In our search for the ultimate law, P, that allows us to encode the whole of reality we have come across a very fundamental obstacle. As Deutsch argued, P cannot be all-encompassing, simply because it cannot explain its own origins. We need a law more fundamental than P, from which P can be derived. But then this more fundamental law also needs to come from somewhere. This is like the metaphor of the painter in the lunatic asylum, who is trying to paint a picture of the garden he is sitting in. He can never find a way to completely include himself in the picture and gets caught in an infinite regression. Does this mean we can never understand the whole of reality? Maybe so, given that any postulate that we start from needs its own explanation. Any law that underlies reality ultimately needs an a priori law. This puts us in a bit of a ‘Catch 22’ situation. So, are we resigned to failure or is there a way out? Is there some fundamental level at which events have no a priori causes and we can break the infinite regression? What does it mean for an event to have no a priori cause? This means that, even with all prior knowledge, we cannot infer that this event will take place. Furthermore, if there were genuinely acausal events in this Universe, this would imply a fundamentally random element of reality that cannot be reduced to anything deterministic. This is a hugely controversial area, with various proponents of religion, science, and philosophy all having a quite contrasting set of views on this. Often people get very emotional over this question, as it has profound implications for us as human beings. Could it be that some events just don’t have first causes? The British philosopher Bertrand Russell thought so. In Russell’s famous debate with Reverend Copleston on the origin of the world, Copleston thought everything must have a cause, and therefore the world has a cause – and this cause is ultimately God himself.
In our search for the ultimate law, P, that allows us to encode the whole of reality we have come across a very fundamental obstacle. As Deutsch argued, P cannot be all-encompassing, simply because it cannot explain its own origins. We need a law more fundamental than P, from which P can be derived. But then this more fundamental law also needs to come from somewhere. This is like the metaphor of the painter in the lunatic asylum, who is trying to paint a picture of the garden he is sitting in. He can never find a way to completely include himself in the picture and gets caught in an infinite regression. Does this mean we can never understand the whole of reality? Maybe so, given that any postulate that we start from needs its own explanation. Any law that underlies reality ultimately needs an a priori law. This puts us in a bit of a ‘Catch 22’ situation. So, are we resigned to failure or is there a way out? Is there some fundamental level at which events have no a priori causes and we can break the infinite regression? What does it mean for an event to have no a priori cause? This means that, even with all prior knowledge, we cannot infer that this event will take place. Furthermore, if there were genuinely acausal events in this Universe, this would imply a fundamentally random element of reality that cannot be reduced to anything deterministic. This is a hugely controversial area, with various proponents of religion, science, and philosophy all having a quite contrasting set of views on this. Often people get very emotional over this question, as it has profound implications for us as human beings. Could it be that some events just don’t have first causes? The British philosopher Bertrand Russell thought so. In Russell’s famous debate with Reverend Copleston on the origin of the world, Copleston thought everything must have a cause, and therefore the world has a cause – and this cause is ultimately God himself.
Many people in the world of science will often employ terms like 'indeterminacy', 'chance', 'probability', etc., and using knowledge from the world of science they will often attempt to draw philosophical conclusions about the nature of reality as a whole.Claims typically made center around the idea that everything happens by chance, or everything is a result of probability, or that reality is fundamentally indeterminate, etc. But at the root of these claims is a vague and imprecise understanding of what these terms really mean.
Over the last few decades there has been a steadily increasing amount of useful discussion between the fields of science and theology. Robert John Russell has played a major role both as an important scholar and in forming the very effective Center for Theology and the Natural Sciences. Before the twentieth century, science was already remarkably successful and seemed to say that everything happening in our world was completely deterministic. Science now has fundamental laws predicting the probability of particular things happening. The basic and challenging problems or puzzles which the author has selected are of course well recognized by many, and confront any synthesis of science and religion. An electron can never be located at a precise place, nor be known to head in a precise direction. Early in the history of quantum mechanics, many scientists thought that perhaps the unpredictability of phenomena which had been discovered provided a place where God could and was acting.
Even processes that inherently involved chance were pre-determined. Long before dice were used for gaming, they were used for divination. Ancient thinkers thought the gods determined the outcome of a die roll; the apparent randomness resulted from their ignorance of divine intentions. Oddly, modern science at first did little to change that view but it showed that randomness was nothing intrinsic; just a reflection of humanity's lack of information. Here, Brooks examines whether anything in the universe is truly random.
The purpose of this paper is to give a brief survey the implications of the theories of modern physics for the doctrine of determinism. The survey will reveal a curious feature of determinism: in some respects it is fragile, requiring a number of enabling assumptions to give it a fighting chance; but in other respects it is quite robust and very difficult to kill. The survey will also aim to show that, apart from its own intrinsic interest, determinism is an excellent device for probing the foundations of classical, relativistic, and quantum physics. The survey is conducted under three major presuppositions. First, I take a realistic attitude towards scientific theories in that I assume that to give an interpretation of a theory is, at a minimum, to specify what the world would have to be like in order for the theory to be true. But we will see that the demand for a deterministic interpretation of a theory can force us to abandon a naively realistic reading of the theory. Second, I reject the “no laws” view of science and assume that the field equations or laws of motion of the most fundamental theories of current physics represent science’s best guesses as to the form of the basic laws of nature. Third, I take determinism to be an ontological doctrine, a doctrine about the temporal evolution of the world. This ontological doctrine must not be confused with predictability, which is an epistemological doctrine, the failure of which need not entail a failure of determinism. From time to time I will comment on ways in which predictability can fail in a deterministic setting. Finally, my survey will concentrate on the Laplacian variety of determinism according to which the instantaneous state of the world at any time uniquely determines the state at any other time. The plan of the survey is as follows. Section 2 illustrates the fragility of determinism by means of a Zeno type example. Then sections 3 and 4 survey successively the fortunes of determinism in the Newtonian and the special relativistic settings..
In a deterministic theory, one can deduce the state of the universe at any one time from the dynamical laws that govern its evolution and its state at any other time.In particular, one can deduce from the conditions that obtained at some early boundary condition for the universe, its state at all subsequent times.It is a piece of well-received philosophical common sense that there is no room in a deterministic theory for objective probabilities.Arguments will be given below that this piece of philosophical common sense is mistaken, and that a probability measure over the space of physically possible trajectories is an indispensable component of any theory -deterministic or otherwise -that can be used as a basis for prediction or receive confirmation from the evidence.Phase space is the central representational space in physics.It is the space within which all of the states pertaining to a system are represented, and it encodes all of the general information that we have about those states.To take an obvious example (less obvious examples will be given below) the fact that a pair of quantities are represented by different dimensions in phase space encodes the fact that they represent separate degrees of freedom.Physically possible histories are represented by trajectories through phase space and in a deterministic theory, when dealing with a closed system, there is (no more than) one trajectory through each point.Since the universe as a whole is the only truly closed system, this means there is one trajectory through each point in the phase space of the universe.Probabilities may be invoked in applications of theory, when the state of a system or the values of external variables are not known with full precision, but they are eliminable given complete knowledge.And they don't appear in the statement of the laws.The laws serve simply to identify the physically allowable trajectories.About Newtonian dynamics, Laplace famously said "given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings who compose it -an intelligence sufficiently vast to submit these data to analysis -it would embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom; for it, nothing would be uncertain and the future, and the past, would be present to its eyes."ii It is a short step from this to the idea that probabilities invoked in classical contexts are subjective rather than objective.If they represent anything, it is facts about our epistemic states, not facts about the world.iii Popper, and Lewis, and other influential figures have endorsed this view, categorically rejecting any role for objective probabilities indeterministic contexts.In Popper's words:
When investigating various interpretations of quantum mechanics one notices that each interpretation contains an element which escapes a complete and full description. This element is always associated with the stochasticity of the individual event in the quantum measurement process. It appears that the implications of this limit to any description of the world has not been sufficiently appreciated with notable exceptions of, for example, Heisenberg, Pauli and Wheeler. If we assume that a deeper foundation of quantum mechanics is possible, the question arises which features such a philosophical foundation might have. It is suggested that the objective randomness of the individual quantum event is a necessity of a description of the world in view of the significant influence the observer in quantum mechanics has. It is also suggested that the austerity of the Copenhagen interpretation should serve as a guiding principle in a search for deeper understanding. In recent years, a significant increase of interest in the foundations of quantum mechanics can be observed. This increase is certainly related to the immense progress made during the last two decades in experiments with individual quantum systems. This technological progress has made it possible to really perform more and more of the famous gedanken experiments which were so important in the early days of the theory. Not only did these experiments confirm the theory in every detail, they also opened up avenues for new experimental directions which might even lead some day to new technology. While such applications are certainly still far away, areas like quantum cryptography[1], quantum computation[2] and interaction-free measurement[3], just to name a few examples, certainly deserve the attention they receive. All this activity has also drawn more attention to the problems of understanding and interpreting quantum mechanics. It seems that there, a definitive consensus has not yet been reached. As witnesses quote authorities like Feynman as saying[4]: I think can safely say that nobody today understands quantum mechanics, whereby he apparently included himself, or like Roger Penrose[5], who describes his opinion remarking that while the theory agrees incredibly well with experiment and while it is of profound mathematical beauty, it makes absolutely no sense. Why did even physicists who have contributed so significantly to quantum theory Feynman was even rewarded the Nobel Prize for one of its mathematical formulations choose such emphatic and strong formulations? Why is it that the average physicist hears very little about such problems during his/her education? Why is the comprehension of the theory very often focused on formalism while questions that probe for deeper meaning are usually not tackled? To take a closer look at the situation, let us turn to a brief analysis of the interpretation of quantum mechanics. We note that there are at least two levels of interpreting a formalism, a physical theory. The first, basic, level supplies the rules that determine which element of the formalism corresponds to which measurable quantity or to which observable fact in a concrete experimental situation. Theses rules are a large, mostly not explicated but only implicit, set of instructions. These instructions concern the manner of working with the statements of the theory in order to obtain predictions for future experiments or events, and they concern the instructions on how to proceed in experiment in order to demonstrate or test a theoretical