What is time? Everyday experience tells us that time is something that passes, measured by the ticking of a clock. If everyone synchronises clocks, and those clocks are mechanically perfect, we might expect that everyone will agree on the time for evermore. We exist in the present, and we are comfortable defining the present moment as ‘now’. Since we all agree on what time it is, therefore we must agree on what ‘now’ means. This implies that the past is gone, fading in memory as a canvas dims with age, and the future is yet to come.
What is space? Space feels like the arena within which things happen; a giant box containing Earth, Moon, Sun, planets and stars. Two people could measure the distance in space between Earth and Moon at an agreed time on perfectly synchronised clocks with perfectly calibrated rulers, and they would agree.
In this chapter, we will follow Einstein in discovering that the obvious statements in those last two paragraphs are wrong: we will discover that time and space are not what they seem. This will lead us to consider the startling possibility that Monet’s magical summer’s day may have an existence beyond his ageing canvas. As the great physicist and mathematician Hermann Weyl wrote, ‘The objective world simply is, it does not happen. Only to the gaze of my consciousness, crawling along the lifeline of my body, does a section of this world come to life as a fleeting image in space which continuously changes in time.’
But we must start at the beginning, and think carefully about how concepts such as distances in space and intervals in time are treated in physics. The first steps towards the modern understanding of space and time were arguably the first steps along the road to modern science itself. Our story begins in the seventeenth century with Galileo, Newton, and the systematic study of the motions of the planets and Earth’s place in the Solar System.
One of Claude Monet’s most famous works, Coquelicots (Poppies), captures a perfect moment in time, on one summer’s day in the French countryside in 1873.
Our story of the modern understanding of space and time begins with the early astronomers, shown in this 1692 engraving: from left to right, Galileo, Hevelius, Aristotle, Brahe, Copernicus and Ptolemy.
Galileo’s diagram of the Copernican (heliocentric) system of the Universe. It also shows his own discovery, the four moons of Jupiter.
Life on a spinning, orbiting planet
The study of motion has a long and controversial history that stretches back many thousands of years. At first sight it is hard to imagine how the study of motion could ever be controversial; it seems like such a basic thing. The origin of the controversy was, in part, due to the fact that we live on a spinning planet that is hurtling around the Sun. That statement was still problematic in Newton’s time, partly for well-known theological reasons but also because it really doesn’t feel as if we are moving. Common sense informs us that we are standing still, and common sense of the ‘I might not know much about science but I know what I think and feel’ variety has a profoundly negative effect on public discourse in the twenty-first century – never mind in the seventeenth. If the feeling that we are standing still at the centre of the Universe on an immovable planet really were reliable, Galileo and many others would have been saved a lot of bother.
It is sometimes the case that remarkable ideas become so embedded in culture that they cease to feel remarkable simply because they are familiar. The motion of the Earth around the Sun and the sheer hidden violence of the celestial dynamics that Nature conspires to conceal from us is an excellent example of this conundrum. Most of us give very little thought to what’s actually happening to the ground beneath our feet because we’ve been taught to hold difficult concepts in our heads with reckless intellectual abandon. An educated person probably knows that we’re all walking around on the surface of a sphere of equatorial circumference of 40,000 km and mass 6 thousand million million million tonnes, spinning around an extravagantly tilted axis once every 24 hours, and that the whole vast spinning thing is barrelling around the Sun at close to 30 kilometres per second in order to make it around the 940-million-kilometre orbit every year. Such a person probably doesn’t find it amazing that we don’t notice this on a day-to-day basis. It’s dizzying.
The reason why we don’t notice is a deep one, and to appreciate it we need to explore precisely what we mean by motion. Before the seventeenth century it was widely believed that things move when they are pushed and stand still when they are left alone. Aristotle is usually credited with the expression of this intuitive view, based on the idea that everything that happens must have a cause. Since motion is something that happens, involving a change in the position of an object over some interval of time, it must have a cause. If the cause is removed, the motion should stop. Intuitively reasonable perhaps, but not correct.
It is true that if you push an object along a table, it moves, and if you stop pushing it, it stops. That is because friction between the object and the table slows it down. If there is no friction and you give the object a push, it will carry on moving until you give it another push. This is known as the principle of inertia, and it is a remarkable thing when you think about it.
The incomparable Nobel Prize-winning physicist Richard Feynman described how his father introduced him to the concept of inertia when he noticed something whilst playing with a toy wagon and a ball.
‘“Say, Pop, I noticed something. When I pull the wagon, the ball rolls to the back of the wagon, and when I’m pulling it along and I suddenly stop, the ball rolls to the front of the wagon. Why is that?”
‘“That, nobody knows,” he said. “The general principle is that things which are moving tend to keep on moving and things which are standing still tend to keep standing still, unless you push them hard. This tendency is called inertia, but nobody knows why it’s true.”
‘Now, that’s a deep understanding. He didn’t just give me the name.’
I like this because it illustrates something important. There are some questions about Nature that have the answer ‘because that’s the way our Universe is’. There have to be answers like this, because even if we knew how to derive all of the laws of Nature from first principles, we’d still need to know what those principles are. The law of inertia, as expressed by Feynman’s dad, is one such principle as far as we know. One of the most difficult things in modern physics is to find out which properties of the Universe are truly fundamental and which follow from a deeper principle or law. This book is all about asking ‘Why?’ Sometimes, the answer is ‘because it is’. This may be wrong – there may be a deeper reason for something that we haven’t yet discovered, but it isn’t a superficial answer.
The frontispiece of Isaac Newton’s seminal work, The Principia Mathematica, published in 1687, which expressed his principle of inertia.
Isaac Newton expressed the principle of inertia in the first of his three laws of motion, which he published in 1687 in The Principia Mathematica. Virtually everyone today can recite it word for word, or at least remembers a time at school when they could:
‘Absolute, true and mathematical time, of itself, and from its own nature flows equably without regard to anything external …’
– Isaac Newton.
‘Every object continues in a state of rest or uniform motion in a straight line unless acted upon by a force.’
EVERY OBJECT CONTINUES IN A STATE OF REST OR UNIFORM MOTION IN A STRAIGHT LINE UNLESS ACTED UPON BY A FORCE.
There is a subtlety here. If we are to say that an object is moving, then we have to answer the question ‘relative to what is the object moving?’ Newton certainly thought about this question, and almost got the answer right. His writings on the subject are illuminating, and go to the heart of questions about the nature of space and time, and how they are linked to motion. Newton stated the assumptions behind his laws clearly.
‘Absolute, true and mathematical time, of itself, and from its own nature flows equably without regard to anything external …’
That’s the intuitive view that time ticks along,
and everyone agrees on the rate at which it ticks.
‘Absolute space, in its own nature, without regard to anything external, remains always similar and immovable … Absolute motion is the translation of a body from one absolute place into another.’
Truly deep concepts often sound like utter pedantry. This is one of the few similarities between physics and philosophy.
A 360-degree panoramic view of the Milky Way over the ALMA radio telescopes in the Atacama desert of northern Chile.
This is Newton’s assertion that there is some sort of giant box within which everything happens. We can go a little further and imagine a series of grid lines crisscrossing the box, against which we can mark the position of anything in the Universe. We could then define absolute motion as being motion relative to this universal grid, which we assert to be standing absolutely still in absolute space. This giant grid is an example of what we’ll call a frame of reference. In order to define absolute motion, Newton is assuming that there is a very special frame of reference: the frame corresponding to the universal grid, at rest with respect to absolute space, against which all motion is measured.
Then, wonderfully, Newton makes a further observation;
‘…. but motion and rest, in the popular sense of the term, are distinguished from each other only by point of view, and bodies commonly regarded as being at rest are not always truly at rest.’
Newton is saying that it is impossible to determine whether or not an object is ‘actually’ in motion in a straight line, or ‘actually’ standing still. We might not be ‘truly at rest’, as he puts it, but we can’t tell. This is the reason why we don’t feel as if we’re moving around the Sun while we are standing on the surface of the Earth; on minute-to-minute timescales, we are almost travelling at constant speed and approximately in a straight line. Newton was correct in noticing that if this is the case we won’t feel as if we are moving; indeed, we are at liberty to claim that we are at rest, even though we might not be, in his language, ‘truly at rest’.
Let us make an apparently philosophical aside that has extremely important consequences for the development of Einstein’s theory of relativity. If it’s impossible to decide whether or not we are moving, even in principle, then what use is the concept of absolute space? Is there, in reality, no special frame of reference against which all motion can be judged? Shouldn’t we just jettison the idea? Yes, that is correct, we should, but Newton never did. The wonderful thing is that his laws of motion do only deal with relative motion, and do not rely on his assumption about the existence of a special frame of reference against which all motion should be calibrated. He got the equations right, but then saddled their interpretation with the unnecessary philosophical baggage of absolute space. All of this might seem like pedantry without relevance, but it isn’t. The redundant but comforting idea that space is the fixed arena within which ‘stuff happens’ is positively harmful to our understanding of nature. Jettisoning it allowed Einstein to construct an entirely new theory of space and time, which delivers a more accurate description of the natural world than Newton’s laws.
This does not mean that we want to jettison the concept of a frame of reference – far from it! I’ve realised something about physics during my years of trying to understand it for myself and explain it to others. Truly deep concepts often sound like utter pedantry. This is one of the few similarities between physics and philosophy. Our careful introduction to the idea of frames of reference is a good example; it may seem that we’ve been almost too careful, but we’ll need to take care if we are to understand the somewhat cryptic comments we’ve made so far about the implications of Einstein’s Theory of Special Relativity. With that in mind, let’s take a brief diversion to explore frames of reference in more detail. The effort will be worth it.
An important aside: frames of reference
We can imagine erecting a set of grid lines that span the Universe, just as Newton did. The positions of objects can then be measured with reference to the grid. This grid represents a frame of reference.
Reference frames are more than an interlocking set of rulers, however. We also need to measure time. Let’s also imagine an array of identical clocks scattered across the Universe. All of the clocks sit at fixed positions with respect to the grid. We can now go ahead and measure where and when an event happened; it happened at some position in space (we can use the grid to record precisely where) and at some particular time (we can use the clock adjacent to the event to record precisely when).
It isn’t overstating things to say that the whole of physics can be reduced to understanding the relationships between events. This is why we are taking care to set up the framework (quite literally) that we will use to record the positions in space and time of events. Care is necessary: we need to be very clear on how to measure the time of an event.
To illustrate why, let’s consider a particular event: a firework exploding. The time of the explosion event is the time recorded on a clock sitting next to the firework when it explodes. This is different to the time measured by someone watching from a safe distance away, because the flash of light from the firework will take a small amount of time to reach the person watching. Light travels at approximately one foot per nanosecond, or 30.48cm in a billionth of second, if you’re of metric persuasion. I always think that, if there is a creator, this is evidence that She worked in imperial units. Another way of appreciating why we need to be careful is that we must make no assumptions regarding the rate at which all the clocks tick. We said that they are identical clocks, so you might think they all merrily tick together. But that would be an assumption, and as we will discover later on, that is wrong. This is why we have to be very clear in defining precisely how we should measure the time.
A reference frame is also a way of establishing our point of view; our perspective on the Universe. We are free to erect our imaginary frame of reference, and somebody else is free to erect their own imaginary frame. Generally speaking, any two frames of reference might be moving with respect to each other (imagine one array of clocks and rulers sliding past a second array of clocks and rulers). The range of possible reference frames is limitless, but in his Theory of Special Relativity Einstein singled out a special set of reference frames. Specifically, he introduced the idea of an ‘inertial reference frame’.
Let’s consider a particular event: a firework exploding. The time of the explosion event is the time recorded on a clock sitting next to the firework when it explodes. This is different to the time measured by someone watching from a safe distance away, because the flash of light from the firework will take a small amount of time to reach the person watching.
You are at rest in an inertial frame if you observe that an isolated object is either sitting at rest or moving in a straight line at fixed speed. Frames that are spinning, such as the frame you are currently sitting in on the rotating Earth, are not inertial. Many of the things we take for granted in our lives, from the behaviour of storm systems to the ebb and flow of the tides, are the result of the fact that we are spinning, and therefore not in an inertial frame of reference, even though we don’t feel it. We will see how this works when we explore the ocean tides and the behaviour of storm systems.
As we’ve already mentioned, there isn’t a ‘special’ inertial reference frame; all inertial reference frames are as good as each other. If you’re in an inertial reference frame, you are allowed to say that you are standing still, and there is absolutely no measurement you can make that will tell you otherwise. It is because we are approximately sitting in an inertial reference frame on the surface of the Earth that we don’t feel as if we are moving from moment to moment.
Einstein elevated the requirement that all inertial frames are equivalent to a fundamental principle. This means that identical experiments carried out in different inertial frames will always lead to the same results. To put it another way, the laws of Nature do not change as we switch our point of view between inertial reference frame
s; if they did, we could tell the difference between the reference frames! I don’t want to give the game away early in the chapter, but this ultimate democracy between inertial frames turns out to be such a severe constraint on the laws of Nature that Newton’s laws and the laws of electricity and magnetism cannot both be right. This may not sound too serious, but we will see in Chapter Four that the laws of electricity and magnetism are one of the great pillars of physics alongside Newton’s laws. They describe so many things we take for granted in our everyday lives; the action of electrical generators and motors, the formation of a rainbow, the action of lenses, the optical fibres that bring the internet into your home, and, when merged with quantum theory, the structure of atoms and molecules; the list is virtually endless. It is inconceivable that the framework we use to describe one of the four fundamental forces of nature could be incompatible with the theoretical framework we use to describe motion. This conflict is what motivated Einstein to develop a new theory of space and time. We’ll get to that. For now, let’s explore the idea of describing the world from different points of view, which is to say using different reference frames, within a Newtonian framework. This will lead us to an understanding of the passing of the seasons, the rotation of storm systems and the ocean tides.
Forces of Nature Page 8
