## In Memorium

Posted by on Wednesday, February 7, 2018

There is some sad news to report this month, with the passing in January of one of my friends and mentors, Dr. Fred Cooperstock. Not only was he an accomplished physicists making significant contributions to the study of the general theory of relativity, but he was also a much loved and respected instructor to generations of physics students at the University of Victoria.

As a theoretical physicist he was best known for the Cooperstock Energy Localization Hypothesis, which argued that gravitational fields only contain energy in the presence of non-gravitational fields or matter. In vacuum the energy vanishes. Although general relativity has been studied extensively for over a decade, there is still an open problem on calculating how much energy the gravitational field contains, and whether that energy contributes to the curvature of spacetime. Because gravity is essentially an illusion created by the curvature of spacetime, and for other more technical reasons, it is difficult to calculate its energy in a definitive manner. As yet the energy localization hypothesis remains just a hypothesis, but if it is eventually proven then it will have a major impact on our understanding of gravity and the Universe.

Another important contribution that he made was the Cooperstock-Tieu solution of Einstein's field equations which describes the properties of spacetime in and around galaxies such as our own Milky Way. Although galaxies have also been studied by astronomers and astrophysicists for decades, it had always been assumed that the traditional Newtonian gravity would be an adequate approximation to the full general relativistic gravitational fields. In the mid-2000s Cooperstock and his graduate student solved Einstein's equations for a reasonable approximation of the mass distribution of a galaxy, and demonstrated how Newtonian gravity might not be adequate. (I must mention here that there was a flaw in their solution which lessened the impact of their discovery, in that they had inadvertently included an additional massive disc inside the galaxy which resulted in additional gravitational forces. This was corrected in later research papers.)

On a more personal note, Fred Cooperstock was also a friend and mentor to many physics students over the course of his long career, including me. I first met him in September 1997 when I took his class in advanced classical mechanics, and would go on to learn general relativity and relativistic electrodynamics with him when I was a graduate student. In the latter class I was the only student by the end of the course, and often our classes were in the form of one-on-one discussions on a wide range of topics in theoretical physics. (When I was in my final years as an undergraduate student we even started on a formal research project together with plans to publish, which would have been the first academic papers of my own research career, but outside forces prevented it from happening. ) After the class was finished, we continued having these chats about modern physics for another ten years, ending only with my graduation and his retirement. Dr. Cooperstock was the first person to really teach me how to simplify complex theories and ideas for students, and how to present research to an audience of my peers.

He was a good teacher, mentor and friend to generations of students and colleagues, and he will be missed by many.

Rest in Peace.

As a theoretical physicist he was best known for the Cooperstock Energy Localization Hypothesis, which argued that gravitational fields only contain energy in the presence of non-gravitational fields or matter. In vacuum the energy vanishes. Although general relativity has been studied extensively for over a decade, there is still an open problem on calculating how much energy the gravitational field contains, and whether that energy contributes to the curvature of spacetime. Because gravity is essentially an illusion created by the curvature of spacetime, and for other more technical reasons, it is difficult to calculate its energy in a definitive manner. As yet the energy localization hypothesis remains just a hypothesis, but if it is eventually proven then it will have a major impact on our understanding of gravity and the Universe.

Another important contribution that he made was the Cooperstock-Tieu solution of Einstein's field equations which describes the properties of spacetime in and around galaxies such as our own Milky Way. Although galaxies have also been studied by astronomers and astrophysicists for decades, it had always been assumed that the traditional Newtonian gravity would be an adequate approximation to the full general relativistic gravitational fields. In the mid-2000s Cooperstock and his graduate student solved Einstein's equations for a reasonable approximation of the mass distribution of a galaxy, and demonstrated how Newtonian gravity might not be adequate. (I must mention here that there was a flaw in their solution which lessened the impact of their discovery, in that they had inadvertently included an additional massive disc inside the galaxy which resulted in additional gravitational forces. This was corrected in later research papers.)

On a more personal note, Fred Cooperstock was also a friend and mentor to many physics students over the course of his long career, including me. I first met him in September 1997 when I took his class in advanced classical mechanics, and would go on to learn general relativity and relativistic electrodynamics with him when I was a graduate student. In the latter class I was the only student by the end of the course, and often our classes were in the form of one-on-one discussions on a wide range of topics in theoretical physics. (When I was in my final years as an undergraduate student we even started on a formal research project together with plans to publish, which would have been the first academic papers of my own research career, but outside forces prevented it from happening. ) After the class was finished, we continued having these chats about modern physics for another ten years, ending only with my graduation and his retirement. Dr. Cooperstock was the first person to really teach me how to simplify complex theories and ideas for students, and how to present research to an audience of my peers.

He was a good teacher, mentor and friend to generations of students and colleagues, and he will be missed by many.

Rest in Peace.