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Many-Worlds Quantum Theory

ManyWorlds may be representable by Density Matrices, by Bernoulli Shifts, and by Surreal Numbers.

What Does Many-Worlds Mean?

According to John Cramer's Alternate View 48:

"... The Many-Worlds interpretation of quantum mechanics ...[was originated by]... Hugh Everett III, ... a graduate student working with Prof. John A. Wheeler at Princeton University in the mid-1950s. ... Everett's PhD dissertation presented his new QM interpretation, a radical approach which uses neither collapsing wave functions nor observer knowledge. Instead it proposes a deceptively simple alternative: the wave function never collapses. Instead, at every occasion where a quantum event has more than one outcome (e.g., when an electron may strike one atom or another), the universe splits. We have one universe where the electron hits atom A, another where it hits atom B, and so on for all of the possible outcomes. Similarly, if a light photon might be transmitted or reflected, if a radioactive atom might decay or not, the universe splits into alternative worlds, with one new universe for each and every potential outcome. This is the Many Worlds (MW) interpretation. From the MW viewpoint, the universe is like a tree that branches and re-branches into myriads of new sub-branches with every passing picosecond. And each of these new branch universes has a slightly different sub-atomic "history". Because an observer happens to have followed one particular path through the diverging branches of this Universe-Tree, he never perceives the splitting. Instead he interprets the resolution of the myriad of possibilities into one particular outcome as a Copenhagen-style collapse. But the observer plays no active role in the splitting. Events at the quantum level, of course, must lead to consequences in the every-day world. There should be a MW universe in which every physically possible event has happened. There should be MW universes where the dinosaurs dominate the planet ... Even as you read this sentence your universe may be fragmenting into a number of branches too large to count. ...

... in Physical Review Letters [66 (1991) 397] ... Joseph Polchinski has demonstrated that ... non-linear [Quantum Theory] ... [unblocks] observer-to-observer EPR communication. ... Polchinski describes such an arrangement as an "EPR telephone". ...[in which]... Separated measurements on the same quantum system begin to "talk" to each other and faster-than-light or backward-in-time signalling becomes possible. ...

... Polchinski .. goes on to describe ... in non-linear QM ... an "Everett-Wheeler telephone" ... in the Many Worlds scenario in which ... a measurement performed in one MW universe can ... "talk" ...[to]... a measurement made in another ... and can be used for transmission of information from one MW branch universe to another. With Polchinski's non-linear quantum telephones you could talk to yourself at an earlier time or to your alter ego in an alternate universe. ...

[ In Physical Review Letters [66 (1991) 397] ( a copy of which paper was sent to me by Lloyd David Raub ) Joseph Polchinski says: "... In ... nonlinear extensions of quantum mechanics ... there are nonlinear observables in addition to the usual linear ones. Heuristically, the greater number of observables suggests that there is more information in the wave function than in the usual linear theory. This in turn raises the possibility that ... the EPR apparatus might be used to send instantaneous signals. In this Letter I determine the constraints imposed upon observables by the requirement that transmission not occur in the EPR experiment. ... I find that forbidding EPR communication in nonlinear quantum mechanics necessarily leads to ... communication ... between different branches of the wave function. ... This is an Everett phone ... Communication between branches of the wave function seems ... bizarre ... but it is not clear that it represents an actual inconsistency. ... It means that ... [t]he many-worlds interpretation of quantum mechanics becomes the natural one, with communication between the worlds now possible. ... in the present thought experiments the evolution equations are mathematically consistent and allow a consistent interpretation. ...

... what are the experimental implications of these results? ... communication between branches of the wave function invalidates most previous attempts to analyze the experimental consequences of nonlinearities ... because these analyses ignore previous branchings of the wave function and treat macroscopic systems as though they begin in definite macroscopic states. A complete analysis requires consideration of the entire wave function ... and is therefore rather complicated. Naively, it would seem that nonlinear effects will be very much diluted by the enormous number of branches ...". ]

... is quantum mechanics [of the Standard Model Electromagnetic, Weak, and Color forces] non-linear? Atomic physics experiments have been used by several experimental groups to test Weinberg's non-linear theory. So far these tests have been negative, indicating that any non-linearities in the quantum formalism are very small, if they exist at all. In my [John Cramer's] view the negative results are not surprising because the atomic transitions involve only a few electron-volts of energy. If quantum mechanics does have non-linear properties, I [John Cramer] would expect them to depend on energy and to appear only at a much higher energy scale. ...

[ Such Non-Linear EPR and EW telephone phenomena are also characteristic of Non-Equilibrium Quantum Theory described by Anthony Valentini, in which the Born Rule does not apply.

Non-Linearity appears in the Many-Worlds Quantum Theory of the D4-D5-E6-E7-E8 VoDou Physics model through:

Some Non-Linear and Non-Equilibrium phenomena may be manifested through Resonant Connections. ]

... The transactional interpretation [invented by John Cramer] is suggested by the formalism of quantum mechanics itself. The predicted "expectation value" of some property p of a physical system, in the QM formalism, is:  <p> = INTEGRAL dv(Y* P Y), where P is a mathematical operator describing the measurement of p, INTEGRAL dv is a volume integration over 3-dimensional space, and Y is a wave function, the solution of the Schroedinger wave equation which describes the system being measured. We call Y a retarded wave because it has a built-in time delay so that it arrives at some distant location later than it started. The wave function Y* is the time-reverse (or complex conjugate) of Y. It is an advanced wave which arrives earlier than it started. In other words, Y* is a wave that travels backwards in time.

The transactional interpretation takes the QM pairing of an advanced and a retarded wave quite literally. It describes any quantum process as a transaction, a handshake across space-time performed by the two-way exchange of advanced and retarded waves between the initial system andthe final system, a two-way contract between the future and the past for the purpose of transferring energy, momentum, etc.

The transactional interpretation is explicitly nonlocal because, through such handshaking, the future in a limited way is affecting the past on the same basis that the past affects the future. A delicate balance in the formalism (in QM lingo, the commutation of separated-measurement operators) suppresses "advanced effects" and ... faster-than-light and backward-in-time signalling (EPR communication). ... In the transactional interpretation the Schrödinger waves act in the external world as precursors of a quantum transaction. ...

[ The extent of a Transaction in time is related to Quantum Consciousness and Radin-Bierman Presponse phenomena. ]

... even now [1991], six decades after... Werner Heisenberg and Erwin Schrödinger ..., the meaning of the QM formalism remains controversial. ... The choice between interpretations has been decided by taste, aesthetics, and what you were taught in graduate school. Non-linear quantum mechanics may change that. ...".


The natural Clifford algebra structure of the D4-D5-E6-E7-E8 VoDou Physics model produces a Many-Worlds Quantum Theory.

The Discrete HyperDiamond Generalized Feynman Checkerboard and Continuous Manifolds are related by Quantum Superposition:

Volumes of Spaces of Superpositions of other given Sets of Basis Elements correspond to Volume of Physical SpaceTime and Volume of Internal Symmetry Space represented by those Basis Elements.

In the D4-D5-E6-E7-E8 VoDou Physics model, Many-Worlds means the Everett Relative State interpretation, with the addition of the interpretation basis of David Deutsch (Int. J. Theor. Phys 24 (1985) 1-41) to require that worlds of measure zero occur with zero probability. See David Deutsch's parallel universes web site for more details.

For Deutsch's interpretation basis to be well-defined, kinematic independence in the distant past must be assumed. Therefore, the Many-Worlds branch toward the future (not toward the past), and an arrow of time and an entropy can be defined without using either ensembles or coarse graining such as used in the decoherence theory of Gell-Mann and Hartle.

A fundamental form of decoherence, distinct from the consistent (or decoherent) histories interpretations of Griffiths, Omnes, Gell-Mann and Hartle, is

GRW Dynamical Collapse based on Compton Radius Vortex Particles and GravitoEM Induction Region Virtual Gravity Waves

with fundamental parameters a = 1 micron = 10^(-4) cm and T = 3 x 10^14 sec.

Click here to see some more points of view from which to look at GRW Dynamical Collapse.


Although Everett has said that people cannot feel the other branches of his Many-Worlds interpretation, Deutsch describes a gedanken experiment in which an observer can feel himself having been split into two branches that have now merged into his present branch, in the sense that, although he accurately remembers only one branch, he can infer that "... there was more than one copy of himself (and the atom) in existence at that time, and that these copies merged to form his present self."

Deutsch's paper only constructs the interpretation basis for quantum theories with finite-dimensional state spaces. The construction was not done for field theories or for relativistic theories. If such construction is done, then, as Deutsch says: " least for those who find Everett's interpretation acceptable, the 'problem of measurement' and the problem of interpretation of quantum theory in general, would be solved. Quantum theory could be regarded without reservation as a universal physical theory."

In its lattice formulation, the D4-D5-E6-E7 model has, at least locally, a finite-dimensional state space (although the finite dimension is very large) and has relativistic structure inherent in its D4 lattice structure. Therefore the construction of Deutsch shows that the fundamental lattice D4-D5-E6-E7-E8 VoDou Physics model with Many-Worlds quantum theory is an example of a universal physical theory.

In the D4-D5-E6-E7 HyperDiamond Feynman Checkerboard lattice model, correlated states, such as a particle-antiparticle pair coming from the non-trivial vacuum, or an amplitude for two entangled particles, extend over a part of the lattice that includes both particles. The stay in the same World of the Many-Worlds until they become uncorrelated.

In the Many-Worlds Quantum Theory of Andrew Gray, in quant-ph/9804008 and quant-ph/9712037, entire Cosmic Histories are Selected over all space and time, with a probability for selection assigned to each possible history. As this probability depends on the whole history, and is not merely composed of the product of probabilities for each step in the history, the theory is not a causal theory. Gray shows that this violation of causality is usually completely unobservable and confined to the microscopic world.

Each entire Cosmic History is selected by calculating both the product of probabilities for each step in that history and the product of the interference factors, which measure interference with other possible histories, at each time. It is the interference factor which makes the theory intrinsically non-causal at the microscopic level.

For example, a particle, when deciding which branch to take if faced with a choice of going in two directions, which are apparently equally probable from a local perspective, will always choose one route if the other results in a definite destructive interference with another particle at some stage in the future. It is as if the particle knows what will happen to it in the future if it goes one way or the other. From the perspective of the History Selection formulation of Many-Worlds Quantum Theory, there is nothing mysterious about this, the probability of a history in which the particle goes one way is zero, the probability of a history in which it goes the other way is non-zero, so at the branching point it always goes one way. However, though this may not be mysterious from the point of view of a Massless Lightcone life form that perceives the whole of its space-time world line, it might seem very mysterious from the local perspective of Material life forms such as humans, from whose perspective the probabilities for its various actions now are influenced by what could happen in the future.

Gray also shows that in certain special circumstances it is possible to exploit the intrinsic non-causal nature of the theory to violate causality at the macroscopic level. A design for a device which can exploit this effect is shown in quant-ph/9804008. As Michael Gibbs has noted, how easily the device can actually be constructed depends, among other things, on how easily a down converter can be built that has the desired properties. Such a device would effectively enable one to see into the future, or perhaps modify the future, and is thus a kind of time machine.

Gray's device is described in more detail HERE, where you can see an argument by Nick Herbert that Gray's device would violate diffraction constraints, and my speculation that using a curved screen might allow Gray's device to avoid violation of diffraction constraints.

Gray's device may be related to the structure of Dolphin brains.


Many-Worlds and the Born Rule

According to a Many-Worlds FAQ:

"... Everett demonstrated ... that observations in each world obey all the usual conventional statistical laws predicted by the probabilistic Born interpretation, by showing that the Hilbert space's inner product or norm has a special property which allows us to makes statements about the worlds where quantum statistics break down. The norm of the vector of the set of worlds where experiments contradict the Born interpretation ("non-random" or "maverick" worlds) vanishes in the limit as the number of probabilistic trials goes to infinity, as is required by the frequentist definition of probability. Hilbert space vectors with zero norm don't exist (see below), thus we, as observers, only observe the familiar, probabilistic predictions of quantum theory. Everett-worlds where probability breaks down are never realised. ...

... What Everett asserted, and DeWitt/Hartle derived, is that the collective norm of all the maverick worlds, as the number of trials goes to infinity, vanishes. ...".

David Wallace, in quant-ph/0211104, said:

"... Of the two main problems generally raised with Everett-type interpretations, the preferred-basis problem looks eminently solvable without changing the formalism. The main technical tool towards achieving this has of course been decoherence theory, which has provided powerful (albeit perhaps not conclusive) evidence that the quantum state has a de facto preferred basis and that this basis allows us to describe the universe in terms of a branching structure of approximately classical, approximately non-interacting worlds. ...

... The other main problem with the Everett interpretation concerns the concept of probability: given that the Everettian description of measurement is a deterministic, branching process, how are we to reconcile that with the stochastic description of measurement used in practical applications of quantum mechanics? ... It is useful to identify two aspects of the problem.

The first might be called the incoherence problem: how, when every outcome actually occurs, can it even make sense to view a measurement as indeterministic?

Even were this solved, there would then remain a quantitative problem: why is that indeterminism quantified according to the quantum probability rule (i. e. , the Born rule), and not (for instance) some other assignment of probabilities to branches?

In my view, the incoherence problem has been essentially resolved by Saunders, building on Parfit's reductionist approach to personal identity. ...

This then leaves the quantitative problem as the major conceptual obstacle to a satisfactory formulation of the Everett interpretation. Saunders himself has claimed ... that the quantitative problem is a nonproblem: that once we have shown the coherence of ascribing probability to quantum splitting, we can simply postulate that the quantum weights are to be interpreted as probabilities ...

... David Deutsch has claimed ... to derive the quantum probability rule from decision theory: that is, from considerations of pure rationality. ... the Everett interpretation is assumed from the start ... Defining quantum games ... What form does the decision problem take for a quantum agent? Our (mildly stylised) description of the problem in classical decision theory involved an agent who was confronted with some chance setup and placed bets on the outcome. This suggests an obvious quantum version: our agent measures some quantum state, and receives a reward which depends on the result of the measurement. ... Decision theory provides a framework in which we can understand what is involved in deducing quantitative probabilities for quantum branching, and then shows us that this can be done satisfactorily even when questionable assumptions like additivity are abandoned. Furthermore, the relevant links between quantum probability and non-probabilistic facts can then be satisfactorily established. ...".

Simon Saunders, in quant-ph/0211138, said:

"... the derivation of the Born rule that we shall present is independent of decision theory, independent of the interpretation of probability, and independent of any assumptions about the measuring process. ... Deutsch invokes ... the zero-sum rule ... The zero-sum rule is the statement that the most that one will pay in the hope of gaining a utility is the least that one will accept to take the risk of losing it. We may take it that this principle, as a principle of zero-sum games, is perfectly secure. And evidently any quantum experiment can be used to play a zero-sum game; therefore this principle also applies to the expected utility of experiments. ... With a further application of payoff additivity there follows ... the Born rule. ... As Wallace has shown, this ... can be derived from much weaker axioms of decision theory, that do not assume additivity. ... Decision theory can evidently play a role in the derivation of the Born rule, but it is only needed if the notion of probability is itself in need of justification. That may well be so, in the context of the Everett interpretation ...".

My two comments are:



Experimental Support for Many-Worlds


In Science 292 (4 May 2001) 823-825, Charles Seife says:

"... Zap an atom hard enough ... and its electron flies free, like a rock boosted beyond Earth's escape velocity. So an electron in an atom should be able to store only so much energy, even if it is hit with a huge barrage of photons. "You would expect, wffft! The atom is ionized--nothing more would happen," says Pascal Salieres, a physicist with France's Atomic Energy Commission in Gif-sur-Yvette. Au contraire. A little more than a decade ago, scientists experimenting with lasers discovered that atoms could absorb hundreds of photons beyond their binding energy and could emit photons with much more energy than should be allowed. "By the 1990s, there was much confusion on how to describe these phenomena," says Gerhard Paulus, a physicist at the Max Planck Institute for Quantum Optics in Garching, Germany. "It was a big controversy." ... Most quantum theorists had tackled the problem by using the Schroedinger equation to find the distribution of electron wave functions -- smeary particle-wave beasties that inhabit a large parcel of space all at one time. Feynman, on the other hand, treated electrons as ordinary point-particles that circle their nuclei ...

... To make the [ Feynman ] method work, physicists had to take all possible orbits into account simultaneously, rather than just one as in classical mechanics. Ordinarily, the infinite variety of possible orbits makes Feynman's method impractical. But on page 902, Salieres, Paulus, and colleagues show that the method does indeed hold the key to solving the mystery of the superionized atoms. ...".


In Science 292 (4 May 2001) 902-905, Feynman's Path-Integral Approach for Intense-Laser-Atom Interactions, Salieres, Carre, Le Deroff, Grasbon, Paulus, Walther, Kopold, Becker, Milosÿevic, Sanpera, and Lewenstein say:

"... Atoms interacting with intense laser fields can emit electrons and photons of very high energies. An intuitive and quantitative explanation of these highly nonlinear processes can be found in terms of a generalization of classical Newtonian particle trajectories, the so-called quantum orbits. ... the ... formulation of quantum mechanics developed by Feynman in terms of path integrals builds on the familiar Lagrangian concept of the action of an orbit in space and time and appears to be much closer to classical concepts. In Feynman's formulation, the probability amplitude of any quantum-mechanical process can be represented as a coherent superposition of contributions of all possible spatio-temporal paths that connect the initial and the final state of the system. The weight of each path is a complex number whose phase is equal to the classical action along the path. Even though this approach turned out to be very useful in quantum field theory, it has, nevertheless, received much less practical use, due in part to the large number of different paths required to describe most phenomena. Recently, the path-integral interpretation has set the frame for a unified view of the physics of nonlinear laser-atom interactions. Indeed, some phenomena that take place in intense fields have only recently been partly elucidated. For example, in the process of above-threshold ionization (ATI) an atom may absorb many hundred more photons than necessary to get ionized, ejecting an electron of very high energy, Under the same conditions, the atom may emit photons having harmonic frequencies, that is, multiples of the incident-laser frequency v. The harmonic frequencies can reach and exceed 300 v and extend well into the water window , i.e., the region of the light spectrum between x-ray and ultraviolet (XUV) for which water is transparent. Such high-harmonic generation (HHG) is making available brilliant table-top sources of coherent XUV radia-tion, with pulse durations potentially in the sub-femtosecond regime. ... The path integral formalism suggests we envision these processes in terms of "quantum orbits," i.e., space-time trajectories of the participating electrons. These quantum orbits have, however, imaginary parts related to tunneling ionization that determine the probability of the process. Quantum orbits have been able to explain subtle features of HHG and ATI. We report experimental and theoretical results that demonstrate the pervasive presence of quantum orbits as the basic building blocks for the probability amplitudes of these processes. Despite the complexity of the highly nonlinear laser-matter interaction, a very small number of clearly identified quantum orbits is sufficient to describe ATI or HHG processes ... in ATI spectra generated by a laser with elliptical polarization, each part of the spectrum can be attributed to one particular pair of quantum orbits. Moreover, we show how the contribution of a single quantum orbit can be isolated in phase-matched HHG, allowing for a direct measurement of the corresponding classical action. ... Notwithstanding the combined complexities of atomic physics and nonlinear laser-matter interaction, HHG and ATI spectra can be reproduced with a small number of quantum orbits. The identification of these orbits and the measurement of the corresponding action offer a unique way of controlling these processes and opens the possibility of new applications. ...".



Many-Worlds Cosmology

In the D4-D5-E6-E7-E8 VoDou Physics model, interaction is by exchange of gauge bosons. From the Many-Worlds Quantum Theory viewpoint, an interaction is a measurement of the quantity (charge, polarization, position, etc.) that is involved in the interaction. Therefore a graviton interaction can measure the structure of spacetime, including the selection of a time-like axis and space-like section that is used in the local description of the D4-D5-E6-E7-E8 VoDou Physics model.

Since Black Holes are information sinks for electromagnetic, weak force, and color force information, such interactions with a Black Hole are not measurements that destroy correlations of the time axis and space sections of spacetime at the Black Hole.

In the D4-D5-E6-E7-E8 VoDou Physics model, our universe was formed as a single Cosmological Expanding Instanton, so it has a Fundamental Correlation with respect to time axis and space sections.

In the cosmology of the D4-D5-E6-E7-E8 VoDou Physics model, the universe contains cold dark matter (CDM) Black Holes with mass at least the Planck Mass, 10^-5 gm. Primordial Black Holes may retain the fundamental spacetime correlation of our universe.

Gravitational interactions involving local inhomogeneities of mass distribution can produce the effect of local curvature of spacetime. The tilting of lightcones can be seen as arising from an effective theory of gravity, whose underlying fundamental theory of gravity (in the D4-D5-E6-E7-E8 VoDou Physics model) may provide, in principle, a non-trivial correlation among the lightcones with respect to the fundamental underlying 4-dim Feynman checkerboard structure.

As the universe evolves, quantum vacuum creation of virtual bosons (and fermion-antifermion pairs, and black hole pairs) at any part of spacetime should occur with respect to the fundamental underlying 4-dim Feynman checkerboard structure, and so be correlated with respect to time axis and space sections.

As the CDM Black Holes within our universe should retain their correlation, their 4-pair graviton interactions with ordinary matter should correlate a particle with which a CDM blackhole interacts, and a neighborhood of the particles. (To determine what is meant by "neighborhood", consider that: Planck mass = 10^-5 gm; the density of CDM black holes in a present-day flat universe is 4.5 x 10^-30 gm/cm^3 = 4.5 x 10^-25 CDM black holes/cm^3, and that Avogadro's number = 6 x 10^23 atoms/cm^3.)

The CDM Black Holes may act like the incoherent dust of Brown and Kuchar to couple with the metric and introduce into spacetime "a privileged dynamical reference frame and time foliation. The comoving coordinates of the dust particles and the proper time along the dust worldlines become canonical coordinates in the phase space of the system. ... This has three important consequences. First, the functional Schrodinger equation can be solved by separating the dust time from the geometric variables. Second, the Hamiltonian densities strongly commute and therefore can be simultaneously defined by spectral analysis. Third, the standard constraint system of vacuum gravity is cast into a form in which it generates a true Lie algebra."

The privileged frame of Brown and Kuchar is consistent with Deutsch's preferred interpretation basis of states.

A fundamental form of decoherence is

GRW Dynamical Collapse based on Compton Radius Vortex Particles and GravitoEM Induction Region Virtual Gravity Waves

with fundamental parameters a = 1 micron = 10^(-4) cm and T = 3 x 10^14 sec.

Ford describes decoherence from vacuum fluctuations.

Tegmark describes decoherence from scattering processes.

Gisin and Percival describe Quantum State Diffusion, that is compared to grw in an article by Mark Buchanan entitled Crossing the Quantum Frontier in The New Scientist of 27 April 1997, pages 38-41, which states: "... In 1992, Mark Kasevich and Steven Chu of Stanford University directed two beams of sodium atoms along different paths some 15 centimeters long, and found the pattern expected from normal quantum theory. So the [QSD] fluctuations - if present - didn't have noticeable effects. These experiments would be sensitive enough to detect the fluctuations if they take place in around 10^(-44) seconds. But the fluctuations may well be more rapid yet. ... [improved experiments} should provide a more sensitive probe within the next few years. ...".

Plaga shows that finite decoherence time may permit experimental communication of information among the Many Worlds.

Anglin, Paz, and Zurek mention experiments by Brune et al in which the increase of the decoherence rate as the square of the separation scale is confirmed over a limited range of separations. Anglin, Paz, and Zurek show that decoherence can be very complicated due to such things as colored noise, dissipative terms with memory, backreactions, temporal and spatial non-linearity, and non-locality. Such things can cause saturation of decoherence at long distances and other interesting things.

Hawking and his students propose that creation of virtual pairs of Planck-energy black holes (a phenomenon that should also occur in the D4-D5-E6-E7 model upon reaching the energy scale of its Planck length lattice) should cause macroscopic black holes should evaporate down to Planck size and then disappear in the sea of virtual black holes.

The virtual pairs of Planck-energy black holes are similar to fermion particle-antiparticle pairs and to the quantum information theory virtual qubit-anti-qubit pairs of Cerf and Adami, which they call ebit-anti-ebit pairs, that are related to negative conditional entropies for quantum entangled systems.


Click on the next line to see

Many-Worlds Quantum Computing



Worlds, Histories, Links, and Vertices

and LifeForms

Each World of the Many-Worlds D4-D5-E6-E7 model is described by a configuration of bosons on links and fermions on vertices in a 4-dimensional HyperDiamond lattice spacetime.

In the D4-D5-E6-E7 model, the Many-Worlds Sum over Histories is a sum over all paths, each path being a history in a 4-dimensional HyperDiamond lattice spacetime World.

Each path is a vertex-link-vertex-link-...-vertex sequence in a D4 lattice spacetime World.

To the extent two paths coincide, they may be said to be in the same World of the Many-Worlds. Where they differ, they are in different Worlds.

A given link can only link two nearest-neighbor vertices in a 4-dimensional HyperDiamond lattice spacetime World containing that link.

A given vertex can be connected to a nearest-neighbor vertex in many possible 4-dimensional HyperDiamond lattice spacetime Worlds.

Consider 4-dimensional HyperDiamond lattice spacetime, with vertex structure like this stereo pair representation with blue(+) to red(-) color coding for the 4th dimension:

There are 8 links leading away from a given vertex to a nearest neighbor in a given 4-dimensional HyperDiamond lattice World.

The 4 future lightcone links in the 4-dimensional HyperDiamond lattice form a vertex figure that is the future (blue) tetrahedron:

After a 4-dimensional rotation, it is clear that the figure can be called a quantum pentacle:

In the Many-Worlds Quantum Theory, any given vertex may be connected to a number of 4-dimensional HyperDiamond lattice Worlds.

Therefore, each of the 4 quaternionic unit vector HyperDiamond future lightcone links {(+ 1 +/- i +/- j +/- k)/2 } (with an even number of + signs) at the given vertex is a SUPERPOSITION of all possible links leading from the given vertex to one of the possible Worlds.

A given quaternionic unit vector HyperDiamond future lightcone link leading from the given vertex does not really look like a single link from the given vertex, but like a bundle of a finite (but large) number of links from the given vertex to destination vertices, each in its own future history World:

If the links are regarded as such superpositions, the HyperDiamond future lightcone figure

can be called a HyperDiamond Quantum Pentacle.

In this picture, physics on a single link is reversible.

Irreversibility comes from the branching of the Many-Worlds, manifested by the fact that a single link is only one part of the superposition of links that is a quaternionic unit 4-dimensional vector originating at the origin vertex.

Consider a given link within the superposition .

By being at the origin vertex at the "start" of the the "experiment", you have effectively selected a particular World containing the origin vertex.

To select the given link within the superpostion, you must select a particular future history World at the destination vertex.

Then, the amplitude of each link in a superposition is determined by:

the fermion state of the given origin vertex;

the boson state of each of the other 7 lightcone links at the origin vertex in the World containing the prior history of the given origin vertex;

the fermion state of the destination vertex; and

the boson state of each of the other 7 lightcone links at the destination vertex in the World containing the future history of the destination vertex.

The probability of the link (in a sense, the probability of observation of the link) is the product of amplitude with its complex conjugate, where the complex conjugate of the amplitude is the amplitude for the same link with past and future interchanged by time reversal. (Compare the transaction picture of Cramer, Rev. Mod. Phys. 58 (1986) 647-687)

Three Types of Beings:

Massless Lightcone Beings

Massive Spacelike Beings


Abstract ManyWorlds Beings

A being made of massless light-cone particles

lives on the boundary of the light-cone. It exists in all times and sees alternative Worlds branching at all times. The quantum phase, taking values in the helical covering space of U(1), is the means by which a light-cone being determines the order of events and how amplitudes interfere. In other words, the quantum phase is the means by which a light-cone being "tells time".

From the lattice point of view, 
the quantum phase is an internal symmetry 
related to the coassociative internal symmetry space, 
whose relative size to the associative physical spacetime 
is the Golden Ratio PHI.  
For each physical spacetime time-step, 
the phase should advance by PHI radians, 
or by the fraction    2 pi / PHI    of a circle (about 222.5 degrees). 
Although pi is transcendental (e^(i pi) = -1) and PHI is algebraic, 
the continued fraction for PHI = 1 + 1/ 1 + 1/ 1 + 1/ 1 + ... 
shows that PHI is the most irrational number, and 
that steps of  2 pi / PHI  give a maximally uniform distribution 
of phases throughout time (non-unique, as  2 pi / PHI^2  is just as good, 
see Kappraff - Connections, McGraw-Hill, 1991). 
Therefore, a light-cone being always knows when/where it is 
by its phase, in a maximally efficient way. 

"In a world of light there are neither points nor moments of time; beings woven from light would live 'nowhere' and 'nowhen'; ... One point of CP3 [the 'Penrose paradise'] is the whole life history of a free photon -- the smallest 'event' that can happen to light." (Yu. I. Manin, Mathematics and Physics, Birkhauser (1981), pp. 83-84)

Light-cone beings in our low-energy regime could be made up of any massless (not SU(2) weak bosons or scalar Higgs) and unconfined (not SU(3) gluons) gauge bosons, i.e., photons and gravitons,


of massless neutrino fermions.

For Light-cone beings to be STABLE, they must be made of stable photons, gravitons, or neutrinos.

A being made of massive spacelike particles

lives in the interior of the light-cone. It has spacelike extent, and evolves in time. It exists in a limited spacetime neighborhood with one past history (although a few others may be experimentally detectable) and can see alternative future histories branching only near its present time.

"What binds us to spacetime is our rest mass, which prevents us from flying at the speed of light, when time stops and space loses meaning." (Yu. I. Manin, Mathematics and Physics, Birkhauser (1981), p. 84)

Spacelike beings in our low-energy regime could be made up of massive SU(2) weak bosons, scalar Higgs, and confined SU(3) gluons,


of massive lepton and quark fermions.

For Spacelike beings to be STABLE, they must be made of stable first-generation massive lepton and quark fermions.

Interactions between STABLE Lightcone beings and Spacelike beings could be through Lightcone neutrinos, photons, and gravitons interacting with Spacelike massive first-generation lepton and quark fermions.

ManyWorlds Abstract life forms

that live and move among the ManyWorlds would not be restricted by the lightcone structure of spacetime. Their structure is described by the information theory of quantum computers. As Cerf and Adami have shown, quantum information processes can be described by particle-antiparticle diagrams much like particle physics diagrams.

Consequently, the underlying structure of ManyWorlds abstract life forms should be fundamentally similar to that of Light-cone life forms and Massive life forms, which are also based on particle physics.

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Quantum Consciousness



Advanced Waves from the Future

Jack Sarfatti comments on a paper of Hoyle and Narlikar 
(Rev. Mod. Phys. 67 (1995) 113-155):
Classically, if "we use only retarded electromagnetic waves 
that propagate on the future light cone of their source events, 
conservation of energy for an accelerating classical point charge 
implies HN's Lorentz-covariant tensor eq. 2.2 on p.116
md^2a^i/da^2 = eFret^i k da^k/da + 
+ (4/3)e glk(d^3a^i/da^3 da^l/da - d^3a^l/da^3 da^i/da) da^k/da 
The first term on the RHS is 
the external Lorentz force for the point charge. 
The second term involving the third derivative of 
the particle's postion relative to the proper time along its world line
is the self-force or radiation reaction. 
This equation cannot be deduced from the Lagrangian of 
traditional classical electrodynamics for point charges 
in purely retarded causal electromagnetic fields. 
It is put in adhoc in order to obey conservation of energy. 
If you choose a time symmetric sum of advanced and retarded waves 
there is no radiaton and no radiation reaction. 
Anti-causal advanced waves propagate 
on the past light cone of their source events. 
Dirac used HN's eq. 2.3
which is half the difference of the retarded and advanced waves.
                          R^i k = (1/2){Fret^i k - Fadv^i k} 
Dirac ... 
showed that the individual self-fields diverge for the point charge, 
but their difference is finite and it is exactly equal to 
the adhoc radiation reaction term in eq. 2.2 above. 
The classical self-force when quantized is responsible 
for the spontaneous emission of bound atomic electrons 
in excited energy levels. 
This is amazing and highly suggestive 
that we are close to the secrets of Einstein's 'Old One'.   
HN then develop the quantum version of their classical theory 
using the Feynman path method. 
The quantum 'influence functional' of the future of our Universe 
replaces the classical absorber boundary condition. 
They show that there are no renormalization infinities 
in the delayed action-at-a-distance theory at the quantum level 
because of damping by 
the cosmological influence functional of the entire future Universe 
on every charged particle ...
[HN say that:] 
     '... the apparently local behavior of a quantum system 
      actually involves the response of the Universe 
      via an influence functional 
      which arises when we take into account 
      how the absorber reacts back (via advanced potentials) 
      on the local system. 
      The influence functional enters into any probability calculation 
      in the path integral approach whenever 
      the effects of external variables on the local system 
      are integrated out. 
      It is a double integral over paths and conjugate paths. ... 
      the conjugate paths arise in the calculation of 
      probability for spontaneous transition of the atomic electron, 
      involving the response of the Universe, 
      when the effects of the individual absorber particles 
      are integrated out.' p. 147 
The congugate paths in this case carry negative energy em waves 
propagating backwards in time.
They ... replace the virtual photon vacuum fluctuations 
of the traditional quantum electrodynamics."  

Quantum Mind, Zeno and Anti-Zeno, and Fate

In the cosmology of the D4-D5-E6-E7-E8 VoDou Physics model, the universe is open.

Does it obey the quantum version of the total absorber boundary condition?

YES, because the open universe is also a totally Many-Branched universe, in the sense that any future world-line from any chosen point will eventually encounter a "new universe" branching off from the chosen universe.

A quantum mind could interact with the anti-causal advanced conjugate paths coming from anything in either the future part of the chosen universe or from any of the new universe Many-Branches.

HOW MIGHT A QUANTUM MIND BE ABLE TO SELECT which of the Many-Worlds it will experience in the future?

Fred Wolf uses the Watched-Pot property of quantum theory (also called the Quantum Zeno Effect) to provide part of the answer. The Watched-Pot property is just the fact that, if some types of quantum systems are observed constantly, their states do not change.

In Temporal behavior and quantum Zeno time of an excited state of the hydrogen atom, quant-ph/990501, P. Facchi and S. Pascazio of Bari, Italy, say: "The quantum Zeno time of the 2P-1S transition of the hydrogen atom is computed and found to be approximately 3.59 x 10^(-15) s (the lifetime is approximately 1.595 x 10^(-9) s). The temporal behavior of this system is analyzed in a purely quantum field theoretical framework and is compared to the exponential decay law. ...".

For some types of quantum systems, there is a Quantum Anti-Zeno Effect, whereby observation accelerates change of state. The Quantum Anti-Zeno Effect is described in quant-ph/9901060 by M. Lewenstein and K. Rzajzewski. Their abstract states: "... near threshold decay processes may be accelerated by repeated measurements. Examples include near threshold photodetachment of an electron from a negative ion, and spontaneous emission in a cavity close to the cutoff frequency, or in a photon band gap material.".

Pascazio and Facchi, in their paper quant-ph/9904076 entitiled Modifying the Lifetime of an Unstable System by an Intense Electromagnetic Field, say: "... We shall look at the temporal behavior of a three-level system ... where level #1 is the ground state and levels #2, #3 are two excited states. The system is initially prepared in level #2 and if it follows its natural evolution, it will decay to level #1. The decay will be (approximately) exponential and characterized by a certain lifetime, that can be calculated from the Fermi Golden Rule. But what happens if one shines on the system an intense laser field, tuned at the transition frequency 3-1? ... the so-called quantum Zeno effect ... the lifetime of the initial state depends on the intensity of the laser field. In the limit of extremely intense field, the decay should be considerably slowed down. ... for physically sensible values of the laser field, the decay can be enhanced, rather than hindered. This can be viewed as an "inverse" quantum Zeno effect. The whole problem is related to electromagnetic induced transparency ...".

In Towards a quantum Zeno tomography, quant-ph/0104021, by P. Facchi, Z. Hradil, G. Krenn, S. Pascazio, and J. Rehacek, the abstract states: "... We show that the resolution "per absorbed particle" of standard absorption tomography can be outperformed by a simple interferometric setup, provided that the different levels of "gray" in the sample are not uniformly distributed. The technique hinges upon the quantum Zeno effect and has been tested in numerical simulations. ...".


Both the Quantum Zeno Effect and Quantum Anti-Zeno Effect could be used by a

Quantum Mind to choose a Branch of the Many-Worlds.


Uncertainty Principle

Cerf and Adami have shown that information theory of quantum computers can give negative conditional entropies for quantum entangled systems. Therefore negative virtual information can be carried by particles, and quantum information processes can be described by particle-antiparticle diagrams much like particle physics diagrams.

Consequently, the underlying structure of Many-Worlds abstract life forms should be fundamentally similar to that of Light-cone life forms and Massive life forms.

To get an idea of how to think about Many-Worlds on lattices, 
here is a rough outline of how the Uncertainty Principle works: 
Do NOT (as is conventional) say that a particle is 
sort of "spread out" around a given location in a given space-time  
due to "quantum uncertainty".  
Instead, say that the particle is really at a point in space-time
BUT that the "uncertainty spread" is not a property of the 
particle, but is due to dynamics of the space-time, 
in which particle-antiparticle pairs x-o are being created
sort of at random.  For example, in one of the Many-Worlds,
the spacetime might not be just 
but would have created a particle-antiparticle pair
                x - o 
If the original particle is where we put it to start with, 
then in this World we would have 
                x - o x 
Now, if the new o annihilates the original x, 
we would have 
and, since the particles x are indistinguishable from each other, 
it would APPEAR that the original particle x was at a different 
location, and the probabilities of such appearances would 
look like the conventional uncertainty in position.  
In the D4-D5-E6-E7-E8 VoDou Physics model, correlated states, 
such as 
a particle-antiparticle pair coming from the non-trivial vacuum, 
an amplitude for two entangled particles, 
extend over a part of the lattice that includes both particles. 
The stay in the same World of the Many-Worlds 
until they become uncorrelated. 



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