Quantized Spacetime
By Rex Pay
Introduction
An alternative view of the universe comes into view when space and time are considered as quantized rather than being continuous, as is usually assumed. Quantization provides a different account of the material contents of the universe and the forces acting on them. For example, quantized spacetime (QST) finds that the unknown gravity that speeds the rotation of galaxies comes not from dark matter but from empty space, and that nothing goes into a black hole, being stopped at its surface by a spherical shell of photons nourished by more coming from its accretion disk.
This alternative view acknowledges much of general relativity, quantum electrodynamics and chromodynamics, and known universal constants. But it treats space and time as having an ultimate smallest size, as mass and energy do. It is based on a successful line of thinking initiated by Leucipus and Democritus in the Sixth Century BCE. Leucipus claimed matter is formed from a set of uncuttable atoms, that is quantized. They were moving in a void, empty space, which was their source. His follower, Democrates, used this atomic theory to explain how all the substances in the world could arise from a few simple atoms. Even other stars and planets might exist, populated by other civilizations.
Importantly, regarding spacetime as quantized rather than continuous gives some insight why it took till 1998 to find we had overlooked 95 % of the mass-energy of the universe (1,2). The new perspective came from measurements of the rate of recession of distant nova. This led to recognition that beyond the 5% we thought was the whole universe, 25% appears to provide invisible extra mass found in a cluster of galaxies by Fritz Zwicky in 1932 (3) and by Vera Rubin in individual galaxies in 1980 (4). The remaining 70% has not been identified. It may be involved in expansion of the universe.
The Quantum
At present, we view all matter as made up of families of quarks, electrons and neutrinos, which emerged at or shortly after the appearance of continuous spacetime. These are fermions, uncuttable elementary particles that combine in various ways to produces protons, neutrons, atoms, molecules, and chemicals. All the materials in the universe. In a comparable way, physical forces and the radiation associated with them also emerged as uncuttable elementary particles, known as bosons, such as the photon and the two particles carrying the weak force.
Matter and radiation are all quantized. This understanding began with Max Planck’s discovery early in the twentieth century of the smallest piece of energy a particle of light could carry. He called it the quantum of energy.
If space and time are quantized in a way that matches their elementary contents, there will be a limit to their divisibility, so that one can ultimately find the smallest pieces of space and time. These spacetime quanta may be surrounded by an intriguing region where space and time no longer exist.
Space-time and Spacetime
We have found, largely through Einstein’s development of relativity, that space and time are not independent of each other but are inseparable in a combination referred to as space-time. We have an instinctive recognition of this from our experience whenever we move. There is no instantaneous jump from one place to another. We always move through both space and time, with the two intervals moved being related by our speed of movement.
Currently, we assume that space and time are continuous and infinitely divisible. This implies that infinitely small objects can be infinitely close together. We find that elementary particles of matter behave like points that have position but no diameter or length. But if we assume they can be infinitely close together, we find calculations of their properties can give non-sensical answers, such as infinity or probabilities larger then one.
Richard Fynman noticed that. He questioned this assumption as threatening the legitimacy of the renormalization process essential in getting rid of unwanted infinities in quantized electrodynamics. (He received a Nobel prize as a co-inventor of this.) In 1985 he wrote ". . . perhaps the idea that two points can be infinitely close together is wrong . . . If we make the minimum possible distance between two points as small as 10-100 centimeters . . .the infinities disappear, alright -- but other inconsistencies arise, such as the total probability of an event adds up to slightly more or less than 100%, or we get negative energies . . . " (4A). Quantization of space and time removes such difficulties.
So what is proposed here is the quantization of continuous space-time: the replacement of continuity with a universal matrix of the smallest uncuttable elements of spacetime (no hyphen in QST). The joined space and time components in a quantum are related by the speed of light.
Spacetime Matrix
Quantized Spacetime must provide the symmetries in space and time required to meet energy and momentum conservation laws (5). Over large distances QST must impose no preferences on the location or direction of movement of elementary particles and fields of force like gravity, electromagnetism and the weak and strong forces. For this reason, quanta of spacetime must be uniformly spherical and tightly packed into a random spacetime matrix. Spherical to provide the same path length across the quantum in any direction; random because symmetrical packing of spheres would produce regular but different path-lengths in different directions. Even tight packing leaves spatial gaps between particles, which is helpful for waves traveling with moving particles. But randomness means we can only predict the probability that a moving particle will arrive at any specific place. This is similar to the situation in quantum electrodynamics.
“Does this mean that physics, a science of great exactitude, has been reduced to calculating only the probability of an event, and not predicting exactly what will happpen? " asked Richard Feynman. His answer was, “Yes. That’s a retreat. . . but that’s the way nature is. . . Yet science has not collapsed.” (6 ). The viewpoint in quantized spacetime is that the randomness in packing of spherical quanta is essential to a universe providing biological evolution. And it must be truly random to prevent biasing that evolution in a particular direction.
The random matrix is not a mathematical coordinate system, it is the physical 'landscape' of spacetime. It may be described by various types of coordinate system, just as one can choose between coordinate systems for mapping Earth. For example, with different coordinate systems, one can show that North and South Poles exist, another can show that they do not exist. Fortunately, the coordinate system has no physical effect on objects, from elementary particles to stars and galaxies.
Spacetime Quantum Size
To find the size of the spacetime quantum, you need to specify how to recognize it. One approach is to define the quantum as the smallest piece of space able to hold one bit of information (7). Our two recognized theories describing the universe approach this idea from opposite directions, based on particle mass. Relativity sees a black hole radius increasing as the mass of the hole increases. Quantum mechanics sees the length of the wave traveling with a particle decreasing as the particle mass increases. Calculation shows the two theories meet near the Planck mass of 2.18 x 10-8 kg, where both lengths for the minimum aspace are very close to 1.616 x 10-35 meter, the Planck length. As the diameter of a sphere, this becomes the length across a spacetime quantum. Dividing the quantum length by the speed of light gives the quantum time interval: 5.391 x 10-43 second, the Planck time.
In the absence of gravity, a spherical quantum and its surrounding gaps in the matrix occupy about a cube of space whose side is the Planck length. From this, the volume occupied by a quantum is 4.22 x 10-105 of a cubic meter. The number of quanta in a cubic meter is 2.37 x 10104. The number in the visible universe is about 10185. With such minuscule dimensions, spacetime quanta have escaped detection, even though their numbers are legion.
In QST elementary particles move from quantum to quantum at a speed equal to the quantum diameter divided by the transfer time. The speed of light sets an upper limit. A particle with energy but no mass, a boson like the photon, requires just one Planck time interval per transfer. A fermion with mass, like an electron, moves slower and requires several time intervals.
The spacetime quantum, having no other dimensions (such as mass, electrical charge, spin, or quark color) conserves the intrinsic dimensions of elementary particles within it.
Gravity
Gravity appears when a mass particle enters a quantum. The action of mass is the opposite of the tension acting as a negative pressure keeping a quantum spherical in dimensionless energy. Mass causes a quantum to shrink. In a population of empty quanta, a uniform mass appearing in one quantum would cause it to shrink radially. The pressure of tight packing causes surrounding quanta around it to undergo a compression that will decrease radially in an inverse square law from the center of the quantum with mass. No gravitational field. Just the rearrangement of space at the speed of light by mass.
Put two mass particles in two different quanta separated by empty quanta and the doubled shrinkage between them will cause them to move together. The rest of general relativity probably follows, without aid of a boson carrying gravitational energy from place to place. In quantized, spacetime, general relativity and quantum mechanics can be integrated.
The Second Universe
Spherical quanta allow elementary particles to move freely from quantum to quantum across their points of contact, even though maximum packing distributes the contacts randomly across sphere surfaces. Outside of each quantum and its contacts is a gap between other quanta. It is part of a labyrinth of gaps throughout the tightly packed matrix. This labyrinth forms a second universe about a third the volume of the spacetime universe, sufficient to hold electromagentic and other waves and the invisible energy recently discovered from nova measurements. The lack of spacetime dimensions in the gaps denies the bulk of the energy mass and therefore gravity.
Juan Maldevena (8) discovered that a dimensionless second universe in contact with a dimensioned universe like ours could gain one time and two surface dimensions from the first across their mutual zero-thickness boundary. In quantized spacetime the boundary is the surface of quanta. Maldevena considered two different universes in contact in continuous space-time. One was like our own with gravity, particles, time and three space dimensions. The other was without gravity but had particles, time and two surface space dimensions. The interaction of the universes across their common interface enabled study of quantum effects with and without gravity.
Mark van Raamsdonk (9) used this technique to investigate relationships between quantum field theory and gravity. His findings hinted at existence of spacetime quanta: the degree of quantum entanglement in his model influenced the formation of individual space-time fragments. In QST, the fragments are spacetime quanta.
Quantized Early Universe
The prexistence of bulk energy with no spacetime dimensions and therefore no boundary is assumed in QST. From this perspective, the QST quantum is a bubble within bulk energy. Such bubbles might emerge at the beginning of the universe as a phase change in the bulk. This is comparable to the emergence of ice crystals when water freezes. To obey the law requiring conservation of energy, the bubbles will contain the bulk energy they displace. Entering the spacetime quantum, this energy gains space and time dimensions and so becomes a particle with mass, M = E/c2.
As the precipitation of spacetime quanta continues, groups become bound by their mutual gravity and their time pulses become synchronized by a cooperative process. Growing clumps combine, forming the seeds of galaxies, and eventually the expanding quantum matrix reaches the size of the visible universe. If the expansion is fast enough, the universe will be homogeneous in all directions, as appears to be the case. In general, the evolution and distribution of collections of mass and radiation particles follow that described in continuous spacetime. Differences appear at the scale of black holes and galaxies.
QST Black Shells
Buried in dimensionless energy, quanta surfaces are initially circular as a result of a tension in their surface. In the gravitational collapse of a star, its material forms into a massive spherical object that generates a spherically uniform gravitational compression against the tensions of the quantum spheres. The compression wins and the star matter shrinks into a spherical ball. To maintain spherical symmetry, a series of concentric spheres of spacetime-quantum shells forms. These shells decrease in thickness as the center of star matter is approached and the gravitational field rises. The diameters of individual quanta in a shell shrink in the direction of the center of mass.
At the compression intensity of a black hole surface, the quantum radial length shrinks to zero and the quantum becomes a circular disk with three instead of four dimensions. To achieve this the final compression intensity breaks up fermions into bosons in the form of photons moving at the speed of light. The crushed matter must reach the emerging fully-collapsed object at the speed of light because the object’s escape velocity is the speed of speed of light. The two velocities must be equal to maintain conservation of energy.
Stages in the crushing process can be seen around a black hole with an accretion disk. This disk crushes elementary particles together about 40 times more efficiently than nuclear fusion. This intensity will be exceeded in the sudden radial shrinking of the mass of an entire star.
Photons produced in the accretion disk during break up of hadrons (combinations of fermions and bosons) move to a photon ring around the blackhole. In turn, the ring feeds a fraction of its photons to the black hole where they arrive tangentially to the black hole surface (event horizon), adding to the existing photons.
A black hole, or black shell as it is in quantized spacetime, may be formed initially by complete collapse of a star five times the mass of the sun. In continuous spacetime that mass enters into the black hole and disappears through an aperture the size of a spacetime quantum. In quantized spacetime the mass remains in spacetime, as photon tracks spread throughout a spherical shell of spacetime quanta at the event horizon. Knowing the mass of the shell and its radius, the number of photons in the shell can be calculated. Combined with the mass that each photon provides to the shell (from the E=Mc2 equation) the formula for the temperature of the shell can be found. It is identical to the one accepted in continuous spacetime.
Galaxy Virtual Mass
The bulk energy within spacetime lacks the dimensions of spacetime: no length, breadth, height, or time. These dimensions are on the other side of its interface with the fermions and bosons of the spacetime universe. Within the bulk universe, the spacetime quanta appear as bubbles, their areas of contact providing a zero-thickness interface between the bulk and spacetime. This shared surface with two space dimensions and one time dimension allows interaction between spacetime and bulk energy.
If a particle is within the quantum, it has the spacetime dimensions of the quantum. If the quantum is empty, two spatial dimensions and one time dimension reach the local bulk surface, converting its local surface energy into surface mass , in accordance with the Einstein equation M = E/c2. Since we associate mass as being carried by an elementary fermion, mass formed without a fermion is a virtual mass.
Its gravitational field radiates into spacetime, combining with the fields produced by fermions in spacetime. In their trillions of trillions, these minute surfaces of virtual mass can supply the invisible extra mass detectable in galaxy clusters and in galaxies. Hitherto this extra mass has been attributed to dark matter particles. But no dark matter particle has been found, and the conclusion is increasingly put forward that dark matter is neither dark nor is it matter. Of course it’s not; it’s virtual mass.
References
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2. S. Perlmutter, M. S. Turner, and M. White, Constraining Dark Energy with Type Ia Supernovae and Large-Scale Structure. Phys. Rev. Lett. 83, 670 – Published 26 July 1999
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5. E. Noether, Invariante variationsprobleme. Nachricten von der Gesellschaft der WissenSchaten zu Gottingen. Mathematisch-Physikalische Klasse. pp. 235-257 (1918).
6. R. F. Feynman, The Strange Theory of Light and Matter. Princeton University Press, 1985.
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12/28/2022