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Is Space a Substance?

One of the most important things that Newton established in his mechanics was the irrelevance of absolute motion to questions of physics. Instead, his account focuses on inertial frames, and the idea that any non-accelerated frame is equivalent when plugged into equations of motion. When considering, therefore, a ball bounced inside a train, we need not concern ourselves with the train's (constant) movement across the landscape. Instead we can limit the model we draw up to the motion of the ball within the carriage, and view the carriage as a stationary frame through which the ball moves. We may say, therefore, that Newton's mechanics need no account of absolute motion, and there need be no single magnitude or direction attributed to a body before we are able to describe the body's motion.

The case of acceleration, however, is very different. If we consider a car starting, from the perspective of a pedestrian standing on the pavement, the car begins at rest, and then accelerates, until it is moving at a considerable velocity relative to the pedestrian. From the perspective of the driver, however, the car is stationary: it is, to her, the pedestrian that accelerates away from her, until the pedestrian is moving at a considerable velocity away from the car. We know, however, that the cases are not entirely symmetric, because forces are required to induce the acceleration in the car, whereas the pedestrian expends no energy to accelerate relative to the car. Since, according to Newton's account, objects remain in inertial motion unless acted upon by a resultant force, the case of accelerated motion is different in that a force acting upon one of the bodies causes that body to accelerate absolutely. Consider a cup of coffee sat on the passenger seat, and one held by the pedestrian. When the cup inside the car is subjected to acceleration relative to the pedestrian, the coffee spills; the cup held by the pedestrian, however, does not spill, despite its acceleration relative to the car. We have good grounds, therefore, to deny that the two cups are in an identical situation with respect to acceleration: we want to say (and it seems to be correct to say) that the cup on the passenger seat is really accelerating, whereas the one held by the pedestrian just looks like it is to the car driver.

Since the advent of Einstein's special, and later general, relativity, the physics landscape has not been quite as simple. Einstein showed that such a conception of space as a series of 'snapshot' hypersurfaces, that can be stacked in order and experienced through time is unsatisfactory. He showed that the speed of light is constant in any inertial frame, and that it wasn't possible to 'slow down' a beam of light by following it at speed - it would still move away from you at just the same velocity as it would if you were stationary (in some inertial frame). This might at first sound like it meant that light does in fact have some absolute velocity, but on closer reflection this is not what it means. Light does not have some privileged, absolute inertial frame, but instead seems to move at the same velocity regardless of which direction it is going, and the observer's velocity. If Einstein's predictions did show that there was some sense in which absolute motion was important, it would still appear that an observer's absolute motion could be subtracted from that of a light beam when observing how quickly it was moving, and this simply isn't so.

Instead, Einstein suggested that our concept of space as separate from time was incorrect. Instead of space and time, we should have space-time, a four-dimensional manifold. In effect, the faster you move, the more time slows down for you, so light is able to move at a constant velocity away from you even when you move at high speeds, because time slows down for you when you do so. There are many counter-intuitive results of such a change in world-view, not least the relativity of simultaneity: no longer is an event simultaneous simply in virtue of occurring in the same spatial time-slice, instead simultaneity is relative to the observer, and two events that may be simultaneous for X may not be simultaneous for Y. It follows from this that we cannot have a simple conception of 'space', but instead find that it is inextricably woven in with time. In light of such revelations, few physicists would support any longer the suggestion that there is such a thing as real, or substantial, space. We must, instead, turn our interest towards whether space-time is a substance.

If acceleration is absolute, therefore, it is argued, there must be something relative to which this acceleration is taken - there must be a privileged inertial space-time frame relative to which 'real' acceleration occurs. Such a view is generally dubbed (neo-)Newtonian, though simply referring to it as a substantivalist or absolutist view would seem more accurate, and is opposed to a Leibnizian, relationist view. The relationist holds that all physical facts can be described in terms of properties of objects and the relations between them, and denies that there are additional facts, such as those about what direction all these objects are facing.

A central test case in the debate is whether there would be any difference in facts about the world were the whole universe shifted fifty miles to the north. Whilst an absolutist will presumably take such a change to be substantial, since every object in the universe would be in a different place relative to absolute space(-time), the relationist will hold that the possible world described is identical with the actual world, since all the relational facts about the matter in the universe will be preserved. It is occasionally suggested that in formulating the example we have simply shown that the absolutist is correct - for how could we describe such a shift of the entire contents of the universe if not as relative to substantial space? Such a claim seems to me very much to be assuming just what it is trying to prove. It is exactly the suggestion that when we talk about shifting every object in the universe fifty miles north we are making a meaningful statement that the relationist will want to deny - they will say that such talk of a universe exactly like our own, but fifty miles further north is nonsense, since objects do not have an absolute position, but can only be considered relative to other objects (which, of course, might be observers). Leibniz, and his followers, will simply invoke the Principle of the Identity of Indiscernables, which, roughly speaking, states that if two objects share all the same (perceptible) properties, they are the same object. Absolutists will have to deny this principle.

The relationists seem largely to have won this round - and whilst intuitions seem to be divided as to whether talk of identical worlds, simply in different positions is reasonable, they seem to side against the absolutists if supporting either side. Clearly the question of whether identical but moved possible worlds will be the same possible world is not going to be empirically verifiable, so the debate is not going to be answered experimentally. It does not take a particularly hard line verificationist view to wish to deny that identical-but-differentially-located worlds could exist, especially since the answer will clearly have no effect upon science.

The privileged position of acceleration, however, seems to hint at empirical grounds upon which the absolutists might defend their position. Whilst the exact position of the total mass of the universe might not be a matter of fact, this does not rule out the possibility that there must be a frame against which acceleration is to be measured. The relationists, however, argue that even this can be explained in terms of relations between matter: namely that it is an object's acceleration in relation to the collective mass of all the matter in the universe that marks acceleration out as absolute. Clearly there will be some largest inertial frame - namely the one with the largest amount of matter stationary relative to it. Newton's mechanics, in fact, need not even deny this, all it need say is that there is no reason why such a frame need be invoked in mechanical equations, since any other frame will do just as well.

The chief argument employed by the absolutists to defend their suggestion that absolute space (or space-time) is needed to explain the privileged frame in which absolute acceleration occurs is known as the 'bucket experiment'. They argue that, in the same way that when a bucket is spun the contents attempt to recede from the centre, were we given two massive spheres attached together by a cord in an otherwise entirely empty universe, and these spheres orbited one another, there would be tension in the cord, as if the spheres were trying to recede from one another. I must say that I am wholly bemused by the claim that this case shows the absolutists to be correct. There seems to be no basis on which for them to claim that such recession will occur, except extrapolation from experiments performed in a universe where there is considerably more matter that just that of the test objects. The suggestion that acceleration forces will not be felt in the absence of this matter is just what is being claimed by the proponents of the view that this example supposedly disproves. Furthermore, the very suggestion that two objects could 'orbit' one another - i.e. be in constant acceleration with respect to one another - in any real sense, in the absence of other matter (and thus frames) is at least debatable, especially since the relationist view can happily deny that there can be any debate about these objects' position, and since the choice of whether they are moving inertially (as opposed to circling) is only a factor of the arbitrary inertial frame relative to which we consider the objects. This experiment, therefore, might be a test case, in that if there were tension in the cord, it would indeed show that acceleration was unrelated to the rest of the matter in the universe, but such a thought experiment isn't going to prove anything. It isn't even a particularly good test case, since clearly it involves an experiment that we simply will not be able to stage.

Sklar points out that the problem with theories such as that which posited the ether as the medium through which light travels, is that it is certainly not clear why, even if the ether existed, we should equate it with space. The fact that there would be an inertial frame through which light travels says nothing about whether that inertial frame is stationary. Clearly there is nothing to which the absolutist might appeal in order to deny that frame in which acceleration occurs is itself inertial, except just the verificationist tendencies to which the relationists appeal. If we are allowed to posit an ether to be the invisible, intangible inertial frame in which light moves, there is nothing to stop us positing the blether to be the invisible, intangible inertial frame in which the ether moves.

Overall, therefore, I would suggest that there is little evidence to counter the claim that acceleration could be absolute relative to the whole mass of the universe, though clearly there is much work to be done to complete such a theory. There will, of course, be difficulties about how this matter might exert 'forces' upon the accelerating object at such great distances, and uniformly throughout space, but this certainly should be a more likely prospect than for an intangible object such as 'space-time' to exert these forces. It seems very likely to me that forces due to acceleration will be a product of physical objects, rather than unverifiable ones posited simply to account for tendencies without any explanation of how these objects might account for these tendencies. Not to be mention the bizarreness of discussing whether space is a substance when there seems no viable explanation of what we mean by substance apart from just that stuff that this space-substance is supposed to contain: namely matter.