i'm going to talk about bandwidth and
actually just to be really old-fashioned
about this it's 60 symbols video and
it's got a symbol which would be delta f
because it's a range of frequencies
essentially what bandwidth is it is
related to
the amount of information you can get
down the fiber so you know the bandwidth
of your broadband is telling you how
much information you're actually getting
there it's largely limited by how much
you're prepared to pay your broadband
company
but there's a sort of fundamental
physics limit as to how much information
you can actually get down say a piece of
fiber optic cable you can apply this
concept to anything to sounds to radio
waves to light down a
optical fiber whatever you like but the
idea is the same which is that
essentially light sound whatever comes
in waves right and the classic sound
wave or light wave is a sine wave a
little app here which will produce
a tone there we go
there we go
that's a sine
wave and there's no information content
in there at all right you can't use that
to actually transmit information if you
actually want to convey information in
particular if you want to convey digital
information you need ones and zeros and
that essentially means you need pulses
you can't do it with just a sine wave
like that you need a little you know a
beep and then nothing then beep then
nothing you need you need to break it up
into pulses
and you can't do that with a single
frequency because a single frequency
always sounds like that it's just a
single tone professor couldn't you turn
it on and off
i could turn it on and off but actually
then it wouldn't be a single frequency
anymore let's back up a little bit okay
let's do something a little bit more
sophisticated which is so there's my
tone and i've got brady's iphone here my
phone is tuned to produce a tone of a
kilohertz 1 000 hertz and i've set
bradies up to produce a tone of a
thousand and one hertz okay so you know
we can play bradys
that's what a thousand one hertz sounds
like
and that's
and that's what a thousand hertz sounds
like
really very similar not very much to
tell between them the interesting thing
that happens is if we play them both at
once
and if you listen carefully you can hear
that there's this strange beating effect
that it's sometimes louder sometimes
quieter
but one way might make it clear is if i
change the frequency a bit you'll hear
that the beat change so if i take
brady's phone from a thousand one hertz
to a thousand and two
you'll hear that the beats get quicker
so let's turn off the annoying noises
for a moment please so
physically what's happening is you've
got these two waves of slightly
different frequencies and that means
they're just kind of over time drifting
in and out of phase with each other and
when they're in phase the waves all add
up and you get a louder sound and when
they're out of phase the waves cancel
each other out and then it goes quieter
again so you get these beats of loud and
quiet and what i really want is i just
want one of those beats i don't want a
whole series of them i want kind of one
one blip and i can't quite do that with
only two frequencies well i've got only
got two frequencies here but if i had
lots of frequencies then actually i can
produce a single beep a single blip okay
that's not because then basically
everything agree you know adds up
incoherently at one point so you end up
with lots of sound there but then it
destructively interferes everywhere else
so i can produce a single little pulse
of beep
and that's really what i want to do if
i'm going to convey information
digitally i want to send a whole string
of these beeps but in order to do that i
needed to combine different frequencies
together right it wasn't just one
frequency it was a whole range of
frequencies
and there's this very simple
relationship between the range of
frequencies i add up and how short the
beep is and essentially so let me write
this one down so essentially if i've got
a range of frequencies
delta f and i'll produce pulses duration
delta t so the bit the bleeps i end up
producing the product of the two
always comes out to be approximately
equal to one and so you see
if i want to produce very short pulses
if i want to produce you know if i want
to pack a lot of information in a finite
period of time i want to produce very
short pulses i can produce you know a
whole load of code in a very short
period of time so you can see from this
formula if i want delta t to be small
and the product of delta f and delta t
has to be one as this term gets smaller
the only way i can do that is by making
this term bigger in other words to make
shorter and shorter pulses of sound or
light or whatever it is i need a wider
and wider range of frequencies to do it
and the fundamental limit to putting
information down a fiber optic cable is
what range of frequencies can i put down
because although a fiber optic cable you
know it'll probably let blue light go
through and red light go through it
won't let x-rays through or radio waves
through it's just not you know optical
fibers don't work that way and so
there's a finite range of frequencies a
bandwidth
of light that i can put down a fiber
optic cable and that fundamentally
limits how short a beep i can send down
how short a blip of light i can send
down
and that's what limits the amount of
information you can put down the fibre
optic cable so professor when i'm using
the internet and i get a one is that
what's happening to create the one
they're interfering all these different
colors of light except a certain one to
so if some of that if some of the path
between you and whatever server is that
you've got that one from is down a fiber
optic cable that's exactly what's
happening a little blip of light has
been sent down that fibre optic cable to
represent the one
and to produce a little blip of light
you need a whole range of frequencies of
light to do it it's not just a single
color they can't just switch something
on and off but eat like morse code okay
so that's the weird thing right even if
you've got
supposedly so everyone thinks like a
laser produces light every single color
okay single wavelength single frequency
actually that's only true if you leave
it on forever if you leave it on forever
so you're not switching then you do
indeed have a sine wave that goes on
forever and that is indeed strictly a
single frequency as soon as you switch
it on and off over some finite period
it's no longer a single frequency
so even a laser so let me again maybe a
picture will help with this right if
i've got my light you know my light wave
that goes on and on forever that really
is if i were competent at drawing a
single frequency a single wavelength of
light if however i just switch it on for
a little while
so it's off then i've got a pulse of
light
and then it's off again
okay this no longer has a single
wavelength associated with it it looks
like it because you can see well it's
going up and it's going down but
actually to produce something like this
this is clearly different from this and
to go from having a real single wave to
having this i've got to add a whole
bunch of waves together of slightly
different frequencies to produce
something like this and so this is
actually the superposition of a whole
bunch of slightly different frequencies
even a laser which you think of as well
it's a single wavelength of light if you
switch it on and switch it off again
you've actually produced a pulse of
light that has by its nature to contain
more than one frequency if i have a
laser i can just switch it on and off i
don't have to do anything clever i'm not
saying oh i'm producing a little bit of
this red light and then this little bit
that's a bit bluer and this little bit
that's a bit redder in order to make a
pulse right nature does all that for you
that actually by switching it on and off
the laser instead of producing this
single wavelength of light is actually
producing the right superposition of
wavelengths of light to make a pulse
so there are a bunch of engineers and
experts that had to come up with a way
to make all these things interfere and
no no no it's all done you know that
nature that takes care of it that just
by switching the thing on and off at the
right wavelength sorry
the frequency you want to switch things
on and off at so at the you know
producing pulses that by its nature
produces light which is no longer a
single wavelength but it turns out that
actually there's a quantum mechanical
application of all this as well right
and one of the things that people know
about quantum mechanics is this
wonderful thing called the uncertainty
principle that says there are various
things that you can't measure at the
same time so you can't measure the
position of a particle and its momentum
at the same time
and one of the other
forms of the uncertainty principle is
that you can't measure the time when
something arrives and its energy
at exactly the same time so if you
measure the energy of something and the
time of arrival then there's an
uncertain you can you can trade them off
against each other you can measure times
very accurately and then you get rubbish
measurements of energy and vice versa
and it turns out this is a simple
example of exactly that and the reason
is we go back to this
equation again for a second that the
frequency here instead of thinking in
terms of of these pulses of light and
the classical picture of waves think
about photons and when a photon arrives
if we've got a pulse of light like that
we know that the light has to arrive
sometime within this time so the photon
we detect is going to arrive within some
finite time rather and so because of
this relationship up here because it's
some finite time of arrival that means
there's also a finite range of
frequencies that that photon can have
what the frequency that we actually
measure for the photon and in terms of
frequencies of light there's a very
simple formula that says that the energy
of a photon
is related to its frequency
by this relation planck's law right that
the energy of the photon is planck's
constant times the frequency of the
light so an uncertainty in the frequency
of the light
then translates into an uncertainty in
the energy of the photon we have this
trade-off right we can either measure
the energy of the photon arrival very
accurately but because of this
uncertainty relation that means that we
can't predict exactly when it's going to
arrive so we don't know what type of
time of arrival will be or alternatively
we can very tightly force a photon to
arrive at a particular time by saying
well we'll switch the laser on and off
very quickly which means we know exactly
when the photon took off which means we
know exactly when it's going to arrive
so we know when it's going to arrive but
because it was then a very short pulse
that means there's a very large range of
frequencies in that pulse which means
the energy we record for the photon is
very large
and so there's this trade-off this
uncertainty relation that says that you
can't measure these two properties of a
photon or indeed any particle
simultaneously you can't measure both
its energy and its time of arrival very
accurately the ultimate limit for how
much information you can squeeze down
the fiber optic cable is set by exactly
this because you might think well you
know i can just keep pushing my pocket
if i want to pack more information down
well i'll just make my pulses shorter
and i can send them through quicker that
way but actually as each time you make
the pulse shorter the range of
frequencies of the light in that pulse
get wider and eventually you're going to
reach a point where that some of those
frequencies are the kind of light that
won't go down the fibre optic cable
anymore so this really is from an
engineering point of view this is the
fundamental limit as how much
information you can squeeze down a piece
of fiber optic cable is set by this
relationship and what is the limit
what's the shortest pulse
ah
i'd have to look it up actually i've got
the calculation if you want to know i
can tell you ah which lecture
that one maybe so it's a few
femtoseconds a few times 10 to the minus
15. so this means for if you've got a
fiber optic cable that just works in the
optical part of the spectrum so just in
terms of rough numbers that works from
kind of blue light to red light it turns
out that the shortest pulse you can send
down that
is about a femtosecond so that's ten to
zero point fifteen fourteen zero's one
so ten to the minus fifteen so that's
the shortest pulse that you can actually
send down that and that that pulse
actually contains light all the way from
the red to the blue end of the spectrum
if you try and make your pulse any any
smaller the range of frequencies will
push you out of the optical part of the
spectrum so you could get zeros where
you were going for a one so you could i
mean basically your pulse would fall
apart you can't make a nice neat pulse
anymore because you suddenly some of the
frequencies you need to make that very
neat pulse won't actually travel down
the fiber at all then it will get
horribly messed up in terms of
data transfer that basically i think it
works out you could send
the ultimate limit as you could send
about a terabyte of data down a fiber
like that in a few hundredths of a
second