But it illustrates a point: Objectively, there seem to be no hard rules to be violated. I have a hard time justifying a four-sided triangle, but it presumes that three is not identical to four. Pretty obvious, but is that true given no rules at all? — noAxioms

"contradictory statements cannot both be true in the same sense at the same time"
https://en.wikipedia.org/wiki/Law_of_noncontradiction

So if in one sense you mean wheels only as those on which the car currently travels and in another sense also as a spare wheel, your statement about the wheels is consistent. A contradiction arises only when something is asserted and denied in the same sense.

In arithmetic, four is not identical to three. It is the successor of three. So to claim that four is identical to three in the arithmetical sense is a contradiction.

So if all these outcomes exist, why do empirical measurements find more occurrences of the probable ones than the improbable ones? — noAxioms

The only reason I can think of is that the more probable outcomes occur in more worlds than the less probable outcomes. But I heard that this is still an unsolved problem in MWI because it is not clear how to calculate frequentist probabilities when there are infinitely many worlds. Maybe the number of worlds that split at a measurement cannot be infinite. Maybe a unified theory of QM and gravity will give the answer? (just my lay speculation)

The other solution is that some realities are more probable than others, and in the case of your proposed view, it means some things are more logically consistent than other things. This world exists more than the possible but more improbable ones. — noAxioms

I don't know what it would mean that some things are more logically consistent than others.

I don't know what it would mean that some things are more logically consistent than others. — litewave

I think the decay case can be swept under the rug saying there are infinite, but as many universes on one side of the half life as on the other. Mathematics supports at least that since all the positive reals (or rationals for that matter) on one side of any arbitrary division can be mapped to the reals on the other side. There are more little numbers than big ones, in that sense.

So the more worrisome case is the discreet ones like the measurement of spin along some axis. For a typical particle, that is a 50/50 shot, but for two particles, you get four outcome permutations. If the two particles are entangled, you can select the probability of correlation by the similarity of the axes between the two measurements. Nearly parallel axes means pretty much full correlation. So four worlds result from the two measurements, and they have probability of say 40, 40, 10, 10 percent. That is just four worlds, two of which are four times as probable as the other two. They all are logically consistent, so they all exist, but two of them seem to be more consistent. What does that mean??? It can't mean that there are 4 of one world and 1 of the other, since four of them would be identical, and thus violate the law of identity.

Yes, the physicists are trying to work that one out, and I suspect their answer is going to shed some empirical light on the whole ontology matter. The ontology of worlds within the one context of QM rules/logic is still a different from context-free ontology where there seem to be almost no rules, making me question even stupid things like why 3 is not 4. I think some axiom (something unproven) is needed to demonstrate the inconsistency of that.

It can't mean that there are 4 of one world and 1 of the other, since four of them would be identical, and thus violate the law of identity. — noAxioms

You can have copies of a world that are the same as that world. Their only difference would be their different position (place) in reality.

You can have copies of a world that are the same as that world. Their only difference would be their different position (place) in reality. — litewave

Worlds have positions?? Can I say which is left of the other? Can these four identical worlds be put in some kind of order?
You're assigning nonexistent differences to the same thing and contradicting your own definitions now.

Worlds have positions?? Can I say which is left of the other? Can these four identical worlds be put in some kind of order?
You're assigning nonexistent differences to the same thing and contradicting your own definitions now. — noAxioms

A space can consist of identical points, that is, points that are the same except for their position in the space they make up. Now imagine that the points are worlds - again, identical except for their position in the space they make up.

Worlds have positions?? Can I say which is left of the other? Can these four identical worlds be put in some kind of order? — noAxioms

If the worlds are supposed to exist in the same reality, and they are numerically distinct (despite having the same qualitative properties) from one another then I cannot see how that makes sense without saying that they occupy different regions of some kind. How they are distributed may be a problem to explain in detail, but it seems to necessarily be one that it has to deal with.

A space can consist of identical points, that is, points that are the same except for their position in the space they make up. — litewave

Physical space has no coordinate system except an arbitrary one assigned in an abstract way. Physical space sans matter is not space at all since matter defines it. One can define an abstract empty coordinate system with no objects in it, but our universe seems not based on such geometry.

Anyway, the issue once again can be broken down into simple abstract cases. Consider that a square seems to be distinct from a square in a coordinate system. A square is just a square, and as such all four sides and vertices are identical to each other. Sure, relative to one, there is a far one and two (again identical) other ones to either side. The far one is unique. But that is true of any of them, so they are all identical without the coordinate system. But if they're identical, the square has only one side and thus seems not to meet the requirement of being a square. So I am not going to push the issue. Four identical things are still in relation to each other and despite lack of coordinates, seem to be still four distinct things. A circle is worse, with an infinite number of identical points. Is there one point then without the coordinates? Well, there are relations, so no, they're not the same point.

So maybe our answer lies in here somewhere. The sides of the square are identical, and thus are one side, but it exists four times as much as center point of the thing.

Coordinates complicate matters, but simplify it in other ways. It gives the vertices of the square identities and makes them non-identical, but the assignment of the coordinates requires definition of A) an origin, B) the orientation of the X axis, and C) the sign of the orthogonal Y axis. In our universe, it seems that five things need definition. We need an origin point in spacetime, an arbitrary orientation of any three of the four axes, and the sign of the last one. Yes, the temporal axis can be arbitrarily assigned. If its orientation could be locally discovered by some empirical method, relativity would be disproved.

If the worlds are supposed to exist in the same reality, and they are numerically distinct (despite having the same qualitative properties) from one another then I cannot see how that makes sense without saying that they occupy different regions of some kind. — Mr Bee

Of some kind, yes. But the spatial relation that exists between the Earth and the Moon is not it, nor is it the temporal relation between an ice cube and that cube melted an hour later. Both those relations can be measured in linear terms and thus can be assigned meaningful coordinates. The relation between Earth and the Earth with the unicorns is not expressible in linear terms. It is a different kind of separation, not one that can be ordered or have distances like spatial and temporal relations.

I think 'Hilbert space' names the mathematics that describes this sort of relation, but it is not yet another linear dimension.

Of some kind, yes. But the spatial relation that exists between the Earth and the Moon is not it, nor is it the temporal relation between an ice cube and that cube melted an hour later. — noAxioms

Is it? We are talking about something related to physics which means we are dealing with something physical here. So it seems closer to say that these worlds, if they should exist, exist within a physical space rather than say the space of abstract ideas (not a Platonist myself or anything but I'm just saying). These parallel worlds could be said to exist in another dimension of space for instance, and not necessarily the dimensions that we are normally accustomed to either.

So maybe our answer lies in here somewhere. The sides of the square are identical, and thus are one side, but it exists four times as much as center point of the thing. — noAxioms

Or we can say that one abstract line is instantiated in four particular lines. The abstract line and the four particular lines are five different things.

[a relationship] Of some kind, yes. But the spatial relation that exists between the Earth and the Moon is not it, nor is it the temporal relation between an ice cube and that cube melted an hour later.
— noAxioms

Is it? We are talking about something related to physics which means we are dealing with something physical here. So it seems closer to say that these worlds, if they should exist, exist within a physical space rather than say the space of abstract ideas (not a Platonist myself or anything but I'm just saying). These parallel worlds could be said to exist in another dimension of space for instance, and not necessarily the dimensions that we are normally accustomed to either. — Mr Bee

I didn't say it wasn't a physical world. I said the relationship between this world and another one is neither temporal nor spatial. It can be said that exists in an alternate dimension, but that dimension is not of space, which nor is it a linear dimension at all. Linear dimensions can be measured and the events along them have the property of being ordered. Alternate worlds are actually still physically part of each other, sharing common events that lay outside the light cone of the quantum decoherence event that separated them. So if I perform some experiment that measures a decay and potentially kills a cat based on it, both the dead cat and the live one share the same Mars, at least for a while. Schrodinger's theoretical box prevented that light cone, and thus the two cats also shared a common Schrodinger, which is why it is meaningful to assert that the cat is both dead and alive.

They have made such boxes in the lab, but they don't look like boxes, and they can be used to do strange things like alter the past.

Or we can say that one abstract line is instantiated in four particular lines. The abstract line and the four particular lines are five different things. — litewave

My gripe was this violated the definition of identical. Worlds do not have coordinates, not even arbitrarily assigned abstract ones like you have with respect for space. They're quite identical and are not in different places.

The coordinates of a world (of an event actually, worlds don't have identities, but their events do) can be specified by listing the outcome of every quantum decoherence event in the past light cone of that event. If multiple-worlds are how the probability problem is solved, identical ones all have the same coordinates, and thus be truly the same world. I can arbitrarily assign different coordinates to the corners of the square, but there is no way to do that (even abstractly) with identical worlds.

I didn't say it wasn't a physical world. I said the relationship between this world and another one is neither temporal nor spatial. — noAxioms

I would say that any things that are differentiated from each other make up a "space" of some kind, in which they are differentiated from each other. So you could have a one-dimensional space of natural numbers, or a two-dimensional space of complex numbers, or a space where on one axis is the price of a product and on another axis is the demanded quantity of the product (the demand curve can be said to exist in such a space). Or if you don't want to use the word "space" in such a general sense, just use the word "collection", "set" or a "multiset". Multisets are sets that treat identical copies of their members as different objects.

I would say that any things that are differentiated from each other make up a "space" of some kind, in which they are differentiated from each other. So you could have a one-dimensional space of natural numbers, or a two-dimensional space of complex numbers, or a space where on one axis is the price of a product and on another axis is the demanded quantity of the product (the demand curve can be said to exist in such a space). — litewave

Every example above is a linear case. Complex numbers have magnitude and can be meaningfully added and subtracted from each other. I can add and subtract demand or price and say there is more demand for this than that.

Or if you don't want to use the word "space" in such a general sense, just use the word "collection", "set" or a "multiset". Multisets are sets that treat identical copies of their members as different objects.

This is better. No addition or subtraction is meaningful between two members. I didn't say space, but I said 'spatial'. The latter is a linear thing. Hilbert space is not linear, so 'space' is a more general term like this multiset, a term I had not heard before.

So our physical universe can be modeled by the set of all possible chess states where each state includes its history. The set is finite (there is entropy and thus a longest possible chess game), but beyond that the analogy is pretty good. There are two spatial dimensions, and it is meaningful to state the distance between two pieces (which make up the elementary particles). Time is measured in moves, and this forms a tree of legal states. Each move is like a quantum decoherence event and it creates a set of worlds. Once move X has been made, the world where Y was made becomes inaccessible. The coordinates of any particular state is simply the history of moves leading up to it, corresponding to the history of quantum events that led to event X (say me posting this comment). This space is not linear. It is not meaningful to reference the distance between a first chess position and a second one that is possible but not possible from the first position.

The chess analogy poorly illustrates weighted existence. All the legal states exist, and the introduction of favoritism of win/lose/draw states is required to model differing weight, and that model would not correspond to how QM works (I think), so it seems pretty pointless to explore that.