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The B-theory of time is a name given to one of two positions in the philosophy of time. B-theorists believe that time is tenseless, rather than tensed, and therefore temporal becoming is not an objective feature of reality. Theories such as four-dimensionalism and eternalism draw upon the B-theory.

Origin
The labels, A-theory and B-theory, are derived from the analysis of time and change developed by Cambridge philosopher J. M. E. McTaggart in 'The Unreality of Time' (1908), in which events are ordered via a tensed A-series or a tenseless B-series. A-series is closely related to presentism while B-series is closely related to eternalism.

Events (or 'times'), McTaggart observed, may be characterized in two distinct, but related, ways. On the one hand they can be characterized as past, present or future, normally indicated in natural languages such as English by the verbal inflection of tenses or auxiliary adverbial modifiers. Alternatively events may be described as earlier than, simultaneous with, or later than others. Philosophers are divided as to whether the tensed or tenseless mode of expressing temporal fact is fundamental. To assert that both are equally fundamental is to land in McTaggert's Paradox, since it would require of any event that it is both present and future, which is contradictory.

Those who (like Arthur Prior ) take the tensed notions associated with the past, present and future (rather than merely before, during, and after) to be the irreducible foundations of temporality and our conceptions of temporal fact, are called A-theorists. A-theorists usually deny that past, present and future are equally real, and maintain that the future is not fixed and determinate like the past. A-theorists also believe that a satisfactory account of time must acknowledge a fundamental metaphysical difference between past, present and future. Those who wish to eliminate all talk of past, present and future in favour of a tenseless ordering of events are called B-theorists (such as D.H. Mellor and J.J.C. Smart ), who believe that the past, the present, and the future are equally real. B-theorists concede that the distinction between past, present, and future is central to our concept of time, but argue that this concept is not self-evidently correct.

B-theory in metaphysics
A-theorists believe that a satisfactory account of time must acknowledge a fundamental metaphysical difference between past, present and future. The difference between A-theorists and B-theorists is often described as a dispute about temporal passage or 'becoming' and 'progressing'. B-theorists argue that this notion is purely psychological, and embodies serious confusion about time. B-theorists also argue that The past, the present, and the future feature very differently in deliberation and reflection. We remember the past and anticipate the future, for example, but not vice versa. B-theorists maintain that the fact that we know much less about the future simply reflects an epistemological difference between the future and the past: the future is no less real than the past; we just know less about it. Many A-theorists argue that in rejecting temporal 'becoming', B-theorists reject time's most vital and distinctive characteristic. It is common (though not universal) to identify A-theorists' views with belief in temporal passage.

The debate between A-theorists and B-theorists is a continuation of a metaphysical dispute reaching back to the ancient Greek philosophers Heraclitus and Parmenides. Parmenides thought that reality is timeless and unchanging. Heraclitus, in contrast, believed that the world is a process of ceaseless change, flux and decay. Reality for Heraclitus is dynamic and ephemeral. Indeed the world is so fleeting, according to Heraclitus, that it is impossible to step twice into the same river. The metaphysical issues that continue to divide A-theorists and B-theorists concern the reality of the past, the reality of the future, and the ontological status of the present.

B-theory in theoretical physics
B-theorists argue that in special relativity, the relativity of simultaneity implies there is not a unique present, and many of special relativity's counter-intuitive predictions such as length contraction and time dilation are a result of this. Relativity of simultaneity implies eternalism (a block universe) and hence a B-theory of time, where the present for different observers is a time slice of the four dimensional universe. Thus it is also common (though not universal) for B-theorists to be four-dimensionalists, that is, to believe that objects are extended in time as well as in space and therefore have temporal as well as spatial parts. This is sometimes called a time-slice ontology.

A-theorists will counter in one of two ways, depending on how philosophically rich that the B-theorist intends special relativity to be. They can deny the special theory of relativity, for example, arguing that special relativity gave way to general relativity, which has cosmic time that can serve as the absolute 'now'. Less radically, A-theorists can also argue that special relativity does not imply that there is no absolute simultaneity. Ned Markosian draws a distinction between two different interpretations of the special theory of relativity. STR+ is a philosophically robust interpretation of STR, containing enough philosophical baggage to make it imply that there is no such thing as absolute simultaneity. STR- is a philosophically austere interpretation of STR that is empirically equivalent to STR+. Any argument from science or from empirical observation that supports STR+ will support STR- equally well. The A-theorist can then argue that one has good a priori reasons to believe in the A-theory, and therefore prefer STR-.

An A-theorist might argue that the neo-Lorentzian interpretation of relativity, which is empirically equivalent to the Spacetime (Minkowskian) interpretation, is correct. Under the neo-Lorentzian model, there is a privileged time and reference frame. Distances shrink up and clocks slow down for objects in motion relative to said frame. Mellor states that "while it is physically possible to determine whether two objects or events are simultaneous relative to a particular frame of reference, it is not physically possible to determine whether two objects or events are absolutely simultaneous." Therefore, special relativity is consistent with absolute simultaneity. It is also consistent with absolute presentness.

A-theorists have argued that relativity is even more compatible with relativity than the B-theory is. Geoffrey Builder has also argued that the non-relativity of rotation and acceleration imply the existence of absolute space and time, giving support to the neo-Lorentzian theory. In arguing for this model, Simon Prohovnik states that time dilation and length contraction "are by no means independent and that both may in fact be consequential on a single more fundamental concept." Ettore Minguzzi and Alan Macdonald suggest that the existence of a frame of reference where the speed of light has a round-trip speed of c, regardless of the motion of its source, is that one fundamental concept which explains both time dilation and length contraction on a neo-Lorentzian model.

Quentin Smith argues that temporal becoming, a feature incompatible with the B-theory of time, is an irreducible and essential part of physics. He states that references to the present cannot be construed in a fashion compatible with the B-theory without seriously altering their explanations. Terms like "the present value of the Hubble age" cannot mean "the value of the Hubble age at the time when I, the physicist, state this." Such a paraphrase would restrict by definition, its range of values to times when conscious organisms exist.

Irreducibility of tense
Opponents argue that the B-theory of time is burdened with heavy philosophical problems. Earlier B-theorists argued that one could paraphrase tensed sentences (such as "the sun is now shining") into tenseless sentences (such as "on September 28, the sun shines") without loss of meaning. Later B-theorists argued that tenseless sentences could give the truth conditions of tensed sentences or their tokens. Quentin Smith states that "now" cannot be reduced to descriptions of dates and times, because all date and time descriptions, and therefore truth conditionals, are relative to certain events. Tensed sentences, on the other hand, do not have such truth conditionals. The B-theorist could argue that "now" is reducible to a token-reflexive phrase such as "simultaneous with this utterance," yet Smith states that even such an argument fails to eliminate tense. One can think the statement "I am not uttering anything now," and such a statement would be true. The statement "I am not uttering anything simultaneous with this utterance" is self-contradictory, and cannot be true even when one thinks the statement. Finally, while tensed statements can express token-independent truth values, no token-reflexive statement can do so (by definition of the term "token-reflexive"). Current proponents of the B-theory argue that the inability to translate tensed sentences into tenseless sentences does not prove the A-theory of time.

Arthur Prior has also drawn a distinction between what he calls A-facts and B-facts. The latter are facts about tenseless relations, such as the fact that the year 2025 is 25 years later than the year 2000. The former are tensed facts, such as the Jurassic age being in the past, or the end of the universe being in the future. Prior asks the reader to imagine having a headache, and after the headache subsides, saying "thank goodness that's over." Prior argues that the B-theory cannot make sense of this sentence. It seems bizarre to be thankful that a headache is earlier than one's utterance, anymore than being thankful that the headache is later than one's utterance. Indeed, most people who say "thank goodness that's over" are not even thinking of their own utterance. Therefore, when people say "thank goodness that's over," they are thankful for an A-fact, and not a B-fact. Yet, A-facts are only possible on the A-theory of time.

Identity over time
Opponents also charge the B-theory with being unable to explain personal identity over time. The two leading explanations for this phenomenon are endurantism and perdurantism. The former states that objects are persisting individuals that are wholly present at every moment of their existence. The latter states either that objects exist at each instant, and do not have identity over time, or objects are extended in time, and therefore have temporal parts. Hales and Johnson explain endurantism as follows: "something is an enduring object only if it is wholly present at each time in which it exists. An object is wholly present at a time if all of its parts co-exist at that time." Under endurantism, all objects must exist as wholes at each point in time. The indescernibility of identicals states that if two objects are the same, then they have identical properties. However, an object such as a rotting fruit will have the property of being not rotten one day and being rotten on another. On eternalism, and hence the B-theory, one is committed to two conflicting states for the same object. The spacetime (Minkowskian) interpretation of relativity adds an additional problem for endurantism under the B-theory. On the spacetime interpretation, an object may appear as a whole at its rest frame. On an inertial frame, however, that same object will have proper parts at different positions, and therefore will have different parts at different times. Hence, it will not exist as a whole at any point in time, contradicting the thesis of endurantism.

Opponents will then charge perdurantism with having numerous difficulties of its own. First, it is controversial whether perdurantism can be formulated coherently. An object is defined as a collection of spatio-temporal parts, which are defined as pieces of a perduring object. If objects do not have identity over time, this clashes with our beliefs about personal identity. If objects have temporal parts, this leads to other difficulties. For example, the rotating discs argument asks the reader to imagine a world containing nothing more than a homogeneous spinning disk. Under endurantism, the same disc endures despite that it is rotating. The perdurantist has a difficult time explaining what it means for such a disk to have a determinate state of rotation. Temporal parts also seem to act unlike physical parts. A piece of chalk can be broken into two physical halves, but it seems nonsensical to talk about breaking it into two temporal halves. Chisholm argued that someone who hears the bird call "Bob White" knows "that his experience of hearing 'Bob' and his experience of hearing 'White' were not also had by two other things, each distinct from himself and from each other. The endurantist can explain the experience as "There exists an x such that x hears 'Bob' and then x hears 'White'" but the perdurantist cannot give such an account. Peter Van Inwagen asks the reader to consider Descartes as a four-dimensional object that extends from 1596-1650. If Descartes had lived a much shorter life, he would have had a radically different set of temporal parts. This diminished Descartes could not have been the same person on perdurantism, since their temporal extents and parts are so different.

Temporal becoming
B-theorists argue that temporal becoming is an entirely subjective phenomenon, and hence not an objective feature of reality. In the absence of minds, every temporal moment and event simply exists tenselessly; there are no tensed facts; no past, present, or future; nothing comes into existence or happens except in the tenseless sense of existing at certain appointed stations as opposed to others. Philosopher and theologian William Lane Craig states that this leads to a dilemma. The mental phenomenon of temporal becoming is either an objective feature of reality, or it is not. If it is, this amounts to a denial of the B-theory of time. If the B-theorist bites the bullet, stating that there is no temporal becoming of mental states, then this flies in the face of experience. In support of this view, Craig cites early 20th century astronomer and physicist Sir Arthur Eddington who stated: "We have direct insight into 'becoming' which sweeps aside all symbolic knowledge as on an inferior plane. If I grasp the notion of existence because I myself exist, I grasp the notion of becoming because I myself become. It is the innermost Ego of all that is and becomes." . Tim Maudlin said: "Above and beyond and before all these considerations, of course, is the manifest fact that the world is given to us as changing, and time as passing. All the philosophizing in the world will not convince us that these facts are illusions." Caspar Hare concurs with this view, saying that "realism about tense is uniquely capable of making sense of the phenomenology of temporal experience."

Opponents argue that an adequate view of time must explain how or why we can have temporal experiences. Our conception of ourselves as beings caught in the ebb and flow of time is essential to our success as functioning beings in this world, in addition to being one of our most basic cognitive functions. Hence, any adequate philosophical account of time will have to explain it. By not explaining how we could have such experiences, opponents argue that the B-theory cannot adequately explain why we have experiences as of nowness, passage, and change. Craig concludes that B-theory suffers the same incoherence as all theories that time is illusory, namely, that an illusion or appearance of becoming involves becoming, so that becoming cannot be mere illusion or appearance. The idealist or phenomenalist can consistently deny the reality of the physical world, since the illusion of physicality does not entail physicality, but this is not the case with temporal becoming. As an example, Craig cites early 20th century philosopher John Laird who wrote: "Take the supposed illusion of change. This must mean that something, X, appears to change when in fact it does not change at all. That may be true about X; but how could the illusion occur unless there were change somewhere? If there is no change in X, there must be a change in the deluded mind that contemplates X. The illusion of change is actually a changing illusion. Thus the illusion of change implies the reality of some change. Change, therefore, is invincible in its stubbornness; for no one can deny the appearance of change."

Examples in fiction
Four-dimensionalism and consequently B-theory of time and eternalism, is explored in the film Interstellar. In the film, Astronaut Cooper is sent to a region of space called a 'tesseract', built by beings of 5-dimensions. In the tesseract, Cooper is able to perceive time as a spatial dimension. Consequently, Cooper is able to transmit information back to a time in his perceived past. Under the B-theory of time, this is consistent and does not induce a paradox.

These theories also appear in the comic book series Watchmen by Alan Moore, and its film adaptation Watchmen (2009). In one chapter in the comic book series, Dr. Manhattan explains how he perceives time. Since past, present, and future events all occur at the "same time" for him, he speaks about them all in the present tense. For example, he says "Forty years ago, cogs rain on Brooklyn" referring to an event in his youth when his father throws old watch parts out a window. His last line of the series is "Nothing ends, Adrian. Nothing ever ends.".