One of the things we have drilled into our heads as students when first we learn fractions is the idea that there is no “shortest” length or “briefest” time. If you give me any non-zero length, and declare it the shortest possible, I can always just divide it by two to get a length shorter still and, in theory, that process can go on forever. The number line will never run out of room for ever smaller fractions.
Certainly, the number line, as an abstract object, won’t, but what if, in reality, space and time both did? What if there is such a thing as a lower limit on the size of both? What if space-time is not a continuous cloth at all, but is instead a collection of discrete space-time “atoms”?
The idea of a moment in time being made up of a finite number of fundamental time units goes against everything we’ve been taught and fundamentally feel about the nature of existence, and yet that very idea lies at the heart of a new approach to quantum gravity being pioneered by a small group of rogue physicists slaving away in esoteric corners of topology to create something very new and potentially cosmos changing: a unification of gravity and quantum mechanics.
One of the stalwart researchers in this quest for the last couple decades has been Sumati Surya, a self-effacing physicist from India who nearly gave up physics entirely in her youth. As a child, her school teachers were intimidating, so she learned primarily from her parents. Her journalist mother and engineer father would help her with homework and set her challenges that emphasized the pure fun of Figuring Things Out. Intellectually precocious, she figured out by age nine that the answers to the big questions of the universe did not lie in gods and religion, but in the ornate structures-in-progress of natural science.
Confident and curious as an elementary student, Surya’s sense of self-worth nearly unraveled in high school, where the focus was on testing rather than knowledge, and girls were taught that, in science, it was only the boys who could hope to achieve original insights and first-rate statures. Girls, so ran the reigning assumption, could only ever produce second-tier work.
Tragically, in spite of her family’s support and her physicist brother’s strong encouragement, she couldn’t rouse her self-confidence to compete on a level equal to the quality of her mind, and ended up at Madras’s Women’s Christian College, an institution of middling repute, mediocre faculty, and limited resources. In a way, however, the sheer intellectual tepidness of the college was a boon, because it forced Surya back into the rich fields of her own mind. Lacking faculty to guide her or intellectual companions to support her, she undertook a rigorous course of self-education from first principles that soon threw her into the dizzying world of relativity.
As an independent student she shone, and the habits of self-guided deep thinking she developed stood her in good stead as she earned her Master’s Degree in yet another semi-toxic, success-worshipping academic environment, Kanpur’s Indian Institute of Technology.
With so much academic buffeting, a reasonable response might have been to forsake physics for fields less psychologically gnarling, but Surya pressed on, finding her intellectual home at last at Syracuse University with Rafael Sorkin, one of the founding figures of a daring new approach to space-time: causal set theory.
One of the greatest lingering puzzles in physics is the lack of a theory of quantum gravity. Einstein’s theory of gravity as arising from the geometry of space time is outrageously successful on the macroscopic scale, but falls apart at the very small scales where quantum mechanics is successful. Physicists would like a quantum theory of gravity that folds gravitation in with all the other forces currently united in quantum mechanics.
Surya has given us glimpses of a new space-time that are much more than “modest” and we in turn can be much more than thankful to be living in an era of ideas such as these.
The system that typically gets the most press is string theory, or superstring theory, or M-Theory, depending on what moment in time you happen to catch it. It holds that matter is made up of tiny strings whose different oscillations give rise to the universal constituents we know. The complexities of mathematically modeling the 10 or 11 dimensional (depending on whom you ask) space-time which lies at the heart of this theory, however, mean that it could be decades before we find a configuration that accurately models our universe.
Enter causal set theory (CST), which features a very different set of starting premises. It holds that space and time are constructed of finite lengths, that space-time is discrete rather than continuous. There are many reasons why such a theory is attractive – by prescribing a “smallest” length of time, it also ensures a maximum photonic frequency (remember from high school that frequency = 1/period) and therefore a maximum photonic energy (since Energy = h * frequency where h is Planck’s constant). Current theory doesn’t rule out photons of infinite energy – discrete time does. Similarly, limits on how small lengths can be puts lower limits on wavelengths, and therefore upper limits on particle momentum that our current theories also don’t possess.
Sorkin had done foundational work in the 1980s theorizing what the properties of a space-time discretely constituted might be, and after spending some time studying under Sorkin at Syracuse University in the late 1990s, Surya joined the Theoretical Physics Group at the Raman Research Institute in Bangalore. She is now part of that small but devoted cadre of theoretical scientists chipping away at the mammoth task of creating mathematical structures that illuminate how a discrete view of space-time might model our universe and unite quantum theory and gravitation at last.
The job rests on describing the “causal structure” of space-time, which involves developing a mathematical system that explains how events are causally connected to each other, how to describe the distance between events, and how to define sets and elucidate how those sets map to the 4-dimensional manifolds that make up the macroscopic space-time we are used to. The effort requires stretching existing math to new areas and, when that can’t be done, inventing new mathematical objects entirely. It is a dizzying re-imagining of Everything and Surya has contributed numerous papers in its development, though characteristically she describes her own contributions as “modest.”
We won’t let her get off that easily, though, will we? She has written papers on locality, quantum measure, scalar field Green functions, wave functions, and phase transitions in causal set theory that span the range of quantum kinematics, quantum dynamics, and field theory. Along with Lisa Glaser, Astrid Eichhorn, Fay Dowker, and of course Rafael Sorkin, she is adding crucial supports to nothing less than a grand new theory of Reality Itself.
If that theory is right, what a blissfully strange universe we shall suddenly inhabit, but what if it’s wrong? What if, tomorrow, a computer in Berlin goes Ping and spits out an 11-dimensional model of superstrings that reconciles quantum mechanics and gravity and models our universe from the tiniest Planck squiggle to the most grandiose galactic cluster? Will it all have been for naught, then, the work of Surya and Sorkin?
Certainly that’s the risk for any researcher on the crackling edge of theory – for every Darwin there are ten Lamarcks lying bludgeoned by the side of the road – but I don’t see that being the case here. The foundationally discretized universe of causal set theory is so daring in its assumptions and profound in its implications that it is worth knowing, its math worth evolving, even if it doesn’t happen to be our universe. If reality, it is powerful, and if “merely” a cosmic-scale Elseworld, then still it is beautiful. Either way, Surya has given us glimpses of a new space-time that are much more than “modest” and we in turn can be much more than thankful to be living in an era of ideas such as these.
Lead image by Gabriela Secara, Perimeter Institute; republished on Women You Should Know with express permission.
FURTHER READING: Books on string theory are darn-near everywhere, but for Causal Set Theory some digging is required. I recommend this 1999 piece by David Reid as a good mid-level introduction to the field that will prepare you (mostly) for Surya’s own 2011 summary of CST that you can find here. Some familiarity with topology helps and, as always, I’m pushing Munkres as the best source for that. For Surya’s life, there’s a lovely interview with her in The Girl’s Guide to a Life in Science (2011), which is a great collection of talks with Indian women scientists from just about every field you can think of.