call it
10,000 kilm now again I don't know how
true that is but at the end of the day
what's important is that it's a round
number right and that makes sense that's
great for us that the first definition
was a round number which makes sense by
the way although we started adopting the
metric system when it comes to length
and so many other units we did not adopt
it for angles we did not adopt it for
time so that's the reason why we still
have 24 hours and we still have 90° but
anyways what they did after this was
there were a couple of Frenchmen
actually went on expedition to actually
measure exactly how much this distance
is you know in the older units and they
did the conversion whatever distance
they found out to be in their old units
they equated it to 10 million meters and
from that they decid they figured out
how much one meter should be and from
that they created finally the Prototype
earlier meter prototype was made of
different Metals then we realized that
it was not was not good and so we
finally changed it to the Platinum
iridium alloy so where did this
definition of one meter come from from
the size of the Earth and it's from
there the speed of light was calculated
and finally from there we redefine the
meter by fixing the speed of light to be
this value and so now think about this
what if the Earth was slightly bigger if
the Earth was slightly bigger would
probably think nothing would have
changed they would have probably still
decided to call this distance to be 10
million m i mean of course you would
argue that if the Earth was slightly
bigger maybe you know the humanity
wouldn't have evolved at all maybe the
animals would have evolved species would
have evolved completely differently but
that's that's not worry about that you
cut me some slack over here okay but if
they was slightly bigger then we would
have still called this 10 million M then
the size of our meter would have been
slightly bigger right because the Earth
is bigger this distance is bigger if the
size of the meter would have been
slightly bigger then the speed of light
that we would have eventually calculated
would have been slightly smaller in
meters per second right because the
length of the meter is more than the
speed of light I mean this the the
physical distance that light travels in
1 second would be the same but if the
meter size is Big then that distance
travel in terms of that meter that would
have been smaller and if this number
would have been smaller then obviously
the number that we would have fixed
would also have been smaller smaller so
right in front of your eyes you can see
if the Earth was bigger we would have
gotten a smaller number and similarly if
the Earth was slightly smaller then the
meter stick then meter definition would
have been smaller and then we would have
gotten a slightly bigger
number and that's what I told you at the
beginning of the video the reason why
the number happens to be exactly this
number is because Earth happens to have
this specific size booah so what do you
think about this perspective for me this
is a big reminder that um you know the
values of the fundamental constants of
our universe is deeply connected with
our measuring systems which is in turn
deeply connected to the world that we
live in not only is it not only its
political history but even the physical
size of it that I find is truly profound
okay see you