Government of the Autonomous City of
Neuropsychiatric Hospital "José Tiburcio
Borda"
Laboratory of
Electroneurobiological Research
and Journal
Electroneurobiology
ISSN: 0328-0446
Why is
Time Frame-dependent in Relativity? Minkowski's spacetime as a Kantian 'condition
of possibility' for relativistic calculations
Mariela Szirko
and Laboratory of
Electroneurobiological Research, Neuropsychiatric Hospital "Dr. José
Tiburcio Borda"
Government of the
Autonomous City of Buenos Aires
Correspondencia /
Contact: Mszirko [-at–]
Sion.com
Electroneurobiología 2005; 13 (3), pp.
181-237; URL <http://electroneubio.secyt.gov.ar/index2.htm>
Copyright
© 2005
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Abstract
The kinematic consequences of special relativity
can be expressed in three-dimensional language. Remarkably, this does not mean
that, for making special relativity operational, positing a three-dimensional
ontology is as good as positing the four-dimensional ontology. This is a
singular limitation, whose nature is worth close inspection. In exploring it
not just within a traditional, kinematic or geometric perspective but in its
modern scientific context – i.e. as
regards (1) causation, (2) localized observers that physics finds in nature and
are not mere short forms for reference frames, and (3) the semiosis they
develop and use to make reference to distant present objects – this essay
pursues two aims. First, to put on view that the block universe outlook,
regarding the macroscopic-scale universe as a timelessly existing
four-dimensional world each of whose diverse items is composed of temporal
parts, despite its being ontologically incorrect is indeed the only one that is
consistent with special relativity, whose calculations are correct. This is
tantamount to point out that the special relativity's descriptions of the
macrouniverse necessitate to portray time as a dimension, and moreover as an
uncollapsed one; i.e., as a compass
wherein mobility, in the vein of the translocative motion that may occur on
every spatial dimension, ought to be at least conceivable. Second, to probe
arguments defending that special relativity alone can resolve the debate on
whether the extramental macroworld is three-dimensional or four-dimensional. In
particular, since relativity's condition of possibility, namely the imposition
on relativistic observers of describing at once past, present, and future
states along the length of the observed moving entities, has been considered a
proof that past and future components of real entities enjoy an unremitting
mode of existence, the main argument probed in this paper is the one claiming
that "if the world were three-dimensional, the kinematic consequences of
special relativity and more importantly the experiments confirming them would
be impossible." This is acknowledged as exact but it is remarked that,
such imposition being a Kantian condition of possibility, it cannot reveal
anything about what Kant called noumenon, i.e.
extramentality.
The
present essay originated as scholia to Ref. [1]
(Petkov; see "Acknowledgements"), whose structure it thus closely
follows.
1 Introduction
1.1. Struggling
against time.
Explicit or implicit presentism, the view that only the present (the three-dimensional
world at the instant 'now') exists, is the standard view on reality. Some
research in history of ideas [[2]; [3],
pp. 567-823, 963-4] concluded that presentism is generally disowned only in
some human groups where inner coercition is specially important and thus
appreciated, such as very stratified social organizations instanced in rigorist
settings as much diverse as certain pre-Columbian Mesoamerican cultures, the
shoguns' Japan, and academic societies devoted to logic, mathematics, or theoretical
physics. Those rigorisms go along with a societal need of looking for
exemptions to waiting [e.g., for
getting commands done, or for measuring frequency: 3, p. 312] and of denying
reality to the irreversibility of time elapsing, whence efficient extramental
causation becomes denied and imaginarily substituted by relations among
subjective, mental contents; these contents, when generalized, are often
understood as Platonic Ideas, connected not by way of efficient causality but
by their inner buildups or idiosyncratic, essential 'virtues'. In the thus
built reality, no 'present' state of affairs is privileged with the exclusive
possession of powers to metamorphose itself into other states of affairs.
Rather, it is claimed, every situated observer's experience crawls upward along
its worldline collecting sensory information, but incorrectly interprets this
information as meaning that only a
constantly changing reality exists – whereas, in fact, past and future states
are ontologically analogous to the present ones.
1.2. Observation
matters. Yet,
which scientific observation would lend any support to rigorisms? Where on
earth one could witness past and future affairs? A failure of simultaneity
might be of use so long as, in becoming simultaneous, the entities leaving
themselves to be known as arriving from other times retain a label revealing
their formative epoch. Special relativity foresees that if a not-pointlike but
extended entity is described by some eyewitness placed on an inertial frame of
reference in relativistic motion, each distinguishable segment of the lengthy
entity, consecutively positioned along the direction of relative motion, is to
be described at a different present. So, as rigorisms wish, simultaneity seems
to break down: some of those 'presents' did already occur (stay past) and
others not yet occurred (remain future) in an inner or proper-time perspective
taken by an observer located at rest in the very entity's middle segment; such
a segment in the instant of the description is locatable, after some
calculations on the signals' speed, the nearest to the relativistic eyewitness.
This darting eyewitness, in turn, must remotely describe this mid segment of
the extended entity (often visualized as a train of wagons, or as a rod
pointing to the motion's direction) as it was in the past time which lags
behind the outer eyewitness' present exactly by the shortest delay among all
the signals coming from the segments of the lengthy entity – but nevertheless
the entity's segments, which harbor events described as past and future in the
inner, local, rest, or proper-time perspective taken from the middle segment,
should also be described by the outer
eyewitness as in the present scenario. In this way they are simultaneous for
the outer, remote, relativistic eyewitness and sequential for the inner, local,
resting observer.
Whence splitting the subuniverse and shifting
the halves past another at relativistic speeds should suffice to grace with
one's presence both bygone cosmogenesis and remotely impending cosmoclastics.
This cannot help but make up an exciting prospect, whose academic entertainment
depends on neglecting the same calculations for all the signals coming from the
segments of the lengthy entity. The point is discussed below, though anyone seeking
an exception to waiting might find explanative the outline in footnote[1]; key to give good reason
for such sequences' simultaneizing is that, most remarkably, it only occurs
inasmuch as the not-pointlike, extended entity shares in the direction of the
frames' motion. The entity, though often pictured tilted at a certain angle,
ougth to spread itself over a small piece of its path.
But the issue at stake is far more interesting
than estimating Doppler effects on the Pythagorean theorem for a space that
keeps the signals' travel null from their own frame of reference while making
that, from all the other inertial reference frames (only the local ones, in
general relativity), such a null travel be seen to span some distances at speed
c. The said neglect of the mentioned
calculations depends on paying no heed to the very building of the
developmentally-acquired hermeneutical ability to make sense of the physical
semiosis involved in perceiving distant events. On certain historical reasons,
introducing intellectual development into geometrical physics might appear
irritating. Yet, since relativistic calculations relate to items in motion, a
semiosis-installing distance from
those events is indispensable in order to show that observers need not agree on
which events are simultaneous. (For exhibiting this dependence on the state of
motion of the observers, such observers ought to stand in relative motion,
which must be translative; it precludes showing this relativity by analyzing
the simultaneity of the not-spatially-distant mental contents in a
single-observer, or – everything else
unmodified – the perspectives of different observers occupying the same
spacetime point one after another). Here it may be advanced that the mentioned
developmental building of the ability to perceive distant events as distant
involves frame-invariant causation – but this involvement is a matter of
genetic epistemology, an academic department whose relationships with the one
of relativity physics have much been overlooked, if at all minded. Still as a
further, ultimate basis for mystification, the 'exciting prospect' rests on
taking 'to be' as if it only were an intrinsic aptitude to properly accept
combinable predications, rather than recognizing 'to be' as an unexpressible,
non-conceptualizable enactment cancelling nonexistence; this slip-up, moreover,
is one entrenched in social roots. A real stack of misinterpretations, truly.
Deconstructing all of it, even sketchily, will take the remaining of this
transdisciplinary article. Pending such a deconstruction, the imposition on
relativistic observers of describing at once past, present, and future states
along the length of the observed entities has been considered evidence that
past and future components of real entities enjoy a unremitting mode of
existence, authenticating the rigorist denial of presentism.
1.3. Distinguishing
subjective and extramental denotations. In utter contrast to such rigorisms, the
presentist common-sense view reflects the way most people – and probably other
primates and birds [[4]]
as well as reptiles [[5]]
– perceive the world. But in order to deal with world perceptions we need to
clearly tell apart the two denotations of this term, 'world'; namely, its subjective
and its extramental denotations, whose interval modules fairly differ. To this
purpose, let us convene from this point on to reserve the term 'world' for
indicating (save in quotations) 'mental world', i.e. every set of mental contents into which a mind has become
itself differentiated. We will use instead 'subuniverse', confessedly a
graceless name whose valuable coinage is often attributed to J. A. Wheeler, or
'macroworld' when it matters to forget about the 'virtual' particles created
from sub-indeterminacy fluctuations in energy, for denoting the observable
nature where minds and time are found. Associated with these two terms let us
form the pairs moment-world and instant-subuniverse, so as to apply
here the convention deeming
"physical
instant … a very minute period considered the ultimate modulus of
transformational change, namely the minimal interval over which a causal
transformation is at all possible or might be marked off by two different
instants, [while a moment is] the minimal transformational resolution or time
acuity of minds, which is observed to stay in the order of one hundredth of a
second. We do not live and remember physical instants; we live and remember
moments, and the difference between an instant and a moment is a dilation that
stretches physical instants an ascertainable number of times." [[6]]
1.4. Features of
presentisms. Presentism,
taken (not to mix up the issues of dimensionality of the universe in relativity
and in, say, Planck-scale models) as only related to the macroscopic aspect of
the subuniverse, when conceptually refined, features three defining tenets:
1.
The macroscopic subuniverse or actuality displays itself as a plurality of spatial localities
(though, nevertheless, current presentisms may recognize that space is not a
cosmologically fundamental but secondary occurrence). Space spreads forces over
three dimensions; this essay will not discuss the dispersion of forces over
extra dimensions collapsed into tiny magnitudes that might be necessary to
unifiedly describe electromagnetic, gravitatory, and nuclear forces. Yet one
might note that although presentist descriptions can accommodate non-local
effects, e.g. quantum entanglements
over macroscopic distances, in order to reveal relativity (also) in presentisms
these forces' action carriers must be conceived as translocative: no action at
a distance or non-local extramental effect is acceptable. Whence to produce
relativistic descriptions presentists should grant that, in each of those
spatial localities, the frame-invariant causal efficiency of therein-localized
components locally generates changes one by one, and by recording such changes
observers may reconstruct series of events successively occurring in worldines.
2.
Such a subuniverse or actuality thus exists only at the present instant and exhausts itself in its being
present there in full entirety, so that all of the components of every
macroscopic item cannot help but coexist at the same instant yet never on more
than a single instant. Their coexistence enables them for affecting
reciprocally through frame-invariant, efficient causal interactions which
preclude that an event, which is now present, was future, and will be past, in
addition modifies its being earlier than some and later than some of the other
events. Yet, as mentioned in the next paragraph, this coexistence-stemmed
capability to efficiently deploy invariant relationships of precedence and
succession remains unused in certain presentist scenarios which posit causation
to be logical, rather than efficient. In any case, past and future components,
items, events, or situations do not exist and as a result not either coexist
and cannot causally interact. Specifically, no past or future situations,
items, events, or components might be coexistent with the present ones which,
rather, are able to frame-invariantly engage in causal interactions between
themselves. In Indoeuropean-rooted languages past and future nonexistence might
somehow more confoundingly be expressed with a double negation, saying that past
and future 'are' in a certain way or
certain 'mode of being', namely that they 'are' inactual – a supposed 'mode of
being' oftentimes further split into two varieties, so that past states 'are'
inactual and unmodifiable or blocked while, instead, future situations 'are'
inactual and modifiable.
3.
This subuniverse or actuality is three-dimensional, meaning one of the
following alternatives:
3.1. A certain version of presentism, of
pronounced Platonist affinities, pictures this subuniverse or actuality as sheerly
three-dimensional. In this outlook the unchanging universe has no time-like
thickness at all. It thus lacks and always lacked any intervalic extension of actuality which might count as a primary time dimension
secondarily vanished as the magnitude of such a time dimension fully collapsed.
As in this scenario no fourth dimension displays any span, the present
instant's time-like duration is inherently zero; of course, it cannot be
navigated. So in this special presentist outlook absolute uniform motion may
exist but the universe or subuniverse houses no causal change; essential
'virtualities' stand for efficient causation, which – like any change it shapes
– is held as pure appearance and sensory sham. Absence of frame-invariant
efficient causation allows that an event, which appears now as present,
appeared as future, and will appear past, in addition modifies its being
earlier than some and later than some of the other events. It is unclear if
inertia has to exist in it.
3.2. A second, different version of presentism acknowledges a fourth dimension,
although one whose span is fairly meagre. In this fourth-dimensional version of
presentism the changing situations whose sequential delays compose an interval
do no exist simultaneously, but the subuniverse nevertheless also possesses a
particular time-like thickness which – at least in our subuniverse – chances to
be the same that also works for physical changes as their ultimate feasible
interval unit. Thus the present instant's time-like extent is not zero. This
intervalic inner extension of actuality (Fig. 2 below) counts as a
time dimension whose span or magnitude collapsed down to the extent that, for
every locality and segregated modality of interaction (or physical force field),
its residual span accommodates no more, but not either less, than one action of
physical causation at a time. Thus also in this version of presentism this
fourth dimension is unnavigable and neither exception of waiting nor time
travel may either occur, but its span is not nil [3] and all motion is a causal
transformation moving with respect to timelike-thin space, i.e. it is relative. The action units of frame-invariant causation,
by their matching the actuality's collapsed four-dimensional span, can
efficiently run sequential transformations of the timelike-thin actuality
precluding that any therein-enacted event modifies its being earlier than some
and later than some of the other events. Other subuniverses' buildups might
include this fourth dimension either less collapsed or, even, more collapsed,
having varied its span with reference to fundamental requirements of physical
action – with the result that in those subuniverses, whether by excess or by
defect, causal sequences (of transformations in time) could not be sustained,
whereas in our subuniverse, because of the specific magnitude of such residual
span, change exists.
1.5. How do we know
that change is not illusory? Our perception of the external subuniverse reveals it as being indeed
changing. The very causation of this change, however, remains for the most part
unobserved: in 1905-1906 Ehrenfest and Einstein first realized that Planck's
derivations work because physical change comes in integer multiples of hν and a little over fifty years later
Crocco recognized that it entails the unobservability of physical causation
itself. In other words, under observation the efficient causation of physical
change behaves as if coming in microphysical packets which are discrete, i.e. which cannot help but annihilate
themselves to effect the change.
This discreteness, or whatever determines that
behavior, has thus been pinpointed [2, 3, 6] as the reason why one does not
observe the very causation of such a change (whether microphysical or
macrophysical) but just the changes done, except when the change is originated
by one's own mental acts – as in the case of changes derived from the
observer's voluntary behavior, such as the progress in one's writing or
painting – and is observed on time scales large enough, i.e. through not too tight time windows (as commented below). This
makes possible that, as ascertained on consistent observations (summarized, for
example, in [[7]])
carried out over the last three-quarters of century and grounding the quite new
academic field called genetic epistemology, whereas the very causation of outer
changes remains for the most part unobserved, the concept of time and its three
components – past, present, and future – are nevertheless inductively formed
from what we directly perceive: namely, as a part of the individuals'
intellectual development and interactive acquisition of epistemological
adequacy to effectively operate in the surroundings. In those limiting
circumstances, observers gain their metrical impression of duration from the
time needed for their mental acts [cf.
[8],
p. 633].
These modern results about the mechanisms of
intellectual development, a development which each individual must work
together with the surroundings, make clear that time not only elapses for
mental accounts, but also outside of minds: viewing time as purely subjective
is no longer tenable. Its untenabilty has become evinced, among other facts [3,
pp. 81 (fn. 31) and 927], by the developmental acquisition of the animal minds'
epistemological adequacy, whereby "Heraclitus says that the awake share a
unique world, while the asleep turn themselves toward a private world"
(Plutarch, De Superst. 3, 166 C). In
order that, in contrast, time be purely subjective, such adequacy of the mental
contents – on which rests the natural selection of suitable nervous systems'
and cerebral architectures – should rather be achievable through bare
contemplation, as an 'infused knowledge' acquired just by contemplating the
things' reciprocal relations, not interactively: as if an inborn-paralyzed child could be intellectually
bred by exclusively watching television screens. The need, for humans and at
least the other amniotes (i.e., the
mentioned mammals as well as birds and other reptiles) to acquire befitting
knowledge of extramental occurrences, of sequential interactivity[2] wherein the
mind-originated probings enact absolute motion, entails that time, indeed, runs
efficiently in extramental realm.
1.6. Positing that
'everything' exists likewise in regard to time. This settled the issue of the existence of
absolute motion in nature and allows to proceed on topics which, as the one of
simultaneity, logically come later. One should accordingly start by recognizing
that extramental reality, namely how things fit together independently of the
minds, changes in due course. And indeed, Heraclitus argued that the universe
is perpetually changing, though he seems not to have explicitly discussed the
connectionship of change and time. It was attributed to Heraclitus the opinion
that everything flows (pánta rheí: this thereby-appalled Plato ascribed to
Heraclitus in Cratylus 402 a; cf.
Plato's Theaet. 152 d, 160 d),
everything ceaselessly dances in choir (pánta
chórei: this uplifted Aristotle ascribed to Heraclitus in Topikoí… 104 b 21 ss)
[for a popular expose cf. also [9],
p. 65]. Such a dependence making every macroscopic reality likewise contingent
on time and determined by the temporal engagements of the flowing everything (pántoon … reóntoon, Plato's Cratylus 439 c) is contemporarily
contested by scholars pointing that minds are xenochronic [2, 3, 6]. With this
term, they assume that
"natural
science describes… realities of two kinds: observers, also called minds, which
do not generate time inside them (but may emulate any outer course, an aptitude
that may be called xenochronism), and the set of extramentalities, which does
it (and interactively assists minds to emulate outer evolutions). While in
minds memories persist because they do not exist within a coursing of time that
could alter or erase them, extramentalities evolve because the transfers of
causal efficiency make a microphysical time course which the inertial mass of
some but not all elementary particles extends into sizeable scales" [[10]].
But this splitting, exposing that not everything
of what natural science describes behaves identically as regards time, is quite
recent. In ancient times, almost two centuries after Heraclitus, Aristotle
effectively arrived at the conclusion that 'everything' exists likewise in regard
to time. Positing this notable uniformity was not a option, as it was
compulsory in order to found biology. He
"…
conceived knowing, gnoeín, as a
variety of metabolic assimilation only for the purpose, and with the precise
objective, of being able to compose a unique descriptive series with which to
delineate the full variety of living beings – by comparing species among
themselves and comparing the developmental sequences of individuals. With this
conceptual tool, Aristotle was able to achieve his purpose, of attaining
conceptual means suitable for unifiedly and uniformly describing the living
beings found in nature in all their possible forms. His informational view of
knowledge, presenting it as a variety of metabolic assimilation, is thus why
Aristotle managed to institute biology as a unified science. … [I]n view of his
mentioned purpose, it was uninteresting to detect if within the series of
organisms animated by a vegetative-sensitive soul the individuals of some
species included an existentiality circumstanced to sense and move its body.
This is the case of a dog, for example. Other organisms lack such an
existentiality in charge of biological functions, for example a starfish – or
its common ancestors with the dog, if Aristotle could have minded of them. …
These animals lack… any knowledge inasmuch as experience: in these animal
species having an Aristotelian soul but not circumstancing an existentiality
their 'knowledge' is mere information, gnoseologically uncharacterized – and
only metaphorically called 'knowledge' by external observers interested in
keeping Aristotelian homogeneity for the biological series." [ibidem,
Section 2]
1.7. Positing that
'everything' composes the only present 'now' that exists. Therefore, Aristotle's
description would not embrace the mentioned heterogeneity (of xenochronic minds
and time-generating macroworld) as his description could not distinguish
between existentialities or subjectivities and bodily information. (As
notorious, he was also unable to tell between a plurality of existentialities
leaving aside the difference in their mental contents [3, chapter 1.6]). He was
rather to deal unifiedly with all organisms, whether lacking existentiality or
subjectivity or instead possessed with it, so setting a single continuous
series of psychaí ('souls') just
differing in informatical terms. Aristotle further arrived to the conclusion
that such uniform 'everything' exists
only at the moment 'now' since it is this moment that "connects past and
future time" [[11],
p. 301] which themselves do not exist: "one part of [time] has been and is
not, while the other is going to be and is not yet" [11, p. 297].
Besides so portraying all realities in nature –
as uniformly behaving with regard to time and composing in this way the only
present 'now' that exists and in such presence exhausts itself altogether –
Aristotle made another contribution to conceptually refining the presentist
view, by asserting that nature is three-dimensional: "A magnitude if
divisible one way is a line, if two ways a surface, and if three a body. Beyond
these there is no other magnitude, because the three dimensions are all that
there are" [[12]]
(see also [[13]]).
2. Physical and
philosophical connections
2.1. Instant
'thickness' and causation. The three defining features of presentism – asserting that the
subuniverse is causally efficient to transform itself successively through
local change (a feature turned
macroscopic with the acquisition of inertial mass by only a fraction of
elementary particles [3, 10]), exists only at the present instant exhausting itself completely in
such a presence, and is three-dimensional or has its fourth dimension collapsed
– are intrinsically linked: if the macroworld is three-dimensional it exists
only at one instant of time and vice versa;
the time-like thickness or 'duration' of the instant in such a changing
macroworld is determined in relation to features of microscopically local
causation. Namely, in the physical-causation-acknowledging variety of
presentism this time-like thickness of the instant admits neither causal
sequences nor inchoations: it can let in neither more nor less than just one
elementary process of energy transfer or efficient causation; that of course
refers to what may be described as the very transfer of an action carrier of a
force field, not to the response interval or lagging of its direct effects
behind the causal action packet’s instantaneous absorption, i.e. the 'characteristic times' taken by
the transitions caused [3, 6].
2.2. Denial of
efficient causation affirms 'to be' as logical predicability and causal
efficiency as pure outward show. Instead, in the physical-causation-denying,
antichronic variety of presentism, for which transience is unbearable and on no
account deemed basic, the instant's time-like thickness does not exist; 'to be'
boils down to mere predication of attributes (explained below) rather than
fundamental enactment; determinations come only from logical relationships, and
physical change is sensory hallucination: in no way real transformation. As the
therein-revolting prospect that situations could really flow is altogether
denied, reasonings are supplied in order to repute illusive the irrevocability
of time. Augustine of Hippo, still importanly influenced by Plato's antichronic
outlook which instances such denial of reality to time elapsing, made an early
move toward realizing that link by attempting to ascertain the duration of the
'now'.
Augustine decided that the present moment cannot
have any duration: "In fact the only time that can be called present is an
instant... For if its duration were prolonged, it could be divided into past
and future. When it is present it has no duration" [[14],
p. 119]. One should remark that, in order to avoid its being thus divided, there
is no need that it completely lacks duration, as Augustine supposed, since
enacting any division in extramental time demands causal efficiency, so that a
time-like duration shorter than the time needed for enacting causal efficiency
suffices to avert that "it could be divided into past and future" [3,
pp. 309-312]. Yet Platonisms need to pronounce causal efficiency just sense
deceit and pure outward show, reality being rather determined by the essential
virtualities of timeless Ideas.
2.3. Instant's duration
and causal efficiency. One should remark, too, that this instant needlessly supposed of no
duration, i.e. of no intervalic
extension, is thus placed by Augustine into the same scenario that spatial
extension. This combined move presents the universe as sheerly (and, literally,
most narrowly) three-dimensional – otherwise, its time-like thickness makes a
collapsed fourth dimension wherein only
contingently may navigation become unworkable: the nature of such a fourth
dimension's residual span is still alike to that of space – and sustains the antichronic outlook, i.e. Platonisms' denial of reality to irreversible time.
But the topic is intricate, so that to visualize the ties between the
three-dimensionality of the subuniverse and its existence only at the instant
'now' imagine that 'the present moment' names some finite duration. For the
sake of the argument let us forget time courses as determined by physical
causation and, arbitrarily, let that duration be some fixed number of minutes.
(For instance, Petkov [1] chooses ten seconds as his example).
As these minutes are not further distinguishable
into present, future, or past all of them are present. Thus every thing and the
whole subuniverse would be given as a whole, or exist in its entirety both 'at once'
and unchangeably, during all of the (rather, our clock's) instants composing
the imaginarily protracted time-like thickness of the 'now'. Everything, even
if instantaneous, would at least be likewise extended in time. For example,
every mobile item would at once exist at all spatial points of a distance it travels for the fixed number of what we call
minutes. Nevertheless, macroworld's items that are extended in time are
four-dimensional, not three-dimensional. Presentists often remark that we seem
to perceive a realm of items not appearing to exist at more than one instant.
Whence not seldom it is thought [e.g.,
1] that on the presentist view the fact that the subuniverse "is regarded
as three-dimensional implies that the
present moment must be" an instant with no inner transformative
course that could be called duration or 'time taken by such a transformation'.
This entails that in describing presentism one cannot forget (as we did, for
the sake of exemplifying) time courses' being determined by physical causation,
because the interval-like thickness of reality is to be linked with the minimal
possible 'delay' that physical causation imposes in order to enact change [3,
6]. (Only so may a time-like thickness neither to 'hang' nature's
transformations by turning causal courses into a 'legato', i.e. by enmeshing the physical causation of change, nor to prevent
causing transformations altogether.)
2.4. Frame-invariance at the efficient causation's core. Whatever may count as physical causation is of course to be frame-invariant (i.e. no perspective could exist from which it vanishes or cancels) and to come about as every one of the reaction-producing modalities for exchanging energy in a certain energy range. As an interesting instance, when Crocco recognized that the fact that physical change comes in integer multiples of hν entails the outer unobservability of physical causation[3] (which thus displays the extramental transformations as if they were constant conjunction or structural spectacle delineated by certain connectability function, κ, defined as causal), he utilized the frame invariance of causation for presenting sensing as a new fundamental action of nature by way of pinpointing the requisite conservation of feelings in any relativistic description of the sensually-interacting tissue as physical system