section 34 (first updated 1.13.2021)

Newton vs Einstein

Common Misconceptions about Time

A common misconception treats time as if some already-given quantitative measure exists prior to activity, and that activity merely draws from this preexisting stock. In reality, the doing of the activity is the duration of the time taken. Time is not a container into which events are placed; rather, the event itself constitutes the temporal duration. Thinking imagines time before doing, but doing is time unfolding.

A similar misconception applies to space. Space is often imagined as a pre-existing “room” within which objects later arrive. Yet there is no case in which space exists wholly without an object occupying at least some part of it. Once an object is somewhere, a distinction arises between where it is and where it is not. Space is thus not an empty container but the structural differentiation between presences and absences.

Time is the opportunity for things to happen, for thought to think. Phrases such as “running out of time” do not describe a diminishing quantity but express how one determination is overtaken by another. When one is “running out of time” while crossing a street, it is not that time is disappearing; rather, the determination of walking is being overtaken by the determination of oncoming cars, mediated by legal conventions that give each determination its turn.

Similarly, “wasting time” is not about exhausting a resource. It concerns the failed reciprocity of determinations. When a customer travels to meet a seller who never arrives, the trip itself is not the waste; what is wasted is the intended determination (the transaction) failing to encounter its counterpart.

Infinite Regress as Becoming

In this framework, infinite regress is not a problem but the very structure of becoming: each determination presupposes another, which in turn calls forth another, generating the unfolding of time rather than demanding an impossibly fixed beginning.

Time as a General Schema

As Eddington once remarked, “a new theory must take account of well-attested older facts just as much as the latest experimental results.”⁽¹⁾ Thus, any theory of time and space must reconcile classical intuitions with modern physics.

Space and Time as Restrictions and Constructions of the Infinite

Space appears vast and empty because the distances between objects are large relative to the observer. Yet as an observer moves outward, the space between formerly distant objects appears to shrink, and objects appear closer together. What once looked dispersed becomes condensed. Galaxies illustrate this: from afar they are tight clusters, but within them the distances between individual stars are enormous.

This reveals that space belongs to the specific dimensions of the objects under consideration. To treat space as a universal schema within which things simply reside is an abstraction.

Space and Time Are Not Empty

Space, understood as self-externality or indifferent quantity, presupposes its own negation—Negativity. Negativity exists for itself as a positive existence but stands as negation with respect to space. Because space is indifferent, its positivity lies in its neutrality, in simply allowing contents to appear within it. The notion of “empty space” is therefore an abstraction of distance.

Distance

Distance is the measure between two distinct objects by way of a non-distinct quantity—something that is neither object, nor any other particular, but the indifferent medium through which distinction appears. Distance is generated through the interaction of objects: a distinct thing generates the quality opposite to itself—indistinction—to express its distinctness.

Terms such as “interval,” “remoteness,” or “breadth” are relational measures derived from the nature of the object. Breadth, for example, is the span between an object’s extreme points; depth is the internal interval disclosed through its circumference.

Space, as passive quantity, is full of every possibility, not a hollow nothingness. Even the “empty” regions beyond Earth are filled with subatomic particles, radiation, and fields.

Time as Pure Negativity

Time, in contrast, is the pure negativity that limits each content in space. If space contains all possible presences, time restricts them by imposing duration. Time is the activity that gives everything a specific timespan, dividing the totality of being into successive determinations. Every event happens slightly before or after every other event.

Thus, time is abstract activity—negative relative to being, which is positive. Time presses being into becoming. If space is the abstract realm where being becomes, time is the abstract activity where the becoming becomes determinate.

The unity of space and time—modern physics’ spacetime continuum—is the point at which the Idea becomes concrete.

Time, Object, and Negation of Negation

Time is indifferent activity relative to any quality, producing the determinacy by which an object becomes what it is. Time is the natural occurrence corresponding to logic’s principle of identity (P = P). Time is equal to itself as the negative unity of being outside itself: being which, since it is, is not; and since it is not, is.⁽²⁾

Time is also equal to the object, integrated into its essence. As the internal relation of the object, time is continuous like space, but internally rather than externally. Time is to the object what P is to p: the activity (P) pressing the variable being (p) into determinate existence. Conversely, the being of p presses against the abstract universality of time. This tension—negation of negation—characterizes life and death.

Arising and Passing Away

In time, all things arise and pass away. “Life” and “death” are abstractions of these processes, necessary for conceiving the object in temporal becoming. But if one were to abstract space in itself, or time in itself, one would be left with an empty realm and an empty process.⁽³⁾

Such abstraction is impossible because time is the becoming of the object. As Hegel notes, time is “the Chronos who gives birth to everything and destroys his offspring.”⁽⁴⁾

Science, beginning with Descartes, defines matter as extension. Extension is spatial and temporal:

1. Spatial extension: the object occupies a region and fills it with content.
2. Temporal extension: the object persists through moments, each a different configuration of the same extension.

We perceive only one moment at a time—e.g., a person running at 2:00 and eating at 4:00—yet these form a continuous temporal order.

As Hegel notes, although negativity is immanent in everything, time is not adequate to its full essence and thus relates to negativity as its power.⁽⁵⁾

Footnotes

1. Arthur Eddington, The Nature of the Physical World (1928), Summary, p. 165.
2. G.W.F. Hegel, Science of Logic, Book II: The Doctrine of Being, Section on Time.
3. Ibid., discussion of abstract space and abstract time.
4. Hegel, Encyclopedia Logic, §258 Addition: the reference to Chronos.
5. Hegel, Science of Logic, on negativity and time as inadequate to the universality of negativity.

Hegel Strips Time to Its Bare Capacity

Time itself is eternal, for it is neither merely a time nor the moment now, but time as such is a concept. The concept, however, in its identity with itself (I = I), is absolute negativity and freedom. Thus, time is not the power of the concept, nor is the concept within time or temporal. On the contrary, the concept is the power over time, and time is only this negativity in its externality. Nature is therefore subordinate to time insofar as it is finite, whereas what is true—the Idea, the Spirit—is eternal.

Hence, the concept of eternity must not be understood as suspended time, nor as something that comes after time. If eternity followed time, it would be transformed into the future, and thus into a mere temporal moment. Nor should eternity be conceived as a simple negation or abstract elimination of time. For time in its concept is, like the concept itself, eternal, and therefore absolute presence.⁽¹⁾

Hegel §202 “The dimensions of time—the present, future, and past—are only that which is becoming, and its dissolution into the differences of being as transition into nothingness, and of nothingness as the transition into being. The immediate disappearance of these differences into individuality is the present as ‘now,’ which is itself only this disappearance of being into nothingness and of nothingness into being.”⁽²⁾

(1) The Finite Present and the Infinite

The finite present is distinguished from the infinite in that the finite present is this moment now, and thus contains its abstract oppositions—past and future—which stand over against the infinite as over against the concrete unity. Eternity, as concept, contains these temporal moments within itself; its concrete unity is therefore not the moment now, because the “now” is the vanishing oscillation of being into nothingness and nothingness into being. Eternity is instead motionless identity, concrete universality, rather than the flux of becoming.

In nature, where time is always a “now,” the enduring difference of past and future does not appear as something existent; these dimensions exist only in subjective representation—in memory, fear, and hope. The abstract past and future of time find their analogue in space, for suspended space becomes the point, and time is the conceptual analog of the point.⁽³⁾

(2) No Science of Time Analogous to Geometry

There is no science of time analogous to the finite science of space (geometry). The differences of time do not possess the indifference of externality that constitutes the determinacy of space, and therefore cannot be expressed as spatial figures. Only when the understanding paralyzes time—reducing its pure negativity to the fixed unit—does time gain the capacity to be handled as magnitude.

This motionless unit, the sheer externality of thought, becomes the basis for forming external combinations—the numbers of arithmetic. These combinations can be brought under the categories of truth by intuition or by the understanding alone, since the latter is merely abstract while the former is concrete. Mathematics, as such, rests upon the unit as its highest externality and constructs finite relations through equality, inequality, identity, and difference.⁽⁴⁾

Thus, the science whose principle is unity stands opposed to geometry.

(3) Mathematical Treatment of Space and Time

Mathematics has often been invoked to assist in philosophical reflection on space and time, since these subjects lie close at hand. Yet mathematics considers only determinations of magnitude, not time as such—only the unit in its configurations. Although time appears in the mathematical theory of motion, applied mathematics is not an immanent science; it applies pure mathematics to empirical content, rather than deriving determinations from concepts themselves.⁽⁵⁾

(4) On the Possibility of a Philosophical Mathematics

One might conceive of a “philosophical mathematics”: a science that recognizes the concepts underlying the determinations presupposed by conventional mathematics. But since mathematics treats finite magnitudes that remain fixed in their finitude, it is essentially a science of the understanding. It should retain its power to express spatial figures and numerical relations, and avoid contamination by concepts—such as time—which are heterogeneous to its nature.

A philosophical treatment of space and unit would reduce them to logic or to another concrete philosophical science, depending on how their conceptual content was developed. But using spatial figures and numbers to express philosophical concepts is ultimately a superfluous and inadequate task. Such symbols can only express thought externally, ambiguously, and often incorrectly. The Pythagorean system of numbers is the famous example of this—helpful only in the earliest stages of thought.⁽⁶⁾

The more complex the concept, the more insufficient spatial and numerical symbols become. Their abstract juxtaposition destroys the fluidity of conceptual movement. Only explanation, not symbol, can resolve the ambiguity, rendering the symbolism unnecessary.

Other mathematical notions—such as infinity, infinitesimals, factors, powers—receive their true concepts only in philosophy, not in mathematics, where they are used non-conceptually or even meaninglessly. A true philosophical science of mathematics (as the science of magnitude) would be a science of measure, but this presupposes the real particularity of things, available only in concrete nature.⁽⁷⁾

Time as Pure Negativity

Time is pure negativity, and thus it is absolutely identical with itself. It upholds the principle of identity (A = A) precisely by negating the finite existence of objects. Every object is transitory with respect to time; time passes through objects, not objects through time. Time is therefore abstract subjectivity: the object relates to this negativity as to its own determining power.

If space and time are taken as inverse relations of the same being, space is abstract objectivity, whereas time is abstract subjectivity.

Footnotes

1. Hegel, Encyclopedia Logic, §202 (Addition).
2. Ibid.
3. Ibid., on the relation of past and future to space and the point.
4. Ibid., discussion of the understanding’s reduction of time to the unit and the origin of arithmetic.
5. Hegel, Philosophy of Nature, Mechanics section on motion and the application of mathematics.
6. On Pythagorean number mysticism, see Aristotle, Metaphysics A5, and Hegel’s discussion in Lectures on the History of Philosophy.
7. Hegel, Science of Logic, Doctrine of Measure.

Spacetime as Constant

Einstein’s spacetime “fabric,” used to illustrate gravity, assigns a physical structure to the region an object is not immediately in. The so-called fabric of spacetime corresponds to the potential energy a particle contains. Potential energy may be defined as the total set of possible actions, motions, and scenarios available to a particle, while the particle itself is the actualization of one of these possibilities at a given moment.

Modern gravitation theory attempts to explain how a general unifying force relates to the particular actions of bodies. Spacetime, or gravity in Einstein’s sense, describes effects—the reaction of matter—without providing an ultimate account of the action that grounds the cause. For instance, the fact that heavy bodies fall “downward” toward a center is one particular determination taken as a universal rule. The law that matter “falls down” presupposes the concept of downwards as motion toward a center.

But this “center” functions only as a reference relative to an observer, as expressed in the cosmological principle. Motion relative to this center appears “heavy” when directed downward and “light” when upward. We measure “up” and “down” as quantities of heaviness and lightness because they are experienced relative to a constant—the observer himself. In space, stars move up, down, sideways, or radially with no privileged direction.

Aristotle notes:

“Measure means that by which each thing is first known… in length, breadth, depth, weight, and speed. ‘Weight’ means both whatever has gravity at all and whatever has an excess of gravity; and ‘speed’ means both whatever has any motion and whatever has an excess of motion.”⁽¹⁾

These quantitative determinations are objective, but their reference point—their constant of measure—is the observer. The observer is the objective condition grounding the quantities, while the quantities themselves become subject-matter relative to this standpoint.

The Cosmological Constant

It is often claimed that Einstein’s cosmological constant was a mistake because he initially introduced it to obtain a “static universe.” He later abandoned it after Hubble’s discovery of cosmic expansion. But the true error was not in proposing a constant; it was in misunderstanding how a general constant should be applied to the world.

The fallacy lies in attempting to unify two opposed facts (static equilibrium and universal motion) without first understanding each in relation to itself. A universal constant should not be thought of as a rigid, preexisting baseline from which all motion subsequently deviates. If we suppose the first “motion” begins from rigidity, then the beginning of motion cannot be explained. This intuition—of a rigid constant first, and dynamical objects second—is an abstraction of the activity of conception itself. The stability we imagine in the world is projected from the stability of the conceptual standpoint.

The gravitational constant, in Einstein’s formulation, projects this stable reference frame of thought onto spacetime, as though the substratum of the world must be as stable as the conceptual mechanism through which the world is disclosed. The intuition that external matter mirrors the internal structure of conception is not wrong; what is mistaken is to elevate one aspect of conception—its stability—over the other—its activity.

If spacetime is derived from the nature of consciousness, then the active, self-differentiating side of conception must also appear in spacetime. This active aspect corresponds to what physical theory calls the particle, the excited, animated pole opposite to the static reference.

A constant need not be stable; a movement may be constant—constant in motion. When we impose a constant onto the world as a static veil, the understanding gains a sense of completeness: motion appears unnecessary for the sake of a final resting state. Reason, however, disrupts this illusion by demanding an explanation of motion: Why do things move at all if their ground is static? What purpose does motion serve if its origin is immobility?

Gravity as Inversion of the Passive Witness

We say the apple falls downward or helium rises upward only after the fact, ex post facto of our conception. The determination “the apple falls” is its active determination, not the passive impression of witnessing an already completed event. Gravity extrapolates the passive quality of conception—the stability that allows us to witness phenomena without interfering—as though this passive stability were an external active force.

Thus, the conception that remains neutral in witnessing events becomes, when inverted externally, the general active invariant known as gravitational force.

The observer’s conception is constant in that it preserves a stable distinction among objects. Its active side appears externally as objects acting distinctly in space. The no-interference internal aspect of conception becomes, when projected outward, the total interference of a universal force animating all motion. This initial relation is what we call general gravitation. Newton’s gravitational constant (G) expresses that the force between two bodies is always an equilibrium of motion, even when their masses differ drastically.

For example, the Earth and Sun maintain an equilibrium described by distance, speed, and mass. Greater mass corresponds to faster or stronger interaction because more mass occupies more volume—more determinations exist within it. Light, taking up the greatest possible “volume” of activity, is the limit of motion.

Gravity governs these relations as a universal constant, but we do not consider the constant as arising from a particular object. A particular perspective cannot comprehend the full universal magnitude. Just as a single human cannot experientially grasp the reality of billions of individuals—though the number represents them—so universal laws describe magnitudes inaccessible to any single standpoint.

Gravitational Energy and Determination

Gravitational energy is the particular form in which the general gravitational field is determined within a specific object. It is the potential energy an object possesses due to its position relative to another. This represents the application of universal gravitation into a definite direction. When one object uses the asymmetrical structure of another within their common gravitational field, a particular determination arises.

Every single determination emerges from the symmetry of relations among objects. The angle of a diamond, for instance, arises from the symmetry of its crystalline prism.

Footnotes

1. Aristotle, Metaphysics, Book X, Part 1.
2. Einstein, Cosmological Considerations in the General Theory of Relativity (1917); discussion of the cosmological constant.
3. Hubble, “A Relation Between Distance and Radial Velocity Among Extra-Galactic Nebulae,” PNAS (1929).
4. Newton, Philosophiæ Naturalis Principia Mathematica, Book III, on the universal law of gravitation.
5. Hegel, Science of Logic, Doctrine of Being; also Encyclopedia Logic §§94–108 on measure and magnitude.

Space “In and Out” of Something

(With notes on how to connect this to “zooming–contact” and to “time as being and non-being”)

Newton’s Absolute Time and the Externality of Moments

Newton’s conception of absolute time assumes that time has a definite, single direction and that all things move along that direction. Everything moves from past to future, and this movement is independent of all observers. Newton’s view rests on two core assumptions:

1. Time flows uniformly and at an absolutely fixed rate everywhere in the universe.
2. Time exists independently of any perceiver, so that its progression is not altered by differences in spatial position or motion.

This framework makes time measurable, because two observers in different places can agree on the same temporal value. For example, two people standing on opposite sides of a street can both agree that it is 2:00 PM. This forms the everyday intuition that “time is the same everywhere.”

Einstein, however, disrupts this intuition by showing that time is inseparable from space—that spacetime is a unified structure, not two independent entities.⁽¹⁾

Special Relativity and the Magnitude of Space

Special relativity reveals something counterintuitive about the magnitude of space: space is not merely infinitely large; it is also infinitesimally small. Classical intuition sees space as an extensive magnitude—something you can travel “outward” in without end. Light appears to support this: it moves outward indefinitely, implying that space can be traversed endlessly.

Because nothing travels faster than light, light becomes the fundamental magnitude of motion. Any moving object emits light that outstrips it, ensuring that light always “arrives first.” This asymmetry produces a spherical region of disclosure around the object—light arriving from all directions—revealing the object to any possible observer. The internal microstructure of matter mirrors this: the electron mediates the relation of proton and neutron by a field of energy surrounding the nucleus.

Yet relativity also demonstrates the inverse: space is not only vast but also minute. Two objects may be separated by an infinitely small spatial interval, depending on their motion.⁽²⁾ This gives rise to time dilation, length contraction, and the phenomenon that simultaneity is not absolute.

External Observation and Definite Contact

When observers are external to each other—when one object is physically outside another—the observed object appears as a definite thing in a definite moment. Whatever is happening at the present moment seems certain, immediate, and indisputable. A severed hand, for example, is not a matter of interpretation: regardless of what one wants to see, the hand is gone. The event has already happened, and there is no alternative presently available.

This is the domain of contact—direct interaction between object and observer.
(You can insert here the earlier “zooming–contact” material: as one zooms closer into an object, the certainty of contact increases; as one zooms out, space becomes abstraction.)

Newton’s absolute time captures this certainty of contact. A moment, once present, is:

• fully actual,
• irretrievable,
• and independent of what could have occurred.

Newton extrapolates the certainty of this immediate moment to the entire universe, imagining that the whole must be in a definite state at every definite moment, everywhere. Absolute time is therefore:

• a chain of fixed presents,
• continuously sliding forward,
• each one fully actual and no longer alterable.

The Problem Newton Cannot Address

Although a present moment cannot be changed once it has occurred, Newton provides no explanation of what leads to the present moment, or why it occurs at all. His framework treats the unfolding of time as a brute necessity: moments simply happen because time must always have a definite present.

Thus questions such as:

• Why did this event happen instead of another?
• What determines the transition from one moment to the next?

are not answerable within Newton’s model. They are dismissed as meaningless because the present is treated as a given, independent of any inner necessity.

This is where your earlier statement—time is being and not-being—can be inserted. Newton’s time is pure being of the moment, but relativity (and Hegel) show that time is also not-being—the negation through which a moment becomes another. His model ignores the internal becoming that generates each moment.

(This is your second insertion point: connect to Hegel’s “time as the negativity of being” or “time as the being which, since it is, is not; and since it is not, is.”⁽³⁾)

Connecting to “Contact” and “Zooming”

You can now connect the relativity of “closeness” and “distance” to the relativity of the present moment:

• From far away, an object seems fixed and definite (Newtonian contact).
• As you “zoom in,” the certainty dissolves into internal processes, variations, and possibilities.
• From a relativistic frame, events are not absolutely simultaneous; closeness in space alters closeness in time.

Thus, contact becomes scale-dependent, and Newton’s absolute time is simply the external observer’s contact with the world, not the internal structure of becoming.

Footnotes

1. Albert Einstein, On the Electrodynamics of Moving Bodies (1905); see also Einstein, Relativity: The Special and the General Theory.
2. Minkowski, “Space and Time,” (1908); the introduction of Minkowski spacetime demonstrates that spatial intervals depend on the 4-velocity of the observer.
3. Hegel, Science of Logic, Doctrine of Being, §201–203, on time as the negativity of being.

1. The Physicality of Spacetime

The physicality of spacetime is unlike any single physical phenomenon. Many physical processes—ultraviolet radiation, acoustic vibrations, electromagnetic waves—are imperceptible to the naked eye but become detectable once appropriate instruments are used. Each of these exhibits a definite physical structure, a rhythm or vibration, occupying space and time like any ordinary body.

Spacetime, however, possesses no single definable physical form. It cannot be decisively identified as a wave, a field, a vibration, or any other isolated kind of physical entity. Its physicality is indistinguishable from the object resting “on” it, even though it produces effects that go beyond any single object. Spacetime is not reducible to the matter that appears to distort it, because the effects attributed to spacetime propagate outward and alter the behavior of other objects.⁽¹⁾

It is, rather, the possibility for there to be vibrations, waves, or physical interactions at all. Imagine a wavelength passing through an empty room: one sees an object against “space,” and this event—the object-in-space—emerges only after we abstract and isolate the object from its spatial context, and then further abstract space from the time during which the object remains itself. Through this multi-layered process of abstraction, distinctions in nature arise.

Yet spacetime is, in its fundamental form, the indistinguishable element of the universe: the dense, undifferentiated cluster of all possible events. Only when attention fixes upon a particular event do the other possible events fade into the background. That focused event becomes magnified against “empty space,” which functions as the natural measure of distinguishing one thing from another. To isolate an event is not the same as magnifying an object. Magnification singles out an object by making it the center of perception; isolation singles out an event by making it the only present moment.

Whenever a determinate physicality is selected—say, a wave—we thereby obtain an object in spacetime: a localized manifestation of a more general continuum.

2. Determination by Time and the Problem of Universality

If we assume that the condition for being a determination of time is equivalent to being determined by time, we create a conceptual gap. In physical practice, time is often treated as a general schema imposed uniformly across a set of independently acting objects, yet at the level of each particular occurrence, time becomes a local feature, not merely a global frame.

It is not the case that each object has a merely “subjective” time and therefore undermines time’s universality. Instead, each unique occurrence of a particular object reveals how time universally operates as a substantial duration.⁽²⁾ Time appears universal not because it exists “outside” events, but because each event expresses the same underlying structure of becoming.

In physics and mathematics, however, the following tacit assumption often persists:

If time is a determination of the object, then the object must be determined by time.

This makes time function as an imposed measure: a standard by which durations, sequences, and changes become detectable. But the limit governing our conception of duration is not abstract uniform time—it is the form of the object itself. Physics often treats the choice of object as arbitrary (it could be an electron, a stone, a star), yet this “arbitrariness” only means that any object is sufficient to express a universal relation such as motion, gravitation, or illumination.

In this sense, “randomness” in nature is not irrational chaos but an ordering principle. What appears random is the rational process of allowing a determination to fall into its natural state—as leaves stirred by the wind settle onto the ground in accordance with their intrinsic tendencies. Apparent randomness is a test of a determination’s nature.

Every object “must be somewhere before it is anywhere.” Every event must occur—whether sooner or later—because any principle considered in a vacuum expresses its complete domain before it is limited by specific conditions. There is “no place for it to go” because it is already here; “no time for it to happen” because it is already happening.⁽³⁾ This is the metaphysical foundation of time.

3. Absolute Time and General Gravitation

The idea of absolute time bears an intimate relation to the idea of general gravitation. In Newton’s formulation, the law includes both attraction and repulsion (the latter appearing implicitly in his treatment of inertial motion).⁽⁴⁾ Attraction and repulsion together define the magnitude of spatial extension; they generate the balance that produces three-dimensional form.

4. Distorting Spacetime: Einstein’s Revision

Einstein’s general relativity challenges Newton’s conception by arguing that gravity is not a direct force between two objects. Instead, gravity is the consequence of each object’s mass distorting spacetime, the four-dimensional manifold composed of three spatial dimensions and one temporal dimension.

In this view, gravity is:

• not simply the relation between two objects;
• but the relation of each object to a third element—spacetime itself—which then mediates the interaction of objects with one another.⁽⁵⁾

Spacetime is not merely a connector of objects but a feature belonging to all objects. It is their shared condition.

Popular analogies often depict spacetime as a fabric warped by the weight of an object, like a mass placed on a stretched sheet. This analogy is acceptable only insofar as it illustrates that the effects attributed to an object extend outward and influence other bodies—and can even affect something that is not directly observable, such as spacetime curvature.

However, the analogy becomes misleading when it suggests that spacetime and the object are independent entities, such that the object “sits on top” of spacetime. In reality, the observed curvature is not something external to the object’s own constitution. The “warping” of spacetime is the form of the object itself, abstracted. The event does not warp spacetime from the outside; the event is spacetime warped in that particular way.

Spacetime observed around an object is simply the form that space takes over time, the gradient of all the object’s potential interactions. The object is spacetime configured in its peculiar manner. To say that spacetime is distorted by an object is only to say:

An object is spacetime taking on that specific form.

Footnotes

1. Einstein, Relativity: The General Theory; see also Misner, Thorne, Wheeler, Gravitation (1973).
2. Minkowski, “Space and Time” (1908); the interval structure shows that time dilation and proper time demonstrate universality through particularity.
3. This parallels Hegel’s formulation in the Science of Logic that time is “the being which, since it is, is not; and since it is not, is.”
4. Newton, Philosophiae Naturalis Principia Mathematica, Definitions and Laws I–III; repulsion emerges through inertial motion.
5. See Einstein’s field equations (1915); curvature is proportional to the stress-energy tensor: (G_{\mu\nu} = 8\pi T_{\mu\nu}).

1. Entering the Object

Newton conceived time as a general measure applied uniformly to things. Thus, two people in the same region can agree that the time is 2:00 p.m., while in China it is 3:00 a.m. The time difference is still objective, because if one travels to China, one finds precisely that temporal value. Newton’s model assumes that time is determined entirely by external positional differences—by where one is on the earth.

Einstein, however, argued that time is not merely determined by differences in distance between objects. Time also has an internal dimension, a structure implicit within each object. Every object possesses its own proper time and occupies its own infinitesimal spacetime neighborhood.⁽¹⁾ When we say that an object “curves” spacetime, we usually imagine an external indentation. But the so-called “curvature” is better understood as the outermost boundary or event-horizon of the object, the locus where its own inward spacetime begins.

The object has both an inward spatial dimension and an inward temporal dimension. At a sufficiently small—“minute”—scale (minute meaning both small in space and short in time), any object can be entered. For example: viewed from a distance, the earth appears as a solid sphere. But because a human being is extremely small relative to the earth, approaching closer and closer enables one to enter it, reach the surface, stand upon it, move within its atmosphere, dwell in its interior structures, and interact with its materials. One cannot go deeper into the ground simply because one becomes too large relative to the smaller structures that compose the earth’s interior.

Likewise, two people cannot enter one another by mere contact. They can touch, but not penetrate, because at their scale—given their size, weight, density, and molecular structure—each is solid with respect to the other. Yet microscopic organisms freely penetrate human tissue in the same way that a human penetrates the earth’s atmosphere. Thus:

Any object may serve as a dimension for another object, provided the quantitative differences between them are sufficiently large.

This capacity of objects to serve as dimensions for one another is the spacetime implicit within objects. The object itself is a dimension of time—its own infinitesimal corridor of becoming.

2. The Object as a Wormhole of Its Possible Events

An object is a wormhole of infinite potential events. The matter composing an object produces curvature, and that curvature produces an inward “tug” toward the object’s center. The warp that we see as the bending of spacetime is only the external effect an object has on its immediate surroundings. But spacetime does not stop at the object’s outer boundary: it continues inward, forming the very constitution of the object.

From a two-dimensional standpoint, every object appears as a tube—a continuous tunnel through spacetime. This tubular form is the object’s particle state extended as a wavelength. Each infinitesimal segment of that wavelength corresponds to a possible event: all the ways the particle could manifest. Each possibility occupies a slightly different, discrete location in space and time.

This inward infinitesimal structure is the natural meaning of a wormhole. A wormhole is not merely the collapsing of two distant points into proximity in order to permit time travel. Rather, a wormhole is the spacetime structure of the object itself, the condensed network of its possible events. Each object contains:

• an infinitesimal spatial extension inwardly, and
• an infinitesimal temporal extension,

such that all possible events of the object are implicitly contained within it. Any one of these possibilities can be selected as the present actual object.

3. Whitehead’s Extension of Einstein: The Object as a Time

Alfred North Whitehead expands Einstein’s idea of spacetime by asserting that an object is itself a time.⁽²⁾ An object directly observed constitutes an event. Whatever object we experience in the present is really just one of its many possible events abstracted into actuality. The object is therefore a kind of tesseract of events, a four-dimensional volume in which all its potential moments coexist, with one selected as the present.

This explains common phenomena we overlook. Changing one’s position changes the angle from which an object is seen. In elementary geometry, a change of angle modifies a figure’s shape; thus even small positional shifts reveal different geometrical aspects of the same object.

The familiar experience of a wall appearing different when viewed from a different angle is not merely perspectival. A different event of the object is being actualized. By simply walking three steps to the side, one traverses the infinitesimal internal spacetime of the object and activates a different possible moment built into it. That moment becomes the new present.

Thus the event (the form) and the object (the substrate) are indivisible. Each event is the object, and the object is the continuity of its events.

It is telling that an angle is defined as the space between intersecting lines or surfaces near the point of intersection.⁽³⁾ This “space between” is a miniature region of spacetime itself, and every shift in angle enacts a shift through the object’s latent events.

Footnotes

1. Einstein, Relativity: The General and Special Theory; see also the notion of proper time in general relativity, where each worldline possesses its own intrinsic temporal structure.
2. Whitehead, Process and Reality (1929), especially his doctrine of actual occasions as the fundamental units of spacetime and nature.
3. Euclid, Elements, Book I; see definitions concerning angles and their relation to intersecting lines.

Angles, Limits, and the Infinitesimal

An angle is the magnitude approaching a limit. It is not merely the meeting of lines but rather the measure of their approach toward one another. As two lines converge, the region between them becomes increasingly small, tending toward an infinitesimal. The angle represents this approach toward a limit, not the static fact of two lines touching.⁽¹⁾

In our basic mathematical models, we limit the angle to the contact point between two intersecting lines. This abstraction—although incomplete—is pragmatic. If we were to treat the angle as it truly is, namely as the continuous approach toward an infinitesimal point, then we could not measure anything with precision. Every angle would become a passageway into an infinity of other determinations implicit within it, and every geometric form would disclose an unlimited depth of hidden structure. The simplifying abstraction is therefore necessary for practical calculation.

The infinitesimal is not simply the “smallest possible thing.” Rather, the infinitesimal is dense—the point where an infinite number of possible determinations condense into an abstract unity. It is “small” because it is a singularity of possibilities, not because it is a tiny physical object. This is why the infinitesimal functions as the logical prerequisite of continuity and change.⁽²⁾

Wormholes and the Formation of Figures

A wormhole is the way spacetime wraps, bends, and folds itself to form objects. This warping is not external to the object: it is the object. In contemporary physics, the closest analogue is the “string” of string theory—minute, vibrating fibers of spacetime that serve as the raw material for all particles. These strings are not merely spatial lines; they are spatio-temporal fibres, carrying both the shape and the duration that constitute an object’s being.⁽³⁾

Spatial extension—width, length, volume—only accounts for the measurable external form. But every figure also includes qualities that do not vary with spatial expansion or contraction. Light, color, scent, texture, tone, and other qualitative features do not depend on spatial size. The color green, for example, remains identifiably green whether it fills a vast expanse or a tiny point. Empirically, a diluted or stretched pigment becomes pale, yet this refers to a material mixture, not to the essence of green itself.

Such qualities are temporal determinations, because they exhibit instantaneity: they either are or are not what they are. Green is green until it is red; red is red until it becomes another hue. Qualities also possess simultaneity: they coexist at once, and it is only a matter of spatial selection whether one is manifested rather than another.

Thus qualities belong fundamentally to time, not space. They express the instantaneous determination of being, not the extension of matter.

The Series of Events: Inside → Outside → Inside Again

Events proceed in a dialectical rhythm:

It comes out from the inside toward a point on the inside, and then goes inside that outside point, and so on.

This means: an event emerges from an object’s internal spacetime, appears as a point on its boundary (the “outside”), and then folds back inward, being integrated into the object’s total history. Every real event is therefore an infinitesimal selecting itself into actuality.

The reference center of this series is the mind, which navigates the object’s field of possibilities. As consciousness moves outward among these possibilities, some become increasingly concrete until one becomes the real event, the macroscopic present. This is where the infinitesimal sequence terminates in actuality.

The Infinitesimal as Inverted Singularity

The infinitesimal is like an inverted whirlpool: its smallest point is the most abstract, yet it contains the densest multiplicity of possible events. It constrains the entire range of outcomes in a compressed logical unity.

There must be such a singularity because of entropy. Infinite chaos of concrete objects is impossible: masses would interact, cancel each other, merge, or become indistinguishable. True infinite chaos can only exist in the abstract, where concrete physical effects (mass, spin, charge, solidity) are suspended. Two abstract objects can interact without physical deformation, yet this abstract interaction provides the basis for real, physical relations once actualized.

Thus the singularity is the condensation of all possible events, and as event-sequences move outward from potentiality to actuality, they crystallize into the macroscopic world.

Change in Perspective as Change in Determination

A shift in perspective produces a shift in determination. A change in angle yields a new aspect of the object, which is a new event. Thus the “warp” of an object in spacetime is merely its own continuing temporal duration appearing under a new relation. This warping is not external; it occurs infinitesimally within the object itself. It goes inward, inward, inward—yet always in the same place the object occupies.

In other words, what we ordinarily regard as a very simple determination—such as a change in conception or perception, which the mind performs countless times each day—is still a determination within the universe. Although it appears to be the most basic or minimal kind of change, it is in fact the principle of generation itself. We assume that objects already exist “out there,” and that our minds merely alternate between them. But the objects we take as static and objective contain within their very composition an infinitesimal point of uncertainty.

We observe this most dramatically in black holes, where information seemingly enters and never returns: an inherent uncertainty of knowledge for any observer. Yet this uncertainty is also the capacity for infinite potential, the power of a single object to disclose an indefinite number of other objects. This basic structure—the Schwarzschild radius, which is closely related to the notion of zero-point energy—expresses the very same principle that underlies the mind’s capacity to move between objects.

The ability of our conception to differentiate endlessly—both between different “nothings” and within what appears to be the “same” thing—is the mental analogue of the physical uncertainty built into the structure of reality. This simple, ethereal power of the mind has a direct physical counterpart, and the physical world displays the proof of it.

Stars, Singularities, and Internal Wavelengths

A collapsing star reveals a singularity because its entire mass-energy content is exhausted in an extremely short duration. The star is pulled toward its own infinitesimal, its internal spacetime tube, until the beginning and end of its temporal wavelength appear to coincide.

Every object is internally a wavelength of itself. This becomes visible in extreme states—hence the phrase, “my life flashed before my eyes.” The entire extension of the temporal waveform becomes compressed into a single point of awareness.

What appears as a singularity in astrophysics is simply the exposure of the object’s internal spacetime.

Spacetime, Potentiality, and the Observer

Spacetime is the material of the universe, but only in a potential state. Potentiality is defined relative to an observer. What is real for one observer is potential for another; thus actuality and potentiality are in perpetual flux across all observers.

To say “spacetime is the potentiality of everything” means:
it is the potentiality for any single being to conceive the whole. But a single being cannot grasp all at once; if it did, the whole would collapse into a single undifferentiated intuition. Therefore it must conceive the whole as a sequence of single events, each emerging at its moment.

Being, Nothing, and the Selection of Events

The difference between being and nothing is that being is everything, while nothing is not everything—it is a single thing. Spacetime, as the fabric of all possible events, is literally everything. But because we only select one event out of this total, we experience the everything as though it were nothing, and the nothing (the single event) as though it were the whole.

Thus when we “see everything,” we see it as a single finite thing set against nothing.

Ibn ‘Arabi: “Time is the Fluid, Space is the Solid”

The Sufi metaphysician Ibn ‘Arabi writes:

“Time is the fluid; space is the solid.”⁽⁴⁾

This expresses the profound idea that time is the medium of transformation, continuously flowing, while space is the congealed form of that flow. Space is time that has become still; time is space in motion. In this sense, objects are the solidified currents of temporal becoming. We perceive stability only because one infinitesimal moment is selected from among an infinite series of possibilities.

Footnotes

1. Euclid, Elements, Book I, definitions concerning angles and magnitudes.
2. G.W.F. Hegel, Science of Logic, “The Infinitesimal” and the logic of becoming.
3. Brian Greene, The Elegant Universe, on string theory and extra-dimensional structure.
4. Ibn ‘Arabi, Futūḥāt al-Makkiyya, passages on spatial and temporal existence.

Whitehead on the Myth of the Object at One Place at One Time

Whitehead writes:

“Science and philosophy have been apt to entangle themselves in a simple-minded theory that an object is at one place at any definite time, and is in no sense anywhere else. This is in fact the attitude of common-sense thought, though it is not the attitude of language which is naïvely expressing the facts of experience. Every other sentence in a work of literature which is endeavouring truly to interpret the facts of experience expresses differences in surrounding events due to the presence of some object. An object is ingredient throughout its neighbourhood, and its neighbourhood is indefinite. Also the modification of events by ingression is susceptible of quantitative differences. Finally therefore we are driven to admit that each object is in some sense ingredient throughout nature; though its ingression may be quantitatively irrelevant in the expression of our individual experiences.”¹

Whitehead identifies the “simple-minded theory that an object is at one place at any definite time” as the fundamental assumption of classical mechanics. The sensuous recognition of an object gives the appearance of rigidity, permanence, and self-identical endurance across a general timeline. Under classical mechanics—as well as in ordinary consciousness—time is taken as a general and uniform duration within which all things are governed. Because time is applied universally, it is assumed to be a shared principle across all objects. In this latter formulation, time becomes a form of energy, the general capacity for work and the condition for change.

Yet to say that time is a general property of all things tells us nothing about the function of time in each particular thing. It is one thing to claim that everything undergoes temporal duration; it is another to say that each thing possesses the same mode of duration. “Things determined by time” is not equivalent to “time is the determination of things.” The difference is central.

For example, we may say that “the same tree” endures for a thousand years or that “the same man” endures for ninety. Both share time as a factor, but the significance of time is dependent on the activity proper to each being. It would be difficult to claim that a child is simply “the same” as the elderly person he becomes, even though they constitute one human life. Time has not acted identically on the two; nor does the human being occupy the same dimension of time in childhood as in old age.

Thus, different beings possess different determinations of time, even when they occupy the same spatial environment. A tree and a man exist simultaneously in the same physical location, yet their temporal dimensions diverge radically. Their relation is therefore spatio-temporal—neither exclusively spatial nor exclusively temporal. A single moment of experience is one-dimensional temporally, even if the spatial configuration involves three dimensions. Time, unlike space, is not confined by spatial separation: it presents itself as instantaneous points of occurrence, flashes of becoming, analogous to the constant emergence and disappearance of ideas in consciousness.

Quantum mechanics is increasingly revealing the dynamics of these instantaneous “flashes” underlying nature.² Whitehead anticipated this shift. He writes:

“As long ago as 1847 Faraday in a paper in the Philosophical Magazine remarked that his theory of tubes of force implies that in a sense an electric charge is everywhere. The modification of the electromagnetic field at every point of space at each instant owing to the past history of each electron is another way of stating the same fact.”³

Quantum mechanics thus reverses the classical assumption. Classical mechanics claims:
(1) An object is at one place at one time.
Quantum mechanics demonstrates:
(2) An object can be at two places (or in two states) at the same time.

This is not sensible spatially—since physically, an object appears to occupy a single location—but it is intelligible temporally, because an object occupies an indefinite multiplicity of possible events. Quantum theory thereby revolutionizes the meaning of “object.” An object is no longer the same self-identical substance persisting unchanged through time. Instead, its identity is a spectrum, a wavelength—a continuous process of becoming within which any particular actualization still counts as “the same” object.

For example, the human being remains “the same person” in childhood and adulthood because both phases belong to the same spectrum of development. The identity is not a static substance but a continuum of events.

Footnotes

1. Alfred North Whitehead, Process and Reality, corrected edition, ed. D. R. Griffin and D. W. Sherburne (New York: Free Press, 1978), 145.
2. On the temporal discontinuity revealed in quantum mechanics—e.g., quantum jumps, superposition, and spontaneous symmetry breaking—see, for example, Werner Heisenberg, Physics and Philosophy (Harper, 1958).
3. Whitehead, Process and Reality, 146; referring to M. Faraday, “On the Theory of Magnetic Lines of Force,” Philosophical Magazine (1847).

Two Places at the Same Time

When we say that the same object cannot be in two different places at the same time, this is equivalent to saying that two different events belonging to the same identity cannot occur simultaneously. For example, if I am sitting in the living room, I am not in the washroom; when I go to the washroom, I am no longer in the living room. Similarly, if I am having a cup of coffee, I am not dancing, and when I am dancing, I am not having a cup of coffee.

In space, we observe the motion of an object as it occupies one location and leaves another. There must exist a sequence of events connecting both positions to maintain the continuity of the object. We cannot assume that an object can move from one point to another without a substrate that allows for this continuity in space, even if this substrate is not directly apparent in the relation between the two points.

The object in space and time is a realized event, a particle state within a wavelength of potential events. The duality arises because, ordinarily, we observe only one state at a time while the other remains unobserved.

The wave–particle duality in quantum mechanics states that every particle or quantum entity may be described as either a particle or a wave. This distinction reflects the difference between external and internal views of time. Each object, such as a photon, exists as a conjunction of these external and internal relations: it is both particle and wave simultaneously, yet also not simultaneously. Every object is a wavelength in the sense that it encompasses a series of potential events, each occupying a different position in space; and every object is a particle in the sense that, from its first-person perspective, it occupies one potential event at a given moment, forming a continuous identity across events.

This particle state exists within a wavelength of spacetime. Spacetime itself is the substrate that allows objects to affect one another. If there were nothing between two separate objects, one could not influence or exert a gravitational pull on the other. Spacetime acts as the material medium through which one object warps its environment to affect another. This perspective also sheds light on quantum entanglement: objects can influence one another over large distances because their interaction is not merely spatial. Rather, objects relate as a sequence of interdependent events across time, not just as co-located entities.

Mathematically, spacetime is often represented as a simple coordinate grid, which allows us to measure motion, gravity, or mass within small regions. For example, one can calculate the peak of a curve by referencing points along a coordinate plane. However, this grid is an abstraction for technical convenience; it does not fully capture the organic nature of spacetime.

In reality, spacetime is the junction of all qualities and events simultaneously. It is a dimension of infinite diversity, where multiple potentialities coexist. When we isolate a single event, all others appear void. The spatial separation between events allows us to perceive the event within its contextual distance, integrating a sequence of events into a single self-contained moment.

Footnotes

1. Alfred North Whitehead, Process and Reality, corrected edition, ed. D. R. Griffin and D. W. Sherburne (New York: Free Press, 1978), 145–146.
2. On wave–particle duality and first-person versus external observation: Niels Bohr, Atomic Theory and the Description of Nature (Cambridge: Cambridge University Press, 1934).
3. On spacetime as a substrate and quantum entanglement: John Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge: Cambridge University Press, 1987).
4. On the limitations of the coordinate plane in modeling natural phenomena: Hermann Weyl, Space-Time-Matter (New York: Dover Publications, 1922).

Instinct of Time

When we experience an urge to do something, we commonly call this instinct—a fixed behavior in response to a stimulus. Typically, the stimulus is considered an external object, such as another animal or a food source, which triggers a response through the sensory organs. These are direct, tangible forms of stimuli. However, there are more fundamental forms of stimuli, such as time and space, which the sense organs are largely unconscious of, yet for which the mind has an instinctive response.

There is an instinct in response to time, which manifests as an urge in the form of a thought about a possible action or event. For example, when talking to someone who annoys you, the urge to smack them is an instinct toward a potential event. The possible scenario itself enters the consciousness of the present moment, seeking to occupy it, and the observer either acts on that urge or chooses an alternative action.

This is an unconscious recognition of a potential event, which we label as instinct because it is accompanied by an emotional response. What the instinct responds to, however, is not merely the immediate stimulus but a future possibility in time. Smacking someone is a potential event that may follow from the continuation of annoyance, forming a web of interdependent behaviors, where one action presupposes another as long as the initial condition occupies the present. These routes of possibilities emerge from any given action, and the arousal of instinct is the mind’s recognition of these potential events.

There is thus a fundamental instinct for potentiality. When one has an idea of a possibility, one is recognizing a potential event, which becomes real if acted upon. The present transforms into that future when the individual acts on the idea. In this sense, the individual is constantly undergoing a metamorphosis of the present, continually changing into potential events.

The individual is a metamorphosis of the events making up time.

Our conventional image of a timeline obscures the way time actually flows through an individual. Events are not external sequences that the individual enters into; rather, the individual takes the form of the events, integrating them internally. Time is not a series of discrete periods into which an individual steps; these periods are abstractions of recognizable changes. The underlying process—the metamorphosis—occurs continuously within the subject, while understanding abstracts these transformations as external, measurable stages.

We derive the idea of a timeline from the notion of time as internal transformation. Time is the internal transformation of a thing. The mind abstracts from this continuous metamorphosis to identify recognizable changes, then orders them chronologically from earlier to later. Thus, the stages of a life form are ranked from early to late development.

However, this abstraction renders events external to the individual, which has practical and biological reasons. Any given species contains members at different stages of development simultaneously. The existence of all developmental stages at the species level allows for the presupposition and interaction of these stages. An adult gives birth to a child; the child presupposes the adult stage, and the sense of having once been a child emerges. Each individual’s development is abstracted naturally by the simultaneous existence of other members of the species at different stages.

Footnotes

1. On instinct as response to external stimuli: Konrad Lorenz, On Aggression (London: Methuen, 1966).
2. On instinct as a response to time and potential events: Henri Bergson, Matter and Memory, trans. Nancy Margaret Paul & W. Scott Palmer (New York: Zone Books, 1991).
3. On internal transformation and the abstraction of timelines: Alfred North Whitehead, Process and Reality, ed. D.R. Griffin and D.W. Sherburne (New York: Free Press, 1978).
4. On developmental stages in species: Jean Piaget, The Origins of Intelligence in Children, trans. M. Cook (New York: International Universities Press, 1952).

Events Come Out of Each Other

Cause and effect in the spatial domain requires that an object be external to another object in order to have an effect on it. In other words, the compactness of one object comes into contact with the compactness of another, producing some alteration in physical composition. This can occur through gravitational effects, where an object warps spacetime, or through direct collision of masses. These forms of transformation are directly observable and are studied because they exhibit straightforward cause-and-effect dynamics, for example: what goes up must come down.

The impact between two objects produces motion proportional to their momentum and mass. However, there exists a more subtle process of change that does not occur by the external effect of one object on another. Instead, it is internal and subtle, only deducible after a period of time has passed. This form of change is unobservable directly because it occurs within the internal dimension of the object. This is challenging to explain because the internal side of any dimension is inherently unobservable, a principle reflected in Heisenberg’s uncertainty principle. When an observer observes something, the observation cannot simultaneously include the observer observing themselves observing; one either observes the object or the observer as an object, but not the observer observing another object.

The conception of anything inherently includes its inverse, which is not directly conceived and thus represents potentiality. What is not conceived is part of the observation as the ground for what is observed. For instance, when looking at the front of an object, the back is not seen but is implicitly present as the plane supporting the front. Conceiving anything automatically excludes the non-conceived, giving definition to the conceived.

This limitation positively affirms the existence of a definite form while excluding the indefinite. According to general relativity, the mass of an object warps spacetime, and the extent of this warping depends on the magnitude of the mass. What we observe as a terrestrial body orbiting another, such as a planet orbiting a star, is in fact the smaller object circling the outer extremities of the spacetime curvature.

However, this illustration is only a two-dimensional abstraction. In reality, an object bends spacetime in all directions—four-dimensionally. The spacetime surrounding an object collapses toward it from every direction and is thrown back with an equal reactive force, forming a spherical region of spacetime around the object.

Every object has such a sphere of spacetime, and simultaneously, every object possesses a Schwarzschild radius, a point within the object where spacetime enters as an infinitesimal continuum. For example, a black hole absorbs light without reflecting it, yet it remains a continuum of nature, always participating in the broader system, even if abstracted in isolation.

Singularity diagrams often depict a black hole as an infinitely stretching point of spacetime, compressing infinite matter within a finite region. Observing nature closely—for instance, the movement of sparks—often makes it ambiguous whether the sparks are emanating outward or collapsing inward toward the hotspot.

The singularity, as a point of infinite collapse, mirrors the nature of time itself. The development of time is the transformation of one event into another, which can be understood as the collapse of one event into the next. This process involves the conceiving of one event while becoming unconscious of the previous one. Events move into the unconscious as the past, which is also the domain from which potential future events may emerge into the present, becoming consciously apprehended.

Footnotes

1. On cause and effect in physical space: Isaac Newton, Philosophiæ Naturalis Principia Mathematica (1687).
2. On the internal dimension and observation limits: Werner Heisenberg, Physics and Philosophy (New York: Harper & Row, 1958).
3. On mass warping spacetime: Albert Einstein, The Foundation of the General Theory of Relativity, Annalen der Physik 49 (1916).
4. On Schwarzschild radius and black holes: Karl Schwarzschild, Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie, Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften (1916).
5. On time as event transformation and potentiality: Alfred North Whitehead, Process and Reality, ed. D.R. Griffin and D.W. Sherburne (New York: Free Press, 1978).

Spacetime Curvature as Determination

Whether we say that a singularity bends spacetime downward, upward, sideways, or in all directions, we are implying that there is direction in the way spacetime is bent. However, this so-called “direction” is not in terms of ordinary positional motion, such as up, down, left, or right. It is more fundamental than that—it is dimensional, precursory to motion itself. The so-called “warp” of spacetime caused by an object is, in fact, the dimension of the object, or rather the duration and extension of its dimension. This is the domain in which the object changes, develops, and yet remains itself. The dimension of the object is therefore the object itself—it is entering into itself, which is how it maintains its identity as the same object.

The genius of Einstein’s idea of spacetime is that it materializes time for the first instance. Spacetime is the “thinnest” layer of matter, meaning it is the most abstract physical substance yet still produces concrete effects. Spacetime is not a single abstract entity; rather, it is everything in a more abstract state. One of the earliest instances of these physical but abstract states is space itself, which is the quality that allows the motion of a thing from one location to another, or more precisely, facilitates change. Time, in turn, enables change to occur by containing it.

Space is not, as is commonly abstracted, a container of all things. That perception arises because we measure a maximum extent of space and observe a maximum number of objects within it, leading to the conclusion that space contains all things. In reality, the quality of space is simply that something can serve as a realm for something else to act. For example, shining a light on an atom changes its motion or even halts it. This illustrates how one object can act as a dimension for another, or provide the conditions for motion or rest.

A concrete experimental example is laser cooling of atoms (or quantum cooling), in which atomic and molecular samples are cooled to near absolute zero. Laser cooling techniques exploit the fact that when an atom absorbs and re-emits a photon (a particle of light), its momentum changes, gradually reducing thermal motion. In the hypothetical, physically impossible limit of absolute zero, atoms would stop moving entirely.

This motionless state represents the most abstract state of an object—it is space itself. While space provides a realm for change to occur, it is itself changeless. The complementary quality—change itself—is defined by time. Time is not merely the duration measured between events; it is the set of changes themselves, or the process by which possibilities transform into actualities. When a thing changes, those changes constitute time itself.

This perspective naturally connects to the holographic universe hypothesis, which suggests that all information contained within a volume of space can be represented on the boundary surface surrounding it. In this view, spacetime itself encodes all potential events and changes as information, and every point within the universe contains the dimensional potential of the whole. Spacetime curvature, therefore, is not merely a geometric feature—it is a determination of events, possibilities, and actualities, woven into the fabric of the universe.

Footnotes

1. Einstein, Albert. The Foundation of the General Theory of Relativity, Annalen der Physik, 49 (1916).
2. Laser cooling techniques: Metcalf, Harold J., and van der Straten, Peter. Laser Cooling and Trapping (Springer, 1999).
3. On the nature of space and time as abstract physical substances: Whitehead, Alfred North. Process and Reality, ed. D.R. Griffin and D.W. Sherburne (New York: Free Press, 1978).
4. Holographic universe: ’t Hooft, Gerard. Dimensional Reduction in Quantum Gravity, arXiv:gr-qc/9310026 (1993); Susskind, Leonard. The World as a Hologram, Journal of Mathematical Physics 36 (1995): 6377–6396.

Conception Plays Both Roles: Active and Passive

The difficulty arises because conception plays both roles—the active determination and the passive one. When it is active, conception brings to consciousness the knowledge of a fact. This is its active feature, where through examination and analysis of a thing, it comes to know it. This process involves dissecting and unpacking the object, taking knowledge that is already given and converting it into the unknown.

The active and passive sides of conception must be carefully distinguished when analyzing any idea because any concept exhibits both aspects simultaneously, though not necessarily in the same determinate way. For example, “the apple falls to the ground” illustrates the passive aspect: the apple is attracted to the Earth due to its greater mass, an effect of general gravitational interaction. At the same time, the apple moving downward is active in the sense that it moves away from the sky. Conversely, a helium balloon rising toward the sky demonstrates that lighter objects are attracted in the opposite direction to heavier ones, actively moving away from the ground while passively displaced by the surrounding atmosphere.

This illustrates the external sum of all possibilities that is internally contained within the actuality of any of their actual occurrences.

We often depict this concept with a grid and a spherical particle state warping the lines.

In general relativity, the extent to which an object warps spacetime is proportional to its mass. This indicates that an object is a specific point where the mingling of spacetime occurs in a definite way. For an object to affect spacetime, the nature of spacetime itself must yield to the object’s influence. The object represents a discrete measure that discloses the sum set of possible actions and determinations, i.e., its potential energy. The potential behaviors and determinations of an object in spacetime correspond to its internal structure.

For example, the circular motion of a planet inversely corresponds to its internal shape. How an object acts externally in spacetime is an inversion of how it is structured internally. The motion of heavenly bodies is not strictly circular but spherical, where their motion coincides with their form; their form is merely a snapshot of motion at one point in time. In abstraction, a circle is a two-dimensional simplification of a sphere.

Let P′ be the inverse of P with respect to a reference circle. The circle constitutes the first condition for inversion: any point inside the circle maps to a point outside, and vice versa. The circle therefore represents internal and external relations, such that the nearer a point is to the center, the further its inverse lies from the center, and vice versa. This basic principle of inversion geometry becomes far more complex for celestial bodies.

For example, the sun’s motion relative to its star involves more variability than a planet’s orbit. Planetary orbits are analogous to planes flying around the Earth, illustrating that these motions are not perfectly circular but encompass spherical dynamics over millions of years.

This principle also explains Earth’s magnetic field dynamics. Recent discoveries show that the magnetic north pole moves faster than previously anticipated, shifting southward. This movement is an abstraction of the direction in which Earth’s spherical motion is proceeding, reflecting the internal-internal relations of the planet’s dynamics.

Footnotes

1. Einstein, Albert. The Foundation of the General Theory of Relativity, Annalen der Physik, 49 (1916).
2. Whitehead, Alfred North. Process and Reality, ed. D.R. Griffin and D.W. Sherburne (New York: Free Press, 1978), 145–146.
3. Laser cooling example: Metcalf, Harold J., and van der Straten, Peter. Laser Cooling and Trapping (Springer, 1999).
4. Planetary motion and inversion geometry: Milani, A., Nobili, A.M., and Farinella, P. Non-Gravitational Perturbations and Satellite Geodesy (Adam Hilger, 1987).
5. Earth’s magnetic pole movement: Cox, A., et al. “Earth’s Magnetic North Pole Movement Accelerates,” Nature, 2020.

Spacetime Curvature

Gravitational curvature is intimately connected with the geometry of space and time.[^1] Geometric forms are held together as structures through their logical presupposition of one another. The physical manifestation of this structural coherence is gravity. Gravitational “curvature” abstracts the spherical form of spacetime.

Gravity as a pure principle is sometimes described as an “illusion,” illustrated by the equivalence principle: a freely falling observer in a gravitational field does not feel gravity. An accelerating object has a concept of “up” and “down,” but a freely falling object, in relative motion, does not. Motion exhibits relation: in a finite sense, from here to there; in the ultimate sense, self-identical. This freely falling state is an inconceivable conception revealing the object, but insofar as it is an object, there is gravity.

For example, when I move relative to a wall, the wall appears to move relative to me. A stable position arises from the conception that movement across an object makes the object appear in motion. The object, insofar as it is spatially extended, provides the substrate for this perception of motion.

An accelerated observer has a clear notion of “up” and “down.” When such an observer looks up, freely drifting observers and their space stations appear to “fall” toward the floor of the accelerating spaceship. Here, “upwards” is defined by the direction of the spaceship’s acceleration. No gravity exists in this frame; all freely drifting observers agree that the accelerated observer’s perception of falling objects is merely an artifact of the reference frame. It vanishes when switching to a freely falling frame.[^2]

Formation of Spheres

Einstein’s achievement in the general theory of relativity lies in the simple connection of the spacetime continuum, which allows time to be measured by space, and space by time. This conceptual unification defines the complex scope of energy, which is the property of matter manifest as the capacity to perform work. The production of work is identical with its performance.

Spacetime is measured by gravitational curvature, which is directly related to the energy and momentum of the matter present. The curvature is governed by the extent of energy—for example, the denser a black hole, the greater the gravitational distortion.[^3]

But if light has no mass, how can gravity bend it? Gravitational effects result from the warping or curving of the “fabric” of spacetime. Bending of light occurs through gravitational lensing, an effect predicted by general relativity. Mass bends light: the gravitational field of a massive object extends into space and causes light passing nearby to bend and refocus. The more massive the object, the stronger its gravitational field, and the greater the bending of light rays.[^4]

However, extent alone does not explain the form that extent assumes. The curvature of spacetime is not merely the distortion caused by a massive terrestrial body like a star; it also concerns how the fabric of spacetime itself bends and warps to constitute the formation of energy. Analogous structures include squaring the circle, converting a line into a circle, and other geometrical formations that arise from spacetime curvature.

Bodies such as stars are focal points of light concentration. Stars function as centers of attraction and repulsion, synthesizing light whose magnitude is determined by energy concentration. Gravitational attraction organizes light into the physical gas properties of hydrogen and helium, while repulsion radiates elements in the form of heat, including trace elements like neon, iron, silicon, magnesium, and sulfur—these form the basis of rocky planets.

The curvature of spacetime can be viewed as an abstraction of movement from a stable position. From the perspective of spacetime curvature, space is the abstraction of motion, whose energy states are conceptions of moments of process. This is how space is measured by the temporal dimension.[^5]

Time and Causation

According to general relativity, past, present, and future are measurable as spatial dimensions. However, this does not solve the philosophical problem of causation. Treating past, present, and future as points on a continuum does not explain the nature of causation, because it presumes that the past moment leads to the future moment, thereby ignoring the underlying conditions that make such causation possible.

The future is a spatial point on the curvature of spacetime because spacetime itself is in motion. The future is not merely caused; it is a destination to be reached. For example, if I move toward the gym, the gym becomes my future. Consider two points A and B on a moving plane: A is stationary relative to the plane, while B moves on it. B reaches the place where A will eventually arrive; B is therefore the future event of A, as its movement constitutes the point A will ultimately occupy.

Light, Determinacy, and the One and Many

Nothing can exceed the speed of light, because light is the standard of material measurement—the maximum speed at which any object can move. In physics, the speed of any object plus the speed of light equals the speed of light. Light is the minimal substrate implicit in each object. At the foundational level, light precedes all objects, and in the ultimate principle of determinacy, it supersedes all objects.

This principle aligns with the ancient maxim of the “one and many”. The “one” is not merely one thing among many; the “many” are all unified in the one. This relation illustrates how everything can exist within something, a notion echoed in Hindu cosmology through the concept of jewels (ratnas) as multiples reflecting a singular principle.[^6]

Footnotes

[^1]: Einstein Online. “Geometry and the Force of Gravity,” einstein-online.info.

[^2]: Ibid. See also Misner, Thorne, and Wheeler, Gravitation (W.H. Freeman, 1973), Ch. 25.

[^3]: Wald, Robert M., General Relativity (University of Chicago Press, 1984), Ch. 6.

[^4]: Schneider, Peter, Extragalactic Astronomy and Cosmology (Springer, 2006).

[^5]: Penrose, Roger, The Road to Reality (Vintage, 2005), Ch. 22.

[^6]: Radhakrishnan, S., The Hindu View of Life (Orient Longman, 1994), Ch. 3.