[Epistemic status: I am reasonably confident in my thoughts here; I spent a reasonable time thinking about them and asking other people about them. But obviously it’s really speculative. Expected background knowledge: You should be able to understand most of this if you paid some attention in high school science classes. Thanks to everyone who talked to me about this.]

Here’s a physics question I’ve been pondering recently. What’s the simplest set of laws of physics that are close enough to ours that they would support human life?

One candidate is nonrelativistic quantum mechanics. Nonrelativistic QM is a theory of physics which describes the quantum mechanical behavior of particles like electrons, without trying to be compatible with special relativity. It’s the physical theory used for almost all materials science and theoretical chemistry. Is it a good enough approximation to physics that I would survive if I were transported into a universe that obeyed its physics instead of our own universe’s?

Let me phrase the question more precisely. Let’s postulate that the only particles that exist are electrons and nuclei. In this physics, nuclei are fundamental particles that have inherent masses and charges. (We might as well say that nuclei are distinguishable particles, which means that the Pauli exclusion principle doesn’t apply to them.) These particles interact through only the electromagnetic force. (I’m suggesting we include magnetism, which means that this physics has features that the typical molecular Hamiltonian used in chemistry neglects.)

These laws of physics are pretty different from our own. They’re non-local—that is, information can travel arbitrarily fast. They don’t support light. They’re non-relativistic. Given these adversities, if you copy my wavefunction into this universe, and put me in a box with enough food and air and stuff, how long would I last?

Here are some things that I can think of that might be issues.

To start with, the lack of light would suck, because I’d be blind. I don’t think that many processes in my body rely on electromagnetic waves except for sight, though. The only biological processes I’m aware of that involve light are vitamin D production, melanogenesis, and vision. I can get around the latter issue with supplementation, but the fact that the body has some chemical processes which require light makes me wonder if other chemical processes require light too. The paper “What has light ever done for chemistry” doesn’t mention any light-requiring chemical processes which seem crucial to my health, so I’m cautiously optimistic.

Another issue is the lack of black body radiation. In my hypothetical world, heat is only transferred by conduction. This is potentially a really big difference. Eyeballing the results of articles like this one, humans would feel very hot if they didn’t have black body radiation to dissipate heat. I think we’d be able to fix this pretty easily by putting me in air that is much colder than the usual comfortable human room temperatures.

I think the biggest problem is probably that relativistic effects sometimes influence chemical properties. For example, if you neglect relativistic effects, mercury isn’t a liquid, gold isn’t yellow (not that that matters in this lightless world), and lead acid batteries don’t have nearly as much storage capacity. Do any biological processes rely on the chemical properties of heavy elements with enough fragility that this matters?

I’m not sure. It depends a lot on the extent to which relativistic effects influence the chemical properties of the molecules in our bodies, and also a lot on how much tolerance for error our body has.

According to Jensen, “Introduction to Computational Chemistry”:

In terms of total energy, the relativistic correction becomes comparable to the cor- relation energy already for Z~10, while it becomes comparable to the exchange energy for Z~50. Since the majority of the relativistic effects are concentrated in the core orbitals, there is a large error cancellation for molecular properties. Relativistic effects for geometries and energetics are normally negligible for the first three rows in the periodic table (up to Kr, Z = 36, corresponding to a “mass correction” of 1.04), the fourth row represents an intermediate case, while relativistic corrections are necessary for the fifth and sixth rows, and for lanthanide/actinide metals.

[…]

The general conclusion is that relativistic effects for geometries and energetics can normally be neglected for molecules containing only first and second row elements. This is also true for third row elements, unless a high accuracy is required.

Hmm, I’m not liking the sound of “unless a high accuracy is required”. I have no idea how much accuracy my body requires for things. I normally think of biological processes as being pretty robust, but there’s no reason for them to be robust to things like “suddenly your iodine-containing thyroid hormones have a significantly different chemistry, and the basal metabolic rate that it controls is totally broken”.

I’m particularly scared of iodine, because it’s by far the biggest atom that we use in our body. It seems like a particularly plausible place for a chemical process to go wrong. The next heaviest element we use is molybdenum (which has a whole lot of biological roles), and the next after that is possibly strontium. If my molybdenum doesn’t work, it might cause isolated sulfate oxidize deficiency, which causes generalized seziures and severe developmental delays—that disorder is caused by an inability to make a molybdenum-requiring enzyme.

I think that these effects are pretty likely to kill me. Humans use a gazillion different enzymes, and I’d get very sick if even a small proportion of those enzymes stop working. I guess I still don’t understand whether things are more likely to change efficiency or totally stop working. Like, I think I’d be okay if a particular enzyme was now ten percent more or less effective. 90% would be more of a problem. If I wanted to investigate this question further, I’d probably try to learn more about how robust these biological processes are.

Overall, I am quite uncertain about whether these effects would turn out to be a problem.

So what’s my probability distribution of how long I’d last?

Here are some things that could happen:

  • I disintegrate totally and my remains are not clearly human. (This is what happens if you teleport me into a classical mechanics universe.) I think this is 5% likely.
  • I mostly stay together, but I die instantly, because my cell walls all rupture or my brain doesn’t at all work or something. I think this is also 5% likely.
  • I die within minutes or hours because I’m unable to regulate my metabolism or something, because of some chemical process or because something gets too hot as a result of the lack of black body radiation. 30%.
  • Something is broken and I die at the same pace as people who don’t eat iodine or who have sickle cell anemia or who take a drug which stops a particular biological process. This means I would die over the course of days or weeks or months. 30%.
  • I live for more than a year. I think this is 30% likely.

My biggest concern is probably that an essential biological process breaks because it relied on relativistic effects. Could I try to add in some of these relativistic effects without making the model that much more complicated?

In the context of chemistry, the main relativistic effect is that kinetic energy grows faster at high velocities. In classical mechanics, kinetic energy is \(\frac12 m v ^ 2\). Relativity amends the formula for kinetic energy so that it takes infinite energy to accellerate something to the speed of light. It’s given by the formula

$^$ \frac{mc^2}{\sqrt{1 - v^2/c^2}} - mc^2 $^$

This formula is well approximated by \(\frac12 m v ^ 2\) if \(v\) is much smaller than \(c\). You can get a better approximation by taking the Taylor series of this equation and looking at the next term in \(v\), which is \(\frac{3 mv^4}{8c}\).

So we could better approximate a relativistic universe by asserting that in this universe, kinetic energy is given by \(\frac{mv^2}{2} + \frac{3 mv^4}{8c}\). In that universe, I’d be much less worried about various biological processes failing on me.

I care about this because I feel that nonrelativistic quantum mechanics is underrated. It’s only slightly more complicated than classical mechanics, but it allows an enormously richer universe—a universe of molecules and atoms and maybe even humans. (And even if it doesn’t support human life, I think life could evolve in it which would have reasonably similar chemistry to the life in our world.) A universe of nonrelativistic quantum mechanics has stuff in it which is is unmistakeably like the stuff in ours. Classical mechanics doesn’t.

I’m still slowly working on writing some explanations of nonrelativistic quantum mechanics. It’s my goal that after someone reads these explanations, they’ll feel that they understand how it leads to a theory of physics close enough to our everyday experience of matter that I think I might be able to survive in it.