The power of armchair physics

Mathematics has a well-deserved reputation of being an armchair endeavour. You sit down armed with some concepts and wander off into many wonderful directions by just digging deeper into these concepts. Physics on the other hand has traditionally been a laboratory science. One tried to understand the physical universe with experiments and codified the results with the help of mathematical tools. Einstein however came along and blurred this distinction. He changed the way we view the universe `simply by thinking about it.’ I will, in one of my next posts, show how the postulates of special relativity can be derived in a purely mathematical way in much the same way Einstein might have done. Newtonian physics recognised gravity as one of the fundamental forces that shapes our universe but was unsuccessful in explaining how and why objects attract other objects. Einstein, armchair and all, unraveled this mystery in his theory of general relativity. He visualised space-time as a fabric that stretched and curled through the universe. An object that is plonked on this fabric creates a deformity or depression that sucks in objects around it. The heavier the object, the bigger the depression and greater its powers of attraction. Simple and profound. Einstein was nothing if not that! Armed with this model, it is but natural to conclude that objects which are so plonked onto this fabric create waves that ripple across the fabric. These are the gravitational waves that EInstein’s General Relativity predicts and which are yet to be observed experimentally.

It was under this mathematical framework of general relativity that Stephen’s Hawking made his celebrated conclusion that black holes emit radiation. Whilst being a tour de force in mathematical reasoning, it hasn’t won him a Nobel prize because it hasn’t being verified experimentally! And then along came Edward Witten and others and the traditional barriers between mathematics and physics have all but dissolved.

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