The Ontology of Spacetime
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Clarke argues that since the curvature of the water occurs in the rotating bucket as well as in the stationary bucket containing spinning water, it can only be explained by stating that the water is rotating in relation to the presence of some third thing—absolute space. Leibniz describes a space that exists only as a relation between objects, and which has no existence apart from the existence of those objects.
Motion exists only as a relation between those objects. Newtonian space provided the absolute frame of reference within which objects can have motion. In Newton's system, the frame of reference exists independently of the objects contained within it.
London: Methuen. While he did not deny the existence of phenomena like that seen in the bucket argument, he still denied the absolutist conclusion by offering a different answer as to what the bucket was rotating in relation to: the fixed stars. Home Questions Tags Users Unanswered. Several problems with this kind of program make themselves felt immediately. Spatial measurements are used to quantify how far apart objects are, and temporal measurements are used to quantitatively compare the interval between or duration of events. The challenge of uniting quantum theory and general relativity in a successful theory of quantum gravity has arguably been the greatest challenge facing theoretical physics for the past eighty years. The Logical Leap.
These objects can be described as moving in relation to space itself. For almost two centuries, the evidence of a concave water surface held authority. Another important figure in this debate is 19th-century physicist Ernst Mach. While he did not deny the existence of phenomena like that seen in the bucket argument, he still denied the absolutist conclusion by offering a different answer as to what the bucket was rotating in relation to: the fixed stars.
Mach suggested that thought experiments like the bucket argument are problematic. If we were to imagine a universe that only contains a bucket, on Newton's account, this bucket could be set to spin relative to absolute space, and the water it contained would form the characteristic concave surface. But in the absence of anything else in the universe, it would be difficult to confirm that the bucket was indeed spinning. It seems equally possible that the surface of the water in the bucket would remain flat.
Mach argued that, in effect, the water experiment in an otherwise empty universe would remain flat. But if another object were introduced into this universe, perhaps a distant star, there would now be something relative to which the bucket could be seen as rotating. The water inside the bucket could possibly have a slight curve. To account for the curve that we observe, an increase in the number of objects in the universe also increases the curvature in the water.
Mach argued that the momentum of an object, whether angular or linear, exists as a result of the sum of the effects of other objects in the universe Mach's Principle. Albert Einstein proposed that the laws of physics should be based on the principle of relativity.
Baptiste Le Bihan
This principle holds that the rules of physics must be the same for all observers, regardless of the frame of reference that is used, and that light propagates at the same speed in all reference frames. This theory was motivated by Maxwell's equations , which show that electromagnetic waves propagate in a vacuum at the speed of light. However, Maxwell's equations give no indication of what this speed is relative to.
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Prior to Einstein, it was thought that this speed was relative to a fixed medium, called the luminiferous ether. In contrast, the theory of special relativity postulates that light propagates at the speed of light in all inertial frames, and examines the implications of this postulate. All attempts to measure any speed relative to this ether failed, which can be seen as a confirmation of Einstein's postulate that light propagates at the same speed in all reference frames.
Special relativity is a formalization of the principle of relativity that does not contain a privileged inertial frame of reference, such as the luminiferous ether or absolute space, from which Einstein inferred that no such frame exists. Einstein generalized relativity to frames of reference that were non-inertial. He achieved this by positing the Equivalence Principle , which states that the force felt by an observer in a given gravitational field and that felt by an observer in an accelerating frame of reference are indistinguishable.
This led to the conclusion that the mass of an object warps the geometry of the space-time surrounding it, as described in Einstein's field equations. In classical physics, an inertial reference frame is one in which an object that experiences no forces does not accelerate. In general relativity, an inertial frame of reference is one that is following a geodesic of space-time.
An object that moves against a geodesic experiences a force.
An object in free fall does not experience a force, because it is following a geodesic. An object standing on the earth, however, will experience a force, as it is being held against the geodesic by the surface of the planet. Einstein partially advocates Mach's principle in that distant stars explain inertia because they provide the gravitational field against which acceleration and inertia occur. But contrary to Leibniz's account, this warped space-time is as integral a part of an object as are its other defining characteristics, such as volume and mass.
If one holds, contrary to idealist beliefs, that objects exist independently of the mind, it seems that relativistics commits them to also hold that space and temporality have exactly the same type of independent existence.
The position of conventionalism states that there is no fact of the matter as to the geometry of space and time, but that it is decided by convention. This view was developed and updated to include considerations from relativistic physics by Hans Reichenbach. Reichenbach's conventionalism, applying to space and time, focuses around the idea of coordinative definition. Coordinative definition has two major features.
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The first has to do with coordinating units of length with certain physical objects. This is motivated by the fact that we can never directly apprehend length. Instead we must choose some physical object, say the Standard Metre at the Bureau International des Poids et Mesures International Bureau of Weights and Measures , or the wavelength of cadmium to stand in as our unit of length. The second feature deals with separated objects. Although we can, presumably, directly test the equality of length of two measuring rods when they are next to one another, we can not find out as much for two rods distant from one another.
Even supposing that two rods, whenever brought near to one another are seen to be equal in length, we are not justified in stating that they are always equal in length. This impossibility undermines our ability to decide the equality of length of two distant objects. Sameness of length, to the contrary, must be set by definition.
Such a use of coordinative definition is in effect, on Reichenbach's conventionalism, in the General Theory of Relativity where light is assumed, i. After this setting of coordinative definition, however, the geometry of spacetime is set.
Introduction (D. Dieks). The Implications of General Covariance for the Ontology and Ideology of Spacetime (J. Earman); The Disappearance of Space and Time. Purchase The Ontology of Spacetime II, Volume 4 - 1st Edition. Print Book & E- Book. ISBN ,
Building from a mix of insights from the historical debates of absolutism and conventionalism as well as reflecting on the import of the technical apparatus of the General Theory of Relativity, details as to the structure of space-time have made up a large proportion of discussion within the philosophy of space and time, as well as the philosophy of physics.
The following is a short list of topics. According to special relativity each point in the universe can have a different set of events that compose its present instant. This has been used in the Rietdijk—Putnam argument to demonstrate that relativity predicts a block universe in which events are fixed in four dimensions.
Invariance, or symmetry, applies to objects , i. Covariance applies to formulations of theories, i. This distinction can be illustrated by revisiting Leibniz's thought experiment, in which the universe is shifted over five feet. In this example the position of an object is seen not to be a property of that object, i. Similarly, the covariance group for classical mechanics will be any coordinate systems that are obtained from one another by shifts in position as well as other translations allowed by a Galilean transformation.
In the classical case, the invariance, or symmetry, group and the covariance group coincide, but they part ways in relativistic physics. The symmetry group of the general theory of relativity includes all differentiable transformations, i. The formulations of the general theory of relativity, unlike those of classical mechanics, do not share a standard, i. As such the covariance group of the general theory of relativity is just the covariance group of every theory. A further application of the modern mathematical methods, in league with the idea of invariance and covariance groups, is to try to interpret historical views of space and time in modern, mathematical language.
In these translations, a theory of space and time is seen as a manifold paired with vector spaces , the more vector spaces the more facts there are about objects in that theory. The historical development of spacetime theories is generally seen to start from a position where many facts about objects are incorporated in that theory, and as history progresses, more and more structure is removed.
For example, Aristotelian space and time has both absolute position and special places, such as the center of the cosmos, and the circumference. Newtonian space and time has absolute position and is Galilean invariant , but does not have special positions. With the general theory of relativity, the traditional debate between absolutism and relationalism has been shifted to whether spacetime is a substance, since the general theory of relativity largely rules out the existence of, e.
One powerful argument against spacetime substantivalism , offered by John Earman is known as the " hole argument ". Define a function d as the identity function over all elements over the manifold M, excepting a small neighbourhood H belonging to M. Over H d comes to differ from identity by a smooth function.
These considerations show that, since substantivalism allows the construction of holes, that the universe must, on that view, be indeterministic. Which, Earman argues, is a case against substantivalism, as the case between determinism or indeterminism should be a question of physics, not of our commitment to substantivalism. The problem of the direction of time arises directly from two contradictory facts.
Firstly, the fundamental physical laws are time-reversal invariant ; if a cinematographic film were taken of any process describable by means of the aforementioned laws and then played backwards, it would still portray a physically possible process. Secondly, our experience of time, at the macroscopic level, is not time-reversal invariant. We have memories of the past, and none of the future. We feel we can't change the past but can influence the future.
One solution to this problem takes a metaphysical view, in which the direction of time follows from an asymmetry of causation. We know more about the past because the elements of the past are causes for the effect that is our perception. We feel we can't affect the past and can affect the future because we can't affect the past and can affect the future.
There are two main objections to this view. Science, Logic, and Mathematics. Space and Time in Philosophy of Physical Science.
Singularities and Black Holes
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