## Axioms of Quantum Semiotic

Peder Voetmann Christiansen

IMFUFA, RUC

## The sign relation

- The quantum mechanical state vector is a
sign.

- A
signorrepresentamen(R), according to Peirce, is afirststanding in such a genuine triadic relation to asecond, called itsobject(O), as to be capable of determining athird, called itsinterpretant(I), to assume the same triadic relation to its object in which it stands itself to the same object.(note 1)

- The representamen R in a quantum semiotic sign relation
mediatesbetween the quantum mechanical object O and the interpretant I:

I-R-O

- The interpretant I is a potential, actual, or general purely physical result of measurement.

- The
sign links( - ), in the dyadic parts R-O and I-R of the sign relation areinteraction bondscorresponding to the physical processes ofpreparation(the R-O link) andregistration(the I-R link).

- Each sign link is characterized by the Peircean categories as either 1:
potential, 2:actual, or 3:general.

- The category numbers,
fandg, of the R-O link and the I-R link are restricted by the selection rule:gf.

- The
qualisign11 (g=f= 1) is the continuum of theHilbert space. TheHsymbol(g=f= 3) issynthesizedfrom the lower signs by successiveactualizationsofpotentiallinks (1 2) andgeneralizationsofactuallinks (2 3).

- The six classes of signs (
gf) are connected with Peirce's semiotic definitions and Dirac's bra-ket notation in the following way

(33)

symbol

qp(13)

iconic legisign

p(23)

indexical legisign

p(11)

qualisignH(12)

iconic sign

(22)

indexical sinsign## The measurement process

- A
measurementis a permanentregistration. The physical setting of an interpretant (the I-R link) preceding the registration is anirreversibleprocess.

- Registration is a
dissipativeandnoisyprocess.

- For a dissipative admittance the quantum noise on the current, whose spectrum is given by the fluctuation- dissipation (FD) theorem (note 2) corresponds to a time-series of
discrete events

- For a dissipative device with mobility and relaxation time the average number of events up to time
tfollowing an event at time 0 at zero temperature according to the FD theorem is given by

- The
collapseorreductionof the state vector requires the setting of a dissipative sign link corresponding to the appropriate ray ofHbeforethe measurement. The projection on the ray is the first of the quantum events predicted by the FD theorem. (note 3)

- The collapse of a state vector for more than one particle requires
prospectivecoincidence counting.

- The violation of Bell's inequalities and other
superclassicalcorrelations is due to a common context of detection of several particles represented bypreset coincidence counters.

- Quantum Mechanics is
strictly localand all the so called "non-local" effects can be simulated in a purely classical and local scenario provided there is a common context for the registration of individuals. (note 4)## Notes:

Collected Papers, ed. Hartshorne & Weiss,CP2.274.- H. B. Callen and T. A. Welton,
Phys. Rev.,83, 34 (1951).- P. V. Christiansen,
The Semiotics of Quantum-Non- Locality, IMFUFA text no. 93 (1985).- See my paper "Peircean local realism does not imply Bell's inequalities", Joensuu 1990.

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