Very recently, the "Pacing the Frontier" petition was published. I want to focus on the comment from Alex Zhao, researcher at OpenAI:
My opinion is that while coordination between American labs is feasible and could potentially be straightforward, the much larger and more significant threat is from a geopolitical arms race with China. Much as the Manhattan Project thought they might ignite all of the oxygen in the atmosphere but chose to run a test detonation anyways, I’m afraid that due to future geopolitical competition, actors will take terribly excessive safety risks in the name of this international arms race. As a result there could be catastrophic side effects from deployment without due safeguards, potentially resulting in the destruction of key infrastructure or the general disempowerment of humanity.
I'm not qualified to speak on the contemporary concerns of restrictions on the development of artificial intelligence. In the course of writing this article FelonyBench has been created and updated at least 7 times. But let's discuss the antecedent of the analogy.
There are a few storypoints Zhao depends on to make his historical analogue:
Manhattan Project scientists were made aware of the possibility that the detonation of an atomic weapon might trigger the ignition of the entire troposphere, and possibly higher layers of atmosphere, killing all life on the surface of the planet. We might call this an alarm bell raised internally at Los Alamos.
Oppenheimer tells Groves that "the chances are near zero" (i.e. cannot say it will not happen).
The Manhattan Project conducts their atomic test, unsure of whether Everyone Will Die. Everybody Dies™ does not occur, so they get away with it.
Only the first point is undoubtedly true, the second is at best a dramatization, and the third is entirely false. Christopher Nolan generally does the world no favors by continually promulgating movies not true to their literary or real-world inspirations, cf.The Odyssey (2026). But in this case, Nolan got it right; in the film, and in real history, Edward Teller's theory of atmospheric ignition dies on the blackboard at Los Alamos. When they publish their findings in 1946, Teller himself is an author.
the actual science
In a nuclear reaction, there are reactants and products, each some entity of some type with some energy. We particularly discuss nuclear fission.
The input to the reaction is always a neutron denoted and, in the case of the Trinity test, one atom of plutonium-239 denoted. Because quantum mechanical phenomena are involved, the reaction is not the same every time. But fission is the most likely outcome of the collision[1]; the atom splits in one of many ways into two or more nuclei, some number of neutrons, and spare change in the form of excitation and other (photon, neutrino, etc.) particles. You are likely familiar with the idea that these neutrons may initiate further fission reactions. In a fission reaction, momentum and charge are conserved, but kinetic energy is not. A phenomenon occurs which is not explainable by simple mechanics; the sum of kinetic energies of the products is larger than the kinetic energies of the reactants. Simultaneously, the products are lighter than the reactants. We can easily recall which famous equation perfectly predicts the rate at which mass is exchanged for energy.[2] This energy is measured in electron-volts, with the usual SI prefixes (kiloelectron-volt), , and so on.
The nuclear physics picture of fission is quite complicated. The takeaway is that fission releases energy which is carried on small particles with high kinetic energies. In a fission bomb many of these particles are released rapidly in a small space.
what was teller worried about?
The aforementioned high-energy particles are not propagating into empty space, but into the atmosphere, which contains many gas molecules. Particles proceeding from fission will collide with air particles and these will in turn collide with slower-moving air particles. Such an increase in median kinetic energy of a collection of particles is the phenomenon we call heat, which is measured by temperature. Hot air exerts more pressure by the gas laws, so it propagates upwards and outwards. This creates the famous mushroom-shaped cloud. The air is extremely hot, but, to reiterate, it doesn't burn! So "fireball" is a bit of a misnomer.
Teller was concerned that this very hot air might allow some troubling downstream phenomena. Generally, the fusion of nuclei is generally restricted by two factors. First, nuclei in the wild are surrounded by electrons, which repel each other due to both having negative charge. This is often used by intelligent but smarmy schoolchildren to say that nothing ever touches anything else. Second, nuclei themselves repel each other because they contain protons which repel one another. But, if the nuclei have enough energy to shed their electrons (because they are hot enough to become plasma) and collide despite electrostatic repulsion, they can fuse.
in favor of doomsday scenario
Los Alamos sought to investigate what they saw as the possibility "most to be feared", which was the fusion of nitrogen nuclei in the air. They reasoned that, from a nuclear physics perspective, the remaining significant fractions of the atmosphere are oxygen, carbon, and noble gases, all "much more stable than nitrogen". In context, stability denotes nuclear stability, where the nuclei store less energy available to be released by some kind of reaction[3]. Of concern are a series of possible outcomes of the fusion . The one that might release the most energy is the fusion to releasing . But they call this reaction "certainly infrequent... as reactions of this type always are" compared to the result [4]. Despite other outcomes of this reaction possibly yielding less energy, they steelman the argument and suppose that every reaction will yield a net .
They also assume that every collision between nitrogen nuclei (with sufficient energy to overcome electrostatic repulsion) results in fusion, corresponding to a cross section of roughly 2 barns (given the size of nitrogen nuclei). They knew this was a pessimistic estimate, that "certainly the reaction cross section will be exaggerated". Indeed, with the benefit of hindsight and better equipment, we now know the cross section probably never exceeds even 1 barn[5].
They also account for low-energy nitrogen collisions, where the total energy is less than the amount necessary to overcome electrostatic repulsion. In this case, fusion is still possible due to quantum tunneling, where the probability increases with energy, by the Gamow factor.
Other possible reactions are ruled insufficiently frequent to be of concern:
Any reaction involving, because nitrogen-15 is only 0.38% of naturally-occurring nitrogen.
, too rare because the cross section of at attainable neutron energies was already known to be "on the order of an eighth of a barn", and the cases of a neutron and proton "should not differ much". This argument also applies to interactions with alpha particles[6].
The heavier products of nitrogen-14 fusion could react with nitrogen. But every large nucleus produced has more binding energy per nucleon than nitrogen, so these reactions produce less energy (more than an order of magnitude less than the feared ). Since these reactions would be less efficient at releasing energy while still consuming the supply of nitrogen, they are not of concern. The objective of the analysis is to discuss a worst-case scenario.
against doomsday scenario
Having studied the proposed mechanism by which energy might be produced, the report then examines the mechanisms by which energy might be lost, that is, converted to a form which cannot give kinetic energy to nitrogen atoms to encourage their fusion.
They first consider bremsstrahlung (German "braking radiation") of electrons. At thousands of Kelvin or higher, electrons do not meaningfully associate with nuclei and we air becomes a plasma. This applies here because a nuclear weapon can create temperatures in the millions of Kelvin. Under such conditions, nuclei, which are charged, will transfer energy to one another and to electrons as they attract and repel each other. As electrons then interact with various charged particles, their acceleration and the conservation of momentum necessitate the release of lost kinetic energy as photons, called bremsstrahlung. These photons have no rest mass, so they cannot impart kinetic energy to nitrogen nuclei and, as far as nuclear reactions are concerned, can be considered lost energy.
Electrons may also impart energy to photons via the inverse Compton effect, where an electron and photon interact and energy is transferred to the photon as they leave. Los Alamos presents this as an additional mechanism, but not the primary mechanism, by which catastrophe is prevented.
In order to start a supposed chain reaction, it is also necessary to heat an initial volume of air. Heating too small of a volume means that energy will be carried away by fast-moving particles and radiation, meaning the volume will not stay hot. Heating too large of a volume is simply impossible given the amount of energy released. It was supposed that heat would be carried primarily by the alpha particles from nitrogen-nitrogen fusion, for "no particle produced in air is more energetic than they". The alphas produced by fusion would have about[7], known to travel 57 meters on average in air[8]. Thus, a sphere of this radius would be required to ensure the kinetic energy held by the alpha particles is transferred, possibly indirectly, to nitrogen nuclei as to sustain the hypothetical chain reaction.
In fact, the entire volume of air must be hot enough. Nitrogen nuclei must not often encounter a much slower-moving particle before fusing, lest the former lose its energy. This requires that virtually every particle in the sphere have kinetic energy of around . This translates to billions of degrees Kelvin throughout the entire sphere. We previously established that only millions are reached, and this is the maximum at the center of the detonation, not over a considerably larger sphere of air. Considering how a great deal of available fission energy (99%) is released in unusable forms, the Trinity bomb was about 8 orders of magnitude sort of heating a sufficient volume of air.
The atmosphere also does not obey a model where heat first heats a central region to billions of Kelvin before the heat spreads elsewhere. A ball of hot air cannot stay in one place and will exert outward pressure, thus cooling by transfer of heat to surrounding air. So the yield of the bomb would need to be even higher.
resultant p(doom)
The crucial analysis of the paper is, for a relevant volume, determining whether the rate of energy loss from bremsstrahlung will be sufficient to offset the rate of energy gain from fusion.
The relevant rules governing bremsstrahlung are as follows.
The mean of electron energies is initially not known, but if this mean is known, the distribution of electron velocities around the mean can be known. We are at billions of Kelvin, so the non-relativistic model no longer holds. The relativistic model is instead applied. The rate of bremsstrahlung is known at each velocity, so it is integrated over the distribution of velocities. In summary, the mean of electron energies can be used to determine the rate of energy loss due to bremsstrahlung.
Nuclei preferentially undergo charged interactions with particles of similar mass (i.e. other nuclei and nucleons). Nuclei will also interact with electrons, albeit less frequently because electrons are about times lighter. So some energy will be transferred to electrons, at a rate given by the mean energies of the nuclei and of the electrons.
The mean of electron energies will take the value which balances the rate at which electrons gain energy from nuclei against the rate at which electrons emit bremsstrahlung.
So to find the rate of energy loss from bremsstrahlung:
We fix the mean energy of nuclei to some quantity. From this we can state the rate of energy transfer from nuclei to electrons, and equate this to the rate of bremsstrahlung. The mean energy of electrons appears on both sides, and remains unknown.
We can then solve for the mean electron energy and re-compute the rate of bremsstrahlung. Because bremsstrahlung in this context is principally an interaction between an electron and a nucleus, we express the result as some energy lost per unit time per nitrogen atom present.
The rate of energy gain from fusion is computed in this way:
The number of reactions must relate to the quantity of reactant available. The more nitrogen is available, the more likely our one nucleus can fuse with another.
We understand that not every pair of nitrogen nuclei will interact with one another, let alone fuse with one another. We again fix the average energy of nuclei, and from this derive the distribution of nitrogen velocities. The Gamow factor is a function of the velocities of the two nitrogen nuclei involved in the reaction. We can integrate the Gamow factor formula over the distribution of these two velocities to get a probability of fusion of two nitrogen nuclei. This too is a pessimistic estimate (i.e. overestimating the rate of fusion) because the cross section for fusion is less than assumed.
By multiplying the quantity of available reactant by the probability of fusion, we attain an expected number of fusion events. We then multiply by the previously assumed . This is also pessimistic, because this one of multiple possible, reasonably likely paths for fusion. This quantity is also expressed in energy per unit time per nitrogen atom.
In any volume of air considered, at any average energy of nuclei, the rate of energy loss from bremsstrahlung alone would never be less than 1.6 times the rate of energy gained.
While 1.6 is indeed quite a close call, it was estimated that the inverse Compton effect could add up to 340% to this margin, depending on the average energy. An alternate scenario driven by the reaction is also proposed. Because this produces stable nuclei only, and no alpha particles, the sphere of air under examination may have a radius of only 7 meters[9].
However, this reaction produces less energy than the magnesium[10]-producing one, so the safety margin is even greater.
In essence, the argument of the paper is:
Energy loss from bremsstrahlung is, at lower energies, thousands of times faster than energy gain from fusion.
At high energies of , the rate of bremsstrahlung is only 60% greater than the rate of energy gain. However, it is impossible by several orders of magnitude of energy to sustain this temperature in a sufficiently sized volume of air. Failure to heat a large enough volume of air results in heat losses due to alpha particles escaping without transferring away their energy.
Hot air expands, so the temperature is even harder to maintain, if achieved.
The inverse Compton effect makes energy loss even faster.
Nitrogen fusion is certainly less likely than assumed.
Nitrogen fusion does not always take the most exothermic path.
Specifically, if it resulted entirely in the production of oxygen and carbon, it would require a smaller sphere to be heated, but it would produce even less energy and the reaction, if started, would succumb even sooner to the aforementioned mechanisms of energy loss.
So, perhaps, a more accurate telling of this story would be:
Edward Teller raises a doom scenario.
The team works on computing p(doom). The circumstances here are disputed, including the timeframe, It is quoted in an interview with Arthur Compton (on the Manhattan Project, and for which Compton scattering is named) that their acceptable p(doom) was , but there are reasons to doubt Compton's account[11].
p(doom) is found to be zero with reasonable certainty, and work continues.
The Trinity bomb test predictably does not trigger the fusion of any appreciable fraction of the atmosphere's nitrogen inventory, equivalent to tons of TNT[12].
what does this mean for AI?
Clearly all powerful technology has the capacity to be used toward various ends. It is reasonable, as Zhao has done, to consider nuclear energy, being one such technology, as a historical analogue to AI:
[W]hen our ancestors sharpened flint stones to make knives, they used them both to cut hides for clothing and to kill each other. The same can be said of other more advanced technologies, such as the energy produced by the fusion of atoms... which could be used to produce clean, renewable energy or to reduce our planet to a pile of ashes... [N]ow that human beings have fashioned complex tools they will see their lives shaped by them all the more.
Others are certainly more informed and more qualified than me to draw parallels, but here are some.
X is a versatile technology
While the supposed recklessness of frontier labs clearly doesn't have a parallel in the proposed nitrogen fusion doomsday scenario, let's examine some comparisons nonetheless.
The laws of physics are, of course, not naturally aligned, but nuclear physics has been used to make clean, versatile, and nearly emissionless power. It has revolutionized medical diagnostics and therapies. It has also been used to kill hundreds of thousands, and assassinate defectors. Nuclear safety incidents, principally at Chernobyl and Fukushima, leave 2,000 square miles of Earth uninhabitable today.
Knowledge of nuclear physics, particularly weapon development, is seen as both offensively and defensively relevant in potentially armed conflict between major world powers. Major actors take steps to secure their own supply and attempt espionage to steal scientific knowledge and learn the extent of the others' degrees of development and stockpiling.
developers of X are uncertain about doom scenarios
The Los Alamos science team[13] not only erred, but veered on the side of caution on their analysis, and we should too:
Because of the uncertainties in the knowledge of these processes, the policy should be adopted of exaggerating the dangers at any point which appears at all questionable.
If we distill their report down to its more emotionally charged statements, the mood seems mixed. There is good news in the abstract (excerpts abridged):
whatever the temperature[,] no self-propagating chain of nuclear reactions is likely to be started[,] even with rather extravagant assumptions
[on the close call of 1.6x]: It is impossible to reach such temperatures even if bombs greater than 1000 cubic meters [of fissile material] are employed... a chain reaction in air [is] impossible
To end their report, they first show that even if nitrogen fusion began, it would die out due to unsustainable rates of energy loss as the reaction propagated. Then, they say the following. Perhaps their fears are not entirely quieted:
There remains the distant possibility that some other less simple mode of burning may maintain itself in the atmosphere.
Even if the reaction is stopped within a sphere of a few hundred meters radius, the resultant earth-shock and the radioactive contamination of the atmosphere might become catastrophic on a world-wide scale.
One may conclude that the arguments of this paper make it unreasonable to expect that the reaction could propagate. An unlimited propagation is even less likely. However, the complexity of the argument and absence of satisfactory experimental foundations makes further work on the subject highly desirable.
sources and reading
There is an urge in popular depictions of this episode to gloss over the physics, especially the math. I have tried to avoid this. The best way to get more detailed is probably to find a physics textbook.
Upload this file into JANIS to see the relative probabilities. The chart plots barns, roughly a unit of probability, given the kinetic energy of the incoming neutron. Note that elastic scattering (i.e. nothing happens except momentum transfer according to classical mechanics) is negligibly unlikely and the cross section for fission dominates. The probabilities of various inelastic scatterings, resulting in the excitation of the nucleus and/or expulsion of nucleons, are not included, because there are too many of them and I don't get paid enough to select them all one-by-one. Note that no proton or neutron is annihilated, which would release about .
About is released on average, about 90% of which is not caught up in nucleus excitation or stored as decay potential and is therefore usable immediately to continue fission.
Nuclei do not have the same mass as their constituent protons and neutrons when they are separated (at arbitrarily great distances apart). This difference between sum of parts and actual nuclear mass is called the "mass defect". Its negation is the "mass excess". These values are usually no more than a tenth of a dalton. In stable nuclei, the mass defect is positive, meaning the nucleus is lighter than its parts measured separately. Mass defect and binding energy by the famous equation, so much so that the mass defect is often expressed not in dalton or amu but in unit , so the binding energy takes on the exact same numerical value in units . A greater mass defect means more energy is liberated and less is stored as mass upon the hypothetical formation of the nucleus from its constituent parts. This means less energy can be gained by some kind of reaction involving this nucleus, because more energy must be spent to dissolve this union of nucleons.
Alpha particles are identical to helium nuclei, so they could be written that way, but alphas are a very common part of nuclear reactions. They are usually written simply as because they always have two protons and two neutrons. Here they are written with Z and A numbers to assist the reader in balancing these quantities in the reaction.
Switkowski, et al. "Measurement of fusion cross sections for 14N + 14N and 12C + 16O at low energies", *Nuclear Physics A*, Volume 274, Issues 1–2, 1976, Pages 202-222, https://doi.org/10.1016/0375-9474(76)90237-2. 1 barn isn't much; the cross section of is in the thousands of barns at typical energies.
No nitrogen-nitrogen fusion reaction produces an alpha, proton, or neutron while also releasing more than , and some of that energy is carried by another product such as a photon or the heavier products. Today, we also have more cross section data than they did: see this on JANIS.
Given the potential fusion reactions and their limited cross section data, they knew enough to conclude as follows: a high-energy alpha, proton, or neutron cannot be produced, and nitrogen does not react with slow-moving/low-energy alphas, protons, or neutrons at a significant probability. But in Christopher Nolan's depiction of Teller's concerns, the equation is depicted as the beginning of an exponentially self-sustaining cycle, against which there are supposedly no restraining factors whatsoever. From the science we see that this doesn't make much sense.
You can easily work out this computation yourself using primary school physics. WLOG, assume the nitrogens had zero momentum. By conservation of momentum, the magnesium and alpha must have zero total momentum (so one momentum is the negative of the other). Their summmed kinetic energies must be . The mass of a magnesium-24 nucleus and an alpha particle are available online. Solving this system confirms that the alpha will have about .
More strongly charged particles have shorter mean free paths because they feel electrostatic attraction and repulsion more strongly and at greater distance. In this case, the only available vehicles of energy transfer would be oxygen and carbon nuclei, which are, respectively, 3 and 4 times more strongly charged than alpha particles.
The reactions proposed in the Los Alamos report suggest that (stable) silicon, aluminum, magnesium, or carbon could be produced. In the spirit of the original quote from Alex Zhao, I computed the energy gained from chemical combustion and oxidation of these elements, even though this would not happen in plasma. As with most chemical, non-nuclear reactions, this is on the order of one electron-volt per atom oxidized (everything we have examined has freed millions of electron-volts from one or two particles). So there really is no sense at all in which anything is "igniting".
Compton claimed "calculations proved the figure slightly less" than the acceptable level, which we see is clearly untrue from the math; the probability was zero. He also claimed that and fusion were of concern, even though this report, in a single phrase, dismisses this class of event as too rare due to reactant scarcity. Perhaps Compton's claims should be taken as apocryphal.
Assume there is of air. Air is mostly nitrogen, assume there is of that. Convert to grams, divide by molar mass (approximate as ), divide by to count reactions, multiply by , convert to joules, divide by to convert to tons of TNT-equivalent.
Very recently, the "Pacing the Frontier" petition was published. I want to focus on the comment from Alex Zhao, researcher at OpenAI:
I'm not qualified to speak on the contemporary concerns of restrictions on the development of artificial intelligence. In the course of writing this article FelonyBench has been created and updated at least 7 times. But let's discuss the antecedent of the analogy.
There are a few storypoints Zhao depends on to make his historical analogue:
Only the first point is undoubtedly true, the second is at best a dramatization, and the third is entirely false. Christopher Nolan generally does the world no favors by continually promulgating movies not true to their literary or real-world inspirations, cf. The Odyssey (2026). But in this case, Nolan got it right; in the film, and in real history, Edward Teller's theory of atmospheric ignition dies on the blackboard at Los Alamos. When they publish their findings in 1946, Teller himself is an author.
the actual science
In a nuclear reaction, there are reactants and products, each some entity of some type with some energy. We particularly discuss nuclear fission.
The input to the reaction is always a neutron denoted
The nuclear physics picture of fission is quite complicated. The takeaway is that fission releases energy which is carried on small particles with high kinetic energies. In a fission bomb many of these particles are released rapidly in a small space.
what was teller worried about?
The aforementioned high-energy particles are not propagating into empty space, but into the atmosphere, which contains many gas molecules. Particles proceeding from fission will collide with air particles and these will in turn collide with slower-moving air particles. Such an increase in median kinetic energy of a collection of particles is the phenomenon we call heat, which is measured by temperature. Hot air exerts more pressure by the gas laws, so it propagates upwards and outwards. This creates the famous mushroom-shaped cloud. The air is extremely hot, but, to reiterate, it doesn't burn! So "fireball" is a bit of a misnomer.
Teller was concerned that this very hot air might allow some troubling downstream phenomena. Generally, the fusion of nuclei is generally restricted by two factors. First, nuclei in the wild are surrounded by electrons, which repel each other due to both having negative charge. This is often used by intelligent but smarmy schoolchildren to say that nothing ever touches anything else. Second, nuclei themselves repel each other because they contain protons which repel one another. But, if the nuclei have enough energy to shed their electrons (because they are hot enough to become plasma) and collide despite electrostatic repulsion, they can fuse.
in favor of doomsday scenario
Los Alamos sought to investigate what they saw as the possibility "most to be feared", which was the fusion of nitrogen nuclei in the air. They reasoned that, from a nuclear physics perspective, the remaining significant fractions of the atmosphere are oxygen, carbon, and noble gases, all "much more stable than nitrogen". In context, stability denotes nuclear stability, where the nuclei store less energy available to be released by some kind of reaction[3]. Of concern are a series of possible outcomes of the fusion
They also assume that every collision between nitrogen nuclei (with sufficient energy to overcome electrostatic repulsion) results in fusion, corresponding to a cross section of roughly 2 barns (given the size of nitrogen nuclei). They knew this was a pessimistic estimate, that "certainly the reaction cross section will be exaggerated". Indeed, with the benefit of hindsight and better equipment, we now know the cross section probably never exceeds even 1 barn[5].
They also account for low-energy nitrogen collisions, where the total energy is less than the amount necessary to overcome electrostatic repulsion. In this case, fusion is still possible due to quantum tunneling, where the probability increases with energy, by the Gamow factor.
Other possible reactions are ruled insufficiently frequent to be of concern:
against doomsday scenario
Having studied the proposed mechanism by which energy might be produced, the report then examines the mechanisms by which energy might be lost, that is, converted to a form which cannot give kinetic energy to nitrogen atoms to encourage their fusion.
They first consider bremsstrahlung (German "braking radiation") of electrons. At thousands of Kelvin or higher, electrons do not meaningfully associate with nuclei and we air becomes a plasma. This applies here because a nuclear weapon can create temperatures in the millions of Kelvin. Under such conditions, nuclei, which are charged, will transfer energy to one another and to electrons as they attract and repel each other. As electrons then interact with various charged particles, their acceleration and the conservation of momentum necessitate the release of lost kinetic energy as photons, called bremsstrahlung. These photons have no rest mass, so they cannot impart kinetic energy to nitrogen nuclei and, as far as nuclear reactions are concerned, can be considered lost energy.
Electrons may also impart energy to photons via the inverse Compton effect, where an electron and photon interact and energy is transferred to the photon as they leave. Los Alamos presents this as an additional mechanism, but not the primary mechanism, by which catastrophe is prevented.
In order to start a supposed chain reaction, it is also necessary to heat an initial volume of air. Heating too small of a volume means that energy will be carried away by fast-moving particles and radiation, meaning the volume will not stay hot. Heating too large of a volume is simply impossible given the amount of energy released. It was supposed that heat would be carried primarily by the alpha particles from nitrogen-nitrogen fusion, for "no particle produced in air is more energetic than they". The alphas produced by fusion would have about[7]
In fact, the entire volume of air must be hot enough. Nitrogen nuclei must not often encounter a much slower-moving particle before fusing, lest the former lose its energy. This requires that virtually every particle in the sphere have kinetic energy of around
The atmosphere also does not obey a model where heat first heats a central region to billions of Kelvin before the heat spreads elsewhere. A ball of hot air cannot stay in one place and will exert outward pressure, thus cooling by transfer of heat to surrounding air. So the yield of the bomb would need to be even higher.
resultant p(doom)
The crucial analysis of the paper is, for a relevant volume, determining whether the rate of energy loss from bremsstrahlung will be sufficient to offset the rate of energy gain from fusion.
The relevant rules governing bremsstrahlung are as follows.
So to find the rate of energy loss from bremsstrahlung:
The rate of energy gain from fusion is computed in this way:
In any volume of air considered, at any average energy of nuclei, the rate of energy loss from bremsstrahlung alone would never be less than 1.6 times the rate of energy gained.
While 1.6 is indeed quite a close call, it was estimated that the inverse Compton effect could add up to 340% to this margin, depending on the average energy. An alternate scenario driven by the reaction
However, this reaction produces less energy than the magnesium[10]-producing one, so the safety margin is even greater.
In essence, the argument of the paper is:
So, perhaps, a more accurate telling of this story would be:
what does this mean for AI?
Clearly all powerful technology has the capacity to be used toward various ends. It is reasonable, as Zhao has done, to consider nuclear energy, being one such technology, as a historical analogue to AI:
Others are certainly more informed and more qualified than me to draw parallels, but here are some.
X is a versatile technology
While the supposed recklessness of frontier labs clearly doesn't have a parallel in the proposed nitrogen fusion doomsday scenario, let's examine some comparisons nonetheless.
The laws of physics are, of course, not naturally aligned, but nuclear physics has been used to make clean, versatile, and nearly emissionless power. It has revolutionized medical diagnostics and therapies. It has also been used to kill hundreds of thousands, and assassinate defectors. Nuclear safety incidents, principally at Chernobyl and Fukushima, leave 2,000 square miles of Earth uninhabitable today.
Knowledge of nuclear physics, particularly weapon development, is seen as both offensively and defensively relevant in potentially armed conflict between major world powers. Major actors take steps to secure their own supply and attempt espionage to steal scientific knowledge and learn the extent of the others' degrees of development and stockpiling.
developers of X are uncertain about doom scenarios
The Los Alamos science team[13] not only erred, but veered on the side of caution on their analysis, and we should too:
If we distill their report down to its more emotionally charged statements, the mood seems mixed. There is good news in the abstract (excerpts abridged):
To end their report, they first show that even if nitrogen fusion began, it would die out due to unsustainable rates of energy loss as the reaction propagated. Then, they say the following. Perhaps their fears are not entirely quieted:
sources and reading
There is an urge in popular depictions of this episode to gloss over the physics, especially the math. I have tried to avoid this. The best way to get more detailed is probably to find a physics textbook.
Upload this file into JANIS to see the relative probabilities. The chart plots barns, roughly a unit of probability, given the kinetic energy of the incoming neutron. Note that elastic scattering (i.e. nothing happens except momentum transfer according to classical mechanics) is negligibly unlikely and the cross section for fission dominates. The probabilities of various inelastic scatterings, resulting in the excitation of the nucleus and/or expulsion of nucleons, are not included, because there are too many of them and I don't get paid enough to select them all one-by-one. Note that no proton or neutron is annihilated, which would release about
About
Nuclei do not have the same mass as their constituent protons and neutrons when they are separated (at arbitrarily great distances apart). This difference between sum of parts and actual nuclear mass is called the "mass defect". Its negation is the "mass excess". These values are usually no more than a tenth of a dalton. In stable nuclei, the mass defect is positive, meaning the nucleus is lighter than its parts measured separately. Mass defect and binding energy by the famous equation, so much so that the mass defect is often expressed not in dalton or amu but in unit
Alpha particles are identical to helium nuclei, so they could be written that way, but alphas are a very common part of nuclear reactions. They are usually written simply as
Switkowski, et al. "Measurement of fusion cross sections for 14N + 14N and 12C + 16O at low energies", *Nuclear Physics A*, Volume 274, Issues 1–2, 1976, Pages 202-222, https://doi.org/10.1016/0375-9474(76)90237-2. 1 barn isn't much; the cross section of
No nitrogen-nitrogen fusion reaction produces an alpha, proton, or neutron while also releasing more than
Given the potential fusion reactions and their limited cross section data, they knew enough to conclude as follows: a high-energy alpha, proton, or neutron cannot be produced, and nitrogen does not react with slow-moving/low-energy alphas, protons, or neutrons at a significant probability. But in Christopher Nolan's depiction of Teller's concerns, the equation
You can easily work out this computation yourself using primary school physics. WLOG, assume the nitrogens had zero momentum. By conservation of momentum, the magnesium and alpha must have zero total momentum (so one momentum is the negative of the other). Their summmed kinetic energies must be
This is called the "mean free path".
More strongly charged particles have shorter mean free paths because they feel electrostatic attraction and repulsion more strongly and at greater distance. In this case, the only available vehicles of energy transfer would be oxygen and carbon nuclei, which are, respectively, 3 and 4 times more strongly charged than alpha particles.
The reactions proposed in the Los Alamos report suggest that (stable) silicon, aluminum, magnesium, or carbon could be produced. In the spirit of the original quote from Alex Zhao, I computed the energy gained from chemical combustion and oxidation of these elements, even though this would not happen in plasma. As with most chemical, non-nuclear reactions, this is on the order of one electron-volt per atom oxidized (everything we have examined has freed millions of electron-volts from one or two particles). So there really is no sense at all in which anything is "igniting".
Compton claimed "calculations proved the figure slightly less" than the acceptable level, which we see is clearly untrue from the math; the probability was zero. He also claimed that
Assume there is
Do you know who ate all the donuts?