From Micro to Macro

Adventures of a Wandering Physicist

Vlatko Vedral

• Publisher: WSPC
• Year: 2018
• ISBN:
  9789813229532
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

-->

This is a popular science book exploring the limits of scientific explanation. In particular, it debates if all sciences will ultimately be reducible to physics. The journey starts with physics itself, where there is a gap between the micro (quantum) and the macro (classical) and moves into chemistry, biology and the social sciences. Written by a practising scientist, this volume offers a personal perspective on various topics and incorporates the latest research.

--> Contents:

• Prologue: The Point of It All
• Physics and its Troublesome Gap
• Chemistry and Computing: Lost in Translation
• Biology: The Biggest Gap of Natural Science
• Uniting the Natural Sciences
• Economics
• Sociobiology
• Conclusion: Can We Bridge the Social-Natural Science Gap?
• Epilogue: The World, the Flesh and the Devil
• Acknowledgements
• References
• Index

-->
--> Readership: Students, general public, academic professionals. -->
Keywords:Interdisciplinary;Reductionism;Quantum;ComputationReview:

"In the course of speculating about unifications that might close the amazing, blatant 'gaps' in our knowledge, Vedral provides a refreshing and engaging tour of those gaps, and of the (apparently) firmer ground between them."

Prof David Deutsch
Oxford University Mathematical Institute
0

CHAPTER I

PHYSICS AND ITS TROUBLESOME GAP

If you want to understand how a car works, you have to get your hands dirty. You have to get up close and personal with its parts (NPI), before you can really understand the beast itself. The micro laws of each part give rise to the macro ones. And this, intuitively, is how it should be. The whole is the sum of its parts.

In physics, we are working on a much smaller scale than car parts, but the logic is the same. We are, of course, talking atoms (and in the context of this book the motion of atoms, rather than types of atoms, which many more books could be written about). The first genius to explain how the individual motions of atoms can be combined to explain the collective behaviour of stupendous numbers of them was Austrian physicist Ludwig Boltzmann. Common sense might tell us that it is impossible to say anything accurate about a gazillion atoms since each of them moves in its own particular and, to a large degree, random way. But randomness is the thing that helps us here, in walking the first line in physics between the micro and the macro.

Let me give you an idea of just how small we’re talking. Atoms are measured in nanometres; a nanometre is the size of 10 atoms lined up next to each other. Mathematically, it is a billionth of a meter. Humanly, it is about the amount your hair (or beard) grows by in a second. In other words, your hair grows by some 10 atoms every second. If you have just had a bad haircut and all you can do is sit and wait for it to grow back, you will have to “hermit-ise” yourself for about a month until your hair gets a few centimetres longer. And that few centimetres is about 100 million atoms sitting next to each other in a straight line.

By comparison, the size of the visible universe is roughly 1000000000000000000000000000 bigger (that is 10 to the power of 27 times bigger). You will be very grey by the time your hair grows that long. In terms of size, the micro to macro transition we are discussing involves traversing this vast space and understanding all the phenomena in between. What could go wrong?

Nowadays, we know that atoms exist because we can actually see them under a microscope (albeit a very special, Nobel Prize-winning microscope), but this was not the case a hundred years ago. Then we only had indirect evidence, and this evidence is one of the key links between some micro and some macro aspects of the physical world. If we could not see them, how could we possibly have known that they existed?

Let us go back to me for a minute. I remember the first time the idea of atoms popped into my head. I was a young spotty teenager taking a flight with my school on a trip to the stunningly beautiful Croatian seaside. I was looking out of the window when it occurred to me that the aeroplane engine must only be half the story behind how aeroplanes could fly. I mean, the engines push the plane forward, but what gives it the upward thrust to lift off? It is obvious with rockets — their engines blast off fuel downwards giving the rocket an upward push (thanks to Newton’s ‘action and reaction’). But not with planes, where the weight of the air above the plane makes it even harder to take off.

The twist in the story is that when the aeroplane is moving, the upward pressure of atoms going below the wings is greater than the downward pressure of the atoms going above the wings. And there we get the upward thrust, the motion of atoms and the pressure they exert when they hit the wings. If there were no atoms, the plane could not fly. This is why planes do not go above 35 thousand feet — there is hardly any air there. And this is what struck me like a bolt of intellectual lightning. The fact that we have flying planes is indirect proof of the existence of atoms (I say ‘indirect’ because direct proof would constitute directly seeing or experiencing them physically). An unusual train of thought for a teenager, but there we go, this is what floated my boat. Yes, before you ask, I was single for a lot of my teenage years.

Not getting the balance right between upward and downward air pressure is actually the cause of more than half of all aeroplane crashes in the last 20 years. If the aeroplane does not fly straight, but at an angle, then at some point it loses the upward thrust, leading to what is known as the ‘aerodynamic stall’. Getting out of the stall — which leads to rapid descent of the plane — requires a careful pilot manoeuvre. But sometimes, it is too late for the pilot to do anything. This is what happened to Air France Flight 447, a scheduled passenger flight from Rio de Janeiro to Paris which crashed on 1 June 2009, killing all passengers and crew, 228 in total.

The Wright brothers flew the first plane in 1903. So already we must have known (though we did not quite know we knew it) that atoms existed. Einstein’s paper in 1905, only two years after the Wright brothers’ flight, was final accepted proof of their existence. Coincidence? He did not use aeroplanes, though the spirit of his logic is remarkably similar. He used particles of dust that execute a random motion we now call Brownian, after a biologist who first observed this motion in the eighteen century. A speck of dust suspended in a tube will move erratically as if it was pushed around by an invisible drunken ghost.

Einstein hypothesised that the reason for this is that the speck was bombarded — not by a drunken ghost (for why would he waste his time pushing specks of dust around?) but by a lot of small objects (atoms) which move about in a random way. He went even further. By measuring the precise details of the motion, he could deduce the number of atoms in the tube where the dust moved about. And he got what is known as the Avogadro’s number, roughly the number of atoms in two pints of water — a one followed by twenty-six zeroes (we like our big numbers in physics).

In the same year, Einstein made another micro to macro connection. This one led Einstein to conclude that if a gas consists of atoms, light also must consist of them. The atoms of light are called photons. To reach this conclusion, he turned around our usual way of using the micro to explain the macro. He started with the macro.

The equation of light in a box (using thermodynamics) gives the same link between its entropy (disorder) and volume as the corresponding equation for a gas comprised of a great number of atoms. Einstein therefore argued that since the behaviour of light and ordinary gas is the same at the macro level, it must have the same underlying micro cause — a powerful reasoning that we will encounter over and over again in various sciences. Ergo, Einstein says, there are atoms of light. Being Einstein, he did not stop there. He went on to propose an experiment that would provide more direct evidence of photons — this was the photoelectric effect for which he was awarded the Nobel Prize in physics in 1921.

Going back even further than Einstein is a rather ingenious discovery made by Daniel Bernoulli. It is particularly ingenious given that scientists doubted the existence of atoms until Einstein’s prolific paper-producing year of 1905. Bernoulli came from one of those miraculous families that produce consistently brilliant children, with Daniel, Jacob, Johann and Nicolaus all making important contributions in science and maths. What Daniel did was connect macro gas behaviour with the micro motion of atoms. This is an important gap-filler if ever there was one. It led to the steam engine.

I remember the exact moment I understood this connection. In high school, aged 16, I finally had my prayers answered and was graced with an inspirational physics teacher, Mrs Bojana Nikić. It was the first and last time in school that I had a great physics teacher — one of the reasons I knew I was meant to be a physicist was that I loved it despite being taught it badly.

Mrs Nikić said to us: ‘I will now use Newton’s laws to derive a thermodynamical equation of state for a gas.’ Most of the kids in our class blinked up at her as if she was talking Yiddish. But not me. This sounded like magic to me. (Yep, still single.)

The equation of state links three properties into one formula — the pressure of the gas, its temperature and its volume. That is the one where the pressure and volume are proportional to temperature. If we increase the volume at the same temperature, we decrease the pressure. Larger volume means that the gas is less dense and molecules hit the walls less frequently — since they have more distance to travel. Hence, the pressure, which is nothing but the force exerted by molecules as they hit the walls, drops. The thermodynamical equation describes the macroscopic properties of a gas and does not at all care about the fact that the underlying microscopic behaviour is based on atoms and molecules.

This deduction of the equation of state from the motion of atoms is the first significant Reduction in physics, and we owe it all to you, Daniel.

Bernoulli imagined that the pressure of a gas is due to its being composed of tiny atoms moving about and hitting the walls of the container the gas is confined to. Then, using Newton’s laws, he was able to argue that the pressure these atoms exert when bouncing on the walls is actually proportional to the number of atoms, their mass and velocity (squared). Subsequently, he used a bit of statistics, which was needed since the atoms are moving about in a completely erratic way — there is an equal chance of finding an atom moving in any direction. After adding this to his logic, Bernoulli showed that the pressure of the gas is actually proportional to the temperature (which is just the energy of the atoms, namely mass times the velocity squared) and inversely proportional to the volume.

And so, the equation of state tells us that any two gases with the same volume and pressure and temperature, actually also contain the same number of atoms. This itself is fascinating, but to think that this comes down to Newton’s law of force = mass/acceleration blew my 16-year-old mind, and still does today. How can one not love physics? It shows us beautifully that seemingly unrelated facts are actually consequences of one and the same rule.

Connecting the macro gas behaviour with the micro motion of atoms is no doubt intellectually pleasing. It is always beautiful when a more complex phenomenon is reduced to a simpler underlying one. But this has technological advantages too, and working at this macro level, explains how the steam engine was made. We heat it up, it expands and by expanding, it can do work. But, if we had access to the micro side of this, the atoms, we could actually use it more efficiently and encode far more information into it. This is why Richard Feynman, Nobel Prize-winning American physicist, wrote a paper called ‘There is plenty of room at the bottom’ (what a title). For Feynman, this meant that if we venture into the nano and quantum domains, we could do much more technologically speaking. The first Reduction changed science, changed technology, and changed the world we know.

Another one of the first big bridging triumphs of quantum physics was explaining the behaviour of large solid bodies (like sugar cubes, or pieces of chalk or anything that is not alive) using the underlying quantum behaviour of atoms. One of (many) puzzles before quantum physics was this: as we put the solid in a hot environment it starts to become hotter itself. As we ramp up the external temperature, the solid absorbs more heat, thereby increasing its own temperature. The puzzle? Classical physics could not explain why this happened! Classical physics suggests that the heat capacity of a solid (as the quantity is known) should be independent of temperature. In reality, it actually goes up with temperature.

The only way to explain this is to suppose that electrons move as the solid heats up and its atoms jiggle about harder and harder. And the higher the temperature, the more the electrons move and the harder the atoms jiggle, hence the higher heat capacity. Classical physics simply cannot account for this. And the first person to point this out was — you guessed it — Einstein again. At some point, he turned against quantum physics (‘God does not play dice’, he tells us firmly), but in the early days, he did more to establish it than any other physicist at the time. Needless to say, his early intuition was the correct one — quantum physics has still not encountered any experiment it is not able to explain with great precision. Physicists love to close gaps. That is why our biggest all-time frustration is the one that remains resolutely open.

THE BIG GAP

Enter Einstein once again, this time with his theories of relativity — the special one is another one of his 1905 papers (it was a busy year) while the general theory of relativity was completed in about 1915. Let us zoom out big time from the quantum level of atoms, right out to one of the forces that governs our universe: gravity.

The universe, we have long believed, is governed by four forces; electromagnetism, gravity, and weak and strong forces. Electromagnetism and weak and strong forces all fit nicely into quantum explanations, and no gaps are left there. But not gravity. This is why quantum physics and general relativity (which explains gravity) do not jell. And this is the biggest gap in physics, and in terms of size, the biggest in our whole understanding of reality. Gravity dominates at large distances, and describes the global features of the universe (planets, stars, clusters of stars, galaxies and so on). Quantum physics describes objects on the very smallest scale. Both theories have been very successful in their own domains. But they just cannot be unified. Like champagne and cigars. Both wonderful, life-giving delights, but they will not work together.

Let me briefly explain how and why (the physics, not the consumables). When quantum physics is applied to the theory of electromagnetism, one of the key consequences is that the energy in electromagnetism cannot be continuous, but comes in discrete chunks, called photons. When we use a laser to excite an electron in an atom, this electron typically goes back to the lower energy state at some point — this process is accompanied by the emission of a photon. The photon is the messenger of the electromagnetic force. Weak and strong forces operate inside a nucleus and when quantised, they also lead to particles (the analogues of photons) that mediate their interactions. The quantum theory of electromagnetic, weak and strong forces (and they can all be thought of in a unified way) is known as the Standard Model and is our best account of all physics. Excluding gravity.

Here comes our trouble-maker. Following the other three forces logically, when we apply quantum physics to gravity, one of the outcomes should be a particle called graviton, the quantum messenger of the gravitational force, in the same way that the photon is the messenger of the electromagnetic force. Maybe graviton is emitted, but the biggest problem is that we, er, cannot even measure it, let alone see it. Now, gravitational force is some 10 to the power of 39 times (1 followed by 39 zeros) weaker than the electromagnetic force. The rate of graviton emission is so small compared to the photon emission that it would take us (much) longer than the age of the universe (13.7 billion years) to ever observe it. Damn.

Surely by logic of the other forces, gravitons exist even if we cannot see them. But we quite like proof of things when it comes to science. Speculation is powerful and important, but experimentation and subsequent evidence is the glue that holds theory together, which is certainly needed if this gap is to be closed. There is also one other tiny problem. Trying to quantise gravity actually leads to predictions that are ridiculous at the other extreme. Namely, rather than forecasting tiny numbers, they actually lead to infinite quantities. The predictions for emission of gravitons I discussed are actually based on truncating this infinity. However, it is hard to do this in a consistent way. There is therefore a mathematical inconsistency at the root of the problem too.

So, here we are, standing at the edge of the biggest gap in physics, one that has kept many a physicist awake at night over the last hundred years. This is a genuine micro to macro gap since quantum is so far all about small objects while gravity concerns planets, stars and galaxies. Will quantum physics and gravity ever be unified? And if they were — what could be achieved?

Solution One: It could be that although quantum physics and gravity cannot be put together in a mathematically rigorous way, this might not be an issue after all since any possible consequences are just too small to ever observe experimentally. The gap is only really a gap in our observations, and there is not too much point losing sleep over something we would never be able to see anyway.

Of course, my eager mind certainly does not want to stop there. It wants to look at Solution Two: Perhaps this gap can be closed — by looking at everything in a different way.

But, wait a minute. What could be the benefits of this gap being closed? Why bother reading seven pages of my Great Reduction hypothesising? Well. Back to what I predicted in the prologue — that uniting the micro and macro will help us both spiritually and technologically. First, there is the spiritually satisfying feeling of understanding the whole physical universe with one theory only. This will either be a new theory of quantum gravity or a realisation that gravity is a consequence of quantum physics. With either theory, the spiritual benefits will be the same — science will provide the comfortable world-view that can now arguably only be found in religion.

The technological benefits of bridging the quantum gravity gap could also be enormous. The possibility of efficient space travel is becoming more and more important. We might not be able to resolve our environmental problems on earth in time to make it continuously habitable. In that case, it is very important to understand gravity properly since it determines to a high degree how far and how fast we can travel. If quantum effects matter in strongly gravitational systems, then maybe quantum gravity could improve our ability to travel to distant places. Also, perhaps quantum effects make the universe work differently, and maybe distant parts are actually somehow quantumly connected. This is all speculation, of course, but speculation is exactly where all theories begin. And maybe, just maybe, this one will be crucial for our future.

A POSSIBLE SOLUTION

Many new ideas in physics are introduced out of desperation. Planck called his quantum hypothesis — when he introduced the idea that energy comes in little chunks and is not continuous as classical physics would have us believe — an ‘act of desperation’. It was an act of desperation because it did not make sense to Planck, other than the fact that it was the only way he saw in which to match theory with the experimental results. But he did not have any deeper way of arguing for quanta. That had to wait another 25 years, for Born, Heisenberg, Jordan, Schrödinger and Dirac to discover the full formalism of quantum physics. Sometimes, the bigger picture of a new theory is revealed later — but the beginning often starts with a leap of faith. So, if you will allow me to leap…

At the heart of my speculations are thermodynamics and information theory. I will go into each in turn and build up my case for how they could potentially become our Great Reduction. Before that, however, it is time for some fun. Perhaps it was Will Hutton at that Oxford dinner party that gave me the taste for this, but I would like to stick my neck out once again.

I would like to suggest that thermodynamics is so robust precisely because its foundations are in...

Table of contents

• Cover
• Halftitle
• Title
• Copyright
• Dedication
• Prologue
• Contents
• Chapter I: Physics and its Troublesome Gap
• Chapter II: Chemistry and Computing: Lost in Translation
• Chapter III: Biology: The Biggest Gap of Natural Science
• Chapter IV: Uniting the Natural Sciences
• Chapter V: Economics
• Chapter VI: Sociobiology
• Conclusion: Can We Bridge the Social-Natural Science Gap?
• Epilogue: The World, the Flesh and the Devil
• Acknowledgements
• References
• Index