Tony Smith's Home Page

Many-Worlds QuantumTheory

ManyWorlds may be representableby Density Matrices, by BernoulliShifts, and by SurrealNumbers.


What Does Many-WorldsMean?

According to JohnCramer's AlternateView 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 PhysicalReview Letters [66 (1991) 397] ( a copyof which paper was sent to me by Lloyd David Raub ) JosephPolchinski says: "... In ... nonlinear extensions of quantummechanics ... there are nonlinear observables in addition to theusual linear ones. Heuristically, the greater number of observablessuggests that there is more information in the wave function than inthe usual linear theory. This in turn raises the possibility that ...the EPR apparatus might be used to send instantaneous signals. Inthis Letter I determine the constraints imposed upon observables bythe requirement that transmission not occur in the EPR experiment.... I find that forbidding EPR communication in nonlinear quantummechanics necessarily leads to ... communication ... betweendifferent 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 actualinconsistency. ... It means that ... [t]he many-worldsinterpretation of quantum mechanics becomes the natural one, withcommunication between the worlds now possible. ... in the presentthought experiments the evolution equations are mathematicallyconsistent and allow a consistent interpretation. ...

... what are the experimental implications of these results? ...communication between branches of the wave function invalidates mostprevious attempts to analyze the experimental consequences ofnonlinearities ... because these analyses ignore previous branchingsof the wave function and treat macroscopic systems as though theybegin in definite macroscopic states. A complete analysis requiresconsideration of the entire wave function ... and is therefore rathercomplicated. Naively, it would seem that nonlinear effects will bevery 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 alsocharacteristic of Non-EquilibriumQuantum Theory describedby AnthonyValentini, in which the Born Rule doesnot apply.

Non-Linearity appears in the Many-Worlds Quantum Theory of theD4-D5-E6-E7-E8 VoDou Physics modelthrough:

Some Non-Linear and Non-Equilibrium phenomena may be manifestedthrough ResonantConnections. ]

... 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 QuantumConsciousness and Radin-BiermanPresponse 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 algebrastructure of the D4-D5-E6-E7-E8 VoDouPhysics model produces a Many-WorldsQuantum Theory.

The Discrete HyperDiamond GeneralizedFeynman Checkerboard and ContinuousManifolds are related by Quantum Superposition:

Volumes of Spaces ofSuperpositions of other given Sets of Basis Elements correspond toVolume of Physical SpaceTime and Volumeof Internal Symmetry Space representedby those Basis Elements.

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

For Deutsch's interpretation basis to be well-defined, kinematicindependence in the distant past must be assumed. Therefore, theMany-Worlds branch toward the future (not toward the past), and anarrow of time and an entropy can be defined without using eitherensembles or coarse graining such as used in the decoherence theoryof 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 Collapsebased on Compton Radius Vortex Particles and GravitoEM InductionRegion Virtual Gravity Waves

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

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

 

Although Everett has said that people cannot feel the otherbranches of his Many-Worlds interpretation, Deutsch describes agedanken experiment in which an observer can feel himself having beensplit 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 (andthe atom) in existence at that time, and that these copies merged toform his present self."

Deutsch's paper only constructs the interpretation basis forquantum theories with finite-dimensional state spaces. Theconstruction was not done for field theories or for relativistictheories. If such construction is done, then, as Deutsch says: "..atleast for those who find Everett's interpretation acceptable, the'problem of measurement' and the problem of interpretation of quantumtheory in general, would be solved. Quantum theory could be regardedwithout reservation as a universal physical theory."

In its lattice formulation, the D4-D5-E6-E7 model has, at leastlocally, a finite-dimensional state space (although the finitedimension is very large) and has relativistic structure inherent inits D4 lattice structure. Therefore the construction of Deutsch showsthat the fundamental lattice D4-D5-E6-E7-E8 VoDouPhysics model with Many-Worlds quantum theory is an example of auniversal physical theory.

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

In the Many-Worlds Quantum Theory of Andrew Gray, in quant-ph/9804008and 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 merelycomposed of the product of probabilities for each step in thehistory, the theory is not a causal theory. Gray shows that thisviolation of causality is usually completely unobservable andconfined to the microscopic world.

Each entire Cosmic History is selected by calculating both theproduct of probabilities for each step in that history and theproduct of the interference factors, which measure interference withother possible histories, at each time. It is the interference factorwhich makes the theory intrinsically non-causal at the microscopiclevel.

For example, a particle, when deciding which branch to take iffaced with a choice of going in two directions, which are apparentlyequally probable from a local perspective, will always choose oneroute if the other results in a definite destructive interferencewith another particle at some stage in the future. It is as if theparticle knows what will happen to it in the future if it goes oneway or the other. From the perspective of the History Selectionformulation of Many-Worlds Quantum Theory, there is nothingmysterious about this, the probability of a history in which theparticle goes one way is zero, the probability of a history in whichit goes the other way is non-zero, so at the branching point italways goes one way. However, though this may not be mysterious fromthe point of view of a MasslessLightcone life form that perceives the whole of its space-time worldline, it might seem very mysterious from the local perspective ofMaterial life forms such ashumans, from whose perspective the probabilities for its variousactions now are influenced by what could happen in the future.

Gray also shows that in certain special circumstances it ispossible to exploit the intrinsic non-causal nature of the theory toviolate causality at the macroscopic level. A design for a devicewhich can exploit this effect is shown in quant-ph/9804008.As MichaelGibbs has noted, how easily the device can actually beconstructed depends, among other things, on how easily a downconverter can be built that has the desired properties. Such a devicewould effectively enable one to see into the future, or perhapsmodify the future, and is thus a kind of time machine.

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

Gray's device may berelated to the structure of Dolphinbrains.

 


Many-Worlds and the BornRule

According to aMany-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 forMany-Worlds

 

In Science 292 (4 May2001) 823-825, Charles Seife says:

"... Zap an atom hard enough ... and its electron flies free, likea rock boosted beyond Earth's escape velocity. So an electron in anatom should be able to store only so much energy, even if it is hitwith a huge barrage of photons. "You would expect, wffft! The atom isionized--nothing more would happen," says Pascal Salieres, aphysicist with France's Atomic Energy Commission in Gif-sur-Yvette.Au contraire. A little more than a decade ago, scientistsexperimenting with lasers discovered that atoms could absorb hundredsof photons beyond their binding energy and could emit photons withmuch more energy than should be allowed. "By the 1990s, there wasmuch confusion on how to describe these phenomena," says GerhardPaulus, a physicist at the Max Planck Institute for Quantum Optics inGarching, Germany. "It was a big controversy." ... Most quantumtheorists had tackled the problem by using the Schroedinger equationto find the distribution of electron wave functions -- smearyparticle-wave beasties that inhabit a large parcel of space all atone time. Feynman, on the other hand, treated electrons asordinary point-particles that circle their nuclei ...

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

 

In Science292 (4 May 2001) 902-905, Feynman's Path-Integral Approach forIntense-Laser-Atom Interactions, Salieres, Carre, Le Deroff,Grasbon, Paulus, Walther, Kopold, Becker, Milosÿevic, Sanpera,and Lewenstein say:

"... Atoms interacting with intense laser fields can emitelectrons and photons of very high energies. An intuitive andquantitative explanation of these highly nonlinear processes can befound in terms of a generalization of classical Newtonian particletrajectories, the so-called quantum orbits. ... the ...formulation of quantum mechanics developed by Feynman in terms ofpath integrals builds on the familiar Lagrangian concept of theaction of an orbit in space and time and appears to be muchcloser to classical concepts. In Feynman's formulation, theprobability amplitude of any quantum-mechanical process can berepresented as a coherent superposition of contributions of allpossible spatio-temporal paths that connect the initial and the finalstate of the system. The weight of each path is a complex numberwhose phase is equal to the classical action along the path. Eventhough this approach turned out to be very useful in quantum fieldtheory, it has, nevertheless, received much less practical use, duein part to the large number of different paths required to describemost phenomena. Recently, the path-integral interpretation has setthe frame for a unified view of the physics of nonlinear laser-atominteractions. Indeed, some phenomena that take place in intensefields have only recently been partly elucidated. For example, in theprocess of above-threshold ionization (ATI) an atom may absorb manyhundred more photons than necessary to get ionized, ejecting anelectron of very high energy, Under the same conditions, the atom mayemit photons having harmonic frequencies, that is, multiples of theincident-laser frequency v. The harmonic frequencies can reach andexceed 300 v and extend well into the water window , i.e., the regionof the light spectrum between x-ray and ultraviolet (XUV) for whichwater is transparent. Such high-harmonic generation (HHG) is makingavailable 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 interms of "quantum orbits," i.e., space-time trajectories of theparticipating electrons. These quantum orbits have, however,imaginary parts related to tunneling ionization that determine theprobability of the process. Quantum orbits have been able to explainsubtle features of HHG and ATI. We report experimental andtheoretical results that demonstrate the pervasive presence ofquantum orbits as the basic building blocks for the probabilityamplitudes of these processes. Despite the complexity of the highlynonlinear laser-matter interaction, a very small number of clearlyidentified quantum orbits is sufficient to describe ATI or HHGprocesses ... in ATI spectra generated by a laser with ellipticalpolarization, each part of the spectrum can be attributed to oneparticular pair of quantum orbits. Moreover, we show how thecontribution of a single quantum orbit can be isolated inphase-matched HHG, allowing for a direct measurement of thecorresponding classical action. ... Notwithstanding the combinedcomplexities of atomic physics and nonlinear laser-matterinteraction, HHG and ATI spectra can be reproduced with a smallnumber of quantum orbits. The identification of these orbits andthe measurement of the corresponding action offer a unique way ofcontrolling these processes and opens the possibility of newapplications. ...".

 

 


Many-Worlds Cosmology

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

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

In the D4-D5-E6-E7-E8 VoDou Physicsmodel, our universe was formed as a single CosmologicalExpanding Instanton, so it has a Fundamental Correlation withrespect to time axis and space sections.

In the cosmology of the D4-D5-E6-E7-E8VoDou Physics model, the universe contains cold dark matter (CDM)Black Holes with mass at least thePlanck Mass, 10^-5 gm. Primordial BlackHoles may retain the fundamental spacetime correlation of ouruniverse.

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

As the universe evolves, quantum vacuum creation of virtual bosons(and fermion-antifermion pairs, and black hole pairs) at any part ofspacetime should occur with respect to the fundamental underlying4-dim Feynman checkerboard structure, andso be correlated with respect to time axis and space sections.

As the CDM Black Holes within ouruniverse should retain their correlation, their 4-pair gravitoninteractions with ordinary matter should correlate a particle withwhich a CDM blackhole interacts, and a neighborhood of the particles.(To determine what is meant by "neighborhood", consider that: Planckmass = 10^-5 gm; the density of CDM black holes in a present-day flatuniverse 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 theincoherent dust of Brownand Kuchar to couple with the metric and introduce into spacetime"a privileged dynamical reference frame and time foliation. Thecomoving coordinates of the dust particles and the proper time alongthe dust worldlines become canonical coordinates in the phase spaceof the system. ... This has three important consequences. First, thefunctional Schrodinger equation can be solved by separating the dusttime from the geometric variables. Second, the Hamiltonian densitiesstrongly commute and therefore can be simultaneously defined byspectral analysis. Third, the standard constraint system of vacuumgravity is cast into a form in which it generates a true Liealgebra."

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


A fundamental form of decoherence is

GRW DynamicalCollapse based on Compton Radius Vortex Particles and GravitoEMInduction Region Virtual Gravity Waves

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


Ford describesdecoherence from vacuum fluctuations.

Tegmarkdescribes decoherence from scattering processes.

Gisin andPercival describe Quantum State Diffusion, that is compared togrw in an article by Mark Buchanan entitled Crossing the QuantumFrontier in The New Scientist of 27 April 1997, pages 38-41, whichstates: "... In 1992, Mark Kasevich and Steven Chu of StanfordUniversity directed two beams of sodium atoms along different pathssome 15 centimeters long, and found the pattern expected from normalquantum theory. So the [QSD] fluctuations - if present -didn't have noticeable effects. These experiments would be sensitiveenough to detect the fluctuations if they take place in around10^(-44) seconds. But the fluctuations may well be more rapid yet.... [improved experiments} should provide a more sensitive probewithin the next few years. ...".

Plaga showsthat finite decoherence time may permit experimental communication ofinformation among the Many Worlds.

Anglin, Paz,and Zurek mention experiments by Brune et al in which theincrease of the decoherence rate as the square of the separationscale is confirmed over a limited range of separations. Anglin, Paz,and Zurek show that decoherence can be very complicated due to suchthings 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 andother interesting things.


Hawking and his students proposethat creation of virtual pairs of Planck-energy black holes (aphenomenon that should also occur in theD4-D5-E6-E7 model upon reaching the energy scale of its Plancklength lattice) should cause macroscopic black holes should evaporatedown to Planck size and then disappear in the sea of virtual blackholes.

The virtual pairs of Planck-energy black holes are similar tofermion particle-antiparticle pairs and to the quantum informationtheory virtual qubit-anti-qubit pairs of Cerfand Adami, which they call ebit-anti-ebit pairs, that are relatedto negativeconditional entropies for quantum entangled systems.

 


Click on the next line to see

Many-Worlds QuantumComputing

 

 


Worlds, Histories, Links, andVertices

and LifeForms

Each World of the Many-Worlds D4-D5-E6-E7 model is described by aconfiguration of bosons on links and fermions on vertices in a4-dimensional HyperDiamond lattice spacetime.

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

Each path is a vertex-link-vertex-link-...-vertex sequence in a D4lattice spacetime World.

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

A given link can only link two nearest-neighbor vertices in a4-dimensional HyperDiamond lattice spacetime World containing thatlink.

A given vertex can be connected to a nearest-neighbor vertex inmany possible 4-dimensional HyperDiamond lattice spacetimeWorlds.

Consider 4-dimensional HyperDiamond lattice spacetime, with vertexstructure 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 nearestneighbor in a given 4-dimensional HyperDiamond lattice World.

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

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

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

Therefore, each of the 4 quaternionic unit vector HyperDiamondfuture lightcone links {(+ 1 +/- i +/- j +/- k)/2 } (with an evennumber of + signs) at the given vertex is a SUPERPOSITION of allpossible links leading from the given vertex to one of the possibleWorlds.

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

If the links are regarded as such superpositions, the HyperDiamondfuture 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 thesuperposition of links that is a quaternionic unit 4-dimensionalvector 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 Worldcontaining the origin vertex.

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


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

the fermion state of the given origin vertex;

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

the fermion state of the destination vertex; and

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


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


Three Types ofBeings:

Massless LightconeBeings

Massive SpacelikeBeings

and

Abstract ManyWorldsBeings

A being made of massless light-cone particles

lives on the boundary of the light-cone. It exists in all timesand sees alternative Worlds branching at all times. The quantumphase, taking values in the helical covering space of U(1), is themeans by which a light-cone being determines the order of events andhow amplitudes interfere. In other words, the quantum phase is themeans 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'; ... Onepoint of CP3 [the 'Penrose paradise'] is the whole lifehistory of a free photon -- the smallest 'event' that can happen tolight." (Yu. I. Manin, Mathematics and Physics, Birkhauser (1981),pp. 83-84)

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

and

of massless neutrino fermions.

For Light-cone beings to be STABLE, they must be made of stablephotons, 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 neighborhoodwith one past history (although a few others may be experimentallydetectable) and can see alternative future histories branching onlynear its present time.

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

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

and

of massive lepton and quark fermions.

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


Interactions between STABLE Lightcone beings and Spacelike beingscould be through Lightcone neutrinos, photons, and gravitonsinteracting with Spacelike massive first-generation lepton and quarkfermions.


ManyWorlds Abstract life forms

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

Consequently, the underlying structure of ManyWorldsabstract life forms should be fundamentally similar to that ofLight-cone life forms and Massive life forms,which are also based on particlephysics.


Click on the next line to see

QuantumConsciousness

 

 


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 lineis 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. 2.3which 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 andAnti-Zeno, and Fate

In the cosmology of the D4-D5-E6-E7-E8VoDou Physics model, the universe is open.

Does it obey the quantum version of the total absorber boundarycondition?

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

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

HOW MIGHT A QUANTUM MIND BE ABLE TOSELECT which of the Many-Worlds it will experience in thefuture?

FredWolf uses the Watched-Pot property of quantum theory (alsocalled the Quantum Zeno Effect) to provide part of the answer.The Watched-Pot property is just the fact that, if some types ofquantum systems are observed constantly, their states do notchange.

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

For some types of quantum systems, there is a Quantum Anti-ZenoEffect, whereby observation accelerates change of state. TheQuantum Anti-ZenoEffect is described in quant-ph/9901060 by M. Lewenstein and K.Rzajzewski. Their abstract states: "... near threshold decayprocesses may be accelerated by repeated measurements. Examplesinclude near threshold photodetachment of an electron from a negativeion, and spontaneous emission in a cavity close to the cutofffrequency, or in a photon band gap material.".

Pascazio andFacchi, in their paper quant-ph/9904076 entitiled Modifying theLifetime of an Unstable System by an Intense ElectromagneticField, say: "... We shall look at the temporal behavior of athree-level system ... where level #1 is the ground state and levels#2, #3 are two excited states. The system is initially prepared inlevel #2 and if it follows its natural evolution, it will decay tolevel #1. The decay will be (approximately) exponential andcharacterized by a certain lifetime, that can be calculated from theFermi Golden Rule. But what happens if one shines on the system anintense laser field, tuned at the transition frequency 3-1? ... theso-called quantum Zeno effect ... the lifetime of the initial statedepends on the intensity of the laser field. In the limit ofextremely intense field, the decay should be considerably sloweddown. ... for physically sensible values of the laser field, thedecay can be enhanced, rather than hindered. This can be viewed as an"inverse" quantum Zeno effect. The whole problem is related toelectromagnetic inducedtransparency ...".

In Towards aquantum 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 standardabsorption tomography can be outperformed by a simple interferometricsetup, provided that the different levels of "gray" in the sample arenot uniformly distributed. The technique hinges upon the quantum Zenoeffect and has been tested in numerical simulations. ...".

 

Both the Quantum Zeno Effect and Quantum Anti-Zeno Effect could beused by a

Quantum Mind to choosea Branch of the Many-Worlds.

 


Uncertainty Principle

Cerf andAdami have shown that information theoryof quantum computers can give negativeconditional entropies for quantum entangled systems. Thereforenegative virtual information can be carried by particles, and quantuminformation processes can be described by particle-antiparticlediagrams much like particle physics diagrams.

Consequently, the underlying structure of Many-Worldsabstract life forms should be fundamentally similar to that ofLight-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                         |                      x                     xxx                   xxxxxxx              xxxxxxxxxxxxxxxxx due to "quantum uncertainty".   Instead, say that the particle is really at a point in space-time                       |                      x 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 createdsort 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                        |                x                             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, 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.   


 

 

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