Being a science professor is no assurance of understanding Newton's mechanics
Keith S. Taber
…this author had just written that
all matter is in uniform motion unless acted upon by an external force
but did not seem to appreciate that
any matter acted upon by an external force will not be in uniform motion
I started a new book today. 'The Watch on the Heath. Science and Religion before Darwin' had been on my pile of books to read for a while (as one can acquire interesting titles faster than find time to actually read them).
'The Watch on the Heath'
by Prof. Keith Thomson
The title is a reference to the analogy adopted at the start of William Paley's classic book on natural theology. Paley (1802) argued that if one was out walking across a heath and a foot struck an object on the ground, one would make very different assumptions if the object transpired to be a stone or a pocket watch. The stone would pass without much thought – there was no great mystery about how it came to be on the heath. But a pocket watch is an intricate mechanism composed of a multitude of especially shaped and arranged pieces fashioned from different materials. A reasonable person could not think it was an arbitrary and accidentally collated object – rather it clearly had a purpose, and so had a creator – a watchmaker.
Paley used this as an analogy for the complexity of the living world. Analogies are often used by teachers and science communicators as a means of making the unfamiliar familiar – a way of suggesting something that is being introduced is actually like something the audience already knows about and feels comfortable with.
Read about analogies in science
Paley was doing something a little different – his readers would already know about both watches and living things, and he was developing the analogy to make an argument about the nature of living things as being designed. (Living things would be familiar, but Paley wanted to invite his reader to think about them in a way they might find unfamiliar.) According to this argument, organisms were so complex that, by analogy with a watch, it followed they also were created for a purpose, and by a creator.
Even today, Paley's book is an impressive read. It is 'one long argument' (as Darwin said of his 'Origin of Species') that collates a massive amount of evidence about the seeming design of human anatomy and the living world. Paley was not a scientist in the modern sense, and he was not even a naturalist who collected natural history specimens. He was a priest and philosopher / theologian who clearly thought that publishing his argument was important enough to require him to engage in such extensive scholarship that in places the volume gives the impression of being a medical textbook.
Paley's work was influential and widely read, but when Darwin (1859) presented his own long argument for evolution by natural selection there began to be a coherent alternative explanation for all that intricate complexity. By the mid-twentieth century a neo-Darwinian synthesis (incorporating work initiated by Mendel, developments in statistics, and the advent of molecular biology) made it possible to offer a feasible account that did not need a watch-maker who carefully made his or her creatures directly from a pre-designed pattern. Richard Dawkins perverted Paley's analogy in calling one of his books 'The Blind Watchmaker' reflecting the idea that evolution is little more than the operation of 'blind' chance.
Arguably, Darwin's work did nothing to undermine the possibility of a great cosmic architect and master craft-person having designed the intricacies of the biota – but only showed the subtlety required of such a creator by giving insight into the natural mechanisms set up to slowly bring about the productions. (The real challenge of Darwin's work was that it overturned the idea that there was any absolute distinction between humans and the rest of life on earth – if humans are uniquely in the image of God then how does that work in relation to the gradual transition from pre-human ancestors to the first humans?)
Read 'Intergenerational couplings in the family. A thought experiment about ancestry'
Arguably Darwin said nothing to undermine the omnipotence of God, only the arrogance of one branch of the bush of life (i.e., ours) to want to remake that God in their image. Anyway, there are of course today a range of positions taken on all this, but this was the context for my reading some questionable statements about Newtonian mechanics.
Read about science and religion
Quantum quibbling
My reading went well till I got to p.27. Then I was perturbed. It started with a couple of quibbles. The first was a reference to
"…the modern world of quantum physics, where Einstein's relativity and Heisenberg's uncertainty reign."
Thomson, 2005: 27
"Er, no" I thought. Relativity and quantum theory are not only quite distinct theories, but, famously, the challenge of finding a way to make these two areas of physics, relativity theory and quantum mechanics, consistent is seen as a major challenge. The theories of relativity seem to work really well on the large scale and quantum theory works really well on the smallest scales, but they do not seem to fit together. "Einstein's relativity" is not (yet, at least) found within the "world of quantum physics".
Still, this was perhaps just a rhetorical flourish.
The Newtonian principle of inertia
But later in the same paragraph I read about how,
"Newton…showed that all matter is in uniform motion (constant velocity, including a velocity of zero) unless acted upon by an external force…Newton showed that an object will remain still or continue to move at a constant speed in the same direction unless some external force changes things."
Thomson, 2005: 27
This is known as Newton's first law of motion (or the principle of inertia). Now, being pedantic, I thought that surely Newton did not show this.
It is fair to say, I suggest, that Newton suggested this, proposed it, mooted it; perhaps claimed it was the case; perhaps showed it was part of a self-consistent description – but I am not sure he demonstrated it was so.
Misunderstanding Newton's first law
This is perhaps being picky and, of itself, hardly worth posting about, but this provides important background for what I read a little later (indeed, still in the same paragraph):
"Single forces always act in straight lines, not circles. Any trajectory other than a straight line must be the result of multiple forces acting together."
Thomson, 2005: 27
No!
The first part of this is fair enough – a force acts between two bodies (say the earth and the sun) and is considered to act along a 'line of action' (such as the line between the centres of mass of the earth and the sun). In the Newtonian world-view, the gravitational force between the earth and sun acts on both bodies along that line of action. 1
However, the second sentence ("any trajectory other than a straight line must be the result of multiple forces acting together") is completely wrong.
These two sentences are juxtaposed as though there is a logical link: "Single forces always act in straight lines, not circles. [So therefore] any trajectory other than a straight line must be the result of multiple forces acting together." This only follows if we assume that an object must always be moving in the direction of a force acting on it. But Newton's second law tells us that acceleration (and so the change in velocity) occurs in the direction of the force.
This is confusing the sense of a change with its outcome – a bit like thinking that a 10 m rise in sea level will lead to the sea being 10 m deep, or that if someone 'puts on 20 kilos' they will weigh 200 N. A 'swing to Labour' in an election does not assure Labour of a victory unless the parties were initially on par.
The error here is like assuming that any debit from a bank account must send it overdrawn:
taking £10 from a bank account means there will be £10 less in the account,
but not necessary that the balance becomes -£10!
Changing direction is effortless (if there is an external force acting)
Whenever a single force acts on a moving object where the line of action does not coincide with the object's direction of travel then the object will change direction. (That is, a single force will only not lead to a change of direction in the very special case where the force aligns with or directly against to the direction of travel.) So, electrons in a cathode ray tube can be shown to follow a curved path when a (single) magnetic force is applied, and an arrow shot from a castle battlement horizontally will curve down to the grounds because of the (single) effect of gravitational force. (There are frictional forces acting as well, but they only modify the precise shape of that curve which would still be found if the castle was on a planet with no atmosphere – as long as the archer could hold her breath long enough to get the arrow away.)
The lyrics of a popular song declare "arc of a diver – effortlessly". 2 But diving into a pool is only effortless (once you have pushed off) because the diver is pulled into an arc by their gravitational attraction with the earth – so even if you dive at an angle above the horizontal, a single force is enough to change your direction and bring you down.
"Arc of a diver – effortlessly"
© Pelle Cass. This image is used with kind permission of the artist.
(This amazing artwork is by the photographer Pelle Cass. This is one of a series ('Crowded Fields') that can be viewed at https://pellecass.com/crowded-fields.)
So, there is a mistake in the science here. Either the author has simply made a slip (which can happen to anyone) or he is operating with an alternative conception inconsistent with Newton's laws. The same can presumably be said about any editor or copy editor who checked the manuscript for the publisher.
Read about alternative conceptions
Misunderstanding force and motion
That might not be so unlikely – as force and motion might be considered the prototype case of a science topic where there are common alternative conceptions. I have seen estimates of 80%+ of people having alternative conceptions inconsistent with basic Newtonian physics. After all, in everyday life, you give something a pull or a push, and it usually moves a bit, but then always come to a stop. In our ordinary experience stones, footballs, cricket balls, javelins, paper planes, darts – or anything else we might push or pull – fail to move in a straight line at a constant speed for the rest of eternity.
That does not mean Newton was wrong, but his ideas were revolutionary because he was able to abstract to situations where the usual resistive forces that are not immediately obvious (friction, air resistance, viscosity) might be absent. That is, ideal scenarios that probably never actually occur. (Thus my questioning above whether Newton really 'showed' rather than postulated these principles.)
So, it is not surprising an author might hold a common alternative conception ('misconception') that is widely shared: but the author had written that
- all matter is in uniform motion unless acted upon by an external force
yet did not seem to appreciate the corollary that
- any matter acted upon by an external force will not be in uniform motion
So, it seems someone can happily quote Newton's laws of motion but still find them so counter-intuitive that they do not apply them in their thinking. Again, this reflects research which has shown that graduates who have studied physics and done well in the examinations can still show alternative conceptions when asked questions outside the formal classroom setting. It is as if they learn the formalism for the exams, but never really believe it (as, after all, real life constantly shows us otherwise).
So, this is all understandable, but it seems unfortunate in a science book that is seeking to explain the science to readers. At this point I decided to remind myself who had written the book.
We all have alternative conceptions
Keith Thomson is a retired academic, an Emeritus Fellow at Kellog College Oxford, having had an impressive career including having been a Professor of Biology at Yale University and later Director of the Oxford University Museum and Professor of Natural History. So, here we have a highly successful academic scientist (not just a lecturer in some obscure university somewhere – a professor at both Yale and Oxford), albeit with expertise in the life sciences, who seems to misunderstand the basic laws of physics that Newton postulated back in 1687.
Prof. Thomson seems to have flaws in his knowledge in this area, yet is confident enough of his own understanding to expose his thinking in writing a science book. This, again, is what we often find in science teaching – students who hold alternative conceptions may think they understand what they have been taught even though their thinking is not consistent with the scientific accounts. (This is probably true of all of us to some degree. I am sure there must be areas of science where I am confident in my understanding, but where that confidence is misplaced. I likely have misconceptions in topics areas where Prof. Thomson has great expertise.)
A balance of forces?
This could have been just a careless slip (of the kind which once made often looks just right when we reread our work multiple times – I know this can happen). But, over the page, I read:
"…in addition to the technical importance of Newton's mathematics, the concept of 'a balance of forces' keeping the moon circling the earth and the earth in orbit around the sun, quickly became a valuable metaphor…"
Thomson, 2005: 27
Again – No!
If there is 'balance of forces' then the forces effectively cancel, and there is no net force. So, as "all matter is in uniform motion (constant velocity, including a velocity of zero) unless acted upon by an external force", a body subject to a balance of forces continues in "uniform motion (constant velocity…)" – that is, it continues in a straight line at a constant speed. It does not circle (or move in an ellipse). 3
Again, this seems to be an area where people commonly misunderstand Newton's principles, and operate with alternative conceptions. Learners often think that Newton's third law (sometimes phrased in terms of 'equal and opposite forces') implies there will always be balanced forces!
Read about learning difficulties and Newton's third law
The reason the moon orbits the earth, and the reason the earth orbits the sun, in the Newtonian world-view is because in each case the orbiting body is subject to a single force which is NOT balanced by any countering force. As the object is "acted upon by an external force" (which is not balanced by any other force) it does not move "in uniform motion" but constantly changes direction – along its curved orbit. According to Newton's law of motion, one thing we can always know about a body with changing motion (such as one orbiting another body) is that the forces on it are not balanced.
But once circular motion was assumed as being the 'natural' state of affairs for heavenly bodies, and I know from my own teaching experience that students who understand Newtonian principle in the context of linear motion can still struggle to apply this to circular motion. 4
I even developed a scaffolding tool to help students make this transition, by helping them work through an example in very simple steps, but which on testing had modest effect – that is, it seemed to considerably help some students apply Newton's laws to orbital motion, but could not bridge that transition for others (Taber & Brock, 2018). I concluded even more basic step-wise support must be needed by many learners. Circular motion being linked to a net (unbalanced) centripetal force seems to be very counter-intuitive to many people.
To balance or not to balance
The suggestion that a balance of forces leads to change occurs again a little later in the book, in reference to James Hutton's geology,
"…Hutton supported his new ideas both with solid empirical evidence and an underlying theory based on a Newtonian balance of forces. He saw a pattern in the history of the rocks: gradually worn down by erosion, washed into the seas, accumulating as sediments, raised up as new dry land, only to be eroded again."
Thomson, 2005: 39
A balance of forces would not lead to rocks being "gradually worn down by erosion, washed into the seas, accumulating as sediments, raised up as new dry land, only to be eroded again". Indeed if all the relevant forces were balanced there would be no erosion, washing, sedimentation, or raising.
Erosion, washing, sedimentation, raising up ALL require an imbalance of forces, that is, a net force to bring about a change. 5
Reading on…
This is not going to stop me persevering with reading the book*, but one can begin to lose confidence in a text in situations such as these. If you know the author is wrong on some points that you already know about, how can you be confident of their accounts of other topics that you are hoping to learn about?
Still, Prof. Thomson seems to be wrong about something that the majority of people tend to get wrong, often even after having studied the topic – so, perhaps this says more about the hold of common intuitive conceptions of motion than the quality of Prof. Thomson's scholarship. Just like many physics learners – he has learnt Newton's laws, but just does not seem to find them credible.
Sources cited:
- Darwin, C. (1859). The Origin of Species by Means of Natural Selection, or the preservation of favoured races in the struggle for life. John Murray.
- Dawkins, R. (1988). The Blind Watchmaker. Penguin Books.
- Paley, W. (1802/2006). Natural Theology: Or Evidence of the Existence and Attributes of the Deity, Collected from the Appearances of Nature (M. D. Eddy & D. Knight, Eds.). Oxford University Press.
- Rosen, E. (1965/1995) Copernicus on the phases and the light of the planets, in Rosen, E. (1995). Copernicus and his successors (E. Hilfstein, Ed.). The Hambledon Press.
- Taber, K. S., & Brock, R. (2018). A study to explore the potential of designing teaching activities to scaffold learning: understanding circular motion. In M. Abend (Ed.), Effective Teaching and Learning: Perspectives, strategies and implementation (pp. 45-85). New York: Nova Science Publishers. [Read the author's manuscript version]
- Thomson, K. (2005). The Watch on the Heath: Science and religion before Darwin. HarperCollins.
- Watts, M. and Taber, K. S. (1996) An explanatory gestalt of essence: students' conceptions of the 'natural' in physical phenomena, International Journal of Science Education, 18 (8), pp.939-954.
Notes
1 Though not in the world-view offered by general relativity where the mass of the sun distorts space-time enough for the earth to orbit.
2 The title track from Steve Winwood's 1980 solo album 'Arc of a Diver'
3 We have known since Kepler that the planets orbit the sun following ellipses (to a first order of approximation*), not perfect circles – but this does not change the fundamental point here: moving in an ellipse involves continuous changes of velocity. (* i.e., ignoring the perturbations due to the {much smaller} forces between the orbiting bodies.**)
[Added, 20220711]: these perturbations are very small compared with the main sun-planet interactions, but they can still be significant in other ways:
"…the single most spectacular achievement in the long history of computational astronomy, namely, the discovery of the planet Neptune through the perturbations which it produced in the motion of Uranus."
Rosen, 1965/1995, p.81
4 What is judged as 'natural' is often considered by people as not needing any further explanation (Watts and Taber, 1996).
5 This reference to Hutton's ideas seems to preview a more detailed treatment of the new geology in a later chapter in the book (that I have not yet reached), so perhaps as I read on I will find a clearer explanation of what is meant by these changes being based on a theory of balance of forces.* Still, the impression given in the extract quoted is that, as with orbits, a balance of forces brings about change.
* Addendum: I have now read on, see: 'Plus ça change – balancing forces is hard work'