There is something essential about the Now which is just outside the realm of science - a constant recollection of the present.

Yourgrau wrote that Gödel found that we can have a world in which there is time or a world in which there is existence, but not both. Gödel made the only rational choice: a world without time because existence is an absolute concept (Yourgrau, 2005, p. 132).
The fundamental premises of this reasoning are the premises that the lapse of time has to be something definite (like existence), and that the lapse of time is definite if and only if it exists in all possible universes and in the same way (that is, as something non-relative). This resembles the hidden premise of the more famous ontological proof of God, namely that God as the perfect being is something definite if and only if it exists in all possible worlds and in some non-relative way. It is interesting that Gödel also tried to formulate his own very subtle version of the ontological proof of God (Sobel, 1987).
The identification of relativistic time dimension with ordinary concept of time is reasonable in usual, every-day conditions but not in extreme geometrical environment or in the whole universe.
The intuitive concept of time simply does not agree with facts, and this indicates its unreality.
A lapse of time, which is not a lapse in some definite way, seems to him absurd as a colored object which has no definite colors.
However, according to Gödel, the concept of existence, cannot be relativized because in such a case it loses its meaning completely. Existence and the lapse of time are absolute concepts, if they refer to something real.
It would be more accurate to say that Gödel meant that, strictly speaking, he proved the radical relativity of the lapse of time which leads us to the unreality of the lapse of time. It doesn’t mean only the usual relativistic meaning of ‘presents’ and ‘Nows’ in regard to the frames of reference of different ‘observers,’ but a deeper relativity in regard to the accidental ‘arrangement’ of the matter in our universe. Someone would say that this does not prove the unreality of time, but in a former remark to his text Gödel said that a relative lapse of time would certainly be something entirely different from the lapse of time in the ordinary sense, which means a change in the existing (Gödel,1990b, p. 203, rem. 5).
It can be said that our world is in principle indistinguishable from a universe in which objective lapse of time is demonstrably absent. The experience of lapse of time and the physical laws are the same in both cases. Does this mean that the time lapse is not real in our world either. Gödel seems to say “yes”.
Gödel proved the essential difference between provability and truth, and similarly he proved the essential difference between the relativistic t-dimension and the intuitive concept and experience of time (T) (ibid.). In both cases, he succeeded to prove his theses by constructing some extreme cases (an extreme case of formalization, an extreme solution of the equations of general relativity).
Yourgrau believes it is something of a scandal that this similarity between the two Gödel’s results has gone unnoticed for so long, and that philosophers did
not recognize the deep meaning and consequences of Gödel’s physical results (Yourgrau, 2005, p. 136–137). According to Yourgrau, there is an important difference between the two Gödel’s results. The incompleteness proof does show that the devices of formal proof are too week to capture all arithmetic truths. The relativistic proof similarly shows that the intuitive concept of time is too weak to be captured by general relativity. The intuitive concept of time simply does not agree with facts, and this indicates its unreality.
Gödel tries to show the radical departure of the relativistic concept of time from any intuitive idea of time and on the lapse of time (Stein, 1990, p. 200). Stein refers to Gödel’s unpublished manuscript on the relationship between theory of relativity and Kantian philosophy.
We know from his short comment on Gödel’s paper in Schilpp’s volume that Einstein believed Gödel’s paper constituted an important contribution to the general theory of relativity, especially to the analysis of the concept of time (Einstein, 1970, p. 478).
Is it always so that time-point B which lies in the ‘past’ part of Minkowsky diagram for a world point P has to be before any point A which lies in the ‘future’ part of the diagram? It seems obviously so because it is possible to send a signal from B to A but not from A to B. The sending of a signal is an irreversible thermodynamic process which is connected with the growth of entropy.
Asymmetry regarding time is not a general trait of physical processes. We know that elementary processes in microphysics are reversible.
Einstein asked himself what would happen if the distance between B and A were far separated apart from each other. Would the assertion ‘B is before A’ still make sense ? Einstein said “certainly not, if there exist point-series connectable by time-like lines in such a way that each point precedes temporally
the preceding one, and if the series is closed in itself” (ibid., p. 688).
In that case the distinction ‘earlier-later’ loses its meaning, at least for world-points which lie far apart in a cosmological sense.
Gödel attacked the concept of lapse of time with the ‘flowing’ experience of Now as something real, and not the idea of time dimension and the time metrics in relativity physics.
t is interesting that Einstein himself felt somewhat uneasy regarding the status of “Now” in physics. Carnap reported in his intellectual autobiography that Einstein told him once that the problem of the Now worried him seriously. For him, the experience of the Now meant something special for man, something different from the past and future, but this important difference does not occur within physics (Carnap, 1963, p. 37).
Einstein answered that these scientific descriptions could not possibly satisfy our human needs; that there was something essential about the Now which is just outside the realm of science.

Is consciousness the sheer ability of one being to position itself between past and future, thanks to memory of some kind ?