THE ALMOST IMPOSSIBLE WORLDS IN QUANTUM INFORMATION

And their Influence on Reality

Vasil Penchev

vasildinev@gmail.com, vaspench@abv.bghttp://www.scribd.com/vasil7penchevhttp://www.wprdpress.com/vasil7penchevCV: http://old-philosophy.issk-bas.org/CV/cv-pdf/V.Penchev-CV-eng.pdf

Worlds and the states of a quantum system

• The many-worlds interpretation (Hugh Everett III, John Wheeler, Bryce DeWitt) of quantum mechanics can identify a possible state of a quantum system with a possible world one-to-one. Both can be considered as possible states of the universe

• The world or the universe can be considered both as a coherent superposition of possible states and as a statistical ensemble of possible worlds, one of which the measurement choices randomly as a principle

Hilbert space

MeasurementChoice

The coherent superposition

of unorderablestates

The well-ordered statistical ensemble

of “worlds”

???“Hidden variables?”

The exact thesis of the many-worlds interpretation:

HILBERT SPACE IMPLIES: STATE = WORLD

No!

The possibility and probability of a state or world

• The quantity of the possibility of a state or world is the probability determined by the corresponding wave function associated with the state or with the world according to the many-worlds interpretation

• Thus possibility is thought in the way of probability, i.e. both as a holistic whole of possibilities (a coherent state) and as a choice among an ensemble of possible worlds

The almost impossible worlds (states)

• A state or world with converging to zero, but nonzero probability, can be designated as an almost impossible one unlike those with exactly zero probability, which are quite impossible

• Thus a coherent superposition of those almost impossible states or an ensemble of those almost impossible worlds can have some nonzero probability

World and quantum state• The identification of ‘world’ and ‘quantum state’

can be generalized from the many-worlds interpretation to quantum mechanics at all thus:

• Quantum mechanics does not differ any coherent superposition from any corresponding ensemble (set) both being described by one and the same mathematical formalism, that of Hilbert space

• That is: It identifies any “much” with a one-to-one defined “many”. Those are the “much” of coherent states and the “many” of possible worlds in the case in question

The exact thesis of the “much – many” interpretation

HILBERT SPACE IMPLIESA COMMON MEASURE

OF “MUCH” AND “MANY” AND THUS “STATE = WORLD”

The unit of that common measure is a qubit: That is: , where are complexnumbers such that: , and are two orthogonal subspaces of Hilbert space normable to two orthonormal bases, e.g. two successive “axes”such as:

The idea of quantum invariance

• That identification of “much” and “many” originating from the common mathematical formalism of Hilbert space can be generalized as a special principle, that of quantum invariance

• It involves the axiom of choice to guarantee a well-ordering of any quantum “much” leading to the corresponding “many”

• Nevertheless the initial “much” excludes any well-ordering and thus the axiom of choice because of the absence of “hidden variables” (Neumann 1932; Kochen, Specker 1968)

A qubit (quantum bit) is the unit of the generalized quantum information:

A qubit is isomorphic to a unit 3D ball, where are represented as any two orthogonal great circles

Classical information1 bit = 1 binary (or any finite) choice

Quantum information1 qubit = 1 infinite choice

The axiom of choiceneedsneedn’t

The unit of information is a choice

01

+𝛽 ¿𝜶

The measurement between a world and a quantum state

• The experimentally verifiable part of quantum mechanics cannot differ ‘world’ with probability one after measuring from ‘state’ with probability less than one before measuring

• The world being randomly chosen among many ones absorbs all probability and thus possibility of them to acquire reality

• The measurement is both the boundary and mediator between “virtuality” (as a whole of possibilities) and the reality of one among all

Measurement is a mapping of the measured into a well-ordering of results

=A unit of information = A unit of measurement

1 qubit 1 quantum measurement=

INFORMATION = MEASUREMENT

MeasurementChoice

Well-ordering

The axiom of choice

Coherent superposition vs. statistical ensemble

• Consequently quantum mechanics underlies and requires the identification of the coherent superposition of ‘states’ before measuring with the statistical ensemble of ‘worlds’ after measuring

• The so-called many-worlds interpretation is not more than an example of a much more general principle contradicting the prejudices of “common sense”

• That general principle called quantum invariance delivers the identity of coherent superposition and statistical ensemble in particular

Quantum information implies: “No hidden variables in quantum mechanics!”

“Hidden variables” means:

The well-orderedstatistical ensembleafter measurement

implies“Hidden variables”order in secret thecoherent super-position of statesbefore measurementAnd thus:

The mapping of “much” into “many” is an identity and that of a coherent state intoa statistical ensemble as well

However quantum information or measurement isjust that mapping turning out to be trivial, empty, or “transparent”

not t

rue

Two kinds of impossible worlds• One can define ‘impossible world’ in quantum

mechanics as a state of a quantum system having zero or converging to zero probability

• Consequently one can distinguish two kinds of impossible worlds in quantum mechanics: quite impossible or almost impossible ones accordingly

• For the absorption of possibilities (probabilities) they differ from each other in their influence on reality or in their capability to turn out transformed into reality: The latters unlike the formers have potency to became reality

Content logical contradictions

Do not content logicalcontradictions

The probability of a single quite impossible world to occur is exactly zero

The probability of a single almost impossible world to occur converges to zero

The probability of anycollections of those is exactly zero, too

The probability of big enough collections of those can be nonzero

Their impossibility is logically necessary

The impossibility of an almost impossible worldis empirical: It occurs withzero probability: However this is a fact but not a logical corollaryTheir impossibility is

“a priori” Their impossibility

separately is “a posteriori”

Almost impossible worlds

Quite impossible worlds

The infinite set of impossible worlds• If the latter is the case, a consisting of those states

set of infinite measure can have a finite nonzero probability

There are two cases according to the corresponding integration ranges for compact sets. For example: or , where is a probability density distribution such that: is finite, and is infinite: symbolizes an almost impossible world from a compact set of ones, and is its probability density ‘almost zero’ for any world of those is ‘almost impossible’

Can reality consist of all quite impossible worlds?

What happens with the quite impossible worlds then? They constitute ... reality caged in space-time:Indeed the well-ordering of time (or space-time) disciplines the quite impossible worlds curing them of contradictions so:The theses and antitheses of the contradictions are divided in different periods of time and that world is cured of the perfect impossibility: Thus it has become a “righteous citizen” of the universe, an almost impossible one

Relativity of the worlds

Space-time

𝒏𝒐𝒓𝒎𝒂𝒍𝒊𝒛𝒂𝒕𝒊𝒐𝒏→

𝒅𝒆𝒏𝒐𝒓𝒎𝒂𝒍𝒊𝒛𝒂𝒕𝒊𝒐𝒏←

probabilitydensitydistribution

𝒅𝒆𝒐𝒓𝒅𝒆𝒓𝒊𝒏𝒈→

𝒘𝒆𝒍𝒍−𝒐𝒓𝒅𝒆𝒓𝒊𝒏𝒈←

One can easily obtain reality caged in space-time and all almost impossible worlds free of space-time thus:

Quantum information [qubits]

Caging in space-time generates the non-zero probability density of reality

All almostimpossibleworlds ()All quite impossible worlds ()

“Cure”: Well-orderingDenormalization

Expanding space-time ()

+

Probabilitydensitydistribution

∞. 𝟎 = .∞𝟎Minkowski space

Quantuminvariance

Hilbert space

The occurrence of the impossible

• One of those “almost impossible” states will happen by the probability of the whole set after measuring the quantum system

• One can utilize the metaphor of “jackpot” for measurement: All possible worlds being even almost impossible participate in the lottery “raffling reality”. Any possible world can win and turn into the real one according to the number of its “tickets” (its value of probability density), but even those “without money for tickets” wishing to participate and keeping the laws (i.e. the almost impossible worlds) have some chance to win

The winner in the quantum lottery of reality

The possible worlds “with tickets”: Their chance separately to win is zero but proportional to the ratio of the numbers of “tickets” of each other

The almost impossible worlds “without tickets”:

Their chance collectively to win can be nonzero, and

proportional to the number of unsold tickets

Possible worlds (a continuum)

Almost impossibleworlds (a continuum)

NeedsThe axiom of choice

The probabilitydensity distribution

Nonzeroprobability

density

Converging to zero

probabilitydensity

The metamorphosis of an almost impossible world into a real one

• Consequently that measurement can turn an almost impossible world into a real one

• One can continue the metaphor: If any possible world is an individual participant, any almost impossible world is a collective sharer among an infinite number of ones. Its collective partakes as an individual participator. If that collective participator wins, a “secondary lottery” within the “primary one” will determine a single almost impossible world as the winner of the jackpot of reality

The democratic constitution of the universe:Reality

The distribution of the lottery winners in the

probability density distri-bution

Almost impossible worlds Slightly possible worlds

Possible worlds Very possible worlds

The universe is dominated by poor by honest (keeping the laws) “citizens” (the almost impossible worlds). The breaches the laws (the quite impossible

worlds) are being removed automatically, deprived of any chance or ... constitute all possible worlds

An example: tunnel junction

• Tunnel junction is a phenomenon, which can illustrate this:

• According to classical mechanics no particle can jump out of a potential well. Tunnel junction in quantum mechanics means that a quantum “particle” can do it with nonzero probability

• Any state of that “particle”, which is out of the well, is almost impossible but such an almost impossible world can win reality after the measurement for the collective sited out of the well possesses a definite nonzero probability according the laws of quantum mechanics

EnergyProbabilitydensity

A quantum anything,e.g. an electron

Position

A potentialwell

The integral probability for the thingto be within the well < 1, e.g. = 0,7

The integral probability for the thing to be out of the well >0, e.g. = 0,3

Almostimpossibleworlds

Tunnel junction

The explanation of tunnel junction

• The prerequisite for it to happen is the measured state to belong to a set of infinite measure:

• It is implemented for any state out of the potential well according to quantum mechanics:

• All probability within the well is rather less than one as to quantum particles commeasurable with the Planck constant, and a big enough ensemble of measurements can verify that “positions” out of the well occur

EnergyProbabilitydensity

Position

The integral probability for the thingto be within the well < 1, e.g. = 0,7

The integral probability for the thing to be out of the well >0, e.g. = 0,3

(No) almostimpossibleworlds

A classical body

=1

=0

All classical is actual and ... grey

(No) tunnel junction in the macroscopic world

• Nothing like this can observed in the macroscopic world: no “unsold tickets” of the lottery of reality:

• The probability of a macroscopic body to leap over the potential barrier is too small to be recorded experimentally

• However special phenomena such as those in tunnel diodes or superconductors are based on the tunnel junction of the physical quantities in macroscopic bodies

Entanglement and quantum information

• Quantum information is that part of quantum mechanics which studies the phenomena of entanglement

• Entanglement is defined strictly as the relation of any Hilbert space to those Hilbert spaces, of which it cannot be a tensor product:

• Since any quantum system and its subsystems correspond to some Hilbert spaces, entanglement can be interpreted physically in terms of those and it has originated historically from quantum mechanics

Quantum system 1Quantum system 2

World 1World 2

State 1State 2

Quantum correlations

≤2√2

Classical correlations≤2

Entanglement

The violation of Bell’s inequalities

A sufficient condition for:

Quantum system 1

Quantum system 2

World 1World 2

State 1State 2

EntanglementA double interaction:

both of worlds and states

Each qubit is for two identicalqubits: the one for the world,

the other for the stateSimultaneous correlation of a pair of conjugates

The entanglement of a set of almost impossible states

• A set of almost impossible states having nonzero common probability is entangled with another of any probability distribution:

• Those almost impossible states share a Hilbert space , and the states of the other share another one :

• However that of the system of both cannot be factorized to those of and . That is:

The commonquantum

system of all

Some otherquantumsystem

All almostimpossibleworldsWorld 2

All almost impossible states

State 2

ℍ𝟏ℍ𝟐

ℍℍ≠ℍ𝟏  ⨂  ℍ𝟐

The deformation of probability distribution for entanglement

• Entanglement will cause some restricting deformation of the probability density distribution

• This is equivalent to the action of some physical force or to the interaction with some physical body or radiation correspondingly with some nonzero mass at rest or energy

• The above case of entangled almost impossible states (worlds) can cause the same effect on the other entangled system as the action of some unknown force or interaction

The commonquantum

system of all

Some otherquantumsystem ℍ𝟏ℍ𝟐

Probability density distributions

A2(x2):Some quantity (A2) of the systemin some point (x2) The conjugate (A1)

in some point (x1)

The entangled almost impossible worlds as a physical force

• Consequently the entangled almost impossible worlds can act as a physical force or interaction determining reality:

• Any of those worlds is impossible separately: Nevertheless a nonzero-measure ensemble of them acts on reality and can be even the most significant force or interaction:

• One can say figuratively that the impossible can be what determines the actual more than the actual itself or the possible

Five scenarios of how one can distribute the entire probability of reality

“Tyranny” (in classical physics)

“Democracy” (in quantum mechanics)

“Communism”

“Oligarchy”

“Socialism”

Probability density distribution ScenariosReality Irreality100% 0%

100% 0%

100% 0%

100%0%

100%0%

Entanglement and Lorentz invariance

• Entanglement is not Lorentz invariant: • This allows the quantum correlation of any region

within the light cone with any other sited outside of it (defined according to the special relativity)

• Thus it can act at a distance, i.e. at any even at infinite distance.

• (By the way Einstein rejecting it called it “spooky” being able to be due only to “God’s gambling in dice”. Nevertheless the experiments prove that is the case)

Entanglement does not depend on the distanceEntanglement is action at any distance (i.e. that action at a distance in classical physics)

Entanglement depends only on the nonorthogonality of any Hilbert spaces associated with any quantum things anywhere

One might say that entanglementis implemented by the mediation of the universe as a whole

Minkowski space

Space-time

The “dark” action of entanglement• It can act beyond the visible universe remains

“dark” as “dark matter” or “dark energy”• The visible universe is the region of space-time and

a segment of the light cone. It can be thought as a potential well having an infinite barrier for anything with nonzero energy within the light cone

• Nevertheless the laws of quantum mechanics allow the tunnel junction across the light barrier and thus all region outside of it (i.e. outside of space-time) is a collection of almost (but not quite) impossible worlds

Space-time = an infinite potential well

Probability density distribution

⇒Tunnel junction outside of it ⇒

All possibleworlds

Entanglement

All almost impossible worlds

The universe as a heart of entanglement

Minkowski space

Minkowski space

Space-time = The visible universe =???= Reality?

Out of the space-time = The dark universe

Probability density distribution

The “socialism” scenario is trueIf “Yes!”:

96% of the universe are dark!4% are visible!

Entanglement as an explanation of “dark” phenomena

It is a possible explanation for these mysterious phenomena discovered recently in physics and designated correspondingly as:Dark matter: the matter of our galaxy, the Milky

way, should be rather more than visible one not to break into parts due to the centrifugal forces according to its rotation speed

Dark energy: the energy necessary to maintain the observed acceleration of the universe expansion

Both can be due to the entanglement with the region outside of the light cone

The visible universe

The Genesis of Being

Probability density distribution

Stage 1:Nothing

Stage 2:The laws

Stage 3:Jail for the breaches

Stage 4:Being

“Let there be the light cone!”4% OF

BREACHES

“Space-time for the breaches!”

“Mathematics!”

96% OF

RIGHTEOUS WORLDS

Entanglement:God’s Love

The dark universe

Who acts: the whole or its element?

• Furthermore, the action of almost impossible worlds cannot be ascribed to any separate entities but only to a whole of such ones

• The action of any single impossible world is practically zero for its probability converges to zero

• Nevertheless the integral action of all impossible worlds, to which that belongs, is finite

• Consequently only the whole influences rather than any single element of it

The set is exactly equal to the sum of its elementsThe interactions between

the elements are exactly zeroThe set is more than the sum of its elements

The sum of the elements is exactly zero and any element as well

The interactions between the elements are more than zero

The set is exactly equal to the interactions betweenthe elements. Mathematically it is an set of emptysets. Physically it is an entangled vacuum. Logicallyit is a set of almost impossible worlds It can be also interpreted as an empty set with some nonzero possibility to be chosen: Indeed, can an empty set be chosen due to the axiom of choice? Obviously, it should be able to

A sum

A systemA wholeness

About the sense for an empty setto be chosen

• The interpretation of the axiom of choice thus that an empty set can be chosen is logically consistent

• The sense: You go shopping and buy that, that, that. All of them are chosen by youYou go shopping and buy nothing. You have chosen an empty setA probability of that to happen can be assigned in both cases

The idea of holistic action• The almost impossible worlds can act only holistically

and be discovered only by means of their effects indirectly remaining “dark” or “hidden” in principle

• The almost impossible worlds can be thought as some holistic being, which is only as a whole, but not as a collection or as a set of any nonzero elements:

• In that sense it can be thought as a set without elements and represented somehow in terms of set theory as an empty set, to which is assigned any finite probability of that to be chosen

• On the base of that probability, its analog in quantum mechanics can act physically

Their wholeness:

Probability = P ≠ 0

Energy = ?

??

h - the Planck constantt – time, ν- frequency

Any element ofentangled

nothing:Probability → 0

Energy = 0 However

the interpretation of is quite “dark”

is Q, quantum information, i.e. thequantity of “much” (for ‘probability’) per a unit of “many” (for ‘time’) = qubits

𝑬=𝒉𝑸

𝑬=𝒉𝑸𝑬=𝒉𝝂=𝒉

𝒅𝑷𝒅𝒕

Thus: Its being is not actual since it is nothingHowever: It can act just as anything from reality

Furthermore: It is physically the most power force forming reality

A wholeness =A probable nothing The “dark”

being Transcendence

The wholeness of reality

(In fact the reality as we know it or imagine to know)

Reality4%

The modality of almost impossible worlds

The being of the almost impossible worlds in quantum mechanics and information can be distinguished as a separate modality possessing unique features:• Taken separately, any almost impossible world

neither exist nor can exist, but yet no prohibition to exist

• Nevertheless it can turn out a real one after measurement thanks to the axiom of choice, and

• It can impact reality in a sense

An almost impossible world can become a real one

• Any almost impossible world can be transformed into a real one after measurement like a possible one though its probability is zero practically

• However that kind of transformation requires it to be somehow chosen among a continuum of similar worlds and thus, the axiom of choice

• Fortunately the axiom of choice and thus its choice is guaranteed by quantum invariance discussed above. Measurement is what implements the choice practically

An almost impossible world can act on reality

• An almost impossible world can act on reality as an element of a set of infinite measure only holistically and thus remaining invisible, “dark”

• One can distinguish an almost impossible world from a quite impossible world only logically after both cannot have any individual verification experimentally

• Physically it means that an almost (unlike quite) impossible world is a bound nothing or nonbeing. Its being consists in its infinite connectivity and can be physically interpreted as the entangled vacuum

‘Dark’ modality• Said metaphorically, that modality of an almost

impossible world can be called ‘dark’• It is an allusion to the concepts of “dark matter”

or “dark energy” in physics recently: There it designates very powerful physical action originating from some missing or unknown source, as if from the physical nonbeing

• Analogically the term of “dark modality” leads to that action, which comes from nonbeing or from the transcendent. Nevertheless it can be founded scientifically

Collective or holistic being

• The being of such a world should be denominated as collective or holistic rather than individual or separate

• Any almost impossible world considered separately is quite impossible and thus it has not any individual being

• However it has that potency to unite with infinitely many other similar almost impossible worlds, which acquire a common collective being jointly

End

Thank youfor your kind

attention!

References:

• DeWitt, Bryce and John Wheeler (eds.) 1968. The Everett-Wheeler Interpretation of Quantum Mechanics. Battelle Rencontres: 1967 Lectures in Mathematics and Physics. New York: W.A.Benjamin.

• Everett III Hugh1957. „Relative state” Formulation of Quantum Mechanics,” Reviews of Modern Physics. Vol. 29, No 3 (July 1957), 454-462.

• Kochen, Simon and Ernst Specker 1968. “The problem of hidden variables in quantum mechanics,” Journal of Mathematics and Mechanics. 17 (1): 59-87.

• Neumann, Johan von 1932. Mathematische Grundlagen der Quantenmechanik, Berlin: Verlag von Julius Springer.