# Is fission/fusion to iron the most efficient way to convert mass to energy?

Is fission/fusion of any element to iron-56 (or nickel-62?) the best way to convert mass to energy, that doesn't involve black holes?

In other words, will we be always limited to convert only about 1% of the mass available to energy? Are there other ways (using strangelets? antimatter?) to go beyond that limit?

I exclude black holes as, as I understand, you can only extract a finite amount of energy by reducing their spin, so they are not viable for energy production on a cosmological scale.

• Happy to exclude black holes, but I wouldn't say that they are not viable on cosmological scale, since many or maybe even all the brightest sources in the universe are powered by the strong gravity processes associated with a black hole. – Andrew Steane Jun 11 '19 at 7:46
• "Are Black Hole Starships Possible" (arxiv.org/abs/0908.1803) is a great article examining the possibility of extracting energy from artificial black holes via Hawking radiation. My layman's take-away from it is that this totally works and is the best thing. – Daniel Darabos Jun 12 '19 at 14:03
• @DanielDarabos Hawking radiation is a separate thing; the main interesting case people have been working with is extracting the gravitational potential energy - fling matter at a black hole so that it spirals down the well, and it will release humongous amounts of energy as (essentially pure) radiation long before it gets close to the event horizon. Nuclear reactions in stars liberate about 1% of the rest mass; accretion on a neutron star around 10% (and it doesn't care about what nuclei are involved). The accretion disk of a rotating black hole gets to around 40%, much better than antimatter. – Luaan Jun 13 '19 at 7:27
• @DanielDarabos Another interesting option is extracting the angular momentum of a charged, rotating black hole - about 20% of the "mass-energy" of a typical stellar-mass black hole is in its rotational energy, and it can be extracted relatively easily. Hawking radiation is essentially useless for stellar-mass black holes - it's only interesting for extremely low mass black holes (e.g. the kind you'd use as a "power source" on a sci-fi space ship). – Luaan Jun 13 '19 at 7:30
• Can you extract momentum from a charged black hole electromagnetically? I.e. could you put it in a coil and see currents generated in the coil? – Skyler Jun 13 '19 at 18:08

## 6 Answers

Matter-antimatter annihilation, such as an electron annihilating with a positron to form two high-energy photons, can convert 100% of the mass into radiation. So fission and fusion are far from the most efficient ways to convert mass into other forms of energy. Unfortunately, the universe appears to contain almost no antimatter.

• Or perhaps fortunately... – user469104 Jun 11 '19 at 12:31
• While this is the obvious answer, I some clarity from the OP may help. While antimatter certainly gives you a 100% efficiency rate, this is only true if you have an easy source of antimatter available. If you have to generate the antimatter, then presumably you have to factor in the efficiency of your antimatter generation process, which (for current technology) is abysmally low. As a result antimatter would best be viewed as an advanced battery technology - not an energy production method, which the OP mentioned in his question. – conman Jun 11 '19 at 14:23
• Unfortunately, about 40% of the incoming mass comes out as neutrino radiation, which is essentially useless for almost any practical purpose. Annihilation is still much more efficient than fission or fusion, though! – Sean Jun 12 '19 at 1:01

The most efficient non-gravitational way of extracting energy from ordinary matter is indeed to convert it into elements in the $$^{56}$$Fe region. There is a fairly broad plateau of nuclides with binding energies of about $$8.7$$ MeV per nucleon, so it does not matter very much which of these you actually turn the source matter into. (However, $$^{56}$$Fe is the optimum, since it has the lowest mass energy per nucleon, and the number of nucleons is conserved. $$^{62}$$Ni has a lower binding energy per nucleon, but it is less stable, since some of its neutrons may be converted to protons to release additional energy; effectively the binding energy does not count the amount of energy that is tied up in the slightly greater neutron mass. On the other hand, much of the energy in that would be released in the conversion of Ni or Co nuclei to Fe is in the form of neutrinos, which would be extremely hard to capture.)

However, the amount of energy that can be released via fusion still pales in comparison with what can be obtained using a deep gravitational potential. This does not need to be a black hole. A neutron star will do. The release of energy in a core collapse supernova comes from the enormous gravitational potential energy that is unlocked when a $$\sim1.4\,M_{\odot}$$ white dwarf (with a radius of thousands of km) collapses into a neutron star (with a radius a just a few km). If you already have a neutron star, you can drop matter onto it and capture the radiation it emits as it accelerates toward the neutron star surface. Under optimal conditions, this can actually release a substantial [i.e. $${\cal O}(1)$$—of order 1] fraction of a dropped particle's entire mass energy.

Finally, there is also direct matter/antimatter annihilation, which lets you get all the mass energy out of the source material. However, it requires you to have ready sources of both matter and antimatter, which is not necessarily possible on large scales. (You cannot manufacture the antimatter without putting in just as much energy as you intend to obtain from the annihilation reaction.) So this option will not function with a generic hunk of source matter as your potential fuel.

• "Under optimal conditions, this can actually release an O(1) fraction of a dropped particle's mass energy." What is the independent variable? – Acccumulation Jun 11 '19 at 14:59
• Nice answer, but the "O(1) fraction" is entirely unclear. Can you clarify what you mean by that? – cmaster - reinstate monica Jun 11 '19 at 18:30
• @mbrig, I believe you can't manufacture antimatter by itself, you can only manufacture equal amounts of matter and antimatter, because of conservation laws. So the net result of the overall process of manufacturing and then annihilating doesn't consume matter, and therefore can't be expected to generate energy. – Harry Johnston Jun 12 '19 at 1:09
• by $\mathcal O(1)$ the author clearly means something like "of order 1", meaning an order of magnitude of 1. Hence around 100%, or at least 10% to 100% efficiency say. – Colin MacLaurin Jun 12 '19 at 3:51
• @HarryJohnston We already know the weak nuclear force breaks the (originally assumed, now proven wrong) symmetry involved; in any case, you don't care matter is produced along with antimatter - what you do care about is that even if you could produce antimatter with 100% efficiency, and annihilate antimatter with matter with 100% efficiency (along with capturing all the neutrinos etc.), you'd only ever break even - you're not going to release any energy you didn't already have. The only reason this would ever be worthwhile is as high-density energy storage, not production. – Luaan Jun 13 '19 at 7:35

You exclude black holes, but Hawking radiation is guaranteed to eventually radiate 100% of the mass energy you throw in as black body radiation. The temperature of the radiation is inversely proportional to black hole size. But if you could get your hands on a very small black hole (which would probably not look black at all), you could theoretically throw anything you don't want in and harvest the radiation.

One problem with this black-hole power plant is that as the size dwarves, the power output approaches infinity. That means that you MUST feed it, or evacuate it.

• The last sentence lacks a physical justification. The energy output per unit of time may go to infinity, but the life expectancy drops to zero. You can't handwave either away. You obviously have a clear upper bound, power integrated over time has to be mc^2. – MSalters Jun 11 '19 at 13:20
• @MSalters The general consensus is that the black hole does explode with gamma ray burst. Calculating it's destructive power sounds like an interesting excercise, I'll look into that. – Tomáš Zato - Reinstate Monica Jun 11 '19 at 13:45
• @MSalters Wikipedia says: "a 1-second-life black hole has a mass of 2.28×105 kg, equivalent to an energy of 2.05×1022 J that could be released by 5×106 megatons of TNT". I doubt that any power plant could be build that would not be destroyed by the equivalent of ten Tzar-Bombs at once... (It doesn't matter that the energy is released over the course of one second, the power plant does not stand the ghost of a chance to deal with so much energy in such a short time.) – cmaster - reinstate monica Jun 11 '19 at 18:48
• @cmaster: True, but what sort of powerplant is running with a 228 ton black hole ?! To keep the thing stable, you'd be feeding that 228 tons of matter per second, to produce 20 Zetawatt of power. That's about a million times the total energy consumption of the whole earth. – MSalters Jun 11 '19 at 22:20
• @MSalters Exactly as Loren Pechtel said. To make things worse, small BHs are tiny. As in "smaller than a proton". And this small bugger is putting out such tremendous radiation. Now try to imagine what would happen if you directed a beam of protons at it. They would simply be blown away, making it virtually impossible to feed the thing. If you want to stand any chance of being able to feed a BH, it must be a lot bigger, a lot heavier, a lot dimmer, so that you can actually feed it. If you fail to feed it and it becomes too small, you better get a planet between yourself and the BH, quick. – cmaster - reinstate monica Jun 12 '19 at 15:48

You exclude black holes, particularly the Penrose process for extracting the rotational energy of a spinning black hole. Forgive me for answering with black holes anyway. Penrose describes three methods in his classic review article "Gravitational collapse" (1969). These are completely impractical by the standards of human technology, but fun, and informative about physics concepts :)

1. Take pairs of black holes in space, let them spiral them around one another until they merge, and harvest the energy of the emitted gravitational waves. Form the new black holes into pairs and repeat the process. Repeat this enough and it approaches 100% efficiency of mass-energy conversion. This proposal is credited to Misner.

2. Slowly lower an object on a rope towards a black hole. Use the force to turn a turbine or something. Think of the energy as released from gravitational potential (see Buzz's answer). Release the object at the horizon. This has up to 100% efficiency. Penrose claims doing this with a rotating black hole, one can release >100%, but without doing the calculations I am skeptical.

3. The "Penrose process".

I have personally researched proposal number 2. Note Gibbons (1972) was the first to analyse the tension in the rope, although there is an error as pointed out by Unruh & Wald (1982) and Redmount (1984). We assume the rope is ridiculously strong. I have generalised from a quasi-static case to a moving rope in any static spherically symmetric spacetime, see MacLaurin 2019, "Cosmic cable", forthcoming hopefully in the proceedings of the 2018 Marcel Grossmann conference.

• You could sell #2 as the plot for a potential James Bond film - "you will be lowered very slowly, Mr Bond, on this ridiculously strong rope". – Dawood ibn Kareem Jun 12 '19 at 4:48

Friction in the accretion disk that forms a quasar, releases an enormous amount of energy, converting anything up to a third (~ 30%) of mass to.energy.

While this is powered by gravitational potential energy (massive black hole at centre), the energy is not actually released as matter meets antimatter, or at the event horizon as matter passes into the BH, or by Hawkings radiation, but by ordinary - and immense - friction.

So potentially, an accretion disk round a neutron star, or other dense object, could have similar effects. NS would be the most obvious non BH candidate....

• The accretion disk of a neutron star can liberate around 10% of the mass of what you throw in as energy; that's an order of magnitude more than any fusion or fission will do (~1%), and it works with any (EM) matter, unlike fusion/fission. But really, there's little reason not to use black holes the same way - the engineering probably isn't significantly more complicated, and you get up to 40% of the mass. As a bonus, since black holes are rotating and charged, you can also extract the rotational energy of the black hole, for another 20% or so. Nothing else quite compares to this efficiency :) – Luaan Jun 13 '19 at 7:41
• The OP specifically asks about ways that "don't involve BH", though. We can't go that far. NS is the next best option. – Stilez Jun 13 '19 at 12:05
• Yeah, but the reason he excludes black holes is "as I understand, you can only extract a finite amount of energy by reducing their spin, so they are not viable for energy production on a cosmological scale.", which isn't true :P – Luaan Jun 14 '19 at 7:03
• Okay, true, that. – Stilez Jun 14 '19 at 14:33

We don't know any better ways today, but we don't know everything.

The problem is that, as far as we know, the total baryon number is conserved. This puts strict limits on what reactions are possible.

If you look at the linked page in the section "Conservation" you will see a couple of theoretical ways this conservation law might be breakable. Obviously, we don't know how to do that, yet, but who knows what the future will bring?