The James Webb Space Telescope
There's recently been a lot of excitement about the images coming in from the so-called JWST, the latest telescope sent out by NASA and the JPL, and commentators and geeky influencers are getting themselves excited with the possibility that the Big Bang Theory might be wrong!! "Please, please, let it not be so!" Don't panic; all future cosmological theories will (probably) incorporate some version of the Big Bang.
As I was watching, at long last, Roger Penrose on YouTube, I was startled for one big reason. In grad school, where I studied all sorts of things (in contrast to a lot of my fellow-students, who were already focused on getting to the research stage ASAP,) my research group---OK, it was just me and my advisor---but he loosely belonged to the group that had collaborated with Roger Penrose and Ezra (Ted) Newman, Paul Todd, John Porter and co, to develop a technique based on complexification of Einstein's theory.
I never could see the point of complexification of spacetime. I loved and was quite at home with Complex Analysis, the mathematics of complex numbers; they are an elegant and unifying approach to various aspects of math, but I had learned physics from a completely non-complex point of view, and I merely endured the idea of complexification, because I did not want to be rude, and I did not want to spend an age before I graduated.
A central idea with complex analysis is that of conformal transformation. This term refers to transforming graphs (bear in mind that a lot of mathematics is about graphs) in such a way that lengths and distances may be distorted, but angles are preserved. Einstein's equations can be transformed conformally as well. (If you transform the geometry of a problem, you can transform the equations as well. Sometimes the equations don't look anything like they used to; sometimes they are hardly changed at all. In this case, the equations were the same except for a non-zero formula that could be divided out from both sides of each equation; what a stroke of luck.)
There is sure to be a print explanation of Penrose's idea on the Web somewhere, but here is the gist of it.
The Boundary of Spacetime
A favorite thing for Penrose and Newman---principally the latter---to do, was to reduce the infinite part of space into a surface. This sort of thing has been done in many cases. For instance, the Number Line (or the Real Line, as it is known to its friends) can be reduced to just a line segment with two endpoints. The whole infinite part of the number line is collapsed---very carefully, obviously---to the two dots at the end of the line segment: minus infinity and plus infinity.
In the case of Spacetime, every point (or event) has to lie on a set of what are called null geodesics, that is, paths of light rays. Now, in principle, light rays will leave every point in every direction. We say that there is a sphere's worth of light rays emanating from each point. Each of these, like the number line, can be reduced to a line segment, with two endpoints. The clever part of the method is that all these endpoints can be formed into a surface. Two surfaces, actually; one in the (infinite) past, and one in the infinite future. The shrinking of spacetime is done conformally, so that the equations are transformed nicely. So this was the basis of my dissertation, and for obvious reasons, I tried to keep it under wraps, because I was vaguely embarrassed by the whole thing.
Heat and Cold under Conformal Transformation
This is where matters stood, until I happened to watch Penrose explain his theory on YT. The first point to note is that if a portion of space is compressed conformally, it becomes hot. Secondly, if a portion of space is expanded, or stretched, it becomes cold. Thirdly, Penrose pointed out, that if the physics of the so-called Big Bang Singularity is stretched out, it becomes quite smooth, and not a singularity at all. (All this has to be proved, but Penrose has apparently demonstrated all this to the satisfaction of those who are interested.)
Now here's the punchline. Penrose says, if you take some sort of catastrophic event, like a supernova for instance, and follow its matter and its light rays all the way out to infinity---in our model, that means chasing it down until it hits the future boundary---we will see how it will appear from the distant future of the entire universe. In fact, Penrose says, it will look very much like the images observed by the JWST as emanating from inside the Big Bang! These sorts of phenomena, the reverse of a Big Bang, have been called a Big Slurp!
To join the dots, it's beginning to look like we're just one of a sequence of spacetimes, and the end of each spacetime is in fact the Big Bang of the next one in the sequence.
This is not a new idea; the model of a cyclic cosmology was one of those shown us in college, in baby relativity class. I never dreamed that that theoretical concept would turn out to be something that astronomical observations would someday nudge us towards!
