Before we start to claim that the world is an amazing place, we ought to convince ourselves that the result we just found is not just some peculiar feature of light clocks. First, let’s be clear about why we chose to think about a light clock in the first place. We did that because we could make direct use of Einstein’s postulate about the speed of light being the same in all inertial frames. If we had been thinking about pendulum clocks then we couldn’t have exploited that postulate so easily. But, with more work, we could have done this calculation using pendulum clocks, or heart beats, or any other type of clock, and the conclusion would have been exactly the same. You can see that this has to be true if Einstein’s second postulate is correct:
The laws of physics are the same in all inertial frames of reference,
or, more colloquially, ‘it is impossible to tell who is moving and who is standing still’. Suppose that the slowing of the light clock is some peculiarity of light clocks and that it doesn’t apply to other clocks. If that were true, person A (on the train) would notice that their light clock was running slow compared to their wristwatch. But that observation would be enough for them to conclude that they are moving, which would be in conflict with Einstein’s first postulate. The only way to keep that postulate alive is to say that if person A’s light clock takes longer to tick according to person B then so to must person A’s wristwatch. It is time to acknowledge that the world is far more remarkable than we had any right to suppose. We have demonstrated that, if Einstein’s two postulates are correct, two people in motion with respect to each other age at different rates.
To finish off, we can compute the time interval between the two events we discussed in the text: the time between Monet placing a dab of paint on his canvas and the turn of the lock in his door. According to Monet’s timepiece, the interval was eight hours. But, according to the formula we just derived, the time interval between the same two events as measured by the aviator is 8 hours/ hours.
Hyperbola
The distance between two events in spacetime, Δs2=c2Δt2–Δx2. Physically, for any two events, although the distance in space Δx and the distance in time Δt will change when measured by observers in different frames of reference, they must change such that the distance in spacetime, Δs, remains constant. Mathematically, this is the equation of a curve known as a hyperbola. Let’s consider a specific example, equivalent to setting the distance between two events in spacetime to be 1 unit. There are two versions of this ‘unit hyperbola’, which have the equations x2–y2=1 and x2–y2 =–1 These are shown in the bottom illustration opposite. If x2–y2 is equal to 1, there are two curves; one in the upper half plane and one in the lower half plane. This is the situation for events that are ‘timelike separated’, i.e. causally connected to each other. For such events, the distance in space between the events, Δx2, is always less than the distance light could have travelled during the time interval between the events c2Δt2. The spacetime interval Δs2 will therefore always be positive. If the events are not causally connected, which is to say that the spatial distance between them Δx2 is always greater than the distance light could have travelled during the time interval between them c2Δt2, then we have the curve x2–y2=–1. These events are known as “spacelike separated”. As we note in the text, the important point is that when we change between inertial frames, the events slide around the spacetime diagram on these four curves, but never hop between them: causally connected events (timelike separated) always have their time ordering persevered, but causally disconnected events (spacelike separated) need not.
1 For a height of 97 metres (the height of the Asinelli tower) at a latitude of 44.5 degrees north (Bologna) and with ω = 7.3 x 10-5/s (the angular speed of Earth), the deflection is equal to 1.8 centimetres. The details of this calculation can be found, for example, in Forshaw and Smith, Dynamics and Relativity (Wiley).
2 You can see this from the definition of distance in spacetime. Set Δx = 0, because you are in your own rest frame, and note that Δs / Δt = c.
The Moth and the Flame
How did life begin? I think this is one of the two most interesting questions in science, and the most important question in the history of human thought. Cathedrals have been built, wars have been fought and empires have risen and fallen as innumerable demagogues have sought universal agreement for their guesses.
How did the Universe begin? I think this is the other interesting scientific question, but we know less about it at the moment. There are speculative theories that suggest the Universe could be eternal, and that there was no beginning. If this is the case, then the Universe has always existed and the question is answered: It didn’t begin. Whether or not this would be a satisfying answer is up to you. I’d be comfortable with it.
Irrespective of what happened at the beginning of time, we know there was a period 13.8 billion years ago when the part of the Universe that we can see today, containing over 350 billion large galaxies and with a diameter of over 90 billion light years, was compressed into a region of space smaller than a single atom. No life could have existed in such extreme physical conditions, so even if the Universe existed in some form before the Big Bang, it’s safe to say that no complex physical structures would have made it through. The observable universe must therefore have been devoid of life at some point in the past, and life must have begun spontaneously somewhere within it, at some point during the last 13.8 billion years. The word ‘spontaneously’ is worth defining here, because it crops up a lot in discussions about the origin of life. In saying that life appeared spontaneously, we are asserting that life is a physical process that emerged as a result of the action of the laws of nature. If we say that the Earth formed spontaneously, we mean that nobody built it; by saying that living things appeared spontaneously, we mean the same thing.
Polarised light micrograph of two Cosmarium sp. desmid daughter cells just after dividing. Desmids are a group of feshwater single-celled algae that have intricate cell walls.
The first atomic nuclei formed in the initial minute or so following the Big Bang, and the first atoms formed in large numbers when the Universe was 380,000 years old. The first stars ignited around 100 million years later, and these assembled the first carbon atoms. It is unlikely that the rich chemistry of life could have begun spontaneously without carbon, oxygen and a handful of the heavier elements beyond the hydrogen and helium atoms that existed before the stars. Life could have got going anywhere in the Universe after this time, and may well have done; we don’t know.
The Blue Marble – Earth in all its glory, as seen on 6 July 2015.
The Earth formed 4.54 billion years ago out of the primordial cloud around the young Sun. It is safe to assume that there was no life on Earth in the early years following her formation; the conditions were too violent and changeable. There is good evidence that life had gained a foothold on Earth around 3.5 billion years ago, and possibly much earlier – we’ll discuss this evidence later. Therefore, we will assume that Earth was once a lifeless world, and that living things appeared at some point in the first billion years after its formation.
Nothing that we’ve said in these opening paragraphs is controversial from a scientific perspective, but there is one assumption we’ll make which is at least contestable. We will assume that life began on Earth, rather than arrived here from space. Since we have discovered no life on planets beyond Earth, this is reasonable, but it is possible that life began on Mars, or perhaps even on comets in the outer Solar System, and was delivered to Earth by impacts from space. This theory is known as panspermia. Unlikely as it may sound, it is a testable theory, and that puts it firmly in the realm of science.
‘Did I request thee, Maker, from my clay to mould me man? Did I solicit thee. From the darkness to promote me?’
– John Milton, Paradise Lost
It is certainly possible that we could discover life on Mars over the next few decades, and if the microbial Martians share our biochemistry and our genetic code, we m
ight be forced to postulate a common origin on either planet, or perhaps somewhere else in the Solar System. This would make the search for the origin of life more difficult, because it is far easier to explore our own planet’s deep history than it is to explore the history of another world. The only way to find out is to do the science, and this is one of the reasons why we send spacecraft to Mars and the potentially life-supporting moons of Jupiter and Saturn. It goes without saying, however, that we shouldn’t stop searching for the origin of life on Earth whilst we build spacecraft to search for life beyond it.
Under the assumption that life began on Earth, it must have been the case that the basic chemistry of life existed on our planet before living things emerged, and that sometime and somewhere chemistry became biology. There is no precise definition of what ‘becoming biology’ means, but it is worth emphasising that biology is just a word for (very) complex chemistry. Living things are constructed from the same set of chemical elements as inanimate things, and they obey the same laws of nature. In this sense we can assert that the Earth is our ancestor and creator, and we would like to know how, where and when the transition from geochemistry to biochemistry occurred.
The dark, narrow streaks that mark the slopes of the Hale Crater on Mars in this NASA image from 2015 provide more evidence that liquid may indeed flow on the planet.
Chemistry is all about the movement of electrons
Living things are made out of simple building blocks with complex interactions. This is obvious in one sense, because everything in the Universe is made out of simple building blocks with complex interactions. We saw in Chapter One that, at the deep sub-atomic level, there are only three building blocks of everyday matter: up quarks, down quarks and electrons. At a higher level, there are protons and neutrons, and higher still are the 92 naturally occurring chemical elements found on Earth. Nobody other than chemistry students or Tom Lehrer remembers all their names, but I am sure virtually every reader of this book will know that they can be laid out in a pattern known as the periodic table, shown on here. Each element has a different number of protons in its atomic nucleus, and an equal number of electrons surrounding it; hydrogen has 1 proton and 1 electron, carbon has 6 protons and 6 electrons, and so on. Chemical and biochemical processes are about the sharing and transfer of electrons between elements, allowing molecules to be formed and broken apart.
At the heart of Mount Ijen volcano lies the largest acidic crater in the world, serene and beautiful, but one of the most extreme natural environments on Earth.
Indonesian miners carry baskets loaded with sulphur from the crater of the Ijen volcano. More than 300 traditional miners work there under extremely difficult conditions.
It’s an alien world that is as beautiful as it is toxic, and one of the few places on the planet where we can glimpse one of the pure ingredients that make up the matter of Earth.
Mount Ijen, lit up by its blue flames at dawn.
All the elements beyond element 92, Uranium, were constructed in laboratories, usually by the bombardment of heavy atomic nuclei by neutrons, or by forcing lighter elements to fuse together. The heaviest goes by the name of Ununoctium, and has 118 protons and 176 neutrons in its nucleus. This exotic nucleus is highly unstable and lives for less than a millisecond.
The periodic table is more than just a pictorial arrangement of the elements; it is the key to understanding how and why elements react together to form molecules. The vertical columns, called groups, contain elements with similar chemical properties. The reason for this is that all the elements in a particular group have the same number of electrons in their outer shells, and it is these electrons that are available for sharing or donating to other atoms; they are the particles that make chemistry happen. We explored the structure of oxygen and hydrogen atoms in some detail in Chapter One. Hydrogen has a single electron. Oxygen has 8 electrons, of which 2 sit close into the nucleus and play no part in chemical reactions. The remaining 6 populate its outer shell, and 2 of these are on their own. Oxygen would dearly like 2 more to complete its outer shell, and it will take them from other atoms given half a chance. This is why hydrogen and oxygen will get together, given a very tiny nudge, to form H2O. I am aware that this anthropomorphic language is a bit unscientific, but to be honest I don’t care. I hope it makes the point, which is that it is the arrangement of electrons inside the atoms of the different chemical elements that leads to chemistry.
The periodic table, showing the tabular arrangement of the chemical elements.
Sulphur has 16 electrons, of which 10 fit close into the nucleus, leaving 6 in its outer shell, just like oxygen. This means that sulphur, just like oxygen, will grab 2 electrons from other atoms if it can. In the presence of hydrogen it will form the molecule hydrogen sulphide, H2S, one of the constituents of the Earth’s primordial atmosphere. Carbon has 4 electrons in its outer shell, and it shares them all to form compounds like carbon dioxide, CO2. Below carbon in the periodic table is silicon, which also has 4 electrons in its outer shell, and it forms similar compounds such as silicon dioxide, SiO2, and so on. As we discussed in Chapter One, electrons are arranged in this highly structured way around atomic nuclei in accord with quantum theory, which is part of the fundamental set of the laws of nature. The important point is that electrons can be transferred or shared between the atoms of different elements, and this is what drives the formation of molecules. Chemistry is all about the movement of electrons, and the movement of electrons can lead to complexity.
A firefly squid glowing with rare luminescence. The reaction between oxygen and luciferyl-adenylate results in the release of energy as blue light.
The manuscript of Mary Shelley’s Frankenstein gave few clues as to its authorship; this and the dark nature of the book made it a notorious novel at the time of publication.
The story of Victor Frankenstein and the creation of his monster brought into public consciousness the debate about the ethics of bringing life from dead matter. This cartoon from 1836 depicts a corpse being revived by a primitive galvanic battery.
Frankenstein’s Monsters
Any discussions about the historical details of the emergence of the modern scientific worldview are at least partly subjective, and academics spend their careers exploring the subject. If a working physicist is asked to identify the first recognisably modern scientific theory, it is likely they will point to Newton’s Principia of 1687, not least because Newtonian physics is still in use today and is taught as part of a twenty-first-century degree course. If you want to send a spacecraft to Pluto, you make the navigational calculations using Newton’s laws. Principia provides a complete and self-consistent model for the geometry and dynamics of the Solar System, with the Sun at the centre and the Earth orbiting around with the rest of the planets. If there was anybody left in 1687 arguing that the Earth occupies a unique physical place, stationary beneath the stars at the centre of creation, they would certainly have had to shut up when presented with a copy of the Principia.
The transition from furious debate about an Earth-centred cosmos to the near-universal acceptance of our physical demotion was relatively rapid once Copernicus and others had opened the intellectual floodgates during the sixteenth century. It’s easy to overlook the philosophical, intellectual and theological storms that the merger between observational astronomy and theoretical physics precipitated.
The Greek philosopher Empedocles, who argued that the Universe originated from four eternal elements – earth, water, air and fire.
Newton was born in 1643, only a year after Galileo died, and Galileo famously encountered quite serious resistance to his support for an orbiting Earth. I’ve written of my admiration for Kepler’s beautiful writing in ‘On the Six-cornered Snowflake’; a distinctly modern voice suffused with wit, curiosity and a careful approach to the exploration of nature echoes down the centuries. Galileo was possessed of a similar confidence and amusing turn of phrase. Here he is, writing to Kepler in 1610, taking a magnificently be
lligerent swipe at the Earth-centred-Universe lobby;
‘My dear Kepler, I wish that we might laugh at the remarkable stupidity of the common herd. What do you have to say about the principal philosophers of this academy who are filled with the stubbornness of an asp and do not want to look at either the planets, the moon or the telescope, even though I have freely and deliberately offered them the opportunity a thousand times? Truly, just as the asp stops its ears, so do these philosophers shut their eyes to the light of truth.’
Galileo would have been at home on Twitter.
Our physical demotion from the centre of all things was well established by the end of the seventeenth century and has continued relentlessly ever since. The entirety of our observable universe is an irrelevant pocket of dust in the wider cosmos, which extends way beyond the visible horizon and is conceivably infinite in extent, and I think society has come to terms with this sort of physical irrelevance. It’s hard to look at the Hubble Ultra Deep Field Image, containing over ten thousand galaxies in a piece of the night sky you’d cover very comfortably with an outstretched thumb, and feel important. Our spiritual demotion, however, is an entirely different matter. By spiritual demotion, I mean the realisation that our very existence has no more significance than our physical location. This is surely the case if life is the inevitable result of the action of the same set of natural laws that formed the stars and planets. Earth must be one of countless billions of living worlds in the Milky Way galaxy alone. This is absolutely not to suggest that our civilisation is not worth celebrating and fighting to preserve – it is my view that civilisations may be extremely rare, even if life is common.
Forces of Nature Page 14
