Difference between revisions of "Eventful Universe"
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===Evolving Transformations System===
===Evolving Transformations System===
Revision as of 13:27, 25 November 2020
- 1 Full Title
- 2 Abstract
- 3 The Model
- 4 Irreversibility and Power Consumption
- 5 What Purpose do Clocks Serve
- 6 How Does Time Evolve?
- 7 Wave Function of the Photon
- 8 The one Photon Hypothesis
- 9 The two Photon Hypothesis
- 10 Summary
- 11 Appendix
- 12 References
The Event-driven Universe is a model focused on the events that happen among objects in the universe.
Thomas C. Jones
- Euclidian three space will be assumed.
- the emission of an entangled photon pair and the subsequent absorption of one of those photons.
The goal is to create a partial ordering of events and then determine if it is possible to use this partial ordering of events to create a time line that can become continuous in the limit. Each partial ordering would be local to the events and so would naturally lead to a relative time line for each locality.
Irreversibility and Power Consumption
Bennet IBM taught us that computing does not need to consume much power.
The problem with these models is that they lead to the static Wheeler-deWitt equation (Ĥ(x)|ψ> = 0) which tell us that the universe does not evolve. Many find that to be a fatal flaw of physics. It simply does not correspond in any way to reality.
Quantum computing is teaching us more about computing and about quantum mechanics, but it is not at all clear where this new knowledge is taking us. In the following we will investigate computing elements that consume something, but it is not clear what, perhaps it is the precursor to entropy. This proposition will not depend on existing knowledge, but rather just explore what is possible if are not completely bound by accepted knowledge. What is created in this endeavor is time itself.
What Purpose do Clocks Serve
How Does Time Evolve?
what about polarization? Need to accommodate linear and circular polarization of photons.
Wave Function of the Photon
It seems that all time begins with the photon, the transport of quanta of energy.
Wave function for the photon
All electromagnetic waves can be superimposed upon each other without limit. The electric and magnetic fields simply add at each point. If two waves with the same frequency are combined there will a be a constant interference pattern caused by their superposition. Interference can either be constructive, meaning the strength increases as result, or destructive where the strength is reduced. The amount of interference depends of the phase difference at a particular point. It can be shown that constructive interference occurs for phase differences of 0-1200, and 240-3600. Thus destructive interference occurs from 120-2400. For two identical waves, no phase shift results in total constructive interference, where the strength is maximum and 1800 phase shift will create total destructive interference (no signal at all).
Df = 2pDx/l Df = 2pDt/T
The phase shift that causes the interference can occur either due to a difference in path length, Dx, or a difference in the arrival time, Dt.
The idealized plane wave is actually infinite in extent. If this wave passes through an aperture, it will diffract, or spread out, from the opening. The degree to which the cropped wave will spread out depends on the size of the aperture relative to the wavelength. In the extreme case where the aperture is very large compared to the wavelength, the wave will see no effect and will not diffract at all. At the other extreme, if the opening is very small, the wave will behave as if it were at its origin and spread out uniformly in all directions from the aperture. In between, there will be some degree of diffraction.
First consider a circular aperture. If a wave with wavelength l encounters an opening with diameter D, the amount of diffraction as measured by the angle, q ,at which the new wave diverges from the opening, measured from edge to edge, will be approximated by q = l/D
Comments on this formula:
- The symbol is used to indicate an approximate result, as opposed to an exact relationship. This result is only valid for relatively small angles, something less than about 200.
- There is some ambiguity in what is meant by this angle. In actuality, the wave does not simply end at this boundary, but falls off smoothly. The exact point which defines the extent of the wave is a matter of definition and there are two standard conventions: the one used here is the ½ power or -3 dB definition.
- The factor of 2 is also an approximation. A more accurate description requires detailed knowledge about the shape of the aperture
- The angle q is measured in radians!
Photon polarization is the quantum mechanical description of the classical polarized sinusoidal plane electromagnetic wave. An individual photon can be described as having right or left circular polarization, or a superposition of the two. Equivalently, a photon can be described as having horizontal or vertical linear polarization, or a superposition of the two.
The description of photon polarization contains many of the physical concepts and much of the mathematical machinery of more involved quantum descriptions, such as the quantum mechanics of an electron in a potential well. Polarization is an example of a qubit degree of freedom, which forms a fundamental basis for an understanding of more complicated quantum phenomena. Much of the mathematical machinery of quantum mechanics, such as state vectors, probability amplitudes, unitary operators, and Hermitian operators, emerge naturally from the classical Maxwell's equations in the description. The quantum polarization state vector for the photon, for instance, is identical with the Jones vector, usually used to describe the polarization of a classical wave. Unitary operators emerge from the classical requirement of the conservation of energy of a classical wave propagating through lossless media that alter the polarization state of the wave. Hermitian operators then follow for infinitesimal transformations of a classical polarization state.
The one Photon Hypothesis
Event: a bundle of energy emitted from an electron in an atom with particular direction or momentum vector and a spin (+ or -). The polarization will be ignored for the moment.
State: Point of no dimension.
Process: Look forward along the direction of momentum 2r units. Examine all space centered at r with a radius r and volume 4/3 π r looking for anything that might absorb the energy. For this cycle only the emitter is considered to be a potential absorber.
State: no absorber found:
Process Look forward 3r units expending the same resources used to look at pervious space, but do not review anything in the circle examined in the previous step.
Create a formula for the radius of the circles created. This should match dispersion.
The two Photon Hypothesis
The model assumes a time sequence for each primitive. In other words there is a predefined partial ordering of primitives where events occur, or not.
Evolving Transformations System
A similar event-based model was created at the university of New Brunswick. The class of processes, i.e. similarly structured processes—with a common generative structure— pervades all levels of consideration in ETS. In particular, the most basic concept, the primitive event, is defined via the classes of primal processes. The ETS then go on to create a collection of primitive events, or transformations that are essentially state machines with a fixed set of inputs and outputs. According to the ETS formalism, photon is not a "particle" but is a (spatially instantiated) stream of structured events.
- Bryce S. deWitt, Quantum Theory of Gravity. I. The Canonical Theory (1967-08-25) Phys. Rev. 160, 1113 https://journals.aps.org/pr/abstract/10.1103/PhysRev.160.1113
- Kyung M Song + 11, (2020-03). Skyrmion-based artificial synapses for neuromorphic computing. Nature Electronics. 3 (3): 148–155. arXiv:1907.00957. [ https://newsroom.intel.com/editorials/intels-new-self-learning-chip-promises-accelerate-artificial-intelligence/#gs.m2dno0 https://en.wikichip.org/wiki/intel/loihi arXiv:1907.00957. doi:10.1038/s41928-020-0385-0
- I. Bialynick-Birual, ON THE WAVE FUNCTION OF THE PHOTON (1994) ACTA PHYSICA POLONICA A http://old.cft.edu.pl/~birula/publ/APPPwf.pdf
- L. Goldfarb + 4, What is a structural representation? Proposal for an event-based representational formalism, Sixth Variation, Tech. Rep. TR07-187 (2007) Faculty of Computer Science, University of New Brunswick http://www.cs.unb.ca/~goldfarb/ETSbook/ETS6.pdf