We’re gonna talk about error bars and to talk about error bars, we’re gonna use Aero bars. These chocolate bars, I don’t think you get them in the US, we certainly have them in the UK. I’ve eaten a lot of this chocolate in my time. It’s full of bubbles Bubbly delicious goodness. So, we’re gonna actually melt the bubbles. Well, we’re gonna melt the chocolate and we’re gonna do it because we’re gonna measure the speed of light with chocolate. This is an experiment that’s… You go anywhere in the internet, You can find lots and lots of people talking about this experiment, lots of people have done this experiment in the past. It’s not so much the experiment itself. What we’re actually doing this for is to put across the key importance of experimental uncertainties and experimental error bars, and I can almost feel the waves of disgust as undergraduate students or any students who might be watching this because Error bars in first-year are something that we spend so much time teaching students about and let’s be honest, they’re not the most exciting aspect of the science. But they are absolutely key because if you quote a result without quoting an error bar, you’re not even wrong. If I can paraphrase Pauli: without that error bar, nobody knows what your uncertainties are, nobody knows how well you did the experiment. You can’t compare your result with any other experiments. So what we’re gonna do with this chocolate is we’re gonna put it in this microwave sitting in this fume cupboard. I should note that the reason we’ve got the fume cupboard, and we’ve got a smoke detector covered up is that earlier today when I was preparing this experiment, I attempted to do it in my office, and I didn’t cover up the smoke detector and the alarm went off in the building and hundreds of people were evacuated. It was a big deal. It was a big embarrassing deal and the security people are not happy with me. It’s a bit like Willy Wonka’s chocolate factory, isn’t it. Brady: Look at that.
Moriaty: Is there gold? No, okay. Right, that’s what it looks like but we’re actually going to use this side. Some of you will have seen this experiment but for those of you who haven’t, what we’re gonna do: I’m gonna put it in here, we’re going to heat it up and it will melt, if the experiment works, in specific places and the places in which it melts are directly related to the wavelength of the microwaves. So what’s absolutely key if anybody does want to do this is you normally have a little rotating thing, the little spindle (That’s the word, spindle.) that sits in here that rotates the the plate around and rotates the food round. We don’t want that. We want it to sit in one place, and they’d be bombarded so it doesn’t doesn’t move around because I will disturb the pattern. Not that I can see anything. [laughs] We might have to do this again. Let’s see where we are, whether we’ve got any.. oh oh no! Yes, it’s definitely worked. There we go. Yeah, okay one last try. It’s melting it already. There we go, 1, 2, 3. Actually that was 20 seconds. Now it’s gonna take five minutes of course. It’s just a mess, you can’t really see ’em. (Bollocks.) Brady: Oh it smells delicious.
Moriaty: Mhm. It’s worked out okay about as well as the the experiment works. It’s a very good experiment to demonstrate this real importance of uncertainties because so often in science is this idea that science proves this and science proves that and evidence so exact, it’s not. So, they went to the microwave and they were blasted for various times between 10 seconds and up to 30 seconds and as you can see, sometimes well decent imprints were formed and then other times it sort of formed a bit of a splodge. In the microwave oven, you’ve got waves of electromagnetic radiation, and it’s those waves that are given rise to the heating of course. Where you have peaks in the electromagnetic radiation, which are called antinodes, you get a lot of power injected into the chocolate and hence it melts. So what we’re seeing this pattern is an imprint of the standing wave pattern in the microwave oven. Normally, if food spins round on that spindle We disabled that spindle because what we wanted was the opposite of what you normally want in your food You don’t want localized hot spots We wanted localized hot spots because also hot spots tell us about the microwaves and the distribution and the pattern of microwaves in the oven So the distance between the peaks Within the oven that is half a wavelength Because that is Hertha, that’s a wavelength is where the whole cycle repeats, this is half a wave event That’s all we need that’s that that’s really we need that and we need one other Equation which are put in the microwave down here, which is this the speed of light? Is equal to frequency of the microwaves? times The wavelength frequency F. Let’s write it up. Here is two point four five Gigahertz I know that because it’s written on the back of the microwave oven so the important thing is that the peaks here Between these tell us lambda over to tell us the wavelength divided by two, so we measure the distance between these Okay, so that’s about eight six about seven, okay, so we’ve got three three measurements we’d like to have more It’s the first thing, but what’s the best thing to do here? Let’s take an average So we’ve got eight centimeters six centimeter and seven centimeter would seem that the best thing to do would you take an aperture? So let’s say a seven centimeters like this is a wavelength of fourteen centimeters So say is equal to F times Fourteen centimeters F we know is two point four five gigahertz Because we read that off the back of the microwave by fourteen centimeters So we want to speed the light which is C Which is in meters per second? So let’s make sure we get were careful with our units so that’s two point four five a Giga is ten to the nine Hertz By in terms of meters, that’s zero point one four meters what we have Is say three point four so zero point two three four three so that’s zero point three four three We could for the physicists among you I know in terms of significant figures, but let’s keep going So see our result is three point four three by ten to the eighth meters Per second That’s the speed of light as determined by chocolate That’s not good Is it? Because we know what the speed of light is and it’s pretty damn close to three by ten to the eighth meters per second So it’s actually three and you’ve got three point four yeah on the basis of chocolate. I think that’s pretty good. How do we know? Good compared to what so can we rarely quote to the four point point four three? How many of those figures are valid or significant or any of those figures significant sometimes we do experiments to try and? Check a previous value and then often we do experiments because we’re reaching out into the unknown How do we know could you do hundred of them another thousand? We could definitely do another hut thousand of them, but still then how do we know even after those a thousand? How do we know anything exactly so what we have to think about as this this value is quoted. We’re not right? We’re not wrong. When are even right? We’re not even wrong we can do nothing with this value because we don’t know what the Experimental uncertainty is we don’t know how well we’ve done the experiment. We don’t know how many of those figures are significant We don’t know You know can we measure to the second decimal place to the fifth decimal place? We don’t know so we find that our value ranges from 12 through 14 to 16 so our value is 14 the best way to quote is that we have lambda is equal to 14 plus or minus 2 centimeters All right How does that translate into? How we quote our value for the speed of light, so we know we’ve got this value this error in in lambda so what we see is we would typically you can either do a big dealt or a little delta typically we call it a little Delta I will do a big Delta because my handwriting is absolutely terrible so Delta Lambda is equal to plus or minus 2 Centimeters or actually we’ll just leave the plus or minus. I Delta lambda is 2 centimeters. That’s our error bar So what we find is see of what we know was C is equal to F times lambda We’re going to assume because it’s written on the back of the microwave that the frequency. We just got we’ve got no idea How you know what error there might be and that’s all we’re just going to assume that it’s a given value That we don’t know what the area is so we’re just gonna treat. It as without an error. It’s it’s a value We’ve been handed down what we need to do is work out the error in C Depending on the error in lambda, but the problem is we’ll see as m/s. And lambda is meters and We can’t compare we can’t just go this is centimeters then We need a value in meters per second, so what do we do here? Well what we have to do is look at something called a percentage error or the relative error so what we know is that? Delta C the error and C in the speed of light over see is equal to delta lambda Over lambda this is just basically percentages That’s all we’re doing we’re expressing our error in C as a percentage of C and that presented the percentage error in C Would be the same as the percentage error in London because we’re assuming this das. Nove an error all right so Delta C over C is equal to two centimeters over fourteen centimeters All right, so our percentage error in C is About well as one over seven and plays our error in C Delta C is one over seven times our value of C which was three point four 3 by 10 to the eighth So if we worked out through work out what 1/7 of 3.43 is 0.49 by 10 to the eighth Now, the standard approach and as long as we all stick to this then everybody can compare the results is that we call to one significant figure or If you’re a bit more careful, and you can justify it like they do in the National Physical Lab or in this, maybe two significant figures. We’re going to do what is done in first-year labs across the world and We’re going to quote that to one significant figure So that means our final results for the speed of light is we’ve quoted this to one decimal place so we need to get this to agree, so we’ll get rid of the the three the second decimal place Without putting our error bar in place the value of C the speed of light from our experiment falls somewhere between Two point nine and three point nine by ten to the eighth meters per second now We can compare that to the speed of light We really shouldn’t because that’s not how you do experimental science because it biases you in one direction We should try and do this as objectively as possible without being skewed But we know in terms of comparing that to the speed of light That we’ve done a pretty good job because the actual speed of light falls within the error bar the problem is and to Often we have to correct this time and time and time again in undergraduate labs the error bar the Experimental error is not the difference of the the value dot dot 3.4 from the speed of light That’s not how you do it. It’s not like it’s a mistake and error is not a mistake. There’s a there’s an inbuilt Uncertainty in our measurements and there’s an inbuilt uncertainty in every single measurement we take doesn’t matter if it’s to the nth decimal place to the tenth the fifteen to twenty eighth decimal place no matter how precise you get You’re never going to be So precise that you’re infinitesimally precise Upside down and when he’s trapped there his mom is you know really worried about him But she figures out that he’s not missing and actually she can communicate with him when he’s in this parallel universe