The Standing Invitation

Posts Tagged ‘Physics

The Origin of Opacity

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A while back I wrote a post about vision and why it is that some things simply can not, even in principle, be described in visual terms. I focused (see how hard it is to avoid metaphors of sight?) on things smaller than atoms, but I didn’t need to go that far. Right now, you are reading these words through at least several inches of air – real-world, macroscale stuff that you are able to feel or hear when it moves, but are unable to see.

Transparency is something magical. As a child I was fascinated by glass: solid, hard, heavier than water – and yet invisible. I asked how this could be possible, and was never really satisfied with any answer I got. And it turns out this is because I was asking the wrong question. It turns out that glass’s seemingly magical transparency is not the phenomenon demanding an explanation. To gain the deep understanding I missed as a child, we must consider the origin of opacity.

Ranked in order of wavelength, the electromagnetic spectrum begins with radiowaves and continues (decreasing wavelength) with microwaves, the infrared, the ultraviolet, x-rays, and gamma rays. Note the omission: I have deliberately excluded visible light. Why?

The portion of the electromagnetic spectrum that we can actually see is vanishingly small. You could blink and miss it, though of course if you blink you do miss it. Visible light – colour – is an astoundingly narrow selection of the available wavelengths between infrared and ultraviolet. One might wonder why this particular chunk of real estate, between 390 and 750 nm, happens to be the one that we can see. And if you ask it in these terms, you are still asking the wrong question.

Recall that you “seeing” something corresponds to your brain detecting a chemical change in a substance called 11-cis-retinal in your eyeball. 11-cis-retinal only absorbs radiation with wavelengths between 390 nm and 750 nm; anything outside this range has no effect, and so is invisible. So this is why only some of the light gets “seen”. But this only pushes the question back one step further. Why do our eyes employ 11-cis-retinal, and not some other chemical with absorbance in another wavelength range?

We can narrow the possibilities using an understanding of chemistry. There are no known chemical compounds that undergo a chemical change on exposure to radiowaves. This means that no organism dependent on chemistry as we know it could ever treat radiowaves as its own personal “visible light”.  The same appears to go for microwaves, though this is contested. X-rays and gamma rays do cause chemical changes in molecules, but with wavelengths such as this it would be quite a challenge to evolve an eye that could handle them (an essay by Arthur C Clarke suggests an animal with a metal box for an eye and a microscopic pinhole to focus it, but only to illustrate the difficulties involved). So from the restrictions of photochemistry we’re limited to a window about 3500 nm wide available for seeing – and yet evolution has caused us to see only a fraction of that. Why? And why did it “choose” for us the wavelength range that it did?

Well, consider some possibilities. What if we saw in the range of about 100 to 200 nm? Chemically it’s possible. But no organism on Earth would evolve to see in that wavelength. Our atmosphere is 80% nitrogen, and nitrogen absorbs light at about 100 nm. If we saw in that range, air would not be transparent: it would be totally opaque. The ability to see in this wavelength range would be worthless, just as it would be worthless to see around 1450 nm, where water absorbs; we evolved from creatures that needed to see in water. Here is the answer to the problem of transparency, and the problem is revealed to be that the question was backwards. Air (or water, or glass) is not transparent by itself; it is transparent to us because eyes that don’t find air transparent would be of no use to us. The transparency of air is the result of the environment our genes have designed us to live in. Of course, a subterranean creature like a mole might welcome a design of eye that makes soil transparent – while simultaneously leaving worms opaque and visible. But the chemistry for that does not exist, and moles have to make do with being blind.

Practical considerations aside, it’s interesting to ask if X-ray vision might have been useful on evolutionary terms. If we saw in the X-ray region, most matter would be transparent to us, including our own bodies. This would be useful for some things, like spotting tumours or broken bones. But we would struggle to pick fruit, or detect approaching thunderclouds, or build tools out of wood. As a species, we are better off with the kind of eyes that can detect the chemical difference between an unripe fruit (green) and a ripe one (red). Evolution has selected for us a sense of vision that operates in the part of the spectrum that is richest in information relevant to our survival. Other animals make use of slightly different wavelength ranges, like bees, who prefer the shorter ultraviolet wavelengths rich in information about the availability of nectar in flowers.

In fact, it’s arresting to imagine an alien world, lit by sun that emits different wavelengths of light to our own – populated by aliens based on very different chemistry to our own, with strange eyes for detecting wavelengths we cannot ever hope to see. If ever they came to visit us, their children might well look at us in fascination, wondering why it is that we humans are as transparent to them as glass…

REFERENCES

http://en.wikipedia.org/wiki/Infrared

http://en.wikipedia.org/wiki/Ultraviolet

Daniel C Dennett: Consciousness Explained

Richard Dawkins: Unweaving the Rainbow

Arthur C Clarke: Report on Planet Three and Other Speculations

Written by The S I

May 6, 2012 at 1:10 am

The Cost of Perfection

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Take two particles.*

Particles are fussy things. They don’t like being too close to each other because atomic nuclei repel each other very strongly; at the same time, the shifting clouds of electrons surrounding the nuclei can be mildly attractive to one another, so they don’t like being too far apart either. This balance of attractive and repulsive forces is familiar from all social gatherings: when you’re talking to someone at a party you want to be close enough to hear them, but if they’re standing right in your face it’s uncomfortable.

What this means for particles is that there’s a sweet spot, an optimum separation between the two particles that makes them both happy. It’s the lowest-energy arrangement of particles, in that once they’re at this distance, it would require an input of energy to push them closer together or pull them further apart.

So this idea of the optimum distance between two particles is straightforward. And the same thing applies when you have billions of particles at once. They will move around at random until they find the lowest-energy arrangement, where the average distance between particles is as close as possible to the ideal separation.

When billions of particles try to reach their lowest-energy arrangement, they will try to form a lattice.

Lattices are three-dimensional patterns of points in space. They are infinitely large, infinitely repeating, purely mathematical constructs that can only be approached, never exactly attained. A lattice is a map of where particles should sit in space in order to be at the right distance from each other.

When particles arrange themselves on a lattice, we call this a crystal. Crystals, like diamond, are simply regular arrangements of particles – and they really are very regular, repeat themselves almost perfectly for millions and millions of layers.

But remember, lattices are mathematical ideals, perfect and Platonic, while crystals are real-world lumps of matter. The particles in a crystal may try to reach the perfect state of a lattice, but they will never reach it. There will always be defects – points at which an atom is not sitting where the lattice says it should be. These are the microscopic imperfections that mean the ideal of a lattice will never be attained. Even though all particles in a crystal would benefit from being in a perfect lattice (achieving the optimum separation from other particles), the defects are nevertheless unavoidable.

There are two kinds of defects: extrinsic and intrinsic. Extrinsic defects are easy to understand. They are simply impurities. A diamond crystal is supposedly a regular arrangement of carbon atoms, but since no source of carbon is perfectly pure, no diamond will be perfectly pure. The most common impurity in diamond is a nitrogen taking the place of a carbon. Diamonds, supposedly pure carbon, are typically 1% nitrogen. As well as being impurities in themselves, the presence of a nitrogen atom causes local distortions in the crystal surrounding it, as the adjacent carbons move slightly from their ideal lattice positions in order to compensate for it.

But even if some perfectly pure source of carbon could be found and a diamond crystal grown from it, would that crystal approach a perfect lattice? Not quite, because of the second kind of defect – intrinsic defects. An intrinsic defect occurs when a particle isn’t where it should be.

These intrinsic defects are interesting because they are unavoidable. They are the inevitable consequence of the great trade-off between enthalpy and entropy. Because although there is an energetic benefit to having particles sitting an ideal distance from each other, there is also an energetic cost to having them perfectly ordered. This again makes sense to anybody who has ever tried to organise anything. Of course you want things organised; things are more efficient when they are organised, and so the more organised, the better – but organising things takes time, effort, and energy. Ultimately a compromise has to be reached: you accept the amount of organisation you can achieve for the amount of energy you’re willing to expend on putting things in order.

Although particles like to be separated by an ideal distance, they also like moving around, particularly at high temperatures. For this reason, truly perfect crystals are impossible to grow. Imperfections will always sneak in. In fact, imperfections are necessary. Crystals exist because it is energetically favourable for particles to be organised; but because of the inevitable cost of organising anything, it is also energetically favourable for there to be defects. And the interesting thing is that because the imperfections are the result of particle movement, and movement depends on temperature, it is possible to predict how many imperfections there will be in a crystal at a given temperature. You can’t say where they will be, but you can say how many there will be per cubic centimetre. The defects obey exact laws that can be understood and exploited. They are perfect imperfections.

 

* In this post, by particles I mean atoms, ions, molecules or some colloids; things smaller than atoms behave rather differently.

Written by The S I

April 9, 2012 at 10:18 am

Things That Don’t Look Like Anything

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When I talk about things like molecules, atoms and particles with nonscientists, a question I am often asked is what these things look like. And they never seem satisfied with my response: that, really, they don’t look like anything at all. It’s not that they’re invisible as such; it’s just that sentences involving what they look like don’t make any sense. You can’t describe their appearance because they don’t have an appearance to describe.

The thought makes people uncomfortable.

The idea of something not looking like anything is not a new one. Sounds do not look like anything. We know that sounds exist, but that physical appearance is not something we can ascribe to them. When we talk about sounds, we describe them in nonvisual terms.

Sounds, or ideas or desires or smells, have a certain abstract quality that seems to excuse this. But particles are stuff. They are physical objects whose masses are known to remarkable degrees of accuracy, and since everything we can see is made up of aggregates of them, it seems impossible that they cannot be described visually.

Let’s consider what happens when you see something, step by step.

An object is illuminated by a bombardment of photons. These photons interact with the surface of the object. Some are absorbed by the object – it is this absorption that gives the object its colour. The photons that are not absorbed are scattered around in all directions, and many of them enter through the pupil of your eye. These photons reach the retina, where they cause chemical changes in molecules like 11-cis-retinal; electrical reports of these changes are transmitted to the brain, where they are interpreted as ‘seeing’ those photons.

So to ‘see’ something means that photons bouncing off the thing cause chemical changes in your eye. This is fine for large objects like apples and oranges, but what if the object is smaller? Most people can’t see objects smaller than 0.1 mm, because there aren’t enough photons reflecting off them to react with our eyes. We get around this problem by using stronger illumination and magnifying lenses, allowing us to see things like blood cells.

But what about objects that are even smaller?

Well, here we start to have a problem. For objects smaller than 0.002 mm, photons of visible light start to be too big to see things clearly. In order to resolve details at this size level, smaller, higher-energy particles than photons need to be used. This is how electron microscopy works: instead of using reflected photons, you use reflected electrons, which are much smaller and better able to probe the surface of what you’re examining.

Is this really ‘seeing’ the object? The microscopic object under examination is not being studied with light, remember. This is why electron microscope images are monochrome. Light isn’t involved in the process at any point until a computer screen shows you, with light, the pattern of reflected electrons. Still, we are presented with pictures of the object’s surface, so it’s certainly like seeing, and the object certainly has an appearance that can be discovered, even if only indirectly.

What if the object is smaller?

Eventually an object can be so small that not even electrons can give you good enough resolution, and even more indirect means of gathering information must be used. One of them, atomic force microscopy, is more analogous to touch than sight: it drags a tiny needle across a surface to register bumps in the surface where the individual atoms are. But apart from the atoms’ location in space, there’s no information here about their appearance. Atoms do not interact with light in a way that gives meaning to the word ‘looks like’. They do absorb light and so might be said to have colour in a technical sense, but no picture of an atom could ever be drawn based on their interaction with light. And smaller particles than atoms don’t interact with light at all. You can’t see them, ever, because there is nothing there to see.

But still, some picture of a very tiny object might be drawn. Questions about its shape, for example, are not meaningless – but on a small enough scale, questions of shape become questions about properties rather than appearance. The question ‘is x round?’ becomes ‘are all the points on x’s surface the same distance from one central point?’. This is a question that can be answered, but only because it is a mathematical question about the properties of a certain type of object. And it turns out that the equations describing these objects reveal the them to be strange and wonderful things – things that behave in ways that make absolutely no sense to people used to objects the size of apples and oranges. They cannot be seen, but they can be described, and this description is better than seeing them. A mathematical description of a particle is more precise and less fallible than the clumsy tool of vision that evolution gave us to survive in a world full of large-scale objects. And we can reach this level of acquaintance with these particles that no one has ever seen because even though we can’t see them, we can imagine them.

Written by The S I

March 26, 2012 at 3:00 am

Burning Curiosity

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Something about writing this thesis makes me think of setting things on fire. This prompted me to wonder exactly what a flame is.

Although a flame appears to be a stable, defined structure, we know that this is an illusion. Particles enter at the bottom and leave at the top, becoming visible for only a part of that journey; the region of space in which they’re visible we call a ‘flame’. It’s rather like a queue: it has a shape, a duration and a certain characteristic behaviour, but nothing about it is permanent. (Remember how no part of our bodies is the same after 20 years…?)

So a flame is really a time-averaged aggregate of microscopic events. But what light-emitting events lead to the thing we call a flame?

Candle wax is made of long-chain hydrocarbons that have a low melting point. Heat turns wax from a white solid to a clear liquid, and then to a gas. Heat rises, and the gas molecules are carried upwards. When they are hot enough, they react with oxygen to form carbon dioxide and water vapour, like this:

 

But this is too simple. The process of combustion is incredibly complex, with countless steps and short-lived intermediates – something a bit more like this.

Many of these reactions give off heat. The heat excites electrons in nearby molecules, and these electrons relax back to their original positions by emitting light. The colour of the light given off depends on how hot the molecule was. It’s how astronomers measure how hot the stars are, and what they’re made of.

The hottest part of a candle flame is the very bottom, where oxygen is plentiful and there is a high density of heat-generating combustion reactions occurring per second, driving up the temperature. The molecules here burn at about 1400 °C and give off a hot blue colour.

These very efficient reactions near the bottom effectively starve the rest of the flame of oxygen. Oxygen still gets in through the sides, but not as efficiently. The result is incomplete combustion: the wax is converted into particles of soot carried upwards by the current of air generated by the heat. These are still hot enough to glow, but the temperature is much lower, and so this region of the flame is a cool yellow.

The flame is only the part of the process we can see. It is misleading to see that soot particles emit light within the flame; better to say that the flame-space is defined as that region within which the particles are hot enough to glow. The tapering shape of the flame comes directly from the low availability of oxygen. When you trap a flame under a glass, the flame extends before going out, because the lifetime of a glowing particle is longer in the absence of oxygen.

This is demonstrated in a lovely picture from NASA of a flame in microgravity. Because there is no ‘up’ for the air currents to go, the flame burns in all directions. This is a much more efficient use of space: oxygen can get in from all directions, so the fire burns strongly, with no soot to give it a yellow colour.

 

REFERENCES

http://en.wikipedia.org/wiki/Candle

Also, see a fascinating and rather whimsical discussion on the ‘philosophy of candles’ by the mighty Michael Faraday here.

 

 

 

Written by The S I

November 8, 2011 at 11:59 pm

Quieten Down

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I dislike noise. When I go to a pub I go there to listen to people, and there is nothing I hate more in a night out than not being able to hear what they are saying.

When you listen to someone speak, you are trying to detect with your ears the audible signals they produce with their mouths; noise is everything you hear that is not a signal. How well you can hear a person depends on how clearly their words stand out against the background: the signal-to-noise ratio.

Signal-to-noise ratios appear everywhere in science where a precise measurement must be taken. In order to understand measurement ­– in order to comment on what it is we can ever hope to know about the world – we have to have a working knowledge of the properties of noise.

Now noise from a Shannon-information perspective is anything that disrupts a flow of information, but generally speaking it is useful to separate noise into two different types: intrinsic noise (or thermal noise), and extrinsic noise (or interference).

Let’s say you want to use a microphone to measure some very faint sound – the sound of an ant chewing a leaf, say. Plug in your headphones and the first thing you’ll hear will be a your neighbour’s washing machine, or traffic on the street outside. This is extrinsic noise and can be reduced by shielding. People build anechoic chambers to reduce extrinsic noise: carefully insulated and coated with foam pads to deaden echoes, they offer some of the quietest places on Earth. According to John Cage, his piece 4’33” was inspired by his experience in an anechoic chamber. Expecting to hear nothing but peaceful silence, he was surprised to hear

two sounds, one high and one low. Afterward I asked the engineer in charge why, if the room was so silent, I had heard two sounds. He said, ‘Describe them.’ I did. He said, ‘The high one was your nervous system in operation. The low one was your blood in circulation.’

What Cage experienced was intrinsic noise, noise that no soundproofing can remove because it originates inside the thing doing the measurement. In his case, the noise came from inside his body, but even an electronic microphone will hiss and crackle from the random motion of electrons in its wiring.

No analytical tool is safe from intrinsic noise, not even a simple ruler, whose length fluctuates randomly on a scale too small for us to notice, but is sufficient to preclude its use for measuring things on the molecular scale. This is all because everything, ultimately, is made of particles that are always in motion ­– tiny, incessant, random movement caused by the ambient temperature.

So that background hiss interfering with your measurement will never go away. It is also totally random ­– and yet, as a consequence of this randomness, it is in some ways completely predictable. Some maths shows, for example, you can increase the accuracy of your measurement simply by taking lots of measurements and averaging them out: the more measurements you take, the more your signal stands out against the background noise. More exactly, if you take four times as many measurements, your signal-to-noise ratio doubles.

But measurements can be costly; noise can never be removed completely; and there is a law of diminishing returns. If a measurement with precision x costs you £10, twice as much precision would cost £40; twice as much again would cost £160. Sometimes the size of the error bars depends on how much you can afford.

REFERENCES

http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf

http://www.physics.utoronto.ca/~phy225h/experiments/thermal-noise/Thermal-Noise.pdf

http://www.lichtensteiger.de/anechoic.html

Written by The S I

October 9, 2011 at 11:59 pm

Life in Freefall

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This is a follow-up to a post about tides, and about how this universally known phenomenon is more complicated and subtle than the standard schoolroom explanation would have us believe.

I put up a diagram of the tides copied from Wikipedia, but my attention was drawn by Yrogirg to this more realistic one that highlights the fact that the semi-major axis of the tidal bulge doesn’t point exactly at the moon; the tide reaches its peak a little bit after the moon passes directly overhead.

The question posed at the end of the earlier post is this: if the tide comes from the Moon’s gravitational pull, why does it also bulge on the other side of the Earth? Surely that is moving against the Moon’s gravity?

Perhaps there is another way of seeing it.

Imagine you have five small, identical objects, A, B, C, D and E; marbles, for example. Imagine you arrange them in your hand in a plus-shaped formation so that B is in the centre with the other four surrounding it. Then, holding them stacked on top of each other like this, you let go.

Naturally the marbles all fall together. The distances between the marbles are the same while they are in freefall, and remain constant right until they hit the floor and scatter. Of course the ABCDE assembly moves faster and faster as it falls ­– it accelerates under gravity. But as long as A, B, C, D and E experience the same acceleration, it doesn’t matter how fast they travel: they will still fall together.

But what if, as they fell, they accelerated at different rates? It can happen. Recall our earlier discussion of gravitational wells: the closer you are to something, the more it attracts you, so in some circumstances, small differences of distance have significant physical effects. What if C fell faster than B, D and E – and B, D and E fell faster than A? What would that look like? Something like this:

If the objects accelerate at different rates based on how close they are to the source of gravity, then the distances between them will increase as they fall.

The next question is: how does this look from B’s point of view?

Well, for B, things look rather odd. B knows there is a source of gravity nearby, represented by the grey ball. And it can readily understand why C appears to be moving towards the gravity source. And yet it also looks as though A is moving away from the gravity source. And if the gravity source is moving around B, then B will always see one marble moving towards it, and one marble on the other side of B appearing to move away.

But B is wrong. Nothing is moving away from the gravity source. Everything is moving towards it – including B – at different rates.

And this applies to Earth and the Moon because, although we do not feel it, we are falling towards the Moon ­– constantly, just as the Moon is falling constantly towards us. But because we are both in motion, we keep missing each other – we fall around one another, in orbit. The tides track the moving target of the Moon, trailing a little behind it as far as an observer on Earth can tell.

Put in terms of bodies in motion through space, the tidal bulge on the opposite side of the Earth makes perfect, intuitive sense. As is so often the case, what lets us down is our unconscious assumption that we are the centre of the universe.

REFERENCES

http://www.astronomy.ohio-state.edu/~pogge/Ast161/Unit4/tides.html

Written by The S I

October 7, 2011 at 11:59 pm

The Slippery Slope

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Let’s go back to school for a moment. A quick science question for you to think about: what causes the tides?

(Actually, the first answer I learned in school for that one was that God had made it that way, but the less said about that the better…)

So we all know the answer: the Moon. And we all probably have the same textbook picture in our minds of how this looks ­– something like this.

So there’s the Earth surrounded by its oceans, and the Moon’s gravitational pull attracts the water towards itself. We also know that the Sun is out there somewhere, and has its own gravitational pull. When the Moon and the Sun are in alignment, you get both forces combined and you get a very strong tide, a spring tide; and when the Sun and Moon are at right angles, you get a neap tide, which is weak.

So it’s mostly down to the Moon’s gravitational pull… right?

Well, actually…

The Moon is near, and the Sun is far away, so the Moon should have the biggest influence ­– but remember, the Sun is massive. In fact, it is two million times heavier than the Moon. How does this affect the balance? I won’t put up the equations here, but it’s actually quite simple to calculate, and it turns out that the Earth feels the Sun’s gravitational pull 177 times more than the Moon’s.

So if the Moon’s effect is so tiny, why do the tides track the Moon, and not the Sun?

What we need to understand here is the concept of a gravitational well.

This is a gravitational well. At the centre is some massive object ­– the Moon, say. We sit on the surface of the well and, if we’re not careful, we can slide down it, faster and faster, until we collide with whatever is at the centre. Key to this concept is the idea that the closer you are to the mass, the steeper the slope is.

When you’re near to the mass you are drawn towards it; if you’re a kilometre closer, you are drawn even more.

But how much that extra kilometre closer really matters depends on how far away you were to begin with. The Sun might be a huge attractor pulling you constantly, but if it’s 93 million miles away an extra step closer won’t really make much difference. The Moon is a much weaker attractor, but because you’re closer to it, distances really do matter.

So yes, we are all affected by the Sun’s gravitational pull, much more than we are by the Moon’s; but we are affected constantly, wherever on Earth we are. The Moon’s effect is much weaker, but much, much more local. It matters if the Moon is overhead or on the other side of the Earth; that extra difference represents a real change in pull, as opposed to the Sun’s stronger but uniform and therefore unnoticed pull.

That’s the gist of it, anyway.

But now we’ve got to thinking about it – look at the diagram again. What’s going on with that tidal bulge on the other side of the Earth to the Moon? We know that exists because we have two high tides every 24 hours, but why? It’s bulging away from the Moon. Surely that makes no sense?

Unfortunately that’s an even weirder story, and we’ll save it for another time.

Written by The S I

October 2, 2011 at 11:59 pm