Time & Fractal

Vasil Penchev, Assoc. Prof., Institute for philosophical research

of the Bulgarian Academy of Sciences

vasildinev@gmail.comForthcoming publication (where this

report is posted):vasil7penchev.wordpress.com

1. According quantum information, a physical meaning has not only 2, but the -function itself.

2. Two ways to describe a physical object exist: from the object to the whole (i.e. as moving object in space time, from the whole to the object (i.e. as a concrete asymmetry of a fractal structure representing the whole).

Five theses:

3. -function represents such a concrete asym-metry of a fractal structure in space-time.

4. Physical quantity representing a linear and Hermitian operator in Hilbert space (i.e. 12 transformation) means some move-ment of an object in space-time expressed by means of a change of its definitive asymmetry with regards to the whole.

5. Being of the physical quantity is information.

And the rest three theses:

The meaning of the report

One of the most difficult problems of the philosophy of physics:

ontological compatibilty of relativity and quantum mechanics

The first one is a local theory, the second is a global one.

For example, compatibility of:

• Relativity:

World line

Time

From a part to

the whole

Constancy

Actuality

• Quantum mechanics:

-function

? Fractal structure?

From the whole to a part

Probability

Virtuality

Building Up of:

World line:

point by point

- any point is a moment of time

from a part (here and now) to the whole as deve-lopment in time

-function:

level by level

- any level is a level of fractal structure

from the whole (here

and now), the 1st le-vel, to the part as

‘th’ level

Meaning of:

• Function of time

Time – t

E = m.c2

d = ict + r

• Fractal structure

Frequency = t-1

E = ħ.d = iE+cp

dA = ds.dE = 0, i.e ‘time “” fractal’

dA = ds.dE = 0, i.e. ‘time “”fractal’2.

(1)

What may it mean for a part not to be ‘’ to the whole?

• a part

an element

• the whole

the set

a: a {a} = a

a: a {a} =

a:1 : (0,1), :0,1 ‘’, ‘’

About

• Constancy: • Probability:

So probability isa relationbetween ‘part’

and ‘whole’

So constancy convertsinto a special case of the relation ofprobability, i.e the relation of‘part’ and ‘whole”

Any element:

• represents the whole as identity of the levels of fractal similarity

• This is the basis of a vector space

(for example Hil-bert space)

• represents it it-self as differen-ce (deflection) between the levels

This is an element of a vector space

So any motion as a relation between two elements may be represented by:• change of the ba-

sis of the vector space (i.e. covari-

ant change)

• change of the ele-ment of the vector space (i.e. contra-

variant change)

Relativity: no experience might differ anyway change of the basis from chan-

ge of the element

From “special” to “general” relativity:

Any motion “by itself” represents a change of a vector space. The simplest special case is then

when the vector space is “flat”: thevector space coincides with its

conjugate space (for example Riesz theorem)

More about that simplest special case:More about that simplest special case:

Any part is independent of the whole, to which ‘belongs’. We mayalso say that the whole is always the same. That’s way the relation

between ‘whole’ and ‘part’ is equal to some property of the part

The simplest special case aboutsubjective and objective probability

• Subjective probability:

waiting for the future

• Objective probability:

experiencing the past

They are if and only if : 1) any future event is independent of any past event;

2) present is but a point

Present is curvature of time!• subjective proba-

bility

• waiting

• objective proba-bility

• experiencing

The “length” of present is the measureof time curvature! This time length is

period of de Broglie’s wave, so it is inversely of mass: the macro-world is

already “timely flat”!

Now about: whether any future event is independent of any past one?

• The future event repeats merely the preceding

• The future event is absolutely independent of any past one

The future event may be causally conditioned by any past one!

Get started a new comprehension of

causality!• Fractal

repetition• Absolute indepen-

dence of future from past (Markov chain)

Causality represented by implicationModel:

Cause ‘0’ ‘0’ ‘1’ ‘1’Effect ‘0’ ‘1’ ‘0’ ‘1’

Causality ‘1’ ‘1’ ‘0’ ‘1’

AB (AB) (A)

• a fractal part:

effect repeats ‘fractally’ cause

• a Markov part:

effect is absolutely

independent of cause

Probabilistic causality means:

Cause causes effect withsome probability ‘p’: AIf cause is available, then

effect is available with probability p. If p = 1:

classical causality; if p=0:A, B are absolutely independent

Which would the difference

between correlation and probabilistic causality

be?• Correlation pre-

suposes that there is a real ‘true’ a real ‘true’ causecause, which is a hidden (compare

with ‘hidden parameter’)

• Probabilistic causality excludes

such a real ‘true”a real ‘true”

causecause

Explaining by Venn

diagrams

• A correlates with B• A causes B ‘probabilistically’

It means for us to reject:

Then ‘probabilistic causality’ means the following:

• The universal setbeing common for

both A, B doesn’texist. We may

think that they belong to two different univer-sal sets

• We may also think that the universal

set changes: t1t2

(AUt1 )

(BUt2

)So some elementsof A may disappear,but new elementsmay appear in B

Returning to classic causality…

• The whole is the same

• Time is Newton one

• Energy is conserved

• Correlation requires for a hidden cause to exist

• Allareequal

Returning back to probabilistic Returning back to probabilistic causality…causality…

• The whole is not the same

• Time is not Newton one

• Energy is not con-served

• There are correla-tions, but there aren’t hidden parameters

This is theThis is the

Realm ofRealm of

quantumquantum

mechanicsmechanics

and infor-and infor-

mationmation

Probabilistic causality generalizes per se… relativity

Now: no diffe-rence whether any part or the whole changes

Probabilistic

causality means

relativity of whole and part

Generalized relativity presupposes that motion of whole and motion of part

are equivalentWe know much

about the motion of

part. What about the motion of whole?

It means change of a frac-tal structure into another. That is not a change in time. Heidegger has spoken of history of being

We would be able to comprehend

‘history of being’ as ‘change of whole’

• On the one hand,

we may think

‘history of being’

as Plato’s eons

changing each other in millenniums

• On the other hand, better to think for

‘history of being’ to be as Braudel’s Braudel’s long run [la longuelong run [la longue

durduréée] e]

From our, human point From our, human point of view…of view…

And now: an unexpected comparison… with the math definition of info:

I=f(t) ln (t) .dt

I=f(t) ln (t) .dt

f(t)– a slow change, long run(t) – an usual run of time

ln – slows down (t) to f(t)

I=f(t) ln (t) .dt – a measureof slow change, of long run

Sat sapienti (a hint in future)

• The function of ln transforms

multiplicative (fast) groups into additive (slow) groups, so a field into a (double) group

• The function of ln transforms an axis of Hilbert space into an inertial reference frame, so a point of it into a world line

Two points of view:Two points of view:1. From the whole -

the motion is motion of whole. So any physical quantity is a li-near (Hermitian) transformation of the whole – in quantum mechanics

2. From the part: the motion is motion of part. So any physical quantity is a linear transformation of part’s world line – in relativity

The concept of (quantum) The concept of (quantum) information units both of information units both of

themthemA= (x) F [*(x)] .dx

I= World line (t).ln (t).dt

Any physical quantity in QMF: (x) F [*(x)] is a trans-formation of the whole – the measuring instrument

More about: I= W (t).ln (t).dt

Granted F: ln (t) = Force{W (-t)}

Full analogy:

Operatorin QM, F

Classical forceacting ‘now’, F

(x) F [*(x)] .dx W (t). F{W(-t)}.dtPhysical quantity

AIInformation of motion I

A general principle in two A general principle in two forms:forms:

• Expressed by the motion of whole:

Quantum mechanics

OperatorPhysical quantity

Reality as virtuality

• Expressed by the motion of part:

Relativity

Force

Motion information

Reality as actuality

A basic idea of the report: A basic idea of the report:A basic idea of the report:

No Already Boundary – since 1989’s falling the wall!

Two ways to describe a physical object exist:

• TA way is: from the object to the whole – as a moving object in space-time

• AAnother way is: from the whole to the object – as a concrete asymmetry of a fractal structure representing the whole

-function represents such a concrete asymmetry of a fractal

structure in space-time

Physical quantity means some motion of an object in space-time

expressed by means of a change of its definitive asymmetry with regards to

the whole

Being of the physical quantity is information