It will be blatantly obvious by now that the ontological implications of quantum mechanics go counter to some of our deepest convictions concerning space, time, and matter.
It is safe to say that the following idea appears self-evident to anyone uninitiated into the mysteries of the quantum world: the parts of a material object are defined by the parts of the space it “occupies,” and the parts of space are defined by delimiting surfaces (boundaries). Because it says, in effect, that the synchronic multiplicity of the world — the word’s multiplicity at any one time — rests on surfaces that carve up space much as cookie cutters carve up rolled-out pastry, we may refer to this idea as the “Cookie Cutter Paradigm” (CCP).
There is considerable neuropsychological evidence that the CCP is “hard-wired”: the way in which the brain processes visual information guarantees that the result — the visual world — is a world of objects whose shapes are bounding surfaces. Vision is based on a neural analysis of the visual field (the optical images falling on the retinas in both eyes) that capitalizes on contrast information. Data arriving from homogeneously colored and evenly lit regions of the visual field do not make it into conscious awareness. The corresponding regions of the phenomenal world are filled in on the basis of contrast information that is derived from boundaries in the visual field.[1–3]
There is, however, a deeper reason why our visual world conforms to the CCP, for our brain works as it does because our mind works as it does — and not the other way round, as we are wont to think. In the Vedantic scheme of things, the original creative principle and dynamic link between UR and the world is a consciousness that, following Sri Aurobindo, we may call “supermind.” The creative action of supermind is primarily qualitative and infinite and only secondarily quantitative and finite. Cosmologically speaking, mind is the agent of this secondary action limiting, defining, dividing, individualizing:
Mind in its essence is a consciousness which measures, limits, cuts out forms of things from the indivisible whole and contains them as if each were a separate integer…. It is this essential characteristic of Mind which conditions the workings of all its operative powers, whether conception, perception, sensation or the dealings of creative thought. It conceives, perceives, senses things as if rigidly cut out from a background or a mass and employs them as fixed units of the material given to it for creation or possession.[4]
Here we have the reason why, when asked to imagine two exactly similar objects in different places, we balk at the logical conclusion that the “two” objects are actually a single object existing, appearing, or manifesting itself in different places. If we perceive things as if rigidly cut out from a background or a mass, then the background or mass from which one thing is cut out differs from the background of mass from which another thing is cut out, even though the two things are cut out from an indivisible whole.
Let’s consider some of the CCP’s implications and how they might lead us up the garden path.
In a world whose synchronic multiplicity rests on surfaces, spatial extension exists in advance of multiplicity, for only what is extended can be cut up by the three-dimensional equivalents of cookie cutters. If, in addition, the parts of material objects are defined by the parts of space, then the parts of space exist in advance of the parts of material objects. This is how we come to think of space as a pre-existent expanse that is intrinsically divided “all the way down.” But if this is how we think, we cannot conceive of fuzzy positions. If parts are defined by geometrical boundaries, the positions of the parts are as sharply defined as their boundaries, and there isn’t anything fuzzy about the way geometrical boundaries are defined.
- CCP: Synchronic multiplicity rests on delimiting surfaces.
QM: Synchronic multiplicity rests on spatial relations. - CCP: Space is a pre-existent and intrinsically divided expanse.
QM: “Space” has two senses: (i) an undifferentiated expanse, (ii) the totality of existing spatial relations. - CCP: All (relative) positions are sharp.
QM: All (relative) positions are fuzzy. - CCP: Space is differentiated “all the way down.”
QM: The spatial differentiation of the world does not go “all the way down.”
Rigid bodies, as the special theory of relativity has taught us, do not exists. (If they did, they could be used for instant signaling, in contradiction of the finite speed limit the theory imposes on the propagation of signals.) An extended material object — an object that “occupies space” — is necessarily compressible. What makes it compressible, however, is the elastic forces that act between its component parts. Its ultimate component parts therefore are neither rigid nor elastic and thus cannot be extended. If we combine the existence of particles without spatial extent with the pre-existence of an intrinsically and infinitely differentiated spatial expanse, we are led on to the notion that such particles are pointlike.
- CCP: A particle without spatial extent (or internal structure) is pointlike.
QM: A particle without spatial extent (or internal structure) is formless.
Although we readily agree that red, round, or a smile cannot exist without a red or round object or a smiling face (the Cheshire cat notwithstanding), we just as readily believe that positions can exist without being properties of material objects. We are prepared to think of material objects as substances, and we are not prepared to think of the properties of material objects as substances — except for one: we tend to think of positions as if they existed by themselves, whether or not they are possessed. The reasons for these disparate attitudes are to be found, not in the physical world, but in the neurobiology of perception.
In brief, the visual cortex is teeming with feature maps. A feature map is a layer of the cerebral cortex in which cells map a particular phenomenal variable (such as hue, brightness, shape, motion, or texture) in such a way that adjacent cells generally correspond to adjacent locations in the visual field. (In the macaque monkey as many as 32 distinct feature maps have been identified.[5]) Every phenomenal variable has a separate map (and usually several ones at different levels within the neuroanatomical hierarchy) except location, which is present in all maps.
If there is a green box here and a red ball there, “green here” and “red there” are signaled by neurons from one feature map, and “boxy here” and “round there” are signaled by neurons from another feature map. “Here” and “there” are present in both maps, and this is how we know that green goes with boxy and red goes with round. Position is the integrating factor. In the brain, and consequently in the visual world, positions pre-exist — in the brain at the scale of neurons, in the visual world at visually accessible scales. They exist in advance of phenomenal objects, and this is another reason why we tend to assume that they also exist in advance of physical objects, not only at the scale of neurons or at visually accessible scales, but also at the scales of atoms and subatomic particles. (The transition from visually accessible scales to subatomic scales is an unwarranted extrapolation, but if one postulates a pre-existent spatial expanse that is intrinsically differentiated at some scales, then it is hard to see why it is not intrinsically differentiated at all scales.)
Features present in the same place thus get integrated into a single object, while features present in different places get integrated into different objects (or different parts of the same object). This is why we are convinced by default that one and the same object cannot be in different places, and that different objects cannot be in the same place. It is also why we are baffled by the apparent ability of a single electron to be simultaneously in different places, and by the ability of two or more particles to be in possession of exactly the same (fuzzy) position. (Helium illustrates this nicely. In the ground state of a helium atom, the positions of the two electrons relative to the nucleus are exactly identical. And in a bottle of superfluid helium, the positions of the atoms relative to the bottle are exactly identical.)
- CCP: Two objects cannot be in the same place simultaneously.
QM: Two particles or atoms can simultaneously possess the same (fuzzy) position. - CCP: The same object cannot be in two places at once.
QM: A particle, atom, or molecule can be simultaneously in (what we tend to think of as) different positions.
Yet another reason why we tend to think of positions as substances is this: the role that position plays in perception is analogous to the role that substance plays in conception. Among the ideas that philosophers have associated with the word “substance,” the following is relevant here: while a property is that in the world which corresponds to the predicate in a sentence composed of a subject and a predicate, a substance is that in the world which corresponds to the subject. It objectifies the manner in which a conjunction of predicative sentences with the same subject term bundles predicates. While substance thus serves as the “conceptual glue” that binds an object’s properties, position serves as the “perceptual glue” that binds an object’s phenomenal features.
Einstein[6] believed that “things claim an existence independent of one another” whenever they “lie in different parts of space.” It is ironic that Einstein based this belief on the demand that things be independent of the perceiving subject, for it is precisely the illegitimate projection of the structure of the visual world into the physical world that underlies it. It is because our minds and/or brains process visual information in conformity with the CCP that we tend to think of space as a pre-existent and intrinsically differentiated expanse, in which objects are separated by “empty space.”
Fact is that the three spins, which may be light years apart, are not independent of one another. Fiction is that they lie in different parts of space. Space is not something that has parts. Nor is there such a thing as empty space — not because space is “filled with vacuum fluctuations” as the dumbed-down literature has it, but because in the physical world there is no such thing as an unoccupied location or an unpossessed position. Space is the totality of existing (=possessed) spatial relations. Where there is nothing (no thing) there is no “there.” (In another sense, space is an undifferentiated expanse. Instead of dividing things, it unites them by its utter lack of parts.) If we add to this that all existing relations are self-relations — relations between UR and UR — we find that there is neither a structural nor a substantial basis on which physical things could “claim an existence independent of one another.”
1. [↑] Hubel, D.H. (1995). Eye, Brain, and Vision, Scientific American Library.
2. [↑] Hoffman, D.D. (2000). Visual Intelligence: How We Create What We See, W.W. Norton and Company.
3. [↑] Enns, J.T. (2004). The Thinking Eye, the Seeing Brain: Explorations in Visual Cognition, W.W. Norton and Company.
4. [↑] Sri Aurobindo (2005). The Life Divine, Sri Aurobindo Ashram Publication Department, pp. 173–174. Emphases added.
5. [↑] Clark, A. (2000). A Theory of Sentience, Oxford University Press.
6. [↑] Einstein, A. (1948). Quantenmechanik und Wirklichkeit. Dialectica 2, pp. 320–324.
This Quantum World 