A Contemplation of Causality

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    When I wake up in the morning my perception of the world begins anew. I become aware of sights and sounds and immediately begin resolving those percepts into concepts. One after another images come into my mind, showing me a collection of objects engaged in a sequence of events. My mind responds to the flood of percepts by organizing them into patterns. But a full organization of our percepts requires some way of relating one set of them to another: we want a kind of genealogy of objects and events. The possibility of creating such a genealogy leads us to the concept of causality, the idea of cause and effect.

    We understand effect as something we observe that tells us that an event happened. But we also assume that something else made the event happen and we call that something else the cause of the event. It may seem unimportant, but we want to understand causes because we assume that such an understanding will enable us to control the happening of events. In order to cope successfully with the world, to live well in it, we want the ability to make some predictions of the occurrences of events with good accuracy. We want the ability to forge chains of inference, using syllogisms as links, and to succeed at that we must be able to work out cause and effect. This natural ability, which we need in order to survive, passes over into our philosophy in the manner of an analogy. We do not accept chaos in our natural world, so we do not accept it in the artificial world of our philosophizing.

    So what does the word "cause" denote? How can we describe cause as a thing-as-perceived and how can we relate that description to the thing-in-itself (insofar as we can say anything meaningful about that concept)? To answer those questions we must lay out the properties of cause and effect and see what pattern we discern in them.

    Most fundamentally the words cause and effect denote events; thus, for example, I do not have a cause but my birth and growth do. Further, in order to participate in the chain of cause and effect a thing must exist. We say that the thing must have a material (from the Latin for mother) organized into a pattern (from the Latin for father), but we need not go into detail. In order to verify that a thing exists we need only determine that the thing possesses the property of inertia, the quality through which objects respond to forces. As an example of what that statement means, consider light.

    In 1873 and 1876 respectively, James Clerk Maxwell used his electromagnetic theory and Adolfo Bartoli used the second law of thermodynamics to show that light exerts pressure upon any object that reflects it or absorbs it. That exertion of pressure, confirmed by experiment, tells us that light carries linear momentum. Because light carries linear momentum it can suffer a change in that linear momentum, either in quantity (e.g. as in the gravitational Doppler shift) or in direction (e.g. as in the deflection of starlight passing the sun), which means that light responds to force; thus, we can infer that, in some respect, light possesses inertia; therefore, light exists as an entity that can participate in a chain of cause and effect.

    What determines the form of a cause? It doesn’t seem to inhere in space; it seems to associate with particles. Thus, both cause and effect involve bodies and particles, material objects that serve as actors on the stage provided by space and time. In particular, we apply the words cause and effect to certain changes in the arrangement of bodies and particles in space. In Newtonian physics we say that in an event the effect consists of the changes in the linear momenta of the bodies involved and the cause, which we infer from our observation of the effect, is the force that acted on the bodies.

    As events, cause and effect have both a spatial and a temporal aspect; in particular, a cause and its effect must occur in tight proximity to each other, both in space and time, and the cause must occur prior to its effect. Isaac Newton gave causality its property of contiguity when he abolished action at a distance from his thinking (see Appendix). His laws of motion, requiring contact, replace Aristotle’s bodies knowing their places (via some kind of occult action reaching across space, what Einstein called spooky actions at a distance): in the Newtonian scheme a body responds to only what contacts it and, thus, remains in a given state of motion unless forced to change it. Thus an absolute view of Reality was replaced with a relativistic one (though, just as Koppernigk kept Ptolemy’s circles on circles and had to be corrected by Kepler, Newton kept Aristotle’s absolute space and time and had to be corrected by Einstein.).

    We may also ask whether space and time exist. They don’t fulfill our inertia criterion, but, then, they don’t participate directly in the chain of cause and effect: they merely provide a venue in which those events can occur. But because we perceive space and time directly, because we see a separation between objects and discern changes in some arrays of objects, we can accept the existence of space and time as an axiom in any theory of causality.

    Einstein refined Newton’s work on causality with his work on the relativity of simultaneity. Because of the way in which space and time differ for observers who move relative to each other, two events occur simultaneously for all observers if and only if they occur at the same point in space. Note that we have tacitly assumed that cause and effect occur as two separate events.

    Relativity tells us that spatial and temporal intervals can be transformed, one partly into the other, so we reconceive space and time as a four-dimensional continuum. If we could see in four dimensions, we would see a particle appearing as a thread, a world-line, curving through the spatial dimensions from past to future. An event thus consists of more than one world-line meeting at a point in that continuum.

    Certain kinks in a set of world-lines reveal that a cause has occurred: the kinks constitute the effect from which we infer the cause. As Newton taught us through his laws of motion, we can only observe the effect (change in linear momentum) and infer the cause (force). We must also note that the kinks only occur where multiple world-lines come to the same point in space at the same time.

    Does the cause only exist where and when the kinks occur? It seems more likely that causes exist everywhere at all times and that the lack of an observable effect on a single particle traveling in a straight line comes from symmetry. As the particle travels through space the causes it encounters exert force equally in all directions and, thus, exert no net force on the particle that would change its motion. Only when the particle approaches another particle does it encounter an asymmetry that exerts a net force.

    Proximity gives us a necessary condition but not a sufficient condition for the associated events to be a cause and its effect. Asserting that proximity alone suffices to unite two events as cause and effect leads us into the logical fallacy of "post hoc; ergo, propter hoc" (Latin for "after this; therefore, because of this"). Expressed as a syllogism, the fallacy states that

A occurs,

then B occurs;

therefore, A caused B.

    To avoid the fallacy we add to the concept of causality the properties of uniqueness and necessity. Thus, each specific cause must lead necessarily to the same unique effect. That statement means that if we see the effect, we know that the cause has occurred, and if we see the cause, we know that the effect will occur, without exception.

    The property of uniqueness is also the basis for determinism. When we view that fact in the light of the quantum theory, we discover that instead of finding an atom of causality we may find causality evaporating altogether, vanishing before our increasingly focused gaze.

    Heisenberg’s indeterminacy principle implies the idea that we can no longer determine uniquely the connection between cause and effect. Instead of the sharp, precise calculations of Newtonian dynamics, we must use fuzzy probabilistic calculations in the quantum theory. When we consider the smallest scales physics becomes myopic and Reality appears blurred.

    Note that the reference to Heisenberg’s indeterminacy principle obliges us to alter the geometric frame in which we plot cause and effect. Rather than the 4-dimensional spacetime of Relativity, we must use an 8-dimensional continuum, relativistic phase space, that consists of spacetime plus the 4-dimensional continuum on which we plot the linear momentum and energy of an event. Taking the elapse of time as our independent variable, as we must, we see the world-lines of particles curving and kinking in space. In the four dimensions of momentum-energy we also see lines associated with particles, call them motion-lines, and we see in those lines the kinks that represent the events that reveal cause and effect.

    Again, if we could see in four dimensions, we would see a world-line curving through space as a thread, passing through the point labeled Here and Now, and then fraying as it passes into the future light cone. That fraying represents the possible world-lines available to the particle in accordance with quantum indeterminacy.

    As an example of the quantum blurring of causality, consider radioactive decay. We cannot say with any precision at all when a given neutron will decay; we can only offer the probability that it will decay in some interval, representing that probability through the half life. But if we have many neutrons gathered together, we can determine with good accuracy the rate at which they decay, often to a theoretical precision greater than that of the detector, which is itself a quantum-limited device. Thus, the production of radiation appears to be a deterministic phenomenon, but only because a large population of producers is involved.

    How does an indeterminate world manifest the determinism of classical physics? We don’t have perfect knowledge of the position and momentum of an electron, but if it is locked to an atomic nucleus we know its position and momentum more or less as being the same as those we would expect of an object traveling with that atom. And if the atom is part of a solid body, then its position and momentum can be taken to be determined by the position and motion of the gross body of which it is part. Such constraints, putting particles into bound relationships with other particles and agglomerations of particles, create a kind of faux determinism: the de Broglie wavelength of the whole is shorter than the spacing among its components, so the quantum indeterminacy in its position is smaller than the error inherent in any measurement of that position. The world appears deterministic, but only on some scales.

    Time reversal gives a glimpse of a world that is deterministic on all scales, from the cosmological to the subatomic. Consider the decay of a neutron again. If we bring the decay products together, we have no guarantee that they will combine into a neutron. But if we reverse time, the products come together and inevitably combine into a neutron. What makes this comment meaningful is the knowledge that a proper relativistic quantum description of matter necessarily requires that a part of the wave function describing each particle expand backward in time.

    So, if we run time backward, we find that determinism is not only possible, but necessary. How else can we explain the traces of a unique past? Consider the Burgess Shale, which contains the remains of creatures that lived in the sea some six-hundred million years ago. Each of those remains represents a creature that definitely existed at that time and that would have to be resurrected if time ran backward. But we have no similar traces of the future (or, more precisely, the futures).

    Now time reversal raises a new question: does effect become cause and cause become effect? Consider a two-particle collision. As time elapses forward we observe the particles coming to the same point in space and suffering changes in their linear momenta. We take those changes as the effect of the collision and infer the occurrence of a force as the cause of that effect. Now imagine time elapsing backward. Again we observe the particles coming to the same point in space and suffering changes in their linear momenta, albeit those changes reverse what we observed before. Because we observe those changes and because they are essentially the same as the changes we observed before, they constitute an effect, from which we infer the existence of a cause that occurred just prior to their becoming manifest.

    But look at what time reversal does to the world-lines. As time elapses forward, taking us into the future, the ever-present Now ravels up the threads of all possible world-lines into a definite History of Reality. In the Now, as time elapses backward, the causes unravel that single determinate world-line of the past into the splayed out array of possible world-lines of the future. In both cases we infer the existence of causes altering the world-lines.

    Finally we must ask the important question – Does cause actually exist? Or is it merely an illusion caused (there’s that word again) by our psychological need for explanations? We know that we receive percepts from which we devise the concepts that we associate with effects, but we receive no percepts to give us the concepts that would yield a mental image of a cause: the idea of cause comes to us purely as inference. But if causality is an illusion, it is a compelling and persistent one.

Appendix: Forcefields

    Although scientists dismissed the idea of action at a distance, they nonetheless knew of three phenomena that look very much like such a thing – gravity, electricity, and magnetism. Michael Faraday resolved the dilemma early in the Nineteenth Century when he sprinkled iron filings onto a sheet of paper near a magnet. He saw that the filings responded to the magnetic force by forming a pattern vaguely resembling the furrowed pattern of a plowed field, so he postulated the existence of a field of magnetic force (or forcefield) permeating the space around the magnet. Faraday’s concept of forcefields filled the gap that Newton’s "I frame no hypotheses" had left in the understanding of causality. The forcefield extends contiguity from the forcing object, through space, to the forced object; thus, action at a distance is avoided. But how does the forcefield do it?

    We assume that as an extended entity the forcefield exists, point by point, in contact with itself. At each and every point there exists a potential force that only comes real when an appropriately charged particle occupies that point. Thus at each and every point there exists a cause, which only acts when an appropriate object occupies that point.

    We know that space and time exist as a continuum, an infinite set of infinitesimal points and instants. Each point or instant comes arbitrarily close to zero without actually reaching it. Objects in space must have finite extent in order to have any chance of coming into contact with each other. By that same reasoning the cause associated with one particle must have a finite extent in order to touch another particle and be activated.

    Does a cause adhere to a particle and move with it or does it, like a virtual particle, exist inherent in space only to be realized when a particle comes to it and touches it? The existence of forcefields, especially the electromagnetic forcefield, implies the latter. Now we need to account for the form of the forcefield, particularly the inverse-square law.

    In this case we assert that the charge emits virtual particles, virtual photons in the present case, that realize virtual (or potential) causes from the vacuum just as a real particle realizes real causes. Because the density of those photons diminishes according to the inverse square of distance, we get an inverse square in the density of realized causes. Why not just use the photons alone in the theory? The lack of a screening effect implies that the photons pass a particle unaffected, that they simply realize the cause and move on.

    And how do we know that the virtual photons themselves are not the direct cause of the force in the field? We assert that a point-like electric charge emits a stream of virtual photons. Now surround that charge with a thin shell of an equal charge of opposite sign. Outside the shell the electric fields must cancel (due to symmetry), but if the photons are the direct cause of force, then the photons from the point charge will not penetrate the shell and the point-shell ensemble will display an electric field outside the shell. We thus infer that the virtual photons do not cause force directly, but realize the potential cause at a point in space as they cross that point.

    So just as the quantum vacuum is filled with virtual particles that can become real under the right circumstances, so it is also filled with virtual causes that can be realized into potential causes by contact with virtual photons and then made to exert a real force when contacted by real particles. As we can see, then, we can mimic action-at-a-distance with a ghostly action-on-contact. Thus we have forcefields.


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