Posts Tagged ‘physics’
Canto: Well, Karl Kruszelnicki is one of our best science popularisers as you know, and therefore a hero of ours, but I have to say his explanation of the blueness of our daily sky in his book 50 Shades of Grey left me scratching my head…
Jacinta: Not dumbed-down enough for you? Do you think we could form a Science for Dummies collaboration to do a better job?
Canto: Well that would really be the blind leading the blind, but at least we’d inch closer to understanding if we put everything in our own words… and that’s what I’m always telling my students to do.
Jacinta: So let’s get down to it. The day-sky is blue (or appears blue to we humans?) because…?
Canto: Well the very brief explanation given by Dr Karl is that it’s about Rayleigh scattering. Named for a J W Strutt, aka Lord Rayleigh, who first worked it out.
Jacinta: So let’s just call it scattering. What’s scattering?
Canto: Or we might call it light scattering. Our atmosphere is full of particles, which interfere with the light coming to us from the sun. Now while these particles are all more or less invisible to the naked eye, they vary greatly in size, and they’re also set at quite large distances from each other, relative to their size. The idea, broadly, is that light hits us from the sun, and that’s white light, which as we know from prisms and rainbows is made up of different wavelengths of light, which we see, in the spectrum that’s visible to us, as Roy G Biv, red orange yellow green blue indigo violet, though there’s more of some wavelengths or colours than others. Red light, because it has a longer wavelength than blue towards the other end of the spectrum, tends to come straight through from the sun without hitting too many of those atmospheric particles, whereas blue light hits a lot more particles and bounces off, often at right angles, and kind of spreads throughout the sky, and that’s what we mean by scattering. The blue light, or photons, bounce around the sky from particle to particle before hitting us in the eye so to speak, and so we see blue light everywhere up there. Now, do you find that a convincing explanation?
Jacinta: Well, partly, though it raises a lot of questions.
Canto: Excellent. That’s science for you.
Jacinta: You say there are lots of particles in the sky. Does the size of the particle matter? I mean, I would assume that the light, or the photons, would be more likely to hit large particles than small ones, but that would depend on just how many large particles there are compared to small ones. Surely our atmosphere is full of molecular nitrogen and oxygen, mostly, and they’d be vastly more numerous than large dust particles. Does size matter? And you say that blue light, or blue photons, tend to hit these particles because of their shorter wavelengths. I don’t quite get that. Why would something with a longer wavelength be more likely to miss? I think of, say, long arrows and short arrows. I see no reason why a longer arrow would tend to miss the target particles – not that they’re aiming for them – while shorter arrows hit and bounce off. And what makes them bounce off anyway?
Canto: OMG what a smart kid you are. And I think I can add more to those questions, such as why do we see different wavelengths of light as colours anyway, and why do we talk sometimes of waves and sometimes of particles called photons? But let’s start with the question of whether size matters. All I can say here is that it certainly does, but a fuller explanation would be beyond my capabilities. For a start, the particles hit by light are not only variable by size but by shape, and so potentially infinite in variability. Selected geometries of particles – for example spherical ones – can yield solutions as to light scattering based on the equations of Maxwell, but that doesn’t help much with random dust and ice particles. Rayleigh scattering deals with particles much smaller than the light’s wavelength but many particles are larger than the wavelength, and don’t forget light is a bunch of different wavelengths, striking a bunch of different sized and shaped particles.
Jacinta: Sounds horribly complex, and yet we get this clear blue sky. Are you ready to give up now?
Canto: Just about, but let me tackle this bouncing off thing. Of course this happens all the time, it’s called reflection. You see your reflection in the mirror because mirrors are designed as highly reflective surfaces.
Jacinta: Highly bounced-off. So what would a highly unreflective surface look like?
Canto: Well that would be something that lets all the light through without reflection or distortion, like the best pane of glass or pair of specs. You see the sky as blue because all these particles are absorbing and reflecting light at particular wavelengths. That’s how you see all colours. As to why things happen this way, OMG I’m getting a headache. The psychologist Thalma Lobel highlights the complexity of it all this way:
A physicist would tell you that colour has to do with the wavelength and frequency of the beams of light reflecting and scattering off a surface. An ophthalmologist would tell you that colour has to do with the anatomy of the perceiving eye and brain, that colour does not exist without a cornea for light to enter and colour-sensitive retinal cones for the light-waves to stimulate. A neurologist might tell you that colour is the electro-chemical result of nervous impulses processed in the occipital lobe in the rear of the brain and translated into optical information…
Jacinta: And none of these perspectives would contradict the others, it would all fit into the coherence theory of truth…
Canto: Not truth so much as explanation, which approaches truth maybe but never gets there, but the above quote gives a glimpse of how complex this matter of light and colour really is…
Jacinta: And just on the physics, I’ve looked at a few explanations online, and they don’t satisfy me.
Canto: Okay, I’m going to end with another quote, which I’m hoping may give you a little more satisfaction. This is from Live Science.
The blueness of the sky is the result of a particular type of scattering called Rayleigh scattering, which refers to the selective scattering of light off of particles that are no bigger than one-tenth the wavelength of the light.
Importantly, Rayleigh scattering is heavily dependent on the wavelength of light, with lower wavelength light being scattered most. In the lower atmosphere, tiny oxygen and nitrogen molecules scatter short-wavelength light, such as blue and violet light, to a far greater degree than long-wavelength light, such as red and yellow. In fact, the scattering of 400-nanometer light (violet) is 9.4 times greater than the scattering of 700-nm light (red).
Though the atmospheric particles scatter violet more than blue (450-nm light), the sky appears blue, because our eyes are more sensitive to blue light and because some of the violet light is absorbed in the upper atmosphere.
Jacinta: Yeah so that partially answers some of my questions… ‘selective scattering’, there’s something that needs unpacking for a start…
Canto: Well, keep asking questions, smart ones as well as dumb ones…
Jacinta: Hey, there are no dumb questions. Especially from me. Remember this is supposed to be science for dummies, not science by dummies.
Canto: Okay then. So maybe we should quit now, before we’re found out…
‘Why is the sky blue?’, from 50 shades of grey matter, Karl Kruszelnicki, pp15-19
‘Blue skies smiling at me: why the sky is blue’, from Bad astronomy, Philip Plait, pp39-47
Canto: Well, we’re celebrating this month what is surely the greatest achievement by a single person in the history of science, the general theory of relativity. I thought it might be a good time to reflect on that achievement, on science generally, and on the impetus that drives us to explore and understand as fully as possible the world around us.
Jacinta: The world that made us.
Jacinta: Well, first can I speak of Einstein as a political animal, because that has influenced me, or rather, his political views seem to chime with mine. He’s been described as a supra-nationalist, which to me is a kind of political humanism. We’re moving very gradually towards this supra-nationalism, with the European Union, the African Union, and various intergovernmental and international organisations whose goals are largely political. Einstein also saw the intellectual venture that is science as an international community venture, science as an international language, and an international community undertaking. And with the development of nuclear weapons, which clearly troubled him very deeply, he recognised more forcefully than ever the need for us to take international responsibility for our rapidly developing and potentially world-threatening technology. In his day it was nuclear weapons. Today, they’re still a threat – you’ll never get that genie back in the bottle – but there are so many other threats posed by a whole range of technologies, and we need to recognise them, inform ourselves about them, and co-operate to reduce the harm, and where possible find less destructive but still effective alternatives.
Canto: A great little speech Jas, suitable for the UN general assembly…
Jacinta: That great sinkhole of fine and fruitless speeches. So let’s get back to general relativity, what marks it off from special relativity?
Canto: Well I’m not a physicist, and I’m certainly no mathematician, but broadly speaking, general relativity is a theory of gravity. Basically, after developing special relativity, which dealt with the concepts of space and time, in 1905, he felt that he needed a more comprehensive relativistic theory incorporating gravity.
Jacinta: But hang on, was there really anything wrong with space and time before he got his hands on them? Why couldn’t he leave them alone?
Canto: OMG, you’re taking me right back to basics, aren’t you? If I had world enough, and time…
Jacinta: Actually the special theory was essentially an attempt – monumentally successful – to square Maxwell’s electromagnetism equations with the laws of Newton, a squaring up which involved enormous consequences for our understanding of space and time, which have ever since been connected in the concept – well, more than a concept, since it has been verified to the utmost – of the fourth, spacetime, dimension.
Canto: Well done, and there were other vital implications too, as expressed in E = mc², equivalating mass and energy.
Jacinta: Is that a word?
Canto: It is now.
Jacinta: So when can we stop pretending that we understand any of this shite?
Canto: Not for a while yet. The relevance of relativity goes back to Galileo and Newton. It all has to do with frames of reference. At the turn of the century, when Einstein was starting to really focus on this stuff, there was a lot of controversy about whether ‘ether’ existed – a postulated quasi-magical invisible medium through which electromagnetic and light waves propagated. This ether was supposed to provide an absolute frame of reference, but it had some contradictory properties, and seemed designed to explain away some intractable problems of physics. In any case, some important experimental work effectively quashed the ether hypothesis, and Einstein sought to reconcile the problems by deriving special relativity from two essential postulates, constant light speed and a ‘principle of relativity’, under which physical laws are the same regardless of the inertial frame of reference.
Jacinta: What do you mean, ‘the initial frame of reference’?
Canto: No, I said ‘the inertial frame of reference’. That’s one that describes all parameters homogenously, in such a way that any such frame is in a constant motion with respect to other such frames. But I won’t go into the mathematics of it all here.
Jacinta: As if you could.
Canto: Okay. Okay. I won’t go any further in trying to elucidate Einstein’s work, to myself, you or anyone else. At the end of it all I wanted to celebrate the heart of Einstein’s genius, which I think represents the best and most exciting element in our civilisation.
Jacinta: Drumroll. Now, expose this heart to us.
Canto: Well we’ve barely touched on the general theory, but what Einstein’s work on gravity teaches us is that by not leaving things well alone, as you put it, we can make enormous strides. Of course it took insight, hard work, and a full and deep understanding of the issues at stake, and of the work that had already been done to resolve those issues. And I don’t think Einstein was intending to be a revolutionary. He was simply exercised by the problems posed in trying to understand, dare I say, the very nature of reality. And he rose to that challenge and transformed our understanding of reality more than any other person in human history. It’s unlikely that anything so transformative will ever come again – from the mind of a single human being.
Jacinta: Yes it’s an interesting point, and it takes a particular development of culture to allow that kind of transformative thinking. It took Europe centuries to emerge from a sort of hegemony of dogmatism and orthodoxy. During the so-called dark ages, when warfare was an everyday phenomenon, and later too, right through to the Thirty Years War and beyond, one thing that could never be disputed amongst all that disputation was that the Bible was the word of God. Nowadays, few people believe that, and that’s a positive development in the evolution of culture. It frees us to look at morality from a broader, richer, extra-Biblical perspective..
Canto: Yes we no longer have to even pretend that our morality comes from such sources.
Jacinta: Yes and I’m thinking of other parts of the world that are locked in to this submissive way of thinking. A teaching colleague, an otherwise very liberal Moslem, told me the other day that he didn’t believe in gay marriage, because the Qu-ran laid down the law on homosexuals, and the Qu-ran, because written by God, is perfect. Of course I had to call BS on that, which made me quite sad, because I get on very well with him, on a professional and personal basis. It just highlights to me the crushing nature of culture, how it blinds even the best people to the nature of reality.
Canto: Not being capable of questioning, not even being aware of that incapability, that seems to me the most horrible blight, and yet as you say, it wasn’t so long ago that our forebears weren’t capable of questioning the legitimacy of Christianity’s ‘sacred texts’, in spite of interpreting those remarkably fluid texts in myriad ways.
Jacinta: And yet out of that bound-in world, modern science had its birth. Some modern atheists might claim the likes of Galileo and Francis Bacon as one of their own, but none of our scientific pioneers were atheists in the modern sense. Yet the principles they laid down led inevitably to the questioning of sacred texts and the gods described in them.
Canto: Of course, and the phenomenal success of the tightened epistemology that has produced the scientific and technological revolution we’re enjoying now, with exoplanets abounding, and the revelations of Homo floresiensis, Homo naledi and the Denisovan hominin, and our unique microbiome, and recent work on the interoreceptive tract leading to to the anterior insular cortex, and so on and on and on, and the constant shaking up of old certainties and opening up of new pathways, all happening at a giddying accelerating rate, all of this leaves the ‘certainty of faith’ looking embarrassingly silly and feeble.
Jacinta: And you know why ‘I fucking love science’, to steal someone else’s great line? It’s not because of science itself, that’s only a means. It’s what it reveals about our world that’s amazing. It’s the world of stuff – animate and inanimate – that’s amazing. The fact that this solid table we’re sitting at is made of mostly empty space – a solidity consisting entirely of electrochemical bonds, if that’s the right term, between particles we can’t see but whose existence has been proven a zillion times over, and the fact that as we sit here on a still, springtime day, with a slight breeze tickling our faces, we’re completely oblivious of the fact that we hurtling around on the surface of this earth, making a full circle every 24 hours, at a speed of nearly 1700 kms per hour. And at the same time we’re revolving around the sun at a far greater speed, 100,000 kms per hour. And not only that, we’re in a solar system that’s spinning around in the outer regions of our galaxy at around 800,000 kilometres an hour. And not only that… well, we don’t feel an effing thing. It’s the counter-intuitive facts about the natural world that our current methods of investigation reveal – these are just mind-blowing. And if your mind doesn’t get blown by it, then you haven’t a mind worth blowing.
Canto: And we have two metres of DNA packed into each nucleus of the trillions of cells in our body. Who’d’ve thunkit?
I think it would be amusing – for me anyway – if my blog posts were connected by threads, one leading to another. For example, the last post on aerosinusitis resulted from comments on my previous one about my recent air travel, and this one results from comments about pressure differentials in the last one, and so on and on.
Well, anyway, Boyle’s law.
Boyle’s law describes how the pressure of a gas increases as its volume decreases.
Take a set amount of gas – that’s to say, a certain mass of gas – and decrease its volume. Then the pressure it exerts increases in proportion. That’s to say, the relationship between volume and pressure is inversely proportional, given a constant temperature and mass. This relationship can be expressed in the formula PV = k, where k is a constant. In ‘word’ terms, the product of pressure and volume is constant, controlling for the other factors. If the pressure is calculated as 6, and the volume 2, then if the volume is doubled to 4, then the pressure will be halved to 3, with, on both occasions, the constant being 12. Another way of expressing this relationship is P1V1 = P2V2.
The English chemist/physicist, or ‘natural scientist’, Robert Boyle, first published the relational law in 1662, though he wasn’t the first to notice a relationship between pressure and volume. Nor did he fully understand the reason for the relationship, because gases were not then seen as molecular, with the molecules in kinetic relationship to each other. However, Boyle’s thinking was moving in the right direction, as he theorised that air – the gas on which he experimented – was ‘a fluid of particles at rest in between invisible springs’. Edme Mariotte of France independently formulated the law a little over a decade after Boyle.
The best physical explanation for the law emerged more than two centuries later, with work on the kinetic theory of gases by James Clerk Maxwell and Ludwig Boltzmann. This theory explains pressure within a container as a result of atoms or molecules colliding with the container at various rates and velocities. It provides a molecular, microscopic accounting of such macroscopic measurements as pressure, volume and temperature. Einstein’s work on Brownian motion, the motion of dust or pollen particles as seen under a microscope, helped confirm the theory, on a level kind of in between the molecular and the macroscopic. Interestingly, the idea that macroscopic conditions might be the result of microscopic bodies in collision was put forward by Lucretius nearly 2000 years ago.
Boyle’s law treats of an ideal gas, something not known or considered at the time because gases under standard conditions of temperature and pressure behave essentially like ideal gases. Other ideal gas laws include Charles’ law, which is a law of volumes, Gay-Lussac’s law, which treats pressure, and Avogadro’s law, which covers the proportional relationship between volume and the number of moles present (molar volume). As always, improvements in technology led to the observation of a wider range of conditions requiring new hypotheses, the confirmation of which led to new knowledge – in this case, the kinetic theory.