From: mk_thisisit
Sir Roger Penrose, a mathematical physicist, received the Stanisław Lem Prize in 2024 for his fundamental contributions to the development of physics [01:10:00]. He describes himself as more inclined towards physics than mathematics, with his heart lying with the part of twistor theory that relates to physics [08:17:00].
Nobel Prize for Proving Singularity
Roger Penrose was awarded the Nobel Prize for demonstrating the falsity of the statement that complex systems would not lead to singularities [00:38:00], [07:09:00]. He proved the existence of singularities given a specific criterion of collapse, a place beyond the point of no return that he called a “trapped surface” [04:55:00]. His work aimed to show that black hole singularities were not just artifacts of specific, unrealistic models [04:10:00].
Challenging the Oppenheimer-Snyder Model
A famous article by Oppenheimer and Snyder, published around 1939, described a dust cloud that collapsed into a singularity of infinite density [05:14:00]. However, this model was widely disbelieved at the time because it did not include pressure and assumed perfect spherical symmetry, leading to an unrealistic collapse to a single point [05:36:00].
Furthermore, observations of active phenomena in distant galaxies suggested bodies beyond the scope of the Oppenheimer-Snyder model [06:01:00]. Two Russian physicists, Lvshica and Kalatnikov, published a paper attempting to prove that in complex, irregular systems, singularities (infinite density) would not appear, and bodies would rotate and escape [06:40:00]. This view significantly influenced the scientific community [06:59:00].
Penrose’s theorem was formulated in response to these arguments [06:13:00]. He analyzed the work of Lvshica and Kalatnikov and found an error, which was later corrected by Beliński, who confirmed that oddities (singularities) were common [07:15:00]. Penrose independently demonstrated the necessity of an error in their claims using completely different, previously unused methods [07:41:00].
Penrose’s Unique Approach
Instead of writing down and solving equations, Penrose developed techniques for looking at causal structure and analyzing the general characteristics of space-time [09:31:00]. He focused on concepts like “trapped surfaces,” which were not previously considered [11:13:00].
A trapped surface is a two-dimensional surface that, if imagined as a flash of light, would have light rays on both its inside and outside converging [11:19:00], [12:32:00]. This concept, along with the theorem that every point on the boundary of a space-time future must lie on a ray of light, allowed him to prove the existence of singularities without assuming specific situations like the Oppenheimer-Snyder model [10:14:00], [10:57:00].
Collaboration with Stephen Hawking
Penrose frequently collaborated with Stephen Hawking [00:44:00]. Penrose states that on the topic of black hole singularities, he was the main author, and the key ideas were his [00:47:00], [13:13:00]. He also credits Brandon Carter for correcting errors in Hawking’s early work [13:16:00]. While Hawking developed certain techniques more than Penrose, the fundamental concepts originated with Penrose [13:48:00]. Hawking’s most important independent contribution concerned the evaporation of black holes (Hawking radiation) [13:53:00].
Conformal Cyclic Cosmology (CCC)
Penrose has developed a cosmological model, Conformal Cyclic Cosmology (CCC), which proposes that the universe did not begin with a single Big Bang, nor will it end [17:01:00]. Instead, the Big Bang of our eon is the end of a previous eon, and our eon will transition into a future one [17:17:00].
Key elements of CCC include:
- Gravitational Wave Signals: Collisions between black holes, particularly supermassive ones, produce gravitational wave signals [17:31:00], [18:06:00]. These signals create “rings in the sky,” which Penrose suggests may be confirmed by discoveries like Priscilla Lopez’s galaxy circles [17:36:00].
- Hawking Radiation: Hawking discovered that black holes are not completely cold but have a temperature [19:25:00]. Larger black holes have lower temperatures [19:37:00]. As the universe expands and cools, it will eventually become cooler than black holes, causing them to evaporate over an incredibly long time (estimated 10^100 years) [19:48:00].
- Signals in Microwave Background Radiation: The radiation from evaporating black holes passes into the next eon, causing “single point explosions” that create signals in the sky, heating certain regions [20:07:00]. Penrose claims these spots in the sky are observed with a high confidence level of 99.98%, and conventional theory does not explain them [20:37:00].
Penrose views these predictions as belonging to conformal cyclic cosmology [21:08:00]. He speculates that CCC might eventually be combined with twistor theory, though currently they are separate [21:22:00]. His book, Cycles of Time, provides a description of the transition from one eon to the next [21:32:00].
The Birth of Conformal Infinity and Twistor Theory
Penrose’s interest in relativity theory deepened through his work on gravitational waves with Herman Bondy [24:26:00]. A key insight came from understanding Ray Sax’s “flaking theorem” regarding the behavior of the radiation field [24:38:00]. Penrose realized this was connected to conformality, leading to the birth of “conformal infinity” [25:08:00].
His understanding of conformal invariance of Maxwell’s equations and the importance of separating positive and negative frequencies, explained by his office-mate Engelbert Schuking, led him to the development of Twistor theory [25:41:00], [26:01:00].
“I don’t differentiate between fun and serious learning.” [14:34:00]
Penrose considers mathematical physics largely as “fun,” driven by the desire to solve problems and the pleasure derived from exploring topics like causal spaces and the boundaries of the future [14:55:00]. He notes that the mathematical techniques he used for his Nobel Prize-winning theorem were developed for fun, not necessarily to prove that specific claim [15:24:00].