Alternatives to the Multiverse
Many interpretations are vastly more appealing, if only we can understand them.
Nobel laureate, Steven Weinberg, at my alma mater the University of Texas at Austin, in 2017 published an article called “The Trouble with Quantum Mechanics” in which he laments the lack of a clear interpretation of quantum mechanics. This is, as he says, a debate that has been raging for 100 years with no signs of stopping.
The problem is simply that the current mathematical formalism of quantum mechanics and quantum field theory includes no model or indication of how measurements arise from the predictions of the theory. Rather the theory presents us only with probabilities based on a wavefunction state vector. To quote Erwin Schrödinger, describing a radioactive decay experiment,
the emerging particle is described … as a spherical wave … that impinges continuously on a surrounding luminescent screen over its full expanse. The screen however does not show a more or less constant uniform surface glow, but rather lights up at one instant at one spot ….
There are a handful of interpretations of this phenomenon. These can be classed into complete and incomplete interpretations. Complete interpretations are those that say that the quantum wavefunction is a complete description of a quantum system. Incomplete interpretations are sometimes called hidden variable theories. Albert Einstein favored these.
I have written several articles (see the end of the page for links) on the simplest incomplete interpretation: Bohmian mechanics.
In this article, I want to spend some time talking about complete interpretations. The multiverse or Many World Interpretation (MWI) of quantum mechanics can be considered to be a complete interpretation. The so-called “wavefunction collapse” or Copenhagen interpretation of Heisenberg is also a complete one.
In the last 40 years many more sophisticated interpretations have been developed, many of them with almost no exposure outside their small communities. This has given the impression to both scientists and the public that MWI is much more dominant in science than it is. For those who study interpretation theories, it isn’t even a strong competitor.
First, let’s talk a little bit about how measurements in quantum mechanics work. The thing you measure about a quantum state like the position or momentum of a photon, a particle of light, is called an observable. The observable for a particle is divided into several probable observations, any of which may be measured. Before a particle is measured, it exists as a wavefunction state vector which evolves in time. The wavefunction contains each observation in what is called superposition, meaning it can contain many observations at once. These can be contradictory observations in superposition such as the particle being in different locations at once.
When we make a measurement, the wavefunction is radically altered to become one, and only one, of the contradictory observations of the observable. This is called the postulate of wavepacket reduction or WPR and is what Herr Schrödinger is talking about quoted above.
Schrödinger’s equation that governs the evolution of the wavefunction works fine when we don’t measure things but as soon as we do it is completely violated. It is not random like the measurement, and it does not model WPR. Thus, the primary equation we use to model quantum mechanics doesn’t actually apply to measurements. It doesn’t matter if you switch to Heisenberg’s equivalent equations either. Measurement appears to be outside the scope of quantum mechanics.
Therefore, quantum interpretations are methods of attempting to restore or resolve this violation of quantum theory.
Since we want to talk about alternatives to the MWI, let’s talk about the logic behind interpretation theories. Quantum mechanics makes two basic assumptions:
The quantum mechanical wavefunction is a complete description of a quantum “microsystem” such as a particle.
Interactions between measurement apparati (including lab equipment and people), i.e. macrosystems, and microsystems are governed completely by Schrödinger’s equation.
Suppose we have a wavefunction that has two states in superposition, which we know can be prepared in the lab, such as vertical and horizontal polarization of light. Schrödinger’s ensures that, when they interact with a piece of lab equipment, they put the lab equipment into two superimposed states as well.
That we do not observe those two states but only randomly observe one exists nowhere in the quantum theory.
Some have taken issue with the reasoning above, arguing that macroscopic objects are too complex to interact with microscopic particles in a simple way and that the surrounding environment must also play a role. Surely that would be sufficient to collapse the wavefunction.
It turns out, however, even taking all these considerations into account in a very general measurement scheme that includes the entire universe, you still get superpositions of macroscopic objects as long as your measuring equipment is reliable enough to clearly distinguish the two states in superposition.
Thus there really is a missing link between what quantum mechanics says happens and what we observe to happen.
You have three options to deal with the problem:
Violate assumption #1 and expand beyond the wavefunction to hidden state variables as Bohmian mechanics does.
Violate assumption#2 and expand beyond Schrödinger’s equation.
Keep both assumptions and reinterpret what the wavefunction means.
You can read my other articles for my take on #1. In this article, we are only talking about #3. I’ll talk about #2 in a follow up.
If you take this route, there are three possibilities:
Reinterpret what you can observe.
Reinterpret what properties a wave function has.
Reinterpret what we perceive.
Let’s talk about each.
Specifying what can be observed
Superselection
One class of theories is called superselection which suggests that we cannot distinguish quantum superpositions of states from classical mixtures of states. This is either because quantum mechanics really limits what we can observe that way, which is unlikely, or because it limits what macroscopic observers can observe, which is more likely.
It is important, in this approach, to understand what a quantum vs classical state is. A quantum superposition of states is a single state containing two observations, meaning that it is both those observations at once, not one or the other. In fact, it is one or the other with 0% probability and both with 100% probability. A classical statistical mixture of states is one where the state is one or the other with some probability, e.g., 50/50, not both, but we don’t know which. So the states are “mixed” until we look. Thus, the classical state can be 50% one or 50% the other, but 0% both.
Superselection says that we cannot, in practice, distinguish the superposition state that is both from the mixed state that is 50/50. This method, therefore, suggests that if a particle that is in a superposition of vertical and horizontal polarizations hits a detector it puts that detector into one consistent with vertical or horizontal polarization. We cannot observe the detector in a pure superposition of states even if it is in that state because of what are called superselection rules which govern what we are allowed to observe.
Although superselection enjoyed great popularity in the past, it suffers from a major drawback in that it cannot specify why the same exact wavefunction would appear as either one or another mixed state while retaining its full superposition. So this approach doesn’t really answer the mail as far as interpretations go.
Specifying what properties a system has
Modal Interpretation
The modalist says that quantum wavefunctions have two states:
Their dynamical state that defines what may be true and evolves with Schrödinger’s equation
Their value state that defines what properties they actually have.
This is not unlike hidden state models but, unlike those, the hidden state is not modeled by an additional function but exists in the wavefunction statevector itself. From there, you can get into many different mathematical ways of showing it, but basically it suggests that the wavefunction contains both what may be true and what is true and that these evolve with time.
It is hard to differentiate modal interpretations from hidden variable theories and so while it is technically complete it lacks some ideal features of completeness. Consider that a modal interpretation requires you to accept that in two different experiments the exact same wavefunction statevector can have two different values. This seems like slight of hand to me and has a similar problem as superselection.
Consistent (Decoherent) Histories
This approach also fits into the limits on properties box. Its inventor calls it “Copenhagen done right” and shows that there is no measurement problem at all.
The histories approach says that the universe is fundamentally random and provides histories of particles that are both consistent with Schrödinger’s while obeying classical rules of probability.
Basically, histories are like moving pictures that you assemble from snapshots of particles and experimental measurements (anything really) at different times. These snapshots can be organized into separate sequences called histories based on the consistency of the snapshots with one another.
You can think of this as like a big stack of photographs. Each photo describes part of a story. Histories says you can put all these photos into consistent stories based on certain rules. Each history has a probability associated with it. In this sense, it is a generalization of the rules of classical mechanics which only tells one story with certainty. Histories takes into account that a wavefunction can have properties that contradict one another and resolves it by snapshoting out the different properties randomly.
Unlike modal, MWI, Copenhagen, and others, the histories interpretation places no special emphasis on the role of measurement. Rather, measurement is simply a way for a scientist to determine what history has unfolded and jump into that history.
The key rule in the histories approach is the choice of a framework. You can think of a framework as like a sack of balls of different colors. Each ball is a history (a sequence of states at different times.) Choosing the sack is like how you choose to set up your experiment. Once you’ve chosen your sack, you must choose balls (histories) from that sack. Choosing a ball out of your sack is like making a measurement (or choosing not to make one). You cannot choose balls from different sacks and mix and match them. That is, you cannot take one experimental setup and apply the results from it to those of another experimental setup, unless the two setups are similar enough to fall into the same framework.
This is not something that you have to deal with in classical physics which has only one framework.
The histories approach resolves quantum paradoxes such as Schrödinger’s cat. There is no framework where the cat is both dead and alive. What you are doing is mixing incompatible frameworks (sacks of balls) which is not allowed. There are sacks where the cat is dead or alive but none where the cat is both dead and alive. The theory says these are incompatible in a framework. Instead, what you can say is that if you observe a particular outcome, such as the cat is alive, then you can infer that the quantum particle was not in a state such as to trigger the poison.
Unlike MWI, histories never suggests that there are multiple coexisting realities. Rather, the universe continually chooses what reality is at each moment in time randomly, selecting out properties whether we observe them or not. You are free to choose a framework within which to interpret measurements you make of the universe, but that is more like a point of view, not a set of realities.
Unlike superselection, as well, it provides real mechanism for translating from quantum superpositions to classical mixtures that doesn’t restrict what can be observed. Instead, it restricts what properties are there.
Of all interpretations, I think this one is closest to what Niels Bohr, one of the founding fathers of quantum theory, wanted in his interpretation because it is essentially a relativity-like theory for quantum mechanics. So I would agree that this is Copenhagen done right. It was introduced by Griffiths in 1984 and continues to have a strong following. There is a non-mathematical book on it called Quantum Philosophy by Omnès.
Specifying what we perceive
If we don’t limit what can be observed or what properties that things can have, then we have to limit our own perceptions. This is literally a more subjective point of view. It says the universe is exactly as Schrödinger’s says it is and that we somehow get caught up in that evolution when we make an observation.
There are two basic approaches to this: the well-known MWI and an alternative called the Many Minds Interpretation (MMI). The MWI says that the entire universe splits when an observation is made that is inconsistent at the macroscopic level. This gets into the same problem as other “shifty” interpretations that suggest that some shift happens when a measurement is made. As mentioned above, the histories approach does not suffer from this problem.
The MMI is a stranger form that suggests that there is only one universe and that our minds actually split when a measurement is made. So one mind observes one outcome and the other observes another. The universe, meanwhile, continues to have many superpositions of states and never splits. This interpretation suggests that our minds force us to view the world in some sort of consistent way and that the inconsistency of observation causes our minds to split.
Thus, our split minds experience an increasingly diverse set of realities, even ones where we die, but all of these are contained in one complete universe. Why our minds have such a need for classical consistency is not clear. This would have to be a property of consciousness itself.
Those who study quantum interpretations do not take these two very seriously because they are so radical, and they are inherently subjective because they explain the measurement problem as a property of the subject’s perception (you, me, or the apparatus). Also they don’t solve some of the other problems that quantum interpretations should solve like the micro-macro shift problem. They are more popular among non-experts, probably because they are so easy to understand while the others are couched in dense mathematics and jargon.
Which one is correct?
Hidden variable models like Bohmian mechanics are appealing because they present the world in a more intuitive way. Unfortunately, quantum mechanics severely limits our ability to assign specific properties to particles, so Bohmian mechanics gets around this by explicitly modeling what we measure and the wavefunction separately. The mathematics for this is simple to present but ugly to try to solve since the Q function, which represents the hidden particle positions, has to be inserted into the wavefunction to solve for it. It also is nonlocal and dealing with relativity has been a major challenge.
The most irking aspect of it for me is that the hidden particle positions appear not to influence the wavefunction at all, which cannot be true since they represents the reality we observe. Somehow that has to loop back around. It cannot be a one-way street any more than Einstein’s theory of gravity is. In that theory, matter tells space how to curve and space tells matter how to move. Why would Q not tell the wavefunction how to evolve? The mathematics is silent on this point.
Of the completeness approaches we’ve looked at, the histories approach is probably the most convincing philosophically. It does introduce some new mathematics because it has to specify rules for frameworks and consistent histories, but it doesn’t challenge the completeness of the wavefunction or of Schrödinger’s. It also doesn’t have the micro-macro shift problem that most completeness interpretations have. Objections to it (that is it logically inconsistent) have been soundly addressed by Griffiths, so it is hard to point to specific issues with it. It does say that God plays dice with the universe. In fact, it is fundamentally random. It also does nothing to address the anthropic principle. We are here because random histories were selected that put us here. On the other hand, one of the bonuses that I didn’t cover is that it solves the nonlocality problem in that it is a local theory and doesn’t require instantaneous (faster than light) communication. Most other quantum theories have faster than light communication built into them.
Science proceeds by experiment so it is hard to distinguish different interpretations at this point. All we have to guide us is philosophy and the soundness of arguments in favor of one or the other. Someday we may find that an even better idea comes about that puts all these questions to rest by evidence.
I do not believe in the multiverse, the case for realism
The multiverse, the idea that the universe is constantly splitting into parallel copies of itself, appeals to atheists…medium.com
Bohmian Relativity: Quantum matter may create time
What is time? Quantum theory may have the answer.medium.com
Bell-type Field Theory: the universe may be made of particles not fields
The alternative quantum field theorymedium.com
Bohmian Mechanics: the past and future may not exist
A 70 year old interpretation of quantum mechanics challenges everything we think we know about the universe.medium.com
References:
Weinberg, Steven. “The trouble with quantum mechanics.” The New York Review of Books 64.1 (2017): 51–53.
Schrödinger, E., 1935, “Die gegenwärtige Situation in der Quantenmechanik”, Die Naturwissenschaften, 23: 807–812, 823–828, 844–849; English translation by John D. Trimmer, 1980, “The Present Situation in Quantum Mechanics: A Translation of Schrödinger’s ‘Cat Paradox’ Paper”, Proceedings of the American Philosophical Society, 124(5): 323–338, reprinted in Wheeler and Zurek 1983: 152–167.
Bassi, Angelo, and GianCarlo Ghirardi. “Dynamical reduction models.” Physics Reports 379.5–6 (2003): 257–426.
Lombardi, Olimpia and Dieks, Dennis, “Modal Interpretations of Quantum Mechanics”, The Stanford Encyclopedia of Philosophy (Spring 2017 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/spr2017/entries/qm-modal/>.
Griffiths, Robert B., “The Consistent Histories Approach to Quantum Mechanics”, The Stanford Encyclopedia of Philosophy (Summer 2019 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/sum2019/entries/qm-consistent-histories/>.
Griffiths, Robert B. Consistent quantum theory. Cambridge University Press, 2003.
Omnès, Roland. Quantum philosophy: understanding and interpreting contemporary science. Princeton University Press, 2002.