2. Parts of the Physical Universe

The parts of the physical universe are called objects.

Parts of the physical universe share the dimensionality of the physical universe, even if they are atomic (although atoms have only unit measure in each dimension). For example, parts of a four dimensional universe must be four dimensional entities. The parts of the physical universe are called objects : since the universe is considered to be (at least) four-dimensional, another word for these objects might be events (where it is implied that the events have a nonzero duration). The physical universe contains all of us as objects: we are each a part of it. Since from a physical perspective our minds are our brains, they too are a part of the universe. Therefore, parts of perception (percepts) and parts of conception (concepts) are kinds of objects, at least when they are understood non-referentially. This is represented in the following figure:

All objects occupy a nonzero interval of time.

What are the primitives of reality? Are there things out of which reality is composed, such that there is a unique decomposition into these things? Both conceptually and physically, it seems unlikely that there is a unique decomposition; the world may be partitioned in numerous different ways. However, is it possible to at least characterize which types of things constitute valid parts? For example, things can be described as either spatial things which endure through time, or as things which have an inherent temporal aspect. In other words, are things three-dimensional, and do we perceive most of them, or are they four-dimensional, and of them do we perceive only a slice?[46] To address this question we look at several findings from modern physics.

One of the more interesting findings from physics is that when one attempts to measure a physical object, a trade-off is encountered between knowledge of its position (the spatial location) and knowledge of its momentum (which is the velocity of an object in a given direction multiplied by its mass). According to quantum physics, the product of the standard deviation of these two quantities two cannot be less than a particular constant value. This law, known as Heisenberg's Uncertainty Principle, states that knowledge of one measurement entails imprecise knowledge of the other measurement; knowledge about the position interferes with knowledge about the velocity, and vice-versa (the uncertainty principle may also be stated as a relationship between energy and time).[47]

The uncertainty principle can be understood in at least two fundamentally different ways. According to the first understanding, we cannot know the position and velocity of a particle because our measurement devices are not sufficient. In other words, there is a definite position and velocity, but we cannot measure it. According to the second understanding, there is no definite position and velocity to be measured. In other words, we cannot know these quantities because they do not exist as definite properties of the object. The latter interpretation of quantum mechanics, called the Copenhagen interpretation, is the more popular of the two. In this interpretation, the position and momentum of the object do not exist as precise entities to be quantified in the first place.

Other interesting findings from quantum physics that challenge our assumptions about reality revolve around something called the particle-wave duality. The particle-wave duality refers to the fact that small things such as photons, the particles which constitute light, behave like both waves and particles. When photons impact a surface such as a photographic sheet, we observe them as points: they impact in a very definite location. However, when photons travel through space, they exist as waves.

The particle-wave duality is illustrated in a famous study called the double slit experiment. In that experiment, photons are shot from a source, pass through either one or two narrow openings (slits), and eventually impact upon a photographic plate. In both cases, at the time of impact, the photons act like particles which leave their mark in a well-defined location. When a single slit is open, the pattern of impact on the plate is a normal density, centered on the slit (i.e. there is a Gaussian distribution around the bullseye). However, when two slits are open, there are not two normally-distributed impact patterns as one would expect. In fact, the photographic plate displays an interference pattern; a photon acts as if it goes through both slits, and subsequently interferes with itself. This is not problematic for a wave-like thing, which is distributed in space, but a wave-like thing would not impact the photographic plate in a single point. It is problematic for a point-like thing, since one would expect that the point would go through one slit or the other, and therefore not both (which is necessary to cause an interference pattern). This incongruous behavior is an example of the phenomena called particle-wave duality.

Despite this incongruous behavior, there is a very accurate model of the behavior of the photon which relies on what are called Schrodinger's wave equations. In contrast to the wide acceptance of these equations, however, the interpretation of the phenomena these equations characterize is widely debated. According to the Copenhagen interpretation, the photon travels through both slits as a “probability wave” . That probability wave collapses when it is measured, for example when it hits the photographic plate, and one of the probabilities actualizes. In terms of the equation, this collapse involves setting some number of variables to zero that govern the probabilistic behavior, which coincides with the point-like nature of the particle at that instant. The wave-like nature is explained by saying that the particle exists as a cloud of possibilities, and these possibilities interfere with one another to create the pattern. Of course, this interpretation introduces the need for a theory that explains when and why probability waves collapse, which is where this theory gets particularly controversial.[48] In another theory called the multiple-worlds interpretation, the wave functions do not collapse at all: the multiple alternatives all actualize, each in different physical universes (the universes are said to branch at that instant).

Perhaps one way of accounting for these phenomena is to say that particles are in fact things of high dimensionality (instead of things which are limited to three dimensions). For example, if we consider particles to occupy a region in both space and time, then they would appear like curve segments in spacetime (where the length of the curve corresponds to the relative velocity of the particle). In order to occupy a single location in space, the particle would have to remain immobile for an amount of time greater or equal to its temporal extent (otherwise its location at the beginning would not occupy the same spatial position as its position at the end). Similarly, if a particle is not moving, it is impossible to determine its directionality (and thus its momentum, because it has no temporal orientation). In any case, these are speculations based on the assumption that objects are four-dimensional. If we further assume that objects are five-dimensional, then understanding particles as probability-waves falls out rather naturally (recall the earlier chapter in which the fifth dimension was equated with possibility).[49]

Regardless of one's interpretation of these phenomena, it seems clear that our everyday understanding of physics falters when presented with the evidence gathered from these experiments. However, our misunderstanding in this case may be telling: it may shed light on the nature of our cognition if we can understand why we had this mistaken understanding. One possible answer to this question has to do with the relation between the physical and perceptual universes. In particular, if we suppose that the perceptual universe was a reduced-dimensionality representation of the physical universe, then to base our conception of reality on perception would lead to exactly such an incorrect conclusion. In that case, this lost dimensionality could be recovered, but it would take a good deal of conceptual work.

[46] Four-dimensional objects are also called occurrents (see [ Simons ]).

[47] To put a linguistic spin on Heisenberg's Principle, we might say that the more we know about the object, or the more we characterize it as a noun, the less we can understand about its movement through time, or the less well we may characterize it with verbs. Of course this is a metaphor; Heisenberg's uncertainty principle is intended to apply only to small things in the physical universe, not to the conceptual universe. However, it is also true of the conceptual universe that one cannot exactly identify the noun (spatial position or description) without affecting the verbs (temporal position or description) that apply to an object: the more precisely a noun refers to (or restricts) its referent, the fewer verbs may be applied to that noun. To use a concrete example, if we describe an apple as having the quality of redness, then it becomes difficult to say that the apple ripens, since redness is a quality which changes through the process of ripening. In other words, by placing an increasing number of (spatial) constraints on the apple, the apple becomes less capable of undergoing transformation (without losing its identity).

[48] It is an interesting question what exactly it is that makes a probability wave collapse. Does it have to do with interactions between events, or does it have something to do with the act of observation? This question was formulated by Schrodinger in terms of knowing if a cat in box was alive or dead, but it seems to be the same conundrum as whether a tree falling in the woods makes a sound, even if no one is there to hear it.

[49] When a particle impacts a photographic plate, the space which it occupies along the fifth dimension contracts; physicists say that the probability wave collapses at this point. Given what we have said and will say about changes to the dimensionality of objects, however, we would expect that the probability wave never entirely collapses; even after impact, the photon would continue to occupy a nonzero interval on the dimension of possibility, otherwise this would amount to a reduction in dimensionality.