The Many-worlds interpretation of quantum physics

The Many-Worlds interpretation of quantum physics

From Absolute Indetermination to Relative Solipsism ?

The idea is to dismiss the reality of the collapse, consider that the deterministic evolution without collapse is all what happens, and admit a persisting coexistence of all possibilities in parallel worlds, in each of which things would only "look as if" the collapse happened.

Decoherence

For this, the physical measurement process is analyzed as an emergent macroscopic process called decoherence.
By applying the deterministic quantum evolution of physical states (without measurement) to the case of the measurement apparatus, we deduce that the systems, starting from a "clearly identified" initial state, naturally evolves into a very complex state of correlation with the environment. In an emergent manner, the higher and higher complexity of this entanglement involving larger and larger parts of the environment turns out to be irreversible, so that for all practical purposes the quantum state of the whole system (the measurement apparatus correlated with escaping parts of the environment) behaves as a classically probabilistic superposition of states expressing the possible measurement results, whose probabilities are exactly those that the basic axioms of quantum theory initially expressed on the system that was to be measured.

For details, see my texts :

The trouble with probabilities

The trouble is that, while the result indeed has the right mathematical structure of the expected probabilistic outcome, the ontological meaning of probabilities is lost: the different possible results keep coexisting, carrying weights corresponding to their "probability of being real". But, in this interpretation, there is no more such a thing as a fact of the matter, of which possibility becomes real. All possibilities remain real, so that the problem is to make sense of their "weights" and what can they have to do with the intuitive idea, or the experience, of probability.
These weights (values of the "probabilities" given by Born's rule) need to make objective ontological sense, in order to account for the objective experimental fact that measurement outcomes appear to follow (at least roughly) these probability laws.

A naive idea would be to try identifying the probabilities as the ratio of the numbers of resulting parallel worlds. This cannot work at all. First, because in many cases there is just a small number of possible elementary measurement results, while the values of their probabilities are arbitrary real numbers that have nothing to do with any counting of possibilities. Then, because the only thing that the number of copies of a given possible world really depends on, is the amount of time waited to let it split into more and more divisions before counting them. Clearly, it does not make any sense.

Another idea, followed by David Wallace, would be to develop a concept of subjective probabilities and "rational decisions" to be developed by individual minds in the worlds that split. Such arguments are doomed to remain purely circular and missing the point, as what is to be explained is not the process of a priori guesses that "rational agents", or rather serious students, would need to have correctly calculated in order to pass their exams of theoretical physics, but a posteriori factual observations.

No. In fact, there is a unique mathematically correct solution to this problem that remains faithful to the basic idea of the many-worlds interpretation, and it is very simple. The solution is to accept Born's rule as a postulate, reinterpreted in the absence of measurement, taking weights to mean "amount of existence" instead of "probability".
The problems to be discussed then, are purely philosophical:

Is the divisibility of existence an acceptable ontology ?

If "physical existence" was all what needs to be accounted for, and the heck knows what a concept of "physical existence" might look like and why it should matter, then there would be no problem to conceive physical existence as divisible like a quantity indeed.

The problem comes when trying to apply it to the case of conscious existence as defined by the Artificial Intelligence thesis of consciousness. This thesis says: "an individual has a conscious existence, if the operations of his brain happen to be physically computed".
The problem is, for the laws of physics operate, they must anyway fully and correctly compute what happens in every world that got a nonzero amount of existence, no matter how much this amount is. Therefore, the strict application of the AI thesis of consciousness would result in dismissing the role of the physical amounts of existence, in favor of an equal distribution of conscious existence to every different configuration of a mind that happens to be computed in any world that got at least a bit of physical existence. In this case the Born rule would break down, and would not fit with what we experimentally (subjectively) observe.

The logical solution, then, would be to modify the AI thesis in this way : "The amount of conscious existence of an individual, is defined as the amount of times that the operations of his brain happen to be physically computed".

This way, if there are 2 individuals A and B far away from each other, and if B makes any measure that splits his world into parallel copies but without anyhow affecting (informing) A, then A's total amount of conscious existence remains unaffected by this split: it is the same whether the operations of A's brain are analyzed as happening "once" with the initial total amount of existence it had before B's measure, or as happening "many times", once in each of the worlds resulting from B's measure, but each receiving only a piece of this divided existence (as defined by B's "measurement probabilities").

let us go further : should these "amounts of times" that a mind is computed, be only considered additive when occurring between parallel worlds, or can they also be counted as adding up in case the same computation happened to be repeated in different parts of the same world ?

In fact, if we tried the experiment by cloning A into an identical copy A' at some other place of the same world, then quantum fluctuations would "most probably" soon make this A' behave a little bit differently from A, in the exact same way as another version of A's behavior in some other branch of this continuously splitting world. Thus, since in each world A and A' are actually different while A' is only exactly copying the A of a parallel world, for which their existence had to add up, we clearly have to conclude that conscious existences must add up when they coexist in the same world too.

The shrinked neurons thought experiment

Now it is just a little step further to extend this to the times when A and A' remain identical in the same world (as unlikely as they might stay so any significant amount of time) : the amount conscious existence of a mind has to be counted not only as weighted by the existence of worlds containing him, but also as multiplied by the "amount of material stuff" that operates this computation in this world. And in the same way as a world's existence is quantitative (able of non-rational ratios) rather than counted by integers (numbers of occurrences), the amount of material stuff that operates a mind's computation to give weight to his conscious existence, should be counted as quantitative too.

Now, since distances between copies don't matter, it should not matter either if their locations come to coincide, each neuron of the one staying just aside its copy in the other. Now we get a method to force their behaviors to coincide : oblige each neuron of the one to follow its copy's behavior, as they stay aside each other. Finally, since the amount should be able to be quantitative rather than as a number of copies, we can simplify everything by replacing "2 neurons made to behave the same one aside the other", by "one bigger neuron behaving the same as if it had normal size".

This suggests to consider a new version of the quantum suicide problem, as follows :
Imagine a drug was found with the effect of shrinking the size of neurons, but without actually affecting their behavior. So if you take it, then for sure you don't notice anything, and (unlike in the original version of the quantum suicide problem), other people around won't notice anything either (they will see you alive and conscious just the same), except that, in fact, the size of your neuron shrinks, therefore actually reducing your "amount of conscious existence". For this reason, should this drug be labeled as "dangerous" as much as the quantum suicide experiment (entering the box with Schrödinger's cat) ?

Now, if you had to choose between going with Schrödinger's cat with a 10% risk of death, or take that drug that would shrink your neurons by 20% without any noticeable effect, what would be your choice ?
But, what if it does not shrink all neurons in the same proportions, but, for example, it affects some parts of the brain more than others ? You would need to study some scientific details of which parts of your brain are affected and how before taking a decision, would you ? But why did you never consider the need to make such studies any time before, to find out what kind of mental stimulations "really matter" as forms of happiness or sadness ?

Now, imagine the effect of this drug was temporary: your neurons will resume normal size after a few of days. Would it still have to be considered dangerous ? Or would it be just as safe as if you went for quantum suicide with a 50% risk of dying but a guarantee of being cloned a few days later otherwise ? Why not use it in guise of a method of anesthesia ?

Cosmological interpretation

To try answering the oddness of dividing existence into fractions, some proposed to reinterpret these divisions as those of the infinite number of occurrences of each possible local world in an infinite Universe, where anything than can happen actually happens an infinity of times. This way, the indivisibility of the existence of each individual occurrence is formally preserved in principle, despite the effective divisions of existence in practice. However it remains doubtful whether it is any real improvement : while physical systems can indeed exist in several identical copies in the same space according to the rules of quantum mechanics, identical copies of minds may still be considered philosophically problematic. Moreover it creates 2 new problems :

On the mathematical articulation between the structure of quantum measurement and the frequencies of occurrences throughout the universe : without reading their article (sorry) I'm skeptical of the possibility to make it coherent, unless of course real collapses are introduced, which drives us back to the initial problem instead of resolving it;
It does not fit with the properties of cardinals of infinite sets in mathematics.

The Many-worlds interpretation of the EPR paradox

Imagine a pair of entangled particles, that will be simultaneously measured, each in a specific way, by Alice and Bob, such that for each, the probability is 1/2 to find heads or tails, but globally there is only 10% probability that they get the same result.
So, Alice seeing her measurement result evolves into a superposition (or split) between 2 mental states : Alice-head and Alice-tail, with the same weight of 1/2 each.
In the same way, Bob evolves into a superposition (or splits) into 2 copies : Bob-head and Bob-tail, each with weight 1/2.

Then, Alice and Bob meet again.

Alice-head sees Bob in a superposition of states, composed of 10% of Bob-head and 90% of Bob-tail,
Alice-tail sees Bob in its remaining states, that is a combination of 90% of Bob-head with 10% of Bob-tail.
Bob-head sees Alice as in a superposition of states, composed of 10% of Alice-head and 90% of Alice-tail
Bob-tail sees Alice in a combination of 90% of Alice-head with 10% of Alice-tail.

Then, Alice tells Bob her measurement result.
For her this changes essentially nothing :
When Alice-head says "head" she sees Bob as deterministically evolving from the mixture (10% of Bob-head + 90% of Bob-tail), into the mixture (10% of Bob-head-head + 90% of Bob-tail-head) ; and similarly for Alice-tail who says "Tail".

But bob's experience here is a bit different :
Bob-head sees Alice's state collapsing from the undetermined state of (10% Alice-head + 90% Alice-tail), into either Alice-head (with 10% probability) or Alice-tail (with 90% probability); this splits himself between Bob-head-head and Bob-head-tail with these probabilities.
Meanwhile, Bob-tail sees Alice's state collapsing from the undetermined state of (90% Alice-head + 10% Alice-tail) as he saw her, into either Alice-head (with 90% probability) or Alice-tail (with 10% probability).

The state of the universe at the big bang and its minimal entropy

Let us describe in more details what is the form of the "reality" defined by quantum theory in its many-worlds interpretation, and how.
Basically, only one thing is absolutely real, that is the "universal wavefunction". It comes from the state of the Universe at the time of the Big Bang. In order for things to be mathematically well-defined as needed, this state of the Big Bang needs to be a "completely specific state", i.e. it must describe the contents of the spatial extension of the whole Universe of that time (or at least it must cover all our causal past, that is inside our past light cone, including what is hidden by the opacity of the matter that emitted the cosmological background radiation), in all details in a sense that quantum theory still allows :

either only one elementary state specified in "full details", with zero entropy
or an exactly defined classical superposition of many possible elementary states with definite probabilities, thus with a definite nonzero entropy (but anyway the entropy at the big bang is the lowest amount of universal entropy that ever happened).

More details, and how the idea of objection by the conservation of energy does not work, were moved to a separate page : Time orientation and the big bang

Consequences of the absence of individuality of quantum systems

Let us remember one of the fundamental properties of quantum mechanical systems (as proven necessary by the formalism of quantum theory) : they have no individuality ! They are completely "defined" by their state, that is, the configuration of molecules inside, and there is only a finite number of possible states for all systems with given limits of size and energy. If an individual is defined by his body, then there are only a finite number of "possible individuals" and they have no individual identity. Namely, if the same body happens to be identically repeated in several parts of the universe, then they are not "different individuals similar to each other" but they are the same individual. If it happened to me then the question "which of them am I ?" strictly would not make any sense. Instead, it would only mean that the configuration of the universe around me is undetermined and I am collapsing the state of rest of the universe (or equivalently, splitting myself into my different local copies) by looking at it. You might say that human-sized bodies are so big, with so many molecules inside, that the number of distinct possible bodily states is crazily huge, something like 10^10²⁷, which may be reduced "only" to something, say, in between 10^10¹⁵ and 10^10²⁰ states after adequate file compression, neglecting all insignificant fluctuations to which the body naturally "resists", and ignoring lots of "unrealistic body configurations". Thus, even if the universe is much bigger than the limits of our cosmological horizon, the chances for an individual to identically exist in several place-time locations are quite small. But...
Remember that we are in the many-worlds interpretation. Even if the chances of identical repetition of an individual seem quite unrealistic inside "one universe" in the one-world sense because it is "too small", they become much more significant when you multiply this by the number of alternative histories that could take place in parallel since the Big Bang, say, on a given planet (to not count an individual on a planet as split by random events happening on another planet). Concretely, no single brain can ever "remember" the whole evolutionary history of life on his planet. Therefore, it must be "compatible" with many such histories. Formally, the Many-worlds interpretation of quantum physics says that the past evolutionary history relatively to a given individual (especially one who is not a paleontologist), is largely undetermined.
Thus, as the role of the "absolute reality" of the universal wave-function (in its way of defining or "creating" specific realities), is ultimately reducible to its way of distributing respective weights ("amounts of existence") to all possible states (configurations) of biological systems as measured by their "total amount of connection" to the initial state of the universe (the big bang), we can notice that its computation of this distribution is quite strange and indirect : the weight it gives to each individual comes by adding up the weights of all possible evolutionary histories that may lead to it !
The same thing happens for the astronomical data relatively to an individual who is not an astronomer: the rest of the universe is in a state of indeterminacy, between many possibilities obtained by adding up the weights of all possible histories of the Universe corresponding to the different possible outcomes of quantum fluctuations that could occur shortly after the Big Bang, and that could lead to the same planet (or at least the same given individual no matter his planet) but with different "rests of the Universe".

How the universal wavefunction defines and distributes reality

Then, this universal wavefunction distributes partial "amounts of existence" between all possible individuals. The mathematical operation defining the measure of this existence, is a tensorial operation, that is a sort of dot product, bilinear with respect to these 2 data :

The state of the big bang (which defines the universal wavefunction)
The state of the individual. But it only needs to be conceived as a partial information, that is, some information about one's own body that needs not be exhaustive, and ignoring all what is outside the body.
Just like in any dot product operation, the product operation itself, which connects together both things to be multiplied, can be seen as a third object in the list of things that are multiplied. Here, this third object that multiplies both above states (the state of the universe at the big bang and the state of the individual), represents the shape of all the space-time between the big bang and the individual. This would make clear sense in the formalism of quantum field theory, where it can be summed up as the data of the space-time location of the individual inside the universe (with respect to the big bang), that is defined in the absolute independently of all the material content of the rest of the universe (leaving unclear, however, the question of its invariance with respect to a global shift of the whole content of the universe; at least this operation depends on the age of the universe). It looks less clear how things can be defined if this portion of space-time is curved by gravity in an undetermined way depending on the material content in between : quantum gravity may be required to make sense of this. The simplest approximate guess we can make here (the classical limit), is that the total thing we need to insert as making up the whole operation of probability computation, looks like the sum of all contributions from the different possible space-time shapes between the big bang and the individual (thus including a sum over all possible ages of the universe), with of course the risk for this to diverge (after all, the occurrence of an infinity of copies of an individual, gives him an infinite amount of existence !).

But apart from this necessary difference between the full definiteness of the state of the big bang and the partial definiteness of the state of the individual (and of course that these states look very different), the product operation between them looks perfectly symmetric (by time-reversal).

Let us point out the natural ontological meaning of tensorial operations : the multiplication means the coexistence of things in different places of same universe, while the addition means the list of alternative possibilities for the same object, that exclude each other ("existing" in parallel bits of universe excluding each other, to be alternatively glued at the same place of the universe). Concretely, this appears in probability operations : we have 2 individuals, A that may be in state A1 or A2; and B that may be either in state B1 or B2. The total probability for A to be in state (A1 or A2) is the sum of their probabilities, while the probability to have ((A in state A1) with (B in state B1)) is the product of their probabilities, if they are not correlated (if they are correlated it also comes from a tensorial product but involving vector spaces with more dimensions than the simple product of numbers...).

Correlations between experiences or parts of memory

If I exist, then I have the same feeling of existence no matter what "amount of existence" the universe gave me, so, what difference does it make for me ? Directly, not much. However, the laws of physics have 2 effects on me : one for my past which I could verify, and the other for my future, which I can predict.

As for the past, it concerns the correlations between my past perceptions. This can be equivalently expressed in 2 ways :

The immediate correlation that I can find now between the different parts of my memory, assumed to be a material memory. It is is computed exactly as above, where the state of my brain (thus my memory) contains all this information, thus contains the tensor product between these bits of memory.
The correlation between my past experiences themselves, that is, the states of sensorial perceptions I had at the different times of the past, provided that I remember them (I have the information about them in memory). Again the operation is multilinear with respect to these different perceptions, but taken as inserted in the space-time locations where they respectively occurred.

So, the laws of physics define a probability law between all possible combinations of perceptions, that is, a distribution of amounts of existences between them.
The effect of this, which I can verify, is that my experience is "not too untypical" with respect to this law.

The relative existence between objects or individuals, and "probability predictions".

The next thing of interest I can get from the laws of physics, is the state of the universe, or more concretely, the state of some specific object A (in the sense of the "probability distribution" between the possible states of this object), no more in the absolute as above but relatively to me. It is defined as follows:

(Probability for A to be in state x relatively to me) =

Amount of existence of (me with (A in state x))
my amount of existence, ignoring anything else

Indeed the mathematical structure from which the amounts of existence are calculated from the universal wavefunction, as defined above, ensures that the sum of the "probabilities" so defined for all possible states of A, equals to 1 (i.e. the sum of amounts of existence of me with each possible state of A, equals my amount of existence ignoring A).

Now the question is, how can these quantities so defined, be of any interest to me, so that I can meaningfully call them "probabilities" event though the Many-Worlds has no true probabilities but only a distribution of amounts of existence ?

Answer : Insofar as I'm going to measure A, the next versions of myself with the additional memory content expressing each possible result of this measurement, are going to get the respective shares of my current amount of existence, as defined by these "probabilities" of states of A relatively to me.

However, the real amounts of existence of these possible future states of myself, might still differ from these shares (namely, exceed them), in case I would lose a part of my memory in between, letting me coincide with other versions of myself where the state of this lost part of memory was different (thus adding up the amounts of existence of the initally different versions of myself, in a common pot). Anyway I won't notice any effect from this fusion :) and, rationally speaking, I don't have to care.

Where is time gone ?

However, this leaves a big unknown : what is time, finally ? Is time anything else than a space dimension among others ? If there is "going to be" a next version of myself, that is, with some more experiences and that will receive "some amount of existence", in which meaningful sense can it be said that : "that will still be me" and "that is my future" ? Or equivalently, how can the past experiences that I remember, be said to be "my experiences" and "past to me", if all there is, is... just different possible states of people getting diverse amounts of existence, all in bulk ?

Relative Solipsism

The notion of "how are things relatively to me", actually constitutes another wavefunction of the universe, aside the universal wavefunction that was mentioned above.

Let us call it "my universal wavefunction". It is defined as follows (where "me" means more precisely "me now", i.e. without time extension):
To every object A (space-time location defined relatively to me) that is outside my past cone (i.e. it is either in the future or independent of me), it gives the state that is "the state of A relatively to me" which we defined above.
This indeed has all the properties of a wavefunction, in the sense that it satisfies the same law of evolution (Schrödinger equation) as the universal wavefunction that was mentioned above. In order for this to be the case, the above definition had to be restricted to the A that are outside my past light cone, so that the operation involves A only by its past light cone and not by its future light cone. Precisely, it is operated by (only depends on) the region of space-time that is the union of both past light cones of me and A, by which these 3 things are connected: me and A at the future ends of the region ; the Big Bang at the past end of the region.

But then I can also extend my universal wavefunction to my space-time neighborhood including my past, by taking the part we just defined and applying the Schrödinger equation to rebuild the rest; even if it does not coincide with some more directly definable and meaningful result. For example, if I measured an object (such as a spin) successively in 2 ways, and from the first measure I deduced that the second measure necessarily had probabilities 50% to give either result, and I got one of these result, then (due to the time-symmetry of the Schrödinger equation) my universal wavefunction gives 50% chance for the first measurement result to have been what it was, which is absurd since I know what it was. However such reasonings are dubious anyway, since it can be absurd to claim applying the Schrödinger equation backwards when describing processes that are seen at the same time as thermodynamically irreversible, such as measurement processes.

Precisely, my universal wavefunction differs from the universal wavefunction, as it replaces its initial definition (the state of the Big Bang that was taken as origin of space-time) to be extended to its future by the Schrödinger equation, by the following :

Integral for all possible intermediate shapes and contents of space-time with all possible relative positions and speeds (or possible space-time shapes) between me and the Big Bang, of
(The wavefunction of me here now at rest, multiplied by the state of the Big Bang regardless "however long ago at whatever speed")/(my amount of existence)

Note that:

While I can afford to leave the time of the Big Bang (age of the universe) and its speed (relatively to me) in that state of indetermination, I still cannot ignore it altogether, otherwise (without assuming the past to have had lower entropy than the present) it would not let me define any wavefunction at all (attributions of probability distributions to states of things relatively to me).
My universal wavefunction differs from The universal wavefunction, by these properties:

According to My universal wavefunction, almost everything is undetermined, except Me; and there is a nonzero probability for the universe to have started by some big bang (as certainty here would be incompatible with the definiteness of my own state).
According to The universal wavefunction, everything except the big bang was in an even much worse state of indeterminacy.

Reference of a related thought experiment : The Information Argument

Where is Reality gone ?

Finally, the many-worlds interpretation itself suffers the exact same problem as the Bohm interpretation, only with a different choice of "physical pointer":

Bohmian mechanics takes the hidden variables as the pointer (arbitrarily given from nowhere) that defines which world "physically exists" inside the many-worlds landscape, but this specific world (given by the values of hidden variables) still depends on the structure of the many-worlds (that is, the wavefunction, that "contains" all its other possible worlds) for expressing its law of evolution.
Everett's many-worlds takes the universal wavefunction as the arbitrary pointer that defines the "physical existence" of a specific many-worlds (a specific distribution of amounts of existence between all possible worlds or organisms) inside the Hilbert space, but the law of behavior (Schrödinger equation) of this specific wavefunction, still depends on the structure of the whole Hilbert space, with all its other elements (that are other wavefunctions) implicitly required to somehow also exist. There is no objective reason to consider some specific wavefunction in that space to be more real than other wavefunctions, such as, for example, my universal wavefunction.

Any temptation to see a theological interpretation in the structures of the above reasonings (that naturally came, let us remember, as logical consequences of trying to interpret the physical world in the absence of any fundamental role of consciousness), may be, after all, not a purely fortuitous coincidence. Indeed the Mind makes collapse interpretation will give this "coincidence" all its meaning.

Related texts by other authors

Not explicitly about many-worlds but about very related metaphysical concepts:

References about many-worlds

The Interpretation of Quantum Mechanics: Many Worlds or Many Words ? (with a small poll of opinions from University of Maryland Baltimore County, 1997)

The Emergent Multiverse: Quantum Theory according to the Everett Interpretation by David Wallace (2012)

‘Many Worlds? Everett, Quantum Theory and Reality’, edited by Simon Saunders, Jonathan Barrett, Adrian Kent and David Wallace (2010) (see reviews on the site).
Many worlds: quantum theory and reality? review by Iñaki San Pedro
Review by Jeremy Butterfield