MORE THAN IMPOSSIBLE:

NEGATIVE AND COMPLEX PROBABILITIES AND THEIR INTERPRETATION

Vasil Penchev

• Bulgarian Academy of Sciences: Institute for the Study of Societies and Knowledge (Institute for Philosophical Research): Dept. of Logical Systems and Models

• Vasildinev@gmail.com

Modal Metaphysics: Issues of the (Im)Possible IV ⦁Bratislava, Slovakia (Klemensova 19) ⦁

August 30-51, 2016 ⦁

More than impossible?• What might mean “more than impossible”?

For example, that could be what happens without any cause or that physical change which occurs without any physical force (interaction) to

act ⦁• Then, the quantity of the equivalent physical force, which would cause

the same effect, can serve as a measure of the complex probabilityFurthermore, the same effect is interpretable as re-ordering and thus as

a certain quantity of information ⦁• One can write a very intriguing equation:

𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝐹𝐹𝐹𝐹𝐹𝐹𝑃𝑃𝐹𝐹 = 𝑇𝑇𝑃𝐹𝐹 𝑆𝑆𝑃𝑃𝑆𝑆𝐹𝐹 𝐸𝐸𝐸𝐸𝐸𝐸𝐹𝐹𝑃𝑃𝐸𝐸 = 𝐼𝐼𝐼𝐼𝐸𝐸𝐹𝐹𝐹𝐹𝑆𝑆𝑃𝑃𝐸𝐸𝑃𝑃𝐹𝐹𝐼𝐼.

Information

Relation of probability(distributions)

(Re-ordering)Relation of orderings

Synchronic viewpoint Diachronic viewpoint

Definition in Shannon Definition in Kolmogorov

The conceptof physical force

The space-time interpretationof quantum information

My presentation now

The conceptof curved space-time

More than impossible? Of course, quantum mechanics

• Quantum mechanics introduces those fluctuations, the physical actions of which are commensurable with the Plank constant

They happen by themselves without any cause even in principle ⦁

• Those causeless changes are both instable and extremely improbable in the world perceived by our senses immediately for the physical actions in our world are much, much bigger than the Plank constant

The problem:NEGATIVE AND COMPLEX PROBABILITY

LINKED TO FORCES IN SPECIAL AND GENERAL RELATIVITYFAQ:What is the intrigue?

That cherished bridge between quantum mechanics and general relativity (including special one, or more exactly special relativity including general one) built by stones of

quantum informationHow or how far?

Absolutely, for complex probability implies quantum information and thus quantum mechanics

Kinematics for dynamics

• Meaning that negative and complex probabilities which have been already linked to physical forces in quantum mechanics valid in the Plank scale, one should research that way for them to be introduced in special and general relativity, which should be valid in both macroscopic and microscopic (Planck) scale

This implies one to use only the kinematic formulation neglecting the dynamical one for the latter involves mass and energy right

distinguishing the scales from each other practically as the distances are unified as macroscopic according to the real

apparatuses for quantum phenomena ⦁

‘Reference frame’ as the key to kinematics

• Particularly, ‘force’ is defined per a unit of mass (energy), and therefore equated to acceleration after kinematic consideration

‘Reference frame’ is the key concept as it is properly kinematic ⦁• Still one restriction is representability in terms of quantum

information, and more especially, by the concept of qubit One needs it for the consistency and coherence of the

considerations in quantum mechanics (and information) and both special and general relativity ⦁

What a qubit is:

• A qubit is defined as 𝛼𝛼 0 + 𝛽𝛽|1⟩, where 𝛼𝛼 and 𝛽𝛽 are two complex numbers so that 𝛼𝛼 2 + 𝛽𝛽 2 = 1, and 0 , |1⟩ are two orthogonal subspaces of the complex Hilbert space(abbreviated as “cHs” further)

For any two successive axes (𝐹𝐹𝑖𝑖𝑖𝑖𝑖𝑖, 𝐹𝐹𝑖𝑖 𝑖𝑖+1 𝑖𝑖) of cHs can be interpreted as those 0 , |1⟩, cHs or any point in it can be

represented as a series of qubits (𝑄𝑄𝑖𝑖), correspondingly “empty” or “fulfilled” by the values 𝛼𝛼𝑖𝑖, 𝛽𝛽𝑖𝑖 ∈ 𝑄𝑄𝑖𝑖 ⦁

Qubit as space-time and thus kinematics• Any qubit is isomorphic to a unit ball in the usual 3D Euclidean space if

two points are chosen in that ball: the one in the ball (including its surface, which is a unit sphere), and the other in the surface

Thus, a qubit (being a 3D ball) means the same what Minkowski space is a certain moment of time ⦁

• That isomorphism is both elementary and crucial for our consideration Indeed, it guarantees the equivalent transfer of negative and complex

probabilities between quantum mechanics (the former, “left side” of isomorphism) and both special and general relativity (the latter, “right

side”) ⦁

0

1

𝛼𝛼 0 + 𝛽𝛽 1

∅ = 2𝑃𝑃𝐸𝐸

Minkowskispace

Imaginarysubarea

The past

11

ImβReβ

β

0

ReαImα

α0

A qubit as an inertial reference frame

• Indeed, a qubit, already as a unit ball with two points “recorded” in it, allows for another interpretation as an inertial reference frame 𝒓𝒓𝟎𝟎, 𝒗𝒗 :

The point (vector) within the ball (𝜶𝜶 = 𝛼𝛼𝑥𝑥 , 𝛼𝛼𝑦𝑦, 0) corresponds to the zero of frame (𝒓𝒓𝟎𝟎 = 𝑥𝑥0, 𝑃𝑃0, 𝑧𝑧0) and that on its surface (𝜷𝜷 = 𝛽𝛽𝑥𝑥, 0, 𝛽𝛽𝑧𝑧)

to the speed of inertial frame 𝒗𝒗 = 𝑣𝑣𝑥𝑥, 𝑣𝑣𝑦𝑦, 𝑣𝑣𝑧𝑧 ⦁• The one-to-one mapping of the components of a qubit and those of

an inertial frame is what is implied:

𝑥𝑥0 = 𝑃𝑃𝛼𝛼𝑥𝑥𝐸𝐸0; 𝑃𝑃0 = 𝑃𝑃𝛼𝛼𝑦𝑦𝐸𝐸0; 𝑧𝑧0 = 0; 𝑣𝑣𝑥𝑥 = 𝑃𝑃𝛽𝛽𝑥𝑥; 𝑣𝑣𝑦𝑦 = 0; 𝑣𝑣𝑧𝑧 = 𝑃𝑃𝛽𝛽𝑧𝑧

0

1

𝛼𝛼 0 + 𝛽𝛽 1

11

ImβReβ

β

0

ReαImα

α0

Space position in 𝐸𝐸 = 𝐸𝐸0:𝑥𝑥0 = 𝑃𝑃𝛼𝛼𝑥𝑥𝐸𝐸0; 𝑃𝑃0 = 𝑃𝑃𝛼𝛼𝑦𝑦𝐸𝐸0; 𝑧𝑧0 = 0

Relative velocity:𝑣𝑣𝑥𝑥 = 𝑃𝑃𝛽𝛽𝑥𝑥; 𝑣𝑣𝑦𝑦 = 0; 𝑣𝑣𝑧𝑧 = 𝑃𝑃𝛽𝛽𝑧𝑧

This means:complementarityinterpreted asindependence(orthogonality)

0

1

𝛼𝛼 0 + 𝛽𝛽 1

1

0

Space position in 𝐸𝐸 = 𝐸𝐸0:𝑥𝑥0 = 𝑃𝑃𝛼𝛼𝑥𝑥𝐸𝐸0; 𝑃𝑃0 = 𝑃𝑃𝛼𝛼𝑦𝑦𝐸𝐸0; 𝑧𝑧0 = 0

Relative velocity:𝑣𝑣𝑥𝑥 = 𝑃𝑃𝛽𝛽𝑥𝑥; 𝑣𝑣𝑦𝑦 = 0; 𝑣𝑣𝑧𝑧 = 𝑃𝑃𝛽𝛽𝑧𝑧

This means:complementarityinterpreted asindependence(orthogonality)

Thus complementarityrefers to the systemas a single one whole

Thus entanglement

refers to the system

as composed bysubsystems

0

1

𝛼𝛼 0 + 𝛽𝛽 1

1

0

Space position in 𝐸𝐸 = 𝐸𝐸0:𝑥𝑥0 = 𝑃𝑃𝛼𝛼𝑥𝑥𝐸𝐸0; 𝑃𝑃0 = 𝑃𝑃𝛼𝛼𝑦𝑦𝐸𝐸0; 𝑧𝑧0 = 0

This means:entanglementinterpreted asdependence(nonorthogonality)

Relative velocity:𝑣𝑣𝑥𝑥 = 𝑃𝑃𝛽𝛽𝑥𝑥; 𝑣𝑣𝑦𝑦 = 𝑃𝑃𝛽𝛽𝑦𝑦; 𝑣𝑣𝑧𝑧 = 𝑃𝑃𝛽𝛽𝑧𝑧

Thus complementarityrefers to the systemas a single one whole

Thus entanglement

refers to the system

as composed bysubsystems

Another representation of a qubit as an inertial frame

• Any qubit have three independent variables, e.g. 𝑅𝑅𝐹𝐹 𝛼𝛼 , 𝐼𝐼𝑆𝑆 𝑃𝑃 , 𝑅𝑅𝐹𝐹(𝛽𝛽), which can be interpreted e.g. as c. 𝑅𝑅𝐹𝐹 𝛼𝛼 = 𝑣𝑣𝑥𝑥, 𝐼𝐼𝑆𝑆 𝑃𝑃 = 𝑣𝑣𝑦𝑦, 𝑅𝑅𝐹𝐹 𝛽𝛽 = 𝑣𝑣𝑧𝑧

• Then two options appear as the initial position of the inertial reference frame:

𝑥𝑥0 = 𝑃𝑃0 = 𝑧𝑧𝑜𝑜 = 0 (accepted as a convention)An additional and complementary qubit is necessary to

represent any initial position of the inertial reference frame at issue ⦁

• Even more, the former and latter (this) representation can be unified as follows visualized:

SystemSubsystems

Independence Dependence

In Lagrange

In Hamilton

0

1

𝛼𝛼 0 + 𝛽𝛽 1

0

1

𝛼𝛼 0 + 𝛽𝛽 10 1

A bit A bit0 1

OverlapDisjunctionPositionqubit

Positionqubit

Speedqubit

Complementarity Entanglement

SystemSubsystems

Independence Dependence

In Lagrange

In Hamilton

0 1A bit A bit

0 1OverlapDisjunction

Complementarity Entanglement

Ψ ΨNonentangled Entangled

Ψposition ΨspeedΨposition

Ψspeed

A set of inertial RFsA set of noninnertial RFsfor 𝑣𝑣 = 𝑣𝑣(𝑥𝑥)

Interaction orpotential forcefield in classical physics

SystemSubsystems

Dependence

In Lagrange

In Hamilton

Entanglement

ΨEntangled

ΨpositionΨspeed

A set of noninnertial RFfor 𝑣𝑣 = 𝑣𝑣(𝑥𝑥)

Interaction orpotential forcefield in classical physics

General relativity

A world line in the smoothly curved

Minkowski spaceto pseudo-Riemannian

space

A world line ofposition

A world line ofspeed

Minkowski space

The sense of the conventions

• The convention "𝑧𝑧0 = 0; 𝑣𝑣𝑦𝑦 = 0" means that the qubit is correspondingly oriented according to the reference frame unambiguouslyAny nonzero rotation of the unit ball would define a different

inertial frame ⦁• The parameter "𝐸𝐸0" is a conventionally chosen ordinary

moment

And thus a new and more than intriguing equation:

𝐴𝐴 𝑄𝑄𝑄𝑄𝑄𝑄𝑃𝑃𝐸𝐸 = 𝑃𝑃𝐼𝐼 𝐼𝐼𝐼𝐼𝐹𝐹𝐹𝐹𝐸𝐸𝑃𝑃𝑃𝑃𝑃𝑃 𝑅𝑅𝐹𝐹𝐸𝐸𝐹𝐹𝐹𝐹𝐹𝐹𝐼𝐼𝑃𝑃𝐹𝐹 𝐹𝐹𝐹𝐹𝑃𝑃𝑆𝑆𝐹𝐹

A connection to kinematics• Further, the probability "𝑝𝑝" associable with the inertial frame may be

conventionally specified as "𝑝𝑝 = 𝛼𝛼 2" so that 𝛼𝛼 corresponds to the module of wave function just as in the Max Born interpretation of itIndeed, then "𝑣𝑣 = 𝒗𝒗 = 𝛼𝛼 " or as “kinematic momentum” per a unit of mass (energy) might be the “length” of an elementary permutation defined as above, and its change in time would represent acceleration

as “kinematic force” ⦁

A bird’s eye view to the same:

𝐼𝐼𝐼𝐼𝐸𝐸𝐹𝐹𝐹𝐹𝑆𝑆𝑃𝑃𝐸𝐸𝑃𝑃𝐹𝐹𝐼𝐼 = 𝑃𝑃𝐹𝐹𝐹𝐹𝑄𝑄𝑃𝑃𝑄𝑄𝑃𝑃𝑃𝑃𝑃𝑃𝐸𝐸𝑃𝑃 𝐶𝐶𝑃𝑃𝑃𝐼𝐼𝐶𝐶𝐹𝐹 = 𝐴𝐴𝑃𝑃𝑃𝑃𝐹𝐹𝑃𝑃𝐹𝐹𝐹𝐹𝑃𝑃𝐸𝐸𝑃𝑃𝑃𝑃𝐹𝐹𝐼𝐼= 𝐾𝐾𝑃𝑃𝐼𝐼𝐹𝐹𝑆𝑆𝑃𝑃𝐸𝐸𝑃𝑃𝑃𝑃 𝐹𝐹𝐹𝐹𝐹𝐹𝑃𝑃𝐹𝐹: 𝑰𝑰 = ∆𝑷𝑷 = 𝒂𝒂 =

𝝏𝝏𝝏𝝏𝝏𝝏𝝏𝝏

The demarcation of general and special relativity

• Further, the unity of ‘pure imaginary probability’ and ‘force’ as above allows of still one interpretation of the relation of special and general relativityThe new interpretation is consistent to the standard one, but

different from it ⦁• According to the latter, the demarcation line between special

and general relativity is right the quantity of acceleration (𝒂𝒂)of the studied reference frames: zero in inertial reference frames (special relativity) and nonzero in noninertialreference (general relativity)

All you need is tachyon

• According to the new interpretation, one should complement that distinction by the identification of any hypothetical superluminal inertial frame (𝒓𝒓𝟎𝟎, 𝒗𝒗: 𝒗𝒗 = 𝑣𝑣 > 𝑃𝑃)with just one certain noninertial subluminal reference frame 𝒓𝒓𝟎𝟎, 𝒗𝒗, 𝒂𝒂: 𝒗𝒗 = 𝑣𝑣 < 𝑃𝑃

The hypothetical particles with superluminal velocity were called “tachyons”. The new interpretation would add the identification of the tachyons as accelerated subluminal

particles ⦁

General relativity

Interpretation in Lagrange:Speed is the 1st derivative of

position: space-time is smooth,but curved: pseudo-Riemannian

The real subarea of it is redundant, but there are arbitrarily accelerated RFs

That viewpoint implies “forces” & “forcefields“: gravitational field is the unified and

universal background force field, then

Interpretation in Hamilton: Speed and position are two independent variables: space-time is “straight”, but consists of two discrtely divided subareas: Minkowski spaceBoth subareas of it are necessary,but there are no accelerated RFs

Standard interpretation

Now: non-standard interpretation

That viewpoint implies “re-orderings” as “forces” being mappings betweenthe two subareas

General relativity =quantum mechanics

Interpretation in Hamilton: the qubit Hilbert space is the normed

nonstandard equivalent of Minkowski space: each of both

identical subareas is transformed in any of both dual identical spaces

Both dual spaces are necessary being “complementary” to each other

The “forces” & “force fields“ are understoodin an equivalent but opposed way (like in a “negative photo”): as symmetries and thus

conservations (what is not re-ordered)

Interpretation in Hamilton: Speed and position are two independent variables: space-time is “straight”, but consists of two discretely divided subareas: Minkowski spaceBoth subareas of it are necessary,but there are no accelerated RFs

Standard interpretation

Now: non-standard interpretation

That viewpoint implies “re-orderings” as “forces” being mappings betweenthe two subareas

Generalrelativity

Quantummechanics

Forces & Force fields

Interactions

Asymmetries & Re-orderings

Symmetries & conservations

A new fundamental symmetry in cognition,which already was visualized on the

previous slide:

The symmetry to the diagonal:what else is necessary to be transformedonce general relativity is transformed in quantum mechanics

That is the axis of

It implies the symmetryof general relativity

and quantum mechanics

An observer of a tachyon

• Indeed, special relativity identifies the pure imaginary values of speed with those of a reference frame moving with any superluminal relative velocity to an observerThe term “superluminal”, which means a real value ( 𝒗𝒗 = 𝑣𝑣 > 𝑃𝑃),

refers to the relative speed of a hypothetical inertial reference frame to an observer in any usual, subluminal inertial reference

frame ⦁ One can identified the physically interpreted gap between the

sub- and superluminal the mathematically interpreted one between the real and imaginary dimensions of the complex numbers

No any difference!

The physical gapbetween tachyons and subluminal particles

The mathematical gapbetween real and imaginary

numbers

I’m an angrytachyon!!!

I’m an accelerated subluminal particle

Minkowskispace

You’re here!

The observer seeing both physically and mathematically

• That observer should register pure imaginary values as to the velocities in the other, observed reference frame

According to the generally accepted model of special relativity in Minkowski space, time is purely imaginary unlike distance,

which is real ⦁• This implies for speed to be pure imaginary as time, and

acceleration to be real as distanceThe “scholia” is: one and the same gap is seen as that

between different dimensions whether mathematical(ly) or physical(ly)⦁

Mathematically

Mathematically Physically

Dimension 1 Dimension 1

Dimension 2Dimension 2

Superluminal velocity as subluminal acceleration

• Then, an observer in an inertial subluminal reference frame might not distinguish pure imaginary values of velocity from accelerations in other reference frames for both superluminal velocity and acceleration mean one and the same though expressed in two different kinds of terms: correspondingly mathematical or physicalAcceleration being a quantity different from velocity means a new

dimension expressed physically ⦁• Superluminal velocity equated to pure imaginary velocity

according to special relativity means a new dimension expressed mathematically, namely that of imaginary axis in relation to the real one

Gravitational field

• Further, the accelerated inertial frames already according to general relativity implies a force field indistinguishable from the gravitational one in turn represented by curving Minkowski space to pseudo-Riemannian one

Any tensor associable with a point in pseudo-Riemannian space is representable as the tensor product of vectors of Minkowski space as in its real as in its imaginary domain ⦁

• Particularly, the tensor of curvature in a point transforms a vector to another between the imaginary and real domain

In terms of Minkowski space

• Then, the formalism of general relativity is interpretable as presenting transformations within both domains of Minkowski space separately or together unlike that of special relativity restricted only to the one: that associated to the subluminal area usually identified with the imaginary cone (domain)

• The pair of contra- and covariant 4-vectors as to pseudo-Riemannian space is isomorphic to that of

4-vectors in each of the real and imaginary domain as to Minkowski space

THE PHILOSOPHICAL INTERPRETATION:

THE UNITED NATURE OF FORCES AND PROBABILITIES IN:

Ψ QUANTUM MECHANICS AND INFORMATIONΨ SPECIAL AND GENERAL RELATIVITYΨ PROBABILITY AND INFORMATION THEORY

The forces in physics as probabilities in mathematics

• The introduction of complex probabilities unifies forces and probabilities as two dimensions, whether mathematically or physically interpreted, of one and the same nature, that of complex probabilitiesThen both “more than impossible” and even the “squire root

of that more than impossible” acquire a clear mathematical and physical meaning:

• This means that minimal force able to reorder the entities in that more than impossible way, which is observeed

One and the same, universal observer

• All physical forces (interactions) as in quantum mechanics (and therefore in the Standard model) and in special or general relativity are a particular case of the generalized probabilities and relative to the classical, one-dimensional probabilities

Furthermore, the two dimensional (or complex) probabilities unify the subjective probabilities of the observer and the objective

probabilities of the observed, and even the one dimension might be ascribed to the former, the other to the latter ⦁

• This allows of unifying further the concept of ‘observer’ in relativity and quantum mechanics.

Hmm, what ‘observer’ is:

• The concept of observer whether in quantum mechanics or special & general relativity means two dimensions and thus a gap between them, which in modern Western philosophy are designated as “subject” and “object”

One can even think of ‘observer’ as ‘bit’ or ‘qubit’ of information, the two or infinitely many alternatives for choice of which are

interpreted or renamed philosophically as “subject” and “object”: disjunctive for the bit(s) of information or for Descartes’s dualism;

and entangled for the qubit(s) information or for any philosophical doctrine investigating the interaction of subject and object⦁

The generalized observer as the philosophical ‘subject’ as ‘totality’

observing ‘object’ inside or outside of it

𝑇𝑇𝑇𝑇𝑇𝑇𝐴𝐴𝑇𝑇𝐼𝐼𝑇𝑇𝑇𝑇 ≝: 𝑃𝑃𝐼𝐼𝑃𝑃𝑃𝑃𝑖𝑖𝐹𝐹𝑖𝑖𝑖𝑖𝑛𝑛𝑛𝑛𝑛𝑛𝑖𝑖𝑛𝑛𝑖𝑖𝑛𝑛𝑛𝑛

𝐹𝐹𝑄𝑄𝐸𝐸𝑃𝑃𝑃𝑃𝑖𝑖𝐹𝐹

‘Totality’ in definition is what is the same both inside & outside: i.e. topologically, that mathematical object

the internality of which coincides with its externality

Information and its unit philosophically:

TOTALITY⤓TIME⤓

SUBJECT (ITS INTERNALITY) OBJECT (ITS EXTERNALITY)

One can conclude that (quantum) information is the quantity of totality

The observed “inside” and “outside” • Those quantum mechanics and special & general relativity, which

are unified on the base of quantum information and qubits, should unify also their concepts of ‘observer’

The intention of observer is the invariance of both viewpoints, “outside” and “inside”, of the subjective and objective, and

particularly, of subjective and objective probability as in quantum mechanics ⦁

• The following metaphor might visualize that invariance: the observer in special & general relativity observes the other reference frame “outside”, and that in quantum mechanics observes the quantum entity “inside” the apparatus

That invariance implies that both should observer one and the same in the final analysis by means of quantum information ⦁

Generalized observer(from the viewpoint of quantum information)

𝑃𝑃𝐼𝐼𝑃𝑃𝑃𝑃𝑖𝑖𝐹𝐹𝑖𝑖𝑖𝑖𝑛𝑛𝑛𝑛𝑛𝑛𝑖𝑖𝑛𝑛𝑖𝑖𝑛𝑛𝑛𝑛

𝐹𝐹𝑄𝑄𝐸𝐸𝑃𝑃𝑃𝑃𝑖𝑖𝐹𝐹

Observer(from the view point ofquantum mechanics: apparatus)

Observer(from the view point of

S & G relativity: reference frame)

What is observed are smoothprobability distributions

and discrete(quantum)

leaps

What is observed are smoothmotions and discrete(deterministic)probabilityleaps

𝑝𝑝𝐹𝐹𝐹𝐹𝑄𝑄𝑃𝑃𝑄𝑄𝑃𝑃𝑃𝑃𝑃𝑃𝐸𝐸𝑃𝑃 𝑃𝑃𝑃𝑃𝑃𝐼𝐼𝐶𝐶𝐹𝐹𝑛𝑛𝑞𝑞𝑞𝑞𝑖𝑖𝑛𝑛𝑛𝑛𝑞𝑞𝑛𝑛𝑖𝑖𝑛𝑛𝑛𝑛

𝑃𝑃𝑝𝑝𝑃𝑃𝑃𝑃𝐹𝐹𝐸𝐸𝑃𝑃𝑆𝑆𝐹𝐹 𝑃𝑃𝑃𝑃𝑃𝐼𝐼𝐶𝐶𝐹𝐹

𝑃𝑃𝐼𝐼𝐸𝐸𝐹𝐹𝐹𝐹𝑆𝑆𝑃𝑃𝐸𝐸𝑃𝑃𝐹𝐹𝐼𝐼𝑞𝑞𝑞𝑞𝑛𝑛𝑖𝑖𝑞𝑞𝑞𝑞𝑞𝑞 𝑖𝑖𝑖𝑖𝑖𝑖𝑜𝑜𝑛𝑛𝑞𝑞𝑛𝑛𝑞𝑞𝑖𝑖𝑜𝑜𝑖𝑖

𝑆𝑆𝐹𝐹𝐸𝐸𝑃𝑃𝐹𝐹𝐼𝐼

Generalized observer(from the viewpoint of quantum information)

𝑃𝑃𝐼𝐼𝑃𝑃𝑃𝑃𝑖𝑖𝐹𝐹𝑖𝑖𝑖𝑖𝑛𝑛𝑛𝑛𝑛𝑛𝑖𝑖𝑛𝑛𝑖𝑖𝑛𝑛𝑛𝑛

𝐹𝐹𝑄𝑄𝐸𝐸𝑃𝑃𝑃𝑃𝑖𝑖𝐹𝐹

𝑝𝑝𝐹𝐹𝐹𝐹𝑄𝑄𝑃𝑃𝑄𝑄𝑃𝑃𝑃𝑃𝑃𝑃𝐸𝐸𝑃𝑃 𝑃𝑃𝑃𝑃𝑃𝐼𝐼𝐶𝐶𝐹𝐹𝑛𝑛𝑞𝑞𝑞𝑞𝑖𝑖𝑛𝑛𝑛𝑛𝑞𝑞𝑛𝑛𝑖𝑖𝑛𝑛𝑛𝑛

𝑃𝑃𝑝𝑝𝑃𝑃𝑃𝑃𝐹𝐹𝐸𝐸𝑃𝑃𝑆𝑆𝐹𝐹 𝑃𝑃𝑃𝑃𝑃𝐼𝐼𝐶𝐶𝐹𝐹

𝑃𝑃𝐼𝐼𝐸𝐸𝐹𝐹𝐹𝐹𝑆𝑆𝑃𝑃𝐸𝐸𝑃𝑃𝐹𝐹𝐼𝐼𝑞𝑞𝑞𝑞𝑛𝑛𝑖𝑖𝑞𝑞𝑞𝑞𝑞𝑞 𝑖𝑖𝑖𝑖𝑖𝑖𝑜𝑜𝑛𝑛𝑞𝑞𝑛𝑛𝑞𝑞𝑖𝑖𝑜𝑜𝑖𝑖

𝑆𝑆𝐹𝐹𝐸𝐸𝑃𝑃𝐹𝐹𝐼𝐼

The concept of qubit as thenormed superposition of twosuccessive axes:

0 1 = 𝐹𝐹𝑖𝑖𝑖𝑖𝑖𝑖 𝐹𝐹𝑖𝑖(𝑖𝑖+1)𝑖𝑖

The concept of qubit as theunit ball with two its points chosen by a certain rule

0 1 : two its circles, one of which great, and the circle

“0+1” is great as well

The border melting in information• In that final analysis, the border between the physical theories of

quantum mechanics and those of special and general relativity melts in probability and information theory turning out to underlie both

That seeming maybe ridiculous viewpoint can be visualized so:• What is (i.e. [the] being) is (quantum) information. It implies the

kinematic viewpoint as universal. In turn, it generates the dynamic viewpoint dividing the entities in the scale of energy (mass) and thus time. Further, the part of micro-energies in that scale is studied by quantum mechanic, and that of macro-energies by special and general relativity. Back to the kinematic viewpoint of (quantum) information both mean one and the same

The structure of the paper itself instead of conclusions

• Section 1 introduces the concept of complex (negative in particular) probability and its possible physical interpretation as both ‘force’ and ‘information’

• The prehistory and background (Section 2) include the generalization and utilization of ‘negative and complex probabilities’ in quantum mechanics and probability theory

• The narrow purpose of the paper is to be introduced negative and complex probability relevant to special and general relativity and thus to events in our usual perceptive world rather than to microscopic or micro-energetic events studied by quantum mechanics (Section 3)

• Section 4 compares their use in quantum mechanics and information, signal theory, probability theory, and in special and general relativity

• Section 3 & 4 almost coincide with this presentation

The paper:

You can find the entire paper in Internet typing the title

More than impossible: negative and complex probabilityand their interpretation

in any search engine such as Google, Bing, etc.

Thank you so much for your kind attention!Any questions or comments, please!