McTaggart's A-Theory & B-Theory of Time Explained

Einstein's relativity theory implies that different observers can disagree about what events are simultaneous (relativity of simultaneity). For example, two spaceships passing each other at near-light speed might observe flashes of light in different orders. This challenges the A-theory of time (only present is real) and supports the B-theory (all times coexist in a block universe). However, the block universe is a useful tool rather than necessarily reflecting reality, as causality still constrains event ordering.

According to the B theory of time, which states that all points in time are equally real, event B is real in both frames of reference regardless of whether it occupies the present. This resolves the inconsistency that the A theory creates when dealing with the relativity of simultaneity.

Einstein's theory of special relativity fundamentally changed our understanding of time. Before Einstein, time was considered a universal parameter that everyone shared. However, Einstein discovered that the speed of light is finite and the same for all observers, and nothing can travel faster than light. This leads to the relativity of simultaneity—the impossibility to define one unambiguous notion of what happens 'now' that everyone agrees on. Neither observer is wrong or right when they disagree about whether two events happened at the same time. Einstein's mathematical framework combines space and time into one common entity called space-time, leading to the block universe concept where the past, present, and future exist in the same way.

Einstein's relativity suggests the entire universe exists as a static four-dimensional block where all times coexist simultaneously. There is no objective 'now'—all moments are equally real. Different observers moving relative to each other disagree on what events are simultaneous. What one sees as simultaneous, another sees as sequential. Yet causality is preserved—causes must precede effects, preventing paradoxes.

According to Einstein's theory of relativity, the present moment is not absolute but relative to the observer's speed and reference frame. This means that two events that appear simultaneous to one observer may not be simultaneous to another moving at high speed relative to them. The famous Penrose thought experiment demonstrates this by showing that even at low speeds like 15 km/h, different observers can disagree on whether an event in the Andromeda galaxy (2.5 million light-years away) is happening now, happened in the past, or will happen in the future. This leads to the block universe theory, which proposes that all events—past, present, and future—already exist as part of a single, unchanging four-dimensional spacetime block, suggesting that the future may be predetermined rather than freely chosen.

J.M.E. McTaggart, an Oxford philosopher, argued in 1908 that time does not exist. His argument: an event is simultaneously present (in the present), past (in the past), and future (in the future), which is a contradiction. This 'A-series' and 'B-series' argument has been debated for over a century with no consensus. McTaggart's work remains influential in philosophy of time.

McTaggart's argument for the unreality of time faces objections from both A theorists and B theorists: A theorists challenge the ultimacy argument by arguing that change requires only object properties to differ between events, not event properties themselves (as illustrated by a triangular plank where each point maintains its width while the overall shape changes); B theorists challenge the contradiction argument by identifying an equivocation between 'no event can be more than one temporal property at one time' (which is true but insufficient) and 'no event can ever be more than one temporal property' (which is unintuitive), noting that only a C series is needed to make this distinction, not the A series itself.

McTaggart's paradox of time, constructed by J.M.E. McTaggart, is an argument attempting to prove that time is unreal, that temporal distinctions are contradictory, that past, present, and future cannot coexist. The argument begins by distinguishing two ways of thinking about time: the A series, which orders events as past, present, or future, and the B series, which orders events as earlier than or later than each other. McTaggart argues that the A series is essential to time—that change requires events to move from future to present to past, and without this passage, there is no real time. But the A series is contradictory and generates logical problems, therefore time is unreal, is an appearance generated by our temporal perspective but does not correspond to ultimate reality. The paradox emerges from the fact that A series properties are contradictory: every event is past, present, and future. The meeting is future before it occurs, is present when it occurs, is past after it occurs. And so the meeting has all three properties—past, present, and future—which are incompatible and cannot all be instantiated by the same event. The standard response is to say that events have A series properties at different times—the meeting is future at earlier times, present at its time of occurrence, past at later times. This seems to resolve the contradiction by indexing A series properties to times. But McTaggart argues this does not help because now we must ask whether the times themselves are past, present, or future. The same problem recurs. If the time at which the meeting is future is itself past, then the meeting is past and future, and contradiction remains. Indexing to times does not eliminate the contradiction but only pushes it back. McTaggart argues that the only way to avoid contradiction is to eliminate the A series—to accept that events do not really move from future to present to past. That passage is illusory, that reality consists only of the B series, only of earlier-later relations. But the B series without the A series is not real time—it is only a static ordering, lacks the dynamism, lacks the passage that is essential to time. McTaggart's position is a form of idealism about time, treating time as mind-dependent, as not part of the ultimate structure of reality.

John McTaggart, a British philosopher of the 20th century, argued that time is unreal by distinguishing between two series: Series A (dynamic, using past, present, future) and Series B (static, using before/after relations). He demonstrated that Series B depends on Series A, and then showed that Series A is incoherent because it requires events to simultaneously possess incompatible temporal determinations (past, present, and future), leading to an infinite regress when attempting to resolve this contradiction.

This section explores the fundamental question of why time appears to have direction despite time-symmetric physical laws. The second law of thermodynamics states that entropy (disorder) in isolated systems never decreases—it increases or stays constant. This provides time's direction: ice melts, batteries discharge, people age. Despite time-symmetric fundamental equations, entropy increase gives time its apparent direction. Real systems are never truly isolated—they interact with surroundings. Quantum decoherence occurs when systems become entangled with environments, causing irreversible collapse of superpositions. This environmental interaction breaks time symmetry and provides a fundamental arrow of time. Entanglement entropy (increasing system-environment entanglement) complements thermodynamic entropy, explaining why time's direction is real and fundamental rather than merely apparent.

The fundamental distinction between past and future emerges from thermodynamics, not fundamental physics laws. The second law states entropy (disorder) always increases, creating time's arrow. However, what constitutes 'order' is subjective—it depends on how we describe systems (coarse graining). The early universe's low entropy is not inherent but results from our specific interaction with it. We are a special subset of the universe that remembers the past and anticipates the future, giving time its psychological direction. Without entropy production, reversible processes would show no temporal asymmetry.

Fundamental physics laws are time-symmetric, meaning they work the same forward or backward. Yet we experience time as flowing in one direction. This asymmetry emerges from entropy - the measure of disorder in a system. The Second Law of Thermodynamics states that entropy always increases, creating a thermodynamic arrow of time. This explains why hot coffee cools but never spontaneously reheats, and why mixed gases never separate. Our memory formation also follows this direction, as brains create memories through energy-consuming processes that increase entropy. Stephen Hawking called this the 'psychological arrow of time' - our subjective experience of time's direction is tied to entropy increase.

This segment examines the nature of time as the increase of entropy—the measure of disorder in a system. Using the example of a broken glass that cannot naturally return to its original state, the video illustrates the arrow of time. It distinguishes between physical explanations (which describe how matter and energy behave) and metaphysical explanations (which address the fundamental nature of existence and meaning). The video argues that while physics can describe processes, it cannot fully explain why the universe exists at all or what gives it meaning, highlighting the limitations of purely scientific approaches to understanding reality.

Tensed language uses 'now,' 'past,' and 'future' with changing truth values, while tenseless language uses only earlier-than/relations. McTaggart's A-series (tensed) versus B-series (tenseless) distinction shows that tense properties change truth values over time. This linguistic feature, found across all human languages, reflects cognitive adaptations rather than objective time structure. Metaphysical theories attempt to vindicate this experience through various models positing privileged presents.

There are two philosophical theories about time's nature. The tense theory states the future doesn't exist yet and branches out as time progresses. The tenseless theory states the past, present, and future are all equally real, and we are simply traveling along a timeline. These theories represent fundamentally different views on whether time is a dynamic process or a static dimension.

The view of God's relationship to time depends on whether one holds a tenseless or tensed theory of time. A tenseless theory views past, present, and future as an illusion with all events spread out like a line, leading to the conclusion that God exists in a timeless state. A tensed theory views the difference between past, present, and future as real and objective, where things truly come into being and pass away, leading to the conclusion that God is also in time. The speaker argues that the common sense view of time as tensed is correct and comports with our experience. Space can be represented as a disc where the third dimension represents time, with spatial cross-sections at various times. Even if space is finite, if time has no end, there would be an actual infinity of events, though this could be resolved if time comes to an end.

John McTaggart developed the distinction between A series and B series as part of his argument about the nature of time. The A series orders moments in time using tense (past, present, future), while the B series orders moments in time using only earlier-than and later-than relations. On the A series, whether something is present, past, or future is an intrinsic feature of that moment. On the B series, there is nothing intrinsically past, present, or future about moments in time - they are only earlier or later relative to other moments. A theories say that tensed language is the most appropriate language for describing what's really happening with respect to time. B theories say that tenseless language is fully adequate for describing everything going on in time.

Arguments for tensed theory: (1) Tensed sentences correspond to tensed facts and cannot be translated into tenseless sentences, (2) Experience of temporal becoming is veridical. Arguments against tensed theory: (1) McTaggart's paradox results from marrying tenseless ontology with objective temporal becoming, (2) Passage of time is a metaphor for objective temporal becoming. Arguments for tenseless theory: (1) Temporal becoming is compatible with relativity theory under neo-Lorentzian interpretation, (2) Physics time is an abstraction omitting indexical elements. Arguments against tenseless theory: (1) Relations ordering events are only gratuitously regarded as temporal, (2) Mind-dependent becoming is self-defeating.