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Relational or Absolute Space and Time? Leibniz or Newton; Smolin or Penrose

January 29, 2021

This is a question that has intrigued and fascinated me probably ever since I first became acquainted with it. The circumstances of this were twofold. On the one side, I had come to see the power of the basic insight of empirical idealism, that we can only know our own experiences and perceptions with any certainty. On the other side I had read about Newtons attempts to prove that space is absolute based on the curvature experienced by water in a bucket while spinning. The argument, so it goes, is that since there is no evident external force acting on it, and there must be some force, then this force must be a rotation relative to absolute space. My fascination with the problem is that it goes to the core of the question about what space and time and dimensions really are. Are they externally existent things in some sense, or are they merely relational abstractions, ways in which we categorise our experiences?

The debate raged on between Leibniz and Newton at the time regarding this. Leibniz argued that it went against the principle of sufficient reason to have an existent thing that had no effective reason of its action on things. For instance, what would distinguish the absolute space we have from a similar absolute space that was moved a few meters to the left or from one that was magnified by a factor of 10, 100, or even 1 million? It seems nothing within the system could distinguish one such space from the other. And so we would be left as beings within that system as having to hold something as true for which we could distinguish no reason for it being that way. Newton was not too worried, as he imagined there to be some Deistic god who made things as they are originally from the outside, and so, for him there could be reason, if not for us. But this did not satisfy the rationalist, Leibniz, who insisted all things in being and existence must have a reason for their being and existing that we can at least potentially understand as ourselves rational beings.

Moving forward, Kant came along to suggest an epistemology in line with Newtons absolute space and time, by arguing that these particular ways of categorising reality are written into our very subjective observational faculties, like a grid on a telescope that we look through, for instance. And so, there is no need to postulate the space and time as external entities in an arbitrary way, they are merely the necessary filters through which we must perceive all things, and he created a whole metaphysical approach around this idea, that still influences many domains of enquiry to this day. The only problem, of course, is that in the light of Einstein’s theory of relativity we know that Newton’s absolute space and time are incorrect representations of actual space and time. And I can myself give a critique of one of Kant’s own arguments for the absoluteness of a space framework of some kind. Kant argued that a left and a right hand are incongruent, no translation can make one fit neatly on the other. But, what this argument forgets to realise is that by labelling them left and right hands, you are already, tacitly evoking a third dimension of depth, and if you are given the option to flip one of the hands through 180 degrees in that third dimension of depth then you can quite easily make the left and right hand congruent. If such an absoluteness can be removed with a simple mathematical trick of introducing an extra dimension, it hardly seems adequate to ground a whole absolute view of space and time on.

The new point on which I am bringing up all this discussion is in relation to my current reading of the works of Lee Smolin and Roger Penrose. Because, it seems Smolin is an advocate of the purely relational view of space and time, seeing it as a natural outcome of general relativity, while Penrose is not a supporter of this view (I am taking this from a recent interview on youtube between Roger Penrose and Brian Greene where he stated this.)

So we have here an almost 400 year old philosophical debate about the true nature of space and time in which there is still disagreement among top physicists. What does relativity theory really say? Does it indeed take us to a purely relational view of space and time? Now, though I can see and appreciate Smolin’s arguments for it, particularly also in relation to his new way of trying to envision the whole debate in cosmology by developing a cosmological view from somewhere, so to speak, rather than trying to do the old absolutist approach of falsely imagining we can take a view from nowhere of the cosmos. This latter would be an idealised neutral view outside of it, when a more realistic view is that we are inextricably entwined with the universe in key ways. (Of course, it is one thing to state a view like this, but a whole other to make it respectable for theoretical and experimental physics, which is what Smolin tries to do in that book.) Despite of this value of the view, I don’t think we can quite say that relational space and time follow from general relativity. I think, in fact, the question remains open, and in a way general relativity avoids answering it.

The purpose of the field equations is that they can basically be adapted to any empirical, gravitational matter we decide to add to them. We can add them based on directly observed matter, or based on postulated matter. Either way they work the same and we can make models of any kinds of curved space-time we like. They show, yes, that there is no absolute metric for straightness and distance in space-time. This particular metric being determined by what mass is around in that space-time, from which we can then form geodesic paths, as the equivalent of straight lines. But, still its not really a relational view of space and time. A purely relational view would not only state dependence on the specific location of masses for determining space-time curvature, it would also have to do a much better job at explaining Newtons old problem of the spinning bucket. The alternative, relational suggestion of Ernst Mach initially, is that the bucket is spinning not relative to absolute space but relative to the rest of the matter in the universe. Now this remains an interesting speculation, but it has not been shown how this works in any precise physical theory that can also explain the things relativity can. General relativity does not take us this far as far as physical theory goes. It is less committal as to the actual nature of space, time and their curvature. It could be real, it could equally just be a mathematical model, like a climate model, were we are dealing with ever changing possibilities rather than set in stone realities.

So, currently, I would say my instinct is to agree with Penrose on this one. The debate needs to be looked at more in an open-minded way, because it is very easy, based each of us, on our own experience and past training and education, to rush to one conclusion or the other, as a sure judgment always looks better than an uncertain one in our social relations with others. From what I can gather so far on Penrose, his position seems to be that there is some basic reality to space and time, independent of ourselves as observers that can be discovered. This seems more consistent with his general approach of mathematical platonism, where mathematics is argued to be able to model reality accurately. This is a perspective that Smolin criticises and I think is a good subject for a future discussion also.

But, from my own personal way of looking at it, I mean we have the example of the centrifugal force itself, (as is involved also in Newton’s bucket problem) which is claimed as a merely felt force, not a real dynamic force, but that is only based on a postulation of that force happening within a larger space-time arena. Now are we free to make these kinds of postulations or not? I am not sure we are, given a purely relational view, but I am also not sure how a non-purely relational view can avoid making some slightly ad hoc postulations about space and time one way or another, if not quite the extreme position of absolute space and time of Newton and Kant. I will have to explore this point further, as I still have much on this subject to read by both authors over the coming weeks, and will be sure to update with any new insights cropping up that can potentially take us a bit further in this debate.

These issues also of Platonism will come up more, as two of the physicists I am studying, Penrose and Barbour, seem to be more inclined to mathematical Platonism, while Lee Smolin and Stuart Kauffman seem more inclined to a view in which basic reality unfolds from within, so to speak, rather than emerging out of some prior externally existing mathematical framework or structure. This, I think, could reach close to the heart of both the fundamental physical and philosophical question in cosmology and ontology, of what our place and being in the universe amounts to, and warrants much more consideration in future posts.

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