Finding Our Place in the Universe
Andrew Reynolds Notes on History and Philosophy of Science.
1. What is the purpose of this course?
The purpose of this course is to acquaint you with some of the most important
ideas and the methods of modern science. The approach taken here will be quite different
from that typically assumed in science courses. Science textbooks usually present the
theories and results of modern science with only a hint of the history and philosophy that
are always a crucial and essential part of the story. This gives the impression that
science is an abstract and wholly objective discipline, divorced from all other human
concerns and values. The results of science are made to appear certain and inevitable; as
if all it took was the right person to come along and just see what the next step was to
make science advance ever onward in a sequence of uninterrupted progress toward its
ultimate goal of everlasting Truth. That picture of the scientific enterprise is woefully
inadequate, not to mention rather dull. As we will see in this course, science is really a
lot more exciting than the popular image of a bunch of pasty-faced geeks in white lab
coats making fine measurements on expensive-looking machines. Just like the ‘natural
philosophers’ who preceded them, modern scientists are attempting to discover and
interpret the fundamental forces and laws of the universe. By the end of the course I hope
to have convinced you that,
Science is the continuation of philosophy by other means.
In sum then, the objective of the course is twofold: (i) for you to learn the basic principles of modern science (we will be concentrating on physics and biology); and (ii) to gain an understanding of scientific inquiry as a methodical and self-critical attempt to find effective beliefs capable of withstanding the test of experience and logical analysis.
You will not have to learn any mathematics or solve any equations. But you will be expected to learn what some of the more important laws are and what they mean (in qualitative terms of course).
2. The Origins of Naturalistic Explanation
It is longstanding tradition to trace the origins of rationalistic or
‘scientific’ explanation back to the ancient Greeks of the sixth or fifth
century BCE (before the common era). To do so surely ignores those modern cultures that
trace their ancestries back to other ancient peoples. In the last century or so, for
instance, significant contributions played by the ancient Arab-Islamic, Chinese, and
Indian cultures have become better recognized by European and North American historians of
science. There is also a move afoot to pay greater respect to the achievements of African
and Native American societies (of both the Northern and Southern hemispheres). The
‘non-western’ practices of observational astronomy, plant and animal cultivation
(among others) are inherently interesting in their own right. But they fall largely
outside of the line of historical influence with which we will be concerned here.
What is distinct about the ancient Greek thinkers of the sixth and fifth centuries (BCE) is that it is of them that we have records indicating a new means of writing and thinking about the natural world. Earlier writers about natural phenomena (e.g. floods, tides, thunder and lightening etc.) invoked supernatural explanations, such as the capricious and vengeful wills of very human-like gods and spirits. Zeus, Apollo, and the other gods of Olympus are familiar examples of such mythological or anthropomorphic explanations. These supernatural beings were said to have either procreated the world organically, in analogy with human and animal reproduction, or to have commanded it into being, in analogy with the fiat of political and military leaders. These analogical modes of explanation are typically considered to be poetical rather than scientific, for they figure strongly in the writings of such ancient writers as Hesiod and Homer.
Eventually a novel attempt to explain the existence of the world and its natural phenomena arose and spread in the sea-faring merchant towns of what is now Greece and Asia minor (including Iran, Iraq, Macedonia, and Turkey). This new approach is associated with the names of Thales (c. 585 BCE), Anaximander (c. 610-546 BCE), Anaximenes (c. 546 BCE), Anaxagoras (c. 500-428 BCE), Heraclitus (c. 500 BCE), Empedocles (c. 484-424 BCE), and Democritus and Leucippus (c. 460-370 BCE). It is characterized by an attempt to reduce or explain one kind of natural phenomenon by appeal to other natural elements and properties, rather than by appeal to supernatural or anthropomorphic principles. For instance, Thales is known for saying that everything is originally derived from water; Anaximenes that air is the fundamental element; and Heraclitus said fire; while Empedocles chose all four basic elements then recognized: viz. earth, air, fire, and water. Democritus and Leucippus proposed that all matter and all the elements were composed of very tiny indestructible (atomos = Greek for uncuttable) parts, i.e. atoms.
We call such a strategy of explaining one phenomenon in terms of the properties of another reductionism, and it has proven to be an important and highly successful strategy throughout the history of science. Learning the limits of the reductionist approach has occupied a good deal of time and effort on the part of scientists and philosophers. Sometimes this method can prove too simplistic, as for instance when we try to understand human beings on the explanatory model of mechanical machines, or the physics of atoms on the basis of more familiar ‘billiard ball’ models. (This is where quantum physics is called for.)
But despite their penchant for naturalistic modes of explanation, many of the ancient Greeks did not entirely abolish more anthropomorphic principles. Empedocles, for example, wrote that in addition to the four elements, there was a balance between two fundamental forces that he described as ‘love’ and ‘strife.’ We can give this a more charitable reading if we interpret him to mean by love and strife attractive and repulsive forces like those invoked in electromagnetic and subatomic physics. As we will see though, there is a trend throughout the history of science for people to think less and less in terms of explaining things by appeal to the will of gods or one omnipotent, omniscient God, to thinking in terms of natural ‘forces’, and finally—in some cases—to give up on the idea that science should provide explanations and understanding through ‘pictures’ or ‘models’ altogether, settling merely for accurate predictions which may result from nothing more naturally intuitive than mathematical equations.
All of the thinkers discussed so far are generally called ‘pre-Socratics,’ because they antedated the philosopher Socrates (c. 470-399 BCE). Socrates is best known through the dialogues of Plato (c. 429-347), his student and first really systematic philosopher of the Western tradition. Plato is important in the history of science because of his devotion to the nature of mathematical knowledge and structure, topics of obvious importance to science. But for this reason Plato is really less of a scientist than a philosopher of mathematics. For our purposes he is most significant as the teacher of Aristotle (384-322 BCE). Aristotle was much more concerned with the observable world of the senses than Plato, and he developed a philosophical system of the world (what we might call a ‘cosmology’) of amazing breadth and coherence. Aristotle’s philosophy will be important for this course because it was so immensely popular and influential throughout the Christian world. Once the Catholic church had risen to supremacy in the affairs of European politics (by about 1000 AD), it found his theories so conducive to the church’s own agendas and outlook that for years Aristotle was simply referred to as ‘the philosopher.’
You will be happy to hear that as foreign as it is to that of the modern scientific picture, Aristotle’s philosophy is pretty much based on ‘common sense’ and simple empirical observations available to anyone willing to consult their senses. That so much of the history of science is a radical departure from this common-sensical and empirical view constitutes one of the most precious and puzzling philosophical lessons.
3. Aristotle’s philosophy of the physical world
In this section we are going to look at Aristotle’s philosophy of the
physical world, i.e. his cosmology and his physics. A bit later we will look at his
theories of biology and humankind.
Here are the essentials of the Aristotelian model of the universe. The earth sits motionless at the centre of the universe. The universe itself consists of a bunch of invisible ‘crystalline’ spheres (eight in number), each nested within another larger than itself. To each sphere corresponded a ‘heavenly body’, e.g. the moon, sun, and the five planets then known (Mercury, Venus, Mars, Jupiter, Saturn). On the surface of the final outermost sphere are painted the ‘fixed’ stars. They are ‘fixed’ on the outermost sphere’s surface and relative to one another since they never appear to move with respect to one another. Each sphere rotates on its axis, thereby carrying its respective celestial body (moon, sun, the five planets, and the fixed stars) in a circular orbit around the stationary earth. This explains of course why it is that the sun and moon and stars rise in the east and set in the west in regular circular paths across the sky. For the planets things are a little more complicated. But that was a problem for Ptolemy (c. 127-148 AD) to work out, and we’ll get to that a bit later.
Aristotle, like Plato and the Pythagorean brotherhood, believed that the sphere was the most perfect shape. Why? Because it is symmetrical in every direction; any way you rotate or move it, it looks exactly the same. Moreover, all the other ‘regular’ solids (tetrahedron, cube, octahedron, dodecahedron, icosahedron) can be inscribed within it with all their vertices touching its inner surface. When you look out at the sky, either at night or day, it appears to extend all around you from horizon to horizon in a hemispherical shape. Reasoning by symmetry would lead you to suppose that things look the same on the ‘other’ side of the earth; hence the earth is a sphere surrounded by a spherical sky or celestial heaven. (Aristotle invoked other arguments to show why the earth was a sphere and not flat; e.g. the mast is the last part of a ship to disappear and the first to appear when sailing off on the horizon; the shadow of the earth on the moon during an eclipse is visibly circular.) So observation seems to suggest that the earth is at the centre of the universe. And given that the centre of a sphere is a special privileged place (it's the only point that remains still when the sphere rotates), it only makes sense that things should be attracted toward it. That’s Aristotle’s explanation for why heavy things fall to the ground. They are really falling toward the centre of the earth, which just happens also to be situated at the centre of the entire universe.
Once you grant that, it ought to follow that the earth remains perfectly still at the universe’s centre. For if it moved from the centre, then falling objects–continuing to fall straight toward the universe’s centre–would either miss the earth entirely, or at least fall at an acute angle with respect to the ground. Simple observation shows that that is never the case. Ergo, the earth remains at the universe’s centre. But couldn’t the earth be moving on its axis like the other spheres? Suppose the earth is rotating on its axis at the centre of the universe. Aristotle argued that if that were the case, then objects on the earth’s surface ought to be thrown off into space, for we see that is what happens when we spin a ball or disc. Additionally, if the earth were spinning, then birds in flight would have to fly that much faster just to keep up with the ground. And objects dropped from a tall tower should not fall at the tower’s base, but away from it by the amount that the tower had moved with the earth while the earth rotated. (You may recall that Galileo met this objection head on.) Last but not least, we simply don't feel any motion of the earth, we ought to feel a steady wind at least if the earth is spinning. For these reasons Aristotle taught that the earth cannot be either rotating on its axis nor moving transversely through space. This evidence of the senses would seem to be a pretty good argument against the proposition that the earth moves at all.
Alright. So Aristotle has given some rather convincing arguments as to why heavy objects fall to the ground etc. But why then don’t the celestial objects (moon, sun, planets, stars) fall toward the universe’s centre? Recall that they are carried around the earth in a circular orbit by their respective crystalline spheres. The laws of celestial objects therefore are quite different from those of base earthly stuff. This is another important principle of Aristotle’s philosophy that would take a great deal of mental effort for people to overcome (people like Copernicus, Galileo, and Newton). According to Aristotle, the universe is split into two distinct regions or spheres: the superlunary or celestial sphere (from the moon on up), and the sublunary sphere (everything beneath the moon). These two spheres are made up of completely different kinds of stuff and obey completely different laws. The superlunary sphere is perfect and unchangeable. Things there do not decay or arise anew. The sublunary realm, however, is full of change, birth and decay. That is the very essence of biological things. In the sublunary sphere we find the four common elements: earth, air, fire, and water. In the superlunary sphere there is only a special distinct kind of stuff, the fifth essence or 'quintessence', of which stars, planets, and the spheres are made.
Each thing, in Aristotle’s system of the world, had a natural place. Matter belonged at the universe’s centre, stars belonged in the superlunary realm, fire could be seen attempting to escape upwards to its proper place in the heavens. This hierarchical system is known as the doctrine of natural place. (This idea also exerted an important influence on people’s ideas about politics and society right through the middle ages up till the nineteenth century. Every one, it was believed, has a natural place in society; either as slave, peasant, artisan, merchant, nobleman, or monarch.)
In Aristotle’s language, a stone falling toward the earth was ‘striving’ to reach its proper place. It was falling to the earth because it was part of the ultimate plan, so to speak, for heavy things to occupy a spot at the universe’s centre. To rest there is the final goal of heavy objects. Hence, it is said to be the stone’s final cause, or its telos (Greek for ‘goal’ or ‘purpose’). Aristotle drew a distinction between four different types of causes. For example, if we are considering a house, we might ask about its cause. But that is fairly vague Aristotle realized. We might, for instance, be inquiring about its shape, why it is different looking than say a boat. That, Aristotle says, is to focus on its formal cause. Or we might be interested in its structural properties, i.e. that it is built of stone or of wood. That is to ask after its material cause. Perhaps we’re interested in how it came to be; in which case we’d want to know about the carpenters who constructed it, who put its materials together in that particular shape. That would be to ask after its efficient cause. Lastly, we might be asking why the thing was built at all (for shelter), in which case we’d be asking about its final cause. Aristotle and his followers made use of all four of these types of causes, but as we shall see, a good part of the development of modern scientific thought illustrates how the notion of efficient cause came to replace all the others.
4. The Copernican Revolution
The basic design of Aristotle’s geocentric model of the universe was rendered
more precise and suitable for the purposes of observational astronomy by the Egyptian born
mathematician Ptolemy (90-168 AD). Ptolemy presented his system based upon the central
idea that all the celestial bodies moved around the earth in perfect circular orbits in
his treatise the Almagest, (meaning "the great treatise" in Arabic).
Though it has since been resigned to the ashbin of history, it was maintained virtually
without question for 1,400 years. (The Copernican system, in comparison, has only been in
favour for a mere 456 years.) It was amazingly accurate for the degree of precision of the
observations available in its time (pre-telescope).
As mentioned above, one chief difficulty in Aristotle’s model was how to explain the apparent or observable motions of the planets through the night sky throughout the year. ‘Planet’ is actually derived from the Greek term for ‘wanderer.’ The problem is that the planets do not appear to move in perfectly uniform circular orbits through the night sky. Over extended periods of time they exhibit a peculiar ‘retrograde’ motion, whereby they seem to slow down, come to a stop, move backwards relative to the backdrop of the fixed stars, and then return to their normal eastward motion through the ecliptic (the narrow band of sky containing the familiar constellations of the Zodiac: Leo, Cancer, etc.). To explain this retrograde motion was the most pressing problem of astronomy and was known as the ‘problem of the planets.’ To devise a model or theoretical system capable of explaining this motion was to ‘save the phenomena’ (a phrase it seems introduced by Plato). To ‘save the phenomena’ is to devise a hypothesis from which the observed phenomena can be derived. Whether the hypothesis or model in question is a true or entirely accurate portrayal of every aspect of nature remains a separate problem. (Note: even a false hypothesis can make some accurate predictions – this we’ll see makes the scientist’s job a difficult one, and a properly scientific attitude requires that one be willing to accept when one is wrong.)
[We will need to keep in mind that some scientific theories are good for making predictions, and others for providing explanations or 'understanding.' But the two do not always coincide, and the difference between them is a difficult philosophical problem.]
Ptolemy devised a system of explaining the planetary orbits without having to give up the ancient Greek doctrine that celestial objects must move in perfect uniform circles (since being perfect objects they must move in the most perfect closed curve; recall the connection between symmetry and beauty). Ptolemy’s system required the use of many smaller circles centreed upon the main orbits of each of the planets. These smaller circles were called epicycles. The planets then were supposed to spin on these smaller orbits while at the same time making a much larger orbit round the earth at the centre of the universe. Relative to the stationary earth this would explain why at times the planets appeared to move backwards (think of a second hand on a watch moving along its circular path, it moves for a time to the left toward the 9 on the dial and then ‘backs up’ going to the right on its way toward the 3 position).
But as it turned out, even the use of epicycles was not enough to ‘save all the phenomena’ of planetary motion. Ptolemy had to ditch one important presumption of all then current astronomy and philosophy: that each planetary orbit was perfectly centreed on the earth at the centre of the universe. Rather, he had to suppose, the planetary orbits were centreed, not on the earth exactly, but on an abstract point a bit removed from earth lying somewhere in empty space. This device is referred to as an equant.
It is often said that Copernicus (1473-1543) was moved to reject the Ptolemaic system because it was so, shall we say, unGodly complicated. (After all, couldn’t an all powerful and all wise God be relied upon to create a system more simple than Ptolemy’s with all its epicycles?) It is true that Copernicus’s heliocentric model is in some ways simpler. For instance he realized that by attributing to the earth itself a daily rotational motion he could get rid of one circle of motion for each of the planets, the sun and moon, for they no longer need to move about the earth. Because Copernicus still believed that the orbits were circles, not ellipses as Kepler would later show, he too still had to make use of a good number of epicycles. It has often been said that Copernicus reduced the number of epicycles from that required by the Ptolemaic system. But this is debatable; in fact some experts claim that he actually increased the number of epicycles. In any case, what really bothered Copernicus—this great revolutionary scientific thinker and iconoclast—was the Ptolemaic use of equants. Copernicus disliked them it seems because they were so unAristotelian, so aesthetically ugly! Have an orbit centreed on an empty point in space and not something significant like the sun?! Copernicus it seems also had a thing about the sun being some kind of divine being. Like a king ruling from the centre of his domain, the Sun ought to be at the centre of the physical universe he argued. (Ironically Copernicus too ended up having the planets' orbits centered not exactly on the sun but on an empty point just removed from the sun.)
What Copernicus had done was to provide a new model of the universe which was in some ways simpler and easier to use. But it did not catch on right away, and for very good reason (aside from reasons of intellectual and religious conservatism). The problem with the heliocentric theory was that it made almost no sense in terms of terrestrial physics (that is, how objects behave on earth). If the earth is supposed to be in motion—both spinning on its axis and hurtling through space round the sun—then we need a whole new physics capable of explaining why things don’t fly off its surface or get left behind. Remember that everyone still thought in terms of Aristotle’s physics. It would be largely up to Galileo Galilei (1564-1642) to supply an entirely new and unAristotelian terrestrial physics. Until that time people were only willing to accept the Copernican model as a useful fiction, a hypothetical model, good merely for predicting where the planets could be located. But it was not believed to be true. After all, think of the philosophical-theological consequence of Copernicanism: the earth is just another planet, it’s not "special" at all!
[The French Philosopher Auguste Comte (1798-1857) proposed that humankind had progressed through three distinct stages of intellectual development: (1) the mythological-religious stage, (2) the metaphysical stage, and (3) the 'positivist' or scientific stage. In the first phenomena are explained by appeal to gods and other anthropomorphic beings; in the second explanations appeal to occult (invisible) forces, like magnetism and gravity; in the final truly "scientific" stage, humans learn to settle for theories that facilitate prediction and control of phenomena, giving up as pointless metaphysics questions about the ultimate nature of underlying and hidden reality.]
5. Kepler: mysticism and observation
Johannes Kepler (1571-1630) is important for introducing into astronomical theory
the innovatory idea that the proper motion of the planets is not a perfect circle
travelled with uniform speed, but rather an ellipse travelled with varying speeds at
different times. Kepler had two advantages to assist him in his studies: (i) an active
imagination, and (ii) the very precise planetary observations of his mentor Tycho Brahe
(1546-1601). Brahe was the official astronomer and astrologer for the King of Denmark and
the Emperor of Prague. (This during the same time as Shakespeare’s Hamlet, prince of
Denmark.) He was able to make extremely accurate observations with instruments he designed
himself, none of which included the yet to be invented telescope.
With Brahe’s vast collection of data, Kepler set out to trace the paths of the planets. After trying out many different curves he settled on the ellipse. This was a novel and unorthodox idea, seeing as how for centuries it had been unquestioned dogma that the planets travel in circular orbits. Moreover, the elliptical planetary orbits are just barely distinguishable from circles. Textbooks typically illustrate Kepler's laws with a very pronounced ellipse. But that is just for pedagogical reasons. We must also remember that Kepler couldn't just simply look up at the sky to "see" what shapes the planets' orbits were. He had to pore over vast amounts of quantitative data taken from planetary observations and try to fit a curve to it all that had the best fit. In the end, by making this assumption, though, Kepler was able to more accurately describe and predict the positions of the planets, the sun and the moon.
Kepler’s three laws of planetary motion state:
(1) The planets orbit the sun in ellipses with the sun situated at one of the foci.
(2) An arc drawn from the planet to the foci sweeps out equal areas in equal times.
(3) The square of the period of revolution of a planet is proportional to the cube of its mean distance from the sun.
From these results Kepler began thinking that the sun was somehow responsible for the motions of the planets; since the further away they were from it the slower they moved. This too was an important innovation. Prior to this it was assumed that planets just naturally moved on their own (in circles), were carried by the crystalline spheres, or were pushed round by angels. Kepler began speculating that perhaps the sun affected the planets through something akin to the recently studied force of magnetism. In other words, Kepler furthered the tradition of seeking naturalistic explanations.
At the same time, however, Kepler was also a devout Christian who believed that the universe was God’s creation, and so naturally was governed by mathematical laws and order. (Around this time Christians began thinking of God as a divine geometer and mathematician.) Because of this Kepler sought explanations for why there were just so many planets, neither more nor less; and why they were spaced as they were from one another. This expectation of teleology (i.e. that the universe was constructed to fulfill some grand overall purpose) was consistent with the traditional Aristotelian philosophy and with Christian theology. But it ultimately led to a dead end as a scientific research project.
[Hugh Kearney, in his excellent little book Science and Change 1500-1700 (New York: McGraw Hill, 1971) describes three traditions of thought in the history of science and philosophy: (1) Organic, (2) Magical, (3) Mechanical. In the first physical systems are thought of in analogy with living organisms; in the second people looked for hidden laws and mathematical patterns underlying events, and in the last systems were conceived as machines following regular mechanical laws. Aristotle is the best example of the organic tradition; Copernicus and Kepler belong in the magical; and Galileo and Descartes fit the mechanical. Kearney explains how Newton – one of the greatest scientists of all time – straddles both the magical and mechanical traditions.]
6. Galileo and the birth of the new physics
This was the challenge laid out before Galileo. If Copernicus is really right,
then why don’t falling objects land somewhat behind the point from which they were
dropped? Why aren’t objects thrown into the air similarly left behind by a person
supposedly carried along with an earth in motion? Why aren’t things flung from the
earth’s surface if it is spinning rapidly on its axis? Why don’t we feel a wind
from the earth’s motion through space? And if the earth is moving as the Copernican
hypothesis says it is, then what exactly is the path of an object falling freely to the
ground? What are the laws of motion for terrestrial objects corresponding to the
Copernican theory?
One of Galileo’s most important contributions in resolving these difficulties is the idea of inertia. What is inertia? Inertia is simply the tendency for an object in motion to continue in that motion, or an object at rest to remain at rest, unless acted upon by some external influence. Now when people ensconced in Aristotelian philosophy thought about the possibility of a moving earth they were thinking in the following terms: If from a ship moving at a uniform speed on the ocean, a ball is dropped from the top of the mast, won’t it obviously get left behind while in mid-air and land at a point somewhat behind that from which it started? If the ship were moving quickly enough, won’t the ball splash into the water in the ship’s wake? Galileo realized that this little thought-experiment was simply wrong. And it is wrong precisely because it disregards the property of inertia.
Before the ball is dropped it is moving forward with a certain component of motion it derives from the ship. And when it is dropped it then acquires an extra downward component of motion (due to gravity). But the two coexist together, so that while the ball is dropping toward the deck, it still has some of the original forward motion imparted to it by the motion of the ship (via the property of inertia). So the ball is dropping downward and forward at the same time. That’s why the ball drops straight down the length of the mast and not to some point left behind by the mast.
Now if all objects on earth are similarly partaking of its uniform motion forward in space, then by inertia they will follow along with it while in free fall or in the air. The same account explains why the spinning of the earth on its axis does not leave things behind either. When you jump into the air the ground doesn’t move underneath you, because while still attached to the earth you share in its (spinning) motion, and by inertia you retain this motion while jumping. So you are jumping forward and upward, just enough to land back down at the same spot from which you started. Of course, if the ship were to suddenly accelerate forward or slam on its "brakes", i.e. change its speed, after the ball has been dropped, or change its direction of motion, then the ball would fall at a point either somewhat behind or before the mast. But not so long as the motion is uniform, i.e. nonaccelerated.
Galileo revised other features of Aristotelian physics too. According to Aristotelian physics, heavy objects fall towards earth more quickly than lighter ones (because they have more ‘stuff.’). Galileo showed (remember the story about dropping balls from the leaning tower of Pisa?) that two balls of different weight reach the ground at the same time. The answer again involves inertia. While falling the balls are being accelerated, i.e. they are moving faster and faster all the time (their velocity is changing – at the rate of 9.8 meters/second every second, this is due to the earth’s gravitational pull on the balls, but it was Newton not Galileo who talked about this). But inertia is the property of resisting changes in motion. So the balls are resisting being accelerated in their downward fall. Moreover Galileo reasoned that the amount of inertia an object has must be related to the amount of ‘stuff’ it is made up of, that is its mass. Hence the heavier object has more inertia (more resistance to acceleration) than the lighter one, but it is also attracted to the earth more strongly, so the differences between the two end up exactly cancelling out. (This is using Newtonian language of attraction, but we’ll excuse the anachronism for now.)
Aristotle had taught that there were two general kinds of motion: natural and compulsive (or unnatural). Heavy things fall to earth naturally, that’s where they belong. Consequently from the Aristotelian viewpoint there was no need to explain why something heavy picks up speed as it falls to the ground. Aristotle hadn’t conceived of the idea of acceleration. But he did suppose it was necessary to explain why, say, an arrow continued to move after it had left the bow string. The ancients had recognized that without some external force, an object at rest will remain at rest. But they then inferred that the converse was also true: that wherever there is motion there must be some external force. What Galileo did was to revise the very notion of what constituted ‘natural’ motion. For he said that what needs explaining is not uniform (unaccelerated) motion, but accelerated motion. So even stones dropping to earth require more of an explanation than just saying that they’re attempting to get to where they belong. Ironically enough, Galileo did not think that an explanation was needed for why the planets go round the sun (in what he thought was uniform motion), because he believed that inertial motion could either be in a straight line (rectilinear) or in a circle (circular). So like Copernicus Galileo had difficulty giving up some of the old beliefs about the universe.
In addition to his abstract arguments about terrestrial motion Galileo also helped poke holes in the Aristotelian world view by making some of the first observations with the newly created telescope. When he saw imperfections on the moon and sun it fit poorly with the old idea that they were perfect and immutable objects. And when he saw little planets (moons) orbiting around Jupiter, it blew away the whole idea that everything in the universe had to be centred around the earth and humankind.
So now we have the beginnings of a terrestrial physics consistent with the Copernican theory that the earth orbits the sun, just like all the other planets. Copernicus and Galileo had both maintained the traditional belief that celestial objects naturally move in circles. Kepler, we saw, showed that astronomy worked out better if we suppose that they travel in ellipses.
[One very important consequence of Galileo’s research: it doesn’t matter whether objects are moving uniformly on a boat, or on a table which is at rest relative to the earth (which is itself really moving relative to the sun and other planets!) or whatever, the laws of physics remain the same. This hints at the very philosophically significant principle of "Galilean relativity" which will be important for understanding Einstein’s theories of relativity.]
7. Newton: The universe unified
Isaac Newton (1642-1727) was born on Christmas day of the same year Galileo died.
Newton’s great accomplishments are numerous, including inventing the calculus and the
binomial theorem, and developing a theory of light (optics); but for our purposes he is
noteworthy for completing the revision of the Aristotelian world picture begun by
Copernicus, Galileo, and Kepler.
In a nutshell, what Newton did was to formulate a unified theory of celestial and terrestrial physics, according to which the laws of Aristotle’s sublunary and superlunary realms are entirely the same throughout. With his theory of universal gravitation he provided an amazingly accurate and efficient way of understanding the physical world. The theory of universal gravitation says that every bit of matter in the entire universe is attracted to every other bit of matter, with a force proportional to the masses involved and inversely proportional to the square of the distance between them. In symbols:
F = G M1M2
D*2
So the force of gravitational attraction between two bits of matter, M1 and M2, is greater the more massive they are, and the weaker the further the distance, (d2), between them.
And this, Newton realized, means that an object (such as an apple) falls to the earth for the very same reason that the moon orbits the earth and the earth and other planets orbit the sun: i.e. a combination of inertia and the attractive pull of gravity. If it weren’t for the sun’s great mass, a planet would continue to travel in a straight line, but because of the sun’s great mass the planet gets attracted away from its rectilinear inertial path. As this happens at each instant of its motion (and this is why Newton needed to create the infinitesimal calculus), the resulting path is a closed elliptical orbit around the sun, rather than a rectilinear or straight line.
Newton showed by mathematical calculation that if the force of gravity acting between the sun and a planet, or between the earth and the moon, behaved according to anything other than an inverse square law, then the paths of planetary orbits would not be ellipses. So if gravity fell off at a rate inversely proportional to the cube of the distance between the sun and mars say, then mars would not describe the path through the sky that is actually observed. Only a force law that operates as an inverse square will, in other words, "save the phenomena." In other words, Newton’s theory of universal gravitation provided an explanation of Kepler’s laws of planetary motion (in the sense that Kepler’s laws are logical deductions from Newton’s).
According to the Galilean-Newtonian ideas of physics, it follows that your weight is not an intrinsic property of your body, rather it is a relative and combinatory result of the attraction between the mass of your body and the mass of the earth. In fact your weight is the force exerted on your body by the mass of the earth. On another planet with a different mass (and hence a different attractive force) your weight would be different. Your mass, on the other hand, is apparently an intrinsic property of your body. (At least until we get to Einstein’s theory of relativity.)
Newton adopted Galileo’s idea of inertia—the tendency for bodies in uniform motion or rest to continue in that uniform motion or rest—with one slight modification. Whereas Galileo had supposed that inertial motion could be either in a straight line (rectilinear) or in a circle, Newton restricted it to rectilinear motion. An object unacted upon by any force (i.e. not being affected by a mutual attraction between itself and another object) would tend either to remain at rest or to move in a straight line at a uniform speed. In this idea we have the basics of Newton’s three laws of motion.
Important Definitions:
Speed = the rate of change of an object’s spatial position.
Velocity = the speed and direction of an object.
Acceleration = any change in the velocity of an object.
Hence, an acceleration occurs when an object changes either its speed or its direction or both. A car moving with uniform speed round a corner is accelerating. Question: How many ‘accelerators’ does a car have?
Newton’s three laws of motion
1. The Law of Inertia. An object at rest or in uniform rectilinear motion tends to remain at rest or in uniform rectilinear motion.
2. The Force Law. The force acting upon an object is equal to the product of the object’s mass and the acceleration it imposes upon the object. F = ma. In the case of weight (W) W = your mass x g (rate of acceleration at earth’s surface, roughly about 9.8 m/s2).
3. For every force acting on a body, there is an equal and opposite force acting on another distinct body. (Forces always come in pairs and act on different objects.)
The first law describes what would be the case were there only one object in the entire universe, or what would be the case in the limit when two objects are at an infinite distance from one another (or one is of infinitely small mass). But because there is more than one object in the world, the first law is never really true of any situation in the actual world. Objects are continually affecting one another and causing accelerations (however slight in some cases).
The second law provides a way for us to understand what is meant by the notion of physical force. It provides a way to measure both the mass of an object (if we know the mass of another acting upon it), and a way to determine the force acting upon an object (if we know both its acceleration and mass) or the acceleration (if we know both the force acting upon it and its mass). Its basic message is that accelerations are the result of forces acting on objects.
The third law provides further understanding of what is meant by a force. It is something that always acts between two or more objects, and is always balanced by an equal and opposite force. So an object existing entirely on its own in an otherwise completely empty universe could exert no force, nor would it feel any forces acting upon it. (With forces – as in love – you need two.)
Putting the three laws together gives us what amounts to a definition of Newton’s conceptions of physical force, mass and attraction. (Newton’s law of gravity is just a special example of what he meant by a force.) But are the laws themselves true? Are Newton’s conceptions of these notions the uniquely correct ones? There is no way for us (or anyone short of God, should he/she/it exist) to determine that. All that we can say is that Newton’s system provides a very efficient, accurate, and coherent means of describing and predicting physical motions. (And as we’ll see shortly Einstein showed that they require modification when considering motions close to the speed of light and systems of extremely great mass.)
Leaving aside the question of the truth of Newton’s system for now, let’s consider what it says about the age-old question concerning our place in the universe. First, Newton’s system was meant to be consistent with the Copernican model. And he also showed that Kepler’s three laws of planetary motion follow from his own three laws of motion and law of universal gravitation. It has, then, great merit for its unifying capacity. But let us think about some of the other implications of his laws of motion. Newton’s first law states that an object in uniform rectilinear (i.e. non-accelerated) motion tends to remain in that motion. This is supposed to be true even in the case of a single object in an otherwise empty universe. But if there were just one object moving through space, how could we tell that it was in fact moving at a uniform speed and in a straight line? In fact without some other point of reference, how could we tell that it was moving at all and not at rest? Would the question whether it was really moving or not even make sense? Recall the notion of Galilean relativity, that the same laws of physics would apply whether one is moving uniformly in a straight line with respect to some other object or is at rest relative to it. For the occupants of two space ships, for instance, all the same laws of physics should apply. And if the two space ships were floating uniformly out in an otherwise empty space (empty even of distant stars), how could the occupants of either know that they were moving or at rest rather than the other ship? This is another way of expressing the principle of Galilean relativity. Each space ship represents what we call its own inertial (or Galilean) frame of reference; and Newton’s laws of motion work equally well in one such reference frame as any other. Consequently, it has been said that the distinction between rest and uniform rectilinear motion is a purely relative one.
We all know what it’s like to be sitting on a train waiting to leave from the boarding station. If the vehicle begins to move slowly and smoothly enough so that the acceleration is imperceptible, there is a brief moment when we cannot tell by looking out the window whether we are moving or the train next to us is. That illustrates quite nicely the relativity principle. For two or more objects moving in uniform inertial motion relative to one another (i.e. each in its own inertial frame of reference), there is no discernible fact of the matter about which ones are really moving and which ones are really at rest. Its all a matter of perspective; and the laws of mechanics will work equally well in any one.
Recall that Aristotle had believed that a heavier object will fall more quickly than a lighter one. This is, as Galileo noted, not true. All objects of whatever weight fall at the same rate toward the earth. (Of course a feather will not fall as quickly as a ball bearing, but this is due to air friction against the feather. In a vacuum there is no air -- no gases -- and it can be demonstrated that a feather and a hammer hit the ground together at the same time when dropped from the same height. Astronauts on the moon have also verified this.) Although Aristotle was wrong about this, there is a sense in which he was correct. According to Newton's law of gravitation, a more massive object is more strongly attracted to the earth than a less massive one. And weight is just a way of expressing the gravitational force exerted on an object by the earth. (When you step on the bathroom scales what you are seeing is how much force of attraction exists between the mass of your body and the earth's mass.) So Aristotle was right to think that a heavier object is more strongly attracted to the earth. But Aristotle did not know about inertia, as we saw earlier. And if one object is heavier than another, that's because it has more mass. And mass is the measure of inertia; and inertia is the property of resisting accelerations. So although the more massive object (the hammer) is more strongly attracted to the earth, it also resists acceleration more than the less massive feather. The result is that the greater attraction (due to greater gravitational mass) is exactly cancelled out by the greater resistance to acceleration (inertial mass). Mass then has two aspects: a negative one, i.e. inertial resistance to acceleration, and a positive one, i.e. its role in strengthening gravitational attraction/acceleration. It is an odd fact in Newton's physics that inertial mass (as measured by Newton's second law) is equal to gravitational mass (as measured by Newton's universal law of gravitation). This we'll see bothered Einstein. He thought that there must be some deeper explanation for the fact that gravity affects all objects the same regardless of their different masses.
Absolute space
When Newton says that an object in uniform motion tends to persist in uniform
motion, he seems to be assuming that this is true relative to some frame of reference
that is not itself in motion. But which frame of reference is this? Typically in physics
classes we assume that the frame of reference is the laboratory in which we are conducting
experiments, and we assume, for instance, that the lab table is not moving (but balls and
blocks may be moving relative to the table). But this assumes that the room -- which is in
a building attached to the earth-- is not moving. But we know – thanks to Copernicus,
Kepler, Galileo and Newton– that the earth is not at rest; it is rotating on its axis
and orbiting the sun. So perhaps Newton meant that relative to the system of the fixed
stars his first law of motion applies. But how does he know that the stars are fixed? Is
Newton capable of picking out the states of true inertial motion from the states of true
rest? According to the Galilean principle of relativity, Newton’s laws should work
for any of an infinite number of frames of reference moving uniformly and in a straight
line with respect to one another. So if you and I are moving through empty space at
exactly the same speeds and in the same direction, then neither of us will appear to be
moving at all. But what then does it mean to say that in the example we are moving?
It can only mean that relative to some other frame of reference (other than our own
respective ones) that is by assumption at rest. But how do we know that the frame
of reference we assume is at rest is really at rest? After all, all appearances on
earth make it seem like we are at rest when we now know that we are actually moving round
the sun and spinning on our axis. To assume that it makes sense to talk of such absolute
states of inertial motion and rest is to assume that we can do so relative to the entirety
of space or the universe as a whole, which Newton called "Absolute" space to
distinguish it from any merely relative space or frame of reference that you or I might
assume relative to some other merely relative portion of space as a whole.
Newton believed that it made sense to talk about an absolute frame of reference, or Absolute Space, because he thought that without it his laws of motion made no real sense at all. According to Newton, this privileged frame of reference would be absolutely at rest relative to space itself. The idea of Absolute space is premised upon a picture of the universe (or space) as a very big kind of box or container in which stars and planets and other ordinary sized objects are situated. It is consistent with the Aristotelian and Copernican idea that the universe as a whole has a centre. But how could Newton pick out this centre? How, that is, could we know that the sun is at the centre, if all that Newton’s laws tell us is that those laws will work for any of an infinite number of frames of reference which are not undergoing an acceleration?, i.e. are in uniform rectilinear motion or at rest relative to some other? How can we know that the sun is at rest, rather than that the entire observable solar system is moving at a uniform velocity through space? In fact many people, for instance the great philosopher, mathematician and scientist Gottfried Wilhelm Leibniz (1646-1716) (who created a system of doing calculus independently and at roughly the same time as Newton), objected that all motion is merely relative, one object being referred to another object, and that consequently the idea of absolute space is incoherent or simply empty. (Once again, we are seeing glimpses of Einstein’s theory of relativity to come.)
Here’s another way of stating the difficulty. Newton defined an inertial motion as one that covers equal amounts of space in equal amounts of time in a straight line. But how do we measure equal amounts of time? Do we not do so by observing the motion of some physical object such as a watch hand or pendulum? But how do we know that it is moving at a uniform rate? And how can we ascertain its uniform motion but by assuming a uniform passage of time? You see then the quandary we’re in if we cannot appeal to any absolutely uniform motion or absolutely uniform passage of time. Newton realized that no actual physical system could bear the weight of being such a standard, so he proposed that the ultimate standard was an absolute space and time that existed over and beyond all the physical systems we can experience. Absolute space is a mathematical ideal, it is not a physical reality.
But Newton also had an experiment in mind to support his idea of absolute space: the famous bucket experiment. If all motion is merely relative (i.e. the motion of one object compared to another), then how are we to account for the following phenomenon? Suspend a bucket of water from a rope. While the rope is not twisted the water surface will be flat. If we twist the rope and let it go, the bucket of water will begin to spin. At first the water in the spinning bucket appears to be at rest (this is due to the water’s inertia) and remains flat. Eventually bucket’s spinning motion will impart what is called angular momentum to the water, enough so that the water will be moving in a circular motion at just the same rate as the bucket itself and so relative to the sides of the bucket will appear to be at rest. But as it picks up this motion from the bucket the water will begin to climb up the sides of the bucket (this is said to be due to a centrifugal force). Now if we grab the bucket and stop it from rotating, the water will continue to rotate around (so now is moving relative to the sides) and yet still retains the peculiar funnel shape. Because the presence or absence of relative motion between the water and the bucket sides appears to have no effect on the water’s shape, Newton thought that the only answer was that the water was moving up the bucket’s side as a result of a force that could only be referred to absolute space itself, outside of the water-bucket system. (Recall that accelerated motions, such as the water’s climbing up the bucket’s sides must be due to some force, and forces must be referred to some frame of reference.) Here's a simpler example to express the same thing. Imagine a balloon full of water on its own in an otherwise completely empty space. Imagine now that the balloon is spinning quickly about an axis running through its centre. The balloon should experience a centrifugal force similar to that which the earth experiences, thereby distorting the shape of the balloon so that it bulges about its "equator." But what would this spinning motion be relative to in an otherwise empty space, if not to space itself?
What Newton was arguing here is that space is itself a kind of thing, an entity. Indeed in these examples involving rotation and centrifugal forces space is the cause of the centrifugal force and consequent distortion in shape. The nineteenth-century German physicist Ernst Mach objected that the force in the spinning bucket example would have to originate not from absolute space but from the rest of the mass in the universe. As for the idea that space itself can act as a cause of centrifugal forces and consequent motions, Mach pointed out that we have no way of knowing whether this is true, since we have never – nor could we ever – experience what would happen to a single object in an otherwise empty universe. The basic philosophical question here is whether space exists independently of things in space. Is space just a relation between two or more objects, or is it something real over and above (beyond) objects? Some physicists think of space as an entity, others as just a relation between objects. What do you think?
We need to say a word about accelerated systems of reference. First of all, the principle of relativity does not hold for such systems, i.e. the laws of physics would not be the same for an accelerated one. (There are laws for such frames of reference but they become more complicated.) Think about Newton’s three laws of motion. They don't say anything specific about positions or velocities. From the perspective of the laws, the values for the positions and velocities are arbitrary (they don't matter). What the laws are concerned with are accelerations. That’s why the relativity principle holds. It doesn’t matter what two observers in two different frames of reference moving uniformly relative to one another think about the positions and velocities of objects within those systems. Obviously if one person is moving uniformly to another at rest, then they will disagree about whether an object in one system is at rest or is moving (its velocity), and so they may also disagree about the position of things. But one thing they will agree about, no matter how they move relative to one another—just so long as they are moving uniformly, i.e. without acceleration—is the acceleration of objects within either system of reference. Changes in velocity, in other words, will be the same for observers in any inertial system. (Which is just to express the Galilean relativity principle as saying that the laws of mechanics– which describe how velocities change – should be the same for all observers in uniformly moving, i.e. inertial, frames of reference.)
Evidence for Newton’s physics
But how after all, you might ask, do we know that the earth really is moving? Note
first that according to the Copernican and Newtonian systems the earth is undergoing at
least two separate accelerated motions. One is our accelerated orbit about the sun.
The other is our accelerated rotation on the earth’s axis. Newton used the principles
involved in his bucket example to provide evidence for the latter motion. If we accept
Newton’s theory (his definitions of mass, inertia, force, acceleration etc. and his
laws of motion), then the only way to explain certain dynamical phenomena here on
the planet (i.e. phenomena having to do with forces and accelerations, not just
observations of relative motion) is to suppose that the earth is spinning on its axis and
orbiting round the sun. We saw that in the spinning bucket the water was forced outward to
climb up the sides of the bucket. This force is called a centrifugal force. The same thing
happens to the earth as it spins on its axis, only the effect is a considerable bulging
about the equator where the greatest amount of this force is felt, as the earth’s
matter is ‘flung’ outward. How do we know that the earth is bulging at its
equator? Newton predicted that if it were, then the force of attraction between the earth
and a pendulum would be weaker there than at other locations on the earth’s surface.
Recall that the attractive force of gravity is inversely proportional to the square of the
distance separating two objects. If the equator bulges, then the distance from the
earth’s centre (where Newton showed with a nice geometrical argument we can suppose
the bulk of its mass to lie) to its surface will be greater there than at the pole, where
the earth should actually be flattened slightly and so have a shorter distance.
Consequently the pull of the earth’s gravitational force should be less at the
equator than at the poles. Experiments with pendulums do indeed show that these
instruments swing more slowly at the equator than at the poles.
But suppose the earth was not spinning on its axis. This would mean that the entire heavens are rotating about a perfectly still earth; although we could not tell the difference just by looking at the sky, there would be no centrifugal forces affecting the earth and hence no bulging of the equator, (or so Newton says; Ernst Mach pointed out that we really have no way of knowing). And so there should be no variation in the force of gravity at different latitudes and hence no variation in the period or swing time of pendula.
Another demonstration also employs pendulums. A pendulum always swings in the same axis of motion if left to itself (i.e. the bob goes back and forth in a straight line). Now think about setting up such a device (they’re called a Foucault pendulum) at the north pole. As the earth rotates on its axis it should move underneath the swinging pendulum bob which is itself keeping to a straight axis of motion, back and forth across the pole. Watching such a device over an extended period of time shows that the axis of swing appears to move, relative to the ground. If blocks are set up in a circle around the pendulum so that the bob will strike them and knock them over, it will be seen that in 24 hours all the blocks will have been knocked down and the axis of swing will have returned to its initial starting position. So is the earth rotating or the pendulum? Everything we know about pendulums tells us that they do not change their axis of swing unless something forces them to. So the only alternative is that the earth has moved beneath it, just as Copernicus, Galileo, and Newton said. (Learn more about Foucault pendulums.)
And what about the earth’s motion through space and around the sun? How is that shown? One way is purely observational. Back in Copernicus’s time people refused to believe that the earth moved through space because, they said, if it did then the star formations (constellations) ought to look different as we see them from different perspectives (this is called parallax). Since no one could detect any parallax with the naked eye or with the early telescopes—(the nearest stars are much further away than anyone expected)—many disbelieved in the earth’s orbital motion. But the more modern high-powered telescopes do detect parallax.
8. After Newton: Hope for enlightenment
Newton’s system of physics proved extremely effective at explaining the
motions of material objects, and the next few centuries (up until the end of the
nineteenth) consisted in its extension to other types of phenomena (e.g. magnetism,
electricity, heat, gases, light etc.). Newton’s formulation of physics was so
successful that, apart from his own glorification as a great genius, it inspired a great
faith in the ability of human reason to unlock all the secrets of the universe. No longer
need humans feel impotent and humble before the awesome power of nature. This breakthrough
in intellectual accomplishment was complemented by remarkable technological advances. By
the eighteenth century many people believed that further human progress, not only in
science but in social and political matters as well, was nearly inevitable. The instrument
of this faith in the idea of progress was human reason, and a developing notion of
scientific or experimental method.
Newton’s success had been gained by restricting attention to just a few basic properties of natural bodies, viz. mass and acceleration. This inspired a belief that all the natural philosopher need attend to in order to understand nature were the properties of matter in motion. More and more people came to think of the universe as a giant mechanism, a machine which could be fathomed simply by applying to it the concepts of the "Newtonian" philosophy. It is important to note however that Newton himself was no such "Newtonian." Newton still retained a belief in some of the magical elements of alchemy, the proto-science of chemistry, wherein practitioners of the newly evolving experimental method hoped to learn the secrets of turning base elements into gold (the "philosophers stone" of Harry Potter novels), and the secrets of life.
But let us return to the story of finding our place within the physical universe. Newton had put the Copernican model upon a solid foundation, and had shown how to unify the Keplerian celestial physics with the Galilean terrestrial physics. He had wished to retain the ideas of an absolute space and time needed for the comforting and traditional idea of a finite universe. Maybe humans no longer occupied the centre of the physical universe, but it was still assumed that we were not far from it, and that at least we were still at the centre of the creator’s attention. But ironically enough, Newton had also weakened the foundation for this idea of a finite and closed universe with a centre situated in an absolute time and space. For as we saw above, his laws of motion were suitable for any inertial system, whether it was at rest or in motion relative to another. In fact he had actually undermined the idea that there could be any absolute fact of the matter whether any frame of reference was absolutely at rest or in motion. According to his first law of inertial motion, moreover, an object left on its own would not "naturally" proceed to the centre of the universe (as Aristotle had said), but would proceed in a straight line for – well forever in theory. Space, in other words, might not be a finite closed sphere after all, but might just as well be infinite in extension in every direction.
One way of thinking about Newton's achievement is to say that he produced a "Spaceship Physics", that is a physics that you could 'take with you' anywhere in the universe and apply successfully. This is because Newton's physics, unlike Aristotle's, says nothing about a special, unique, or privileged point or location in space (such as the centre of the universe). The very idea of such a privileged place as the centre of the universe is no longer required thanks to Newton. Under Aristotle’s system, if you wanted to know how an object would move you had to know what kind of stuff it was made of and in which direction the centre of the universe was. Under Newton’s system all you need to know is how the objects in the local frame of reference are going to affect the object via the universal property of gravitation.
And what about this mysterious force, gravity? When it came to explaining how it was that gravity was capable of acting instantaneously across great distances of empty space, Newton was famous for stating "hypotheses non fingo", i.e. "I make no hypotheses." According to the methodological guidelines for experimental philosophy that he laid out for himself, one should not attempt to develop hypotheses about things one has no means of experiencing or testing. Some people began to object that this rule should have kept Newton from postulating the legitimacy of an absolute space and time. (Ernst Mach, mentioned above, was one such critic.) For we have no way of knowing whether any uniformly moving system is really at rest or moving relative to any other uniform or inertial frame of reference, let alone relative to "absolute space itself." No experiment or law can decide such a thing. Rest and uniform rectilinear motion are purely relative notions.
9. Maxwell and the theory of light
In the nineteenth century the Scottish physicist James Clerk Maxwell (1831-1879)
developed a theory that showed how to unite the previously distinct phenomena of
electricity and magnetism. Maxwell’s theory of electromagnetism explained that moving
electric charges produce magnetic fields and moving magnetic fields can cause electric
charges to move (and on and on). When Maxwell worked out the speed with which this form of
wave-like phenomena would travel through empty space he found it to be exactly that of the
speed of light. He therefore proposed that light is in fact a changing electromagnetic
wave.
Now all of our experience of wave-like phenomena tells us that a wave must be a wave of something, i.e. that it must have some medium through which to propagate. A wave on the ocean moves through water, a sound wave moves through the gases in the air. So what, people asked, does the lightwave propagate through? The hypothetical medium called the luminiferous (light-bearing) ether was proposed. It was supposed that this ether extended throughout the entirety of space (as it must since we see light from the most distant stars). Another benefit of proposing that such a hypothetical medium existed some people felt was that it would give some more content to Newton’s idea of absolute space. A system supposed to be absolutely at rest might be absolutely at rest relative to the ether. (For if empty space is not completely empty, but contains this ether we might be able to talk about absolute motion relative to it.) But oddly enough this ether had to be so subtle that it could not be experienced by our normal senses. For instance, if the earth is travelling through it at the great speed it is, we certainly don’t appear to detect any "ether wind" do we?
In an attempt to detect this ether wind the physicist Albert Michelson (1852-1931) and the chemist Edward Morley (1838-1923) devised an ingenious experiment. If the earth is travelling through this ether, then a beam of light ought to be slowed down when travelling against a "head wind." The experiment, however, revealed no such slowing down of the light beam. One proposal was that in travelling through the ether the experimental apparatus underwent a shrinking effect (this was called the Lorentz contraction after the physicist who proposed it), thereby cancelling out the delay in the light speed. This attempt to save the hypothetical ether was not very popular however. And yet the idea that lightwaves travel through an entirely empty space (that they are waves of pure nothingness) was not very attractive either.
10. Einstein and the theory of relativity
It is at this point that Albert Einstein (1879-1955) becomes relevant to the
story. At the time Einstein made his most important contributions to the theory of physics
he was a PhD without a university or research position forced to take a job in the Swiss
patent office. He was, perhaps not altogether incidentally, married as a young man to
another physics student, Mileva Maric.
Einstein had been thinking about the nature of light nearly all his (quite young) life it seems. At the age of 26 he wrote the paper that would eventually produce a great revolution in the history of ideas and in the way we think about the universe. It was called "On the electrodynamics of moving bodies." As a young boy Einstein had wondered what it would be like to travel alongside a beam of light, travelling at the speed of 300,000 kilometers per second. Would it look as if it was not moving at all? Would he see both the electric and magnetic fields standing still? He knew there was something paradoxical in this idea, because Maxwell’s theory of electromagnetism implied that such a static field of electricity and magnetism could not exist, not if it were truly light. According to Maxwell’s theory, light should always move with the same speed, regardless of the motion of an observer (i.e. the speed of light is a universal constant). It would seem then that it must be impossible to catch up with a beam of light, impossible to travel as fast as it does. This would explain, moreover, why Michelson and Morley had been unable to detect the ether drag on the beam of light in their experiment. Maybe light always travels at the same speed, no matter even if you yourself are moving very fast relative to some other object or frame of reference. After all, the earth moves pretty fast through space (an average velocity of about 30 km/sec -- which is admittedly very slow relative to the speed of light), and that didn’t seem to affect the measured speed of light.
Einstein knew that this went against the well-established principle of Galilean relativity. That principle declared that if an object is moving at speed X, relative to an observer at rest (relative to the earth say), it would appear to be at rest relative to another observer who is also moving at speed X, (relative to the earth). In other words, the speed with which an object is moving is always relative to the frame of reference under consideration. But if light always travels at 300,000 kilometers/sec (or c as its signified), even for an observer moving very quickly relative to the "fixed" earth, then the principle of Galilean relativity would not apply to it. And if that is the case (that light always travels at the same speed no matter what frame of reference we consider it from), then something else must give in order to make sense of the observed results. Einstein did not want to have to throw out either the experimentally well-confirmed constancy of the speed of light or the principle of Galilean relativity. To give up on the latter would be tantamount to supposing that there was some privileged frame of reference from which to view the universe -- some God's eye view accessible to humans. Perhaps for reasons of humility, but also for very good technical reasons, Einstein could not accept that such a perspective exists. That meant that something else was going to have to go. What went was the intuition that time is an absolute and constant phenomenon.
Consider the following: if A is moving toward B, and A throws a ball at B, then B will catch it sooner than if A and B are moving away from one another. This is because the velocity of A is added to the velocity of the ball. But if A shines a light beam at B, it doesn’t matter whether they are moving toward one another, away from one another, or not moving at all relative to one another, the speed of the light beam, c, will be the same regardless. In other words, when dealing with light, velocities do not add up as we are used to them doing. How can that be?
Einstein began by making two (well-confirmed) postulates. (1) Observers can never detect their own uniform motion except relative to some other body. (I.e. all inertial motion is relative.) If two space ships are floating uniformly out in space, the occupants of neither can decide which of them is moving and which is at rest. An alternative version of this assumption says that in all inertial systems the laws of physics must be the same (including Maxwell's laws of electromagnetism which include the statement that the speed of light is the same for all observers regardless of their motion or the motion of the light source). Both of these statements you should recognize as the principle of Galilean relativity. Einstein's second postulate was the following: (2) The speed of light is always a constant and the same for every observer regardless of their state of motion.
Now if the second postulate were not true it would be in conflict with the first, the postulate of "classical" or Galilean relativity. Consider: spaceship A is moving at a uniform rate relative to spaceship B. According to the principle of Galilean relativity neither crew can decide which of them is really moving and which is at rest. But if the speed of light were not a constant for all observers then they could tell, by making measurements of it, which of them was really moving. For if we know that the speed of light is 300,000 kilometers/second, and crew A gets more than 300,000 km/sec while crew B gets 300,000 km/sec exactly, they would know that crew A was moving toward the light source and that crew B was at rest relative to it.
This also provides some explanation why Michelson and Morley failed to detect any effects of the hypothesized ether. The ether was supposed to be a medium at absolute rest throughout the universe, since light and other electromagnetic phenomena were supposed travel as a wave through it. But if it were at absolute rest, Einstein's first postulate declares that we could never detect it anyway, because we can detect only relative motions.
As stated above, Einstein's postulates were already well established when he raised them to the level of universal truths or postulates. What wasn't well established was the conclusions that followed from them. For instance, if A and B are moving with respect to one another, and yet they both get the same value for the speed of light, then something else in the equation must give. In fact according to the special theory of relativity, both spatial lengths and temporal durations are relative to the frame of reference under consideration. If the difference in motion between A and B is great enough, they will disagree about the lengths of objects and the time elapsed between events, because they agree about the speed of light.
This is the upshot of Einstein’s Special Theory of Relativity. But it might have been more adequately called the theory of absoluteness or the theory of the constancy of the speed of light, since the very thing that forces the conclusion of temporal relativity is the absolute constancy of the speed of light. Einstein’s theory does not, as many people believe, imply that "Everything is relative." It implies that periods of temporal duration are relative to the frames of reference, but it absolutely relies upon the (well-established) premise that the speed of light is not.
So much then for Newton’s notions of absolute time and space. Without an all-pervading and stationary ether what sense can there be in saying that there are absolute positions in space rather than just relative positions? If there is no way to determine that you have occupied the exact same position in space twice, then what sense can there be in talking about absolute space? (Do you recall the joke about the two dim-witted fishermen who wanted to mark the spot out in the middle of the ocean where they had caught a lot of fish, so they placed a styrofoam cup there so they could find the spot the next day? Obviously this won't work because the cup will move with the waves. It would work if the ocean was perfectly and absolutely at rest. But space is not even like the ocean. It is an empty nothingness through which objects move; we can only "detect" space via the motion of objects relative to one another. Extract all the stars and planets etc. from space and there would be no way to differentiate one "spot" in space from another. So we cannot detect absolute motion relative to space itself; we can only detect the motion of one object relative to some other object.)
And if temporal durations are not absolute, but relative to the motion and frame of reference of observers, then what sense can there be in talking about such a thing as absolute simultaneity? How could we ever decide that, for two people travelling at radically different speeds, that some event had occurred for both of them at exactly the same time in any absolute sense? Consider that in order to make any decision about the simultaneity of two events we need to have some signal to compare them to. Light is the fastest signal possible. But if it has the curious property of always giving the same speed no matter how fast or slow observers are going themselves, then there is no way for us to decide whose idea of temporal simultaneity is the correct one.
Consequently, the intuitive idea of a simultaneous time for the entire universe is an empty and unusable one. As the physicists say, it does not correspond to any physical reality.
One way of thinking about Einstein's special theory of relativity is to think of it as expanding the idea of Newton's "space-ship" physics. Einstein showed that you don't need to know where you are in the universe in order to use the laws of physics -- contrary to what Aristotle had supposed. (And, to make Galileo's point against Aristotle clearer: what is the earth but the original space-ship? The earth is travelling through space and the laws of physics work just fine.) Einstein, then, was just showing that your absolute location in space is not only unknowable, but irrelevant for understanding how and why objects move as they do.
It is important to note that what Einstein meant by "time" is not a psychological or abstract entity. Time, Einstein said, is just what we measure with clocks. Any kind of clock. And it is a consequence of relativity theory that clocks "tick" more slowly when moving at speeds near that of light. (This also goes for "biological clocks" like the billions of little cells of which we are all made. And hence we get the famous twin paradox of relativity theory that shows that if one twin goes for a round trip flight into space at near the speed of light, she will have aged more slowly and so be (or appear) younger than her twin who has stayed "at rest" on earth.) There seems no other way of resolving the apparent conflict between Einstein's two postulates. Newton, on the other hand, maintained a conception of "absolute time," time which flows on uniformly and objectively for the entire universe and everyone in it for all eternity. But such a conception of time is inaccessible to us, and so for the purposes of experimental science is without application or utility.
Of course one of the best known results of all modern science is Einstein’s
mass-energy equivalence principle, e = mc2, which tells us that
mass can be turned into energy and vice versa. This equivalence arose out of Einstein's
realization that as an object is accelerated toward the speed of light, it requires more
and more energy to accelerate it any further. Until finally, the amount of energy required
to accelerate an object to precisely the speed of light would be infinite. But that is
just to say that its inertia increases with speed. And as we have already stated above,
mass is the measure of an object's inertia. Hence, mass increases as speed increases.
(These increases in mass are too minute to be detected until the speeds get to about
one-half the speed of light. It is for this reason, among others, that we might say that
what Einstein's theory of relativity amounts to is, not exactly an overthrow of Newton's
mechanics, but an amendment. It integrates the speed of light into Newton's laws of
motion.) Einstein then noted that his equations suggest that even an object at rest
(relative to some frame of reference) possesses a great deal of energy. Ever wonder what
it feels like to move at 99% the speed of light? Well right now as you sit at your
computer, relative to some frame of reference you are moving at 99% the speed of
light. It is this principle that lies at the basis of atomic energy and is what made
possible the atomic bombs that were dropped on the Japanese cities of Nagasaki and
Hiroshima by the allied countries at the finish of the Second World War (1939-1945).
Although Einstein did write a letter to President Franklin Roosevelt urging him to
consider developing an atomic bomb before Hitler and the Nazis did, he was very much
opposed to it ever being used on anyone. In fact he and the British philosopher Bertrand
Russell founded the Pugwash Convention, an anti-nuclear weapons group which still meets
each year in Pugwash, Nova Scotia (though without either Einstein or Russell who have both
been dead for some time).
This is called the special theory of relativity because it is not quite general
enough yet. For it only deals with inertial frames of reference. Einstein’s General
Theory of Relativity applies also to accelerated frames of reference (and so to
motions in general). In it we find the equivalence principle that accelerating a frame of
reference has the same effect as putting that frame of reference in a gravitational field.
For instance, if you were to live in a windowless space ship, there’s absolutely no
experiment you could do that would tell you whether your ship was accelerating due to the
engine’s thrust, or whether you were still sitting on the surface of a massive planet
like the earth. In either case what you would feel is a force pulling you down toward the
floor of the shuttle. The general relativity principle says that accelerations are
equivalent to the effects of gravitational fields. And so it extends the first postulate
of the special theory of relativity to the general postulate that there is no experiment
you could do within the windowless ship that would decide whether you are really moving at
all (either uniformly or with acceleration) rather than at rest. Looking out a window
might provide the appearance of an answer, but that answer would only be relative to your
surroundings.
An important consequence of this is that even light beams should be affected by gravity. For if not then you could perform an experiment in your spaceship with a light beam to detect whether or not you were really moving. If your ship is accelerating through space then the beam of light passing through from outside will move across the inner room of the ship in a parabolic path (because the ship's floor is rising up, while the light beam moves in a straight inertial path). But if Einstein's postulate about not being able to detect absolute motion is correct, then a gravitational field (from a massive planet upon which your spaceship is resting say) ought also to deflect the light beam into a parabolic path. So seeing the light beam describe a parabolic path through the ship would not decide for you whether you are accelerating through space or are at rest in the presence of a gravitational field. And in fact experiments have shown that massive bodies do attract light. (Since light beams have energy -- kinetic energy or energy of motion -- and energy is equivalent to mass, then light beams have mass and hence should be affected by gravitational fields a la Newton's Universal Law of Gravity.) A beam of light from the sun for example is bent slightly from a rectilinear path when it passes by the moon. From this we get the idea that mass actually distorts the shape of space (or rather space-time). In light of the acceleration-gravitational field equivalence the general theory of relativity is also a theory of gravity. And the bending of space-time is its explanation of why objects that would otherwise continue to travel in straight paths are "pulled" in toward massive bodies (as the moon is to the earth for instance). Bodies travel the straightest paths possible in space-time (called geodesics), which are not always straight or flat when in the vicinity of massive objects. In essence this is to say that Einstein got rid of the mysterious gravitational force that was capable of acting instantaneously across great distances and uniformly on all objects. Gravity, in the general theory of relativity, is a function of space-time curvature, and not a real force at all. This also explains why the "force" of gravity affects all objects in the same way no matter how much their masses differ (recall the experiment with the falling hammer and feather). According to Einstein's general theory of relativity, both the hammer and the feather are simply following the "straightest" inertial path they can in the curved space surrounding the earth's massive body. There really isn't a "force" acting on them at all.
Einstein's theory of relativity can be summed up by the phrase "The laws of motion are the same for all observers, no matter what state of motion." This means that there is no privileged perspective, no God's eye-view of the universe from which an absolute correct description of motions and rest can be given. Any of an infinity of different frames of reference are equally valid perspectives, and the motion and rest of objects therefore become relative to those frames of reference.
11. Modern Cosmology and the Big Bang
We have replaced our original Aristotelian picture of a closed and finite universe
with one in which there are an infinite number of equally legitimate frames of reference
from which to look at the universe. None has any intrinsic priority or status over any
other so far as the laws of physics are concerned. And from the standpoint of modern
physics, what cannot be accommodated by the laws of physics has no physical reality. And
so we bid adieu to the concepts of the ether, absolute time and space, the centre of the
universe. We are left with a centreless and possibly infinite universe.
While attempting to solve the equations of his General Theory of Relativity Einstein discovered that one possible model depicted an expanding universe. Would that mean that after all the universe has a centre? Not quite. For the implication is that, from any point in space whatever, light should be affected in such a way that it appears that the space over which it has been travelling has been stretching out. Einstein could not accept this implication and so added to his theory of General Relativity an ad hoc universal constant l which would serve to keep the universe held in static and eternal check. Just like all the other revolutionaries before him, Einstein had difficulty giving up all the old ideas which his own theory would undermine. (As we will see eventually, Einstein spent the latter half of his life rejecting the implications of the quantum mechanical theory of matter which he had also helped to introduce.)
When the astronomer Edwin Hubble (1889-1953) discovered that the light from very distant stars was shifted to the red-end of the light spectrum, the idea of an expanding universe began to take on more credibility. When an ambulance siren moves past us it changes the shape of its sound wave. As it approaches, more of the peaks in the sound wave reach our ear in any given unit of time, and as it recedes fewer peaks hit our ears per unit time. This results in the distinctive change in pitch. This is called the Doppler effect. A similar thing happens to light waves from stars when they are either receding or approaching us. The light from very distant stars is noticeably shifted toward the red end of the spectrum, an effect consistent with their rapid movement away from us. What leads to the hypothesis that the universe as a whole is expanding is that this red-shift is observed in every direction we look.
Hubble inferred from this that if all the stars are now expanding away from each other, then in the past they must have been all much closer together. Running this trend back into the past leads one to suppose that at one time the entire universe occupied a single extremely dense and small point. Could the universe and space-time itself have an origin? But when and where did space and time begin? Modern cosmologists suggest that these are incoherent questions, since to ask them presupposes the prior existence of the very things which by hypothesis are not yet in existence.
Eventually physicists caught up with the astronomers and began to work out the implications of this Big Bang model of the universe. One prediction that they found should be easily testable was that if the universe and all its mass had originated in an incredibly dense ball, then we should be able to detect a now very cool (3 degrees Kelvin) temperature in the outer expanses of the universe. This cosmic background radiation was indeed discovered, by accident, by two radio astronomers working on a very different problem. Arno Penzias (1933-) and Robert Wilson (1936-) were working for Bell Telephone Laboratories, trying to develop better satellite communications. They could not get rid of this 3 degree Kelvin radiation noise no matter what they did. Eventually a colleague more familiar with cosmological theory, Bernard Burke (1928-) an astronomer at MIT, recognized what they had found. Oddly enough Burke did not get to share with Penzias and Wilson the Nobel Prize for physics they received in 1978.
At present the Big Bang theory is the "Standard Model" of modern cosmology. It incorporates both General Relativity Theory and Quantum Mechanics. However, as of yet no one has found a way to render these two very successful theories consistent with one another. Quantum field theory, or the quantum theory of gravity, is a very difficult branch of mathematical physics. Physicists can make predictions about quantum mechanical systems with great accuracy (albeit statistical accuracy), but they have yet to solve the problem of understanding how to do so for accelerated systems moving at near the speed of light.
As for the question "where" did the universe come from?, one of the most popular theories at present is that it was a chance quantum fluctuation in something called a quantum vacuum, or another universe now sealed off from our own. The cosmologist Brandon Carter pointed out that the physical properties in this universe were just right to allow for the emergence of elements necessary for life as we know it (e.g. carbon). Why then should it have come about that just these conditions obtained when it seems that otherwise life would have been so unlikely? This is known as the 'Fine Tuning Problem'. One response is to note that it is not so surprising at all that we find the universe around us to be just right for the presence of life; for if the conditions were significantly different then we would not be here to ask the question. This strategy invokes what is known as the "Anthropic Principle." Some don't find this a very satisfactory answer. It has been proposed, therefore, that perhaps there are a vast number of universes (a hypothesis suggested by some interpretations of Quantum Theory), and in each one the physical conditions are different, some suitable for the formation of life, others not. Advocates of this 'Multiverse' Theory, as it is known, argue that it is not so unlikely that the universe we observe has just the right conditions to allow for life. It is analogous to drawing a particular card from a vast number of alternative decks, as opposed to drawing the right card from just one deck. Recently Stephen Hawking has come out in favour of such a scenario, arguing that the laws of nature are themselves sufficient to account for the existence of our universe, and so -- as the eighteenth century French scientist Laplace said -- we have no need to invoke the hypothesis of a supernatural creator god to explain why there is something rather than nothing. According to the laws of physics, Hawking explains, 'nothing' is unstable and will result in something! These speculations on the nature of the universe and life are the source of great debate among scientists and philosophers. As this should make apparent, scientists may have modified the methods by which they operate, but they have not entirely given up the tradition of philosophy.
© Andrew Reynolds 2002
Last revised Sept. 8, 2010