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\title{\bf Relativity Theory: what is Reality?}

\author{Diederik Aerts\thanks{Department of Theoretical Physics and Center Leo
Apostel, Vrije Universiteit Brussel, 1050 Brussels, Belgium, e-mail:
diraerts@vub.ac.be}}

 

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\date {} 

\maketitle

\begin{abstract}
\noindent In classical Newtonian physics there was a clear understanding of 'what reality is'.
Indeed in this classical view, reality at a certain time is the collection of all what is actual
at this time, and this is contained in 'the present'. Often it is stated that
three dimensional space and one dimensional time have been substituted by four dimensional
space-time in relativity theory, and as a consequence the classical concept of reality, as that
what is 'present', cannot be retained. Is reality then the four dimensional manifold of
relativity theory? And if so, what is then the meaning of 'change in time'? This
problematic confronts a geometric view (as the Einsteinian interpretation of relativity theory)
with a process view (where reality changes constantly in time). In this paper we investigate this
problem, taking into account our insight in the nature of reality as it came by analyzing
the problems of quantum mechanics. We show that with an Einsteinian interpretation of relativity
theory, reality is indeed four dimensional, but there is no contradiction with the process
view, where this reality changes in time.
\end{abstract}

\section {Introduction}

Many textbooks on relativity theory give the impression that the theory is
conceptually very well defined, contrary to textbooks on quantum mechanics, where it
is usually openly admitted that many aspects of quantum theory are not understood at
all. We think that it is actually possible to claim that also relativity
theory, although seemingly very clearly put forward by Einstein himself [1,
2], is not understood in many important aspects. More concretely, it is not at all
clear 'what reality is' taking into account relativity theory.

In a world imagined to be modeled by classical mechanics there is no problem
concerning the question 'what is reality?'. Indeed, in this classical world, reality at
a certain instant of time $t$, is all that exists at this instant of time $t$.
Expressed in ordinary language, reality is all that exists 'at present'. It is
accepted that the 'past' does not exist anymore (it has been real in the past), while
the 'future' does not yet exists (it is a potentiality for possible realities to
come). Now that relativity theory is considered
to describe the world the concept of 'present' is not an unambiguous concept
anymore. In this paper we will analyze this situation in detail and arrive at a
rather amazing conclusion. 

\section{Being and Becoming}

Albert Einstein writes on page 2 of his little booklet on relativity theory [2]:
"The only justification for our concepts and system of concepts is that they serve to
represent the complex of our experiences; beyond this they have no legitimacy. I am
convinced that the philosophers have had a harmful effect upon the progress of
scientific thinking in removing certain fundamental concepts from the domain of
empiricism, where they are under our control, to the intangible heights of the
{\it a priori}. For even if it would appear that the universe of ideas cannot be
deduced from experience by logical means, but is, in a sense, a creation of the
human mind, without which no science is possible, nevertheless this universe of
ideas is just as little independent of the nature of our experiences as clothes are
of the form of our human body. This is particularly true of our concepts of time and
space, which physicists have been obliged by the facts to bring down from the
Olympos of the {\it a priori} in order to adjust them and put them in a serviceable
condition."

I think that Einstein's introduction of special relativity theory and its consequence
for our conception of time and space is one of the examples of a deep
philosophical reasoning that has changed physics forever in a very concrete and determinate
way. We will not repeat here all the subtle steps that make Einstein
proceed to introduce the special theory of relativity (they can be found in [1]) but
just expose shortly some of the main results.

Suppose that we consider two coordinate systems $K_1$ and $K_2$, where
$K_2$ moves with constant velocity $v$ in the direction $x_1$ of coordinate system
$K_1$. An event $\alpha$ can be coordinated in both coordinate systems, respectively
in $K_1$ by four numbers $(x_1, y_1, z_1, t_1)$ and in $K_2$ by four numbers $(x_2,
y_2, z_2, t_2)$. Then the relation between these two ways of coordinating the same
event is given by the Lorentz transformations:

\begin{equation}
x_2 ={x_1 - v \cdot t_1 \over {\sqrt{1 - {v^2 \over c^2}}}}
\end{equation}
\begin{equation}
y_2 = y_1
\end{equation}
\begin{equation}
z_2 = z_1
\end{equation}
\begin{equation}
t_2 = {t_1 - {v \over c^2} \cdot x_1 \over {\sqrt{1 - {v^2 \over c^2}}} }
\end{equation}

\noindent From this it is easy to calculate how the behavior of clocks depend on the
velocity. Let us consider two clocks $C_1$ and $C_2$  that are permanently situated in
the origins of the coordinate systems $K_1$ and $K_2$ respectively. Let us consider
two events $\alpha$ and $\beta$, coordinated in $K_2$ by $(0, 0, 0, 0)$ and $(0, 0, 0,
1)$. This means that the events $\alpha$ and $\beta$ mark respectively the beginning
and the end of one tick of the clock $C_2$, and hence a lapse of time of one second
in coordinate system $K_2$. These events will be coordinated in $K_1$ respectively by
$(0, 0, 0, 0)$ and $(0, 0, 0, {1 / {\sqrt{1 - {v^2 \over c^2}}} })$, which shows that
the laps of time measured in the coordinate system $K_1$, where the clock $C_2$ is
not at rest but moving with a velocity $v$, is not one second, but ${1 / {\sqrt{1
- {v^2 \over c^2}}} }$ second, i.e. a somewhat larger time depending on the
velocity $v$. This relativistic effect is the well knows effect of time dilatation:
time goes slower in a moving coordinate system. From Einsteins general theory of
relativity follows that there is also an effect of gravity on the measuring of time
by clocks: a clock in a gravitational field slows down more and more with increasing
strength of the field.

Mostly this effect of time dilatation makes it not easy to retain the classical
view on reality, were, as we mentioned already, there is a present, which is
the collection of all events that happen at the present time, and a past, the
collection of all events that have happened, and a future, open for the events that
still have to happen. Einstein made a detailed analysis of how the concept of
simultaneously happening events depends on the coordinate system where these events
are considered (see [1]). This shows that we certainly cannot consider the present
as being defined by all the events that happen simultaneously. In the classical
worldview reality is in fact considered to be this 'classical present'. The past and
the future are not real. Although we know from Einsteins analysis of the concept of
simultaneity that we cannot retain the classical view on reality, as being the
collection of all simultaneously happening events, there has not been proposed a real
relativistic equivalence for reality in a serious way. It is important to
remark in this respect that the effect of time dilatation is not interpreted as a
physical effect on the functioning of the clocks itself. If this would be the
case, if we would interpret the effect of time dilatation as a physical effect
on the clocks itself, the classical view can be retained. This is exactly what
the Aether theory interpretations of relativity theory propose. Lets not consider this
possibility for this moment, we'll come back to it later on, and definitely
interpret the time dilatation effect as indicating that a moving reference frame
not only moves in space but also moves in time. With this Einsteinian interpretation
we want to investigate the question :"What is reality?".

Einstein has presented always his theory as a geometrization of time (in the special
theory of relativity) and gravity (in the general theory of relativity). This means
that time becomes a fourth geometrical dimension, behaving differently as to the
metric involved but existing on the same level as the three geometrical dimensions of
space, and the 'real' scenery of reality is then the space-time continuum. There is
however a stupendous but immediate result of this interpretation: if the scenery of
reality is the four dimensional space-time continuum, then there is no change.
Everything, future, present and past, are fixed once ad for all. This conclusion
seems to contradict in a very profound way our daily immediate experience. Often
this contradiction is put forward as a contradiction between a process view on
reality, where there is a being and a becoming, and a geometrical view, where there
is only a being and no becoming. We shall show in this paper that this
contradiction is only due to a incorrect view on what reality is. To make this
clear we first have to introduce some new concepts, and give, completely along the
lines of Einsteins introduction of relativity theory, an operational definition of
reality. Once we have done this we shall prove that reality is four dimensional but
that at the same time it is changing and that our intuitive process view is also
correct and not in contradiction with the geometrical view. 

\section{Where Has Reality Gone To?}

In [3] we have presented a very formal operational analysis of reality,
completely in agreement with Einstein's idea that the construction of reality has to
be related intrinsically with our experiences. The analysis that we have presented
in [3] is inspired by the problem of the nature of reality as it appears in relation
with the problems of quantum mechanics (see [4] and [5]). We shall apply in this
article the analysis of the construction of reality as presented in [3] to the
situation of relativity theory. In a more formal way than we will do
here, we have analyzed some aspects of this problem already in [6] and [7].

We first start with an example that we have used already in [8] to see clear in
what reality is in quantum mechanics. We consider a 'piece of wood'. We have in mind
the property of 'burning well'. A test for this property consists of taking the
piece of wood and setting it on fire. If we perform this test on a dry piece of wood,
the piece of wood will in general be destroyed by the test. So the property of
'burning well' is a property that the piece of wood has independently of the fact that we make the
test or not. Of course it is after having
done a number of tests with certain type of pieces of wood and having always
discovered the answer to be yes, we decide that this one new piece of wood of this
type, whereon we never performed the test, has actually the property of burning
well. What is important to remark, and what can clearly be seen in the example that
we gave here, is that the connection of 'elements of reality' or 'properties' with
the 'experiments to test these properties' is in some sense a subtle one. A property 'is real', or e.g. a specific piece of wood
'has' the property of burning well, now, September 30, 3 pm exactly, if, when we
would have decided to test this property, hence if we would have set on fire the
piece of wood, the test would have succeeded, the piece of wood would have burned.
It is very important for our analysis of reality and relativity theory to
understand deeply this subtle 'empirist' analysis of the concept of reality. Let us
illustrate it further by some more detailed situation. I would like to consider another property of a piece of wood, namely the property that 'the piece of wood
floats on water', and the test in relation with this property
consists of putting the piece of wood on water and seeing whether it
floats\footnote{There exists some sort of African wood 'wenge' that does not float
on water}. We all agree that a specific piece of wood can very well have the two
properties 'at once', it 'floats' on water and 'it burns well'. Clearly however it
is not possible in general to test both properties at once, or even not one after
the other. Indeed if we would first test whether the piece of wood floats on water
and afterwards whether it burns well, then this would not be a good test for the two
properties. Making float the piece of wood changes to much the state of the piece
of wood, such that the test to see whether it burns well becomes irrelevant. The
same is true if we first test whether the piece of wood burns well. At first
sight we would be inclined to
conclude that from an empirist point of view it makes no sense to attribute
these two properties at once to a piece of wood. But, and now we come to the
essential point that we want to make here, this intuitive conclusion does not take
into account the subtle way in which the tests of properties are connected to the
state of reality of these properties. Indeed, if we repeat, and say that the
piece of wood 'has' (now, September 30, 3 pm exactly) the property of burning well
if, when we would have decided to test this property, the test would have come out
positive, and the piece of wood 'has'(now, September 30, 3 pm exactly) the
property of floating on water if, when we would have decided to test this property,
the test would have come out positive, then it is easy to understand that to
attribute 'two' properties at once to an entity, it is not at all necessary that
we are able to perform the two tests connected to these two properties at once.
Indeed, the piece of wood has both properties, burning well and floating on
water, if, whenever we would perform one of them, making it burn 'or' making it
float, we will get a positive outcome. This is the way that we attribute
properties. Before coming to the subject of this paper, relativity theory and reality, because of
the subtlety of the foregoing remark, we introduce a more general scheme in which we can
analyze carefully this subtle empirist remark.

\subsection {Experiences}

Remembering Einsteins remark in the introduction we want to
present a framework in which 'reality' is empirically reconstructed. The basic
concept of our framework is that of an experience. An experience is the interaction
between a participator\footnote{We consciously use here the word 'participator'
instead of the word 'observer' to indicate that we consider the cognitive receiver to
participate creatively in his cognitive act.} and a piece of the world. When the
participator lives such an experience, we will say that this
experience is {\it present}, and we will call it the {\it present
experience} of the participator. When we consider a measurement
then we conceive this situation as the experimentator and his
experimental apparatus together being the participator, and the
physical entity under study to be the piece of the world that
interacts with the participator. The experiment is the
experience.

Let us give some examples of experiences. We consider the following
situation: I am inside my house in Brussels. It is night, the
windows are shut. I sit in a chair, reading a novel. I have a
basket filled with walnuts at my side, and from time to time I
take one of them, crack it and eat it. My son is in bed and
already asleep. New York exists and is busy.

Let us enumerate the experiences that are considered in such a
situation:

\noindent (1) $E_1$(I read a novel)

\noindent (2) $E_2$(I experience the inside of my house in
Brussels)

\noindent (3) $E_3$(I experience that it is night)

\noindent (4) $E_4$(I take a walnut, crack it and eat it)

\noindent (5) $E_5$(I see that my son is in bed and asleep)

\noindent (6) $E_6$(I experience that New York is busy)

The first important remark, referring again to the example of the piece of wood
of the foregoing section, is that obviously I do not experience all
these experiences at once. On the contrary, in principle, I only experience one
experience at once, namely my present experience. Let us suppose that my present
experience is $E_1$(I read a novel). Then a lot of other things
happen while I am living this present experience. These things
happen in my present reality. While 'I am reading the novel' some
of the happenings that happen are the following: $H_1$(the novel
exists), $H_2$(the inside of my house in Brussels exists),
$H_3$(it is night), $H_4$(the basket and the walnuts exist, and
are at my side), $H_5$(my son is in bed and is sleeping),
$H_6$(New York exists and is busy). All the happenings, and
much more, happen while I live the present experience $E_1$(I
read a novel).
 

Certainly it is not because I experience also these other
happenings. My only {\it present} experience is the experience of
reading the novel. But, and this is the reason for this type of
construction, I could have chosen to live an experience
including one of the other happenings {\it in replacement} of my
present experience. Let me put down the list of these
experiences that I could have chosen to experience in
replacement of my present experience: $E_2$(I observe that
I am inside my house in Brussels), $E_3$(I see that it is
night), $E_4$(I take a walnut, crack it and eat it),
$E_5$(I go and look in the bedroom to see that my son is
asleep), $E_6$(I go to New York and see that it is busy).

This example indicates how we have started to construct reality.
First of all we have tried to identify two main aspects of an
experience. The aspect that is controlled and created by me,
and the aspect that just happens to me and can only be known by
me. Let us introduce this important distinction in a formal way.

\subsection{Creations and Happenings}

To see what I mean, let us consider the experience
$E_4$(I take a walnut, crack it and eat it). In this
experience, there is an aspect that is an action  of me, the
taking and the cracking, and the eating. There is also an
aspect that is an observation of me, the walnut and the basket.
By studying how our senses work, I can indeed say that it is
the light reflected on the walnut, and on the basket, that
gives me the experience of walnut and the experience of basket.
This is an explanation that only now can be given; it is,
however, not what was known in earlier days when the first
world-models of humanity were constructed. But without knowing
the explanation delivered now by a detailed analysis, we could
see very easily that an experience contains always two aspects,
a {\it creation}-aspect, and an {\it observation}-aspect,
simply because our will can only control part of the
experience. This is the creation-aspect.

For example, in $E_1$(I read a novel) the reading is
created by me, but the novel is not created by me. In general
we can indicate for an experience the aspect that is created by
me and the aspect that is not created by me. The aspect not
created by me lends itself to my creation. We can reformulate
an experience in the following way: $E_4$(I take a
walnut, crack it and eat it) becomes $E_4$(The
walnut is taken by me, and lends itself to my cracking and
eating) and $E_1$(I read a novel) becomes $E_1$(The
novel lends itself to my reading).

The taking, cracking, eating, and reading will be called {\it
creations} or actions and will be denoted by $C_4$(I take,
crack and eat) and $C_1$(I read). The walnut and the novel
will be called {\it happenings} and will be denoted by
$H_4$(The walnut) and $H_7$(The novel).


\bigskip
\noindent {\it A creation is that aspect of an experience
created, controlled, and acted upon by me, and a happening is that
aspect of an experience lending itself to my creation, control
and action}.
\bigskip
  
An experience is determined by the creation and the happening. Creations are often
expressed by verbs: to take, to crack, to eat, and to read, are the
verbs that describe my creations in the examples. The walnut and the
novel are happenings that have the additional property of being
objects, which means happening with a great stability. Often
happenings are expressed by a substantive.

\bigskip
\noindent {\it Every one of my experiences $E$ consists of one of
my creations $C$ and one of my happenings $H$, so we can write $E =
(C,H)$}.
\bigskip

\subsection{The Empirical Reconstruction of Reality, Present, Past and
Future}
 
Let us again consider the collection of experiences: $E_1$(I
read a novel), $E_2$(I observe that I am inside my house in
Brussels), E$_3$(I see that it is night), E$_4$(I take a
walnut, crack it and eat it), E$_5$(I go and look in the
bedroom to see that my son is asleep) and E$_6$(I go to New
York and see that it is busy). Let us now represent the
'reconstruction of reality' that is made out of this small
collection of experiences.

$E_1$(I read a novel) is my present experience. In my past
I could, however, at several moments have chosen to do
something else and this choice would have led me to have
another present experience than $E_1$(I read a novel).
For example:

One minute ago I could have decided to stop reading and observe that I
am inside the house. Then $E_2$(I observe that I am inside
my house in Brussels) would have been my present experience.

Two minutes ago I could have decided to stop reading and open the windows
and see that it is night. Then $E_3$(I see that it is
night) would have been my present experience.

Three minutes ago I could have decided to stop reading, take a walnut from
the basket, crack it, and eat it. Then $E_4$(I take a
walnut, crack it and eat it) would have been my present
experience.

Ten minutes ago I could have decided to go and see in the bedroom whether
my son is asleep. Then $E_5$(I go and look in the
bedroom to see that my son is asleep) would have been my
present experience.

Ten hours ago I could have decided to take the plane and fly to New
York and see how busy it was. then $E_6$(I go to New
York and see that it is busy) would have been my present
experience.

\bigskip
\noindent
{\it Even when they are not the happening aspect of my present
experience, happenings 'happen' at present if they are the happening
aspect of an experience that I could have lived in replacement
of my present experience, if I would have decided so in my
past.}

\bigskip
\noindent The fact that a certain experience $E$ consisting
of a creation $C$ and an happening $H$ is for me a
possible present experience depends on two factors:

\medskip
\noindent
(1) I have to be able to perform the creation.

\smallskip
\noindent
(2) The happening has to be available.

\medskip
\noindent For example, the experience $E_2$(I observe that I am
inside my house in Brussels) is a possible experience for me, if:

\medskip
\noindent
(1) I can perform the creation that consists in observing the
inside of my house in Brussels. In other words, if this
creation is in my personal power.

\smallskip
\noindent
(2) The happening 'the inside of my house in Brussels' has to be
available to me. In other words, this happening has to be contained
in my personal reality.

\medskip
\noindent
{\it The collection of all creations that I can perform at the
present I will call my present personal power}.

\smallskip
\noindent
{\it The collection of all happenings that are available to me
at the present I will call my present personal reality}.

\medskip
\noindent
I define as my present personal reality the collection of these
happenings, the collection of happenings that are available to one of
my creations if I would have used my personal power in such a
way that at the present I fuse one of these creations with one
of these happenings.

\medskip
\noindent
{\it My present personal reality consists of all happenings that
are available to me at present. My past reality consists of all
happenings that were available to me in the past. My future reality
consists of all happenings that shall be available to me in the
future.}

\medskip
\noindent
{\it My present personal power consists of all creations that I
can perform at present. My past personal power consists of all
the creations that I could perform in the past. My future
personal power consists of all creations I shall be able to
perform in the future.}

\medskip
\noindent
Happenings can happen at once, because to happen, a happening
does not have to be part of my present experience. It is
sufficient that it is available, and things can be available at
once. Therefore, although my present experience is only one, my
present personal reality consists of an enormous amount of
happenings all happening at once.


\section{The Reconstruction of Reality and Relativity Theory}


We will concentrate now on the
question 'what is reality in relativity theory?'. Since we have
an operational definition of reality in our framework, we can
investigate this problem in a rigorous way.

Let us suppose that
I am here and now in my house in Brussels, and it is September 21, 1996, 3
pm exactly. I want to find out 'what is reality for
me now?'. Let us use the definition of reality given in
the foregoing section and consider a place in New York, for example
at the entrance of the Empire state building, and let us denote, the center of
this place by $(x_1, y_1, z_1)$. I also choose now a certain time,
for example September 21, 1996, 3 pm exactly, and let me denote this time by
$t_1$. I denote the happening that corresponds with the spot
$(x_1, y_1, z_1)$ located at the entrance of the Empire State building,
at time $t_1$ by $m$. I can now try to investigate whether this
happening $m$ is part of my personal reality. The
question I have to answer is, can I find a creation of
localization $l$, in this case this creation is just the
observation of the spot $(x_1, y_1, z_1)$ at the entrance of the Empire
State building, at time $t_1$, that can be fused with this
happening $m$. The answer to this question can only be
investigated if we take into account the fact that I, who want
to try to fuse a creation of localization to this happening, am
bound to my body, which is also a material entity. I must specify
the question introducing the  time coordinate that I
coordinate by my watch. So suppose that I coordinate my body by
the four numbers $(x_2, y_2, z_2, t_2)$, where $t_2$ is my
 time, and $(y_1, y_2, y_3)$ is the center of mass of my
body. We apply now our operational definition
of reality. A this moment, September 21, 1996 at 3 pm exactly, my body
is in my house in Brussels, which means that $(t_2, x_2, y_2,
z_2)$ is a point such that $t_2$ equals September 21, 1996, 3 pm, and
$(x_1, y_1, z_1)$ is a point, the center of mass of my body,
somewhere in my house in Brussels. This shows that $(x_1,
y_1, z_1, t_1)$ is different from $(x_2, y_2, z_2, t_2)$, in the
sense that $(x_1, y_1, z_1)$ is different form $(x_2, y_2, z_2)$
while $t_1 = t_2$.

The question is now whether $(t_1, x_1, y_1, z_1)$ is a point of
my  reality, hence whether it makes sense to me to claim
that now, September 21, 1996, 3 pm, the entrance of the Empire State
building 'exists'. If our theoretical framework corresponds in
some way to our pre-scientific construction of reality, the
answer to the foregoing question should be affirmative. Indeed,
we all believe that 'now' the entrance of the Empire State
building exists. Let us try to investigate in a rigorous
way this question in our framework. We have to verify whether
it was possible for me to decide somewhere in my past, hence
before September 21, 1996, 3 pm, to change some of my plans of action,
such that I would decide to travel to New York, and arrive
exactly at September 21, 1996, 3 pm at the entrance of the Empire
State building, and observe the spot $(x_1, y_1, z_1)$. We
could give many concrete ways to realize this experiment,
and we will not give here one in detail, because we shall come
back to the tricky parts of the realization of this experiment
in the following example. But hence the answer is indeed
affirmative: I could have experienced the spot $(x_1, y_1, z_1)$
at September 21, 1996, 3 pm, if I would have decided to travel to New
York somewhere in my past. Hence $(t_1, x_1, x_2, x_3)$ is part
of my reality. It is sound to claim that the entrance of the
Empire State building exists right now. And we remark that this
does not mean that I have to be able to experience this spot at
the entrance of the Empire State building now, September 21, 1996, 3
pm, while I am inside my house of Brussels. I repeat again,
reality is a construction about the possible happenings that I
could have fused with my actual creation. And since I could have
decided so in my past, I could have been at the
entrance of the Empire State building, now, September 21, 1996, 3 pm.

Until this moment one could think that our framework only will
confirm our intuitive notion of reality but our next example
shows that this is certainly not the case. Indeed, let me
consider the same problem, but now consider another point of
space-time. I consider the point $(x_3, y_3, z_3, t_3)$, where
$(x_3, y_3, z_3) = (x_1, y_1, z_1)$, hence the spot we envisage
is again the entrance of the Empire State building, and $t_3$ is
September 22, 1996, 3 pm exactly, hence the time that we consider is, tomorrow 3 pm. If I
ask now first, before checking rigorously by means of our operational definition
of reality, whether this point $(x_3, y_3, z_3, t_3)$ is part of my present
 reality, the intuitive answer here would be 'no'. Indeed,
tomorrow at the same time, 3 pm, is in the future and not in the
present, and hence it is not real, and hence no part of my
present  reality (this is the intuitive reasoning). If
we go now to the formal reasoning in our framework, then we can
see that the answer to this question depends on the
interpretation of relativity theory that we put forward. Indeed,
let us first analyze the question in a Newtonian conception of
the world to make things clear. Remark that in a Newtonian
conception of the world (which has been proved experimentally wrong, so here we are just
considering it for the sake of clarity), my present  reality just falls together with
'the present', namely all the points of space that have the same
time coordinate September 21, 1996, 3 pm. This means that the entrance
of the Empire State building tomorrow 'is not part of my present
 reality'. The answer is clear here and in this
Newtonian conception, my present personal reality is just the
collection of all $(x, y, z, t)$ where $t = t_2$ and
$(x, y, z)$ are arbitrary. The world is not Newtonian,
this we know meanwhile experimentally, but also if we put
forward an Aether theory interpretation of relativity theory (let
us refer to such an interpretation as a Lorentz interpretation)
the answer remains the same. In a Lorentz interpretation, my
present personal reality coincides with the present reality of
the Aether, namely all arbitrary points of the Aether that are
at time $y_0$, September 21, 1996 3 pm, and again tomorrow the
entrance of the Empire State building is not part of my present
 reality.

For an Einsteinian interpretation of relativity theory the
answer is different. To investigate this I have to ask again the
question of whether it would have been possible for me to decide
in my past such that I would have been able to make coincide
$(x_2, y_2, z_2, t_2)$ with $(x_3, y_3, z_3, t_3)$. The answer
here is that this is very easy to do, because of the well known, and
experimentally verified, effect of 'time dilatation'. Indeed, it
would for example be sufficient that I go back some weeks in my
past, let us say the beginning of September 1996 and then decide to step
inside a space ship that can move with almost the velocity of the
speed of light, such that the time when I am inside this space
ship slows down in such a way, that when I return with the space
ship to planet earth, still flying with a speed near the
velocity of light, I arrive in New York at the entrance of
the Empire State building while my personal  watch
indicates September 21, 1996 3 pm, and the watch that remained at the
entrance of the Empire State building indicates September 22, 1996 3
pm. Hence in this way I make coincide $(x_2, y_2, z_2, t_2)$ with
$(x_3, y_3, z_3, t_3)$, which proves that
$(x_3, y_3, z_3, t_3)$ is part of my present  reality.
First I have to remark that in practice it is not yet
possible to make such a flight with a space ship. But this is not a
crucial point for our reasoning. It is sufficient that we can
do it in principle\footnote{We have not yet made this explicit
remark, but obviously if we have introduced in our framework
an operational definition for reality, then we do not have to
interpret such an operational definition in the sense that
only operations are allowed that actually, taking into account
the present technical possibilities of humanity, can be
performed. If we would advocate such a narrow interpretation,
then even in a Newtonian conception of the world, the star
Sirius would not exist, because we cannot yet travel to it.
What we mean with operational is much wider. It must be
possible, taking into account the actual physical knowledge of
the world, to conceive of a creation that can be fused with
the happening in question, and then this happening pertains to
our personal reality}.  

\subsection {Einstein versus Lorentz: Has Reality Four
Dimensions?}

We can come now to one of the points that we want to make in
this paper, and that clarifies the paradox of time that makes the
difference between an Aether interpretation of relativity
(Lorentz) and an Einsteinian interpretation of relativity. Why
would we come to a different result concerning the foregoing
question, depending on whether we advocate an Einsteinian
interpretation of relativity theory or an Aether interpretation.
To see clear in this we have to come back to the essential
aspect of the reconstruction of reality of our framework, which is
the difference between a creation and a happening. We have to
give first another example to be able to make clear what we
mean.

Suppose that I am a painter and I consider again my
present  reality, at September 21, 1996, 3 pm, as indicated on
my personal  watch. I am in my house in Brussels and let us specify: the
room where I am is my workshop, surrounded by paintings, of which
some are finished and others I am still working on. Clearly all
these paintings exist in my presents reality, September 21, 1996, 3
pm. Some weeks ago, when I was still working on a painting that
now is finished, I could certainly have decided to start to work
on another painting, a completely different one, that now does
not exist. Even if I could have decided this some weeks ago, all
of you will agree that this other painting, that I never started to
work on, does not exist now, September 21, 1996, 3 pm. The reason for
this conclusion is that the making of a painting is
a 'creation' and not a happening. It is not so that there is
some 'hidden' space of possible paintings such that my choice of
some weeks ago to realize this other painting would have made me
to detect it. If this would be the situation with paintings, then
indeed also this painting would exist now, in this hidden space.
But with paintings this is not the case. Paintings that are not
realized by the painter are potential paintings, but they do not
exist.

With this example of the paintings we can explain very well the
difference between Lorentz and Einstein. For an Aether
interpretation of relativity the fact that my watch is slowing
down while I decide to fly with the space ship nearly at the speed
of light and return at the entrance of the Empire State building
while my watch is indicating September 21, 1996, 3 pm and the watch
that remained at the Empire State building indicates September 22,
1996, 3 pm, is interpreted as a 'creation'. It is seen as if
there is a real physical effect of creation on the material
functioning of my watch while I travel with the space ship, and
this effect of creation is generated by the movement of the
space ship through the Aether. Hence the fact that I could observe
the entrance of the Empire State building tomorrow September 22, 1996
3 pm, when I would have decided some weeks ago to start
traveling with the space ship, only proves that the entrance of the
Empire State building tomorrow is a potentiality. Just like
the fact that this painting that I never started to paint could
have been here in my workshop in Brussels is a potentiality. This
means that as a consequence the spot at the entrance of the Empire
State building tomorrow is not part of my present reality, just as
the possible painting that I did not start to paint is not part of
my present reality. If we however put forward an Einsteinian
interpretation of relativity, then the effect on my watch during
the space ship travel is interpreted in a completely different
way. There is no physical effect on the material functioning of
the watch\footnote{Certainly if we take into account that most
of the time dilatation takes place not during the accelerations
that the space ship undergoes during the trip, but during the
long periods of flight with constant velocity nearly at the
speed of light}, but the flight at the velocity nearly the speed
of light 'moves' my space ship in the space-time continuum
such that time coordinates and space coordinates get mixed. This
means that the effect of the space ship travel is an effect of a
voyage through the space-time continuum, which brings me at my
personal time of September 21, 1996, 3 pm at the entrance of
the Empire State building, where the time is September 22, 1996, 3 pm.
And hence the entrance of the Empire State building is a
happening, an actuality and not just a potentiality, and it can be
fused with my present creation. This means that the happening
$(x_3, y_3, z_3, t_3)$ of September 22, 1996, 3 pm, entrance of the
Empire State building, is an happening that can be fused with my
creation of observation of the spot around me at September 21, 1996, 3
pm. Hence it is part of my present  reality.
The entrance of the Empire State building at September 22, 1996,
3 pm exists for me today, September 21, 1996 3 pm.

If we advocate an Einsteinian interpretation of relativity theory
we have to conclude from the foregoing section that reality is
four dimensional. This conclusion will perhaps not amaze those
who always have considered the space-time continuum of
relativity representing the new reality. Now that we have however
defined very clearly what is the meaning of this, we can start
investigating the seemingly paradoxical conclusions that often
are brought forward in relation with this insight.

\subsection {The Process View Confronted with the Geometric
View}

The paradoxical situation that we can try to solve
now is the confrontation of the process view of reality with
the geometric view. Often it is claimed that an interpretation
where reality is considered to be related to the four
dimensional space-time continuum contradicts another view of
reality, namely the one where it is considered to be of a process
like nature. By means of our framework we can now understand
exactly these two views and see that there is no contradiction.
Let us repeat now what is the meaning in our framework of the
conclusion that reality is four dimensional. It means that, at a
certain specific moment, that I call my 'present', the collection
of places that exist, and that I could have observed when I would
have decided to do so in my past, has a four dimensional
structure, well represented mathematically by the four dimensional
space-time continuum. This is indeed my present 
reality. This does not imply however that this reality is not
constantly changing. Indeed it is constantly changing. New
entities are created in it and other entities disappear,
while others are very stable and remain into existence. This is
as much the case in all of the four dimensions of this reality.
Again I have to give an example to explain what I mean. We
came to the conclusion that now, at September 21, 1996, 3 pm the
entrance of the Empire State building exists for me while I am
in my house in Brussels. Then this is not a statement of
derterministic certainty. Indeed, it is very well possible that by
some extraordinary chain of events, without me knowing about
these events, the Empire State building had been destroyed, such
that my statement about the existence of the entrance of the
Empire State building 'now', although almost certainly true, is
not deterministically certain. The reason is again the same,
namely that reality is what I would have been
able to experience, if I would have decided differently in my
past. The knowledge that I have about this reality is complex
and depends on the changes that go on continuously in it. What I
know from experience is that there do exist material objects,
and the Empire State building is one of them, that are rather
stable, which means that they are into existence without changing
to much. To these stable objects, material objects but also
energetic fields, I can attach the places where I could observe
them. The set of these places has the structure of a four
dimensional continuum. At the same time all these
objects are continuously changing and moving in this four
dimensional scenery. Most of the objects that I used to shape my
intuitive model of reality are the material objects that surround
us here on the surface of the earth. They are all very fixed in
the fourth dimension (the dimension indicated by the $t$ variable, and
we should not call it the time dimension) while they move easily
in the other three dimensions (those indicated by the $x$, $y$, and $z$
variables). Other objects, for example the electromagnetic fields,
have a completely different way of being and changing in this
four dimensional scenery. This means that in our framework there
is no contradiction between the four dimensionality of the set of
places and the process like nature of the world. If we came to
the conclusion that the entrance of the Empire State building,
tomorrow, September 22, 1996, 3 pm exists also for me now, then our
intuition reacts more strongly to this statement, because
intuitively we think that this would mean that the future exists
also and hence is determined and hence no change is possible.
This is a wrong conclusion which comes from the fact that during
a long period of time we have had an intuitive image of a
Newtonian present, that would be determined completely. We have to
be aware of the fact that it is the present, even in the newtonian
sense, which is not determined at all. We can only say that the
more stable entities in my present reality are more determined
to be there, while the places where they can be, because these
places are stable with certainty, are always there.


\subsection{The Singularity of the Reality Reconstruction}

We want to come back to the reconstruction of reality in our
framework that we have confronted here with the Einsteinian
interpretation of relativity theory. Instead of wondering about
the existence of the entrance of the Empire State building
tomorrow, September 22, 1996, 3 pm, I can also question the existence
of my own house at the same place of the space-time continuum.
Clearly I can make an analogous reason and come then to the
conclusion that my own house, and the chair where I am sitting
while reading the novel, and the novel itself, and the basket of
wall nuts beside me, etc..., all exist in my present reality at
September 22, 1996 3 pm, hence tomorrow. If we put it like that, we
get confronted even more with a counter-intuitive aspect of
the Einsteinian interpretation of relativity theory. But it is a
correct statement in our framework. We have to add however that
all these objects that are very close to me now September 21, 1996, 3
pm, they indeed also exist in my present reality at September 22, 1996,
3 pm, but the place in reality where I could have observed them
is of course much further away for me. Indeed, to be able to get
there, I have to fly away with a space ship at nearly the
velocity of light. We now come to a very peculiar question that
will confront us with the singularity of our reality construction.
Where do I myself exist? Do I also exist tomorrow September 22, 1996, 3
pm? If the answer to this question would be affirmative, we
would be confronted with a very paradoxical situation.
Because indeed, I myself, and this counts for all of you
also, cannot imagine me to exist at different places of time. But
indeed our framework clarifies this question very easily. It is
impossible for me to make some action in my past such that I
would be able to observe myself tomorrow September 22, 1996 3 pm.
Indeed, if I would have chosen to fly away and come back with the
space ship such that I observe now, September 21, 1996, 3 pm on my
personal watch, the inside of my house tomorrow September 22, 1996, 3
pm, then I can do this, and as we remarked already, it proves
that this inside of my house tomorrow is part of my present
personal reality. But I will not find myself in it.
Because to be able to observe my house tomorrow September 22, 1996 3
pm, I have had to move out of it. Hence, in this situation I will
enter my house, for myself being still at September 21, 1996, 3 pm, but
my house and all things in it, being at September 22, 1996, 3 pm. This
shows that there is no paradox.

\section{Introducing an Additional Time Parameter?}

There is an approach to relativity theory that could be interpreted conceptually as we put forward
in this paper. It has been developed by Stueckelberg, Horwitz and Piron [9, 10, 11, 12, 13, 14,
15]. One introduces explicitly a parameter $\tau$ that would correspond to the time of the
processes and changes going on in reality. The variable $t$ is interpreted as being a geometrical
variable. In this mathematical model, recently technically more and more developed by Horwitz and
his collaborators [14, 15], it would be very interesting to see how the conceptual framework that
we put forward here, with a very definite interpretation of 'what reality is' could be elaborated.
It is one of the aims of the author to work on such a conceptual elaboration in the near future.

\section {Acknowledgments}

This work was supported by the Federale Diensten voor
Wetenschappelijke, Technische en Culturele Aangelegenheden; IUAP-III
n$\circ $9. The author is a Senior Research Associate of the Fund for Scientific Research.   

 


\section{References}

[1] Einstein A., {\it Relativity}, Methuen and Co, LTD, London, (1954). 

\smallskip
\noindent 
[2] Einstein A., {\it The meaning of relativity}, Chapman and Hall, Science
Paperbacks, London, (1967). 


\smallskip
\noindent 
[3] Aerts D., {\it The construction of reality and its influence on the 
understanding of quantum structures,} Int. J. Theor. Phys., {\bf 31} 
1815, (1992).



\smallskip
\noindent 
[4] Aerts, D., {\it A possible explanation for the probabilities of quantum
mechanics,} J. Math. Phys., {\bf 27}, 202,  (1986).



\smallskip
\noindent 
[5] Aerts, D., {\it  An attempt to imagine parts of the reality of the
micro-world,} in the proceedings of the conference {\it Problems in Quantum Physics ; Gdansk
'89,} World Scientific Publishing Company, Singapore, 3,  (1990).


\smallskip
\noindent 
[6] Aerts, D., {\it Framework for a possible unification of quantum and relativity
theories,} Int. J. Theor. Phys., {\bf 35}, 2431, 1996.

\smallskip
\noindent 
[7] Aerts, D., {\it Time, Space and Reality and Modern Physics}, Elservier
Publishing Company, ed. P. Baert, to appear 1997.

\smallskip
\noindent 
[8] Aerts, D., {\it Description of Many Separated Physical Entities Without the
Paradoxes Encountered in Quantum Mechanics}, Found. Phys. {\bf 12}, 1131, (1982). 

\smallskip
\noindent 
[9] Stueckelberg, E.C.G., Helv. Phys. Acta {\bf 14}, 372 (1941).

\smallskip
\noindent 
[10] Stueckelberg, E.C.G., Helv. Phys. Acta {\bf 15}, 23 (1942).

\smallskip
\noindent 
[11] Horwitz, L.P. and Piron, C., Helv. Phys. Acta {\bf 46}, 316 (1973).

\smallskip
\noindent 
[12] Horwitz, L.P., Schieve W.C and Piron, C., Ann. Phys. {\bf 137}, 306 (1981).

\smallskip
\noindent 
[13] Piron, C., in Nato Advanced Study Institute on Quantum Electrodynamics and Quantum Optics,
Itsanbul, Turkey, Aug. 1989.


\smallskip
\noindent 
[14] Saad, D., Horwitz, L.P. and Arshansky, R.I., Found. Phys. {\bf 19}, 1125, 1989.

\smallskip
\noindent 
[15] Land, M.C. and Horwitz, L.P., Found. Phys. Lett. {\bf 4}, 61, 1991.


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