To: Christopher F.
From: Geoffrey Klempner
Subject: Space and time: substantivalism vs. relationism
Date: 9th December 2008 11:36

Dear Chris,

Thank you for your email of 28 November, with your essay towards the Associate Award, 'Substantivalism vs. Relationism in Space Time Theories.'

This reads like a useful summary for physicists who are looking to be informed about the history of the substantivalism vs relationism debate, together with some pointers to the current state of debate. However, I was a bit disappointed that there was not more philosophy here.

It could be argued that the debate between substantivalism and relationism is a perfect example of a problem which was once thought 'philosophical' but has now been taken over by science: in other words, an illustration of Comte's theory of 'positivism'. The ultimate aim of science is to overcome philosophy. However, so long as we lack the requisite scientific knowledge, we have to make do with philosophical 'speculation'.

However, even hardnened scientific critics of philosophy would regard that picture as too simplistic, at least with regard to the problems of space and time. There are still deep philosophical issues to get into, even if we have to accept that our questions cannot all be resolved a priori.

It is fair to say that the majority of philosophically informed readers would have lost the thread of the essay long before the end. Your summary of the most important historical arguments -- Leibniz's application of the identity of indiscernibles (plural!) and Kant's point about incongruent counterparts, the bucket thought-experiment, the Kantian idea that space is not a 'thing in itself' nor a mere 'relation' but rather the 'a priori form' of experience -- is far too swift. These deserve more space (of the conceptual variety).

There are also comparatively recent discussions, which I may have mentioned to you: Peacocke's 'Holistic Explanation' developing Kant's view of space in terms of the 'holistic explanation' of experience in terms of simultaneous hypotheses concerning spatial positions and properties exemplified at those positions, as well as Swinburne's ingenious argument for relativism regarding space combined with absolutism regarding time. I cite these as evidence that science does not have the last word, even if philosophy doesn't either.

One way to get a handle on this is to imagine possible universes, i.e. universes where the laws of nature might have been different but which are nevertheless conceivable in the sense that, in Kantian terms, 'experience is possible'. For example, suppose that all the evidence (contrary to what has in fact turned out to be the case) pointed to the truth of Newton's theory. Would that necessarily refute Leibnizian relationism? Why? or why not?

But let's look at the bucket experiment, which plays a very important role in all of this. You remark laconically that according to Mach, 'inertial forces associated with rotation as observed by the 'bucket' experiment might originate from the relative acceleration of different material bodies with respect to each other.' How, exactly? Come again?

In abstract terms, that *seems* to make sense. But what does that mean? In the context of Einstein's General Theory of Relativity, we are asked to believe that there is *no empirical difference* between revolving a bucket and making the water inside the bucket rise, and revolving the universe around the bucket, thus creating gravitational forces which cause the water in the bucket to rise. (God could do it.)

Anyone with a dose of common sense would say that this is utterly crazy. Physics talks about abstract setups. You consider a system and all its interconnections at a given time, or during a given time slice. It is irrelevant how the system came to be there in the first place. But it is not at all irrelevant that *we rotated the bucket*. There is a basic story about time and causation here. Of course, from the abstract perspective of General Relativity, you can explain the physical movements -- or space-time distribution -- of the subsystems colloquially known as 'human beings' which interact with the bucket subsystem following which the water rises. But that isn't the whole truth. If you think it is, or could be, then you have to be prepared to throw out rather a lot. This is scientific reductionism with a vengeance.

The Special and General Theories of Relativity are empirical theories based on evidence (although admittedly the first 'test' of General Relativity came long after it was first proposed). Apart from the evidence, however, they have a beauty and simplicity which strongly inclines us to believe that they must be true. There is no priviledged frame of reference from which the laws of nature can be discovered. The universe is deeply 'symmetrical', in the sense that you would come to the same results wherever you stood.

As you observe, Einstein didn't in fact believe that he had succeeded in implementing Mach's principle. Now physicists argue over whether maybe you can plug the gap or maybe you can't. But the general point remains, that -- without taking anything away from science -- it does not necessarily tell the whole story. Either *we* rotated the bucket, or the existence of the human world is a mere illusion.

All the best,

Geoffrey