Minkowski

INTERPRETATION OF THE CONCORDANCE RESULT USING MINKOWSKI’S METRIC- Raju Chidambaram, Ph.D (4/10/08) The author presented in previous papers the basis for a mathematical model of spirituality along with some analysis of that model (Ref 1). Among the results of the analysis was one which indicated that there is a strong correspondence between the time-space relationship in Einstein’s Special Relativity Theory and the relationship between spiritual detachment and suffering in Vedantic teachings. This correspondence suggests that the nearly equivalent use of the terms “space” and Consciousness”, (as well as “light” and “knowledge”) found throughout in Vedantic scriptures appear to be more than just a simile. The correspondence between Vedanta and Relativity Theory stands out more clearly when the Minkowski’s Metric for time-space continuum is used. To start the discussions, consider Fig 1 below with a jeeva of uniform detachment θ. Let AB and CD be two time arcs and PQ the radial at angle θ intersecting the two time arcs at P and Q respectively. PQ = is the distance between P and Q in the ` space. Let us denote PQ by δS.

Fig 1M `: Cosmic Mind Space

D Q δS

B

δG θ

P

δτ

R

A

C

PR= δS.cosθ is the incremental experienced time, denoted by δτ, over the time interval δS. RQ = δS.sinθ, denoted by δG, is the incremental goodness or “merit” over the same time interval. We have the relation δS2 - δτ2 = δG2 ……. (1) This is similar to the Minkowski’s Metric of distance (or time) in Relativity Theory for the 4 dimensional time-space continuum:

δs2 – δt2 = δd2 ------- (2) where δs = the distance in the ordinary three dimensional Euclidean space, δt = c.time, δd = the metric (distance or time) in the 4 dimensional time-space continuum, and c being the speed of light. For convenience, the units of measurement of time and space may be set such that c = 1. This equation shows how time and space are related and why two observers moving in the Euclidean space relative to each other experience time and space in different ways. Physicists sometimes explain the basic relationship between time and space in a way that is particularly helpful to our discussions (Ref 2). Everybody and everything in this universe, they point out, is constantly moving through the time-space continuum at the speed of light. Even objects stationary in space are also traveling at that speed, except that their travel is in time dimension only. They are moving through time at the fastest speed possible, namely speed of light. We may say that time moves the fastest for these objects. When something or somebody is moving through space, it is in fact diverting part of its speed in time dimension to accomplish travel in the three dimensional space. Because of this diversion, its speed in time is reduced; that is “time slows down” for it. In the extreme, time stops for an object moving through space itself at the speed of light. All these observations are of course cast in robust mathematical terms in relativity physics. We can re-write Eq. (2) as follows: δd2 – (iδt)2 = δs2 ------- (3) where i = √-1 is the unit imaginary number. Comparing equations (1) and (3), we see the correspondence between the following pairs of terms: a) the four dimensional time-space continuum d with the space `; b) the imaginary time i.t with experienced time τ on the horizontal axis; and c) the three dimensional Euclidean space s with G, the vertical axis of Pure Witness or Consciousness. The time-space relationship of Special Relativity Theory can be readily translated now in spiritual terms as follows. Everything and every jeeva, as discussed in Ref 1, is in the Mahat (` space) and all move constantly at the speed of cosmic time, just as everything is moving at the speed of light in the time-space continuum1. This is the basis for the mathematical model proposed in Ref 1. In the Fig 1 above, for example, the universe, which is in the arc AB at a certain time, is in the arc CD after the elapse of δS in cosmic time. All things and beings must also necessarily move with the universe. However, spiritual beings, or 1

Jesus puts it more eloquently: "For in him we live, and move, and have our being; ...” Bible Acts 17:28

jeevas, possessing detachment divert part of this speed to advance in the dimension of Self (or Goodness, along the vertical axis). This reduces their speed in the dimension of “experienced time” τ (along the horizontal axis). The speed component along the vertical axis is δG/δs. This equals sinθ which we defined as the “Relative Awareness”, a comparative measure of the Goodness and Knowledge the jeeva has relative to that of a fully Realized “Perfect Being”. Higher the vertical speed component, lower is the horizontal speed component. Stated differently, more the jeeva’s relative awareness, less is its suffering. This of course is the inverse relationship between Love and Suffering , the “fundamental law of spirituality”. The Minkowski’s Metric thus provides a clearer basis for interpreting the concordance result. The two components δτ and δG could perhaps also be related to the “temporal” and “spatial” components of identification with Self that are discussed in Ref 1. REFERENCES 1. Towards a Mathematical Theory of Spirituality Based on Advaita (Parts I and II)- Raju Chidambaram, Sixth WAVES Conference, Houston, TX July 2006 2. The Fabric of the Cosmos- (Page 48, First Edition) Brian Greene, Alfred Knopf, New York, NY 2004