Since Hegel’s death there have been further - revolutionary - developments in science, and it is appropriate to ask whether Hegel’s philosophy of nature is compatible with such devel
opments. This is not a question that can be answered fully here, but to end this chapter I offer a few thoughts on the relation between Hegel's philosophy of nature and Einstein’s theories of relativity.
Dieter Wandschneider argues - in my view, convincingly - that Hegel accepts Galileo’s principle of relativity. According to this principle, one cannot tell purely from the behav
iour of physical objects within a closed space whether that space is in a state of rest or uniform motion. Which state an object is in can only be determined by comparison with other objects that serve as a frame of reference. Uniform motion is, therefore, always rela
tive to other objects.191 Hegel also explicitly acknowledges that light has ‘absolute velocity’
(iabsolute Geschwindigkeit)}92 Since the principle of relativity (in a more generalized form) and the constancy of the speed of light are the two postulates on which Einstein's special theory of relativity is founded, Hegel's philosophy of nature would thus appear prima facie to be compatible with that ground-breaking theory (even though Hegel clearly had no inkling himself that such a theory could ever be developed).193 One can also point out that Hegel endorses another idea central to the special (and general) theory of relativity, namely the idea that space and time form a single unity: space-time.
Yet what about the startling effects predicted by Einstein's theory: time dilation and length contraction? The special theory of relativity states that ‘time elapses more slowly for an individual in motion than it does for a stationary individual' and that ‘observers per
ceive a moving object as being shortened along the direction of its motion'.194 Could Hegel really countenance such revolutionary propositions? Perhaps.
Hegel maintains that space and time are universal in the sense that all matter is extended in three directions and is constantly vanishing into the past. By itself, however, this does not commit him to the view that time always and everywhere passes at the same rate or that the length of an object will always be the same, regardless of the frame of reference within which it is measured. Furthermore, Hegel denies that space and time themselves provide an independent, universal frame of reference for the measurement of distance or the passage of time. He states explicitly that space and time are not pre-existing ‘contain
ers’ (Behdlter) within which matter is located, but prove logically to be the extendedness and vanishing of matter itself.195 This means that, for Hegel, motion is never motion in relation to ‘absolute’ space and time, but always only motion in relation to other matter.
‘motion as such has meaning and existence simply and solely in a system of several bodies that stand in relation to each other'.196 This is not to say that Hegel in some way ‘anti
cipates' special relativity eighty years before Einstein: such a claim would be wholly inappropriate. Hegel’s rejection of the idea that there is an independent, universal spatio- temporal frame of reference does, however, leave room for the idea that the rate of aging and the length of an object may depend on the velocity at which that object moves in relation to other objects. In this sense, his philosophy of nature is compatible with special relativity.
Einstein’s general theory of relativity is a theory about gravity. It states that a body, such as the sun, warps or ‘curves’ the space around it and that the greater the mass of the body concerned, the greater the curvature it produces.197 Other bodies moving without external buffeting through the space around a massive body like the sun will follow the nearest thing to a straight path in such curved space. Such a path, which is the path of minimum dis
tance between two points but is itself curved, is called a ‘geodesic’.198 Due to the warping of space, bodies (or light beams) travelling ‘straight ahead’ in the vicinity of the sun will thus actually follow a curved trajectory rather than move in a straight line. This explains the phenomenon of gravity: the ‘gravitating’ of a body towards the sun is simply the motion that is produced by the curvature of the space through which that first body travels. If the curvature of that space is strong enough, and the body's speed and direction of travel are
right, die body will be guided into an orbit around the sun. According to the general theory of relativity, therefore, a ‘planet orbits the Sun in an elliptical orbit not because of a grav
itational force of attraction exerted on the planet by the Sun, as Newton affirmed, but because the mass of the Sun warps the space around it, altering its geometry’ and the motion of the planet is determined by the shape of that warp. For Einstein, there is thus no such thing as a force of gravity: gravitational motion is motion due to the distorted geometry of space.199
Einstein also made the suggestion that space might be not only locally warped by matter but positively curved or ‘closed’ as a whole in such a way that light travelling in a constant direction away from its source would eventually return to its point of origin. Such space would be unbounded in that it would have no discoverable limit or ‘edge’; but the fact that light would ultimately return to its point of departure, rather than continue to move away from its source indefinitely, means that this space would be finite. The general theory of relativity, however, does not itself fully determine the global shape of the universe - it pre
dicts only that the fabric of space will be locally ‘warped’ by the presence of matter - and there is currently no definitive proof that space overall is positively curved.200
Is Hegel’s philosophy of nature compatible with general relativity? Two things suggest that the answer might be yes. First, as we saw earlier, Hegel insists on the identity of iner
tial and gravitational mass, and P. M. Kluit argues that this brings him close to Einstein, for whom the equivalence of the two types of mass is the starting-point for the general theory of relativity.201 Second, Hegel agrees with Einstein - against Newton - that gravity is not a force exerted by one body on another. For Hegel, gravitational motion is grounded in the inherent nature of matter and, ultimately, in the very nature of space and time them
selves. In this sense, one could say of Hegel, as Brian Greene says of Einstein, that he ‘wove gravity into the basic fabric of the universe’.202
There are two things, however, that suggest Hegel’s philosophy of nature might not be compatible with general relativity after all. The first is this. According to general relativity,
‘figures constructed out of light rays do not satisfy Euclidian geometry if the light rays propagate in the presence of gravitating matter’because, in taking the shortest path between two points, those rays follow a curved rather than a straight line. In Einstein’s own words, therefore, ‘the space-time continuum cannot be regarded as a Euclidian one’203 Hegel, by contrast, clearly assumes that space is Euclidian. The proposition that the straight line is the shortest between two points is said by him to be ‘the most correct definition’. More
over, he argues that Pythagoras’ theorem, with which Book 1 of Euclid’s Elements con
cludes, can be derived directly ‘from the Concept’ and so be proven a priori to be true.204 Yet does Hegel’s commitment to Euclid inevitably pit his philosophy against general relativity? I think not. Brian Greene notes that ‘in the absence of any matter or energy, Einstein envisioned that space would be flaf: light would thus propagate in straight lines that behave in accordance wit^-the axioms of Euclid.205 Einstein could also be said, therefore, to hold that space in itself is Euclidian. He argues, however, that the presence of matter warps space and thereby renders it locally (and maybe even globally) non- Euclidian. The question to consider is thus whether Hegel could also accept that matter might distort space that is otherwise intrinsically Euclidian.
For Hegel, there is no space prior to matter, because space-time itself proves logically to be nothing but matter-in-motion. In particular, it takes the form of independent central bodies - stars and planets - that are separated by the vastness of empty space. Hegel clearly assumes that not only the space far removed from matter but also that in the vicinity of matter will be Euclidian. As far as 1 can tell, however, there is nothing in Hegel’s conception of matter that logically precludes the possibility of matter’s distorting the surrounding
space. Any such distortion would have to be considered contingent from the philosophi
cal point of view, since nothing makes it logically necessary; but it does not appear to be definitively ruled out. In this sense, Hegel's understanding of space as inherently Euclidian is not irreconcilably at odds with general relativity.
Nor does the idea that space might be positively curved globally, and so finite, conflict with Hegel's claim that space must be continuous and unbounded. According to Hegel, one can travel as far as one likes, but one will always be able to go further and will never reach a definitive limit or edge to space: ‘however remotely I place a star, I can go beyond it, for the universe is nowhere nailed up with boards'.206 This conception o f space as con
tinuous and unbounded is, however, compatible with either the infinity of globally ‘flat' (but locally curved) space or the finitude of space that is overall positively curved. After all, even in a positively curved, finite universe, one could still travel forever in a uniform direc
tion without reaching an edge to space; one would just return at some point in time to one’s place of departure. The fact that space is necessarily continuous and unbounded does not, therefore, determine by itself whether space is infinite or finite. It is thus a matter of contingency, from the philosophical point of view, which is the case - or indeed whether space is negatively curved (like a saddle) - and it is up to natural science to determine the true state of affairs.207
There is, however, a second problem. In Hegel’s view, the fall or orbital motion of a body is due not to the action of an external force upon it but to the inherent tendency of matter to seek unity with other matter. Matter thus gravitates freely - of its own accord - towards or around other matter. According to general relativity, by contrast, bodies such as planets do not gravitate o f their own accord around their sun. Their motion is determined by the curvature of the space through which they pass. In this sense, from the Hegelian point of view, Einstein's account of gravity closely resembles Newton’s: for in neither account do bodies actively move or gravitate towards or around another body. In both accounts, bodies fall towards or orbit around another body because they are caused to do so by something outside themselves - either by a force exerted upon them or by the warping of the sur
rounding space. There is thus a clear tension between Hegel’s conception of gravitational motion and Einstein’s. This tension is, of course, of no concern to the physicist, but it is a serious problem for the philosopher who claims that philosophy and science study the same realm of nature and that ‘agreement with actuality and experience’ is essential to philosophy.208
So is it possible to dissolve this tension between the philosophy of nature and general relativity? Well, we could conclude that Hegel’s derivation of gravity from the nature of space and time is misconceived. We would, however, have to show precisely where that derivation goes astray and how it can be amended. On the other hand, we could choose to reject the general theory o f relativity. This would, however, be unwise, since ‘no deviations from the predictions of general relativity have been found in experiments performed with our present level of technology’.209 The third option is to suggest that, perhaps, both the philosophy of nature and general relativity capture something of the truth. Perhaps planets move in orbits around their sun both because the space through which they travel is warped by the mass of the sun and because they have an inherent tendency to gravitate around that sun - a tendency rooted in the fact that they form part of a unified system of celes
tial bodies into which intrinsically gravitational matter has organized itself.210 If this third option has merit, Hegel’s philosophy of nature would, after all, be compatible with general relativity.
These remarks are certainly not meant to be the last word on the relation between Hegel and Einstein. They are meant to do no more than prom pt those better qualified than I to
examine that relation in detail. In my judgement, Hegel’s philosophy of nature is intended not just to systematize the scientific knowledge of Hegel’s own day but to determine what is made logically necessary by nature itself. If it is successful in this task, there will still remain a huge am ount of work for science to undertake, but no future scientific discovery will be fundamentally incompatible with the insights of philosophy. If discoveries incom
patible with philosophy are made, however, then the philosopher will clearly have to think again. For this reason, although physicists may well be able to ignore Hegel, students of Hegel’s philosophy of nature cannot, in my view, afford to ignore modern physics.
This concludes my examination of Hegel’s mechanics. I have discussed this section of the philosophy of nature in some detail in order to help readers to follow the twists and turns of Hegel’s logical analysis and see for themselves the subtle way in which Hegel relates his analysis to the findings of science. I also wished to explain as clearly as I could how it is that Hegel finds the seeds of freedom and spirit in the most unlikely of places, namely in the barrenness of space itself. Not all readers will be convinced that Hegel’s philosophy of nature rewards intensive study, but I hope that some might be tempted to press on and examine the further dialectical development of nature.
Following his account of celestial mechanics, Hegel goes on to argue that matter must take the form of light, physical objects (with density, cohesion and heat) and chemicals. In the process matter proves to be held together not just by gravity but also by magnetism, electricity and chemical bonds. Matter also proves to be more and more explicitly self
determining and self-moving. The philosophy of nature culminates in an account of the most explicitly self-determining matter that nature produces, namely life. In the next chapter we consider Hegel’s analysis of life and then briefly trace the logical process whereby life mutates into freely self-determining, embodied spirit