Effective Theories of Classical Gravity
If the concepts underlying Effective Theory were appreciated from the earliest days of Newtonian gravity, Le Verrier’s announcement in 1845 of the anomalous perihelion precession of Mercury would have been no surprise. Furthermore, the size of the effect
- PDF / 273,092 Bytes
- 28 Pages / 439.37 x 666.142 pts Page_size
- 35 Downloads / 242 Views
Effective Theories of Classical Gravity
Abstract If the concepts underlying Effective Theory were appreciated from the earliest days of Newtonian gravity, Le Verrier’s announcement in 1845 of the anomalous perihelion precession of Mercury would have been no surprise. Furthermore, the size of the effect could have been anticipated through “naturalness” arguments well before the definitive computation in General Relativity. Thus, we have an illustration of how Effective Theory concepts can guide us in extending our knowledge to “new physics”, and not just in how to reduce larger theories to restricted (e.g., lower energy) domains.
3.1 Introduction The purpose of these lectures is to introduce the concepts of Effective Theories to students of Philosophy, Mathematics and Physics who have a shared interest in the philosophy and history of physics. The concept I wish to discuss, Effective Theory, is a thoroughly modern notion; nevertheless, I wish to illustrate it with a very old and intuitively accessible problem in physics: Mercury’s anomalous perihelion precession. Le Verrier announced in 1845 a small discrepancy in the precession rate of Mercury’s perihelion compared to Newton’s theory, even after taking into account all the disturbing influences throughout the solar system such as the effect of other planets’ orbits.1 This came as a surprise, and more or less nobody believed at the time that it was the fault of Newton, but rather the fault of observers who had not seen the other celestial bodies that must surely be perturbing Mercury’s orbit. Historically, that is the beginning of the problem. Le Verrier believed that an as-yet unobserved mass distribution inside the orbit of Mercury was the source 1
In 1859 Le Verrier gave a number for this advance: 35 arcseconds per century (Le Verrier 1859). It was later reevaluated by S. Newcomb (Newcomb 1882), who determined the correct value of 43 arcseconds per century. J. D. Wells, Effective Theories in Physics, SpringerBriefs in Physics, DOI: 10.1007/978-3-642-34892-1_3, © The Author(s) 2012
15
16
3 Effective Theories of Classical Gravity
of the discrepancy. He and others advocated the existence, for example, of a new small planet (“Vulcan” as it was sometimes called) that would be observed when astronomers developed the instruments necessary to find it (Roseveare 1982). Such was not the case. By the 1890’s it became clear to most that new large-scale object(s) was not the explanation (Oppenheim 1920), despite some ill-fated protestations otherwise (Poor 1921). The resolution of the problem came with Einstein’s General Relativity, which predicted precisely the 43” of arc per century observed, and the case was closed. However, I want to argue that anticipation of the “problem” could have occurred much before Le Verrier. What prevented scientists from anticipating Mercury’s perihelion precession was not lack of mathematical skill, or lack of experimental abilities. It was solely due to not having the right mindset. Unlike perhaps in decades and centuries gone by, no c
Data Loading...
