Groping towards quantum physics

I started reading Jim Al-Khalili’s book Quantum: a guide for the perplexed on the 3 March 2010, courtesy of Nottinghamshire libraries. I finished it on the 10 March.

First, thanks to Jim for the jokes - essential light relief from a subject so challenging!

The main thing I’ve learnt, I think, is that ’microscopic’ things don’t behave anything like ’macroscopic’ things.

These two terms seem to have nothing to do with what I know as a microscope - in fact things classed as microscopic by physicists can’t be seen at all - even with the most state-of-the-art electron microsocopes. Basically, the term seems to apply to atoms and anything smaller than atoms. Anything that can be seen using visible light is by definition macroscopic.

Weird etymology, this: I’m sure biologists, geologists and other serious researchers, for whom the old-fashioned optical microscope is an indispensible tool, would take exception to the physicists redefining their jargon.

The second thing I’ve learnt is that there is no reason why I should expect microscopic things to behave like macroscopic things (physicist’s definitions). Newton’s laws of gravitation simply do not apply at the subatomic level. For all I know (which is still precious little), it may be that some of the entities or waves on which the quantum physicists concentrate actually make Newton’s laws happen - as in actually causing gravity. In that case you could hardly expect them to be affected by gravity - not in any normal way, at least. Even Prof Jim admits that this looks like a cop-out, but it was already obvious, a quarter of the way through the book, that it’s true.

Talking of Newton’s laws, first published in 1687, they do work in the macroscopic world until speeds approach that of light - 186,000 miles or 300,000 kilometres per second. Since we’re never likely to travel at even a fraction of that, let alone at these ’relativistic velocities’, I don’t think we really need to worry!

I feel relieved about this. What the book seems to be telling me is that what goes on inside atoms, or in radiation, doesn’t necessarily undermine my attempts in this diary to build a model of the macroscopic universe that makes reasonable, intuitive sense to me. Even though I’ve begun to see how essential quantum phenomena are to what are now everyday modern technologies, and indeed to the whole working of the universe, I think my ’Newtonian’ model is probably pretty sound. There’s just an awful lot more going on behind the scenes than I’d realised!

I do have one of two gripes about this beautifully produced book. There are far too many points at which Jim says things like ’as I will show in Chapter 6’. There are also entities he calls ’boxes’ (overgrown sidebars) written by himself and other authors, and it’s often far from clear where the reader should divert from the main text to read these. Early on, I thought I might have to read the thing twice to make real sense of it - even if that wasn’t an altogether over-optimistic expectation -but I think I’ve probably got as much out of it as I’m going to in one pass.

To pick a few nits, there are some examples of sloppy proof-reading: I just don’t understand how, with modern publishing technologies and a professional publisher’s editor at every author’s elbow, this can still happen.

Having read the book with considerable interest and some real enjoyment, I can’t say I’m a great deal wiser than when I started. Quantum physics and quantum mechanics seem to deal in a lot of probabilities and not a lot of certainties. There’s a thing called a wavefunction, which seems to be a graphical representation of the probabilities of a particle being in different locations, and which seems to be the nearest physicists can get to determining where the particle is without their measurements sending it somewhere else. That much I can accept, but when the wavefunction is talked about as if it is real - more real than the particle to which it relates, it sometime seems - I begin to lose my grasp.

Anyway, quantum physics and quantum mechanics have obviously been around for a lot longer than I thought, and are thoroughly mainstream. However, any real understanding requires vastly more maths than my bare pass at O-level in 1959, so I think they’re safely left to the physicists. A bit like some of the implications of what Prof Jim repeatedly refers to as ’quantum weirdness’: he whimsically suggests these should be left to the philosophers, ’who have nothing better to do with their time’.

It is clear, though, that there is a lot of stuff going on inside atoms and molecules. However, one of the more counter-intuitive facts is that almost the entire volume of every atom consists of nothing but empty space (unless, of course, you are seduced into seeing wavefunctions as real entities rather than probability graphs). An atom consists of a nucleus - which in turn is a structure of heavy neutrons, which have no electrical charge, and equally heavy protons, which have a positive charge - surrounded by what is nowadays called an electron cloud, within which very light electrons orbit. The old model, which looked very much like our solar system, has been replaced - thanks to quantum physics - with something more subtle, but the basic idea of the electrons being trapped in orbits by the attraction between their negative charges and the protons’ positive ones still holds: it’s just that an orbit governed by an electromagnetic force (and therefore by quantum mechanics) behaves very differently from one governed by gravity (and therefore by Newton’s laws).

The really amazing figure is that the radius of an atom’s electron cloud is more than ten thousand times that of its nucleus, where all the atom’s mass, which we experience as weight, momentum and inertia, is concentrated. A few (or, in heavy elements, many) massless electrons whizz about in the cloud, but the rest is just space. Despite the lack of ’stuff’ in the cloud, its is only the electrons in the outermost ’orbit’ that can form bonds with other atoms, to form the molecules of compounds, so it is the size of the cloud that defines the real, practical size of the atom.

Just to get this into perspective, Wikipedia tells us that the atomic radii of different elements range between 30 and 300 picometres. A picometre is one trillionth (1/1,000,000,000,000) of a metre or one billionth (1/1,000,000,000) of a millmetre. It follows that all the mass of one atom of the lightest element is concentrated in something with a radius of three ten-billionths of a millimetre.

Accepting that the volume of a solid is proportional to the cube of its radius, the volume of an atom’s electron cloud must be of the order of ten-thousand-cubed times that of the nucleus. If I’ve got all this right, that is one trillion times!

So our bodies, like everything else in our macrosocopic world, are made up of an infinitesimally small amount of very dense solid stuff and a vast amount of nothing - not even fresh air! That’s one of the weirder notions, because it implies that most of the volume of any form of matter (including us) is actually a hard vacuum. I still struggle with the idea that I’m mostly made of water - never mind a couple of cubic feet of absolutely nothing!

We macro-people naturally think that this would suck in air - but, of course, atoms of oxygen and nitrogen can’t possibly be sucked inside other atoms. This again reinforces the vast difference between the macro world and the micro one. The suggestion that all matter is composed of dense nuclei scattered very thinly in a vacuum otherwise populated only by electrons in their orbits, the whole held together by electromagnetic forces, takes a lot of believing.

Michael Moseley, in the recent BBC series The Story of Science: Power, Proof and Passion, came up with a spectacular illustration: if we could take the entire six-billion population of our planet and ’get rid’ of the empty space, what was left would fit into a space smaller than a sugar cube! Now that is weird...

And why aren’t we transparent - or even invisible? Presumably because each atom is far smaller than the wavelength of visible light, so the nuclei - while unimaginably tiny individually - are actually very tightly packed together in terms of light, so visible light waves can’t pass through them. In fact, as will become clearer in a moment, the very idea of light going through an atom doesn’t really make sense.

First, though, to get this into perspective... Ignoring the stuff about whether light is a ray or a stream of particles or both (quantum weirdness again), light of a specific colour is accepted to have a specific frequency or wavelength (two ways of looking at the same thing: high frequency equals short wavelength and vice versa. Remember radio stations being identified by wavelengths in metres rather by frequency in kilohertz or megahertz? BBC Radio 4 long-wave’s familiar 1500-metre wavelength translates to a frequency of roughly just under 200 kilohertz - a hertz being one cycle per second and a kilohertz 1000 cycles per second. The visible colour with the shortest wavelength is violet, with a wavelength of 420 nanometres (billionths of a metre or millionths of a millimetre). Think that’s small? The diameters of the largest atoms are in the area of 300 picometres (trillionths of a metre or billionths of a millimetre) - around a thousand times smaller than the wavelength of violet light, and the smallest are just a tenth of that size.

This, of course, evades the question of why some materials are transparent or translucent. And why the transparent ones are capable of bending (refracting) a beam of light - a phenomenon without which cameras, binoculars and telescopes wouldn’t work. Wikipedia has a useful bit about this.

Basically, a light ray (or a stream of photons - take your pick) striking an atom can interact with the atom’s electrons in several ways.

Pause for thought... The Wikipedia page cited refers to photons as ’individual packets of light energy’. I had a lightbulb-on-top-of-the-head moment when I read this, because I know about packets in the context of computer data, and this offers quite a tasty analogy. The data comprising this web page arrived in your computer down a single wire in the form of a voltage switching on and off: on represents 1 and off represents 0. If you looked at this oscillating voltage, which you can do on a device unsurprisingly called an oscilloscope, you would see a waveform - a rather untidy one, with on and off periods of varying lengths, but still a waveform - the untidiness explains the horrible noise produced when early home computers loaded their programs from ausio cassettes!. This continuous data stream is chopped up into packets which computers can see as discrete entities. If you were to connect a photoelectric cell, which turns light energy into electrical energy, to your oscilliscope, you would also see a waveform (provided the cell and the instrument could react fast enough). So if something (the electron, perhaps) could react to a brief burst (packet) of light energy as if it were a particle, you could call that particle (real or virtual - who cares?) a photon.

So whatever the packet is - and please remember that we’re operating at the quantum level here - it and one of the atom’s electrons meet. And what happens? One of ’several’ things, of which the Wikipedia page cites four:

1. The electron absorbs all of the energy of the photon and re-emits it with different color, giving rise to luminescence, fluorescence or phosphorescence which we see as the matter glowing (emitting light energy).
2. The electron absorbs the energy of the photon and sends it back out the way it came in - reflection or scattering.
3. The electron cannot absorb the energy of the photon (why?) and the photon continues on its path - transmission or, as we know it, transparency.
4. The electron selectively absorbs a portion of the photon, and the remaining frequencies (colours) are transmitted in the form of spectral color (a waveform can be a mixture of lots of lesser waveforms).

Actually, not ’one of several things’ but more likely a mixture of two or more.

Not all photons are identical - a photon can be of any colour, and the way it interacts with matter depends on some unspecified property of the electron it encounters. Since all electrons are identical (I hope!), this property must derived from the atomic structure in which the electron exists. Whatever, we get either a glow (old-fashioned TV screens offer the obvious example), the light coming back unchanged, transparency or the light coming back a different colour (which makes the matter appear to have a colour of its own).

(Actually, the word ’colour’ in this context is misleading. The term ’photon’ is used to describe a particle (or packet) of any kind of electromagnetic radiation. The spectrum is unbelievable, extending from frequencies way below what we can hear to gamma rays and x-rays.)

Enough. If you want some more, have a look at the section headed UV-Vis: Electronic transitions on the Wiki page.

And why do things ’feel’ solid? That’s easier: because one atom (even a little one) can’t pass through the empty space inside another (even a big one).

If that doesn’t convince you that the quantum world is very different from the macro world, nothing will! To be honest, I have no idea how much sense what I have written here makes, but it does incline me to take all this quantum stuff very seriously - even if I haven’t a hope of really understanding it.

So what are we made of?

My Dad, who was an industrial chemist and compiled a massive book that started as Solvents Manual in 1954 and was retitled Solvents Guide for the second edition in 1963 (and which can still be found in various university library online catalogues, and even on Ebay), had a profound contempt for theoretical physicists. He accused them of inventing a new particle every time one of their equations wouldn’t work, and then of rushing around desperately trying to find it. That was some decades ago, and interestingly Prof Jim says in his section on quarks (don’t panic - some, if not all, will shortly be revealed) ’By the second half of the 20th century, so many new elementary particles had been discovered that physicists began to question whether they were truly elementary at all. Just as the atoms of the 92 different kinds of elements [once thought to be indivisible] were found to be made up of just three particles: protons, neutrons and electrons, so perhaps were all these particles composed of just a few even more fundamental constituents.’

I first heard about quarks in 1977 in Nigel Calder’s BBC documentary The Key to the Universe. I remember a drunken discussion about it with some fellow teachers, one of whom claimed to have ’understood’ the programme. The rest of us freely admitted that we had not, and accused him of bullshitting.

But I digress. The theory that some of what were previously believed to be elementary particles are actually composed of different types (or ’flavours’) of quarks seems to be surviving the test of time, but it was refreshing to read one of the ’boxes’ in Prof Jim’s book, contributed by Frank Close, Professor of Physics at Oxford. His introduction says: ’At various stages in history the candidates for the fundamental building blocks have difffered. A century ago, the atomic elements were believed to be fundamental; by the 1930s it was electrons, protons and neutrons. Today, the electron is still on our list but protons and neutrons are known to be made from yet smaller particles - the quarks. An obvious question, with history as our guide, is whether the electron and quarks are indeed fundamental, or made of yet smaller pieces like Russian dolls. The honest answer is: we don’t know! All we can say is that with the best experiments we are able to do today. there is no hint of deeper structure. There are also hints that there is something special about this layer of the "cosmic onion".’ How refreshing (especially after trying to read Roger Penrose’s impenetrable epic) - a physicist who writes clear, plain English and cheerfully admits that it’s all just theory!

Anyway... Prof Jim tells us that the hypothesis that protons and neutrons are composed of quarks ’was confirmed...In an experiment [in which] high-energy electrons were scattered from protons and neutrons. ...the directions in which the electrons bounced back revealed that hidden inside each nucleon [the collective name for the protons and neutrons that comprise the nucleus] were three tiny lumps of matter. The quark idea had been vindicated.’

Apparently there were originally thought to be three flavours of quark, but ’We now know there to be six in total’. Know? Prof Frank, above, says ’We don’t know!’. However, for the purpose of this section, it doesn’t really matter because the nucleons are apparently made up of only two types: a proton contains two ’up’ quarks and one ’down’ quark, while a neutron has two ’down’ quarks and an ’up’ quark.

Conveniently, we are told that an ’up’ quark carries a positive charge equal to two-thirds that of a electron and a ’down’ quark carries a negative charge equal to one-third that of an electron. The proton’s two ’ups’ and one ’down’ balance out at one electron’s worth of positive charge, while the neutron’s two ’downs’ and one ’up’ add up to no charge at all. So, as we knew all along (but not quite why) all nuclei have as many electrons’ worth of positive charge as they have protons, which allows them to hold the same number of negatively-charged electrons in ’orbit’. The neutrons and protons cannot be held together by the electromagnetic force, because this would drive the positively charged protons apart and would neither attract nor repel the neutral neutron. The ’cement’ is ’the strong nuclear force’ (to distinguish it from ’the weak nuclear force’, about which I have yet to read). While the lighter elements have equal numbers of protons and neutrons in their nuclei, the heavier ones tend to have more neutrons.

So it seems that all the matter in the Universe, including you, me and Prof Jim, is built from just three simple blocks: electrons, ’up’ quarks and ’down’ quarks. Oh yes - and an awful lot of empty space.

What the other four flavours of quarks and the various other particles contribute, I don’t yet understand (the ’yet’ might be optimistic). But we are all made of atoms, and all atoms are made of just those three components (unless, of course, the theory really is a load of old cobblers!).

Anyway, according to the current models, everything (and that really does mean everything) was in an extremely hot and dense state - a singularity. What sort of state it might have been in previously and how it got into that hot and dense state and how long it had been in that state do not seem to be explained in any text I can make sense of.

Anyway, some 13.7 billion years ago the singularity began to expand rapidly (terms like that seem to be defined differently from how they are in common usage!), which resulted in the expansion we still see today. It also resulted in cooling (also a relative term!), allowing energy to be converted into various subatomic particles. From the Wikpedia page I’m using as a source, it is unclear where the quarks fit into this sequence, because the particles are said to include protons, neutrons and electrons - the components of atoms. It would, apparently, have taken ’thousands of years’ for these particles to combine to form atoms (the mere blink of an eye - there have been 13,700,000 ’thousands of years’ in the life of the universe).

Anyway, the first elements created were a lot of hydrogen (the simplest and lightest) and ’traces’ of helium and lithium (the next two in terms of ’heaviness’). These atoms were not distributed quite evenly through space, so gravity created discrete clouds which fell in on themselves to form stars, whose density went on increasing until each became a monstrous nuclear fusion reactor. Within these, the lighter elements were created - up to and including iron. It seems that these hyperactive early stars were (relatively) short-lived, and it was the collossal explosions of their deaths - supernovae - that created the remaining, much heavier elements and scattered them all over the cosmos.

The process of the birth and death of stars continued, only now working on a much wider range of heavier elements as well as the ubiquitous hydrogen. 13.7 billion years and an awful lot of nuclear fusion after the Big Bang, here we all are.

Talking of The Big Bang...

I found some clarification of the process described above on the website of the Large Hadron Collider which has just got back into gear following its very disappointing breakdown when it was first fired up:

’At the earliest moments of the Big Bang, the Universe consisted of a searingly hot soup of fundamental particles - quarks, leptons and the force carriers. As the Universe cooled to 1000 billion degrees, the quarks and gluons (carriers of the strong force) combined into composite particles like protons and neutrons.’

I love ’As the Universe cooled to 1000 billion degrees’ - you have to ask just how hot is ’searingly hot’... Anyway, what went on at the birth of the Universe wasn’t just quantum-weird: it was inconceivably-bloody-hot-weird, too. If you want to know more than I’ve said above about quarks, and what leptons and the force carriers (which I haven’t mentioned before) are, I suggest having a go at Prof Jim’s book.

Combining these two sources, it seems that everything there ever was, and is, started out as pure energy, concentrated in one very tiny space. We know from combustion, fission and fusion that matter and energy are interchangeable, but in everyday life we are only familiar with the transition from matter to energy. The Universe, it seems, began with a collossal conversion of energy into the most basic building blocks of matter.

Zero and infinity again!

Oh yes: at some point, Prof Jim drops in, as a self-evident fact, the assertion that any number divided by zero equals infinity. This contradicts what I said in Infinity a bit closer to home, where I demonstrated to my own satisfaction (if to nobody else’s) that neither zero nor infinity are actually numbers. Now I’d be the first to admit that, when it comes to a disagreement on anything mathematical between the 67-year-old holder of a bare pass in maths at O-level, gained 51 years ago, and a professor of physics, there is no contest. However, I still hold to my view that zero and infinity aren’t numbers in arithmetic, except in the sense that (and only in the case of zero), when dealing with whole numbers and fractions in the decimal (or any other base system) you need a symbol for ’none in this column’ - no whole leftover hundeds or tens, and no spare tenths, or thousandths, or whatever:

102.000123

says this quantity consists one hundred, no spare tens, two ones, no tenths or hundredths or thousandths, but one ten-thousandth, two hundred-thousandths and three millionths - or a hundred and twenty-three millionths. The zeros are simply an agreed convention. To add just zero to or subtract it from a real quanitity, or to multiply a number by zero - let alone to divide a quantity by zero - is arithmetical nonsense.

My computer backs me up, insisting that any attempt to divide a number by zero generates an error. If a computer can’t do it, I certainly can’t!

As for infinity, it doesn’t matter how big a number is: in arithmetic, you can always add one to it and get a bigger number. So infinity can’t be the answer to an arithmetical problem. And division is just arithmetic. Sorry, Prof!

Fusion power - just around the corner?

Finally, I was greatly cheered by Prof Jim’s confident prediction that nuclear fusion power stations will definitely be built within decades. Pity I won’t be around to see the benefits (unless I’m very wrong in my beliefs about religion).