ISSN: 2638-6062
Patrice F Dassonville*
Received: November 17, 2020; Published: December 03, 2020
*Corresponding author: Patrice F Dassonville, Department of Biomedical sciences, Freelanceresearcher, France
DOI: 10.32474/PRJFGS.2020.04.000185
Space as such has no materiality ; the empty space is a mathematical concept.
Keywords: Imaginary Space; No Materiality of Space; Use of Zero
The modeling of phenomena often imply space under various forms ; therefore it requires that physical space and empty space must be defined. The definitions will help us to uncover the nature of space and that of empty space. Moreover, a good definitionusualy leads to theoretical developpements, some unexpected.
In the everyday language, it is commonly said that we« see
the space » in front of us, that we« measure the length » of a
table. Unfortunately it is a faulty language. For example, from the
summit of Assekrem (2790 m) (Hoggar February 1973) you can
seemountainpeaks in the fore ground, mountains in the sandmist
in the background, and the sky: we seeobjects, not « space » as
such Space is a difficult issue to address for various reasons, which
constitutes obstacles to be imperatively circumvented Here are
three currentexamples :
• Definitions and descriptions of dictionaries and specialized
works are unacceptable because they are systematically locked
up in semantic dead ends.
• The intuitive approach, which is guided by sensitivity and
repetition of receivedideas, is sterile.
• Dialectics , in which elementary reasoning and primary logic
dominate,fails in it sown language.
Two unusual approaches deserve to be reminded :
• An investigation through Latin literature show us how authors
have gradually conceptualized the notion of space from the
observation of their environment For example, the Latin
scholar Cicero (106-43) uses distant (remote), longitudo
(length), spatium (large clearance) [1]. Afterobserving, Latin
authors name what they see, what they feel about : either
through new words or by extending the meaning of existing
words, the sensitive approach if fruitfull, however it remains
powerless for defining space.
• Define somethin gunderstudy is very important because the
definition must say what it is about. In addition, we noticed
that the more a definition is effective, the more itadduces
theoretical extensions. We enforce a very elementary approach
by saying that a distance is defined by« what separates two
objects ».We have defined physical space by« what is between
two objects ». Define space using two objects seems primary,
so simple it is ; but sometimes things are simpl erthan we fear
about. In this case, some theoretical extensions have already
been emphasized [2]. We briefly recalltwo of them : on the one
hand the properties of space, and on the other hand the nature
of the empty space.
We have shown that the properties of spacedepend on the experimental field in which we operate. For example, in special relativity, space is covariant [3] it means that the values of spatial data exchanged between the laboratory and a relativisticreferential (aparticle or a star),change depending on the speed of the referential. For example a traveller moving at 150,000 km/s looks smaller : 1m 47 instead of 1 m 70.First, the phenomenon is reversible ; the traveller seems smaller to the observer, and the observer seemssmaller to the traveller. Second, in fact the traveller as well as the observer are not smaller : the Lorentz equations allow us to counteract a technical effect of field by re-establishing the proper data. Covariance is a mathematical property : space has no physical properties ; it only owns mathematical properties. We conclude by saying that space is a polymorphic mathematical concept. How can we assert that the above relativistic experiment is not a physical experiment on space ? The answer is provided by our « elementary definition » of space : indeed, the experiment is made on« the two individuals », instead of their « size », instead of spaceas such.It is important to recall that spatial data, like « size », have no physical properties ; no experiment can be made on spatial data as well as on spacegenerallyspeaking. There is an interesting consequence ; length measurements and space measurements, that are kinds of experiments, are impossible ; in fact we measure « what separates the two objects ». Three examples :
• The zoologistdoes not measure the length of apolarbear’
sfootprint, because « length » is a concept : in fact, hemea
sures what separates the two ends of the footprint ; the result
is called « length of the footprint » (Figure 1 and 2).
• The geographer does not measure the distance between Paris
and New York, instead, heme asures « what separates Paris
and New York » ; the result is called « distance Paris/New York
».About curved space, it could be added the difference between
physical distance and mathematical distance ; for example,
Paris and New York are approximately separated by 5840km
for airlines, and 5600 km for mathematicians (Figure 3).
• The Greek geographer Eratosthenes (276-194) succeeded
in evaluating the value of the terrestrial circumference by
simultaneaously comparing the shadows of two identical
sticks located in twodifferent places ; with an incredible
accuracy lessthan 2%.Eratosthenesdid not measure the «
length of the shadows », because « length » is a concept :
heme asured what « separated the two ends of each shadow »
(Figure 4). It is a technical effect of field which makes us think
that we can measure a length, a distance, a surface, a volume,
a space; Indeed these five words designate five concepts on
which no experiment is possible, including measurements.
The misleading results from everyday language which we must
be wary of.
The empty space could be easily defined by an energy density «
ρ »equal to zero (the Greek letter « ρ »)(the matter is included with
the energy):
ρ = 0
which requires that the variation« dρ » of the energy density is
zerotoo :
dρ = 0
But according to the uncertainty principle of the German
physicist Werner Heisenberg (1901-1976) the more the accuracy on energy is low the less the precisionon time is high. In other
words, if the variation of energy density is zero, the duration of
measurements is infinite. The quatum physics has observed «
quantum fluctuations » in an alleged empty space [4]: it simply
means that the quantum void is not an empty space ; well, our
concern is the « empty space ».About that, we would like to return to
what we call « the induction rule » and the use of « zero » [2]: inside a
system, the induction rule prohibits the introductionof a parameter
of zero value when the system does not owns this parameter. Think
that the non-existence of a parameter is equivalent to zero valueis
an excessive and in appropriate mathematization which results
from a model effect of field. Example : we may not say about the
one who has no boat, thatheownszero boat ! Or that heowns a
boat of length zero! It’s about being wary of everyday language :
we must replace « energy density equal to zero » by « no energy
density ».We obtain « no energy density » as soon as the two objects
that have been used to define distance and space are removed. It
leads to the lack of any parameter and the disappearance of the
mathematical properties. Thereforeit is impossible to build a
definition : in clear, the emptyspace has no physical existence, itis
a pure mathematical concept. The major consequence is that space
as such has no materiality: itdoes not exist. The famous questioning
of the German mathematician and philosopher Leibniz (1646-
1716) « Why is theresomethinginstead of nothing ? » is a sophism
because « nothing » is not an option to « something » :« something
» is necessary. Leibniz was deceived by a technical effect of field.
For his black hole theory, Stephen Hawking introduced an «
imaginary time » [5] :
t = iτ (the Greek letter « τ »)
which is of course unrelated to symbolist or surrealist poetry.
He might do it because time is a concept. We have defined the «
imaginary time » by « what separates two states (imaginary or not)
of an imaginary system ». It allows us to introduce an imaginary
space, defined by « what separate stwoimaginarys ystems. Given
that space is a concept, the imaginary spaces hould not lead to
theoretical obstacles in the case we needit in the futur.
Space is neither observable nor measurable because it has no physical properties. It does not mean that the relations with this concept are disrupted. Fortunately we keep the ability of observing and measuring in accordance with definitions, with a different but rich approach, and respecting the accuracy of the words.
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