Recent history of minimal length scale?

[arivero]

I noticed that the three seed articles about space-time quantisation are aligned in 1994.

https://inspirehep.net/literature/371960 Garay
https://inspirehep.net/literature/386329 Doplicher et al
https://inspirehep.net/literature/379391 Rovelly-Smolin

I wonder, does anybody remember why this kind of research was triggered then? Was it some new mathematical insight or technique? Or some basic paper or talk that launched the business.

 

[Vanadium 50]

I have a hard time thinking of 28 years ago as "recent", nor of 3 papers as a trend. I assume there is no answer to your question in the papers themselves or their references, so I would chalk it up to coincidence.

 

[arivero]

Only the first one from Garay cites old references on the topic, and only a two old ones that didn't start to get regular citations until this year (1994), https://inspirehep.net/literature/46600 Mead and https://inspirehep.net/literature/220203 Padmanabhaan, the later definitely impulsed by Sabine Hossenfelder review of the topic in 2012, https://inspirehep.net/literature/1095226.

There is an interview with Mead elsewhere where he explains that nobody was ready to take a minimal distance seriously. So 1996 could be a coincidence but of a different tone, the moment that the discoveries from String Theory, Non Commutative Geometry and Loops make the idea palatable for the audience.

By the way, the motivation to look now into this is the recent public demolition, by Sabine, of a paper arguing very hand-wavy about relations between gravity and quantisation; I was trying to compare the old arguments with the one given in the old physicsforums thread
https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/, that I uploaded to https://arxiv.org/abs/gr-qc/0404086 . What I find a bit puzzling is that the idea of "Kepler Length" does not extend to General Relativity, as it has not a covariant presentation. So Compton Length only emerges in the non-relativistic limit.

 

[Hengri]

The Planck-Einstein relation: E = h f and c = f λ [λ = wave length].
It shows that the wave length is the only non-constant. That is remarkable because the equation represent physical reality. So how is it possible that the wave length isn't a multiple of a constant of length (the minimal length scale). Moreover, electromagnetic waves arrives from everywhere, thus the constant of length is directly related to the unit of quantised space. Or better, it shows the structure of the basic quantum fields.

 

[ohwilleke]

By the way, the motivation to look now into this is the recent public demolition, by Sabine, of a paper arguing very hand-wavy about relations between gravity and quantisation;

To be clear, Sabine wasn't demolishing the concept one way or the other, she was demolishing a truly crappy paper making that argument.

 

[arivero]

Nobody should be confused about that, but it is not bad to stress the point. As mentioned before, she is the author of one of the main reviews on the topic, https://link.springer.com/article/10.12942/lrr-2013-2

 

[Hengri]

Nobody should be confused about that, but it is not bad to stress the point. As mentioned before, she is the author of one of the main reviews on the topic, https://link.springer.com/article/10.12942/lrr-2013-2

The concept of quantised space originates from Parmenides of Elea, a Greek philosopher and mathematician who lived about 500 BC. He is the "father" of the ontology in philosophy and he strongly influenced philosophers like e.g. Plato and Aristotle. He reasoned that motion isn't possible without an underlying creating reality. A bit comparable with our "modern" interpretation of quantum fields. Most of Parmenides' work is lost, what we know is what other philosophers in ancient Greece wrote about him. His model of the universe as an enormous volume has a metric and one of his arguments with other philosophers is that real emptiness cannot exist in the universe. There is some uncertainty about the origin of the word "atom" because Parmenides' model suggests the existence of units that cannot be divided any more, although the units can change their shape (like a flame). In the ancient Greek language the word atom has not the meaning of "rigid".

The paper of Sabine Hossenfelder describes a short history about the search for the metric of the universe. In the first half of the 20th century Heisenberg, Moglich, Goudsmit, etc. tried to find a metric with a size of about 1 x 10^-15 m. Partly to solve the infinities and partly because there must be a related minimal wave length of electromagnetic radiation.

As far as I know it was Gerard 't Hooft who advertised the Planck units (about 1985-1990). Before, it was thought that the Planck units were quite obscure. Because the electromagnetic field is a term for the universal electric field and its correponding magnetic field. So Planck used the Planck constant for his derivation of the units but not the related vectors of the magnetic field. Instead he used the gravitational constant without showing the direct relation. Moreover, someone has to elucidate why there is the enormous gap of 1 x 10^20 between the Planck length and the minimal length scale of about 1 x 10^-15 m. His paper was really speculative. So maybe it was 't Hooft who inspired others to publish about the minimal length scale a couple of years later (the papers on top).

There is another aspect about the quantisation of space because Einstein's concepts of space and time ("spacetime") are absolutely not comparable with Newton's axioms (space and time as a continuum). For Einstein space and time are just "tangible" phenomena. For Newton space and time have an ontological meaning, comparable with Parmenides' thoughts about the universe. (Einstein was influenced by Ernest Mach, the Austrian philosopher/physicist, who advertised that everything that is not "tangible" must be ignored). Einstein had the bad habitude to use terms without much insight in the concepts (like time is what the clock hands show).

 

[mitchell porter]

The concept of quantised space originates from Parmenides of Elea ... He reasoned that motion isn't possible without an underlying creating reality ... His model of the universe as an enormous volume has a metric

Are you the only person who thinks this? The usual interpretation of Parmenides is that he denied the reality of change and emphasized the Oneness of all things.

 

[Hengri]

So you think that Parmenides as a famous mathematician who calculated the orbits of the then known planets of the solar system denied the reality of change? See "A Model of the Cosmos in the ancient Greek Antikythera
Mechanism" (Nature scientific reports: https://doi.org/10.1038/s41598-021-84310-w).

There is a difference between absolute reality and relational reality (phenomenological reality). Absolute reality envelopes relational reality but not the opposite. The universal conservation laws (energy and momentum) and the 2 universal constants (quantum of energy and the speed of light) describe relational reality, the dynamical part of the universe (that is what physics is about). Parmenides model is about absolute reality and he stated that the observable dynamics of the universe originate from the "underlying" part of absolute reality. What he describes is nowadays comparable with a type of self generating fractal. A nice article about this type of concepts is from Fotini Markopoulou (https://arxiv.org/abs/1201.3398).

 

[Nugatory]

This thread has drifted far from its original topic and is no longer connected with any sort of empirical science, so is closed as off-topic for PhysicsForums.

As with all thread closures, it can reopened for further discussion of the original post.