Happiest Thoughts: Great Thought Experiments of Modern Physics Kent A. Peacock Department of Philosophy University of Lethbridge 1. Introduction: Of Chickens and Physicists A physicist can be defined as a person for whom a chicken is a uniform sphere of mass M. The point of this joke (which this author first heard from a physics professor) is that physicists shamelessly omit a lot of detail when they attempt to model and predict the behaviour of complex physical systems; indeed, one of the important skills that physics students must learn is knowing what to leave out when setting up a problem. This penchant for simplification does not necessarily mean that physicists are hopelessly out of touch with reality, however; for one can learn a surprising amount about how real things behave by thinking about apparently simplistic models. A typical textbook example of a physical model might be the block sliding down an inclined plane. The plane is at a definite angle with respect to the force of gravitation; the block (a rectangular chunk of indefinite stuff) has a given mass, and there will be a certain coefficient of friction between the block and the plane. The assignment might be to calculate the coefficient of friction that would be sufficient to prevent the block from sliding down the plane, as a function of the angle of the plane. Now, no block of material in the world is perfectly uniform, no planar piece of material is perfectly flat and smooth, no actual coefficient of friction is known to arbitrary accuracy, and gravity is never exactly uniform in direction and magnitude. And yet, there are many physical systems in the real world which are sufficiently like idealized models such as this, to a definable degree of approximation, that their observable behavior can be predicted using such models. Models are therefore useful not only because they help us to picture how basic physical principles work in a concrete situation, but also as frameworks on which to hang a practical calculation. Even textbook problems couched in terms of simple models such as the inclined plane amount to thought experiments of a sort. Usually, though, we reserve the honorific Gedankenexperimente for idealized scenarios that give us new insights into the meaning or limitations of important physical concepts, usually by testing their implications in extreme or highly simplified settings. Suppose, for example, that I confusedly believe that all objects fall at a rate that is a function of their mass. Galileo has an elegant thought experiment that shows that To appear in James Robert Brown, Yiftach Fehige, and Michael T. Stuart (eds), The Routledge Companion to Thought Experiments. Preprint posted to philsci archive, August 6, 2016. Comments, corrections, and objections are welcome; contact the author at [email protected]. Happiest Thoughts Page 1 of 34 my notion is a mistake: all objects in a uniform gravitational field must fall with the same acceleration (ignoring air resistance), on pain of outright contradiction.1 Galileo’s thought experiment, like most typical textbook models, can be translated into experiments that can actually be performed. But sometimes one can learn a lot even from thought experiments that cannot be done, at least in the simple terms in which they are first described. Mach invited us to rotate the entire universe around Newton’s bucket of water. No granting agency will fund that feat, and yet Mach’s insights contributed (in a complicated way) to the construction of a theory (general relativity) that has testable consequences (Janssen, 2014). In this chapter I describe several thought experiments that are important in modern physics, by which I mean the physical theory and practice that developed explosively from the late 19th century onwards. I’m going to mostly skip thought experiments that merely illustrate a key feature of physics2 in favour of those that contributed to the advancement of physics. Some thought experiments (such as Galileo’s) provide the basis for rigorous arguments with clear conclusions; others seem to work simply by drawing attention to an important question that otherwise might not have been apparent. Many of the most interesting thought experiments have ramifications far beyond what their creators intended. I’ll pay special attention to one particular thought experiment, defined by Einstein and his collaborators Boris Podolsky and Nathan Rosen (1935). The Einstein-Podolsky-Rosen (EPR) thought experiment dominates investigations of the foundations of quantum mechanics and plays a defining role in quantum information theory; I will suggest that it may even help us understand one of the central problems of cosmology. In the form in which Einstein and his young colleagues first described it, the EPR experiment was another idealization that probably cannot be performed. Despite this, it has evolved into practicable technology. While the thought experiments to be discussed here are key turning points in the history of modern physical theory, in several cases (including the EPR experiment) their full implications remain to be plumbed. It is an extraordinary fact that most of the definitive thought experiments in twentieth century physics were born from the fertile imagination of one person, Albert Einstein. This forces us to ponder the importance of individual creativity in the advancement of science. Music would be very different, and much diminished, had Beethoven died young. If Einstein had not lived, would others have made equivalent discoveries? It seems likely that many of his advances would have been arrived at by other competent physicists sooner or later—except perhaps for general relativity, for the very conception of the possibility of, and need for, such a theory was due to the foresight and imagination of Einstein alone. 2. Sorting Molecules: A Thought Experiment in Thermodynamics We’ll start with Maxwell’s Demon, a thought experiment that bridges 19th and 20th century physics. 1 For a nice analysis of Galileo’s thought experiment, see (Arthur, 1999). 2 Such as the double-slit experiment. For a lucid exposition, see (Feynman, Leighton, & Sands, 1965 Ch. 1). Happiest Thoughts Page 2 of 34 James Clerk Maxwell (1831–79) is best known for his eponymous equations for the electromagnetic field. He also made important contributions to statistical mechanics; in particular, he was the first to write the Maxwell-Boltzmann probability distribution which describes the statistics of particles in a Newtonian gas. Although Maxwell did not originate the concept of entropy (which was due to Rudolf Clausius, 1822–88) he was well aware of the Second Law of Thermodynamics, which, in the form relevant to our discussion here, states that no process can create a temperature difference without doing work. Maxwell fancifully imagined a box containing a gas at equilibrium, with its temperature and pressure uniform throughout apart from small, random fluctuations (Norton (2013a)). A barrier is inserted in the middle of the box, and there is a door in the barrier. A very small graduate student with unusually good eyesight is given the task of tracking the individual gas molecules and opening or closing the door so as to sort the faster molecules into (say) the left side, and the slower molecules into the right. Apparently, then, a temperature difference can be created between the two sides by means of a negligible expenditure of energy. The problem is to say precisely why such a violation of the Second Law of Thermodynamics would not be possible. There is a large literature on Maxwell’s demon, which we can’t hope to do justice to here. (For entry points, see (Maroney, 2009; Norton, 2013a).) It is well understood that there is a sense in which statistical mechanics would, in principle, allow us to beat the Second Law— albeit, in general, only for extremely brief periods of time. The easiest way to create a temperature difference between the two boxes is simply to leave the door open for a very, very long time. Eventually enough fast molecules will, by pure chance, wander into one side and enough slow molecules, again by pure chance, will wander into another, to create a measurable temperature difference between the gasses in the two boxes, at least until another fluctuation erases the gains made by the first. Now imagine that the hole has a spring-loaded door which could snap shut as soon as a specified difference in temperature Δ푇 was detected between the two partitions. The thermometer and door mechanism will have some definite energy requirement, but this can be made independent of Δ푇. If we want Δ푇 to be large enough that it implies an energy transfer greater than the energy requirements of the door mechanism, all we have to do is wait long enough and eventually a large enough fluctuation will probably (not certainly) come along—although the larger we want it to be, the longer we (again, probably) have to wait. (Let’s call this process “fishing for fluctuations”; like ordinary fishing the result can never be guaranteed.) As soon as the desired temperature difference is detected, the door snaps shut and we would have “trapped a fluctuation” in a way that apparently violates the Second Law. This example underscores the point made by Ludwig Boltzmann (and apparently well understood by Maxwell), which is that the Second Law is a statistical statement. Violations of the Law by pure chance are possible. In trying to exorcise Maxwell’s demonic assistant we are dealing with a question of what is overwhelmingly probable, not what is certain in a law-like way. The question is not whether energetically-free sorting against entropic gradients (such as temperature or concentration) could be done at all, but whether it can be done reliably, repeatedly, and in a time span shorter than the life of the observable universe.