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                                     Quantized Spacetime

By Rex Pay

  1.    Introduction (Below)

  2.    Summary

  3.    Quantized Spacetime (QST)

  4.    Singular Waves

  5.    Expanding Universes  

  6.    Black Shells

   7.     Appendix 1. Black Shell Temperature              

   8.     Appendix 2. Twin Slit Experiment             

1.  Introduction       2302

95% of Universe Hidden

In 1998, two teams of astronomers made a momentous discovery when measuring how fast distant galaxies are moving away from us. Their measurements indicated   we had overlooked 95% of the energy in the universe. That is like suddenly finding the Earth’s population is not 8 billion but 160 billion, without knowing where the extra 152 billion are hiding. Cosmologists, who study the nature of the universe, estimated it had become 69% dark energy, 26% dark matter, and 5% familiar matter and energy. 

Such a realignment in perspective suggests something may be wrong with our view of the universe. And perhaps the most sweeping error possible could be how how we view space and time.

Einstein and Makowski showed these two so-different types of dimension are an essential unity, now known as spacetime. But, as we have for millennia, we still think of spacetime as continuous. Perhaps it is quantized, like the energy and elementary particles within it. Energy comes quantized into in small indivisible amounts that cannot be divided. So do elementary waves or particles, the basis for matter and radiation throughout our 5%. Perhaps we might understand our newly acquired energy better if we think of spacetime itself as quantized. It would then match the structure of its contents.

The following investigation pursues this idea. It suggests why the universe has an amazing degree of uniformity over astronomical distances, how other universes may have formed, and why our most successful account of universes’ contents, quantum mechanics, has to deal with randomness. This leads to probabilities rather than certainties, and appears necessary because the randomness is the essential driver of biological evolution.

Personal Confession

This investigationt has not been  reviewed by experts in its subject matter in the way scientific papers usually are. At 91 my time is too sort for that. So you read it at your own risk. My background is a masters degree in electrical engineering, gained with a thesis based on of random noise in semi-conductors. There might be a bias towards randomness in the material that follows.

In quantized spacetime, that randomness arises in a universal matrix of spacetime quanta, packed tightly together. Waves travel through the matrix via random strings of quanta, each string different to all others.  To get from one randomly oriented quantum to another, a wave must often change its direction of motion. This gives the wave a random pattern of deviations as it goes through the matrix. It achieves these by small increments of momentum at right angles to its path, A different pattern of these increments is stamped on every wave moving through the matrix. There, all quantum waves are different. This has enormous consequences. It means matrix waves cannot combine and increase their energy level. Therefore they they provide exactly the right level of energy in sensitive biological interactions. In contrast, unmodified waves would automatically combine and deliver dangerous amounts of energy.

It was because waves in quantum mechanics were assumed to be perfect, and therefore sure to combine and transmit the wrong level of energy, that photons were invented. Einstein assumed photons would to deliver exactly the right level of energy throughout spacetime. Singular waves in quantized spacetime remove the need for photons as intermediaries between biological atoms or molecules. Singular waves can go straight through, from storage level in one atom to the corresponding energy level in another, or in a biological molecule. Critical information for biological interations is communicated directly by singular waves.

Sometimes a developing string of incremental momentum changes sums to a level that violates energy conservation laws. The wave is then diverted to a new track that restores its innocence. This does not last for long, because its energy is likely to be delivered to the wrong biological molecule. It has a good chance, in fact, of causing a genetic mutation. If this is benign, contributing to the genetic drift of beneficial evolution, all is forgiven. Otherwise the recipient may have gained a dangerous mutation.

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Quantized Spacetime

It is not easy to think in terms of a quantized spacetime.  We have believed for thousands of years that space and time are continuous and infinitely divisible. It usually makes our mathematics easier. But in quantum mechanics, which came into being when the quantization of energy was discovered, it soon became apparent that the electrons storing and releasing energy it atoms where quantized. This led to rapid growth in understanding interactions between atoms and molecules, which is the basis of chemicstry.

However, attempts to extend its initial approach to describe the nucleus of atoms were pestered by unwanted zeros and infinities. These occur naturally in continuous spacetime when it is taken all the way down to zero spacetime, which is essential if you believe spacetime is continuous.

The solution has been to not go all the way down to zero. Instead, a calculation is stopped at some point where the intermediate value it should produce is known from an experiment. This value is plugged in to allow the computation to continue.  This has worked very well and has produced many advances in our understanding of quantum mechanics in the atomic nucleus and beyond. But there is a suspicion that is not valid mathematics. It also looks very much as if a short piece of quantized spacetime has been slipped into the calculation. So why not go the whole hog and work in quantized spacetime from the beginning?

The contents of spacetime are already recognized as quantized. Max Planck discovered quantization in his study of the mathematics of iron’s color change as its temperature rises. The change takes place in small steps, indicating that the energy level producing the change moves in steps, not in a smooth continuous rise. It is as if a new brick of energy is put in place each time the temperature rise exceeds a certain value. Planck’s experiment demonstrated that energy was quantized, opening the way to development of the science of quantum mechanics.

We now know that all the elementary particles that make up the universe are quantized, They are not continuous and infinitely divisible. Every quark is identifiable by its specific mass as a quark. Every electron is identifiable by its mass as an electron. They and other elementary packets of energy and momentum cannot be cut into smaller pieces. Each one is quantized.

Spacetime Quanta Spheres

To house or guide quantized energy and matter throughout the universe, spacetime is likely to accommodate them by also being quantized. I suggest spacetime will be made up of the smallest indivisible spheres (for local symmetry) of empty spacetime, each able to hold, or transfer to another quantum, a particle or wave of energy. The sphere provides a quantized container for the contained.

To provide the contained with an environment that does not favor a particular direction of travel (global symmetry) the spacetime quanta must be tightly packed into a predictable but random matrix, so that there is an established spacetime relationship between individual quanta. From the experience in quantum mechanics that random variations in energy and matter intrude throughout spacetime, these spherical quanta appear to indeed have been tightly packed. At random, of course.

The randomness of the matrix will become apparent at very small distances, in sub-microscopic regions of the quantum matrix. But over distances significant for sentient species, random deviations are found to be calculable as meaningful probabilities. The contained will be able to move in a calculable way throughout the universe. And the random matrix will make any large part of the universe very much the same as any other part, an essential feature of the universe we observe.

The Idea of Quantization

The idea that matter is quantized was put forward by Leucippus and Democritus in Greece, about 2,500 years ago. They argued that objects making up the amazing variety of tangible things in the world could be cut into smaller and small pieces until a few uncuttable objects would be reached. In different combinations, these uncuttables (Atomos in Greek) would provide all the variety of objects we find around us.

We have since found that there just over 100 elementary atoms that provide the basis for chemistry. Within these atoms we have found electrons, protons,  neutrons, neutrinos, and few other related particles. Protons and neutrons, in turn, were found to be combinations of simpler particles: quarks and gluons. The neutrino and electron remain indivisible. The possibility might still be open to find some quantized thing even smaller than a spacetime quantum. But first we need to understand the behavior of quantized spacetime quanta and their contents. This might even reveal how massive amounts of energy can be hidden. 

The Importance of Being Quantized

When we investigate the effects of quantizing spacetime, we discover the randomness in quantum mechanics is not an arbitrary nuisance that puzzles quantum mechanics. It has an essential role in the genetic drift of biological evolution and in the evolution of the material universe. Randomness in the spacetime matrix has much to do with everything. But gives future events a certain degree of probability rather than certainty. And it is no shrinking violet. It presents itself for viewing to anyone who looks at the famous twin-slit experiment as an introduction to quantum mechanics.

This is a an experiment that Richard Feyman has described as showing  "a phenomenon which is impossible […] to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery [of quantum mechanics]."

So, here it is: the heart of quantum mechanics, as displayed in both continuous and quantized spacetime.

The Twin Slit Experiment

Figure 1 Shows the cross-sections of a collimated beam of atoms at various intensities, after the beam has been divided by two parallel vertical slits.

Figure 1. Outputs from a twin slit experiment carried out in continuous spacetime using a collimated beam of electrons shows the same development in quantized spacetime when the intensity of the electron beam is successively raised.

The behavior of collimated electrons at low intensities in continuous spacetime, after passage through two slits, is indicated in the first picture (b). After moving a short distance, each electron impacts a sensitive molecule in a photographic plate. This  emits a flash of light, showing where the electron hit the plate. The electrons are moving like particles along tracks that are no longer collimated but have a degree of randomness.

As the intensity of the beam is increased by raising the number of particles delivered to different levels (c,d,e), the electron pattern on the screens begins to show an emerging pattern of waves. Within the random matrix there are now sufficient waves to interact with each other. These form a pattern of standing waves with peaks and troughs at specific locations. The electrons flow through this stationary pattern, clustering and separating in unison as they pass through rise and fall.  The stationary wave pattern becomes increasingly distinct as the number of electrons increases.

This behavior caused Nils Bohr to conclude that in quantum mechanics a quantum of energy, as in an electron, when moving can display two different properties  when it passes through spacetime, depending on the nature of the experiment. It has a duality that enables it to be either a particle or a wave, depending how an experimenter decides to adjust the particle intensity. And that this duality is a distinctive quality throughout quantum mechanics.

 Quantized spacetime views electrons as singular waves, not particles. The first picture (b) shows the electron waves distributed sparsely in the section of the spacetime matrix being observed. If the electron waves were uniformly spaced at initiation of their beam, they will be randomized rapidly by the matrix. In the first screen the location of a few of the random tracks available to the waves can be seen.  The later screens show that electron energy is carried by singular waves that do not combine. Instead they interact in wave fashion to form a stable interference pattern of concentration and dilution at specific distances (details are in Appendix 1). For quantized spacetime’s singular waves there is no duality. They remain as wave and do not change into particles (photons).

 Biological interactions between atoms and molecules make use of electromagnetic singular waves. These can be circularly polarized. Amongst other things, this allows the increments of momentum required to get through the matrix to be summed to detect violation of conservation laws.

Through the Random Matrix

To meet requirements of recognized symmetries throughout the universe,  individual spacetime quanta are tightly packed into a random matrix that provides three dimensions of space and one of time. A singular wave carrying a packet of energy from an atom to a biological destination will travel through a string of spherical quanta via contacts where quanta touch. These contacts are rarely arranged in the exact direction of travel initiated by the originating atom. So the wave will be forced to make small random deviations, involving small changes  in momentum as it moves from quantum to quantum.

Sometimes it will go completely off the original track established by its original momentum, miss its target molecule, modifying instead some unintended molecule. This can be a source of random mutation if an RNA or DNA molecule is the one modified. Over a period of time, such random deviations make an essential contribution to species evolution by genetic drift.

In fact, the random matrix is the source of many different random events that occur both in an organism and in its environment, contributing to random variations in the evolution of species. Understanding the processes involved is the motivation and focus for this investigation of quantized spacetime (beyond investigating the curious case of the missing 95 percent of energy in the universe).

  3/2/2024