What is the maximum Bandwidth? - Sixty Symbols

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

Channel: Sixty Symbols

Views: 779,000

Keywords: sixtysymbols, bandwidth, www, internet, fibre optic

Id: 0OOmSyaoAt0

Length: 11min 38sec (698 seconds)

Published: Thu Oct 03 2013