What are Dimensions and Time?

 Introduction 

Imagine a world where every movement, every interaction, and every phenomenon can be described through a simple yet profound framework: dimensions. From the length of a road to the height of a skyscraper, our three spatial dimensions—length, width, and height—shape the tangible world we experience. But the story doesn’t end there. Enter the fourth dimension: time, an invisible thread weaving together the fabric of the universe, enabling us to not just exist but to journey forward. Together, these dimensions form the dynamic concept of spacetime, a cornerstone of modern physics. Today, let’s embark on a journey to understand how these dimensions define reality as we know it—and even hint at possibilities beyond what meets the eye.

"AI-generated image'' illustrating a dimensional space 

Concept of Dimensions 

In physics and mathematics, the concept of dimensions describes the minimum number of coordinates needed to locate a specific point within a space or an object. For instance, a one-dimensional space, like a line, requires only one coordinate to define a point—for example, the number 5 on a number line. A two-dimensional space, such as the surface of a sphere, demands two coordinates, such as latitude and longitude, to specify a point. In three-dimensional spaces—like the interior of a cube, cylinder, or sphere—you need three coordinates: length, width, and height, to identify a point.

Classical mechanics originally treated space and time as separate categories, with space being a three-dimensional construct. However, modern physics merges these into a four-dimensional spacetime framework, introduced by Einstein's theory of relativity. In this framework, spatial and temporal aspects are no longer absolute, but rather relative to the observer's motion. Minkowski space approximates the universe without gravity, while pseudo-Riemannian manifolds of general relativity include matter and gravity in their description of spacetime.

Theoretical physics ventures even further with string theory and M-theory, proposing 10 dimensions (6 compactified dimensions plus 4 spacetime dimensions) and 11 dimensions (7 hyperspace dimensions plus 4 spacetime dimensions), respectively. Quantum mechanics transcends physical dimensions, utilizing infinite-dimensional function spaces for state-space representations.

Interestingly, dimensions are not confined to physical reality. In mathematics and sciences, high-dimensional spaces are often abstract and appear in parameter or configuration spaces, such as those used in Lagrangian or Hamiltonian mechanics. These dimensions provide tools for understanding complex systems beyond the physical realm. 

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

This illustrates the progression of dimensions, from simple to complex, using geometric shapes:

1. 1D - Line Segment: A single dimension, represented by two points connected by a straight line. Only one coordinate is needed to describe a point on this line.
2. 2D - Square: By connecting two parallel line segments, we create a square—a two-dimensional shape. Now, two coordinates (length and width) are required to locate any point within the square.
3. 3D - Cube: Extending further, two parallel squares can be connected to form a cube. A cube exists in three dimensions, necessitating three coordinates (length, width, and height) to specify a point inside it.
4. 4D - Tesseract: Finally, the leap to the fourth dimension introduces the tesseract (or hypercube). It’s the four-dimensional counterpart to a cube, created by connecting two parallel cubes. Visualizing this is challenging since humans perceive only three spatial dimensions.

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

This description highlights the progression of dimensions through the properties of geometric shapes:

• Square: A 2D shape confined to a flat plane, with boundaries made up of 1D line segments. A square illustrates how two coordinates (length and width) suffice to define any point within it.
• Cube: Moving into 3D space, a cube is enclosed by six 2D squares as its faces. To specify a point within a cube, three coordinates (length, width, and height) are required.
• Tesseract (Hypercube): Transitioning to the 4D realm, the tesseract (or hypercube) is a four-dimensional counterpart of a cube. Its boundaries are composed of 3D cubes, and understanding it requires four coordinates. While it's challenging for us to visualize a tesseract in its entirety, projections and representations help us grasp its structure conceptually.

This analogy elegantly connects lower dimensions to higher ones, revealing the increasing complexity as we move through dimensions. 

Nature of Time as the Fourth Dimension

In modern physics, the concept of time goes far beyond its everyday perception as a ticking clock. It emerges as the vital fourth dimension within the unified framework of spacetime, a cornerstone of Einstein's theory of relativity. This unification demonstrates that every event in the universe is characterized not only by three spatial coordinates but also by a temporal one, seamlessly weaving space and time together. One of relativity's most profound implications is that time is not absolute—it is remarkably relative, varying with an observer's frame of reference. This leads to fascinating phenomena like time dilation, where the passage of time slows with increasing velocity, and gravitational time dilation, where stronger gravitational fields similarly slow the flow of time.

While spacetime treats time as a dimension akin to space, our subjective experience is guided by the "arrow of time," a seemingly unidirectional flow from past to future. This flow is influenced by several factors, such as the increase of entropy as dictated by the second law of thermodynamics, the ongoing cosmological expansion of the universe, and our psychological perceptions of causality and memory. Though time is a fundamental physical quantity precisely measured within the SI system, its behavior in quantum mechanics often contrasts sharply with its treatment in general relativity. This divergence presents one of the greatest challenges in the search for a unified theory of quantum gravity. Ultimately, understanding time as the fourth dimension reveals a reality far more dynamic and interconnected than it might initially seem, with ongoing research continually uncovering its deeper mysteries and profound implications for the cosmos.

Hermann Minkowski, a brilliant German mathematician, laid the groundwork for this transformative understanding of spacetime. Born in 1864, Minkowski made significant contributions to number theory and geometry but is best remembered for his revolutionary concept of unifying space and time into a four-dimensional continuum—now known as Minkowski spacetime. This concept provided the mathematical framework for Einstein’s theory of special relativity and redefined the structure of the universe.

 In 1905, a young patent clerk, Albert Einstein (1879–1955), introduced the special theory of relativity (left), and Hermann Minkowski (1864–1909) (right), Einstein’s math professor who pioneered the use of space-time diagrams. Pic ref and credit: https://aetherczar.substack.com/p/52-relativity

Interestingly, Minkowski was once Einstein's mathematics teacher at the Polytechnic Institute in Zurich. Initially, Einstein dismissed Minkowski's geometric interpretation of relativity as unnecessarily abstract. However, he later embraced it, recognising its profound significance. Minkowski’s work not only clarified the essence of special relativity but also influenced Einstein's development of general relativity, solidifying spacetime as a cornerstone of modern physics.

Minkowski's visionary approach transformed our understanding of the universe, showcasing the deep interconnection of space and time. His legacy continues to inspire physicists, mathematicians, and thinkers to explore the nature of reality.

Is Time an Illusion? 

In my own viewpoint, if there is no time, there are no changes. Imagine a world that just freezes. Time is a measuring unit for the process of every change. Literally, time practically exists. Imagine when a movie is paused indefinitely, nothing progresses, nothing regresses, and everything just is, which is meaningless. There would be no past, present, or future, no sequence of events. The universe is expanding, and the rate of this expansion is measured by the Hubble constant. Hubble constant is estimated to be around 70 kilometers / second / megaparsec (km/s/Mpc) So, a galaxy that is 1 megaparsec away would be receding from us at a speed of 70 km/s, a galaxy 2 megaparsecs away would be receding at 140 km/s, and so on. This rate of expansion suggests that the farther away a galaxy is, the faster it appears to be moving away from us. This is a cosmic scale that we are able to measure because of the existence of TIME.

The Hubble constant (H₀) is a key value in cosmology that describes the rate at which the universe is expanding. It is part of Hubble's Law, which states that the farther away a galaxy is, the faster it appears to be moving away from us due to cosmic expansion. 

Hubble's Law: The relationship is expressed by Hubble's Law: v=H0​×d where:

• v is the recessional velocity of the galaxy (how fast it's moving away).
• d is the distance to the galaxy.
• H0​ is the Hubble constant.

Units: The Hubble constant is most commonly expressed in kilometers per second per megaparsec (km/s/Mpc). This unit indicates that for every megaparsec (approximately 3.26 million light-years) of distance, galaxies recede at a certain speed in kilometers per second.

It's also worth noting that by simplifying the units, the Hubble constant can be seen to have units of inverse time (s⁻¹), which relates to the age of the universe. The reciprocal of the Hubble constant is known as the Hubble time.

Current Value and the "Hubble Tension": Determining the precise value of the Hubble constant is an ongoing challenge in cosmology. There are different methods to measure it, leading to slightly different results and a discrepancy known as the "Hubble tension."

Ancient Preserve That Universe Operates In A Cycling Nature 

Ancient civilisations had an entirely different way of perceiving and measuring time compared to our modern clock-driven world. Their understanding was deeply rooted in natural cycles and celestial observations, making time feel more organic and interconnected with daily life.

The passing seasons were among the most significant markers of time, shaping agricultural activities and daily routines. The rising and setting of the sun dictated the rhythm of life, while the moon’s phases provided a recognisable pattern for tracking months. Many societies organised their calendars around lunar cycles, using each new moon as the start of a fresh period.

Celestial bodies played a crucial role in timekeeping. The movement of the sun led to the development of sundials, where shadows provided an indication of hours. In Egypt, obelisks functioned as primitive time markers, casting long shadows that helped people track different parts of the day. Stars also served as nighttime clocks. Egyptian astronomers used instruments like the merkhet to align with the Pole Star, carefully observing how other stars shifted across the sky to determine hours after sunset. Certain stars, such as Sirius, had specific cultural and practical significance. The annual rising of Sirius coincided with the Nile floods, signalling an important time for farmers.

"Using plumb-lines called "merkhets", the Egyptians could calculate time at night, provided the stars were visible. Used since at least 600 BC, two of these instruments were aligned with Polaris, the North pole star, creating a north-south meridian. By observing certain stars as they crossed the line created with the merkhets, they could accurately gauge time"
Pic Credit&Reference: https://www.pinterest.com/pin/242279654927657424/

Planetary movements influenced timekeeping as well. Civilisations like the Mayans incorporated the cycles of Venus into their highly detailed calendars, adding another layer to their understanding of cosmic rhythms.

 Nine Points of the Venus Cycle as observed on Earth.
Pic Credit&Ref: https://www.johnpratt.com/items/docs/lds/meridian/2013/venus_patterns.html

The ingenuity of ancient timekeeping devices reflected the need for accurate measurements without the benefit of mechanical clocks. Sundials were among the earliest tools, evolving into portable designs suited for different regions.

Clepsydra image
Pic Credit: AI Gemini

Water clocks, known as clepsydras, allowed time to be measured even at night by controlling the flow of water from one container to another. In Asia, marked candles and incense sticks helped estimate time by observing how much had burned, while hourglasses eventually emerged as reliable tools for tracking specific intervals.

The division of the day into hours varied greatly across cultures. Egyptians first divided daytime into twelve parts, but these hours were not of equal length—they expanded in summer and shortened in winter. The concept of standardised, fixed-length hours came later, thanks to Greek influence.

Calendars played a fundamental role in organising time for agricultural planning, religious observances, and social coordination. Most ancient calendars were lunisolar, attempting to balance the lunar cycle with the solar year. This often required adjustments, with extra months inserted occasionally to correct discrepancies between the seasons and calendar dates. Civilisations like the Sumerians, Babylonians, Egyptians, and Mayans developed remarkably advanced calendar systems based on their astronomical observations.

Pic serves as an illustration

To ancient people, time was fluid rather than rigid. It was a force tied to nature, divinity, and cosmic events. Today, time feels more precise and structured, but perhaps it has lost some of its organic connection to the universe. The way early civilisations perceived and measured time reminds us that, beyond numbers and schedules, time was once an experience—something observed, lived, and deeply felt.

Conlusion 

Journey through the concept of dimensions reveals a universe far more intricate and interconnected than our everyday senses might suggest. From the simple line to the mind-bending tesseract, each added dimension unlocks new possibilities for understanding the fabric of reality. And at the heart of this framework lies time, the enigmatic fourth dimension, which, alongside space, forms the dynamic stage upon which all events unfold. While our modern world meticulously measures time with precise instruments, the echoes of ancient civilisations remind us of a time when its rhythm was deeply intertwined with the natural world and celestial cycles. Ultimately, whether perceived as a rigid framework or a flowing experience, the exploration of dimensions, and particularly the nature of time, continues to be a profound and ongoing quest, pushing the boundaries of our understanding of the cosmos and our place within it.