Executive Knowledge Lines

but depend on the state of motion of the observer. Further, they are inextricably interconnected and manifest as space-time continuum.

Accordingly, events occur in the 4-Dimensional fabric of space-time.

In other words, we live in a 4-D world! In our daily life, we are familiar only with three spatial dimensions - length, breadth and height. We see and feel 3-D objects around us including ourselves. Representation of 3-D objects on a 2-D sheet of paper itself is difficult, let alone more dimensions! But then, we can’t escape some mental gymnastics if we must conceive more abstract geometrical shapes.

General Theory of Relativity (GTR) was published in 1915. It views gravity, not as a force as Newton conceived, but as the influence of matter in curving the space-time fabric in its vicinity. Gravity was thus transformed to a geometrical concept of curvature! Two mindboggling consequences of GTR are that (i) A light beam can be bent by gravity and (ii) A clock is affected by gravity-stronger the gravity, slower the clock !

Einstein used nothing but paper and pencil. He was the epitome of a theoretical physicist. All predictions of his abstruse Theory of Relativity have long since been proven true by other physicists. By the way, the now famous equation, E=mc2 is a direct consequence of STR. Except for this equation whose benevolent (nuclear power generation) and malevolent (nuclear bomb) effects are widely known even among lay public, other consequences of Relativity - both STR and GTR - remain aloof from the layman. However, GPS (Global Positioning System), without which life has now become impossible, is a significant exception.

GPS This helps us determine our position on land, waters or skies with an accuracy of a few meters. It employs a system of Navigation Satellites circling the earth in different orbits about 20,000 km above the surface.

Perfect timing is the key to its satisfactory performance, which is achieved with a network of accurate, rock-steady atomic clocks on the ground and onboard the satellites. A little known fact is that, without taking both STR and GTR effects into account, the position errors would build up at the rate of 10 km/day rendering GPS a colossal waste (several billion US Dollars)! Because the satellites are moving at 4 km/second in the orbit, the onboard clock would seem to run slow by 7 microseconds/day relative to us (‘Moving clocks run slow’).

Besides, at a height of 20,000 km, the earth’s gravity is only about 5 % of what is here on the ground with the result that the onboard clocks 16Executive Knowledge LinesDecember 2011