Finding the Foundations Supported by the Whole

I’ve just finished reading Roberto Torretti’s Relativity and Geometry, a somewhat demanding philosophical discussion of the foundational ideas of Einstein’s two theories of relativity. Over the course of the book, as he discussed those foundational ideas of relativity, he builds up to a conclusion which is true enough, but does beg some questions. He points out that Einstein was able to avoid the philosophical assumptions of empiricism, axiomatic systems, and conventionalism.

So what did Einstein do, what sort of thinking did he engage in while being such a creative storm in theoretical science? More generally, what does it mean to think so that we’re not unduly bound by empiricism, axiomatic systems, and conventionalism? Is there a more positive way to speak of such a way of thought?

Torretti gives one example of one mathematical physicist who was not able to escape the bonds of conventionalism circa 1900. Poincare was in a position to develop a full-blown special theory of relativity before Einstein did so, but the great French scientist held a conventionalist viewpoint that prevented him from seeing the possibility that the equations he’d developed might be pointing to a greater truth. In fact, he’s one of the thinkers mentioned in a Wikpedia article, Conventionalism, where we can read the definition:

Conventionalism is the philosophical attitude that fundamental principles of a certain kind are grounded on (explicit or implicit) agreements in society, rather than on external reality.

[The article is weak but the definition checks out well enough so I kept this reference for convenience.]

In Empiricism, we can read:

In philosophy, empiricism is a theory of knowledge that is practical rather than abstract, and asserts that knowledge arises from experience rather than revelation.

Finally, in Axiom, we can read:

In traditional logic, an axiom or postulate is a proposition that is not proved or demonstrated but considered to be either self-evident, or subject to necessary decision. Therefore, its truth is taken for granted, and serves as a starting point for deducing and inferring other (theory dependent) truths.

I should point out that our primary knowledge does arise from experience and that there are truths which are so self-evident as to be built into the very functioning of our physical bodies. There are also social aspects to the specific problems chosen by particular scientists, in the way they state even the most abstract of truths, and so on. However, we seem to be able to somehow access domains of knowledge of abstractions, generalizations from our experiential knowledge and the truths built into our very brains and fingers — all colored by our social situations, that includes possibilities not known to be realized and even possibilities which can’t be realized in our universe. I’ll leave that issue undeveloped in this entry. Any reader wishing to read more about my take on the nature of Creation and the human mind can explore this blog. It might be a good idea to start with the earliest entries in Christian in the Universe of Einstein and Mind.

Einstein was pursuing a better formulation of the truth about the physical world and was first led on by the conflicts in the basic assumptions of reality between Newtonian mechanics and Maxwell’s statement of electromagnetic theory — the impossibility of reconciling Galilean relativity with Maxwell’s equations was perhaps the major problem. After the special theory of relativity was established, he wanted to reconcile intertial mass with gravitation mass (weight). Einstein achieved that second goal by developing the general theory of relativity and, perhaps to his surprise, found that he’d developed a theory that could be used to define and describe a universe as well as various strange objects inside the universe — such as black-holes.

As it turned out, a theory that reconciles inertial mass and gravitational mass (weight) describes such fundamental aspects of a universe that it’s a definition and description of important aspects of a universe, at least of possible universes similar to this one.

We can think of gravity as that which unifies our universe and it is longer surprising that a reconciliation of inertial mass and gravitional mass leads to Einstein’s field equation giving a relationship between the shape of space-time and the distribution of matter-energy for an ‘isolated’ gravitationally bound system which can be merely a black-hole or it can be an entire universe or it can even be a more ordinary object in this universe which can be treated as gravitationally isolated. As Wittgenstein might have said: Einstein had penetrated to the foundations and found they were being supported by the entirety of the structure.

Einstein himself has been quoted as defining a scientist as an unscrupulous opportunist, a way both humorous and dramatic to say that good science is often the result of seeing the importance of an unexpected result and exploring it in a fruitful manner. Some of the dramatic examples are in the experimental fields but the fruitful explorations of Einstein’s field equation from the general theory of relativity provide another good example. While it was interesting and important that observer’s were able to see light being bent by the sun’s strong gravitation field and most of the perhelion shift of Mercury was explained, the real action was along another line of development starting with Schwarzschild’s early solution of the field equation which eventually was seen to be a description of a non-spinning black-hole. The ante was upped when Friedmann found a solution which proved to be for an expanding universe with a bounded space-time. Other solutions were found, including that of Godel in which the entire universe rotated and could be detected as rotating and in which time could move in either direction.

Not only had ‘universe’ been defined in a scientific manner, but a small number of possible universes had been described, one of which — corresponding to Friedmann’s solution — is at least similar to our universe. Not only had general relativity given a way of defining a universe, it had provided an abstraction so that various possible universes could be defined. In a sense, Einstein had not only found a way back to the so-called Big Bang, he had found a way to pass through it and explore parts of Creation which are at least one phase closer to what I call the Primordial Universe, the manifestation of truths that God had selected for Creation, from which truths He had shaped this particular universe.