Time: an objective definition of time

 To determine the objective definition of "time" following Ayn Rand's methods and instructions, I will proceed step by step:

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### Step 1: Reduce the concept of time to its perceptual-level roots and its basic fundamental axioms, lemmas, and general principles.

**Perceptual-level roots**:

- Time is observed through the sequential nature of events and changes in reality. It is experienced directly through the progression of actions, the movement of objects, and the succession of events.

- Time is not a sensory object but is understood conceptually through the observation of change and motion within the physical world.

**Basic fundamental axioms, lemmas, and general principles**:

- **Axiom of Identity**: Reality is composed of entities that exist with specific natures. Change can only occur within entities that exist, and time is the measurement of that change.

- **Axiom of Existence**: Time exists as a relational concept that depends on the existence of entities and their actions or changes.

- **Axiom of Consciousness**: Human consciousness allows for the observation and integration of sequential events, thus forming the concept of time.

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### Step 2: Identify the perceptual-level roots of the concept.

The perceptual-level roots of time involve:

- Sequential experiences: Observing one event following another (e.g., the sun rising and setting, a clock ticking).

- Relationships between events: Recognizing that certain actions or processes take place over intervals (e.g., the time it takes for a fruit to ripen, for a person to walk across a room).

- Duration and change: Observing that entities persist over measurable extents of change or motion.

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### Step 3: Identify intermediate steps and principles necessary to reconstitute the concept of time.

**Intermediate principles**:

1. Time is a relational measurement—it does not exist independently as a "thing" but is a conceptual framework derived from the relationship between entities and their changes or motions.

2. Time is a means of integrating and quantifying the succession and duration of events.

3. Time is measured using consistent units derived from observable phenomena (e.g., the Earth's rotation, oscillation of a pendulum).

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### Step 4: Use reason to identify the observable and measurable essential characteristics and distinguishing characteristics of time.

**Essential characteristics**:

1. Time is the measurement of change and motion.

2. It is observed through the succession and duration of events.

3. Time is conceptualized through consistent and repeatable standards (e.g., seconds, minutes, hours).

**Distinguishing characteristics**:

- Time is not a physical entity but a conceptual tool used to understand and measure the progression of reality.

- It is defined by its dependence on motion, change, and human consciousness to integrate and structure these observations.

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### Step 5: Define the concept of time in terms of genus and differentia, and its essential characteristics and distinguishing characteristics.

**Genus**: Time is a relational concept of measurement.

**Differentia**: Time is the measurement of the succession and duration of changes and motions within reality.

**Definition**: Time is the relational measurement of the succession and duration of changes and motions, as conceptualized through the observation of events and quantified using consistent standards.

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This definition eliminates any mysticism, subjectivism, or floating abstractions, adhering strictly to the observable and conceptual nature of time within the framework of reality.

In addition:

Time is the continuous progression of existence that unfolds in an apparently irreversible sequence from the past, through the present, and into the future. It is a fundamental dimension in which events occur in a specific order, allowing the measurement of durations, intervals, and rates of change in reality or conscious experience[1].

At its perceptual root, time relates to the observation of events, changes, and sequences—qualities and actions perceived as happening one after another. These aspects correspond to basic entities in reality such as objects undergoing changes, actions occurring, and events unfolding with relationships ordered by before and after.

Fundamental axioms and principles underlying time include:

Causality: Every effect has a cause occurring earlier in time.

Irreversibility (Arrow of Time): Time flows in a single direction from past to future, not backwards.

Continuity: Time is continuous rather than discrete at macroscopic scales.

Universality: Time applies universally to material reality and experiential phenomena.

Spacetime Unity: In modern physics, time is inseparable from space, forming a four-dimensional continuum (spacetime).

Intermediate principles necessary to reconstruct the concept are:

The ability to measure time, often relative to periodic phenomena (e.g., Earth's rotation, atomic vibrations).

The concept of duration and intervals that can be compared.

Temporal ordering to understand the sequence of events.

The influence of physical conditions (e.g., velocity, gravity) on the rate of time’s passage.

The measurable essential and distinguishing characteristics of time are:

Sequential Order: Events are arranged in a linear, irreversible sequence.

Quantifiability: Time can be measured as intervals using consistent units.

Universality: Time affects and applies across all events in the universe.

Continuum: Although measured discretely, time itself is continuous at macro scale.

Relativity: Time’s rate can vary based on relative speed or gravitational field (relativistic effects).

Definition of time (genus and differentia):

Time is a fundamental continuous dimension (genus) of reality, characterized by the irreversible, sequential progression of events from past to future (differentia), whose passage is universally measurable as intervals, orders the causality of events, and integrates with space into the four-dimensional spacetime continuum.

Criteria for an objective definition of time include:

Grounding in perceptually verifiable realities—observable events, changes, and orders.

Consistency with fundamental physical laws (causality, continuity, relativity).

Being free of mysticism, subjective mental states, or arbitrary conventions.

Universality, applying to all physical reality without exception.

Clarity, precision, and the ability to be operationally measured.

The above definition meets these criteria: it is based on empirical observation, universal principles in physics, measurable characteristics, and excludes subjective or mystical elements.

Based on current scientific understanding, this definition of time is general and universal, applicable across classical and modern physics as well as everyday human experience[1].

References:

[1] Time

https://en.wikipedia.org/wiki/Time

[2] Time What Is Time - song and lyrics by Blind Guardian

https://open.spotify.com/track/3I4iklkGcZyjwLmJ4FjhBi

[3] Time What Is Time - Remastered 2007

https://open.spotify.com/track/1Gac3BjYY98hH9YgQEl7Lm

[4] Blind Guardian - Time What Is Time (Lyrics)

https://www.youtube.com/watch?v=lY_oEw7kyXQ

[5] Time What is Time (Revisited)

https://www.youtube.com/watch?v=ZS85-mLG0V8