New souls come from wherever they came from in the first place

Unless your world has time as a closed loop, then the souls had to be formed in the first place. If you are assuming that life originated on this planet, then there was some time in the distant past when there was no life, and thus no hosts for your souls.

Therefore, one of the following three things must be true:

1. The system is not in fact closed, either in space or time (time meaning, souls come back from the future).


2. There is some mechanism for psychogenesis, the creation of souls from either some form of energy present on Earth, or from nothing.


3. There are no souls; or, souls cannot be expressed as energy and/or matter.

Since 1 and 3 are precluded by your assumptions, there must be some reaction that turns chemical/electromagnetic/thermal/whatever energy into souls.

There is also the problem of species extinction, by your criterion. There are a lot of dinosaur souls that no longer have a place to go, since there is no cross-species soul migration. Thus, there must also be some mechanism for souls to return to energy.

You are looking at the "wrong" closed system.

In the entire Universe there are countless inhabited worlds. For a world with growing population, there will be one with decreasing population. The souls will migrate trans-worlds to keep the 1:1 ratio.

When an observer, like you did, limit the investigation to just one world, it might look like the ratio is violated.

From this it follows that life will follow the same route over and over in all the worlds where it can develop, leading to humans.

You need to examine your assumption (unstated) that the number of souls is limited to less than some number of bodies.

If, for instance, there are a trillion souls out there in the ether, then we are unlikely to outstrip the supply any time soon. Or how about 10 trillion? Why should there be a limit which just happens to correspond to the current (more or less) population?

The fact of reincarnation requires only that some souls are better than others at latching on to new-born (or newly-conceived) bodies, as these will preferentially inhabit bodies when there aren't enough to go around. Or perhaps the act of being embodied gives a soul an overwhelming boost in its ability to grab a body (practice makes perfect).

The energy does come from elsewhere.

Just because energy is a conserved quantity and souls need some energy, it does not follow that souls are a conserved quantity.
If you need some amount of energy differential to create a soul, this sets no limitation as to where this energy is coming from.

You can have your soul-attribution system work such that

• unoccupied souls are recycled first


• when no soul is available at the moment, a new one is crafted from a tiny bit of sunlight or whatever energy source the great soulmaster has at their disposal

Of course, you do run out at some point, but that only happens when there is no source of energy available in the whole universe, which bears the sweet name of Heat death of the universe. At that point your species has likely gone extinct from something else anyway.

Your conditions are very specific ...

The intent of this is that each soul needs exactly one body, and that
each body needs exactly one soul, with only brief periods of
detachment allowed. If strictly meeting this criteria isn't possible,
then it's allowable to consider that each soul needs exactly one body,
but not every body needing exactly one soul.

If it is true that each soul needs exactly one body, and each body needs exactly one soul then clearly the population has always been at its current level (give or take those in temporary transit) and always will be. Logic and mathematics dictate this and there is no escape from it.

If each soul needs exactly one body but not every body needs exactly one soul then the number of bodies with souls has been and always will be constant. Therefore any excess population will consist of soulless zombies.

Note

My answers above assume that souls are immortal and all souls are indivisible.

If souls are mortal after inhabiting a certain number of bodies, and are not replaced by new souls, then over time, the population will all become zombies.

If souls can be split into smaller souls then as the population increases each person's soul will be smaller. Perhaps this will lead to a more secular society. When population decreases, small souls may be able to coalesce into larger ones and so a smaller population would become more spiritual.

Post-clarification of intent:

I would suggest that souls lead two lives at each turning of the wheel, a life within the body, and a separate, but similar, life outside the body. This life outside the world we physical beings live in includes equivalents of all the activities we take for granted, including the creation of children, in the form of new souls. As to the energy balance of the system as a whole, there are two worlds each of which absorbs and traps, for a time, energy from the sun or it's equivalent. In the material world that energy is used for fuel by humanity in the soul world it goes into making new souls.

Pre-clarification of intent:

You haven't stated that a body needs a soul, only that a soul needs a body, this then is an answer if not a particularly palatable one. The world has run out of souls, some time ago in fact, that's why, on average, people are consistently less emotionally stable and less harmonious at each generation, more and more of the population are born without a soul at each generation.

The soul is the software of the brain, as such it is constantly changing. Now we tend to think of ourselves as having an identity that doesn't change over time, we can reconcile this with the reality of the constantly changing software that the brain is running, by attributing the changes in the software to information that we've acquired over the course of time. But this picture is only approximately valid as information can also be erased, it doesn't fully capture all relevant brain processes.

While the number of souls is not conserved, there is then a maximum number of souls. This follows from the fact that the total amount of information that can be present in the visible universe has an upper bound. The set of all possible programs that can be run in the universe is thus finite.

There are far more souls than there are bodies AND there is net "soul immigration" to Earth. The question should be, what does a soul, who has recently died and wants a new body, do about the shortage of bodies?

Also, a soul can split and become two souls -- but neither one is diminished or in any way less than the original.

One reason why so many people are dead set against abortion, contraception, and any form of nonreproductive sex (gay sex, etc.) is that they're afraid of a shortage of bodies for the next lifetime and want to encourage "more babies for everyone whether they want them or not". (I myself am not encouraging this.)

While the usual ratio is one soul to one body, you can have one soul to many bodies (a colony, like an ant colony) or many souls to one body (a cluster).

The ancient Buddhists define Samsara as the "endless cycle of birth and death", where one is so attached to the physical universe that one MUST begin a new lifetime somewhere. I'm not sure what happens when one must (Samsara) and one can't (shortage of bodies). Perhaps the "losers" have to downgrade from human to animal bodies, or worse, become a soul in charge of someone's body part (like the left leg). Escaping Samsara is an ancient but elusive goal.

I suppose a compromise would be to let yourself be reborn, but reborn in a body/family of your liking. We all have the ability to specify what we want for our next body, just some have it more than others (and no, whether you've been good or bad is NOT a factor).

While I'm at it, what do you call a soul who wants to be one gender but (accidentally) picks up a body of the other gender? (Oh, this is SO easy.)

It's a shame this thread is on Worldbuilding, a fiction thread, because I consider reincarnation to be a literal fact. But there is really no other place on SE for this.

Do I have references to back up these statements? I don't see how that would be possible for this subject, as the best I could do is to back up my opinion with references that are themselves opinions. But it is all nonetheless true.

The delay between reincarnations gets shorter as the population grows.

This breaks your "short detachment" criteria, but otherwise meets all other requirements. So long as your total number of available souls is greater than the population, then you can simply have shorter and shorter delays between reincarnations. This avoids souls having to "fight" for bodies as well; it's a simple first-in-first-out system.

One of my favorite short stories of all time addressed this issue. Like you, the author assumed that souls were human and not transferable with animals. I'm afraid I don't know the author or title of the story anymore, though it's somewhere in a stack of magazines I kept. It's from Fantasy and Science Fiction and was probably published in 1979-1980.

In the story, there were a finite number of souls available but humanity didn't hit the limit until the world's population went over a certain amount (a number that was not reached at the time the story was written...not sure about now).

So people shared souls (this was not something under anyone's control, it just happened). If you did not have a soul to use at any given time, you were in a coma.

If you assume souls are real and tangible in some way and reincarnated, you basically have 3 ways to go:

1) You run out of souls at some point (and maybe the number available is so high we'll never exceed it).

2) Souls are not subject to the usual mass/energy constraints.

3) Souls can transfer between humans and nonhumans. I know you don't want to go this route but do consider that pretty much every religion that believes in reincarnation allows for at least some human/nonhuman soul transfer.

The Universe is Infinite

With probability 1, if the universe is infinite, then the population of your species is infinity. Aleph null, to be specific.

Why is this? That's because there's a small chance on every planet of that species developing. Really small, since it has to have the correct DNA. But, its not 0. So, the expected number of worlds will have that species is aleph null.

Then, our problem is the same as Hilbert's hotel. Even if the population on every planet is increasing, you can "shuffle around" souls so that you have a 1-1 correspondence between bodies and souls.

I'd say souls are free from the time dimension meaning that it doesn't make sense to place a limit to the number of souls you can have at a given time.
For example when a person dies maybe his soul reincarnates on a newborn 2000 years from now. Not meaning that they are dormant for 2000 years but that they simply skip the time in between.

Another option is that "the reality of souls" is universal and therefore there are not only animal souls but also alien's souls, but the total population of souls in the universe always remains the same through some quantum effect. If some alien is born and there are no souls left maybe that would make an old human on the blink of death die.

The world does run out of souls.

This is one idea. Maybe contrary to expectations, the world actually can run out of souls: Say, as the world population reaches a certain level, the global birth rate starts rapidly declining, because of the decreasing availability of free souls.

The manga Spirit Circle explores this idea somewhat, in the Lafalle arc. The setting does violate rule 3 of your conditions, though—it's established in-universe that some of the protagonist's previous lives have overlapped in time. However, if you ignore that, it still explores some interesting aspects of the idea of a limited number of souls:

In this arc, it is the 34th century, and science has developed to the point where "Sleeping Towers" can host the brains of people who have lost their bodies due to accidents or illness, keeping them alive in a state of dreaming. The people kept in these "Sleeping Towers" are known as the "non-living".



However, the human population has been shrinking: There are 10 billion "non-living", but only 500 million living people.



The protagonist realizes later on that the population is shrinking because of the souls that are trapped in the Sleeping Towers: People aren't dying, and thus aren't being reborn.

Chicken Soup for the Pool of Souls

A possible soulution for your problem is that the human body(the vessel itself) does contribute to the pool of available souls. Upon death, the body's decay contributes not just nutrition to the soil in the usual physical cycle of life, it also contributes soul-stuff to the realm where reincarnation plucks its subjects from. This can be a byproduct of a "used vessel" being imprinted from once having a soul residing in it.

However, since your setting respects the laws of thermodynamics, what this creates is a system where the human body consumes energy in the form of food and other resources to produce souls upon death, wherein reincarnation will then put souls back in bodies, and so on. An ever increasing population of both human bodies and souls will consume an ever increasing amount of resources, creating an overpopulation problem just like real life. Without an infinite amount of resources(potential energy) to use, this system is not infinitely sustainable and will eventually fail.

When your world becomes unable to support the amount of humans in it, it'll have no choice but to be declared insoulvent. The resulting crash will most likely result in the collapse of the ecosphere and death for huge swathes of the population through starvation. This could plausibly be the extinction of the human race as we know it if you want to go that way.

Maybe I just did not understand that there is need for individual souls from your question, if it was meant this way, I am sorry.

Do souls stay the same, do they mix, or even re-form?
Is the composition static, meaning that if a soul is reincarnated it existed before (e.g. my Soul is Napoleon), or do I have maybe just the soul-equivalent of Napoleon's nose but some other guys soul-ears?

In the static condition: You have a number of n souls, therefore population cannot be > n.
If we say that souls consist of some kind of matter and this matter can mix in between reincarnation: You have an amount of n units of soul matter, therefore population cannot be > n/amount of matter needed per soul.
But this gives you another possibility, saying that souls don't have to be necessarily of the same quality (or size). Would lead to that in a more populated world the occurrence of "big" souls descends.

I would probably prefer a more "scientific" approach, you could say that the matter is made of some physical resource, so if a body dies, the soul decays like the flesh, only to be re-formed in some later stage, giving you your closed cycle.
Although this defies the whole use of souls in some way, it gives you the chance to keep your world in balance. Soul matter = water means the more humans needing a soul the less water on the planet.

Ashen one, be sure to bring more souls.

I would invite you to take a look at the dark souls series where there really is only one human soul. It gets more and more fragmented as time passes on. Most humans become more and more hollow as the humanity is drained from them, destined to live a life of despair until they die (or not, if they are cursed). Some are more powerful and amass vast amounts of souls, further fueling their might. They are bound to become great and to fulfill the proficy of rekindling the first flame.

You could reformat that so that each person gets less and less of a soul, until most of them are basically just existing, doing the same job, the same routine for years on end without any real desire or goals, only making marginal progress.

Some however resist this and can hold on to their humanity or even increase it. These would naturally be your protagonists and antagonists. This could be done through sheer willpower, fate or something else. Maybe you can even actively take it away from someone else?

The energy required is miniscule and it's mainly a force outside the known ones that regulates it. So the ambient energy around a person is many times more than need to sustain the soul. The act of birth triggers the creation of a new one.

At death it dissipates back to potential until another birth nearby makes it coalesce. So it would never be exactly the same soul. Sometimes there is an issue and you get Jack The Ripper, other times there is an issue and you get Mother Theresa. Either way each individual soul will be unique.

Eventually there would not be enough energy, but first all the suns would have to die and the universe implode.

Interminable Dimensional Souls

Assume the closed loop is Earth, but dimensionally-speaking all humans who ever have, do, or will live do so in a non-closed time circuit. Assume also that souls are not confined to our particular dimensionality. Under these premises, there is, has been, and always will be precisely the number of souls required for all of humanity. The souls themselves become a closed system. This also allows for alternate realities in which the population is not booming, or has never boomed, and in which the population of humans on Earth in 2018 is 20 billion or 5 million. It's probably sloppy from a story perspective, though it could be made interesting if handled properly.

Soul reaping

Souls are a resource beyond our comprehension (true), which are harvested and reaped as supply and demand fluctuate. This might also assume that souls have some sort of shelf life - a limited number of reincarnations available or a limited amount of universal time in which they "live", but that new souls are formed/grown/developed from the aether in some manner or another.

Notes on Logic or "Science"

You did ask for as scientific an explanation as possible, which of course is still going to be derivative of logic since there is no science that covers souls. Considering that, the initial question is - where did souls originate? What is their genesis? Did souls exist before life or did life exist before souls - or... did they come into being simultaneously?

If souls existed before life, it violates your requirement that every soul needs a body. However, it could point to souls being something even further beyond the scope of our understanding than they already are. If life existed before souls, it violates your requirement that every body needs a soul, however it would point to souls actually being a byproduct of life. If they developed simultaneously, it could lend itself to the idea that souls are, in fact, tied directly to life, which leads to the next possible option:

Soul Mitosis

At least for most offspring, where two parents are needed, each parental soul splits a portion of itself to lend to the creation of a new soul for the new life. This doesn't fit directly into the scope of reincarnation, but hear me out.

Just as life doesn't always succeed (some eggs, fetuses, etc are not viable), some souls don't always succeed. When a soul is not viable, an existing soul finds that host and reincarnation of the soul occurs. This accounts for the number of souls needed, as well as accounting for why some folk seem to remember/feel past lives - are "old souls" and some do not find themselves in this position. This would require that reincarnation is not an assured phenomenon, but one that can occur. From a logic perspective, this one makes the most sense to me. It seems to cover all of the bases except that a soul requires a body - but if we accept concepts like ghosts and spirits or the like, it leads one to believe that there may, in fact, be souls without bodies, or that souls have somewhere to go while they wait (could be heaven/hell, or Valhalla, or... who knows. Literally could be anything).

Soullessness

Of course, it could be that we have entirely run out of souls. It would explain a lot with regard to the modern world in which we live, if we assume that souls are the source on conscience/goodness (though that's a stretch since, at least via Abrahamic religions, "bad" souls go to hell). It could be that some other energy fills that void, and thus bodies don't need souls, per se, but an energy that sustains life. A TV needs to be plugged into a wall, but if you give it enough batteries, it WILL power up for a while (if DC is properly converted and such). Actually, that leads to:

Energy Transformation

Energy is energy, and different types can become or be used as different types. Kinetic energy can become heat (friction), light energy can become electricity (solar conversion), et cetera. Who is to say that something else can't become, or take the place of, soul energy?

One interesting way to look at this, and while not scientific in any way isn't entirely implausible logically given that we don't know what souls are (or if they even exist), is that psychic energies can condense into souls. Christmas babies are incredibly kind because they are born during a time when the world is at peak-kindness. War babies are fearful or decisive or quick to anger. This takes an almost astrological view applied to souls and the states of humanity, and sounds somewhat like ancient East Asian philosophies on life. New souls are created from the detritus of vast human emotion.

There is only one soul in the universe.

Every being is a unique refraction of it just as every snowflake uniquely refracts sunlight.

As per Hindu mythology , there are 84 lakh (8.4 million) distinct species of which humans are one of its kind. So in this religion the holy books preach that human are the most supreme species of all and any creature born as human may attract soul from any source of species that have lived off in past.

What happens post death?

As per the mythology the soul is the supreme driver of the life , once the life ends the body is burnt to ashes while the soul spirit escapes to the infinite universe and unless it becomes completely purified (free from any sins , greeds and motive of the last birth) it's then set free to enter in to a new borne species. So the soul is independent of whether the person is human or any animal.

So for this theory , we can assume that since many species are getting extinct their soul's might be getting transferred into humans.

A newborn body calls to Souls, but if no soul is available then a new one may grow from embedded fragments of the parent souls that spawned it.

The real question is what happens when there's a mass die-off of the species and there are too many souls!

You can take inspiration from the Lifestream concept from the video game Final Fantasy VII. In a nutshell, there is a finite amount of "soul-energy" contained in the planet. When a living being is born some of this energy infuses into its body, thus giving it life. When this being dies, the energy exits its body and returns to the planet's pool of energy, and somehow blends with it.

This can have some interesting ramifications: while there may be cap on the total number of beings on the planet, there is not a fixed number of individuals for a given species. Also, you can play with the concept of some species using more of this energy than others, so you could have plenty of "low level" beings such as plants or bacteria, or fewer "high level" intelligent species that hoard on this energy, therefore preventing other parts of the planet's ecosystem from developing (this is reminiscent of the video game's plot).

I think this does not contradict your assumptions but requires that the souls only have an identity as independent beings when they are inside a body.

There is plenty of souls - trillions, quatrillions, quintillions perhaps. There is no way that the incarnated population ever needs all souls at a time; it would destroy the planet's ecosystem.

Time traveler souls

I propose the following: Souls are time travelers.

A soul can reincarnate in a body that is born in the past respect to the moment of death of the previous body. That is, when a person dies, its soul could go to a new born in the past.

Thus – assuming souls have identity – there could be two bodies in the same time period that are being occupied by the same soul, except one of them is an early version, and one of them is a later version.

Furthermore, there could be only one soul per species, and without any need of soul fragmentation.

Oh, and before you consider it... No, sex is not part of souls… some species can change sex midlife.

Physics

This is a possible framework for what I suggest above

You say souls have energy. However, it appears souls do not have mass. If this is true, free souls (souls not attached to a body), would move at the speed of massless objects (the speed of light). If this is true, in the frame of reference of the souls time does not pass, that is, all instants are the same for the free soul. This also means that souls do not need bodies, nor do they experience the time outside a body.

I also want to bring a philosophical interpretation of Feynman diagrams… these diagram represent particle interactions, with one of the axis of the diagram being time. However, these diagrams remain valid when rotated, except that when you rotate them half turn, what used to be electron is now a positron (and vice-versa). Under this interpretation, a positron is an electron traveling backwards in time from your frame of reference (and vice-versa). Going further, there could be only one electron/positron that travels back and forth in time, and as a result all electrons/positron are the same.

Note: electrons are indistinguishable from one another, same for positrons… and any fundamental particle actually.

Then why electrons – and other particles – have the particular properties they have? Well, because there is only actually one of each, and this is how they were created.

I am suggesting that souls behave similar to that, traveling back and forth in time. Why a soul is of a particular species? Because that is how they were created (or how they always have been, if your cosmology has no creation), along with the universe.

Conservation of energy and time travel

Evidently the soul won’t be like the electron (electrons have mass and have a distinct antiparticle), but like photons (that have no mass and are their own antiparticle). Thus, a soul is a soul going backwards or going forward in time, it makes no difference for the soul.

Yet, photons have energy, if they go back in time, won’t that mean that a moment in the past would have more energy than one in the future?

Well, these particle that go back in time are virtual particles. They are only one of the infinite paths that particles take in an interaction. Under Copenhagen interpretation, particles go into a superposition of all the paths, including those that go back in time… and these can break conservation of energy. However, when the particle interacts with another, it collapses in such way that the interaction respects conservation of energy.

Souls would be like that. When free from a body, they go into a superposition that can break conservation of energy and time travel. However, to enter a body, there would be an interaction with it, such that conservation of energy is preserved.

Thus, if the soul adds energy to the body, some energy must be lost. In fact, under the assumption that the body-soul link is in stable equilibrium, it must be a low energy state, thus it makes sense that energy is released…

Yet, it cannot be released to the environment, at least not at the time of linking (that would still result in more total energy in the universe), instead, it must be released to the time from where soul comes from. Well, the soul comes from the body of the prior incarnation is dying.

Thus, in time A: some energy is lost because the soul leaves, the dead body. Then the soul goes to another time B. In time B: the soul links to the new body adding energy. In consequence equivalent energy leave the body and is send to time A. Then in time A: that energy is released.

Consequences: conservation of energy is preserved, and the energy release when the soul leaves the body could be detectable. In what form is that energy released? Use your artistic license. Addendum: Scientis could think that that is the soul, it isn't. Perhaps this is an excuse for ghosts if you want them in your setting.

Biology

These are some ideas on the biology of species tied souls

Perhaps souls species needs some wiggle room. As we know individuals of the same species differ biologically. Yet, they would all be viable vessels for the same soul.

If scientists create new variants of a given species, souls could still populate these bodies.

However, perhaps a body is that has mutated too much could not host a soul.

If scientist create a new species – out of genetics and bio-engineering – these might or might not host souls depending on whatever or not they are a close match for existing species.

Why would a body need a soul? If we need excuses for souls as postulated here, I would say that souls shape the growth of the body. In that way there is rational link between the species of the soul and the species of the body.

This would also suggest that if the attachment of the soul to the body is not ideal, the body may have uncontrolled growth, I mean, cancer. From another point of view, if the DNA of parts of the body is damaged in such way that it does not match the species of the soul, the attachment of the soul to the body would be severed, preventing it from shaping its growth, leading to cancer.

An interesting consequence of this idea (if you choose to allow it in your setting) is that if you could, by means of science or magic (again, if you allow it in your setting), force a soul into a body, that body would start to resemble the species of that soul. This also opens a backdoor for chimera creatures, lycanthropes and such.

About the moment the soul enters the body… I would say that it happens at some point between the conception and the first cell division.

This also imply that eggs do not necessarily have souls by themselves.

Ah, and I would remind you that there are some virtually immortal cancerous human cells that are used for research (HeLa). Under my proposal, her soul is not trapped there.

Couple of possibilities

We're still some distance away from that problem

There are 16 gigasouls: 2^34. Always were. In the early days, when they died, they slept thousands of years before coming back around. Now they're sleeping for decades. Souls need sleep. The less sleep they get, the greater the odds of the planet experiencing a Malthusian die-off of one kind or another. The dice came up badly for the Black Death, World War II and since then we've partly gotten happy dice, and partly human will has influenced the dice.

As the number of living souls approaches 16GiS, the chance of a Malthusian event approaches 100%.

This is simply animals, graduating

Some religious doctrine believes that souls move up and down from differnt stages of animal (amoeba, ant, shark, snake, mouse, dog, dolphin) to human.

Souls are getting their act together. The graduating classes are getting very crowded. This is all a good thing, this is the evolution of souls. More of them are graduating to humans, so there are more humans.

All the logical reasons (technology, food efficiency etc.) are just the manifestation. If there were 500 billion souls graduated to human, this planet would look like Coruscant and somehow that would all just work. And there will be convenient explanations for why it works, such as there was with the Green Revolution.

Possibly souls are immortal but not eternal. Souls are immortal once created but the god or gods in charge of reincarnation can create new souls for human bodies at any time they may be needed.

So human population growth can result in an increase in the number of souls while human population decrease doesn't result in a decrease in the number of souls, merely a decrease in the g frequency of incarnations for an average soul.

It is also possible that the number of souls is so vast that an average soul might wait for hundreds, thousands, or even millions of years between incarnations, so human population growth would only result in a minor increase in the frequency of incarnation for a soul.