Gazing at the sub Planck Length realm using Philosophy of Science

(With inputs from ChatGPT)

Immanuel Kant (1724-1804) argued that we could only have knowledge of the world as it appears to us (phenomena) and not the world as it is in itself (noumena).

In other words, noumena represent things in themselves that are beyond our direct experience, whereas phenomena are the appearances or manifestations of those things that we can perceive and understand. 

A nice article on the Kantian perspective of noumena & phenomena is at Allzermalmer. 

Another interesting description(below), it's inspired by the Kantian point of view though it's a description in terms of the lens of human emotions. Arthur Schopenhauer's philosophy. Schopenhauer was a German philosopher who was deeply influenced by Immanuel Kant:

(Brief commentary on the above: The Schopenhauerian progression in "Tristan and Isolde" can be seen as an artistic exploration of the human experience and the underlying Will, which is related to the realm of noumena in Immanuel Kant's philosophy. The opera delves into the deep emotional and metaphysical aspects of human existence, providing a glimpse into the world beyond mere appearances or phenomena.)

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And now, let us take a quick look at Henri Poincaré's worldview and then use it to gaze at the realm below the PLANCK LENGTH:

Henri Poincaré (1854-1912) a French mathematician, theoretical physicist, and philosopher of science, however, revised Kant's view in a more optimistic direction. He believed that while we may not be able to directly access the noumena or unobservable entities postulated by scientific theories, we could still indirectly gain knowledge about them through the study of their relations or structure. In Poincaré's structuralist view, scientific theories offer a way to describe and understand the structure of the world, even if we cannot directly observe all the entities involved.

And this brings us to a very intriguing aspect of Physics, the PLANCK LENGTH. What could lie below it, could Poincaré's philosophy help here?

While it's not possible to provide a definitive answer about what could lie below the Planck length from Poincaré's perspective, we can try to relate his ideas of noumena and phenomena to our current understanding of the Planck length and theoretical physics.

The Planck length (about 1.6 x 10^-35 metres) is the smallest meaningful length scale in current theoretical physics, which arises from combining fundamental constants like the gravitational constant, Planck's constant, and the speed of light. At or below this length scale, our understanding of space and time, as described by classical and quantum theories, breaks down. It is generally believed that a complete theory of quantum gravity is required to describe phenomena at such scales.

In the context of Poincaré's views on noumena and phenomena, one might argue that the Planck length represents a boundary between what we can currently describe as phenomena (our current scientific understanding of the world) and what might be considered noumena (unobservable aspects of the world that are beyond our current theoretical framework).

Since Poincaré emphasised the importance of structural relationships in understanding scientific theories, it is possible that he would have been open to the idea that a new theoretical framework, such as a successful theory of quantum gravity, could provide us with an indirect understanding of what lies below the Planck length. This would be in line with his belief that we can gain knowledge about unobservable entities through their structural properties.

However, Poincaré's views were developed in a different scientific context, and his ideas on noumena and phenomena might not map perfectly onto modern theoretical physics. The specific details of what lies below the Planck length would depend on the development of a complete theory of quantum gravity, which remains an open question in contemporary physics.

Poincaré lived between 1854 and 1912, a period that saw significant developments in mathematics and physics, but many of the key concepts and theories we now consider fundamental, such as quantum mechanics and general relativity, had not yet been developed or were in their infancy.

The concepts of noumena and phenomena, as discussed by Poincaré and Kant, pertain to the distinction between things as they are in themselves (noumena) and the way those things appear to us (phenomena). While these philosophical concepts can still be relevant to modern discussions in the philosophy of science, they might not perfectly align with the more specific and detailed concepts in contemporary theoretical physics.

For example, modern theoretical physics deals with a variety of phenomena that were not known or understood in Poincaré's time, such as the behaviour of particles and fields in quantum mechanics.