Not all universes need to be considered alternative versions of each other, not even all universes existing inside the same multiverse. Sometimes two different universes can just be seen as being two different independent universes, not being versions of each other at all. This is always a matter of point of view as well. Everyone can easily define their subjective definitions for what makes a universe to be an alternative version of another and what makes it just another different universe. There are several different types of alternative universes described below. Anything not following on any of those types would be considered as just another different universe instead of an alternate version. This case as been defined as Type 0.
It is possible for higher level verses than that of universes to also have alternative versions. Like an alternative version of a multiverse or above, in the extreme to alternative versions of the omniverse which would correspond to other altarcae.
Many of these realities were likely formed from the Polyverse.
These universes can not be seen as alternative versions of each other by any of the definitions of the other types. Usually they are universes which have not all derived from the same singularity, each one having started from its own or even having different beginnings. Also, their origins are also not related in anyway, with each having started with a different and independent singularity instead of having a common or related single cause for their beginning singularity. They usually also don't share a temporal dimension, meaning that their timelines are not comparable.
Sometimes the terms "alternative universe" are still used to describe these universes although it is being used in an inexact manner in those cases. In other cases the distinction becomes muddy and hard to spot. Given any two universes, it can be hard to say if they are alternative versions of each other or not. An exact answer would require knowledge about the structure of their containing multiverse.
a) Momentary Global State
This possibility corresponds to the Many Worlds Interpretation of Quantum Physics, also known as a Level 3 Multiverse.
According to observer effect and quantum mechanics, the act of observing a particle changes the state of said particle, causing a wave function collapse into a probabilistic state which is then observed. As this state is probabilistic, any other possible state could have been observed instead, each possible observation having a certain probability of occurring. This creates a fundamental distinction between the observer and the observed where the observed is undefined and probabilistic before being observed by the observer but the observed does not, or at least appears to not share such properties with it.
One of the possible solutions to this paradox is the so called many-worlds interpretation of quantum mechanics. This interpretation recognizes the wave to be the fundamental reality and states that the wave collapse only appears to occur but is not actually real. Instead the wave collapse corresponds to the establishing or choosing of one of many possible realities. The observer ends up observing the particle in a certain state but that observer is also in an uncertainty state himself. In fact, for each observation the observer exists as observing all the possible states of the particle at the same time, each of those different observations of the same thing are all different alternative versions of the same reality that all exist parallel to each other. They can be seen as being created at the moment of the observation, having exactly the same past but diverging from that point on. It is important to state that the term observation does not imply a sapient or even sentient being. Any interaction between two particles at any level counts as an observation in the sense that it causes a wave collapse forcing those particles to choose one state among all possible ones.
This set of alternative versions of the universe contains all possible versions of said universe that differ from each other in one or more observed particle states. All such universes are effectively the same universe in all its different possible states. They have the same laws of physics ruling their behavior, the same dimensions with the same properties, the same size, the same shape and topology, etc. Their time passes in the same way, always synchronized with all of them. Each such versions of the universe can be defined as a possible global state of such universe.
All such universes would have been, at the first point in time, where the universe was just a singularity, a single universe. After that single point in time the different possible versions would have started to diverge as particles started to interact with each other creating new possible global states. For each particle interaction a new group of versions of such universe is created, one universe for each possible state resulting from said interaction. As it can be seen, only global states that are reachable or possible from the common single original state exist as alternative versions of said universe. Other global states not reachable from that point are impossible and do not exist as alternative versions of it.
The number of global states that are possible for a given universe is based on several factors: The number of fundamental particles existing inside it, how many states each can exist in and how many points in space they can be at. Multiplying all those numbers one gets the number of all possible global states which will be infinite if any of those numbers is also infinite. If all those numbers are finite though, the number of possible global states will also be finite, although possibly arbitrarily large. Just being infinite does not mean that all imaginable states are possible. It is possible to have an infinite number of possible global states while there existing many other impossible global states as well. In the same way that the number of even numbers is infinite but there are still many other numbers that are not even, an infinity of them actually.
This type of alternative universes only compares the global state of a defined moment in time. It does not care how different or similar they where in the past and it does not care how much they will differentiate in the future. It is assumed that all of them share a single timeline and that, despite any current differences, they all have been merged into a single global state on some point in the past. Also, in the unlikely possibility that two different past global states resulted in a currently identical one, those two versions of the universe collapse into a single one which is considered the same in this case.
The set of all of these universes, corresponding to all possible current states of the universe, is sometimes known as quantum foam (not to be confused with the material of the same name) as a reference to a way of looking at them as if they where just a massive superposition of all the possible states of the entire universe. In some cases it is possible to somehow travel between these different branches or states or timelines, causing a dramatic increase in their overall complexity because any such jump will inevitably create new multiple possible states. These cases are called spaghettiverses.
b) Full Past Global State
It is possible to add to the set of all alternative versions of a single universe by adding another factor for comparison. If, instead of just comparing a well defined temporal coordinate, instead the comparison is made across the entire time dimension.
In this case, while comparing versions one should compare not just the global state of each version in a defined temporal coordinate but across all past temporal coordinates. If two versions of the same universe differ in their global state at any temporal coordinate of the past they are considered to be different. They are only the same if they have always been and still are identical in every way.
This increases the number of possible versions enormously for one must now multiply their number by the number of possible temporal coordinates from the beginning of time up to the current one.
This option can also exist for a universe that has no beginning of time but, instead, has never started and have also existed in some way. If that is the way and if for every point in time in the past there are more than one single global state possible, there is necessarily an infinite number of possible pasts of such universe, therefore there are necessarily infinitely many possible alternate versions of this universe.
It is possible that for every unique version of this type of a particular universe, there is an entire set of all type I-a alternate versions of it.
c) Full Temporal Global State
Like the previous type but with the comparison necessarily being made from outside of their time line so that it can be compared in full. Two alternative versions of the universe are considered different as long as any point in time, no matter if in the past or the future, is different in any way. If they remain the same for the entirety of the time line except in the end of time point, they are still considered different versions of the universe. If they are identical, diverge in a single time coordinate and then become identical again right after that they are also considered different versions. This means that when a multiverse contains all versions of this type of a universe there are a lot of almost identical or practically indistinguishable ones inside it.
What this type implies is that there exists already an alternative version of the universe for every possible future of it. Alternative versions are not created when a wave collapses into a possible state, instead they all exist from the beginning of time, only becoming different when those differences manifest themselves.
This leaves open the possibility that maybe not all possible futures come to exist, therefore there are more identical copies at a given point in time than those that will ever be differentiated from each other. If, instead, the number of identical copies at any point in time is exactly the same number of possible futures that will actually occur. If one assumes that not all possible futures will eventually happen and there is only one copy per future that will actually happen, then that means that either destiny or some similar force must exist for the number of possible futures yet to happen is somehow known prior to them happening. If the number of existing copies is equal to all futures that could possible happen, than that is not the case. What it means for a possible future to not happen in this context is the possibility of an observation causing the wave collapse of a specific particle into a specific state never occurring. The number of occurring futures is related to the number of observations that are actually made or the number of wave collapses that occur. But the number of all possible futures that could happen is the number of all observations or all wave collapses that could occur, not just those that do.
This option applies even for infinite timelines where time never ends. Assuming that there exists the possibility of different global states at each and every point along the time line than it is required that for any single global state at any point in time there exist an infinite number of possible futures, therefore there are necessarily an infinite number of possible alternate versions of this type for such universe.
It is possible that for every unique version of this type of a particular universe, there is an entire set of all type I-b alternate versions of it.
Weak vs Strong Comparisons
The comparisons of the different versions of the universes based on their global states can either be weak or strong.
As described above they are all strong comparisons. A weak comparison would be a comparison made using less detail, or in a "sloppier way". A weak comparison is one that does not compare all states of all fundamental particles of the universe. Instead if makes the comparison at a higher level of detail only.
Maybe it only compares the states of all atoms of the universe, instead of all the fundamental particles. Or maybe it makes the comparison at the level of individual molecules or even at the level of macroscopic items only.
In the other direction, an omniscient based comparison would take into account all information inside the universe, even that which cannot be obtained from inside it due to Heisenberg's uncertainty principle or similar laws preventing it. A comparison at this level would require absolute precision in all the values of all the properties of each individual fundamental particle and its corresponding wave function, all at the same time.
The higher the level of the comparison the less details are taken into account for it. The less zooming is required to perform it.
Weaker comparisons are much easier to make and probably result in much less versions of the same universe.
A note on discreteness
Some of these comparisons can only make sense or be possible if we assume that time is discrete, that is, that it can be divisible into a minimum interval. Only that way can one talk about a global state of the universe at any given time. Otherwise, if time is continuous and infinitely divisible in smaller and smaller intervals it is only possible to talk about a global state at a given interval which can include multiple different states different in time along such interval. A possible solution is if there is a minimum interval of time required for even the smallest change of state in the smallest of the fundamental particles. If that is the case that interval can be considered to be the quanta of time and used for the comparison. Otherwise only intervals can be compared and there are an infinity of them, therefore there will automatically be infinitely many alternate versions of such universe.
The same applies for space and for the states in which particles can be at. If any of those is not discrete, it is always possible to zoom in and find additional differences, giving way to an infinite number of variations.
These alternative versions of a universe are harder to compare than the ones sharing their dimensions for they are not comparable. It is not possible to say that the set of coordinates (w,x,y,z) in one version corresponds to the set of coordinates (a,b,c,d) in another. Alternative versions of this type occur when all those originate from the same big bang singularity or whatever their point of origin is. They just develop each with its own different dimensions. So it is perfectly possible that for each alternative dimensions of that universe, there exists a full set of type I alternative versions as well.
In order to calculate their number one just needs to multiply the number of alternative versions of the type I used by the number of alternative versions of the different set of dimensions. It is possible that only a few of the dimensions are different instead of all of them being so. In that case, the more the number of dimensions different, the higher the number of alternative versions. The most common case is for the temporal dimension to be different, the space dimensions to be all different or both but it is also possible for just some of the space dimensions or a few of the space and the time dimensions to be different while other space one to be the same.
One way to understand this is to imagine two versions of a universe, both with the same global state and the same past and future as well. But one of them has its time, and therefore its past, starting earlier than the other, such that one has a larger past than the other. They can have fully identical pasts back to that point where one no longer goes back in time for its time starts there while the other can continue to go back and have an additional past. This will necessarily make them different. The same comparison could be made for their future, with one lasting more than the other.
It is possible that for every unique version of this type of a particular universe, there is an entire set of all type I alternate versions of it.
Type III - Different laws
a) Different fundamental constants
This possibility corresponds to the Level 2 Multiverse of other existing Post-Inflation Bubbles.
Another type of alternative versions of a universe is given by the set of all possible fundamental constants used by the laws of physics that govern said universes. The baseline universe would just be one on such a set, represented by its own fundamental constants. Each other universe in there would have one or more of such constants slightly different. This set is sometimes seen as coming out of string theory.
It is possible that for each universe in this set there would be a set of all type I or even II alternative versions of it.
b) Different laws of physics
This possibility partially corresponds to the Level 4 Multiverse of other mathematical structures.
More than just having different constants, this set of universes contains a universe for every possible combination of laws that could be called laws of physics. Each variation of the laws, no matter how small or large, from removing some laws to adding others or to simple small changes to already existing laws.
It is possible that for every unique version of this type of a particular universe, there is an entire set of all type III-a alternate versions of it.
c) Different laws of mathematics
Like above but for the set of all possible different mathematical systems. This possibility probably better corresponds to the Level 4 Multiverse of other mathematical structures.
It is possible that for every unique version of this type of a particular universe, there is an entire set of all type III-b alternate versions of it.
d) Different laws of logic
Like above but for the set of all possible different logic systems.
It is possible that for every unique version of this type of a particular universe, there is an entire set of all type III-c alternate versions of it.
e) Higher differences
One can continue this reasoning to an arbitrarily high level.
As long of an all encompassing set of all the possible variations of the category above can be generalized into something more abstract, a new set of all possible variations of that more abstract thing can also be made and so on to an arbitrarily high level.
A Note on the Level 1 Multiverse: Regions Beyond Our Cosmic Horizon
This page considers an entire universe as a whole and does not concern itself with smaller parts of that whole. Other parts of the universe beyond a cosmic horizon would still be part of that same universe, no matter how far away. Therefore they do not count as alternative versions of that universe in the context of this page.
Type IV - Multiple copies of the same universeSome strange multiverses could contain multiple fully identical versions or copies of the same universe, of any arbitrary type. These copies would be fully indistinguishable from each other with the exception of their individual location within their containing multiverse.
It is also possible for the exact same universe to exist inside two different multiverses at the same time. These can either be exact copies or they can actually be the exact same universe. The only way to tell the difference is by changing one of them. If that automatically also changes the other, then they are the same one, existing in both places at the same time, otherwise they were just identical faithful copies.
The problem with minds and souls
All these possible existences of different versions of the same universe can cause a problem or be contradictory with some spiritual beliefs. If one believes that the mind is just a product of the material particles, their states and interactions, than there is no problem in having multiple identical copies or even slightly different versions of minds. In realities where this is the case, multiple versions of universes can exist without a problem. In this case there is no difference between personality and the network of particles and their states in the brain of a creature so the number of possible different versions of a universe remain the same.
But in realities that match the belief that minds are actually souls or spirits and that each one is unique it is not so simple. By mind or soul it is meant the sum of individuality, personality, feelings, emotions, ideas, creativity, knowledge, memories, intelligence, sanity, sense of humor, and any other property that could apply. There are several possible solutions for this situation though:
- The same soul inhabits all the bodies of the same entity existing in all of the alternative versions at the same time. That way each of the copies is just a different manifestation of the same unique soul. How these manifestations vary is the new question that appears naturally then. Does this mean that only alternative versions of that creature that share a similar personality are possible or is it possible to have extremely different personalities because each soul is simultaneously manifesting itself in all possible different ways? This second hypothesis would have the consequence that souls don't have necessarily specific or unique personalities.
- Different souls inhabit each body, even the multiple versions of it, no matter how similar. This means that the same creature can have extremely different personalities in each version, no matter how close those versions are physically. The implication is that the reverse is not true. There's no reason to expect that any two versions of the same creature would ever act in a very similar manner except by pure coincidence, therefore versions of the universe similar in such ways would become more unlikely.
- Souls also actually have different versions of them. This is contradictory with the idea that they are unique but that is not necessarily a problem. For each version of a given creature there is also a version of its soul. As stated this option results in no change on the number of possible versions of a universe. But it also opens up the possibility of a new type of versions for if there exists some number of creatures inside the universe and for each of those creatures there exists some number of souls, there is also the option that every soul could inhabit any of those creatures instead of all the versions of a soul being restricted to all the versions of the body of its corresponding creature. If one removes this correspondence it becomes a new variable on the calculation of the number of possible versions of the universe.
- Souls can be nothing special but just some combination of the properties indicated above like individuality and personality, among others that haven't been understood yet. That way, they could be like a particle or a group of particles each with its own current state and with each soul being a different particle or a similar particle in a different state. This would also just add a new set of variables to the calculations but wouldn't otherwise change much.
- Souls are actually unique individualities that cannot be copied or have different versions of themselves. If that is true there are probably no alternative versions of the universe with alternative copies of the creatures inside it. There can exist alternative versions that are different in more limited ways but all those changes imposed by some living creature do not create new versions. Each unique individual only exists in a single version of the universe at a time. With this option, full alternative versions can only exist if contradictions are possible inside such a reality. That way it would possible to for alternative versions of individuals to exist and not exist at the same time.
Classifying multiverses based on what type of universes they contain
These different types of alternative versions of universes can define different types of multiverses. One multiverse can contain a single universe with all its altverses of a given type while another multiverse also contains a single universe but with all its altverses of a different type. Other multiverse can contain several otherwise unrelated universes with all the altverses of a given type of each of those universes. And even another multiverse just contains unrelated universes without any altverses on it.
This also opens up the possibility of having multiple multiverses containing the same universe, maybe with each multiverse having the alternative versions of a given type for said universe.
It becomes possible to classify multiverses according to these definitions: a multiverse of type X(n) corresponds to a multiverse containing n unrelated universes and all the type X altverses of each of those n universes. So a type I(1) multiverse would contain a single universe and all its type I altverses while a type 0(∞) multiverse would contain an infinite number of otherwise unrelated universes and no alternative versions of any of them. It would be possible to have more complicated types of multiverses like I(10)/II(3) or whatever combination for a multiverse having 10 universes with all the type I altverses of those and another 3 universes with all type II altverses of those but this becomes confusing very fast.
- A multiverse containing a manageable number of universes inside it, all alternative versions of each other, either type I-a or I-b would work well for this example. This means that not all possible versions of the universe exist here, only an arbitrary limited set of them. Souls exist here and are unique but each soul expresses itself over all the multiple alternative versions of each body. Everyone has many versions of themselves across the multiverse, all sharing the same soul. The life energy of each person or soul is divided by all the versions of that individuality. This means that whenever one version dies, its part of the life energy is absorbed by the remaining ones, making them stronger, more powerful, just better in general. If anyone would manage to kill all alternative versions of themselves, they could become very very powerful, with different theories and beliefs about what could actually happen, from them becoming a godlike entity to the multiverse being destroyed.