Scientific literacy and desk accessories in science fiction
Keith S. Taber
Is the principle of conservation of mass that is taught in school science falsified all the time?
I am not really a serious sci-fi buff, but I liked Star Trek (perhaps in part because it was the first television programme I got to see in colour 1) and I did enjoy Blakes7 when it was broadcast by the BBC (from 1978-1981).
Blakes7 was made with the same kind of low budget production values of Dr Who of the time. Given that space scenes in early episodes involved what seemed to be a flat image of a spacecraft moving across a star field with no sense of depth or perspective (for later series someone had built a model), and in one early episode the crew were clearly given angle-poise lamps to control the craft, it was certainly not a case of 'no expense spared'. So, it was never quite clear if the BBC budget had also fallen short of a possessive apostrophe in the show title credits or Blakes7 was to be read in some other way.
After all, it was not made explicit who was part of Blake's 7 if that was what the title meant, and no one referred to "Blake's 7" in the script (perhaps reflecting how the doctor in Dr Who was not actually called Dr Who?).
Blake's group was formed from a kind of prison break and so Blake was something of a 'rough-hero' – but not as much as his sometime unofficial lieutenant, sometime friend, sometime apparent rival, Avon, who seemed to be ruled by self-interest (at least until the script regularly required some act of selfless heroism from him). 'Rough-heroes' are fictional characters presented in the hero role but who have some traits that the audience are likely to find morally questionable if not repugnant.
As well as Blake (a rebel condemned as a traitor, having 'recovered' from brainwashing-supported rehabilitation to rebel again) and Avon (a hacker convicted of a massive computer fraud intended to make himself extremely rich) the rest of the original team were a smuggler, a murderer and a petty thief, to which was added a terrorist (or freedom fighter if you prefer) picked up on an early mission. That aside, they seemed an entirely reasonable and decent bunch, and they set out to rid the galaxy of 'The Federation's tyrannical oppression. At least, that was Blake's aspiration even if most of his companions seemed to see this as a stop-gap activity till they had decided on something with more of a long-term future.
At the end of one season, where the fight with the Federation was temporarily put aside to deal with an intergalactic incursion, Blake went AWOL (well, intergalactic wars can be very disruptive) and was assumed dead/injured/lost/captured/?… for much of the remaining run without affecting the nature of the stories too much.
Among its positive aspects for its time were strong (if not exactly model) roles for women. The main villain, Servalan, was a woman – Supreme Commander of the Federation security forces (and later Federation president).
In Blake's original team (i.e., 7?), his pilot is a woman. (Reflecting other SciFi series, the spacecraft used by Blakes7 require n crew members to operate effectively, where n is an integer that varies between 0 and 6 depending on the specific plot requirements of an episode.) In a later series, after Avon has taken over the role of 'ipso facto leader-among-equals', the group recruits a female advanced weapons designer/technologist and a female sharpshooter.
When I saw Blakes7 was getting a rerun recently I re-watched the series I had not seen since it was first aired. Despite very silly special effects, dodgy story-lines, and morally questionable choices (the series would make a great focus for a philosophy class) the interactions between the main characters made it an enjoyable watch.
But, it is not science
Of course, the problem with science fiction is that it is fiction, not science. Star Trek may have prided itself on seeking to at least make the science sound feasible, but that is something of an outlier in the genre.
This is clear, for example, in an episode called 'Orbit' where Avon discuses the tachyon funnel, an 'ultimate weapon', with Egrorian, a renegade scientist. Tachyons are hypothetical particles that travel faster than the speed of light. The theory of special relatively suggests the speed of light is the theoretical maximum speed anything can have, but some other theories suggest tachyons may exist in some circumstances. As always in science, theories that are widely accepted as our current best understanding of some aspect of nature (e.g., relativity) are still open to modification or replacement if new evidence is found that suggests this is indicated.
In the Blakes7 universe, there seemed to be a surprisingly high frequency of genius scientists/engineers who had successfully absconded from the tyrannical and paranoid Federation with sufficient resources to build private research facilities on various obscure deserted planets. Although these bases are secret and hidden away, and the scientists concerned have normally been missing for years or even decades, it usually transpires that the Blakes7 crew and the Federation manage to locate any particular renegade scientist during the same episode.
This is part of the exchange between this particular flawed genius scientist and our flawed and reluctant 'rough hero', Kerr Avon:
Egrorian: You've heard of Hoffal's radiation?
Avon: No.
Ah… Hoffal had a unique mind. Over a century ago he predicted most of the properties that would be found in neutron material.
Neutron material?
Material from a neutron star. That is a… a giant sun which has collapsed and become so tightly compressed that its electrons and protons combine, making neutrons.
I don't need a lecture in astrophysics. [But presumably the scriptwriter felt the audience would need to be told this.]
When neutrons are subjected to intense magnetic force, they form Hoffal's radiation. Poor Pinder [Egrorian's lab. assistant] was subjected for less than a millionth of a second. He aged 50 years in as many seconds. …
So neutrons are part of the tachyon funnel.
Um, eight of them … form the core of the accelerator.
From the script of 'Orbit' (c) 1981 by the British Broadcasting Corporation – made available 'for research purposes'
Now, for anyone with any kind of science background such dialogue stretches credibility. Chadwick discovered the neutron in everyday matter in 1932, so the neutron's properties could be explored without having to obtain samples from a neutron star – which would certainly be challenging. When bound in nuclei, neutrons (which are electrically neutral, thus the name, and so not usually affected by magnetic fields) are stable.
Thinking at the scale of a neutron
However, any suspension of disbelief (which fiction demands, of course) was stretched past breaking point at the end of this exchange. Not only were the generally inert neutrons the basis of a weapon that could destroy whole worlds – but the core of the accelerator was formed of, not a neutron star, nor a tonne of 'neutron matter', but eight neutrons (i.e., one for each member of Blake's 7 with just a few left over?)
That is, the intensely destructive beam of radiation that could destroy a planet from a distant solar system was generated by subjecting to a magnetic field: a core equivalent to (the arguably less interesting) half of a single oxygen atomic nucleus.
Now free neutrons (that is, outside of an atomic nuclei – or neutron star) are unstable, and decay on a timescale of around a quarter of an hour (that is, the half-life is of this order – following the exponential decay familiar with other kinds of radioactivity), to give a proton, an electron and a neutrino. The energy 'released' in this process is significant on the scale of a subatomic particle: 782 343 eV or nearly eight hundred thousand eV.
Eight hundred thousand seems a very large number, but the unit here is electron volt, a unit used for processes at this submicroscopic scale. (An eV is the amount of work that is done when one single electron is moved though a potential difference of 1v – this is about 1.6 x10-19 J). In the more familiar units of joules, this is about 1.25 x 10-13 J. That is,
0.000 000 000 000 125 J
To boil enough water at room temperature to make a single cup of tea would require about 67 200 J. 2 So, if the energy from decaying neutrons were used to boil the water, it would require the decay of about
538 000 000 000 000 000 neutrons.3
That is just to make one cup of tea, so imagine how many more neutrons would have to decay to provide the means to destroy a planet. Certainly, one would imagine,
more than 8.
E=mc2
Now since Einstein (special relativity, again), mass and energy have been considered to have an equivalence. It is commonly thought that mass can be converted to energy and the equation E=mc2 tells you how much of one would be converted to the other: how many J per kg or kg per J. (Spoiler alert – this is not quite right.)
In that way of thinking, the energy released by a free neutron when it decays is due to a tiny part of the neutrino's mass being converted to energy.
The neutron's mass defect
The mass (or so called 'rest mass') of a neutrino is about 1.67 x 10-27 kg. In the usual mode of decay the neutrino gives rise to a proton (which is nearly, but not quite, as heavy as a neutron), an electron (which is much lighter), and a neutrino (which is considered to have zero rest mass.)
| Before decay | Rest mass / 10-31 kg | After decay | Rest mass / 10-31 kg |
| neutron | 16 749.3 | proton | 16 726.2 |
| electron | 9.1 | ||
| neutrino | – | ||
| total | 16 749.3 | 16 735.3 |
So, it seems like some mass has disappeared. (And this is the mass sometimes said to have been converted into the released energy.) This might lead us to ask the question of whether Hoffal's discovery was a way to completely annihilate neutrons, so that instead of a tiny proportion of their mass being converted to energy as in neutron decay – all of it was.
Mass as latent energy?
However, when considered from the perspective of special relativity, it is not that mass is being converted to energy in processes such as neutron decay, but rather that mass and energy are considered as being different aspects of something more unified -'mass-energy' if you like. Energy in a sense carries mass, and mass in a sense is a manifestation of energy. The table above may mislead because it only refers to 'rest mass' and that does not tell us all we need to know.
When the neutron decays, the products move apart, so have kinetic energy. According to the principle of mass-energy equivalence there is always a mass equivalence of any energy. So, in relativity, a moving object has more mass than when it is at rest. That is, the 'mass defect' table shows what the mass would be if we compared a motionless neutron with motionless products, not the actual products.
The theory of special relativity boldly asserts that mass and energy are not the independent quantities they were once thought to be. Rather, they are two measures of a single quantity. Since that single quantity does not have its own name, it is called mass-energy, and the relationship between its two measures is known as mass-energy equivalence. We may regard c2 as a conversion factor that enables us to calculate one measurement from the other. Every mass has an energy-equivalent and every energy has a mass-equivalent. If a body emits energy to its surroundings it also emits a quantity of mass equivalent to that energy. The surroundings acquire both the energy and mass in the process.
Treptow, 2005, p.1636
So, rather than thinking mass has been converted to energy, it may be more appropriate to think that the mass of a neutron has a certain (latent) energy associated with it, and that, after decay, most of this energy is divided between products (according to their rest masses), but a small proportion has been converted to kinetic energy (which can be considered to have a mass equivalence).
So, whenever any process involves some kind of energy change, there is an associated change in the equivalent masses. Every time you boil the kettle, or go up in an elevator, there is a tiny increase of mass involved – the hot water is heavier than when it was cold; you are heavier than when you were at a lower level. When you lie down or burn some natural gas, there is a tiny reduction in mass (you weigh less lying down; the products of the chemical reaction weigh less than the reactants).
How much heavier is hot water?
Only in nuclear processes does the energy change involved become large enough for any change in mass to be considered significant. In other processes, the changes are so small, they are insignificant. The water we boiled earlier to make a cup of tea required 67 200J of energy, and at the end of the process the water would not just be hotter, but also heavier by about
0.000 000 000 000 747 kg
0r about 0.000 000 000 75 g. That is easy to calculate 4, but not so easy to notice.
Is mass conserved in chemical reactions?
On this basis, we might suggest that the principle of conservation of mass that is taught in school science is falsified all the time – or at least needs to be understood differently from how it is usually presented.
| Type of reaction | Mass change |
| endothermic | mass of products > mass of reactants |
| exothermic | mass of products < mass of reactants |
Yet, the discrepancies really are tiny – so tiny that in school examinations candidates are expected to pretend there is no difference. But, strictly, when (as an example) copper carbonate is heated in a crucible and decomposes to give copper oxide and carbon dioxide there is a mass decrease even if you could capture all the CO2. But it would not be measurable with our usual laboratory equipment – so, as far as chemistry is concerned, mass is conserved. 'To all intense and purposes' (even if not absolutely true) mass is always conserved in chemical reactions.
Mass is conserved overall
But actually, according to current scientific thinking, mass is always conserved (not just very nearly conserved), as long as we make sure we consider all relevant factors. The energy that allowed us to boil the kettle or be lifted in an elevator must have been provided from some source (which has lost mass by the same extent). In an exothermic chemical reaction there is an extremely slight difference of mass between the reactants and products, but the surroundings have been warmed and so have got (ever so slightly) heavier.
| Type of reaction | Mass change |
| endothermic | energy (and equivalent mass) from the surroundings |
| exothermic | energy (and equivalent mass) to the surroundings |
As Einstein himself expressed it,
"The inertial mass of a system of bodies can even be regarded as a measure of its energy. The law of the conservation of the mass of a system becomes identical with the law of the conservation of energy, and is only valid provided that the system neither takes up nor sends out energy."
Einstein, 1917/2015, p.59
Annihilate the neutrons!
So, if we read about how in particle accelerators, particles are accelerated to immense speeds, and collided, and so converted to pure energy we should be suspicious. The particles may well have been destroyed – but something else has now acquired the mass (and not just the rest mass of the annihilated particles, but also the mass associated with their high kinetic energy).
So, we cannot convert all of the mass of a neutron into energy – only reconfigure and redistribute its mass-energy. But we can still ask: what if all the mass of the neutron were to be converted into some kind of radiation that carried away all of its mass as high energy rays (perhaps Hoffal's radiation?)
Perhaps the genius scientist Hoffal, with his "unique mind", had found a way to do this (hm, with a magnetic field?) Even if that does not seem very feasible, it does give us a theoretical limit to the energy that could be produced by a process that converted a neutron into radiation.6 Each neutron has a rest mass of about
1.67 x 10-27 kg
now the conversion factor is c2 (where c is the speed of light, which is near enough 3 x 108 ms-1, so c2 =(3×108ms-1)2 , i.e., about 1017m2s-2), so that mass is equivalent to about 1.50 x 10-10 J 5 or,
0.000 000 000 150 J
Now that is a lot more energy than the 1.25 x 10-13 J released in the decay of a neutron,
0.000 000 000 150 000 J
>
0.000 000 000 000 125 J
and now we could in theory boil the water to make our cup of tea with many fewer neutrons. Indeed, we could do this by annihilating 'only' about 7
448 000 000 000 000 neutrons
This is a lot less neutrons than before, i.e.,
448 000 000 000 000 neutrons
< 538 000 000 000 000 000 neutrons
but it seems fair to say that it remains the case that the number of neutrons needed (now 'only' about 448 million million) is still a good deal more than 8.
448 000 000 000 000 neutrons
> 8 neutrons
So, if over 400 million million neutrons would need to be completely annihilated to make a single cup of tea, how much damage can 8 neutrons do to a distant planet?
A common learning difficulty
In any reasonable scenario we might imagine 8 neutrons would not be significant. This is worth emphasising as it reflates to a common learning difficulty. Quanticles such as atoms, atomic nuclei, neutrons and the like are tiny. Not tiny like specs of dust or grains of salt, but tiny on a scale where specs of dust and grains of salt themselves seem gigantic. The scales involved in considering electronic charge (i.e., 10-19C) or neutron mass (10-27 kg) can reasonably said to be unimaginatively small – no one can readily visualise the shift in scale going from the familiar scale of objects we normally think of as 'small', to the scale of individual molecules or subatomic particles.
Students therefore commonly form alternative conceptions of these types of entities (atoms, electrons, etc.) being too small to see, but yet not being so far beyond reach. And it is not just learners who struggle here. I have even heard someone on a national news programme put forward as an 'expert' make a very similar suggestion to Egrorian, in this case that a "couple of molecules" could be a serious threat to public health after the use of chemical nerve agent. This is a preposterous suggestion to a chemist, but was, I am sure, made in good faith by the international chemical weapons expert.
It is this type of conceptual difficulty which allows scriptwriters to refer to 8 neutrons as being of some significance without expecting the audience to simply laugh at the suggestion (even if some of us do).
It also explains how science fiction writers get away with such plot devices given that many in their audiences will readily accept that a few especially malicious molecules or naughty neutrons is a genuine threat to life.8 But that still does not justify using angle-poise lamps as futuristic spacecraft joysticks.
Works cited:
- Einstein, A. (1917/2015). Relativity. The special and the general theory. (100th Anniversary ed.). Princeton: Princeton Univerity Press.
- Treptow, R. S. (2005). E = mc2 for the Chemist: When Is Mass Conserved? Journal of Chemical Education, 82(11), 1636. doi:10.1021/ed082p1636
Notes:
1 To explain: For younger readers, television was first broadcast in monochrome (black and white – in effect shades of grey). My family first got a television after I started primary school – the justification for this luxury was that the teachers sometimes suggested programmes we might watch.
Colour television did not arrive in the UK till 1967, and initially it was only used for selected broadcasts. The first colour sets were too expensive for many families, so most people initially stayed with monochrome. This led to the infamous 'helpful' statement offered by the commentator of the weekly half-hour snooker coverage: "And for those of you who are watching in black and white, the pink [ball] is next to the green". (While this is well known as a famous example of misspeaking, a commentator's blooper, those of a more suspicious mind might bear in mind the BBC chose snooker for broadcast in part because it might encourage more people to watch in colour.)
My father had a part-time weekend job supervising washing machine rental collections (I kid you not, many people only rented such appliances in those days), to supplement income from his full time job, and this meant on Monday evenings after his day job he had to visit his part-time boss and report and they would go throughout the paperwork to ensure things tallied. I would go with him, and was allowed to watch television whilst they did this – it coincided with Star Trek, and the boss had a colour set!
2 Assuming water had to be heated from 20˚C to 100˚C, and the cup took 200 ml (200 cm3) of tea then the calculation is 4.2 x 80 x 200
4.2 J g-1K-1 is the approximate specific heat capacity of water.
Changing these parameters (perhaps you have a small tea cup and I use a mug?) will change the precise value.
3 That is the energy needed divided by the energy released by each neutron: 67200 J ÷ 1.25 x 10-13 J/neutron = 537 600 000 000 000 000 neutrons
4 E=mc2
so m = E/c2 = 67 200 ÷ (3.00 x 108)2 = 7.47 x 10-13
5 E=mc2 = 1.67 x 10-27 x (3.00 x 108)2 = 1.50 x 10-10
6 Well, we could imagine that somehow Hoffal had devised a process where the neutrons somehow redirect energy provided to initially generate the magnetic field, and perhaps the weapon was actually an enormous field generator producing a massive magnetic field that the funnel somehow converted into a beam (of tachyons?) that could pass across vast amounts of space without being absorbed by space dust, remaining highly collimated, and intense enough to destroy a world.
So, perhaps the neutrons are analogous to the core of a laser.
I somehow think it would still need more than 8 of them.
7 That is the energy needed divided by the energy released by each neutron: 67200 J ÷ 1.50 x 10-10 J/neutron = 4.48 x 1014 neutrons
8 Of course molecules are not actually malicious and neutrons cannot be naughty as they are inanimate entities. I am not anthropomorphising, just alliterating.