Involved in the foundations of physics, as a Jesuit
Jesuit Scholars in a Postmodern Age meeting
April 23, 1995Ron Anderson, S.J.
I have attached copies of two papers [1][2] related to a project I have been working on for several years with some physicist friends at Melbourne University. They are on rather technical topics in the foundations in physics and not that accessible without a background in physics and mathematics. However, I will try to use them and my involvement in this work to address some of the concerns of our Jesuit Scholarship in a Postmodern age project.
In the following I will introduce the subject matter of these papers in a way that hopefully gives an indication of the disciplines the project involves and some hint of the general sorts of problems addressed by the papers. My main focus will be on the shorter paper that appeared in a journal in February this year. I will also say something about how I became involved in this project, its importance to me, and the way I work in this area. At our meeting on April the 23rd I'll say a bit more about all of these issues.
My aim is to allow this example of a research project to provide a basis on which to get at the underlying issues as to how we do our work as Jesuit scholars today, how we undertake choices in what to do, and how we inform our research projects with certain habits of mind and heart. There is also the tantalizing question of how the practice of scholarship in particular disciplines and contexts could inform the way we practice our Jesuit lives.
1) General comments on the project:
There are various sorts of number systems. The one we are most familiar with (the "real" numbers) includes integers (1, 2, 3.....etc), "rational" numbers (e.g. fractions such as 1.25, 1.5 etc), and negative numbers (-1, -2...). We do various things with these numbers such as add, subtract, and multiply them, and we form abstract systems of mathematics such as algebra to describe their properties (e.g. the addition of two numbers can be represented by "a + b = c," an expression which represents an infinite number of such operations of adding two particular numbers to get a third, such as 1 + 2 = 3).
To describe nature requires we use numbers and abstract number systems. Using imagery from another discipline, one could say that the language best suited for texts about nature is mathematics. There has been considerable reflection on the significance of the fact that parts of nature can be successfully described with mathematics, a feature that has been referred to as the "unreasonable effectiveness" of mathematics in physics. The main focus of the 1993 paper was to explore one particular way this seems to happen, and to argue that certain directions in the development of mathematics, in particular, increasing abstraction and generalization, lead to the type of mathematics most likely to be used in new physical theories.
As well as the standard real numbers mentioned above, there are also other systems of numbers with similar properties. A number system of mathematics objects now know as "complex numbers" was discovered in the 17th century, and "quaternions" were discovered in 1843 by the Irish mathematician and physicist, William Hamilton. Complex numbers have two "parts" to them, while quaternions have four. Complex numbers and quaternions have all the properties of the familiar real numbers when it comes to operations such as multiplication, addition etc. There is only one other (it can be formally proved) number system that has these properties.
Complex numbers now have a well established place in physical laws. While quaternions are useful in some situations, their place is not as central as complex and real numbers. The project is to do with exploring the implications of the use of quaternions in particular physical theories.
The project also invites a more general reflection on the very role and place of "number systems" in describing nature.
2) Disciplines woven into the project:
Physics:
This is most to the fore in the 1995 paper. This paper considers a form of quantum mechanics using quaternions, and the implications for particular physical situations. Quantum mechanics was developed in the early decades of this century and deals with the microscopic world. In its standard form complex numbers are an important part of the theory. The 1993 paper considers various physical theories that use quaternions.
Mathematics:
The 1993 paper deals with some of the "pure" mathematical properties of quaternions. Also, since the project is one to do with theories in theoretical physics, mathematics is an intrinsic part of the project, although the concerns are not directly those of mathematicians.
History of Physics and Mathematics:
The argument in the 1993 paper is based on historical evidence as to how mathematics has been used in physics. The 1995 paper is on a contemporary systematic topic, however, the historical dimension is present in the way it locates itself with respect to previous work in the standard way of "review of the past"
Philosophy (or Foundations) of Physics:
The argument in the 1993 paper ? that certain types of mathematics are likely to be productive for the development of new physical insights ? is, in one sense, a "meta-argument" about the nature of physics, and therefore could be placed in the camp of philosophy of physics. Still, if true, then it has implications for the practice of physics, and in this sense is directly relevant to the practice of physics and thus part of physics.
The 1995 paper is on the metaphysical implications of quantum mechanics. This theory has shown that there exist influences (described as "spooky" by Einstein) that occur between events at places widely separated from each other, and between which there appears to be no causal influence of a readily understandable sort. Parts of our world are strangely "entangled" or "correlated" with each other. The idea in this paper was to explore how quantum mechanics using quanternions differs from standard quantum mechanics in what it says about these correlations. Here we are addressing some fairly traditional concerns in the philosophy of nature.
It's difficult to separate out the various disciplines involved in this project. Pursuing certain questions means drawing on elements from various "mainstream" disciplines.
3) The people and place involved in this project:
Girish Joshi was the supervisor for my degree in physics from Melbourne University. S. P. Brumby, one of the authors on the 1995 paper, is one of his present graduate students. Most of my years within the Australian Jesuit Province were spent in Melbourne and one of the attractive features of this project is the contact it provides me with people and places there.
4) Mode of developing papers:
Girish Joshi normally visits Boston around the middle of the year, and I usually visit Melbourne in December. The project is somewhat of a background one for me, where little is done on it for months, and then a good bit of time is put in when the final form of a paper is being developed. Currently we are in a quiet period in which the general ideas for the next paper are being thought out. While the time together on these visits is an important part of the collaboration, most of the details to do with working out papers takes place on e-mail. In many ways I have found e-mail to be a more efficient way for developing papers than working together in one place, as it forces texts to be generated which form the basis for papers. In developing these papers one person had "control" of the text, while others fed in comments, written sections for inclusion, proposals for redrafts of sections etc. It's a process involving compromise and criticism, and it is often hard to separate out various contributions to the final set of ideas that form the paper.
My experience is that it's a process that allows inspiration for new ways of thinking to arise by one being forced to understand and respond to the various contributions from others. In the 1995 paper there were places when various parts (even sentences) when through numerous redrafts (over many days) before the final form was agreed upon.
The immediacy of the type of connection with e-mail is such that at times, when working with those in Melbourne, I find myself consciously noting the time zone of Melbourne, and when to expect responses (also, there are now ways of finding out from afar if computers are on and when they were last used).
5) My own research agenda in this project:
I find that questions that most interest me in the philosophy of physics are ones that draw on the particular content of physical theories. Working with those full time in physics is an excellent way to keep in contact. As well, due to time constraints as well as limitations of my own abilities, collaborating with those working directly in physics enables me to explore questions in a way I could not on my own.
6) Some aspects that attract me about this work:
1) Finding out how the world "works" has been one of my long standing interests, and the general site I usually place myself in, the philosophy and history of physics, is such to allow me freedom and scope to pursue this interest.2) I also find I enjoy trying to understand something that is beyond me such as (in an obvious sense) the world, and will forever be beyond me, something that's objective and steadily and coolly present to me, something that I can only grasp by respecting the way it is. I find myself at home with this sort of "recalcitrant fixity" that characterizes nature, which is somewhat in contrast with my unease with the fixity one can find affirmed in human constructs of institution and culture with their claims of authority and exercise of power.
3) Working in this discipline gives me a sense of being connected with the world. I'm exploring theories such as quantum mechanics which deal on some level with every material thing.
4) I also enjoy working with others on collaborative projects and this provides me with another sense of connectedness.
5) Mathematics is a discipline to do with many possible mathematical forms and structures. Only some seem to be relevant to describing the work. Searching out and hunting down those which seem to be relevant, and reflecting on why they are relevant is attractive. The results are often unexpected and sometimes initially strange and unsettling.
6) I also have some long term interests in matters to do with God's relationship to the world such as the problem of how one can understand God's action in the world. I occasionally worry about these issues, but at the moment I defer working on them directly. It seems better that I be directly absorbed in trying to understand parts of nature.
7) Possible Jesuit dimensions:1) This project brings me into contact with others in a common activity to understand aspects of nature, and the "larger" issues about the meaning of this understanding. To be part of such an activity as a Jesuit gives me a sense of making my Jesuit world, with its particular commitments, part of this activity.2) A collaborative project such as this keeps me in touch with the different places in the world that are woven into my life, and works to "spread" out my life, and its Jesuit dimension beyond my local world.
3) Working in this area gives me a sense of the continually changing and growing nature of our understanding of nature, a sense which I suspect influences my view of many other elements of my life, including the way I view my Jesuit life.
4) Related to the continually changing nature of scientific understanding, there's an "iconoclastic" spirit that permeates the practice of science, a spirit (at least in the ideal) that rigorously resists any forces other than those that bring one closer to understanding nature. I would hope this spirit works in "analogous realms" in my Jesuit life. Also, when working on new approaches to a problem one is required to be suspicious of other approaches (a spirit that is instinctive in the practice of science), but suspicious in a way that's balanced by accepting many of their elements. As time goes on I recognize that this sort of "critical complicity" is a valuable way to understand my involvement in other areas of my life.
5) In pursuing foundational questions in physics I have become increasingly involved in the history of physics, and aware of the resources there for understanding the present practice of science. This has given me a sense of the power of history for understanding the present and for subverting and challenging theories about science. At the same time issues of historiography of science have become important to me ? questions such as how to represent the past scientific practices and texts, and the type of knowledge needed to understand them. The nature of science generates questions to do with proper approachs to its history that are different from those to do with the history of other disciplines. These issues have made me aware of the important of how we represent our Jesuit past for conceiving of ways of living Jesuit life today.
6) While I don't usually refer to it, within the discipline of the foundations of physics is the issue of the balance between the "constructive" element in knowledge about nature (and mathematics) ? the part contributed by the self ? and the "given" element ? the element independent of the self. To what extent do we create and construct representations of nature that say more about ourselves than nature, and to what extent do we form representations that reflect what exists in nature? On what ground are the foundations of knowledge built? This is one of the old issues in the theory of knowledge, and confronting it in this area of my work invites me to reflect on the parallels of this "constructive"/"given" distinction in my religious and personal life.
1) "Quaternions and the Heuristic Role of Mathematical Structures in Physics," with G. C. Joshi, Physics Essays, 6, 308-319 (1993). Abstract and source2) "Multi-particle Correlations in Quaternionic Quantum Systems," with S. P. Brumby and G. C. Joshi, Physical Review A, 51, 976-981 (1995). Abstract and source
April 12, 1995