Time, a mathematical illusion?

3 minute read


The following is a piece I wrote for an Arts Festival held at my university. You can read the original here.

One of the lesser-known aspects of the life of Kurt Gödel was his endearing relationship with Albert Einstein towards the latter stages of their lives. The two of them often went on long evening walks in and around Princeton University and discussed, at length, the implications of Einstein’s general theory of relativity, on the very nature of time as we know it. Gödel, being a logician first, empiricist much later, put immense faith in the rigours of the process of mathematical deduction, once famously claiming that he didn’t “believe in empirical science”, only “in a priori truth”. This truth, he often held, was mathematical, that it did not need the “real” world to be valid. Thus, when he once pointed out to Einstein that one of the mathematical solutions to his general theory of relativity, was a universe that didn’t just expand, but rotated, Einstein was disturbed. He didn’t take to it too kindly and dismissed the idea in a way befitting someone who preferred the empirical world to esoteric abstractions. Einstein wasn’t a logician, nor was he a mathematician. He was a physicist, and any maths that appeared weird to him, or didn’t make sense, he dismissed it as implausible. Of course, one such naive dismissal would lead him to believe that the universe didn’t expand, that it had no beginning - something that he would later describe as his “life’s greatest mistake”.

Gödel’s idea about the rotating universe, though intriguing, came to Einstein at a time when his personal life was crumbling around him. Moreover, his rejection of quantum physics had by then, already estranged him from the rest of the physics community. Thus, for a variety of reasons - old age being yet another - his discussions with Gödel didn’t lead to anything more fruitful. Gödel, on the other hand, while even on his deathbed, two decades after Einstein’s passing was still working on equations, trying to calculate the angular momentum of the universe - hoping to find some evidence, however small, that the universe was indeed rotating.

The truth was, what Gödel had discovered - hidden deep within the cold equations of the general theory of relativity - was a universe that, by rotating on an axis, mixed space and time in a way that would allow anyone undertaking a long-enough trip, to travel back and forth in time. Gödel, the ever-immaculate logician, had an interesting interpretation of this theory. He opined that if time-travel is possible, then what has passed has not really passed, if the laws of physics - encoded in abstract mathematical equations - allowed one to revisit it. He thus came to a conclusion which was scarcely less startling than his more famous Incompleteness Theorems: that in such a universe, that could very well be ours, time could not exist.

Gödel and Einstein Gödel and Einstein at Princeton. Image courtesy https://www.discovery.org/a/2444/

Reference: Yourgrau, P. (2009). A world without time: The forgotten legacy of Gödel and Einstein. Basic Books