QST: Introduction
Studies of the recession rates of ancient supernova (1,2) have shown that we have been unaware of 95% of the mass and energy in the universe until the last decade of the twentieth century. We now recognize that 26 % of that mass-energy may be the source of hidden mass in galaxies and in the network they form. That leaves another 69% that might be involved with the expansion and other phenomena in the remaining 5% that is our familiar spacetime universe. The surprising drop from 100% to 5% may have been thrust on us because we had assumed spacetime is continuous and infinitely divisible, allowing points within it to be infinitely close together.
But Richard Feynman in discussing the origin of quantum electrodynamics noted that while it brought unprecedented order into quantum calculations it is not proven to be mathematically consistent. He added “perhaps the idea that two points can be infinitely close together is wrong – the assumption that we can use geometry down to the last notch is false.” (3)
And there are other indications that spacetime may be discontinuous rather than continuous. Energy has an indivisible minimum, the quantum of energy; radiation is quantized into photons. Elementary mass particles also appear quantized: they cannot be infinitely close together and their mass is indivisible. These different types of quanta populate the material universe. The expectation that the spacetime containing them should be quantized too is the basis for Quantized Spacetime (QST).
In QST spacetime quanta are spherical and packed into a tight spacetime matrix. Elementary particles move freely from quantum to quantum across their points of contact. The quanta are packed randomly, but even tight packing leaves interconnected gaps between quanta throughout the matrix. This labyrinth of gaps forms a second universe about a third the size of the spacetime universe, sufficient to hold the invisible energy recently discovered. But lack of spacetime dimensions in the labyrinth denies its bulk energy mass and gravity, making it difficult to detect.
Juan Maldevena (4) found that a dimensionless second universe in contact with a dimensioned universe like ours can acquire one time and two surface dimensions from the first across their mutual boundary. Mark van Raamsdonk used this technique to investigate relationships between quantum field theory and gravity. His findings (5) hinted at existence of spacetime quanta: the degree of quantum entanglement in his model influenced the formation of individual spacetime fragments.
General relativity and quantum mechanics can agree that the minimum length for holding one bit of information may be the Planck length of 1.63 x 10-35 meter (6). I suggest this defines the diameter of the spacetime quantum. Dividing this length by the speed of light yields a minimum quantum time of 5.39 x 10-43 second, the Planck time. As a repeating time interval within a spacetime quantum this provides the passage of time. I assume the quantum dimensions are rigid to the forces of the standard model but shrink in the direction of a gravitational field, while keeping the speed of light constant. Being responsive to gravity ensures that space and time within the matrix have a dynamic form, changing as energy, stars and glaxies move through it.