"Continuum versus Discrete" Physics: brief note on Endo- and exo-observer of a physical system

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by  David Vernette

”Continuum versus Discrete” Physics: brief note on
Endo- and exo-observer of a physical system.
David Vernette and Michele Caponigro
7 We argue about the following concepts:(i)introduction of endo and exo-observer of a physical
0 system(ii)possiblerelation betweenendo,exo-observerandcontinuum/discretenatureofthesame
0 system (iii)the distinction about two categories of observers do not help to solve the basic nature
2 (continuum/discrete)ofthesystemconsidered. Wearguethatdiscrete mathtoolutilizedtodescribe
behaviorofaphysicalsystemistoascribetotheexo-observerdescription. Inotherwords,discrete-
n
a ness nature of a system is due at the presence of an external observer description, the observation
J act. Viceversa,weretain,thatendo-observerdescriptiongiveusacontinuumnatureofthesystem
but only in a Platonic realm. Finally, we retain that a real theory of the state of matter could to
5
1 build a real independence from the observer. These brief considerations open a discussion on the
foundationsofdiscretemathtoolsandtheirrelationwiththeobservationact,includedthepossible

] extension to foundations of thequantum mechanics.
h
p
- INTRODUCTION: ROLE OF THE OBSERVER We think that above assumptions are not sufficient
n
e to distinguish the basic nature (continuun/discrete) of
g Recently many workshave beendedicated to informa- a physical system. We will analyze this point next sec-
s. tionalapproachestothephysics,especiallyinthefieldof tion. Of course, the ideal hypothesis is that exist a met-
c quantum mechanics (Fuchs, Peres, Zeilinger[1]). We are alanguage where any endo/exo-observer can be formu-
i
s interestedtoanalyzingthisapproachrespecttheproblem lated. We do not see (until now) the existence of a
y
ofcontinuum/dicretenatureofphysicalsystem. First,we (neutral) metalanguage. We will argue that the pos-
h
p retain that: sible existence of a metalanguage must be linked with
[ a real theory of the state of matter. For this reason,
• 1)The informational approach is not a preroga- our brief analysis will be more general and will diverge
1 tive of quantum mechanics.The structure of infor- from Primas[2] position: Inescapably, the study of the
v
mational approach is applicable in many fields of endo/exo-dichotomy must be conducted in a metalan-
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6 physics. guage. The language in which any endo/exo-theory can
1 ever be formulated is neither part of the [...] endo and
• 2)The approach is based on: i) a subjective in-
1 exo-observer description. We agree,instead,with the fol-
0 terpretation of probability ii)the equivalence be-
lowing Primas[2]definition, which he calls ”the observer-
7 tween physical reality and our knowledge of phys-
free”(quantum endophysics):the study of the Platonic
0 ical reality,this position is supported through the
/ heaven, the realm of non-spatial, non-mental, timeless
s irreducibly random nature of individual quantum
but nevertheless real entities. According Primas: A
c events.
i hard-boiled positivist may have difficulties to appreciate
s
y As we have seen, the approach is centered on the such a quantum endophysics since it refers by definition
h fundamentalroleoftheobserver’sdescription. Weretain to some kind of a Platonic universe, and not to empiri-
p that the presence or apparent absence of the observer cal facts. The aim of the study of quantum endophysics
:
v is an important step to establish the nature of physical is not the hope to find the true and real values
i system. What we intend with observer? Which is the for all endophysical observables(these do not exist!)
X
nature of the ”relation” with the correspondentphysical but to formulate universally valid natural laws endophys-
r
a system? ically in view of theoretical derivations of operationally
meaningful exophysical descriptions.
We adopt the following general assumptions:
• 1)We call exo-observer system: a physical sys-
CONTINUUM VS DISCRETE: PLATONIC
tem which is mathematically dependent from an
REALM VS INFORMATION
externalobserverdescription(e.g. mathdescription
of the system depend by external observer).
First,wedonotretainanegativeelementthe”subjec-
• 2)Wecallendo-observer system: aphysicalsys- tivity” in a description of a physical system. We argue
temwhichisnotmathematicallydependentbyany simple that the ”exo-observer act” introduce a discrete
external observer description. behavior of the physical system. Vice versa, we retain,
2
thatendo-observerdescriptiongiveusa”continuum”na- The following table summarize our brief considera-
ture of the system but only in a Platonic realm. The tions:
tension between discrete and continuous aspects seem
without a definitive solution. As we know, from ancient
Endo-Observer Exo-Observer
philosophy the question of the nature, for instance, of
1.Physical Law 1.Information
space (atomicity vs.infinite divisibility) and its consti-
2.”Continuum”(in Platonic realm) 2.Discreteness(Idealism)
tuting elements has played a great part in metaphysical
3.Universality 3.Contextuality
studies. This question raised some problems that still
4.Possible Onticintepretation 4.Epistemic interpretation
make up interesting research topics not only in philoso-
phy but in mathematics and cognitive sciences as well.
What does constitute space? Here, our intentions are
not to get into philosophical analysis, but rather to try
to evidence the fundamental role of the observer in the
description of the system.
Discrete (respectively continuous) can be related to: CONCLUSION
time, real space, phase space etc. This analysis could
be done under different levels: a) computational tech- In conclusion, both approaches do not give us a
niques (i.e.informationalapproach)b) natureofthe phe- definitive response on the continuum/discrete nature of
nomenon (i.e. quantum nature). The meaning of ”con- physical system. How we can go out? We retain that a
tinuous”, for instance, seem less ambiguous in physics real theory of the state of matter could to build a
than in mathematics. real independence from the observer, the metalanguage
Whicharetheimplicationsoftwoobserver’scategory? auspicate from Primas.
• A)endo-observer ⇒This hidden observer usually
is introduced under form of ”physical laws” (Pla-
tonic Observation). For instance, the Shr¨odinger’s
equation: i¯h∂Ψ= HΨ)→ is an example of
∂t
”Platonic observation”.
• B)exo-observer⇒This case is introduced under
——————
form of ”information” (Subjective Observation).
⋄David Vernette:QuantumPhilosophyTheorieswww.qpt.org.uk
For instance, the collapse of wavefunction →is an
[email protected]
example of ”Subjective observation”.
⋄MicheleCaponigro: UniversityofCamerino,PhysicsDepartment
Wearguethatbothcategoriesofobserversdonotsolve [email protected]
the basic nature of continuum/discrete dichotomy of the
physical system. How we can infer and to support these
statements? Where are the theoretical reasons?
• 1) Until now, Exo-observerdescription implies→
a discrete nature of the physical systems (included
the unsuspicious classical systems). The preroga- [1] C.Fuchs Quantum Mechanics as Quantum Informa-
tion(and only a little more).
tive of this description is the subjective interpreta-
http://arxiv.org/abs/quant-ph/0205039
tion of mathematical data.
C. Fuchs, A.Peres Quantum theory needs no’interpreta-
• 2) Until now, Endo-observer description implies→ tion’ ” Physics Today page 70, March 2000
J.Kofler J, A.Zeilinger, Sciences et Avenir Hors-Srie No.
a ”continuum” nature of the system but only in
148, November2006
the Platonic realm (The Math models and Physi-
[2] H.PrimasEndo-andexo-theoriesofmatter,Publishedin:
cal Laws). In other words, we have not any real EndoandExo-ConceptsofObservationandKnowledgein
”continuum” definition of a physical system out of Physics, Philosophy, and Cognitive Science,Pp. 163-193
Platonic realm. (1994)