January 2008: Issue Four: Page 7



Student Comment: (continued...)
One of the advantages to a post-Newtonian view of the law is that it would spare lawmakers from making artificial distinctions. Tribe continues:
The most basic substantive principles affecting the kinds of things that government may do in its dealings with people should not depend on accidents of form and appearance—like the accident of whether the government exerts pressure through a single administrative regulation instead of through a series of judicial rulings, or by imposing a fine on those who do something instead of offering a benefit only to those who agree not to do it. Id. at 37.
The purpose of this student comment is to provide an example from General Relativity to further illustrate the folly of artificial distinctions. According to Newtonian Mechanics, gravity is a force which pulls massive objects together. But, because the Earth has not gone crashing into the Sun, Newtonians had to posit the existence of a force that counteracts gravity when one object is circling the other. This force, the centrifugal force, differs from other forces in that no object seems to cause it. It simply appears when needed. Alternatively, according to General Relativity, the Earth stays in its orbit because it is traveling a geodesic, the shortest path given the curvature of spacetime. It is not necessary to invoke the centrifugal force as a way of balancing gravity because gravity is not a force—it’s the result of spacetime curvature.
Marek Abramowicz, a professor of astrophysics at Göteborg University, one of the major universities in Europe, likes the idea of the centrifugal force because when we drive around in a circle it feels like a force is pushing us outward. So he extended the concept of centrifugal force to the arena of General Relativity. See Marek Abramowicz, Black Holes and the Centrifugal Force Paradox, Scientific American (March 1993). He took the curvature of spacetime and carved its effects into “gravity” and “centrifugal force.”
Unfortunately, when an object is in orbit close enough to a black hole, the “centrifugal force” pushes in the same direction as gravity, rather than against it. In order to save intuitions about the “centrifugal force,” Abramowicz proposed that we change what we mean by “outward” and “straight” so that it sounds like the centrifugal force always points in the right direction. However, the definitions he devised for these terms are artificial, designed only to fit the case of an object moving in a circle around a black hole. It turns out that if the object orbits in an ellipse instead of a circle, his new definitions fall apart. (To see the mathematics behind this statement, please click here).
The problem with redefining terms to suit a specific situation is that the definitions are unlikely to behave well everywhere. It is not surprising that Abramowicz’s attempt to save the relativistic version of centrifugal force failed when considering alternative situations given that his new definitions of “outward” and “straight” were introduced to save “centrifugal force” from clashing with intuition.
In General Relativity, “gravity” and “centrifugal force” are really two sides of the same thing. It’s possible to make the distinction between them and treat them differently, but doing so can have bad consequences. Similarly, in law, imposing a fine for doing something is just the other side of offering a benefit for not doing it. As Tribe concludes:

Plant: (continued...)
“Once you start to get those kinds of divergent interests all focused on one common goal, that’s when you hit a real tipping point and things start to change.”
Further evidence that there has been a real shift in public thinking is the success of the GEO, an office created by Governor Ritter on April 16, 2007. The GEO is helping to transfer technology from research labs into the marketplace, accruing new technology from various research projects, and stimulating “this emerging economic opportunity of renewable energy and energy efficiency,” says Plant.
“Overall we have the much larger focus of really changing the paradigm of how we consume energy and how we emit pollutants into the air. We realize that we cannot continue down this same road. So there need to be some very profound shifts in the amount of pollutants we are putting into the air. It’s going to come through a variety of things, but primarily we are seeing it come through conservation going on across the state and renewable energy taking the place of more traditional fossil fuels, so that we end up with more of a mix of energy resources as opposed to having a large reliance on one very polluting form of energy.”
Plant believes that CEES plays an important role in this change. “I think House Bill-1203 [which provided CEES with a grant to study Colorado’s energy use, please see EESI News Issue One for more information] was a very important step for the state in recognizing that if we are going to make changes in all the ways we have been talking about, we need to first quantify what the best ways are to get there, what our current resources are, what our current opportunities are, and what we need to do so that we can develop that well integrated plan. It’s a fairly large challenge, but the work of CEES is going to really help us be able to achieve that.”
