Ed claps, touches the ground, and one second later there’s a wall. Every time I see it, the same dumb question pops up: how much would that actually cost? Not “is it magic”, but how many joules, how many seconds and what machine you’d need.

I ran the numbers with real physics, one source at a time, and ran into something I didn’t expect: physics almost never objects to the what. Walls, diamond, steel, even gold: all of that exists and gets made. The problem is the how long. Doing it in one second takes a power and a heat that would destroy both the object and the alchemist. And where alchemy fails in the story, it fails in physics too.

What the story says (and what it doesn’t)

Before bringing in physics, we need to pin down what the story actually claims. I only use Hiromu Arakawa’s manga and Fullmetal Alchemist: Brotherhood; the 2003 anime changes important rules and I keep it separate.

  • Three stages: comprehension, deconstruction and reconstruction of matter. That’s the definition Brotherhood opens with.
  • The Law of Equivalent Exchange, split in two: conservation of mass (as much mass comes out as goes in) and the Law of Natural Providence (the product has the same nature as the material: you can’t get stone out of water).
  • Transmutation circle: a conduit that focuses the flow of energy. People who’ve seen the Gate use their own body as the circle and clap.
  • Taboos: making gold (ch. 3) and human transmutation, which never works.
  • Energy: the official version says it comes from tectonic movement.

What the story never says is how each stage works: what force breaks the bonds, how the atoms get placed or how much energy it takes. Arakawa warns in volume 1 that her alchemy has nothing to do with the real thing. That gap is exactly what I want to fill.

Equivalent exchange is Lavoisier without Carnot

Lost? Lesson: Can you make something from nothing? Conservation, no fear

The story’s law looks a lot like real laws, but it only covers part of them:

Law in FMAPhysics equivalentDoes it fit?
Conservation of massConservation of atoms in chemistry (Lavoisier, 1789)Yes, almost word for word
Natural ProvidenceConservation of elements; more generally, of charge and baryon numberYes, if “nature” means elements
(missing)Conservation of energyCovered up with tectonic energy
(missing)Second law: ordering matter forces you to dump heatNever mentioned

It’s a mass balance, not an energy or entropy balance. And thank goodness: if an alchemist could create mass from nothing, they’d have to pay E = mc². One gram is 9×10¹³ joules, about 21.5 kilotons of TNT. An alchemist without equivalent exchange would be a walking nuclear weapon. The law isn’t a plot ornament: it’s what keeps that world in one piece.

What recomposition is (and what it costs)

Lost? Lesson: Why doesn't diamond turn into graphite?

Of the three stages, the first two happen inside the circle and you can’t see them: comprehension (knowing what you have and what you want) and deconstruction (breaking the material down). The third, recomposition, is the flash and the rising wall. It’s the one you see on screen, and the one with the most explaining to do.

If you ask that third phase to follow physics, recomposition has three costs, and the story only shows the first:

  1. Energy to form the new structure. Sometimes it’s negative: forming chemical bonds releases energy.
  2. Information: knowing where each piece goes and applying it. That’s the circle’s job.
  3. Heat. Every irreversible placement step dissipates energy. The second law of thermodynamics doesn’t let you put matter in order for free: since Landauer (1961) we’ve known that even erasing one bit of information has a minimum cost in heat.
The bill for a recompositionA receipt with three lines. Energy to form the new structure: in the story the alchemist pays it. Information, knowing where each piece goes: the circle carries it. Heat, because every irreversible placement dissipates energy: in the story nobody pays it. At the bottom: what really limits you is power, energy divided by time.BILL · RECOMPOSITION2.Informationknow where each piece goesThe circle carries it3.Heatevery irreversible step leaksNobody pays itThe limit isn't the total:it's power = energy ÷ time
The three costs of recomposition. The story shows the first, hints at the second and never mentions the third.

Energy isn’t power

Lost? Lesson: Joules, watts or calories? Energy and power without fear

Lost? Lesson: How much is 7×10²⁷? Huge numbers without fear

This is the core of the post, and I’ll explain it with the most extreme case: assembling a human body atom by atom.

FigureValueSource
Atoms in 70 kg~7×10²⁷Freitas, Nanomedicine
Heat if each placement dissipates just 1 eV1.1×10⁹ JMy own calculation
Temperature rise if that heat can’t escape~4600 KMy own calculation, with the specific heat of tissue

One electronvolt per atom is a ridiculously small amount, but there are 7×10²⁷ atoms. Here’s that heat, depending on how long you take to release it:

Build timePowerWhat it means
1 s, as in the story1.1 GWA whole nuclear reactor inside a body: it vaporises before it’s finished
1 hour312 kWOver 3000 times your metabolism
9 months48 WHalf your metabolism (2000 kcal a day is about 97 W)

The energy is the same in all three rows. What changes is the power: energy divided by time. And here’s the beautiful part: biology already solved the recomposition of a human being, and it solved it by taking nine months.

Try it yourself: pick what to build and how long to give it.

Power needed depending on build timeLog-scale chart: time from 1 second to 1 year across, power from 1 watt to 10 gigawatts up. Each object is a falling line: the more time, the less power. A human body needs 1.1 GW if built in 1 second, 312 kW in 1 hour and 48 W in 9 months, close to a human metabolism (97 W). Top reference line: a typical nuclear reactor, 1 GW.1 s1 min1 h1 day1 month1 year1 W1 kW1 MW1 GWBuild time (log scale)PowerA nuclear reactor, ~1 GWYour metabolism, ~97 W1.1 GW312 kW48 W
What you build
In 1 s: 1.1 GW

That's 1.1 nuclear reactors running at once, packed into a single object.

If someone offered me alchemist powers, I’d ask for a good cooling system first. Creating isn’t the problem; cooling down is.

Four levels of creation

Not everything costs the same. The story’s creations can be ranked by how much has to be broken and how much has to be known to rebuild them, and all three costs grow with the level:

The four levels of recompositionA four-step staircase climbing from left to right. Level 1, shape: nothing breaks, it moves; in the story, walls and stone spears; today, volumetric printing in 30 to 120 seconds. Level 2, material: chemical bonds break; Greed's diamond or steel; today, CVD diamond at 100 microns per hour. Level 3, element: nuclei break; the Youswell gold; today, picograms at the LHC. Level 4, life: what's missing is information; human transmutation; today, only biology, in nine months.Each step: more to break and more to know1 · ShapeWhat breaksNothing: it movesIn the storyWalls, stone spearsTodayVolumetric: 30–120 s2 · MaterialWhat breaksChemical bondsIn the storyDiamond, steelTodayCVD diamond: 100 µm/h3 · ElementWhat breaksNucleiIn the storyThe Youswell goldTodayLHC: picograms4 · LifeWhat breaksMissing informationIn the storyHuman transmutationTodayBiology: 9 months
Levels 1 to 3 are a matter of energy and power. At level 4, what's missing is information.

Level 1: shaping

Lost? Lesson: Joules, watts or calories? Energy and power without fear

It’s the most common creation in the story and the easiest to defend. The material doesn’t change: it gets moved, compacted and welded together. That takes three steps: bring the earth into the new shape, compact it to squeeze out the gaps, and join the grains so it’s solid. Joining them means sintering (heating until the grains weld together) or cementing.

With Ed’s wall, made of granite and 3 × 2 × 0.3 m:

Ed's wall in cross-section, with what it costsCross-section of a 3 × 2 × 0.3 metre wall (4.8 tonnes). Outside, a 2 cm sintered ceramic skin that comes out hundreds of degrees hot; inside, compacted earth. On the right, the 1.8 cubic metre hole left in the ground, because the mass has to come from somewhere. Costs: lifting it one metre, 47 kJ; with a sintered skin, about 1 GJ; sintering all of it, 5.8 GJ; making it from nothing, 4.3×10²⁰ J.1.8 m³ holethe mass comes from hereCompacted earth3 × 2 × 0.3 m · 4.8 t2 cm ceramic skinComes out hundreds of degrees hotWhat it costsLift it 1 m47 kJWith a sintered skin1 GJSinter all of it5.8 GJMake it from nothing4.3×10²⁰ J
The skin is exaggerated so you can see it: it's 2 cm. The hole in the ground has the same volume as the wall.

Moving earth is cheap: lifting the wall one metre costs 47 kJ, a small car engine’s power for one second. The expensive part is turning earth into rock. Sintering all of it takes 5.8 GJ, and in one second that’s 5.8 GW: several nuclear reactors for one wall. The realistic design is different: weld only a 2 cm skin and compact the inside. The cost drops to ~1 GJ, and the wall comes out steaming, hundreds of degrees hot.

The story almost never shows two details. The first is the hole: because mass is conserved, the wall comes from somewhere, and in front of it or under it there’s a 1.8 m³ hole. The second is that compacted earth isn’t granite: without sintering or cementing, it holds far less than it looks like it would.

The closest thing today

It isn’t regular 3D printing, which goes layer by layer. The closest thing to a transmutation circle is making the whole volume at once:

Three ways to make things: layer by layer, by volume, and with a circleThree panels. One: layer-by-layer 3D printing, a nozzle lays material from the bottom up and takes hours. Two: volumetric printing, light enters a spinning vial of resin from many angles and cures the whole object at once, in 30 to 120 seconds. Three: the transmutation circle read as a template, a flat drawing on the ground creates a three-dimensional field that forms the whole object; that part is fiction.ExistsLayer by layer3D printing: bottom totop, in hoursExistsAll at onceVolumetric: light frommany angles, 30–120 sFictionWith a circle2D template → 3D field→ whole object (fiction)
The first two exist. The third is the physical reading of the circle: a flat drawing that defines a 3D field.
  • Volumetric printing. It projects light from many angles onto a spinning resin, and the accumulated dose cures the whole object at once: centimetre-sized parts in 30–120 seconds, with 0.3 mm detail (Kelly et al., 2019). A later version gets under 30 seconds (Loterie et al., 2020).
  • Acoustic holograms. A 3D-printed plate shapes an ultrasound field that pushes particles, gels or cells into place, without touching them and in a single step (Melde et al., 2016 and 2023). It’s a flat pattern that, once powered, places matter in 3D. All it lacks is scale: it moves particles, not walls.
  • Solar sintering. ESA and DLR concentrated sunlight with 147 mirrors to melt simulated moon dust: a 20 × 10 × 3 cm brick in about 5 hours.

Verdict: possible with engineering, in minutes rather than one second, and with a wall that burns.

Level 2: changing the material

Lost? Lesson: What is a wall made of? Atoms and elements without fear

Lost? Lesson: Why doesn't diamond turn into graphite?

Here alchemy changes the chemistry: the same atoms, in another compound or another structure. The story has three cases that cover the three possible situations, and they’re easier to understand if you draw the energy along the reaction:

Three energy profiles behind FMA's chemistryThree energy charts along the reaction. One, Greed and Ed: diamond sits a little above graphite, separated by a barrier; turning into graphite is downhill (-2.9 kJ/mol), you only have to push it over the barrier. Two, the steel spear: going from iron oxide to iron is uphill, at least 4.9–7.4 MJ per kilo of iron. Three, Mustang: splitting water into hydrogen and oxygen climbs 285.83 kJ/mol and the flame gives back exactly the same; the balance is zero.Greed and EdEnergyDiamondGraphiteBarrier-2.9 kJ/molDownhillThe steel spearEnergyOxideIron+4.9–7.4 MJ/kgUphillyou have to payMustangEnergyWaterWaterH₂ + O₂±285.83 kJ/molBalance: zeroReaction path →
Qualitative shapes: only the labelled numbers are data. What matters is which way each curve goes.

Downhill: Greed and Ed. Greed hardens his skin by rearranging carbon into diamond, and Ed works out that it’s carbon and that its structure decides whether it’s diamond or graphite (ep. 13). At room temperature graphite is the stable one: going from diamond to graphite releases 2.9 kJ/mol. Diamond survives because there’s a barrier; in a vacuum it only turns into graphite at 1500–1800 °C. Ed gets the cheap part: pushing the carbon over the barrier so it falls on its own. Greed gets the expensive part: holding about 6 kg of carbon in a state that today is made at high pressure or atom by atom. Growing a 1 mm shield by vapour deposition would take about 10 hours.

Uphill: the steel spear. The iron in the ground is oxidised, and reducing it to metal costs at least 4.9–7.4 MJ per kilo of iron: 10–15 MJ for a 2 kg spear. A real blast furnace uses about 48 MJ for that spear. You also have to gather the iron: the crust is 3.9 % iron, so it takes about 51 kg of earth for every 2 kg of iron. The cost is in breaking the iron–oxygen bonds, not in ordering the atoms.

Up to come down: Mustang. In his fight with Lust (ch. 38; ep. 19), Mustang splits the water in the room into hydrogen and oxygen and lights it. Splitting water costs 285.83 kJ/mol, and the flame gives back exactly the same: the balance is zero. Mustang uses alchemy to charge a chemical battery with the room’s water and discharge it all at once. He doesn’t gain energy; he gains power, because the discharge lasts milliseconds.

Verdict: plausible if chemical assemblers working in massive parallel ever exist. Today only biology works that way.

Level 3: changing the element

Lost? Lesson: What is a wall made of? Atoms and elements without fear

In chapter 3 of the manga, Ed turns mine waste into gold bars to con a corrupt official, then turns them back into rocks (Brotherhood doesn’t adapt the scene). Changing an element means changing the number of protons in the nucleus. It’s possible, and it’s been done since 1919; what you can’t do is use chemistry for it. To see what it costs, you need the most important curve in nuclear physics:

Binding energy per nucleon: why gold is expensiveChart of binding energy per nucleon, in MeV, against mass number, from 0 to 240, with AME2020 data. The curve rises fast from hydrogen, peaks at iron and nickel (8.79 MeV) and slowly falls to uranium (7.57 MeV). Marked: carbon-12, oxygen-16, silicon-28, iron-56, gold-197 and lead-208. Going from lead to gold costs 77 MeV per atom, because 3 protons and 8 neutrons have to be torn off. Going from carbon to gold would release about 46 MeV, but the electric repulsion between nuclei stops it. Left of iron, fusion releases energy; right of it, fission does.0246804080120160200240Mass number (protons + neutrons)MeV per nucleonC-12O-16Si-28Fe-56Iron peak: the most tightly bound nucleiAu-197Pb-208Pb → Aucosts 77 MeV/atomC → Au would release ~46 MeV……but electric repulsion blocks itfusion releases energyfission releases energy
AME2020 data. The higher up, the more tightly bound the protons and neutrons in the nucleus are.

From lead, gold isn’t downhill: 3 protons and 8 neutrons have to be torn off, and that costs 77 MeV per atom. An ounce of gold is 1.2×10¹² J, about 0.28 kilotonnes of TNT.

The fun detail is that coal-mine waste contains carbon, and building gold out of carbon would release energy, about 46 MeV per atom. It doesn’t happen because nuclei repel each other electrically, and the repulsion grows with every proton. Not even stars make gold that way: they do it by capturing neutrons very fast, in events like the neutron-star merger observed in 2017.

What has actually been achieved: the ALICE experiment at the LHC saw about 89,000 gold nuclei form per second in lead collisions. Over a whole four-year run they added up to 2.9×10⁻¹¹ grams, and they break apart almost immediately. There’s a proposal, not yet peer reviewed, to produce gold in fusion reactors: about 2 tonnes a year per thermal gigawatt, in a reactor that doesn’t exist yet, and the gold would come out radioactive for about 14 years.

Verdict: possible, but in another energy league, and with radioactive waste the story never shows.

Level 4: creating life

The story’s most famous scene is the ingredient list for a human body, which according to Ed you could buy with a kid’s pocket money. Here it is next to the ICRP’s 70 kg “reference man”:

Ed’s ingredientAmountIn the reference body
Water35 L~42 L (60 % of the mass)
Carbon20 kg16 kg
Ammonia (nitrogen)4 L1.8 kg of nitrogen
Lime (calcium)1.5 kg1.0 kg of calcium
Phosphorus800 g780 g
Salt (sodium and chlorine)250 g100 g of sodium and 95 g of chlorine
Saltpetre (potassium)100 g140 g of potassium
Sulphur80 g140 g
Iron5 g4.2 g

The list is nearly right: the right elements in the right order of magnitude. That’s what makes it interesting, because it shows the ingredients aren’t the problem. The problem is order, information and time.

Nature has its own transmutation circle: the ribosome. It reads a template (messenger RNA) and assembles matter (amino acids) into a specific shape (a protein).

Three machines that read a template and buildA drawn table with three columns and three rows: template, machine and product. Transmutation circle, fiction: the chalk drawing is the template, the alchemist with their energy is the machine, and out comes a wall. Acoustic hologram, real since 2016: a plate with a relief is the template, an ultrasound emitter is the machine, and out come particles placed in the shape of an image. Ribosome, real in every cell: messenger RNA is the template, the ribosome is the machine, and out comes a folded protein, at 12–21 amino acids per second in trillions of cells at once.TemplateMachineProductCircleFictionChalk drawingAlchemist + energyA wallAcoustic hologramReal, 2016Plate with a reliefUltrasoundParticles in placeRibosomeReal, inside youMessenger RNARibosomeFolded protein
The same structure in all three: a template, a machine that reads it and a shaped product.

A bacterial ribosome chains 12–21 amino acids per second, and an animal one 4–5. Making the ~11 kg of protein in a body in one second would take about 3×10²⁴ ribosomes working at once. Biology spreads it over nine months, across trillions of cells, with the heat carried away by the mother’s blood. That’s why it comes out at ~48 W.

And even with all that, human transmutation would fail for three reasons:

  1. The recipe isn’t the person. With the list and a genome you could, in theory, build a human body. Not Ed and Al’s mother: that takes that person’s information (her neural connections, her memories), and that information was lost when she died.
  2. Building it in one second destroys it. That’s the heat table above.
  3. A body isn’t an object. It’s alive because it keeps up a constant flow of energy. Assembling the parts doesn’t start the metabolism, just as assembling an engine doesn’t switch it on.

The story fits all three: what the Elrics create isn’t their mother.

Verdict: impossible.

With Ed’s list I’d have money left over for another hat. What you can’t buy is whatever the list leaves out.

Where does the energy come from?

Lost? Lesson: Joules, watts or calories? Energy and power without fear

The official explanation is energy from tectonic movement. The real Earth has something similar: its internal heat leaks out of the surface at about 92 milliwatts per square meter (Davies and Davies, Solid Earth, 2010). A one-square-meter circle would need six days to gather what it takes to lift Ed’s wall, and about 2,000 years to sinter it. For one ounce of gold, 400,000 years.

So the official version can’t work. You need a store: energy collected over a long time and released all at once. And here’s the lovely part. The story’s reveal is that Amestris’s alchemists are unknowingly drawing on a Philosopher’s Stone hidden under the whole country, made from the souls of an entire city. The plot twist matches what physics demands: a giant battery under everyone’s feet. The story turns a physical limit into the moral engine of the plot.

The gap

Lost? Lesson: How much is 7×10²⁷? Huge numbers without fear

Putting the four levels together, this is the distance between the story and the best demonstrated technology. The fusion proposal is hatched because that reactor doesn’t exist:

How long reality takes to do what Ed does in a secondHorizontal bars on a logarithmic time scale, starting at 1 second, which is what the story takes. A small part by volumetric printing: 1 min. An ounce of gold with a proposed fusion reactor that doesn't exist: 8.2 min. A 1 mm diamond shield: 10 h. A human body, by pregnancy: 9 months. Ed's wall by solar sintering: 1.7 years. An ounce of gold at the LHC's rate: 4.3×10¹² years, hundreds of times the age of the universe.10⁰10³10⁶10⁹10¹²10¹⁵10¹⁸10²¹Time (log scale, seconds)1 yearAge of the universeThe story: ~1 sShape · small partvolumetric printing1 minElement · 1 oz of goldfusion reactor (proposal)8.2 minMaterial · diamond shieldCVD, 1 mm10 hLife · a bodypregnancy9 monthsShape · Ed's wallsolar sintering (ESA)1.7 yearsElement · 1 oz of goldLHC (ALICE)4.3×10¹² years
Each tick on the axis multiplies the time by a thousand. The story always takes one second.

Volumetric printing is just two orders of magnitude away from the story: it’s the closest thing to a transmutation circle that exists. At the other end, an ounce of gold at the LHC’s rate would take hundreds of times the age of the universe.

Three things people often get wrong

  • “It costs so many joules, so it’s impossible.” The total energy is usually manageable; what makes it impossible is dividing it by the one second the scene lasts. Always look at the power.
  • “Creating always costs energy.” Forming bonds releases heat, and that heat has to go somewhere too. From carbon to gold, even nuclear physics would come out ahead if it weren’t for electric repulsion.
  • “A nanobot places a million atoms per second.” That’s a theoretical projection by Drexler from 1992, not a measurement. What’s been demonstrated by 2026 is dozens of carbon atoms placed one by one at 4 K (−269 °C) in a vacuum. In 1990, IBM took about 22 hours to write its logo with 35 atoms.

The cheapest licence

Putting it all together, FMA’s alchemy can be described as programmable matter powered by an energy store. With that model, almost every rule in the story falls out on its own. That leaves three licences no known physics hands out for free:

  1. An energy store of nuclear density that discharges on demand. The story pays for it: the Stone costs souls.
  2. A field that can place matter at atomic scale throughout a volume. Today it exists at the micron scale (sound) and in resins (light).
  3. An almost unlimited heat sink. The story never mentions it, and it’s what would make the speed believable.

The verdict

LevelCan it be made?In one second?
ShapeYes: today, centimetre parts in seconds and bricks in hoursNo: it needs a gigawatt source and the wall comes out burning
MaterialYes: diamond in hours, steel in blast furnacesNo: tens of megawatts for each spear
ElementYes, with nuclear energy, in picogramsNo: kilotonnes of energy for each bar
LifeA body, in theory; that person, neverNo: a gigawatt of heat inside a body

If you keep one idea, make it this one: always separate what gets made (almost always chemically possible) from how long it takes (almost always impossible). The story gets the first right and allows itself the second.

And one more thing stays with me: Arakawa warns that her alchemy has nothing to do with the real thing, and then builds a system that respects conservation of mass and of elements, needs an energy store (and makes it the center of the plot) and fails exactly where physics says it should. For “not science”, it’s better physics than plenty of films that brag about being scientific.

Sources

Numbers without their own link are my own calculations from these sources.

How this post was made: from my physics notes, with help from Claude to organise and write them up. The numbers come from the sources above. The drawings are my own: no screenshots or official art from the series.