1.0 Traditional religious views
1.1 The Hindu Vedas describe a cyclical cosmology of time, in which the universe goes through repeated cycles of creation, destruction, and rebirth, with each cycle lasting 4,320,000 years. Hindu comsology also argues "There are innumerable universes besides this one ... they are unlimitedly large (Bhagavata Purana c750 CE).
1.2 The Hellenic views were diverse, but it is possible to derive some dominant opinions. Aristotle for example ties time to quantifiable change and movement. Only the Prime Mover is at absolute rest. The universe as a whole was ungenerated as well as indestructible, but finite in size. In contrast Epicurus and Lucretius argued that space (like time) was not bounded.
1.3 The Abrahamic religious perspectives tended to argue for a universe of finite space and time ("in the beginning", "day of judgment"), a view shared by John Philoponus (Christian), Al-Kindi and Al-Ghazali (Muslium), and Saadia Gaon (Jewish). Only God could be infinite, not the material world.
2.0 Physicalism and Idealism
2.1 The ontological physicalist is that time and space have an existence apart from conceptions. The idealist perspective varies from a rejection of independence from a mind (e.g., a theological position) or, from an experiential position from phenomenology.
2.2 The Kantian perspective in Critique of Pure Reason argued that space and time were ordering principles of the mind, which allowed us to comprehend sense experience. They are not considered substances, or learned from experience, rather they are a priori and synthetic; the predicate of which is not logically or analytically contained in the subject (i.e., synthetic) but the truth of which is verifiable independently of experience (i.e., a priori).
3.0 Absolutism and relationalism
3.1 A significant debate in the philosophy of space-time was whether space and time were absolute, that is, they had an independent existence, or whether the were relational between objects. Samuel Clarke (following Issac Newton) argued the absolute perspective and corresponded with Gottfried Leibniz who argued the relational view (1715-1716).
3.2 Leibniz argued space exists only as a relation between objects, and which has no existence apart from the existence of those objects. The Newtonian view provided an 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. These objects can be described as moving in relation to space itself.
3.3 The contributions of James Clerk Maxwell and especially Albert Einstein suggest that the Newtonian absolute concepts of space and time provide an highly approximation to general relativity, which combines special relativity (lightspeed in a vaccuum, universal physical laws) and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of spacetime.
3.4 The special theory of relativity replaces absolute time with the notion of a time that is dependent on reference and spatial position. Rather than an invariant time interval between two events, there is an invariant spacetime interval. Special relativity predicts the equivalence of mass and energy, the mass-energy equivalence formula E = mc^2.
4.0 Geometry of Spacetime
4.1 The Hellenic mathematician Euclid established a small set of axioms, and deducing many other propositions (theorems) from these, starting from plane geometry, and then into three dimensional geometry. The postulates are; (i) A straight line segment can be drawn joining any two points. (ii) Any straight line segment can be extended indefinitely in a straight line. (iii) Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center. (iv) 4. All right angles are congruent. There is a fifth postulate, unproven, (v) If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough.
4.2 Non-Euclidean geometry arises when either the metric requirement is relaxed (distances are undefined) leading to kinetic geometry, or the parallel postulate is set aside. In the latter case one obtains hyperbolic geometry and elliptic geometry.
4.3 An accurate geometry of spacetime requires a conceptual separation of the the space of locations from the space of vectors (velocity, acceleration, fields, etc) leading to 'manifold space', the set of all possible locations.
5.0 The Arrow of Time
5.1 Time appears as a one-way direction" or "asymmetric" (c.f., Arthur Eddington, 1927). This can illustrated by cosmological, thermodynamic, and radiative principles. But see also Davies, who points out that if the universe did lack critical initial mass, it would eventually shrink - "big crunch" - as a space shrank, time would reverse. There is also the issue of how quantum uncertainty gives rise to entanglement; "spooky action at a distance.
5.2 Under our current cosmology, effective time travel is available in certain scenarios the most well known being the effects of time dilation due to relativistic velocity where one object does not go forward in time as fast as another. A variety of well-known paradoxes could result from this; the physicist Novikov argues that if any event that would result in a paradox or change a relativistic past, then the probability of that event occurring is actually zero.
Philosophy Forum, August 3, 2014