relativity - Science-Education-Research

The missing mass of the electron

Annihilating mass in communicating science

Keith S. Taber

An episode of 'In Our Time' about the electron

The BBC radio programme 'In Our Time' today tackled the electron. As part of the exploration there was the introduction of the positron, and the notion of matter-antimatter annihilation. These are quite brave topics to introduce in a programme with a diverse general audience (last week Melvyn Bragg and his guests discussed Plato's Atlantis and next week the programme theme is the Knights Templar).

Prof. Victoria Martin of the School of Physics and Astronomy at the University of Edinburgh explained:

If we take a pair of matter and antimatter, so, since we are talking about the electron today, if we take an electron and the positron, and you put them together, they would annihilate.
And they would annihilate not into nothingness, because they both had mass, so they both had energy from E=mc² that tells us if you have mass you have energy. So, they would annihilate into energy, but it would not just be any kind of energy: the particular kind of energy you get when you annihilate an electron and a positron is a photon, a particle of light. And it will have a very specific amount of energy. Its energy will be equal to the sum of the energy of electron and the positron that they had initially when they collided together.
Prof. Victoria Martin on 'In Our Time'

"*An electron and the positron, and you put them together, they would annihilate…they would annihilate into energy*" – but this could be misleading.

Now, I am sure that is somewhat different from how Prof. Martin would treat this topic with university physics students – of course, science in the media has to be pitched at the largely non-specialist audience.

Read about science in the media

It struck me that this presentation had the potential to reinforce a common alternative conception ('misconception') that mass is converted into energy in certain processes. Although I am aware now that this is an alternative conception, I seem to recall that is pretty much what I had once understood from things I had read and heard.

It was only when I came to prepare to teach the topic that I realised that I had a misunderstanding. That, I think, is quite common for teachers – when we have to prepare a topic well enough to explain it to others, we may spot flaws in our own understanding (Taber, 2009)

So, for example, I had thought that in nuclear processes, such as in a fission reactor or fusion in stars, the mass defect (the apparent loss of mass as the resulting nuclear fragments have less mass than those present before the process) was due to that amount of mass being converted to energy. This is sometimes said to explain why nuclear explosions are so much more violent than chemical explosions, as (given E=mc²): a tiny amount of mass can be changed into a great deal of energy.

Prof. Martin's explanation seemed to support this way of thinking: "they would annihilate into energy".

An alternative conception of particle annihilation: This scheme seems to be implied by Prof. Martin's comments

What is conserved?

It is sometimes suggested that, classically, mass and energy were considered to be separately conserved in processes, but since Einstein's theories of relativity have been adopted, now it is considered that mass can be considered as if a form of energy such that what is conserved is a kind of hybrid conglomerate. That is, energy is still considered conserved, but only when we account for mass that may have been inter-converted with energy. (Please note, this is not quite right – see below.)

So, according to this (mis)conception: in the case of an electron-positron annihilation, the mass of the two particles is converted to an equivalent energy – the mass of the electron and the mass of the positron disappear from the universe and an equivalent quantity of energy is created. Although energy is created, energy is still conserved if we allow for the mass that was converted into this new energy. Each time an electron and positron annihilate, their masses of about 2 ✕ 10^-30 kg disappear from the universe and in its place something like 2 ✕ 10^-13 J appears instead – but that's okay as we can consider 2 ✕ 10^-30 kg as a potential form of energy worth 2 ✕ 10^-13 J.

However, this is contrary to what Einstein (1917/2004) actually suggested.

Einstein did not suggest that matter could be changed to energy

Equivalence, not interconversion

What Einstein actually suggested was not that mass could be considered as if another kind/form of energy (alongside kinetic energy and gravitational potential, etc.) that needed to be taken into account in considering energy conservation, but rather that inertial mass can be considered as an (independent) measure of energy.

That is, we think energy is always conserved. And we think that mass is always conserved. And in a sense they are two measures of the same thing. We might see these two statements as having redundancy:

In a isolated system we will always have the same total quantity of energy before and after any process.
In a isolated system we will always have the same total quantity of mass before and after any process.

As mass is always associated with energy, and so vice versa, either of these statements implies the other. ¹

Two conceptions of the shift from a Newtonian to a relativistic view of the conservation of energy (move the slider to change the image)

No interconversion?

So, mass cannot be changed into energy, nor vice versa. The sense in which we can 'interconvert' is that we can always calculate the energy equivalence of a certain mass (E=mc²) or mass equivalence of some quantity of energy (m=E/c²).

So, the 'interconversion' is more like a change of units than a change of entity.

Although we might think of kinetic energy being converted to potential energy reflects a natural process (something changes), we know that changing joules to electron-volts is merely use of a different unit (nothing changes).

If we think of a simple pendulum under ideal conditions ² it could oscillate for ever, with the total energy unchanged, but with the kinetic energy being converted to potential energy – which is then converted back to kinetic energy – and so on, ad infinitum. The total energy would be fixed although the amount of kinetic energy and the amount of potential energy would be constantly changing. We could calculate the energy in joules or some other unit such as eV or ergs (or calories or kWh or…). We could convert from one unit to another, but this would not change anything about the physical system. (So, this is less like converting pounds to dollars, and more like converting an amount reported in pounds {e.g., £24.83} into an amount reported in pence {e.g., 2483p}.)

Using this analogy, the electron and positron being converted to a photon is somewhat like kinetic energy changing to potential energy in a swinging pendulum (something changes), but it is not the case that mass is changed into energy. Rather we can do our calculations in terms of energy or mass and will get (effectively, given E=mc²) the same answer (just as we can add up a shopping list in pounds or pence, and get the same outcome given the conversion factor, 1.00£ = 100p).

So, where does the mass go?

If mass is conserved, then where does the mass defect – the amount by which the sum of masses of daughter particles is less than the mass of the parent particle(s) – in nuclear processes go? And, more pertinent to the present example, what happens to the mass of the electron and positron when they mutually annihilate?

To understand this, it might help to bear in mind that in principle these process are like any other natural processes – such as the swinging pendulum, or a weight being lifted with pulley, or methane being combusted in a Bunsen burner, or heating water in a kettle, or photosynthesis, or a braking cycle coming to a halt with the aid of friction.

In any natural process (we currently believe)

the total mass of the universe is unchanged…
- but mass may be reconfigured
the total energy of the universe is unchanged…
- but energy may be reconfigured; and
as mass and energy are associated, any reconfigurations of mass and energy are directly correlated.

So, in any change that involves energy transfers, there is an associated mass transfer (albeit usually one too small to notice or easily measure). We can, for example, calculate the (tiny) increase in mass due to water being heated in a kettle – and know just as the energy involved in heating the water came from somewhere else, there is an equivalent (tiny) decrease of mass somewhere else in the wider system (perhaps due to falling of water powering a hydroelectric power station). If we are boiling water to make a cup of tea, we may well be talking about a change in mass of the order of only 0.000 000 001 g according to my calculations for another posting.

Read 'How much damage can eight neutrons do? Scientific literacy and desk accessories in science fiction.'

The annihilation of the electron and positron is no different: there may be reconfigurations in the arrangement of mass and energy in the universe, but mass (and so energy) is conserved.

So, the question is, if the electron and positron, both massive particles (in the physics sense, that they have some mass) are annihilated, then where does their mass go if it is conserved? The answer is reflected in Prof. Martin's statement that "the particular kind of energy you get when you annihilate an electron and a positron is a photon, a particle of light". The mass is carried away by the photon.

The mass of a massless particle?

This may seem odd to those who have learnt that, unlike the electron and positron, the photon is massless. Strictly the photon has no rest mass, whereas the electron and positron do have rest mass – that is, they have inertial mass even when judged by an observer at rest in relation to them.

So, the photon only has 'no mass' when it is observed to be stationary – which nicely brings us back to Einstein who noted that electromagnetic radiation such as light could never appear to be at rest compared to the observer, as its very nature as a progressive electromagnetic wave would cease if one could travel alongside it at the same velocity. This led Einstein to conclude that the speed of light in any given medium was invariant (always the same for any observer), leading to his theory of special relativity.

So, a photon (despite having no 'rest' mass) not only carries energy, but also the associated mass.

Although we might think in terms of two particles being converted to a certain amount of energy as Prof. Martin suggests, this is slightly distorted thinking: the particles are converted to a different particle which now 'has' the mass from both, and so will also 'have' the energy associated with that amount of mass.

Mass is conserved during the electron-positron annihilation

A slight complication is that the electron and position are in relative motion when they annihilate, so there is some kinetic energy involved as well as the energy associated with their rest masses. But this does not change the logic of the general scheme. Just as there is an energy associated with the particles' rest masses, there is a mass component associated with their kinetic energy.

The total mass-energy equivalence before the annihilation has to include both the particle rest masses and their kinetic energy. The mass-energy equivalence afterwards (being conserved in any process) also reflects this. The energy of the photon (and the frequency of the radiation) reflects both the particle masses and their kinetic energies at the moment of the annihilation. The mass (being perfectly correlated with energy) carried away by the photon also reflects both the particle masses and their kinetic energies.

How could 'In Our Time' have improved the presentation?

It is easy to be critical of people doing their best to simplify complex topics. Any teacher knows that well-planned explanations can fail to get across key ideas as one is always reliant on what the audience already understands and thinks. Learners interpret what they hear and read in terms of their current 'interpretive resources' and habits of thinking.

Read about constructivism

A physicist or physics student hearing the episode would likely interpret Prof. Martin's statement within a canonical conceptual framework. However, someone holding the 'misconception' that mass is converted to energy in nuclear processes would likely interpret "they would annihilate into energy" as fitting, and reinforcing, that alternative conception.

I think a key issue here is a slippage that apparently refers to energy being formed in the annihilation, rather than radiation: (i.e., Prof. Martin could have said "they would annihilate into [radiation]"). When the positron and electron 'become' a photon, matter is changed to radiation – but it is not changed to energy, as matter has mass, and (as mass and energy have an equivalence) the energy is already there in the system.

Energy is reconfigured, but is not formed, in the annihilation process.

So, this whole essay is simply suggesting that a change of one word – from energy to radiation – could potentially avoid the formation of, or the reinforcing of, the alternative conception that mass is changed into energy in processes studied in particle physics. As experienced science teachers will know, sometimes such small shifts can make a good deal of difference to how we are interpreted and, so, what comes to be understood.

Addenda:

Reply from Prof. Victoria Martin on twitter (@MamaPhysikerin), September 30:

"E² = p²c² + m²c⁴ is a better way to relate energy, mass and momentum. Works for both massive and massless states."
@MamaPhysikerin

Work cited:

Einstein, A. (1917/2004). Relativity. The special and the general theory. (R. W. Lawson, Trans.). The Folio Society.
Taber, K. S. (2009). Learning from experience and teaching by example: reflecting upon personal learning experience to inform teaching practice. Journal of Cambridge Studies, 4(1), 82-91.

Notes

¹ In what is often called a closed system there is no mass entering or leaving the system. However, energy can transfer to, or from, the system from its surroundings. Classically it might be assumed that the mass of a closed system is constant as the amount of matter is fixed, but Einstein realised that if there is a net energy influx to, or outflow from, the system, than some mass would also be transferred – even though no matter enters or leaves.

² Perhaps in a uniform gravitational field, not subject to to any frictional forces, with an inextensible string supporting the bob, and in thermal equilibrium with its environment.

Just two things

[Science] fiction reflecting life

Keith S. Taber

I imagine the physicist Henri Poincaré was entirely serious when he suggested,

"the principle of relative motion, which forces itself upon us for two reasons:
first, the commonest experience confirms it, and
second, the contrary hypothesis is singularly repugnant to the mind."
Henri Poincaré (mathematician, physicist, philosopher)

Perhaps Poincaré was reflecting how two opposing schools of philosophical thought had disagreed on wherever the primary source of human knowledge was experience (the empiricists) or pure reasoning (the rationalists), but elsewhere in the same text Poincairé (1902/1913/2015) dismisses the idea that the laws of physics can be obtained by simple reflection on human intuitions. Such intuitions can lead us astray.

If he is being consistent then, surely "the contrary hypothesis is [only] singularly repugnant to the mind" because "the commonest experience confirms…the principle of relative motion". That is, suggestions that are clearly contrary to our common experience – such as, perhaps, the earth is moving? – are readily rejected as being nonsensical and ridiculous.

If that is so, then Poincaré was not really offering two independent lines of argument as his second reason was dependent upon his first.

This put me in mind of some comments of Kryten, a character in the sci-fi series 'Red Drawf',

{responding to a crew suggestion "Why don't we drop the defensive shields?"}
"A superlative suggestion, sir, with just two minor flaws.
One, we don't have any defensive shields, and
two, we don't have any defensive shields.
Now I realise that, technically speaking, that's only one flaw but I thought it was such a big one it was worth mentioning twice."
Kryten (mechanoid assigned to the mining spaceship Red Dwarf)

or alternatively,

{responding to the crew suggestion "I got it! We laser our way through [the 53 doors from here to the science deck]!"}
Ah, an excellent plan, sir, with only two minor drawbacks.
One, we don't have a power source for the lasers; and
two, we don't have any lasers.
Kryten

The principle of relative motion

What Poincairé meant by 'the principle of relative motion' was that

"The motion of any system must obey the same laws, whether it be referred to fixed axes, or to moveable axes carried along in a rectilinear and uniform motion."
the principle of relative motion

In other words, imagine a train passing a station at 10 ms^-1, in which a naughty physics student throws a pencil eraser of mass m with a force of F at another passenger sitting in front on him; while a model physics student observes this from the stationary station [sic] platform.

The student on the train would consider the eraser to be at rest before being thrown, and can explore its motion by taking u=0 ms^-1 and applying some laws summarised by

F=ma,
v=u+at,
v²=u²+2as,
s=ut +¹/₂at²…

From the frame or reference of someone in the the station it is the train that moves,
(Image by StockSnap from Pixabay)
but…

…From the frame of reference of the train (or tram), it seems to be the rest of the world that is moving past
(Image by Pasi Mämmelä from Pixabay)

The student on the platform would observe the eraser to initially be moving at 10 ms^-1, but could calculate what would happen using the same set of equations, but taking u=10 ms^-1

Any values of v calculated would be consistent across the two frames (when allowing for the 10 ms^-1 discrepancy) and other values calculated (s, t) would be the same.

This reflects the relativity principle of Galileo which suggests that there is no absolute way of determining whether a body is moving at constant velocity or stationary: rather what appears to be the case depends on one's frame of reference.

We might think that obviously it is the platform which is really stationary, as our intuition is that the earth under our feet is stationary ground. Surely we could tell if the ground moves?

We can directly feel acceleration, and we can sometimes feel the resistance to motion (the air on our face if we cycle, even at a constant velocity), but the idea that we can directly tell whether or not we are moving is an alternative conception.

For centuries the idea of a moving earth was largely considered ridiculous as experience clearly indicated otherwise. But if someone was kidnapped whilst asleep (please note, this would be illegal and is not being encouraged) and awoke in a carriage that had been set up to look like a hotel bedroom, on a train moving with constant velocity, they would not feel they were in motion. Indeed anyone who as travelled on a train at night when nothing is visible outside the carriage might well have experienced the impression that the train is stationary whilst it moves at a steady rate.

Science has shown us that there are good reasons to think that the earth is spinning, and orbiting the sun, as part of the solar system which moves through the galaxy, so who is to say what is really stationary? We cannot tell (and the question may be meaningless).

Who is to say what is moving – we can only make relative judgements?
(Image by Drajt from Pixabay)

Source cited:

Poincaré, H. (1902/1913/2015). Science and Hypothesis (G. B. Halstead, Trans.). In The Foundations of Science. Cambridge University Press. {I give three dates because Poincaré published his book in French in 1902, and it was later published in an English translation in 1913, but I have a 2015 edition.}

Even Oxbridge professors have misconceptions

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"

(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

Two conceptions of orbital motion (one canonical, the other a misconception commonly offered by students). From Taber, K. S., & Brock, R. (2018). A study to explore the potential of designing teaching activities to scaffold learning: understanding circular motion.

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

¹Though 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'

Albert Einstein and John the Baptist

Keith S. Taber

What is the relationship between Albert Einstein and St. John the Baptist?

Why would someone seeking to communicate scientific ideas to a broad readership refer to St. John?

Spoiler alert: in a direct sense, there clearly is no relationship. St. John lived in Palestine two thousand years ago, was a preacher, and is not known to have had any particular interest in what we think of as physics or science more generally. Albert Einstein was a theoretical physicist, and probably the most famous scientist of the twentieth century, perhaps of all time.

It is fair to point out both were Jewish: John can be considered a Jewish prophet. There has been much speculation on Einstein's religious thought. Of Jewish background, he was subject to the Nazi's fascist policies in Germany and fled to spent much of his life in the U.S.A. Sometimes considered an atheist, Einstein did talk of God (as not playing dice for example – that is, not leaving room in the Universe for completely random events) but it is sometimes claimed he use the idea of God as a metaphor for some kind of pantheistic or general spiritual background to the universe. In general though, he stuck to physics, and campaigned on issues like world peace.

(Read about 'The relationship between science and religion')

So, why raise the question?

My posing this question was motivated by reading something written by Herman Weyl (1885 – 1955) who is described by Wikipedia as "a German mathematician, theoretical physicist and philosopher". In one of his writings Weyl referred to Hendrik Lorentz who (again according to Wikipedia) was "a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and theoretical explanation of the Zeeman effect".

This is how Weyl described Lorentz:

"the Dutch physicist H.A. Lorentz who, as Einstein's John the Baptist, prepared the way for the gospel of relativity."

Weyl, 1952/2016, pp.131-132.

Those studying physics at high levels, or reading about relativity theory, will probably have heard of the 'Lorentz transformations' that are used in calculations in special relativity.

An extended metaphor?

What Weyl is doing here is using a metaphor, or perhaps an analogy. In a metaphor a writer or speaker says that something is something else – to imply it has some attribute of that other thing.

(Read about 'Science metaphors')

In an analogy, one system is compared with another to show that there is, or to suggest that perhaps might be, a structural similarity. Usually analogies are presented as an explicit comparison (X is like Y: i.e., rather than 'Lorentz was Einstein's John the Baptist', perhaps 'Lorentz was like Einstein's John the Baptist in the sense that…')

(Read about 'Science analogies')

As Weyl does not say Lorentz was like a John the baptist figure, or played a role similar to John the Baptist, but that he was "Einstein's John the Baptist" I would consider this a metaphor. However, it is an extended metaphor as the comparison is explained as justified because Lorentz "prepared the way for the gospel of relativity".

That could be seen as a second metaphor in that relativity is normally considered a theory (or two theories, special relativity, and general relativity), and not a gospel – a word that means 'good news'. So Weyl is saying that Lorentz prepared the way for the good news of relativity!

Making the familiar unfamiliar?

When I read this comment I immediately felt I appreciated the point that Weyl was seeking to make. However, I also felt that this was a rather odd comparison to make, as I was not sure how universally it would be understood.

Those communicating about science, whether as science teachers or journalists or (as here) scientists themselves looking to reach a general audience, have the task of 'making the unfamiliar (what people do not yet know about, and may indeed seem odd) familiar'. There are various techniques that can be used, and often these involve some form of comparison of what is being told about with something that is in some ways similar, and which is already familiar to the audience.

(Read about 'Making the unfamiliar familiar')

I attended 'Sunday school' from a young age (I think before starting day school if I recall correctly) at a London City Mission church, and later at a Methodist Church, where I became a Sunday school teacher before i went off to University. I therefore learnt quite a bit about Christianity. Anyone with such a background will have learnt that John the Baptist was a cousin of Jesus Christ, who preached 'the coming of the Lord' (i.e., the Jewish messiah, identified in Christianity with Jesus), and baptised Jesus in the River Jordan as he set out on his mission as a preacher and healer. John is said to have told his congregation to "prepare ye, the way of the Lord!" (the title of a song in the musical 'Godspell').

Someone knowing about Christianity in this way (regardless of whether they accept Christian teaching, or even the historical accuracy of the Baptism story) would likely immediately appreciate that just as John prepared the way for Jesus' ministry in first Century (CE) Palestine, so, according to Weyl, Lorentz prepared physics, laid important groundwork, for Einstein's work on relativity.

When you have the necessary background, such comparisons work effectively and quickly – the idea is communicated without the reader having to puzzle over and interpret the expressions "Einstein's John the Baptist" and "gospel of relativity" or deliberate on what is meant by 'preparing the way'. That is, the if the reader has the relevant 'interpretive resources' then understanding is an automatic process that does not require any conscious effort.

Culture-specific interpretive resources?

But I wondered what someone would make of this phrase ('Einstein's John the Baptist') if they did not have knowledge of the Bible stories? After all, in many parts of the world most people are not Christians, and may have little or no knowledge of Christian traditions. Did Weyl just assume everyone would have the background to appreciate his comparison, or did he assume he was only writing for an audience in certain parts of the world where this was common knowledge?

Certainly, as teachers, our attempts to help our students understand abstract ideas by making references to common cultural phenomena can fall flat if the learners are not familiar with those phenomena. It is counter-productive if the teacher has to interrupt their presentation on some abstract idea to explain the very comparison that was meant to help explain the scientific concept or principle. If you have no idea who 'John the Baptist' was, in what sense he 'prepared the way' for Jesus, or or how the term 'Gospel' came to be attached to the accounts of Jesus' life, then it is not so easy to appreciate what Lorentz was to Einstein's work from Weyl's prose. We can only make the unfamiliar familiar by using cultural references when we share those references with those we are communicating with.

Work cited:

Weyl, H. (1952/2016). Symmetry (New Princeton Science Library edition ed.). Princeton, New Jersey: Princeton University Press.

Is the theory of evolution e=mc²?

Keith S. Taber

Adrian was a participant in the Understanding Science Project. When I spoke to him during the his first year (Y12) of his 'A level' course he told me he had been studying quantum theory, and I asked him about the name 'quantum theory'. He suggested that a theory is an idea that can be proven, but struggled to suggest any other scientific theories.

I suggested the theory of evolution:

What about the theory of evolution? Would you count that as a theory?
Yes, but I am not familiar with it. Was it e=mc²?
That's relativity.
Relativity.
I was thinking evolution?
I don't know that one.
Not sure about evolution at all?
No.

Of course there is more than one theory of evolution, but natural selection was a compulsory topic in the school curriculum, and widely referred to as 'the theory of evolution'. Adrian, however, seemed to have no recollection of hearing about evolution at all. It is inconceivable that he had not met the term in school or elsewhere, but it was not something he was bringing to mind in response to my questioning.