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发帖数: 1240 | 1 Before embarking on a metaphysical critique of the famed "theory of general
relativity" (GR) amidst the fanfare of the recent observation by LIGO of
gravitational wave, an explorative discussion of mathematics is both helpful
and necessary.
In any theoretical investigations, mathematics plays a pivotal role. The
natural question arising herein is then, what is mathematics? And what kind
of roles can we possibly expect of mathematics in any theoretical enquiries
(i.e., by deductions) or in a practical deliberations (i.e., by induction)?
For example, in deductions, we start from a simple premise, which is often
so simplistic that we have to assume its universal validity，which we
express in the verbal form of "it is obvious...", (though not necessarily a
truth, by simple of the simplest , we actually mean that since we can not
enquire about its matter any further as it is apparently presented to us and
give us such and such intuitions) , such examples of premises include, "all
living things die" in biology, obviously this statement is correct as of
now for all living things that ever lived on this earth, but there is no
theory or grounds of a guarantee that this statement should or have to
continue to be true in the very humongousely distant future; nothing can
travel faster than light as in the theory of relativity; time and space are
two facets of the same cosmos entity, the so called spacetime as in the
general theory of relativity; and among many others. As we proceed with such
deduction and often combining synthesis, in the end we often arrive at a
conclusion, sometimes a conclusion that we can hardly believe since it is so
counter-intuitive! For example, the recent observation by LIGO was said to
have confirmed GR's prediction that the curving of spacetime promulgates and
actually manifests as gravitational wave. In inductions, we start with
gathered observations of a certain subject matter, and we proceed by
generalization, in the end we reach a conclusion that can be predicated of
the subject matter, i.e., an analytic. Such examples are numerous as in most
experimental sciences. As we can see in the above illustration, we cannot
expect to extract any empirical validity regarding a subject matter from
either math deductions or math inductions alone. In fact, not surprisingly,
it is said that all mathematics are tautologies, and the sole undefined
concept in any mathematics is, what we mean by "true or false"! In other
words, we usually use "true" or "false" as predicate of other subjects, like
"this and this are true", but we rarely, if possible at all, describe the
very concept of "true" or "false" in terms of its predicates like “Being
true is…”.
Therefore, it might be safe to say that, mathematics are nothing but the
forms to which we have to conform in order that we can organize our thoughts
and thus have any judgments. Or even more radically, since any thinking
processes are through our minds whose vehicles are corporeal, we may
therefore say that mathematics are nothing but a "corporeal instrumentation
＂，an instrumentation that depends entirely, if not solely, on our internal
senses. Since God is the only Infinite and the sole most perfect being (for
the purpose of discussion, lets say God exists), therefore our obvious
finitude as human beings (for among numerous evidences, like all humans die)
demands that we shall not take a synthesis of mathematics and of a premise
originally derived from pure intuition too far. Now, to the formal products
of such synthesis we designate names, these names are what we usually call "
theories", such as, among the numerous, "the theory of general relativity"
by the legendary Albert Einstein.
For readers， if we may at least moderately agree on the above thesis, we
may hence begin our critique of the GR, and for that matter, of theories in
general as a whole.
Since the GR involves fairly complicated and arcane physics and mathematics,
and most of us are neither physicists nor mathematicians by training (i.e.,
we are amateur scientists at the most), it may be helpful to have an
analytic dichotomy of the GR so that we can grasp the whole schema construct
of the GR without compromising its theoretical and mathematical rigors; To
achieve this purpose of not compromising GR’s theoretical and mathematical
rigors while carrying this critique, we will look at GR only in terms of its
premises and its mathematical frameworks without even touching any of its
mathematical details at all, i.e., we look at the synthetic structuring
process of GR in the whole as a set of premises and a set of mathematical
frameworks. Since we must assume (and we are rightly to do so) that the set
of mathematical frameworks involved in GR (which are said to be Lorentzian
geometry, and which, to be frank, I do not understand at all) is correct and
is of the most perfect mathematic rigor, let us then look into the set of
premises involved in GR instead. These premises are (my reading source is
the book “The Road To Reality” by renowned physicist Roger Penrose, if my
summarization should be wrong or inaccurate, please advise): light travels
at the fixed finite speed and nothing travels faster than light; the
equivalence principle; the einsteinian spacetime (a kind of the union of
space and time by abandoning space by itself and time by itself, a notion
initially proposed by Minkowski though, my take of this einsteinian
spacetime is that time and space are like two facets of the same universe
entity conveniently designated as spacetime). Simply put, starting from
these premises by employing the set of mathematical frameworks, Einstein was
able to develop his general theory of relativity.
As my arguments will mainly about the third premise of spacetime, let us
first look at a brief description of various spacetime frameworks that had
been around since very ancient times. The spacetime of Aristotelian physics
has absolute space and absolute time constructed in Euclidean geometry. In
Galilean dynamics, Galileo teaches us that the dynamical laws are precisely
the same when referred to any uniformly moving frame; In light of this
notion, Galilean spacetime framework was reconstructed from Aristotelian
spacetime by adopting relative space but still retaining absolute time, the
so-called spacetime for Galilean relativity. Later, in Newtonian dynamics,
Newton slightly modified the Galilean spacetime but still retained the
overall construct of absolute time and relative space. By abandoning space
by itself and also time by itself (a notion initially proposed by Minkowski
though), and thus abandoning absolute time as well, Einstein was able to
take a revolutionary step in this direction and constructed the Einsteinian
spacetime as a union of space and time. Admittedly, this is a genius and
revolutionary step. Nonetheless, in my humble opinion, this unionized
spacetime is still at least incomplete, if not questionable indeed; For one
reason, this Einsteinian spacetime still views time ontologically in
concreto, which might not be appropriate, and I will try to illustrate my
arguments below.
In a theoretical construction where mathematics is involved, the premises
are usually developed from an intuition that we have when matter or objects,
which we can perceive somehow, are presented to us; as I have discussed in
the very beginning of this critique, the ideal premise shall be based solely
on the purest intuition alone; By purest intuition, I mean, when a single
object alone is apparently presented to us and causes us an immediate
intuition, we shall not even be capable of spontaneously deriving any other
intuition from this immediate intuition than this sole immediate intuition
itself. Why shall I affirm that the ideal premise be based solely on the
purest intuition alone? The reason is that a theory constructed as such
would possess the greatest potential of certainty of its “truthness”.
Among the three categories of certainties, i.e., empirical certainty,
hypothetical certainty, and apodictic certainty (as in mathematics),
apodictic certainty is the highest degree of certainty. Let us take
mathematics as an example. The very reason that we can be so certain of a
mathematical truth is that, as discussed earlier, premise in all mathematics
is based solely on the intuition of “being true” or “being false”,
which is the purest intuition as I mentioned earlier. By this measure of
standards, Einsteinian spacetime is obviously not a premise out of purest
intuition when space instance is presented to us (in this scheme, obviously,
time instance cannot be presented to us in a way that causes an immediate
intuition inside of us, as I will discuss in the following); In this case,
only the perception of space instance is the purest intuition, through this
intuition and by observing various alterations of world events in the space
instance, we perceive time, that is to say, the perception of time (though
only imaginary, because I believe there is no such things as time instances)
is subservient to the perception of space in concreto. As we standing at
this point, it is absolutely necessary to give a clarification as to what is
time?
So what is time? We never touch it, we never smell it, and we never see it,
yet we somehow feel it. It seems that we can measure its interval by clocks,
but even this is only illusory, to be strict, what we actually measure is
only the number of certain periodic cycles of certain movements. Furthermore
, a perceived measuredness does not in anyway mean that we established the
existentiality of the measured. For instance, suppose, there is a person who
has lost his smelling ability, if he was presented with two bottles, one
full of water, the other of pure alcohol, simply by measuring, he is in no
position of telling which one contains water and which one contains pure
alcohol.
So what is time? The answer seems so obvious, but yet whenever we are trying
to grasp its content ontologically, we found ourselves standing on shaky
grounds. Various cultures and religions have their different understandings
of the concept of “time”. In physics as in any other disciplines of modern
sciences, the concept of “time” is so fundamental that the answer to this
seemingly simple enough question will profoundly influence our human
understandings.
In my opinion, rather than a cosmos entity that is external to us, time is a
presupposition that is internal with us, through this presupposition,
whenever we perceive and think, we have to presuppose a time so that we can
organize our thoughts to conform, for example, to certain mathematical
frameworks. Without this presupposition, we cannot even think. As an
evidence of time being internal with us rather than being external to us,
let us look at the following scenario. If time were indeed external to us,
we would be able to imagine things that are not in any ways framed in any “
time”, yet the fact is that we are not capable of even doing this. For
instance, we can imagine a certain point in space at a given time, yet we
can in no way even imagine this same point in space without being
constrained by time. Since this presupposition is universally internal with
us whenever we perceive and think, therefore, it is this presupposition of
time that in effect gives us this illusion as if time is universally present
outside of us,.
At present, let us again look back at the spacetime of Einstein’s general
relativity and several of its ramifications. In this regard, I will quote
from “The road to reality” by Roger Penrose, “…An extreme situation
arises when we have what is referred to as causality violation in which ‘
closed timelike curves’ can occur, and it becomes possible for signal to be
sent from some event in the past of that same event”. Apparently, this
kind of situation demands an explanation. As Roger Penrose has stated in his
book, and I quote, “Such situations are normally ruled out as ‘unphysical
’, and my own position would certainly be to rule them out, …”. In my
opinion, this explanation is anything but satisfactory. In any sound science
, whenever there arises an inconsistency or an absurdity (by whatever
account), you cannot simply say, since it is ‘unphysical’, so let us just
rule them out!
For readers who can bear with me, with my full awareness of my boldness and
humbleness, I will propose my solution to this conundrum. And my proposition
would be, to totally abandon the concept of “time” and to establish a
theoretical construction that is based solely on the concept of “space” in
stead. A theoretical construction of this kind would introduce no ‘
causality violation’, since all world events will be viewed simply as
manifestations of alterations in space instead of as causations and effects.
And I do think that such abandonment of the concept of “time” is not
entirely baseless or completely absurd. For analogy of examples, Galilean
system abandoned the absolute space that is in the old Aristotelian system,
and again the Einsteinian system abandoned the absolute time in the Galilean
system and constructed a union of space and time, or Einsteinian spacetime.
Just as the Einsteinian spacetime requires the Lorentzian geometry to
produce a theoretical formulation, undoubtedly, such a new theoretical
construction would also require an appropriate mathematical framework, which
is certainly beyond my scope of knowledge and mathematical capabilities. | a*******a
发帖数: 1240 | | L****8
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helpful
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【在 a*******a 的大作中提到】
: Before embarking on a metaphysical critique of the famed "theory of general
: relativity" (GR) amidst the fanfare of the recent observation by LIGO of
: gravitational wave, an explorative discussion of mathematics is both helpful
: and necessary.
: In any theoretical investigations, mathematics plays a pivotal role. The
: natural question arising herein is then, what is mathematics? And what kind
: of roles can we possibly expect of mathematics in any theoretical enquiries
: (i.e., by deductions) or in a practical deliberations (i.e., by induction)?
: For example, in deductions, we start from a simple premise, which is often
: so simplistic that we have to assume its universal validity，which we
| a*******a
发帖数: 1240 | 4 翻成中文？
【在 L****8 的大作中提到】
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