Yesterday, I suggested that in rejecting both Descartes's vortex theory and Newton's cosmology (including the law of universal gravitation), Huygens landed with an apparent tension. One the one hand, Huygens claims that solar systems are causally isolated from each other. They are separated by an universal ether* that on my interpretation has five properties I wish to highlight today: (i) it keeps the planetary vertices that make up a solar system in stable equilibrium ("because the æther round it, which is at rest, keeps the parts of it from flying out" ) and (ii) it keeps each solar system causally isolated from each other ("And as their motions do not all intermix or communicate with one another;"). So, I attributed a further property to the Huygensian ether: (iii) that it absorbs and neutralizes any motion/energy from the motions of the solar systems.
Now, one may reasonably doubt that the universal ether is responsible for (ii). For, a more literal reading suggests it is the immense distances among solar systems that is responsible ("in my opinion must the Vortices of Stars be plac’d as not to hinder one anothers free Circumrotations.") This would put Huygens close to the 'solution' that Newton later adopts in the General Scholium. (Newton had worried about solar systems collapsing into each other given universal gravity.)
Yet, the immense distances cannot do the assigned task (of preventing communication of motion among the solar systems) if one is working with a plenum physics. For in a plenum physics, motions can be transmitted along immense causal chains. So, for now I stick with (i-iii).
Discussion with Marius Stan and Chris Smeenk made me realize, however, that there are two ways to understand what Huygens says about the ether: first, one one approach, the ether fills the space(s) between/among solar systems, but is absent inside the solar system. That is, the universal ether is a different kind of material (fluid) from vertices of the solar system. Because of (i) [and (iii)] it also entails that (iv) this ether must have mass (and so is a qualitatively different ether from the one Newton considers--his ether has negligible mass).
The other approach is to treat the ether as a genuinely universal ether that fills all spaces.* (This is how Newton conceives of his ether.) The planetary vertices of the solar system then are carried through this ether. And then according to Huygens somehow this ether maintains the stability of each vortex and the system of vertices. The main problem with this second approach is that ether must have both negligible mass (so as not to retard the planetary motions) as well as considerable mass (so as to keep the system in stable equilibrium from without). Another non-trivial problem is that in the Principia, Newton had shown the orbits would not be ellipses if they had to move through fluids (but spirals); yet Huygens explicitly accepts Newton's result that Keplerian motion is elliptical. So, I reject this approach, and continue to stick with the former conception of the ether.
To return to the apparent tension. On the other hand, Huygens's (v) universal ether explicitly propagates light from one solar system to another. Here, in order to avoid misunderstanding, we need to distinguish between how the wave theory of light is often presented and how Huygens understands his own theory For him light always just is matter in motion, in particular a particle. But the way this is manifested is wave-like. How this is supposed to work in Huygens is unclear (and he himself appealed to God's providence at precisely this point in the Cosmotheoros) because his geometric proofs of the wave light character of light are divorced from his mechanical understanding of light. It is an interesting fact that later, Huygens's wave theory came to be divorced from his own ontology (such that a particle theory of light came to be thought an alternative associated with Newton).
As I hinted yesterday, because Huygens insists that the underlying ontology of light involves particles, he causes two kinds of problems for himself: first, his ether must have negligible mass (so as not to disperse light beams) and, as we have already seen, this is in apparent tension with (v), that is, the ether of having considerable mass (to keep the system of vertices of a solar system in equilibrium). Second, the motions of the solar systems are not causally isolated because particles of light are being transmitted among them across (as Huygens emphasizes) immense distances. I am unsure he recognized the tensions and how he would resolve them.
My interest in these matters was prompted by thinking about how Huygens (and Newton) would have to think about simultaneity. To re-introduce the issue(s) let me recall how Huygens and Newton think about time and also insert some special terminology. The main measures of time were the motions of astronomical bodies (relative to some bodies held fixed, usually the 'fixed stars'). In a series of breakthroughs, Huygens had shown (and Newton had agreed), that it was possible to construct a mathematical equation of time for each planet and use it to calibrate clocks. In addition, Huygens had shown mathematically (see Joella Yoder's great book) that the cycloid was an isochronous curve and that one could construct a pendulum clock which was ischronous. One could treat, as Newton suggested, a solar system as the kind of entity in which the individual equations of time can be coordinated (and unified) with reference to a point external to it. This can help define (at least in thought) a 'temporal frame' (akin to an inertial frame).
Now, let's distinguish between local simultaneity and absolute simultaneity. Local simultaneity is roughly the idea that moments in time are shared within such a temporal frame of a solar system. Absolute simultaneity is the thought that a moment of time spreads out through all the spaces of the universe. Once, in a paper, building on ideas of Nick Huggett, I had claimed that Newton's physics only required local simultaneity. And that this was true for each solar system. But that only theological concerns drove Newton into embracing absolute simultaneity.
I knew this couldn't be the whole truth because Newton's law of gravity was universal, but I had noticed (in the Opticks) that Newton allows the genuine possibility that different galaxies could be governed by different laws of nature (a point I develop in a paper with Zvi Biener). Even so, my approach was treated to very insightful criticism in a wonderful paper by Katherine Brading, who writes, “contra Schliesser, that all three of Newton’s conceptual distinctions between absolute and relative, true and apparent, and mathematical and common time have empirical import (section 5) and are necessary for the project the Principia (section 6).” (emphasis in original)." For now, I leave it to our readers to adjudicate our disagreement.** So, if Brading is right then for Newton, local simultaneity just is a special instance of absolute simultaneity.
By contrast, Huygens was a relativist*** -- in fact, as Howard Stein has shown an amazingly insightful relativist -- about motion. At first glance, it would seem for him there is really no scientific reason to accept absolute simultaneity (recall). This last point seems strengthened by the fact that for Huygens the motions of solar systems are explicitly causally isolated. And, in fact, as I noted yesterday, Huygens's way of thinking seems to allow that different solar systems could have different ways of being locally stable (and so have different kinds of locally apt force laws).+
There is a further reason why Huygens might be cautious about introducing what I am calling absolute simultaneity.++ Imagine two solar systems, A & B, far apart from each other, each with their own temporal frame. We can ask: are equal intervals of time [according to the coordination of the equations of time] for system A *regular* compared to equal intervals of time [according to the coordination of the equations of time] for system B? Here we need a much lower degree of isolation (between A & B) for the problem to arise, at least in principle.+++
Now, the question remains if for Huygens the propagation of light through the ether does not generate pressure to insist on the existence of absolute simultaneity. For this propagation shows (assuming I am right above) that solar systems are not isolated causally. Given that Huygens knows the speed of light and at least some of the the relative distances among solar systems,**** it is at least conceivable for him that one day the motions of a group of solar systems could be brought together (by focusing on light emitted by their Suns) relative to some fixed point (even if within these solar systems there are different empirical force laws governing the motions of system of vertices). While this does not get one from local simultaneity to absolute simultaneity, it would force him to take some steps down that road.++++
*Strictly speaking the ether need not be universal. Huygens flirts with the possibility that there is a (near infinite) vacuum beyond farthest solar systems. How this is supposed to work is unclear because space is explicitly infinite for Huygens. What is clear is that late in life, Huygens rejected quite a few Cartesians principles that he seemed to have accepted earlier.
**I concede that many of her criticisms are fair and make plausible an alternative reading (which, perhaps, is more supported than my own interpretation).
***Recent research is increasingly emphasizing (as I noted in my paper on his philosophy of time) that Newton had a firm grasp of relativistic motion, but that's for a different day.
+So, Huygens only accepts the inverse law as a feature of celestial bodies in our solar system. As I showed with George Smith he explicitly rejects it for bodies on Earth (and so his shape of the Earth is different than Newton's).
++Katherine Brading first alerted me to the issue I am about to discuss. And I am using her way of formulating the issue.
+++If I am not mistaken, in Newton's approach this problem is kind of stipulated away. (But I need to think more about this.)
****He does not know that the speed of light is an upper limit. So he can't rule out solar systems moving faster than the speed of light.
++++This last point is indebted to Brading's criticism of my treatment of Newton. In addition to Stan and Smeenk, I also thank Ori Belkind for discussion of these matters.