The concept of "quantum space" and "quantum time" arises when we try to reconcile the principles of quantum mechanics with those of general relativity. The challenge is that while quantum mechanics describes the behavior of the smallest particles in the universe, general relativity deals with the large-scale structure of the universe, including the behavior of gravity. When we try to apply quantum mechanics to the fabric of spacetime itself, we encounter problems, leading to the search for a theory of quantum gravity.

Carlo Rovelli, a prominent physicist in the field of loop quantum gravity, has made significant contributions to our understanding of quantum space and time. As you mentioned, he suggests that there is a limit to how much we can divide space. This smallest possible length is known as the Planck length, approximately \(1.6 \times 10^{-35}\) meters. At scales smaller than this, the very notion of "space" as we understand it breaks down. Similarly, the concept of time as a continuous flow might not hold true at these scales.

Now, regarding the "quantum of time": If we were to consider the Planck length as a fundamental unit of space, it's tempting to think of the time it would take for light (the fastest thing in the universe) to travel this distance as a fundamental unit of time. Using the speed of light \(c \approx 3 \times 10^8\) meters/second, the time it would take for light to travel a Planck length is approximately \(5.4 \times 10^{-44}\) seconds, known as the Planck time.

However, it's necessary to understand that these are not "quantum" units in the sense that they arise from quantum mechanics. Instead, they are derived from fundamental constants of nature and represent scales at which our classical understanding of physics likely breaks down.

To address your question about using classical mechanics to interpret a Planck-based quantum of time: Classical mechanics, by its very nature, is ill-suited to describe phenomena at the quantum scale. The Planck time and Planck length are derived from constants that appear in both quantum mechanics and relativity, but they don't inherently possess "quantum" properties. They simply represent scales at which new physics, beyond our current understanding, might emerge.

Thus, while the Planck time might serve as a natural "quantum of time" based on the Planck length and the speed of light, it's essential to approach this idea with caution I suppose. The true nature of time, especially at quantum scales, remains one of the most profound mysteries in physics.

Regards

At the end of the first half of the 20th century Werner Heisenberg and others tried to determine the natural metric of space with the help of the size of the smallest wave length and the smallest particles. So they concluded that the metric must be near 1 x 10-15 m. It was not a new idea because about 500 BC the ancient Greek philosopher Parmenides of Elea described the same concept.

That the metric of the minimal length scale exists can be derived with the help of the Planck-Einstein relation. The metric is about 0,486 x10-15 m because the latest experiments show that the radius of a proton is ≈ 0,73 ± 0,17 fm. The consequence is that the constant of quantum time must be ≈ 2,38 x 10-24 second.

The Planck units are derived with the help of Planck’s constant and the gravitational constant G. The use of the gravitational constant is speculative because it denies the unification of the 4 main forces. That means that all the 4 main forces are manifestations of 1 basic force so the differences are caused by the influence of the different configurations of energy concentrations.

The gap between the Planck length and the minimal length scale is about 1020 and that is enormous. So if someone wants to use the Planck units he/she must explain why there are no energy configurations in between both length scales. That is why Planck’s paper about the Planck units was quite obscure for most theorists. However, the Standard model of elementary particles needs the Planck length otherwise the quark/gluon model cannot fit within “physical reality”. Because the measured asymptotic freedom - the imposibility to "split" particles even further (the end of reductionism) - is at about the same scale size as the minimal length scale.

With kind regards, Sydney

Μr Alessandro Rizzo,

Still, we have to consider that SR holds at these scales, since it is a keystone of modern physics i.e mass energybequivslence. Hence, the light constancy inspired definition of Planck time is not so naive..

But i also think the physics of information (Shannon is the unit) might play a crucial role here, since at these scales causal set quantum gravity surfaces mediate energy processes who give rise to time as a out of sub-scale oblivion.. In which sub-scale there is no priviledged variable that acts as time. So time must be defined as the result of a process in which a now macroscopic system choses a variable that acts as time..

“…Time needed to travel a Planck length as a definition of quantum of time?

…..What is quantum space, and what is quantum time?This is, in fact, the problem we call quantum gravity. ….”

- time interval needed to travel a Planck length, lP, is the Planck time, tP, however both these intervals fundamentally cannot be, and so aren’t, some “quantum of space” and “quantum of time”. As that is rigorously proven in the 2007 Shevchenko-Tokarevsky’s “The Information as Absolute” conception, recent version of the basic paper see

https://www.researchgate.net/publication/363645560_The_Information_as_Absolute_-_2022_ed

- actualizations of the absolutely fundamental - “Logos” set elements - phenomena/notions “Space” and “Time” in any informational system, including a system “Matter” as “space” and “time” dimensions, which compose “spacetime”, are fundamentally continuous.

More concretely, as that again rigorously scientifically shown in the SS&VT informational physical model, see

https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics, and

https://www.researchgate.net/publication/355361749_The_informational_physical_model_and_fundamental_problems_in_physics

- the Matter’s spacetime is fundamentally absolute, fundamentally continuous, fundamentally flat, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct), where the ultimate base of Matter – the (at least) [4+4+1]4D dense lattice of primary elementary logical structures – (at least) [4+4+1]4D binary reversible fundamental logical elements [FLE], is placed.

Really everything in Matter is/are some specific disturbances in the lattice, which always constantly propagate in the lattice in (at least) 4D space with metrics (cτ,X,Y,Z) with 4D velocities that have identical absolute values be equal to the standard speed of light, c, [boldmeans 4D vector], what is determined by the main parameters of FLE, i.e. “FLE size” , and “FLE binary flip time interval”, which are lP and tP, c=lP/tP.

All that has fundamentally no any relation to the ‘quantum gravity problem”, which really exist because of that in mainstream physics the GR is standard Gravity theory, which is based on fundamentally wrong postulates that gravitational objects/events/effects in gravitationally coupled systems are determined at interactions in systems “mass-spacetime-mass”; what is fundamentally impossible by scientific definitions of “space” and “time”.

The really transcendent GR postulates were formulated because of in mainstream philosophy and sciences, including physics, including for the GR author, all really fundamental phenomena/notions, first of all in this case “Matter”– and so everything in Matter, i.e. “particles”, “fields”, etc., “Consciousness”, “Space”, “Time”, “Energy”, “Information”, are fundamentally completely transcendent/uncertain/irrational,

- and this completely transcendent passage

“…We learn that there is a limit to the divisibility of space. Below a certain scale, nothing is accessible, or as the Rovelli puts it, “More precisely, nothing exists there”…”

- is a next example. Again, space and time are continuous and below “certain scale”, in this case Planck scale, really FLEs exist that occupy corresponding space volumes.

Gravity is absolutely for sure nothing else than some fundamental Nature force, which is in a number of traits similar to fundamental Electric Force, more about what is Gravity [and Electric] Force see the SS&VT 2007 initial – just Planck scale and principally “quantum” - model of Gravity and Electric Forces in

https://www.researchgate.net/publication/365437307_The_informational_model_-_Gravity_and_Electric_Forces

Quantum nature of Gravity can be observed experimentally yet now, see - http s://www.researchgate.net/publication/215526868_The_informational_model_-_possible_tests ; http://arxiv.org/abs/0706.3979 at least the section 2.1.2. “Monochromatic photon beam distortion”.

Cheers

Dear Philippos Afxentiou

I wholeheartedly agree with your insights. In fact, I've developed a fundamental theorem based on the principle you mentioned. This theorem will interface with Shannon's information theory in my upcoming works. I believe you might find my recent publication on the Golden Ratio Theorem intriguing, as it delves into the framework for interchangeability and self-similarity in complex systems.

The Golden Ratio Theorem: A Framework for Interchangeability and Self-Similarity in Complex Systems.

https://www.researchgate.net/publication/370819046_The_Golden_Ratio_Theorem_A_Framework_for_Interchangeability_and_Self-Similarity_in_Complex_Systems

Your perspective on the role of information physics, especially at scales where causal set quantum gravity surfaces mediate energy processes, is enlightening. I concur that time must emerge as a result of a process, and your thoughts on a system choosing a variable that acts as time are profound.

Thank you for your valuable input!

Warm regards,

Alessandro Rizzo

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Quote: " The concept of "quantum space" and "quantum time" arises when we try to reconcile the principles of quantum mechanics with those of general relativity. The challenge is that while quantum mechanics describes the behavior of the smallest particles in the universe, general relativity deals with the large-scale structure of the universe, including the behavior of gravity."

Exact.

The reason for this dichotomy is that in 1907, Einstein and his colleagues took the decision to ignore the electromagnetic behavior of electrons in Kaufmann's bubble chamber, that was confirmed by Lorentz's analysis in his 1904 article, not even mentioning the confirming analyses of Abraham, Planck, Neumann, Bucherer and Einstein himself, because they were convinced that gravitation applied only at the macroscopic level.

Had they not had this belief, they would have taken the electromagnetic behavior of the electron at the subatomic level into account and would have eventually understood that gravity applies to all levels of magnitude.

Put in perspective in this article, with all historical formal publications put in reference, including direct links to those directly available on the Internet, which is most of them, given that they all are now in the public domain.

Article Introduction to Synchronized Kinematic and Electromagnetic Mechanics