El PDF del libro al completo circula por ahí (yo lo tengo), pero para el que guste de resúmenes, aquí va quasi-todo el meollo:
Key (mostly new) passages from “The Mindful Universe”. (May 14, 2005)
The World of Actions
Werner Heisenberg was, from a technical point of view, the principal founder of quantum theory. He discovered in 1925 the completely amazing and wholly unprecedented solution to the puzzle: the quantities that classical physical theory was based upon, and which were thought to be numbers, must be treated not as numbers but as actions! Ordinary numbers, such as 2 and 3, have the property that the product of any two of them does not depend on the order of the factors: 2 times 3 is the same as 3 times 2. But Heisenberg discovered that one could get the correct answers out of the old classical laws if one decreed that certain of the numbers that are used in classical physics to describe the physical properties of a material system are not ordinary numbers. Rather, they are actions having the property that the order in which they act matters!
This “solution” may sound absurd or insane. But mathematicians had already discovered that logically consistent generalizations of ordinary mathematics exist in which numbers are replaced by “actions” having the property that the order in which they are applied matters. The ordinary numbers that we use for everyday purposes like buying a loaf of bread or paying taxes are just a very special case from among a broad set of rationally coherent mathematical possibilities. In this simplest case, A times B happens to be the same as B times A. But here is no logical reason why Nature should not exploit one of the more general cases: there is no compelling reason why our physical theories must be based exclusively on ordinary numbers rather than on actions. The theory based on Heisenberg’s discovery exploits the more general logical possibility. It is called quantum mechanics.
The difference between quantum mechanics and classical mechanics is specified by Planck’s constant, which is a tiny number on the scale of human actions. Thus this tweaking of laws of physics would seem to be merely a bit of mathematical minutia that could scarcely have any great bearing on the fundamental nature of the universe, or of our role within it. But replacing numbers by actions upsets the whole apple cart. It produces a seismic shift in the nature of reality, and of ourselves. The world of substances is converted to a world of information and actions, and our conscious thoughts become engaged in ways unimaginable in the mechanical framework of classical physics.
What is this change introduced by Heisenberg?
In classical physics the center-point of each physical object has, at each instant of time, a well defined location, which can be specified by giving its three coordinates (x, y, z) relative to some coordinate system. For example, the location of a spider dangling in a room can be specified by letting z be its distance from the floor, and letting x and y be its distances from two intersecting walls. Similarly, the velocity of that dangling spider, as she drops to the floor, blown by a gust of wind, can be specified by giving the rates of change of these three coordinates (x, y, z). If each of these three rates of change, which together specify the velocity, are multiplied by the weight (=mass) of the spider, then one gets three numbers, say (p, q, r), that define the “momentum” of the spider. In classical physics one uses the set of three numbers denoted by (x,y,z) to represent the position of the center point of an object, and the set of three numbers called (p,q,r) to represent the momentum of that object. These are just ordinary numbers that obey the commutative property of multiplication that we all, hopefully, learned in 3rd grade: xp equals px, where * means multiply.
Heisenberg’s analysis showed that in order to make the formulas of classical physics describe quantum phenomena, xp must be different from px. He found that the difference between these two products must be Planck’s constant. [Actually, the difference is Planck’s constant divided by 2π and multiplied by the imaginary unit i, which is a number such that i times i is minus one.] Thus modern quantum theory was born by recognizing, or declaring, that the symbols used in classical physical theory to represent ordinary numbers actually represent actions such that their ordering in a sequence of actions is important. The procedure of creating the mathematical structure of quantum mechanics from that of classical physics, by replacing numbers by corresponding actions, is called “quantization.”
Quantum mechanics, like classical mechanics, uses mathematics to make predictions about empirical phenomena. To connect phenomena to mathematics there must be links between certain features of the mathematics and corresponding features of empirical phenomena It is plausible that mathematical actions should correspond to physical actions, and his turns out to be the case.
The mathematical action x is associated with a certain physical probing action. A physical probing action is an action that elicits a response, called an outcome or a feedback. The probing action associated with the mathematical action x is one such that the feedback would be the number x that would specify the location of (the center of) the object being probed, provided the location of (the center of) that object is well defined. The action p is defined analogously. However, those two particular physical actions exist only as idealized limits of physically realizable probing actions. Indeed, many of the actions occurring in the mathematics do not correspond to physically realizable probing actions. On the other hand, every physically realizable probing action corresponds to some mathematical action. The profound significance of all this, as it plays out in the theory, is that Heisenberg’s replacement of numbers by mathematical actions is associated with a transformation of the basic elements of the theory from numbers that specify internal properties of a system, to probing actions performed upon that system by some “observing” system external to it.
Probing actions play a key role in quantum mechanics. The orthodox formulation of the theory asserts that, in order to connect the mathematically described state of a physical system to human experience, there must be abrupt interventions in the otherwise smoothly evolving mathematically described state of that system. According to the orthodox formulation, these interventions are probing actions instigated by human agents who are able to freely choose which of many alternative possible probing actions they will perform. Each possible probing action separates the physical state of the system being probed into a corresponding set of disjoint component parts, one associated with each of the possible outcomes of that probing action. If an allowed probing action is performed, then one of its allowed feedbacks will appear, and mathematically described state of the probed system will jump abruptly from the form it had prior to the intervention to the component part of that state corresponding to the observed feedback. This means that, according to orthodox contemporary physical theory, the “free” choices of probing actions made by agents enter importantly into the course of both the ensuing psychologically described events, and the ensuing physically described events.
This scenario involving free choices and sudden jumps may seem to you completely bizarre. Indeed, it certainly is completely bizarre from the perspective of the classical idea the nature of the physical world. Nevertheless, this is exactly how orthodox quantum mechanics works!
This scenario is not so strange from the point of view of Descartes. According to the ideas of Descartes there is, in effect, a psychologically described aspect of nature and also a physically described aspect, and these two aspects interact with each other according to definite rules. These rules must allow the psy part both to learn things about the phy part, and also to influence it. These two key conditions are neatly satisfied in the quantum scenario, in which the probing agent’s free choice of which probing action to perform affects the course of both the physically described and psychologically described sequence of events.
If one sets Planck’s constant equal to zero in the quantum mechanical equations then one recovers (the physically incorrect) classical mechanics. Thus classical physics is an approximation to quantum physics. It is the approximation in which Planck’s constant, wherever it appears, is replaced by zero. In this approximation one recovers classical physics, along with the physical determinism entailed by classical physics.
Using the true value of this constant—measured in 1900 by Planck—disrupts classical equations and renders all classically conceivable universes physically unrealizable. The allowed quantum states are, roughly, smeared out versions of the old classically described states, with the minimum allowed amount of smearing being specified by Planck’s constant. This intrinsic smearing, the so-called Heisenberg uncertainty, shrinks to zero in the classical approximation. Thus this approximation pares the smeared out state down to a single unsmeared classical state.
Note that it is the Heisenberg uncertainty that creates the possibility for the interventions of the probing actions. The Heisenberg smearing out of the quantum state provides the latitude within which the chosen probing action acts. The each possible outcome of any probing action corresponds to one of a set of disjoint component parts of the smeared out quantum state. The particular way in which these disjoint component parts are defined, or specified, is determined by the observer’s choice of probing action. When a probing action is initiated, one of these specified component parts of the smeared out state will be selected, and all others banished, by some inscrutable process of nature. But in the classical approximation there is no need for, and no room for, any effects of a probing action. The uncertainties that in the full theory need to be resolved by the intervention of a probing action are already reduced to zero by the replacement of Planck’s constant zero. Thus all effects of the actions chosen by agents on the physically described aspects of nature are eliminated by the classical approximation. Consequently, the physical efficacy of our conscious choices is, within the framework of orthodox contemporary physical theory, strictly a quantum effect. The physical efficacy of our conscious choices vanishes in the classical approximation, which reduces human beings to impotent observers of a mechanically controlled universe.
In view of this fact, it is clear that, within the framework of orthodox contemporary physics, all of the contemporary programs that try to understand the empirically observed physical effects of consciousness within the framework of the classical approximation are irrational endeavours probably doomed to fail. The classical approximation eliminates the causal effects of consciousness
The classical approximation works well in many situations. But it is unable in principle to account adequately for the observed macroscopic behaviours of large physical systems whose macroscopic behaviours depend sensitively upon the behaviours of their atomic constituents. To comprehend the macroscopic behaviours of large systems of this kind one must, in general, use quantum theory.
According to the orthodox interpretation of quantum theory, the interventions of our consciously chosen (probing) actions are “freely chosen” in the very specific sense that they are not determined by any known law of physics. Yet these actions can affect physically described properties. This conjunction of conditions severs in one stroke the dogma of mechanical determinism that has perplexed and hobbled philosophy for three centuries: twentieth century advances in physics have freed philosophy and psychology from the yoke of the doctrine of the causal closure of the physical.
Orthodox contemporary physics leads on, in a completely natural and rational way, to a theory of the mind-brain system that appears to accommodate neatly the empirical data that, on their face, indicate an effect of our conscious choices on the physically described activities of our brains. In this model the conscious choices actually do what they appear to be doing. They are not redundant or ineffectual. But before moving on to an account of that development I shall flesh out the bare-bones account of quantum mechanics just given.
The following passage is from the end of the chapter that examines some core arguments in John Searle’s recent book, Mind. After describing a process of making a complicated conscious choice my account continues with:
My feelings about what is happening, as I review these complex considerations, in order to make my choice, is that I feel a weight for each idea, and am able to make an evaluation based on the net effect of all of these feels together. This evaluation allows a choice to emerge about how to act in the polling booth, and it calls forth a certain resolve to act in accordance with that choice. The strength of that commitment may, or may not, be sufficient to cause me to act in the polling booth in accordance with my choice, in the face of doubts that may later assail it.
What we want to know is: What is really happening when we make such conscious choices about to act? What, in particular, is the role of these mysterious feelings?
What is certainly true is that there is a reality that I call my stream of consciousness. It contains many complex feelings associated with the various ideas and thoughts that populate it. These realities are known realities; not things that need to be, or can be, said to be something other than the experiences that they actually are: the appearance is a reality.
Orthodox contemporary physical theory requires an observing system that contains elements described in experiential terms. This system is allowed to perform probing actions upon a system described in physical terms, and those actions can change that physically described system and elicit corresponding feedbacks from it. In von Neumann’s version the observing system is, or contains, the agent’s stream of conscious experiences, and has no elements describable in physical terms.
Taken literally, orthodox quantum theory says that each conscious choice of a Process 1 probing action originates in the observing system. This theoretical idea is concordant with the empirical fact that each of my conscious choices of how to act seems on the face of it to draw only upon elements in my stream of consciousness: normally, I seem to make my conscious choices on the basis of what I know and can experience, without having or needing any awareness of what’s going on in my brain.
It is logically and theoretically possible to make also that appearance a reality, within the von Neumann ontology, by imposing the condition that the Process 1 choices be, as they prima facie seems to be, determined exclusively by experiential realities. The immediately present content of a stream of consciousness usually contains knowledge received from recent feedbacks, and other inputs into my consciousness from the neural machinery. Hence my choices can depend indirectly on my brain, even if they depend directly only on experiential realities. But there is no logical or theoretical need for this indirect dependence to be coercive: this indirect dependence need not lead to a choice specified in advance by the immediately preceding state of my brain. For the freedom permitted by orthodox quantum theory is only the freedom to choose how, and when, the preceding physical state is to be separated into disjoint parts. By imposing this condition on the nature of Process 4—namely that the conscious choices depend directly on experiential realities alone— we make our reasons, our knowledge, and our feelings the causes of our choices, with these causes all acting within the latitude provided by the purely physical laws, without being coerced by them. This condition on Process 4 brings reality into accord with appearances, in regard to what is causing our choices to be what they are.
Of course, things are not always what they seem: appearances can be deceiving. Still, for a long time now, reality has been persistently assumed by many scientists to be, in large measure, just what classical physics, naively interpreted, said it was, even though that literal interpretation led first to severe difficulties pertaining to the apparent physical efficacy of our conscious thoughts, and eventually to insurmountable difficulties pertaining to the empirical facts physics. Those facts forced a mathematical change that entailed a startling conceptual change: the need to introduce an experientially described realm that can initiate probing actions that are able to change the physically described observed system, and elicit feedbacks from it. This quantum conception accommodates all the empirical facts of physics, while providing also a causal explanation of the physical efficacy of our conscious thoughts. And it can, as just noted, be brought ontologically in line with the pervasive appearance that our conscious choices arise directly from our reasons, knowledge, and feelings.
While these agreements of the theory, realistically construed, with these appearances might be regarded by some critics not as empirical evidence in favor of the theory, but rather as deceptive illusions, it must be objected that agreement of a theory with appearances is the test of the theory, along with rational coherence. Why should the most enduring and consistent appearance in our lives, the appearance that our reasons and feelings are the basis of our conscious choices, and that these choices can guide our physical actions, take a backseat to appearances of other kinds that are often known to deceive. The historical reason is that those primary appearances could not be reconciled with a theory now known to be false. The quantum ontology encounters no such difficulties, and in fact resolves also another problem with the classical ontology, namely how to explain the existence of causally inert or redundant thoughts within an evolutionary context. What a good theory should do is to account for appearances that have no good reason to be doubted. A theory that is generally concordant with appearances is superior to a theory that conflicts with, hence needs to label frauds, the persistent appearances that are the basis of our lives.
The ontology described above is not a complete ontology. I have merely translated into ordinary words what was already essentially present in von Neumann’s work, and extended it by an application of the quantum Zeno effect. The successes at the fundamental level of this quantum conception of reality do not guarantee that it is the literally true and final answer to the question of how our minds are connected to our bodies. Having once been burned, we are rightfully wary of jumping to conclusions about the “truth” of our theoretical ideas concerning the nature of the reality lying beyond our streams of conscious experiences. Nevertheless, the fact that this putative ontology succeeds beautifully on all of these difficult fundamental points where the classical conception fails miserably, and has no known failures of its own, makes it a huge improvement over the conception of reality stemming from classical physics. It is rationally coherent and expands the scope of agreement between theory and appearances, and is the conception of the mind-brain connection most concordant with orthodox contemporary physics
These passages contain the meat of the book