In search of continuity: thoughts of an epistemic empiricist

📝 Abstract

Is the universe digital or analog? In this essay I argue that both classical and quantum physics include limits that prevent us from definitively answering that question. That quantum physics does so is no surprise. That classical physics does so is rather unexpected. In fact, I argue that classical physics is itself really nothing more than a convenient approximation. Either way, it turns out that our knowledge of the universe is discrete and so it is extraordinarily difficult, perhaps even impossible, to determine the underlying continuity of the universe itself.

💡 Analysis

Is the universe digital or analog? In this essay I argue that both classical and quantum physics include limits that prevent us from definitively answering that question. That quantum physics does so is no surprise. That classical physics does so is rather unexpected. In fact, I argue that classical physics is itself really nothing more than a convenient approximation. Either way, it turns out that our knowledge of the universe is discrete and so it is extraordinarily difficult, perhaps even impossible, to determine the underlying continuity of the universe itself.

📄 Content

arXiv:1106.1124v1 [physics.hist-ph] 6 Jun 2011 In search of continuity: thoughts of an epistemic empiricist Ian T. Durham∗ Department of Physics, Saint Anselm College, Manchester, NH 03102 (Dated: November 8, 2021) This essay is dedicated to the memory of my father-in-law Lawrence Brodה′′ע December 30, 1942 - February 6, 2011 I. FRAMING THE DEBATE What does it mean for something to be physically continuous? Does it mean the object can’t be broken down into individual parts or does it simply mean the individual parts are intrinsically linked? And what about reality itself, particularly as it is manifest in the physical universe within which we abide? These are heady questions that have long trou- bled physicists, mathematicians, philosophers, and even theologians. As the great French physicist Louis de Broglie noted, [t]he conflict between the continuous view in Physics, and its opposite, has ex- isted through many centuries with varying fortunes, each gaining an advantage over the other in turn, and neither winning a definite victory. For the philoso- pher there is nothing surprising in this, since the development of theory in every sphere of intellectual activity shows him that, if pushed to an extreme and op- posed to each other, the concepts of both the continuous and the discontinuous are unable to give a correct rendering of Reality, which requires a subtle and almost indefinable fusion of the two terms of this antimony. [1], p. 217 What is perhaps most intriguing about de Broglie’s statement is the last line in which he suggests that a proper rendering of physical reality requires some ‘indefinable fusion’ of the continuous and the discrete. There are two points to be considered here. The first is the most obvious: whether or not reality really requires both continuous and discrete views as opposed to one in lieu of the other. The second is more subtle: are we speaking of physical reality here or merely our rendering (knowledge) of it? It seems to me that these are two distinct questions to be considered for it is entirely conceivable that the continuity of our knowledge about reality might be wholly distinct from the continuity of reality itself. The distinction between states of reality and states of knowledge is described quite suc- cinctly by Spekkens in [2] where he applies the terms ontic and epistemic to refer to states of reality and knowledge respectively. In order to fully understand the distinction between these two types of states, let us look at simple, classical (and uncontroversial) examples of both. The state of a clock, for instance, at a specific time at which we can specify the exact alignment of all the gears, hands, and dials, is considered an ontic state. Conversely, the state of a molecule in a volume of gas, as specified, say, by its translational kinetic energy, is ∗idurham@anselm.edu 2 an epistemic state since it can only be predicted probabilistically using standard statistical mechanics. As Spekkens points out, the distinction between these two types of state breaks down for states of complete knowledge. So, for instance, if we could ‘freeze’ our hypothetical gas at an instant in time and hone in on this one molecule, classical physics assumes that we could specify its exact state (since it allows for the specification of instantaneous values for quantities such as velocity - I will have more to say on this a bit later). Spekkens’ epistemic interpretation of quantum mechanics thus deals specifically with states of incomplete knowledge. But what about those states of complete knowledge? Are they anything more than a pipe dream? Can we ever really know something fully? As it turns out, these questions are intimately related to the debate between the continuous and discrete views. Thus we can frame the continuity debate in terms of ontic and epistemic states. Arguably we are most interested in exploring the continuity of the ontic states since the real point of all this is to understand reality. But what if the only way to get information about ontic states is through epistemic states? Further, what if the epistemic states themselves are discrete? How could we even determine if the underlying ontic states were continuous or not if the ‘lens’ through which we view them is discrete? These questions, however, deal with individual states rather than reality as a whole. The process becomes considerably more murky when we ask questions about reality itself. Is it even possible to reach conclusions about a reality that we are within and thus an integral part of? We may never find answers to some of these questions, but we can still learn a great deal about the universe and our ability to analyze it by considering them. In doing so, however, we will find that the comfortable bosom of classical physics is nothing more than a mirage built on hundreds of years of human instinct and nature. In the process we have so tightly woven mathematics and physics together that it sometimes becomes difficult t

This content is AI-processed based on ArXiv data.