In this final post (for now) on my exploration of quantum mechanics, I will engage in some casual speculation about what our physical reality might be like. (As I wrote in my last post, this is something that most contemporary interpretations do not really try to do in a coherent way.) I will do this within the framework of the primitive ontology approach, which says, roughly, that:
- A fundamental physical theory must specify what are the basic entities that make up physical matter located in space and time.
- Then, that theory must specify how those basic entities behave, in such a way as to produce the macroscopic world that we observe.
Most of the effort so far, by the researchers following this approach, has been directed at specifying the primitive ontology of matter, but it seems to me that to eventually unite quantum mechanics with general relativity, we will also need to think about the primitive ontology of space and time.
Space and Time
The two basic options we have for an ontology of spacetime are continuous and discrete.
If spacetime is continuous, then the way that we usually see space and time as infinitely divisible continuums is correct down to the smallest level. Spacetime forms a smooth manifold just as it does in general relativity; the only differences are quantum fluctuations in the geometry at very small scales. (From a presentist perspective, a continuous four-dimensional spacetime takes the form of a continuous three-dimensional space evolving continuously in time.)
In general relativity, the fundamental variable in the theory is the (four-dimensional) spacetime metric, which controls the geometry of space and the behaviour of matter under gravitational forces. A possible model for quantum gravity has been suggested wherein spacetime is given a privileged foliation in spacelike slices, and the fundamental variable is the (three-dimensional) spatial metric. The spatial metric controls the geometry of space, and the way it evolves from slice to slice is related to the gravitational forces.
In this model, the evolution of the spatial metric is given by a guidance equation derived from the universal wavefunction, similar to how particles are guided by the wavefunction in Bohmian mechanics. It is possible (as suggested by the Wheeler-DeWitt equation) that when quantum mechanics is united with general relativity, the universal wavefunction will be static, unchanging in time. This, I think, makes its role in the primitive ontology approach as a representation of the laws of nature more apparent: combined with the guidance equation, it determines the evolution of every possible configuration of the universe.
If spacetime is discrete, then at very small scales the continuity of space and time breaks down: space itself is made of discrete units and all change occurs in discrete steps. There would be “atoms” of space with some form of connectivity relation between them; spacetime would be represented by a mathematical graph rather than a smooth manifold. The geometry of space would only emerge from vast collections of such atoms. (A presentist would see this as discrete space evolving discretely in time.)
A discrete theory for spacetime has been suggested also, using a guidance equation derived from the universal wavefunction, as before. Here the guidance equation would likely be stochastic, determining the probabilities for the next configuration of space, given the current configuration. Over large enough regions and enough configuration steps, a spacetime manifold (again, with a privileged foliation) would emerge as an approximation.
I am not sure which of these approaches is more likely to be correct, or which will be easier to study. The mathematics of continuous configurations gets difficult: functional derivatives and integrals in infinite dimensional spaces. (Though some of the same mathematics is already needed and being worked on, for the path integral formulation of quantum field theory.) The mathematics of discrete configurations may be simpler, but figuring out how the continuum emerges from that discrete configuration is a hard problem.
Personally, I like the theory of a continuous spacetime, but I think both continuous and discrete ontologies need further investigation. Either way, the dynamics should probably be such that the privileged foliation is not detectable, to agree with the no-signalling theorem.
(You could also have a discrete space with continuous time, so that the discrete structure of space evolves continuously according to a guidance equation derived from the universal wavefunction, for example. Whether such an evolution would be deterministic or stochastic is something that obviously needs investigation.)
Here is where things get interesting, and we think about what everything is made of. Particles, fields, and (so-called) flashes have all been suggested as primitive ontologies for matter.
Perhaps the most obvious choice for the fundamental entities that make up matter is particles. Bohmian mechanics uses a particle ontology to reproduce the predictions of non-relativistic quantum theory, where the particles are guided by the wavefunction. Relativistic generalizations of Bohmian mechanics have been suggested with a particle ontology, where the guidance equation for the motion of the particles is supplemented with a stochastic process for particle creation and annihilation events. In these theories, particles are created, move through space, and are annihilated, all guided by the wavefunction.
Among primitive ontology theorists, there is some question as to whether the primitive ontology should include fermions (matter particles such as electrons and quarks), bosons (radiation and force-mediating particles such as photons and gluons), or both; and, if both are included, whether they should appear in the same form. Usually, non-relativistic Bohmian mechanics includes only electrons and atomic nuclei as the primitive ontology; the electromagnetic force between them appears only in the wavefunction.
It seems to me that the discoveries of quantum physics have shown that, whatever the primitive ontology of nature is, matter, radiation, and forces behave in a fundamentally similar way. Both electrons and photons display both wave and particle natures; in standard quantum field theory, both are considered to be excitations of a quantum field (even though the standard theory isn’t entirely clear about what a quantum field is). So a satisfactory primitive ontology should include both bosons and fermions, and in the same way.
One interesting way of doing this, suggested in this paper, has both bosons and fermions as particles, moving in spacetime and being created or annihilated. Their motion and interaction is guided by the wavefunction, alongside a number of other potentials defined on the configuration space. This theory has the capability of handling gravitons, so it is a possible way of unifying quantum mechanics and general relativity.
A primitive ontology where the fundamental entities are fields is, perhaps, more in line with the spirit of quantum field theory. In such a theory, what everything (or at least, everything physical) is ultimately made of are fields that pervade all of spacetime. Quantum fields have the peculiar property that vibrations propagating through them must possess discrete amounts of energy: this is what allows us to see such excitations as particles.
To me, the field ontology is the most attractive, since it explains in one framework the reason that particles of the same kind have exactly identical properties, the reason each kind of particle has a corresponding antiparticle, the mechanisms of particle creation and annihilation, interactions between different particles, and quantum fluctuations of the vacuum. (Here is an excellent series of articles explaining various features of quantum field theory on physicist Matt Strassler’s site.) However, precisely formulating the actual behaviour of these quantum fields is difficult.
Part of that difficulty is in figuring out how fermionic fields should be represented. (Fermions differ from bosons by being forbidden from occupying the same quantum state. Essentially, two fermions cannot be in the same place at once, which is what makes matter occupy space. This makes fermionic fields more complicated to represent than bosonic fields.)
I have no idea how that problem might be resolved. There are a number of suggestions, reviewed here for example (personally, I think P. Holland’s model is promising). But since the standard theory uses certain mathematical objects called spinors in connection to fermions, I feel like some insight might be gained from geometric algebra, a less well-known set of mathematical concepts that represent spinors much more intuitively (see here for detail) than the usual formulation.
Another significant difficulty in formulating the dynamics of quantum fields is the infinities: fields have an infinite number so degrees of freedom, while any system of particles has only a finite number of degrees of freedom. Interestingly, this could be made easier if spacetime is discrete, since that would reduce the degrees of freedom to a finite number (or, at most, a countably infinite number).
A curious primitive ontology that was first suggested for an objective collapse theory of quantum mechanics has come to be known as the flash ontology. According to a flash theory, matter is nothing more than patterns of flashes – point-like, instantaneous events. (In the context of an objective collapse theory, the flashes represent locations of wavefunction collapse.) Each flash “lights up” a single point in space for a single instant of time, and then it is gone.
From a philosophical perspective, I feel that with the flash ontology, there isn’t enough there for anything to have the causal properties that I believe underwrite the laws of nature. (This paper argues against the flash ontology for the same reason. But perhaps the causal properties are just a part of spacetime itself?) It is an interesting proposal, nonetheless.
In addition to particles, fields, and flashes, other possible primitive ontologies include strings and branes, as found in string theory. (However, I think the prospects of string theory have been overstated, so I find a particle or field ontology to be more likely.) Maybe even the metaphysical forms of this interpretation of quantum mechanics, which I mentioned in my last post, could be thought of as a primitive ontology (though I would consider it closer to idealism than scientific realism).
The dynamics of a primitive ontology theory must specify how the fundamental entities of physics behave. Because of the discoveries that have been made about quantum mechanics, we know that the dynamics will have to have some strange features:
- The behaviour of the primitive ontology may be affected by what is possible for it to do, not just by what it actually does. (This is what we see in the unexpected effects of quantum superpositions.)
- The dynamics will include instantaneous, non-local influences.
- The dynamics will imply fundamental limitations on our ability to measure and manipulate the microscopic degrees of freedom of the primitive ontology (a side effect of which that we cannot exploit the non-local influences to send signals faster than the speed of light).
- Not all of the properties we assign to classical systems can be assigned to quantum systems; some properties will be contextual and depend on how our measurement apparatus is configured.
But there seems to still be a fair amount of freedom in how the dynamics of the primitive ontology could be specified.
Determinism or Indeterminism
Despite the appearance of quantum indeterminacy, there is still the possibility that it remains only an appearance, a result of our ignorance of the details of the actual configuration of the primitive ontology. This is the case in non-relativistic Bohmian mechanics: the motions of the particles are completely determined by the wavefunction and their actual positions. (The analysis in Bohmian mechanics of how randomness arises from a deterministic universe is actually quite insightful, I find.)
Indeterminism, or laws of nature with fundamental randomness, may be required by certain primitive ontologies. Any flash ontology, any particle ontology that includes particle creation and annihilation processes, and any ontology with discrete spacetime all seem to require a component of randomness in their dynamics.
Maybe a way can be found for a field ontology to behave deterministically; the way it looks right now, I suspect that will be difficult. More work needs to be done to answer the question of whether nature is fundamentally deterministic or indeterministic.
Dependent or Independent
The easiest way to implement the strange behaviour of quantum mechanics in the primitive ontology seems to be to use a wavefunction, evolving according to the Schrodinger equation, as an auxiliary variable. Then the behaviour of the primitive ontology is derived from the wavefunction. (Though it is possible to use an object called a density matrix, evolving according to the Lindblad equation, in place of the wavefunction; and it may be possible to go without either, and specify the dynamics directly.)
There are two ways of deriving the behaviour of the primitive ontology from the wavefunction. One is to specify the configuration of the primitive ontology independently of the wavefunction, and use a guidance equation derived from the wavefunction to specify its evolution. This is the approach of Bohmian mechanics.
The other way is to calculate the configuration of the primitive ontology directly from the wavefunction, so that the configuration is dependent. This is the approach of objective collapse theories, when combined with a modification to the Schrodinger evolution of the wavefunction which prevents macroscopic superpositions.
Collapse or No Collapse
The evolution of the wavefunction itself can be specified with or without an indeterministic collapse process. This does not make too much of a difference when you have an independent primitive ontology. However, it produces two very different kinds of theories when you have a dependent primitive ontology.
When the configuration of the primitive ontology is calculated directly from the wavefunction, and an objective collapse process is included in the wavefunction’s evolution, the macroscopic world can turn out pretty much how we expect it to be: macroscopic objects have more or less have a definite location and physical state.
However, if the wavefunction evolves without collapsing, something very strange can happen: superpositions of the primitive ontology, and not just the wavefunction. You end up with multiple macroscopic distributions of matter superimposed on each other, but (after decoherence occurs) not interacting with each other, causally disconnected. This is how you can have a scientific realist version of the many-worlds interpretation of quantum mechanics.
The best analogy I have seen for what this looks like is a radio that is incorrectly tuned. If your receiver isn’t quite tuned to one channel, you can hear two channels superimposed on each other, and, if you were really good at listening, you could even follow both of them at once. On a realist many-worlds theory, reality is like this, containing many independent histories: worlds overlaying each other, branching into even more diverse worlds, all transparent to each other except in the effects seen in coherent superpositions.
Many-worlds interpretations offer a very counterintuitive picture of reality. They raise serious philosophical difficulties with our intuitive concepts of possibility, probability, personal identity, free will, rationality, and moral agency. On an ontological and explanatory level, I think that many-worlds theories introduce an incredible amount of unnecessary complexity into what exists, and so Occam’s razor prefers theories with just a single world.
Because it is also simpler to have no collapse in the wavefunction (and because there are indications that the wavefunction might not actually evolve in a quantum gravity theory, so collapse would not be possible), the best way to do this seems to be to have an independent primitive ontology. The primitive entities of physics are guided by, but not directly calculated from, the quantum wavefunction.
The Nature of Physical Reality
So, after all of that discussion (which turned out to be quite a bit longer than I had originally planned), here is what I believe. A realist theory of quantum mechanics, where the world we observe is made of physical entities existing objectively and mind-independently, seems entirely possible. There is no need to abandon our common-sense view of the physical world – the nature and dynamics of the fundamental physical entities needs to be modified, but their reality can be retained.
Personally, I think a field ontology is the most plausible, either on continuous or discrete spacetime. The particles that our macroscopic world appears to be made of are, if this is correct, excitations in quantum fields that pervade all of space and time. The field behaviour is guided by the wavefunction of the universe, an abstract representation of the laws of physics and the causal properties of the fields. Physical reality comes down to a complex pattern of excitations and disturbances in these fields, like ripples on the surface of a lake.
It also seems to me that the quantum behaviour of the correct primitive ontology, including the ontology of spacetime, will require a privileged foliation. The foliation may be hidden from us, but it grounds the absolute simultaneity required for quantum non-locality. It also means that our common-sense experience of time is correct: there is an objective distinction between past, present, and future. Change and the passage of time are not illusions, but a fundamental part of reality.
If you are an aspiring physicist, I think you should be encouraged: there is much work to be done (so your vocation won’t be going away any time soon), and physical reality can actually make sense. Here are my suggestions for possible research directions:
- Primitive ontology approach: bring scientific realism back into quantum physics. More specifically, I think research is needed in how the primitive ontology approach can be combined with the path integral formulation of quantum mechanics, since it seems to offer a deep insight into the origin of the principle of least action in classical mechanics.
- Geometric algebra: I believe this extension of vector algebra has the potential to simplify at least some of the mathematics in quantum theory, and even in classical mechanics. It even provides a geometric interpretation to some of the imaginary numbers that appear in quantum physics.
- Something different: the wheels have been spinning on things like grand unification, supersymmetry, and string theory for decades, and not much has come of it. Approaching problems in the standard model of physics from a new perspective (such as this proposal for a framed standard model) might be productive.
(I am mostly putting these suggestions down so I can say that I called it when they turn out to be important. That might be overly optimistic, but hey, I can dream.)
And that concludes my discussion of the nature of physical reality. Next, I will begin to explore the highly important question of whether there is anything else.