MU-1: From Bathtubs to Relativity

(This is the first in a series on how maths seems to be the language in which the rules of the universe have been written: the “MU” in this series titles stands for “Mathematical Universe”).

Long, long ago, science could be done by “by watching your bathtub spill over” (as Sabine Hossenfelder put it). All that began to change when Galileo began to argue that “the keys to deciphering the universe’s parlance were mathematical relations and geometrical models”, as Mario Livio put it in his book, Is God a Mathematician?

But it would have to wait until Isaac Newton until someone came up with mathematical relations to describe the universe. In the process, calculus had to be invented because, as Charles Seife puts it in his book, Zero, “calculus was the very language of nature”.

From Newton onwards, all of physics has been stated in mathematical equations. So much so that when Richard Feynman was asked whether we could have a theorist today who was “not mathematically sophisticated but with a very powerful intuition about physics” (a la Faraday), his response was:

“Faraday's models were mechanical--springs and wires and tense bands in space--and his images were from basic geometry. I think we've understood all we can from that point of view.”

Maths, however, was only the language of communication; it did not dictate the content. The content was what physics came up with based on actual observations. This attitude was demonstrated in 2 famous instances:

1)     In 1921, when Alexander Friedmann came up with a couple of solutions to Einstein’s equations of relativity that meant that space itself would be stretching thereby causing the universe to expand, Einstein balked. After all, no observations till date had indicated any such expansion of the universe. Or as Brian Greene puts it in his book, The Hidden Reality, “Einstein refused to be mathematics’ pawn”.

2)     Georges Lemaitre pointed out the Einstein’s equations of relativity implied that the universe began as a tiny speck of unbelievable density. Einstein, after checking and failing to find any errors in Lemaitre’s maths, still refused to accept the implication of the maths and told Lemaitre that the universe had never been expanding. After all, where was any such evidence or observation?

The rest is history. Both #1 and #2 turned out to be true. Edwin Hubble ultimately got the credit for discovering the universe is expanding. And Georges Lemaitre is credited with being the father of what is now famously known as the Big Bang. These two instances may well have been the turning point in why physicists began to trust the maths more and more, even if no observation till date had indicated what the maths of the equations implied.

To be continued…