This paper has two aims. First, to show that the issue of the flow of time is directly connected to that of the dimensionality of the world: the flow of time is objective, if reality is a three dimensional world; if the world is four-dimensional, the flow of time is minddependent. And second, to show that a thorough analysis of the consequences of the special theory of relativity unambiguously proves the four-dimensionality of the world, therefore the minddependence of the flow of time as well.
It may sound paradoxical but a solution of the long-standing
discussion on the meaning of time flow would have been found if
the issue had been discussed in a closer connection (than is
usually the case) with the consequences of the special theory of
relativity. In that case it would not be possible both for the
flow of time to be objective and the consequences of the special
theory of relativity to be true.
To prove this thesis I shall not make use of the argument of
Reichenbach [1] and Grunbaum [2] against the objectivity of time
flow (i.e. against Becoming): "If there is Becoming
(independently of awareness) the physicist must know it". My
reason for not using it is that this argument is necessary
but not sufficient. Objections might be raised that from the
fact that the
flow of time has not been described in physics so far, it does
not follow that it lacks objectivity. To be able to judge
whether the view on the objectivity of time flow is compatible
with the theory of relativity, it should be emphasized that the
alternative - objective or minddependent flow of time - is closely
connected to another alternative - that of the dimensionality
of the world (three-dimensional or four-dimensional world).
Indeed, on the one hand, if the flow of time is an objective fact
it follows that the present moment is objectively privileged in
comparison with the remaining moments of time. The special
status
of the moment "now" presupposes an objectively privileged state
of the
present events as well, i.e. of events occurring simultaneously
at that moment. The privileged state of the present events is taken
to mean that they are the only existing events ; past and future
events are viewed respectively as no longer and not yet existing.
On the other hand, the present (defined as the three-dimensional world at the present moment) is the very class of present events, i.e. the class of material objects existing simultaneously now. Consequently, the flow of time is objective only if reality is a three-dimensional world, i.e. only if events are objectively divided into past, present and future. Conversely, the flow of time would not be objective if events were not divided into past, present and future but had an equal existence. In that case, however, reality cannot be a three-dimensional world since the three-dimensional world is the class of present events only (the past and future events do not have the same status - they simply do not exist if the world is three-dimensional). Past, present and future events are considered equally existent in the four-dimensional spacetime (Minkowski space). Consequently, in a four-dimensional world, where events are not objectively divided into past, present, and future, the flow of time is minddependent. H. Weyl was the first who connected the flow of time with mind and consciousness in the context of special relativity:
"The objective world simply is, it does not
happen. Only to the gaze of my consciousness,
crawling upward along the life line of my body, does
a certain section of this world come to life as a fleeting
image in space which continuously changes in time" [3].
This conclusion seems inevitable: on the one hand, relativity tells us that our body exists equally at all moments of our life (since all events are equally existent) but, on the other hand, we realize ourselves only at the moment "now" which shows that it is the hypothesis of our consciousness crawling along our world line that can reconcile relativity with our everyday experience.
The conclusion that the flow of time is minddependent only
if reality is four-dimensional shows that Reichenbach and Grunbaum are
not consistent in denying both the objectivity of time flow and
the four-dimensionality of the world. Their lack of consistency
is also evident from the fact that they regard the simultaneity of
distant events as a matter of convention whereas an analysis of
the conventionality of simultaneity by taking into account the
issue of the dimensionality of the world shows that simultaneity
is conventional only in a four-dimensional world.
So far the arguments put forward in favor of the four-dimensionality of the world have not provided a definite solution of this problem since they did not analyze the consequences of the special theory of relativity (the underestimated arguments put forward by Rietdijk [4], Putnam [5], and Weingard [6] are an exception). The problem of the dimensionality of the world, however, can be unambiguously solved namely by analyzing the consequences of the special theory of relativity. In the first place this can be done by revealing the meaning of the relativity of simultaneity (see Putnam [5]). Bearing in mind (i) that the present (the three-dimensional world at the moment "now") is the class of simultaneous event at the present moment, and (ii) that observers in relative motion have different sets of simultaneous events (according to the relativity of simultaneity), it follows that the observers in relative motion have different three-dimensional worlds. If we consider the existence of objects as observerindependent (absolute) it follows that the three-dimensional worlds of the observers in relative motion exist equally. This is possible only if reality is a four-dimensional world. In this case the observers in relative motion consider different three-dimensional space-like slices of the four-dimensional world to be their presents (their three-dimensional worlds). The relativity of simultaneity would be impossible if the world is not four-dimensional: if we assume that reality is a three-dimensional world, evolving in time, this world will be the only one that exists; this means that all observers in relative motion, having a common three-dimensional world, will have the same set of simultaneous events which contradicts the theory of relativity. In other words, the relativity of simultaneity is not possible if reality is a three-dimensioanl world. Contradictions with the special theory of relativity are also arrived at in analyzing its remaining kinematic consequences (relativistic length contraction, relativistic time dilatation and the twin paradox) [7].
Another argument against the three-dimensionality (or in
favour of the
four-dimensionality) of the world is the conventionality of
simultaneity. It follows from it that a given observer can
regard as his present an arbitrary three-dimensional
space-like slice of the region outside the light cone (i.e. of
the region Elsewhere). However, if the observer
considers his present to be the only reality, a
conventionality with respect to what exists
inevitably follows form the conventionality
of simultaneity: the observer will be free to
choose which three-dimensional space-like slice to regard as
his three-dimensional world. The conventionality of simultaneity
proves to be trivial (a matter of description) only if reality
is a four-dimensional world. In such a case the entire region
Elsewhere exists (see Weingrad [6]) and for that reason an
observer can arbitrarily consider any slice of it (i.e. any slice
of the four-dimensional world) to be his present.
From what has been said it becomes clear, I believe, that
the world we live in is a four-dimensional one. Consequently, the
flow of time is a minddependent phenomenon. If the consequences of
the special theory of relativity are analyzed consistently and
correctly, this conclusion is inevitable.
Establishing that the flow of time is minddependent is rather a discovery of a new problem (which may prove to be very deep and touching on concepts such as free will ) than a solution of the old problem of time flow.
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