The Utility of Effective Theories
“Effective Theories” are theories because they are able to organize phenomena under an efficient set of principles, and they are effective because it is not impossibly complex to compute outcomes. The only way a theory can be effective is if it is manifes
- PDF / 106,381 Bytes
- 6 Pages / 439.37 x 666.142 pts Page_size
- 59 Downloads / 183 Views
The Utility of Effective Theories
1.1 Definition of Effective Theories and Their Purpose “Effective Theories” are theories because they are able to organize phenomena under an efficient set of principles, and they are effective because it is not impossibly complex to compute outcomes. The only way a theory can be effective is if it is manifestly incomplete. “Everything affects anything” is generally correct, but it saps confidence in our ability to predict outcomes. Effective Theories modify this depressing maxim by pointing out that “most things are irrelevant for all practical purposes.” A tree falling in Peru does not appreciably affect a canon ball’s flight in Australia. Any good Effective Theory systematizes what is irrelevant for the purposes at hand. In short, an Effective Theory enables a useful prediction with a finite number of input parameters. With this definition of Effective Theories it appears that all theories are such, and thus giving it a fancy capitalized name is pointless pedantry. However, the proper name is useful to repeat at times as a reminder that the prominent views of science were not always agreeing that theories were necessarily incomplete, and as a reminder to go beyond it when and if the circumstances may arise. Furthermore, the natural tendency of young students entering science is to believe a theory is either right or useless, when they can never be completely right, but rather merely Effective Theories that are “correct enough for our purposes in this domain.” Frequent and formalized reminders of this are helpful for newcomers to the field. The other purpose of emphasizing the name Effective Theories is to force us to confront a theory’s flaws, its incompleteness, and its domain of applicability as an integral part of the theory enterprise. The most useful Effective Theories are ones where we know well their domains of applicability, and can parametrically assess the uncertainties induced by ignoring the “irrelevant.” They may even have a well-defined procedure for becoming more and more complex as one wishes to compute to higher accuracies. This is the case in many Effective Field Theories of particle physics, such as pion scattering or even graviton scattering. There is J. D. Wells, Effective Theories in Physics, SpringerBriefs in Physics, DOI: 10.1007/978-3-642-34892-1_1, © The Author(s) 2012
1
2
1 The Utility of Effective Theories
a science in understanding the circumstances of when questions can be addressed using accurate, convenient Effective Theories, and it is generally acknowledged that scale separation (Hillerbrand 2013) is one important feature of systems that enable an Effective Theory to separate out well the “relevant” from the “irrelevant”. Indeed the phrase “irrelevant operator” is a technical term used in particle physics (Cohen 1993) to identify small contributions to phenomena caused by dynamics at a much different energy scale than is being probed. This issue arises in one form or another in all Effective Theories and will be seen in the examples presen
Data Loading...
