From: mk_thisisit
Twistor theory, created by Roger Penrose almost 50 years ago, was initially conceived to build a mathematical formalism capable of describing both quantum and classical physics in a similar way [06:04:36]. It proposes a fundamental shift in how physical reality is conceptualized [05:08:29].
Core Concept of Twistor Theory
Most models of the universe, including those with many dimensions, consider points of space or spacetime as fundamental building blocks [04:50:00]. However, Twistor theory departs from this, making a point a secondary object [05:11:00]. Instead, it suggests that a light ray should be considered a more elementary object [05:17:00]. The “twister space” is defined as the space of all such light rays, with an additional degree of freedom, hence the name “Twister” [05:23:00].
The theory attempts to reformulate most of classical and quantum physics in the language of these light rays, such that a point in space-time only emerges at a certain level [05:32:00].
Evolution and Challenges
Initially, the physics message of Twistor theory was unclear, but it proved to solve many problems in pure mathematics, multidimensional geometry, and the theory of differential equations [06:30:00]. This led to physicists abandoning it for a time, while mathematicians took it over [06:47:00].
Mathematical Apparatus and Obscurity
Twistor theory involves a quite advanced mathematical apparatus, which can obscure its underlying physics [04:38:00].
Problem of Quantum Gravity
A major motivation for Twistor theory was the integration of classical and quantum physics [09:13:00]. Physicists are currently stuck trying to use quantum mechanics methods to describe gravitational interactions, suggesting a need to rethink fundamental approaches [00:00:00] [08:52:00]. Traditional attempts since the 1920s and 1930s to build a quantum theory of gravity using quantization laws have not led to success, often resulting in infinities in calculations, a problem physicists call “lack of renormalization” [10:29:00]. This suggests that quantum gravity cannot be built in the same way other theories were [11:10:00].
Most physicists believe that quantum mechanics should remain as it is, while the theory of gravity needs to change [11:31:00]. However, another approach suggests keeping gravity at the level of Einstein’s equations largely unchanged, and instead focusing on understanding and solving the paradoxes of quantum mechanics by incorporating gravitational effects [12:04:00].
Experimental Verification
A significant challenge for Twistor theory, as with other theoretical physics concepts like quantum gravity, is the lack of experimental verification [07:41:00]. Current experiments can only confirm or refute ideas from the 1960s [08:01:00]. Observing phenomena that Twistor theory claims the right to describe, such as quantum gravity, is deemed impossible under current conditions within our galaxy [08:15:00]. This means researchers are “walking blindly” without experimental clues [08:35:00].
Breakthroughs and Applications
Re-emergence in Particle Physics
Around 20 years ago, it was discovered that Twistor theory could greatly simplify calculations for describing interactions or amplitudes of transferred particles, such as photons or gluons [06:52:00]. While describing quark interactions is difficult traditionally, rephrasing them in the language of twists makes it quite easy [07:12:00]. This led string theorists and elementary particle physicists to learn Twistor theory because the calculations were previously impossible for them [07:25:00]. This represents one breakthrough, bringing Twistor theory into mainstream theoretical physics [12:40:00].
Connecting Cosmology and Quantum Mechanics
Another significant breakthrough involves an idea proposed by the speaker that connects the cosmological constant (dark energy) at the edges of the universe with modifications to the Schrödinger equation at the level of a hydrogen atom [22:28:00]. This seemingly “crazy idea”—that what happens at the universe’s edges could influence elementary particles—is supported by calculations at the level of Twistor theory [22:41:00]. This work received first place in an annual distinction for important scientific essays by the Gravity Research Foundation [19:45:00].
This idea proposes a relationship between three elements:
- The expanding universe and dark energy: The universe is expanding at an accelerating rate due to what is called dark energy, or the cosmic constant [21:02:00]. This effect is measurable at the edges of the universe, which has a diameter of slightly less than 100 billion light-years [21:26:00].
- Planck’s constant: A very small constant in physics that describes how quantum effects dominate over classical ones at the scale of a hydrogen atom (10^-10 meters) [22:01:00].
- Twistor theory’s non-locality: Twistor theory is inherently non-local, meaning a point in the theory doesn’t correspond to a localized region but to an infinitely long line or sphere [13:45:00]. Quantum theory is also non-local; for example, an electron’s wave function describes a probability of finding it anywhere in the universe before measurement, and upon measurement, the wave function instantly changes its state across the entire universe [14:03:00]. The speaker and Roger Penrose believe they understand how to describe this quantum non-locality [14:51:00].
The hypothesis suggests that using simple Newtonian gravity, quantum mechanics can be reformulated to explain the collapse or reduction of the wave function [13:22:00].
The Metrizable Problem
The speaker also made a significant discovery in pure mathematics, solving a problem in geometry posed by French mathematician Roger L. at the end of the 19th century, known as the metrizable problem [15:17:00]. This problem concerns whether the concept of distance (metric) can be recreated from a known set of “shortest lines” (geodesics) on a curved space or spacetime [16:49:00]. While it was known by the early 20th century that this isn’t always possible, the challenge was to find a test or theorems to determine when it is [17:09:00]. The speaker’s solution came after nearly a decade of work, demonstrating a different path to understanding mathematical structures [17:17:00].
Reflections on Scientific Practice
The speaker emphasizes the different approaches between physics and mathematics:
- Physics: Ideas are important, and physicists are not ashamed to share them early, even if they turn out to be wrong [18:59:00].
- Mathematics: Credibility is paramount. Mathematicians must ensure there are no gaps in their proofs before presenting a theorem [19:10:00].
The speaker also highlights the importance of finding one’s own way in science, even if it means facing failures or lack of compromise, and not worrying about current trends [24:42:00].