A-Theory: The Past, Present, and Future

In the philosophical debate over the nature of time, the A-theory is the view held among contemporary philosophers that there exist such intrinsic and indivisible properties as pastness, presentness, and futurity. By virtue of having these A-properties, they claim, events in time are past, present, or future. The origin of this theory is found in The Unreality of Time, in which John McTaggart Ellis McTaggart discusses time through what he calls the “A-series” and the “B-series.”


According to McTaggart, the A-series is the “series of positions which runs from the far past through the near past to the present, and then from the present through the near future to the far future, or conversely.”

By “series of positions,” McTaggart means positions in time: Events are positioned in the past if they have already happened; they are positioned in the present if they are happening now; and they are positioned in the future if they have not yet occurred. The property of being in the past, the present, or the future is a temporary, not permanent, property. For example, when it had not yet happened, the event of landing on the moon was in the future; when it was occurring, it was in the present; and now it is in the past.

The “A-series” that McTaggart discusses thus establishes a flow of time, in which each event is at one time future, at one time present, and at one time past, but never any combination of the three at once and never any of the three forever. No event is always present, always past, or always future. His definition also allows for the existence of varying degrees of past and future (next year is, for example, more future than next Tuesday) and different properties that correspond to these different degrees. To talk about events as occurring in either the past, present, or future requires the use of A- sentences, or tensed sentences. An event in the future will take place; an event in the present is taking place; and an event in the past has taken place.


The A-theory combines presentism and non-reductionism. Presentism is the extreme assertion that only the present is real and that nothing exists other than what presently exists. For example, though past objects, such as dinosaurs, did exist, there is no sense in which they do exist. Similarly, while it is possible that future objects, such as the 100th president of the United States, will exist, it is not the case that they do exist. In this context, then, discussion of past or future objects is not a discussion of objects that exist somewhere other than the present, but of properties that did or will exist when other times were or will be present. The strength of presentism depends upon the existence of tenses and is thus an important element of the A-theory.

Non-reductionism, or “taking tense seriously,” is the idea that tense corresponds to a fundamental and ineliminable feature of reality. A tensed proposition, or an A-sentence, is one in which tenses (am, was, will, have, had, etc.) are used. An eternal proposition, or a B-sentence, conversely, is a tenseless sentence. Tenseless sentences use words such as before, after, is simultaneous with, or specify the date. Non-reductionists claim that tensed propositions cannot be reduced to eternal propositions without a loss of information.

For instance, to say “I believe that I am hungry” does not preserve the same truth value if a date—“I believe that I am hungry at 3 p.m. on June 15”—is attached. A sincere statement of “I believe that I am hungry” entails “I believe that I am hungry simultaneously with my utterance,” whereas my statement of “I believe that I am hungry at 3 p.m. on June 15” does not. The A-sentence is true only when it is simultaneous with my saying it. The tenseless sentence, if true, is true at every point in time. This reveals that tensed propositions (A- sentences) convey temporal beliefs that cannot be expressed by tenseless dated sentences.


Despite the pervasiveness of tensed sentences in the English language, many philosophers have argued that the A-theory of time is incompatible with special relativity and is thus invalid. Albert Einstein’s special theory of relativity (1905) consists of two postulates:

  1. The speed of light is the same for all observers, no matter their relative speed.
  2. The speed of light is the same in all inertial frames.

It follows from these two postulates that simultaneity is not absolute but must, instead, be relativized to an inertial frame. For any pair of events, there can be no single fact of the matter as to which event happened first, or whether both occurred at the same time. The precedence of one event to the other depends upon the frame of reference: Relative to one frame of reference, Event 1 might be simultaneous with Event 2; relative to another frame of reference, Event 1 might occur earlier than Event 2; and relative to a third frame of reference, Event 1 might occur later than Event 2.

So, while two events might occur simultaneously for one observer, they will occur at different times for an observer moving in a different inertial frame. An event that is present relative to one frame of reference may well be past or future relative to another frame of reference. Because there are no grounds for selecting any single frame of reference as the “real” frame of reference, there can be no absolute, frame-independent distinction between past, present, and future.


The relativity of simultaneity is found in Einstein’s description of an event occurring on a railway embankment: A long train travels at a constant velocity as depicted in the following picture. A person traveling on the train regards all events in reference to the train. Two strokes of lightning occur, one at point A and one at point B. The distance between point A and point B is measured, and an observer is placed at the midpoint, M. The observer is given two mirrors inclined at 90° so that he can observe point A and point B at the same time. If the observer sees the two flashes of light at the same time, the two strokes of lightning are simultaneous. The passenger, however, will see the light from B earlier than from A. Events that are simultaneous with reference to the embankment, then, are not simultaneous with reference to the train.


As shown in this example, the absence of an absolute simultaneity poses a problem for the A-theory and the use of tenses. If the special theory of relativity is correct, existence according to presentism becomes a frame-dependent matter. According to two different frames of reference, a single event both exists and does not exist.


Some A-theorists have attempted to reconcile the A-theory with the special theory of relativity. Though the special theory of relativity is well confirmed, these philosophers argue, it remains an empirical theory and should not be used to assess metaphysical claims. In this sense, current physics does not completely rule out absolute simultaneity; it just cannot currently conceive of it. An “ideal” physics could detect this currently “unobservable” absolute simultaneity.

Alternatively, A-theorists argue, an absolute simultaneity might never be detectable by physics. The undetectability of absolute simultaneity, however, does not preclude its existence. A final objection posed by A-theorists is that the relativity of simultaneity is itself only an apparent effect. Whether two events are observed simultaneously is one thing; whether they take place simultaneously is another.