Differences in Quantum Field Theory in 4 Spatial Dimensions [closed]

Question

Since I'm thinking about doing some world building on the subject for a potential future story, I wanted to ask some questions on what the fundamental effects on physics in a universe with 4 spatial dimensions would be. For this question, assuming that Quantum Field Theory is at least close enough to a true description of how fundamental particles exist, would there being a 4th spacial dimension effect it in any meaningful way? To clarify, I'm not asking about all the individual subatomic particles or fundamental forces, I'm sure that those would change at least somewhat, for this question I'm wondering how 4D effects the idea of excitement in universal fields being used as a representation of particles and forces, like how a higgs boson is an excitation in the higgs field.

Answer 1

Frame challenge: there is no story to take place in this world

You’ll have a hard time writing an interesting story in this world because, in anything other than a 3+1-dimensional spacetime and thus inverse-square gravity as well as 3 spatial dimensions, stable closed orbits do not exist even in Newtonian gravity. The only stabilizing forces are $F\propto r$ forces (simple harmonic oscillators) and $F\propto \frac{1}{r^2}$ forces (inverse-square forces like three of the four fundamentals, barring confinement). This is stated as Bertrand’s theorem and has been proven.

This might not seem like a huge issue but as it turns out in 4+1D spacetime (and thus $F\propto\frac{1}{r^3}$ gravity) this means that satellites orbiting their primary don’t have a consistent orbit; they either oscillate between a minimum and maximum radius $r_\mathrm{min}$ and $r_\mathrm{max}$ or spin off to infinity. In general, such a system is not stable if there is more than one satellite involved, be it stars around a galactic center or planets around a star or moons around a planet; with multiple planets (which is highly likely given how we’ve observed planets to form; planets are much smaller than the accretion disks that make them), it is likely that they will interact with each other in unpredictable ways and either crash into one another, toss themselves into the Sun, or throw themselves into the cold void of space.

This inverse-cube law isn’t new for just gravity, either. The electromagnetic force is also modified: the reason we have inverse-square laws in 3+1D spacetime is because the surface area of a sphere (i.e. the size of the surface over which a uniform burst of electromagnetic/gravitational radiation is emitted) varies inversely with the square of the radius in 3+1D. In 4+1D the surface area of the hypersphere over which a burst of radiation would be distributed varies inversely with the cube of the radius, which in turn leads to inverse-cube laws for things like gravity and electromagnetism which are mediated by photons and gravitons (radiation). Electromagnetism behaving differently would radically change the entirety of QFT in ways that would be mentally and physically exhausting to explain here, would screw up chemistry in ways that I can’t even rightly predict on my own, and would thus mess with biology in ways that I have a hard time even thinking about. The one thing I can say is that, like planets around the Sun, electron orbitals would be unstable as well and it is unlikely that, in this ultra-chaotic Universe, life would ever come to evolve.

Point being, the world would not be one in which any interesting stories take place. Perhaps revise the concept so that only a certain volume of space has this property; maybe an advanced civilization learned to reverse the compactification of a certain dimension to give the apparent 4 spatial dimensions say on a given planet or solar system.

So if you’re asking about QFT to think about the nitty-gritty details of the world as you prepare to write in it, be warned: your Universe was dead on arrival, and likely contains no life.

Wait, but that’s no fun!

Yeah, it’s not. Physics is specific, and if it were off, we’d all be either dead or never born. If you handwave a physical god coming ex nihilo to flash a bunch of life into existence on a planet orbiting a star alone in a “stable” configuration, the inhabitants of the planet (aside from having wildly-chaotic biochemistries) would see some interesting effects, most notably the instability of their own orbit: the seasons would be unpredictable without numerical analysis of the current state of the planet in space, since the planet would drift all around the habitable zone of the star over the course of 360 degrees around its star. Might want to set $r_\mathrm{min}$ and $r_\mathrm{max}$ within the habitable zone so that they don’t all freeze/incinerate and die.

Why changes to QFT matter at this point is a good question. Life probably won’t last long anywhere in the Universe if we don’t let some external force make it so, and that force has to originate within this Universe (multiversal astronauts would instantly fall apart at the molecular level upon entering this Universe). At this point, it’s better just to wave some hands. Your readers care about the story, not higher-dimensional quantum field theory.