Encountering the Many Worlds Interpretation
Several years ago, I looked into the Many Worlds Interpretation (MWI) of quantum mechanics and concluded that it was not on the right track. It seemed to be creating more conceptual and technical problems than it solved. However, I frequently come across mention of it in the physics literature and in documentaries. Several leading scientists refer to it as a ‘viable’ alternative to the canonical Copenhagen Interpretation (CI); some even calling it the ‘preferred’ interpretation. So, I recently decided to take another look at the MWI. Perhaps there was something I missed, or something important that I did not understand on the first go-around.
My initial instincts have been validated. Reading about the MWI, including papers by its proponents as well as by its detractors, reminded me of the Hans Christian Andersen story called The Emperor’s New Clothes. The Emperor and his ministers believe the hype about a fabric that is allegedly invisible to anyone who is unfit for their position. They pretend that they can see the fabric so as not to feel left out. While the Emperor is parading naked through the town, believing that he is wearing the best suit of clothes, a naïve young boy blurts out that the Emperor is naked! Perhaps I can be that naïve young boy when it comes to untestable ideas like the MWI. I may not be young, but bear with me.
So what is the Many Worlds Interpretation?
As advertised, the main advantage of the MWI is that it solves the measurement problem. I discussed the measurement problem in two previous posts: Quantum Weirdness: The unbridled ability of quantum physics to shock us and Contrary to Popular Belief, Einstein Was Not Mistaken About Quantum Mechanics. The measurement problem results from the apparent need for two distinct processes for the evolution of the state vector: (1) continuous and deterministic evolution according to the Schrödinger equation when no one is looking, followed by (2) spontaneous non-unitary evolution, or collapse, of the state vector upon measurement of an observable. What constitutes a measurement and the dynamics of wave function collapse are not defined in the CI. Additionally, special status is assigned to an intelligent observer who is treated as being outside the quantum system.
As an added bonus, proponents of MWI claim that it enables independent derivation of quantum probability distributions without assuming the Born rule. The Born rule for computing the probability of potential outcomes of a quantum event is an additional postulate of canonical quantum mechanics. According to this rule (which has enjoyed phenomenal experimental verification time and time again throughout the past roughly ninety years), the probability for each potential outcome to become the realized outcome is given by the amplitude squared from the applicable terms in the state vector.
Hugh Everett developed the relative state formulation in his dissertation and his subsequent publication of “Relative State” Formulation of Quantum Mechanics (also available at this link). It was later given new life by Bryce DeWitt in 1970, with his work applying rational decision theory and game theory to quantum mechanics; see Quantum Mechanics and reality. Since then, dozens of papers have been written attempting to patch holes in the theory, or to take it apart.
See the recent article by Sabine Hossenfelder, “The Multiverse is not a paradigm and it’s not shifting anything” for another perspective on multiverses in general.
The MWI hypothesis avoids the measurement problem by assuming that wave function collapse never happens. A single result never emerges from an interaction or quantum measurement. Instead, all possibilities are realized. Each possibility is manifested in a new branching universe. With each observation, measurement, or interaction, the observer state branches into a number of different states, each on a separate branch of a multiverse. All branches exist simultaneously and each branch is ‘equally real’. All potential outcomes are realized, regardless of how small their probabilities.
What is wrong with the Many Worlds Interpretation?
If you have read my earlier post Three Roads to What Lies Beyond Quantum Mechanics, you have already glimpsed my discontent with MWI. You will find statements in the literature that claim MWI solves the paradoxes of the CI, and that it derives quantum probabilities without the use of an ad hoc assumption (as in the case of the Born rule in the CI). Hugh Everett’s main goals when he gave birth to the ‘relative state formulation’, which subsequently became known as the MWI, were to get rid of non-unitary wave function collapse and to relegate the observer to just another part of the quantum system. Unfortunately, MWI and its many variants does not live up to the product’s claims.
The MWI hypothesis requires an unimaginably large, perhaps infinite, number of universes, each spawned essentially instantaneously in a fully evolved state from it’s parent. Your present universe is constantly branching, sprouting multiple universes at a fantastic rate. Each new universe is identical to its parent IN EVERY WAY, except for the record of a single quantum event. I don’t just mean in one you are the Queen or King of your senior prom, and in another you decide not to run for prom royalty. Every quantum interaction, every quantum measurement, a countless infinity of which happen every day in what we conventionally call the universe, leads to multiple new universes.
According to Bryce DeWitt in Quantum Mechanics and reality,
“…every quantum transition taking place on every star, in every galaxy, in every remote corner of the universe is splitting our local world on earth into myriads of copies of itself.”
Cloning and quantum teleportation Star Trek-style should be a breeze if quantum mechanics allows cloning the entire universe a countless number of times each second! This may make for interesting and fun science fiction, but without testable predictions it is not physics.
This multiverse evolves in a continuous and deterministic way. The apparent randomness that an observer in a particular universe (branch) perceives is in his/her mind; a consequence of the particular branch he/she finds him/herself in. The emergence of macroscopic uniqueness, a consequence of state vector collapse in the CI, is just an illusion in the MWI. That sounds like progress, right? But wait.
The different branches are incoherent; they do not interfere with each other and observers in one branch cannot detect the existence of any of the other branches (this is the “no-communication” hypothesis). The wave function collapse hypothesis has been replaced by the no-communication hypothesis. Quantum decoherence has been used to justify and explain the no-communication hypothesis, with varying success. But, it has also been used to justify and explain the wave function collapse hypothesis. So there is nothing gained here by postulating a countless number of universes branching out from all of the interactions occurring throughout our universe.
As John Bell stated (while writing about the MWI, see p. 133 of Speakable and Unspeakable in Quantum Mechanics):
“Now it seems to me that this multiplication of universes is extravagant, and serves no real purpose in the theory, and can simply be dropped without repercussions.”
Probabilities in the Many Worlds Interpretation
Everett sets out to show that the Born probability rule can be derived from within his model, as opposed to having to assume it. He does this by assuming that the square of the amplitudes (from the state vector, same values that the Born rule uses) represent the ‘measure’ that should be assigned to each of the branches. When an observer repeats the same experiment a large number of times, multiple branches appear corresponding to each of the possible outcomes for each performance of the experiment. A particular observer will traverse a particular series of branches out of all the possible combinations of outcomes from all the trials. By applying his weighting scheme, Everett shows that, in most cases, the observer is part of a branch where the relative frequency of the observed results agrees with the Born rule.
What exactly does it mean for different branches to have different weights, if each and every branch is ‘equally real’? Are we to assume that the number of realizations of branches associated with a particular outcome of a particular measurement or interaction is proportional to the branch weight? You may naively think that the probabilities of various outcomes should be related to the number of branches with that outcome (a simple counting measure). What would then happen if the probability was an irrational number? Combinatorial methods fail. Even if you could use simple combinatorial methods, many observers would see outcome distributions that conflict with the Born rule. The Born probability rule has been validated in countless experiments over the past 87 years. Why have we never witnessed a deviation from it in any of the uncountable combinations of branches we have traversed to get where we are today?
In Everett’s theorem, the observer is considered as a purely physical system. This is a central part of his relative state formulation. The observer is just one subsystem in the overall system under consideration. Once one state is chosen for one part of the overall system, then the rest of the system is in a relative state; state X given that the one subsystem is in state Y. This was, initially, an advantage of the MWI compared to the CI. However, attempts to patch some of the holes in the theory have relied heavily on rational decision theory and game theory, thrusting a conscious observer back into the spotlight.
Throwing in Rational Decision Theory and Game Theory
Unfortunately, Everett’s approach to deriving the Born rule has been taken apart due to its use of circular reasoning. David Deutsch used decision theory and game theory to derive the Born rule; see Quantum Theory of Probability and Decisions. He demonstrated that if the amplitude squared measure is applied to each branch, then this value is also the probability measure for those branches. He did this by arguing that it represents the preferences of a rational agent. He considered the behavior of a rational decision maker who is making decisions about future quantum measurements. By rational, he meant that the decision maker’s preferences must be transitive: if he/she prefers A to B, and B to C, then he/she must also prefer A to C. (On a side note – many psychology studies have shown that personal preferences of so-called rational agents in the macro world are often not transitive).
According to Deutsch, if a rational decision maker believes all of quantum theory with the exception of assuming a probability postulate, he/she necessarily will make decisions (behave) as if the canonical probability rule is true. I am not an expert on decision theory, but it seems to me that the strategy chosen by Deutsch’s rational observer is not unique; it just happens to be the one that correlates with the desired end point – the Born probability rule when the amplitude squared values are used as branch weights. Additionally, if you accept Deutsch’s reasoning, methodology, and assumptions, I should think his results could equally well be used to demonstrate why the Born probability rule works in the CI, as well as in the MWI.
Attempts to Make it Consistent
Many attempts to formulate a consistent and defensible version of Everett’s initial ideas have been discussed in the literature since Deutsch’s work. Adrian Kent addresses many of them in One world versus many: the inadequacy of Everettian accounts of evolution, probability, and scientific confirmation. Kent points out some of the inconsistencies and contradictions that these attempts fall victim to, either when compared to each other or within themselves. Given that every potential outcome is actually realized in a branch, regardless of likelihood, a rather tortured path has to be taken to explain the meaning of probability and uncertainty when applying decision theory. Additionally, Kent is concerned by the lack of uniqueness in the assumptions and conclusions that can be made about the so-called rational decision-maker. To apply decision theory or game theory reasoning to quantum mechanical events seems rather surreal to me. But regardless of whether you take the approach seriously, there is little gained from it, unless you want to get extremely metaphysical about the role of consciousness. Which I do not.
So Where Does This Leave Us With Respect to the Many Worlds Interpretation?
“…no matter how high you pile considerations upon nothing, and extend the boundaries of nothing, to nothing it must come at last”
Writings and speeches of Alvan Stewart, on slavery. Ed. by Luther Rawson Marsh. Stewart, Alvan, 1790-1849., Marsh, Luther Rawson, ed. 1813-1902.
The MWI does not deliver on its promises. In particular, it does not solve the measurement problem unless you ignore the extra baggage that comes with the theory, such as the no communication hypothesis, the song and dance concerning rational decision theory, and the surreal role of the observer. Nonetheless, the idea of countless multiple universes has mesmerized popular culture and theoretical physics. The image of an infinite number of copies of ourselves, with slight variations in each universe, is quite tempting. Some people claim that multiverses must be real because we are getting hints of one from multiple theories, including superstring theory, inflationary cosmology, and anthropic reasoning. But each of these predictions are perched upon a mountain of assumptions. And each posits a different cause for the multiverse. It is not at all clear to me that satisfying the multiverse hypothesis of one model would necessarily satisfy that of the others.
The idea that the MWI is the only viable alternative to the CI is a myth. Other viable alternatives already exist; and it is premature to assume no one will ever discover another. These alternatives, such as de Broglie-Bohm mechanics and the Transactional Interpretation, need more work. But at the very least, they serve as proof of concept that we should not be so eager to believe any wild idea offered to us, without evidence. So, if you come across someone endorsing the Many Worlds Interpretation of quantum mechanics, remember the story of the Emperor’s New Clothes. Let them know that you are aware the emperor is naked. MWI does not provide a unique and independent derivation of probability, it does not remove the special treatment of the observer, and it replaces the collapse hypothesis with run-away multiverse branching and the no-communication hypothesis.
My upcoming posts will include:
- Discussion of hydrodynamic quantum analogues. These experiments demonstrate how phenomenon and probability distributions normally associated only with the quantum world can be produced by macroscopic systems and classical dynamics.
- So-called weak measurements that are allowing physicists to directly measure the quantum wave function itself, and monitor its evolution.
- Introduction to de Broglie-Bohm mechanics. Incidentally, wave function collapse does not occur in de Broglie-Bohm mechanics, and it does not require an infinite number of universes (just empty waves…).