right now i'm standing here like a plank
plank length yes what is the plank
length well the first thing to say about
is very very small
and physicists tell us that
it's the smallest length scale
imaginable really the subject today is
the plank length now this is a length of
a plank but this is not what a plank
length is this is about 1.6 meters it's
the height up to about my nose
so that's 1.6 meters
and i want to talk about something which
is a bit smaller well a lot well i can't
give you an idea of how much smaller it
is suppose i take this length and i chop
it into ten equal sections and now that
i take this tenth and i divide that up
into ten one two three four five six
seven eight nine ten and so then i take
this small piece here i can't show you
any more because it's going to be a tiny
little sliver down there that's chopping
it three times in order to get down to
the plank length i had to chop this
35 times that is do this process of
contracting by a factor of 10 35 times
so it goes down to 1.6
10 to the minus 35 meters an
unimaginably small quantity you can see
this length coming down to that that you
can visualize but seeing it done 10 to
the
35 times is ridiculous this is a length
which is smaller than the size of a
proton
by a factor of 10 to the power 20. let
me write it down and do you have to have
to do all these 35 with them
one two three four five six and eight
nine ten and so on and 35 of those zeros
now i'm going to write this number down
so you can see how ridiculously small it
is it's not naught point
no no no
no
that would be five zeroes it's that with
another five
oh that with another five and if i stop
there that would be ten to the minus
fifteen meters which is about the size
of a proton the smallest thing that
people can more or less visualize oh no
you can't visualize it we're going to
carry on one two three four
and that's 10 to the minus 20 not not
not nor
that's
i can't work it out i'm going to have
this plus another 10-15
i feel so ridiculous doing all this but
there it is
down there with these extra four
sets of zeros with the one at the end
that's the distance and then it's 1 6.
so in meters
so this is the planck length it's
arrived at by taking three fundamental
constants planck's constant
the gravitational constant big g and the
speed of light now planck was the first
person to come up with this length
because he just invented quantum physics
by studying black body radiation the
history of it's quite strange because
back in the 1880s
max planck and others were thinking
about the heat energy that was heat and
light energy was coming out of hot
bodies and in the course of that he
started getting a feeling for that there
was something quantum mechanical
happening from that he came up with an
idea of
fundamental units for mass length and
time and the
unit of length is called the planck
length so the planck length
is telling you that when you try to
merge the fields of gravity through
newtonian constant big g
with the velocity of light which is
something comes it comes in
electromagnetism
with quantum mechanics and merge them
all together out of it comes somehow a
natural length called the planck length
let's just write down the three
constants then here's planck's constant
h or is it sometimes written h upon 2 pi
which we could signify like this this is
big g the gravitational constant that
tells us why gravity is as strong as it
is why the earth has got its its
strength of gravity on the surface or
it of course big g and the mass of the
earth determines the orbiting of the
moon around the earth and then the other
constant is
uh c now the curious thing is if you
multiply h bar and g
and then divide by c cube the cube c
that gives you the square of a length or
if you like an area and that's called
the planck length so the planck length
if we now take square roots i want the
length itself we take the square root of
that quantity and that then gives me the
planck length
and if you want to talk about the early
stage of the universe
the period before that it expanded to
the planck length we have no idea of the
laws of physics because to do that we'd
have to have a quantum theory of gravity
and none
exist well if they exist they exist in a
form that nobody knows whether they're
right or not
now what does it all mean physically
well
of course this is this
what it's telling us is that perhaps if
we take quantum mechanics and gravity
into account
space itself is not really properly
defined on length scale smaller than the
planck length maybe
space time gets foamy as they say on
these sorts of length scales and then
all the particle physics guys and these
cosmologists start worrying about their
ideas of bubble universes springing out
out of the plank length but you better
go and talk to a cosmologist or if you
get a black hole
for example if i fell into a black hole
i would be spaghettified turned into
long strands of thing and disappear but
as i go into the black hole
all the entropy associated with me my
complete disorder how my hair is untidy
everything about that will be dissolved
in the black hole and in order for the
laws of thermodynamics to hold
the entropy of the universe must
increase and if the black hole is part
of the universe
the total entry must increase and the
black hole must have an entropy and the
person who wrote down the formula for
the black holes entropy originally was
beckenstein and then
um
stephen hawking and he wrote down the
entropy is equal to
boltzmann's constant
times the area of the black hole
divided by four times the planck length
squared so there it comes in in this
model of the entropy of a black hole
and that is believed by most
theoreticians
despite the lack of any evidence to be
the entropy of a black hole so there is
a practical use for this plank length
well if you're a cosmologist or a
particle physicist i have to say in my
everyday work on semiconductors i don't
use it too much but it's great to think
about because it's such a small length