The utterly fantastic success of Mathematical Analysis (the mathematics of continuous functions of continuous variable) as applied to physics and engineering, tends to blind us to the possibility that the ultimate nature of space and time might be discrete. It is enlightening to recall the resistance of prominent physicists, such as Mach, to the atomic theory. But there is a simple reason why a discrete system can be well modeled by Mathematical Analysis. Completely discrete space-time-state physics, where quantities such as momentum, angular momentum and energy are also discrete, and where those same quantities are conserved (perhaps exactly, as is obviously true of electric charge) will exhibit symmetries, asymptotic to continuous. (A consequence of Noether’s Theorem). As a result, the gross behavior of such microscopically discrete space-time-state systems will be asymptotically well modeled by mathematical analysis. Today, we know that electric charge, angular momentum, matter, photons etc. are discrete, but it’s hard for almost everyone to imagine that space and time could be also be discrete. The major stumbling block is the mathematical beauty and simplicity of the assumption of translation symmetry… along with the absence of any experimental evidence to the contrary. However, I am certain that translation symmetry is an informational impossibility!
Comments
Fortunately the advance of visualisation software has opened up possibilities for new ways of thinking about mathematics. As an example, some wonderful explanation of number systems and more from 3Blue1Brown’s channel on youtube.com (e.g. https://www.youtube.com/watch?v=F_0yfvm0UoU).
On February 11, 2016, a powerful new weapon was handed over to digital philosophers but it appears to have been unrecognized. On that day, discountenancing the speculative aspects of the causation or underlying theory, the Advanced LIGO team essentially announced the observation of a stretching and shortening of the 4 km length between the mirrors of an interferometer arm.
The speculated cause and underlying theory can be referred to in the links below.
From the LIGO News Release http://www.ligo.org/news/pressreleases.php
“At each observatory, the two-and-a-half-mile (4-km) long L-shaped LIGO interferometer uses laser light split into two beams that travel back and forth down the arms (four-foot diameter tubes kept under a near-perfect vacuum). The beams are used to monitor THE DISTANCE between mirrors precisely positioned at the ends of the arms…”
Physical Review Paper http://journals.aps.org/prl/pdf/10.1103/PhysRevLett.116.061102
“Each arm is formed by two mirrors,.. A passing gravitational wave effectively alters the arm LENGTHS… This differential length variation alters the phase difference between the two light fields returning to the beam splitter…”
What is unambiguously reported is a stretching and shortening of the line between mirrors. Nobody is measuring spacetime. Whether a spacetime theory, black holes, MECOs or a gravitational wave passing is responsible for what was measured is a matter for separate contemplation and is distinct from and should not be mixed up with what was actually measured.
Apart from a line now announcing itself to exist as a physical thing and not just a mathematical fiction or concept, the alternate variation in length about the mean 4km, suggests that it has stiffness. The paper’s authors use Strain in their analysis which is Extension/ Unit length and got 10-21, making the alternate lengthening and shortening above and below the 4km length to be about 10-18m.
An opportunity has therefore arisen for digital philosophers to mine this experimental observation that: a line can respond when stimulated.
If a line can alternately shorten and lengthen then it is a physical thing, and not merely a relational concept. By definition, anything that can be acted upon and can move has a substantial reality.
If a line contains an infinite number of points, it cannot be lengthened or shortened when stimulated because either way it will still contain an infinite number of points (zero dimensional). On the other hand, if a line is not infinitely divisible but contains a finite number of points which would then be non-zero dimensional, it can be lengthened and shortened due to an increase and decrease respectively in the number of points therein.
In physics today, we have the ‘relationists’, who believe that Space is just a concept, infinitely divisible and made up of zero dimensional points and the ‘substantivalists’, who hold otherwise and hold that there is a finite limit to the divisibility of space. Most digital philosophers belong to the latter.
If this LIGO finding is correct who has won and who has lost?
The winners will include:
Einstein (a part of him): “…space is endowed with physical qualities” (in his Leiden address); A line responded to stimulus and LIGO has shown that the line is endowed with physical qualities and has a measurable stiffness that make it capable of stretching and contracting.
Newton: “…it is clear that they (philosophers) would cheerfully allow extension (space) to be substance, just as body is, if only extension could move and act as body can”; “…space is capable of having some substantial reality. Indeed, if its parts could move…”. (in De Gravitatione). A line moved. He also has won.
Those who have lost are the Relationists. A line held as nothing, but a relational concept can be continuous and can be infinitely divisible. But it cannot respond to stimulation by lengthening and shortening as there can be no variation in the infinite number of points constituting it.
More on this later, if necessary.
Regards.
The argument that the ‘ultimate nature of reality is discrete’ is supported by many experiments that are not well explained with the current assumption that we live in an objective reality. An example is the double slit experiment. Its become the consensus in the physics community that the results of this experiment are simply weird and can not be explained. However if we adopt a model of reality that is based on information and computing then the results of this experiment are well explained.
Not only is space and time discrete but also the mind (i.e. consciousness ). Understanding the nature of reality ultimately comes down to perspectives at the individual level (then as a society). Perspectives are typically localized to once experiences and environment. To understand the discrete nature of reality one needs a non-local perspective. A person’s perspective is usually related to the quality of the mind which is measured by its entropy ( lower entropy mind computes efficiently). If a mind is at a low entropy it can access variables outside of the local scope allowing it to perceive the non-continuous nature (discrete) of reality.
In any case the digital philosophy is a better model than the one we have now and we as a society will come around to this understanding as we evolve.