Yajnavalkya Space-time and Minkowski Space-time
Yajnavalkya was a Vedic sage who lived in the 8th century BCE. He is known for his philosophical teachings, which are recorded in the Upanishads, a collection of ancient Indian texts. He explained the concept of space and time, when asked by the ancient Indian lady scholar Gargi at the court of the King Janaka in Mithila.
Yajnavalkya's concept of space and time is complex and multifaceted. He describes space as both physical and metaphysical. On the physical level, space is the void that surrounds all things. It is the emptiness that allows for movement and change. On the metaphysical level, space is the source of all creation. It is the infinite potentiality from which all things arise. Yajnavalkya's concept of space is also related to his concept of time. He sees space and time as two aspects of the same reality. Space is the container of time, and time is the movement of space.
Yajnavalkya's concept of time is also complex and multifaceted. He describes time as both physical and metaphysical. On the physical level, time is the sequence of events that unfolds in the universe. It is the measure of change and movement. On the metaphysical level, time is the underlying reality that gives order to the universe. It is the fabric of the cosmos. Yajnavalkya's concept of time is also related to his concept of space. He sees space and time as two aspects of the same reality. Space is the container of time, and time is the movement of space.
Mathematical model of Yajnavalkya concept of Space and Time is hardly known.
To express Yajnavalkya's concept of space and time in a mathematical model, one possible way is to use the concept of Minkowski space. Minkowski space is the modern concept of Space-time. It is independent of Yajnavalkya concept. But it can be parallel understanding understanding of the Space-time in the Modern Physics. Minkowski space is a four-dimensional space that combines three dimensions of space and one dimension of time. It is used in the theory of relativity to describe the physical phenomena in the universe. In Minkowski space, the distance between two events is not fixed, but depends on the relative motion of the observer. This means that space and time are not absolute, but relative.
Minkowski space can be represented by a coordinate system, where the x, y, and z axes represent the three dimensions of space, and the t axis represents the dimension of time. The coordinates of an event in Minkowski space are given by (x, y, z, t). The distance between two events in Minkowski space is given by the Minkowski metric, which is defined as:
ds² = -c²dt² + dx² + dy² + dz²
where c is the speed of light.
The Minkowski metric is invariant under the Lorentz transformation, which is a mathematical operation that changes the coordinates of an event according to the relative motion of the observer. The Lorentz transformation preserves the Minkowski metric, which means that the distance between two events is the same for all observers, regardless of their motion.
The Minkowski space and the Minkowski metric can be seen as a mathematical way of expressing Yajnavalkya's concept of space and time. They show that space and time are not separate entities, but interrelated aspects of the same reality. They also show that space and time are not fixed, but flexible and dynamic. They depend on the perspective and the motion of the observer. They are the manifestations of the infinite potentiality and the cosmic order that Yajnavalkya described in his teachings.