“Time” is a MEASURE of CHANGES
The place of
un-substantive “time” in philosophical hierarchy of
definitions.
Local causality and “local
time”.
Criticisms of incorrect
math abstractions.
Author:
Valeriy Pimenov, research worker of
ROSCOSMOS,
Specialization: General theory of Systems,
computer-models of on-board-systems.
e-mail:
pimenov@roscosmos.ru
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Preface:
The author is
keeping to the un-substantive conception of physical essence of “time”.
Which means that I am strongly convinced that there
DOES NOT EXIST such thing as “time” as
“independent entity”.
Nor “absolute”, nor “relative”, nor “space-time” - NONE!
So, instead of saying “matter exists in space and time” (F. Engels) we should
say:
“Time” is a MEASURE of
CHANGES, evaluated LOCALLY “on the ground” of LOCAL FUNDAMENTAL
PROCESSES.
And you can possibly
guess that I am NOT the first who stated this.
As
far as I know, the first was Titus Lucretius Carus (55
year b.c.(!), Ancient Rome). He
wrote:
So, there is NO “time by itself”, but the
objects
Lead us to discover the previous
ages…
And we will find NO one who could
sense
“Time by itself” – out of MOVEMENTS and peace
of the bodies.
More or less distinctly the “problem of time” was
solved by: Laplace, Descartes and Ernest Mach.
But, if it is “so simple” –
why such a simple question is usually presented so
“misty”?
Ok, possibly, the first reason of “mystification”
is in IDENTITY of LOCAL FUNDAMENTAL PROCESSES, on which ALL
“upper-level” processes are built. And thus, after averaging-out, it looks like ALL
“upper-level” processes HAVE ONE source (etalon, measure) of “pace”. And
people “shift” the position of that “etalon” from the sub-structural level
– to the “out-of-structural” level – making it “out of matter” AT ALL! And
naming it “absolute time”…
That’s why people usually
think about the time as a “global” entity and do NOT identify it with
LOCAL sub-processes.
One man
(you know him, he showed his tongue to you) had grasped, that some
systems could be “essentially local” ("relative") and could have “it`s own
time”. But he could not grasped
either
that the reason of “time” is the LOCAL
PHYSICAL PROCESSES – and started to explain his “relational time” through
the mystical “curvature of
space”…
Another man (Minkovsky)
even found ONE “fundamental PROCESS” (“global revealing plane”), but this
was all what he could “allow yourself” inside his “metric spaces”. So his
SINGLE process should have to be GLOBAL – and thus was independent of
anything that happened locally…
But it was already “wise
enough”, because if ALL local processes has the SAME PACE – this could
give the exact “picture” of Minkovsky’s “global revealing plane”. Alas,
we now know that BASE PROCESSES could CHANGE its PACE (because of
gravitational changes for example) – and thus Minkovsky’s “plane” becomes
something not so “plane”… At the second part of this article I will try to
criticize Minkovsky’s “metric spaces” as practically useless as PHYSICAL
“basement” of ANY physical theory. Mathematical - it could be – at the
most…
Above the question of the
“time” as a MEASURE of CHANGES, there also is a question of time as a
“REASON of CHANGES”.
Even those who admit that time
is “something about changes” – often could NOT make the last step and STOP
thinking about “time” as a “physical entity”. The COMMON base
sub-structures and AVERAGING of base sub-processes – give them a
“subconscious” feeling that there is “something”, which “force all this to
change”…
And this is already about the second problem
with “time” – about its imaginable role as a “reason of
changes”.
But the correct statement is reverse: the
CHANGES are the “reason” of “time” (and NOT
vice-versa).
And what is the reason of changes if NOT
“time”?
Ok, I could only propose the INERTIA as
the “reason of changes”, meaning the “natural” tendency
of ALL STRUCTURED SYSTEMS to its SETTLED STATE. Such transitional
processes are common to ANY SYSTEMS with intra- and extra-interactions,
under which this system is NATURALLY (structurally) trying to return to
its settled state.
But in “math-physics” more common
is the principle of Hamilton (“principle of minimal
action”).
This principle of Hamilton is stated that
among all variations of processes (for given system) – the nature
always selects the one for which the “integral of action” is minimal. The
dimension of “action” is [energy]x[time] – and it is the area under the
curve of “excessive kinetic energy with time”. So, from the state with
MORE kinetic energy the system will return FASTER (the curve is steeper),
and from the state with LESS kinetic energy the system will return SLOWER
(the curve is flatter). So the AREAS under the curves will be THE SAME –
if we will take those integrals WITHOUT the “variation of time-intervals”
(which means that the integration will be made between two STATES of
SYSTEM). So you see, that in such interpretation “the Hamilton
principle” looks like USUAL evaluation of STABILITY MEASURE of any dynamic
SYSTEM. And I, as a specialist in “Theory of Systems” will certainly
prefer the “well-known” methods of systems-parameters evaluations – to the
“vagueness” of Hamilton-principle and all its “consequences” like the
Schrödinger-equation and so on. Mostly because such “equations” do NOT
“have in mind” any particular SYSTEM with all its: ELEMENTS, CONNECTIONS,
INTERACTIONS and BORDERS.
See part 1 with my
attempts to “sort the definitions” of such
“categories”.
At part 2 of
this article I am also trying to criticize the attempts to “directly use”
some MATHEMATICAL models as a “math-PHYSICAL” models. It is a commonly
unjustified assumption that ANY math-model could be also “good physic”.
And thus we see attempts to “live inside the model”. The men simply could
NOT distinct theirs math-models from REALITY – and thus use “time”
inside MODELS as a “real time”. And thus they do try to “change the SIGN
of time” and so on.
I think it
is very important to discuss in this article the principle of “local
causality” – see in the same part 2. But it is not only about LOCAL
processes explaining such phenomena as Newtonian “gravitational force”,
but also about some COMMON PRINCIPLES of ANY physical STRUCTURES. Possibly the
first who tried to formulate this – was Steven Wolfram (“reality is like a set of cell-automata with the
same functions inside every node; nodes (“cells”) interact ONLY with
NEAREST cells”).
At part 2 I am
also trying to discuss the ideas of Carlo Rovelli and
Yang-Mills about “brooding” of “space-time” by the PROCESSES of
interactions of the “elementary particle” with the gravitational
“field”(?).
It is already good that those famous
physicists do NOT “insist” that “curved space-time” exists “by itself” –
but they propose that it is “locally and DYNAMICALLY created” by the
PROCESSES of interactions between “elementary particles” and “quantum
gravitation” (whatever it
means).
Philosophic categories are
usually NOT used in math-equations :O)
And later
(see part 2) we will try re-evaluate current “math-fundamentals” of
current physic, where, as I am convinced, SHOULD be used “local
causality” principle and principle of independent local fundamental
processes (as a measure of local
“time”).
But first
we will try to agree to COMMON TERMINOLOGY. Never mind that it will look
like “a bit of philosophy”. It is still
necessary.
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PART 1
Attempts to build a
hierarchy of
definitions.
CHANGES – a
fundamental property of MATTER, synonym of “general movement” (as a
philosophical category). Synonym of “existence”. “Time” is defined as a MEASURE OF
CHANGES. “Time” is evaluated by the reference to the
LOCAL FUNDAMENTAL
PROCESSES.
PROCESS – a
localized SET of CHANGES, supplied with PARAMETERS, PROPERTIES. Often asked: is such “localization” of some processes is subjective? Ok,
selection of ANY “part of matter” is to some extent “subjective”. But we
see that the “rules” do exist – and thus different “invariants” of
interactions. So, there SHOULD be some REAL “properties” or
“parameters”. The problem is: which one?
:O)
INTERACTIONS –
mutual influences of PROCESSES. We should exclude the “subjectivism” while
defining which of the PROCESSES is “internal” and which is “external”.
Interacted processes usually form some COMMON PARAMETERS. Thus,
interactions are usually a kind of “association” of processes with a
result of getting some COMMON ATTRIBUTE. And thus it is REAL and not
subjective ASSOCIATION.
As we see, INTERACTIONS is an
“interaction of PROCESSES” – and this includes the case of an “external
observer”. And thus “observed events” are NOT “exceptional case” – but
still “the same” interaction (to observer or not). Sometimes the result of
interaction is a DESTRUCTION of one of the system (like absorption of
photon by electron). As you see, it makes no difference whether this process is
“observed” or NOT – it is the same “quantum event” (if system was
destructed as a
result).
PROPERTY – one
of the “attributes” of PROCESS. Or COMMON PARAMETER of some kind of
interactions. About some of the properties have reached “consensus” that
they are REAL and thus it is a
QUALITY.
QUALITY –
INVARIANT-PROPERTY of some INTERACTIONS. Usually by the qualities of
processes we could DISTINCT them, or decide that these are processes of the
same “type” (“similar”). Qualities (invariant-properties) always had
QUANTITY (measure of quality). But we could NOT know this EIGENVALUE
(invariant amount of INTERNAL quality of given system) a-priori (without a
measurement-process). So, in reality we never get the “amount of
quality” itself, but only RELATIVELY MEASURED quantity. But Einstein is
right ONLY in one point – ANY quality of process could be measured ONLY
during INTERACTION and in this sense “relative”. But this does NOT mean
that EIGENVALUES do not exist at all. It is simply the other name of the
“essential descriptors” of the STRUCTURE of some SYSTEM. Most of the
eigenvalues reveal themselves in interactions “implicatively” (indirectly) –
as STRUCTURAL (“parametric”) properties of interacted systems (like
“constant of the thin structure”
etc.).
STATE – state of
the PROCESS (do NOT mix up with the “state of object” (see below)). Applied
to the PROCESSES with PROPERTIES and thus usually used as a “stopped”
(“snapshotted”) process. But it is a big question – should we “quantize” all
processes – or on base-levels processes are
“continual”?
Very often QUANTITATIVE states (still in
the borders of measure) are confused with QUALITATIVE JUMPS, or
EVENTS. I suspect that THIS is the source of most of the
problems with the physical interpretation of “quantum mechanics”. I suspect
that the “states” of quantum mechanics are always the result of some EVENT
(absorption of photon, etc.). But it is always confused with QUANTITATIVE
(continual) states, which are usually the target of classical physic.
Hilbert proposed math-formalism, which
allowed to exclude the “essence of time” from his
equations.
He “invented” the “space of states”, in
which the “time-axis” was formally excluded, but “hiddenly” existed as the
“order of states”. Yes, to me it looks like a step in the right direction. But
this MATH-formalism does NOT solve ALL the problems with PHYSICAL
interpretation of “time” – because Hilbert did NOT “declare” that
PHYSICAL “time” does NOT EXIST “by itself”. He simply proposed “convenient
math-formalism” and did NOT pretend that it was “really so”. And even if
he would have – ALL of his STATES (past, present and future(!)) – do “EXIST”
in his “space of states” – but in reality neither previous nor future states
NOT EXIST “by default”.
STATES could NOT EXIST
until it is consequently “generated” by some
PROCESS.
Below it will be named principle of
local-procedural causality of states.
Each
process could be ONLY in “NOW-state”. Previous states are “lost”. Future
states could be generated ONLY as a result of LOCAL INTERACTIONS (“local
causality”).
Yes, if some process is PERIODICAL then
ALL of his STATES, even future, could be “predictable” and thus looks like
ALL states is already “exist”. But this is a “subjective assumption of
essence”, or our math-model extrapolation – and does NOT have relation to
PHYSICAL REALITY, to REAL physical PROCESS.
If WE
already know ALL STATES of simple pendulum – this does NOT mean that
“pendulum itself” already “know” ALL its FUTURE states. That is where the
“roots” of all “paradoxes” with “reversing of time arrow” and so on. Yes,
we could (sometimes) REVERSE the DIRECTION of some(!) physical PROCESSES.
Especially periodical (:O). But this does NOT means that this way we
“reversed PHYSICAL time”.
Men, FORGET about reversing
“TIME”! All we could really “reverse” – is the direction of some(!)
PROCESSES. But it looks quite IMPOSSIBLE (to me) to attempt to reverse ALL
PROCESSES (with ALL SUB-processes, etc.!) for something bigger than
elementary particle. The difficulty of reversing ALL PROCESSES AT ONCE for
something like amoeba – looks ABSOLUTELY
INSUPERABLE.
One remark about the systems which have
a kind of “memory for previous state”.
Usually it is
the system with the kind of “closed loop” (“back coupling”). This way such
systems could compare CURRENT state with PREVIOUS (which is loop-backed
with some delay) – so it looks like such system do “know” the PREVIOUS state,
which in some sense “exists” there. You understand, that in this case it is
NOT the “previous state itself”, but a kind of COPY, retuned-back by OTHER
INTERACTED PROCESS (loop-back circuit). That is why such loop-backed
systems already has DIFFERENT QUALITIES(!) compared with “linear” systems
– because such system is “forced” to INTERACT WITH ITSELF(!) (with delay)
– and as a result of such “exotic” interaction such system will get
essentially NEW QUALITY. Previous states do not exist but are “regenerated”
(“reconstructed”) there – so the principle of procedural causality
still “works” there. See Part-3 for additional details of relations
between REAL systems and there
MODELS.
OBJECT or SYSTEM
– group of PROCESSES with COMMON (integrating) set of
QUALITIES.
So it is NOT “voluntary selected” group of
processes, but only REALLY INTEGRATED set of processes with common
INVARIANTS.
In most cases the REAL SYSTEM usually
consist of the set of INTERACTIONS with some or other SYMMETRY. Any OBJECT
usually had some sort of SYMMETRY of “internal links”. On the lowest
structural levels it is usually “central symmetry” of internal
“border-processes”.
I could give a “stronger”
proposition: to be the “object”, any set of processes SHOULD have some
kind of SYMMETRY of internal processes. On the BORDER of “object” this
symmetry is usually ends (non-linearly).
But the
problem of “borders of objects” is not really that simple. In more
complicated objects some of the processes could become “borderless”
(irradiation of photon by electron, etc.) – but does this mean that such a
process becomes a “separated object”? We could try to find the answer
together. But NOT in this article :O)
Here we will
try to concentrate on the “problem of
time”.
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PART-2
What
is instead of “time”?
About local
procedural-causality and cellular automata.
“Loop
Quantum Gravitation” of Carlo Rovelli and “Spin networks” of
Yang-Mills.
So, “time” –
is a measure of changes evaluated by reference to the LOCAL
FUNDAMENTAL PROCESSES. If this measure is ONE (common) to ALL LOCAL processes –
what is the difference whether we will use “absolute time” (global measure of
changes) or each local process will have its own local measure of local
changes? Supposing that ALL LOCAL BASISES – are EQUAL?
But the basic sub-processes in DIFFERENT localities
are NOT always equal! The simplest example – is different gravitation on the
Earth and in outer-space…
Ok, we will try to
avoid philosophic “researches” – and will go directly to the selection of
LOCAL-BASIS PROCESSES which could serve to be the local measure of local
changes.
Lets take a laser-clock (etalon of
“time”).
When the base-processes (gravitation,
charge, magnetism) of different exemplars of these clocks are EQUAL – all the processes developed on this basis
will also have EQUAL QUALITIES (and quantities).
So,
if we will take OTHER system (not clock) with the SAME BASE-PROCESSES – we
inevitably get the same measure of changes for this system too (as in
clocks). And we could be certain that our clocks will “measure” the “pace”
of our system and could be used as a “reference system” for measurement of
SPEED of PROCESSES in our system (not clock).
But the
question is – could we be certain that our BASISES are ALWAYS EQUAL “no
matter what”?
Of course NOT!
Neither
gravitation, nor charges, nor magnetism could NOT be considered
unchangeable…
So, in some DIFFERENT localities our
clocks could give different “pace of time”.
It
really does NOT matter, while we will use clocks to measure pace of
PROCESSES in the SAME (or “equal”) LOCALITY where the clock is placed. For
example, ALL of the clocks on the Earth-surface will show “nearly the
same” pace of base-processes (having in mind GRAVITATION
mostly).
But it could be (and IS) DIFFERENT if our
clocks is placed to DIFFERENT conditions of
BASE-PROCESSES.
For example, we could try to send one
of the clocks to the “outer space” (low
gravitation).
It is considered to be “proved” that in
outer space laser-clocks work FASTER (than the same clock on the
Earth-surface). Of course it is NOT “thanks to Einstein”, but just because
we have DIFFERENT CONDITIONS of BASE-PROCESSES in outer-space. Indirectly
this prove that “laser” clocks are really is “sensitive” to the changes of
gravitation as well.
There is one
interesting question – how much “base sub-processes” we should take, to be
sure we get the UNIVERSAL BASIS for ANY real process? In other words,
could we have really “universal” MEASURE OF
CHANGES?
Lets start with Minkovsky’s attempt
to take the “plane of global revealing process”, which “runs away” from any
point with the speed of light. Lets try to use it in nearly the same sense
as our measure of “time”. First I wanted to criticize Minkovsky that his
“revealing plane” is a SINGLE global PROCESS. But later I did understand
that he had in mind that there “existed” an infinity-set of “revealing planes”
– because his “metric space” is continual and thus EVERY “point of space”
is CONSTANTLY “radiating” such “revealing planes”…
Is
it enough for you to understand that it is “pure mathematics”, but NOT
physics?
And, besides, in REALITY there are at least
SEVERAL qualitatively DIFFERENT processes which could be used as a BASIS for all other “higher” processes. But this does not mean, yet, that
Minkovsky was COMPLETELY wrong. In mathematics (and sometimes in physics) it
is usual practice to construct models by ESSENTIAL properties. So
Minkovsky could say that it was “such a model – by essential process
ONLY”…
Unfortunately (for Minkovsky) ALL other processes except
for ONLY ONE PROCESS – his “global
revealing” (used as “pseudo-time”)
was throw-out of his model. By our terminology this process SHOULD
be its own(!) “basis” and its own “measure of
changes”…
To me it looks like “unreal” situation.
What could we “measure” (speed of processes(?) as a “pace of time”) - if
we could NOT organize ANY interactions as a necessary “measuring
procedure”? What could this process “reveal” if NOTHING except SIZELESS (!) and immaterial
“points” exist in this “metric spaces”?
I could NOT believe that after throwing-out
ALL MATTER and all processes, except for a very abstract “revealing procedure”
(revealing of what? Math points?) – we could construct something
“workable”.
And this “ground” was used for the
“officially approved” theory “of everything” – by that well-known man,
which liked to show his
tongue…
Above the criticism of
Minkovsky, I also have more general criticism of attempts to present MOST
of math-models as a “good approximation” of REALITY. But it is NOT that
simple question. See details in Part-3.
Here we will
try to keep to the general problem of this part – which of the base-processes
is “enough”… for what? I will try to remind you
:O)
If “time” does NOT exist – then reality consists of continuum of local “now”.
I spend a lot
of efforts to “assimilate”, that all LOCAL states do NOT “have to”
change “simultaneously”.
So we should NOT bother
about such trifles as the “problem of simultaneity” – local
procedural-causality and spreading interactions is ENOUGH to “solve”
(or to ignore) this problem. We will have something like “in-point”
Maxwell-equations – so we do not need to bother how one local changes will
INTERACT with some other “localities” (or
whether it has “equal pace”) –
because the base-processes in both LOCAL “points” do NOT need to be
“connected” or “synchronized” to “make it ticks”…
In
this sense I agree with Stephen Wolfram (www.wolframscience.com)
in his idea of REAL “space” as a kind of “cellular-automata”. He
states that ALL happens like a set of “local interactions”, spreading from
“cell to cell”, from one discrete “node” to the other – because
the “structure of space” is DISCRETE.
About
sequence of “now”-states he said:
“Should we really imagine that the complete
space-time history of the universe somehow always exists, and that as time
progresses, we are merely exploring different parts of it? Or should we
instead think that the universe--more like systems such as cellular
automata--explicitly evolves in time, so that at each moment a new state
of the universe is in effect created, and the old one is
lost?”
He also understood, that we should NOT treat “time”
the same way as “space”:
“But I very much doubt that any such obvious symmetry
between space and time exists in the fundamental rules for our universe. I
suspect that for many purposes the history of the universe can in fact be
represented by a certain kind of space-time network. But the way this
network is formed in effect treats space and time rather differently...
And in particular--just as in a system like a cellular automaton--the
network can be built up incrementally by starting with certain initial
conditions and then applying appropriate underlying rules over and over
again.”
To my surprise, I have found “thinking in the same
direction” in a book by well-known physicist Carlo Rovelli. I am
talking about his work about “Loop Quantum
Gravitation”:
http://comm.roscosmos.ru/Docs/Carlo_Rovelli_book.pdf
(pdf, 5 Mb)
But
Rovelli does NOT “go directly” to the conception of “time” as a measure of
changes evaluated by base-processes. First he states that space-time is
ingenerated by quantization-processes going “inside elemental particles”
(while interacting with gravitational field(?)). He criticizes Quantum
Field Theory for using “space-time” as a “background”, independent of
quantum-processes in elemental-particles, while particles create some
“non-local structures(?)”. It results in some contradictory (“dualistic”)
theory (“old” Quantum-Field Theory). Rovelli said that such “dualism of
field” is a source of most contradictions of General Relativity (GR) and
Quantum Field Theory (QFT). And that “reduction” (convergence) of
“space-time parameters” of particles to RESULTS of quantum “operations”
(operators) applied to particles – leads to “consolidation” of both
theories.
The main goal of his attempts Rovelli defined
as construction of such math-formalisms of Quantum Field Theory, which
“free us” from the “static background” of “space-time”, while NONE of
PROCESSES with particles going. And for this, Rovelli said , we should
first “become free” from traditional understanding of
“space-time”.
The main math-formalism now (by Rovelli)
should become Hilbert’s “space of states” (filled with operators,
measuring transitive probability-values of physical
properties(?)).
Rovelli’s
new field-theory – Loop
Quantum Gravitation (LQG) based on “uncanonical algebra” which used
“holonomy” of gravitational interactions. “Holonomy” (Wilson`s rings) is a
matrix parallel-movements by closed curves used to define “gauge”
(measure) of something (measure of gravitational interactions in this
case). “Gauges” was first used by Mikle Faraday in the “Theory of
Measurement”. By the way, the same Faraday was the first to propose the term
“field”. He (Faraday) stated that RELEVANT variables should NOT be based
on the “value in point”, but keep the RELATIONAL value of INTERACTION between
this point and its “basis”(?). It was mathematically described (by
Faraday) as “holonomy of measuring (“gauging”) potential
along-the-closed-line”.
In Rovelli’s LQG - holonomy
becomes quantum operators, creating
“loop-states”.
Ok, I will NOT comment Rovelli’s
ideas.
I have supplied some of its details just to show
that it has some similarity to ideas of
Yang-Mills.
The Yang-Mills
theory of “Spinal networks” was proposed some 30 years earlier than
Rovelli’s.
In their theory the “loop-states” have
FINITE “norms” – which means that their “states” do NOT “spread-out over
the
universe”. And some FINITE combination of “loop-states” form a DEFINITE
(exact) “orto-normal basis” of ALL combinations of states of this
“spinal(?) network” in Hilbert’s “space of
states”.
Simply speaking, ONLY those
states (of particles) are “allowed” which are defined by finite combination of states of
the
nearest “spin network” (discrete “field-nodes”) around the particle. But
those “spin network” (nodes) states are NOT independent, and, in their turn,
are “measured” as a result of some “measuring procedure” (or as a result
of “localized” INTERACTIONS with OTHER particles). But it is MY
interpretation of theirs
ideas.
Nor Yang-Mills, nor
Rovelli is NOT a “real physics”, but “pure mathematicians” (from my point of
view) – so they did NOT “labor themselves to death” trying to PHYSICALLY
explain their ideas.
Ok, we will be grateful to them
for their attempt “to free us” from “EMPTY but CURVED
space-time”.
BUT, if we propose that their
“loop-field” or “spin network” is a definite states of PHYSICAL
VACUUM (real medium!) – then all that “mess” FITS TOGETHER and “lay
on proper shelves”.
The particle AND “physical
vacuum” nearest to it - IS a COMMON STRUCTURE (common
system).
The particle (electron for example) in its “quantum
changes” (processes) generates in “vacuum” some decaying wave, which is
necessarily “discrete”, because it spreads on discrete “particles of
vacuum” (“plankeons” etc.) - exactly as on the quantized “spin-network” of
Yang-Mills. And this “discrete wave” generated by electron – is SPREADING
to the OTHER nearest “big particles” (electrons), producing “measuring
effect” - interaction through discrete sub-media with superposition of
influences “stored” (“gauged”) in parameters of “plankeons”. The states of
plankeons around the electron do define (as a “trend”) to which NEXT STATE
this electron is “invited to go”.
In some sense, this
“spin network” (states of “plankeons field”) IS “inertia” - something
which keeps excessive energy of “quantum events” and then use it as a
“background reason” of OTHER QUANTUM EVENTS. So, electron could NOT just
“go by itself”,
without CORRELATING its “steps” with OTHER big particles,
referencing (“gauging”) to the states of nearest “spin particles”
(“plankeons”).
The essence of
Yang-Mills and Rovelli propositions I see in declaration that ALL
math-models of such physical systems should obey to the principle of
local causality. Meaning that, according to the ideas of Stephen
Wolfram, we should use the paradigm of local-process-causal states of every
“locality”, because of the essentially discrete structure of “space” (
consists of “nodes” or
“plankeons”).
Right now I
see only one “shortage” in the Yang-Mills-Rovelli
theory.
Model of Rovelli contains only ONE PHYSICAL
PROCESS – gravitation. And this gravitation is used as a “base-sub-process”
(in “spin-network” or “plankeons”) to “create” ALL EVENTS with
big-particles (electrons).
Of course they “forgot”
about electro-magnetism and some other “trifles”…
And
it is “traditional” for the “pupils” of Einstein (the teacher himself does
NOT “managed” this enigmas too). So their big-particles (electrons)
generate ONLY “gravitational-side” of all possible INTERACTIONS with
sub-particles (“plankeons”). Possibly for the better, because there are
“suspicions”, that this “spin network” (“plankeons”) is principally NOT
able to be responsible for other PHYSICAL MODALITY (electro-magnetism,
etc.).
Yes, electro-magnetism - is already “another
story”… There are suppositions, that this “modality” could be “carried by”
the SUB-SUB-level of the REAL STRUCTURE. For example, there could exist
something like “diffuse matter” – something like “liquid” which is
“placed” AMONG “plankeons” and INSIDE the
big-particles…
Ok, we had
already “gone too far” (by sub-levels of
matter)…
Let’s try to
stick here to the declared theme
– to the physical meaning of “time”.
The one who is
much more interested in SUB-structures of MATTER – could write to me
(pimenov@roscosmos.ru) –
and we will discuss it “privately”
:O)
--------------------------------------------------------------------------------------
PART
3.
Attempts to find physical meaning of some
math-models.
One of my
friends asked me: “could we just throw-out the T (time) parameters from
ALL equations – and then sleep well?”.
If it was so
simple! What could we propose INSTEAD of current (Newtonian) equations
with T as an “independent variable”?
Now it is clear,
that the difference in “pace of processes” for DIFFERENT LOCALITIES
could become measurable ONLY with essentially DIFFERENT conditions for
functionality of BASE SUB-PROCESSES (gravitation, electro-magnetism,
speed of movement in “vacuum”, etc.). We could try to find those equations
(or real processes) in which such base-processes are used
“directly”.
For example, for the systems (and
equations) which work on the Earth-surface – such “nonsense” like
“different gravitational conditions” we could “forget”, meaning that we
could “bravely” continue to use OLD equations with the old
T-parameter.
But when we are trying to understand “what
is wrong” with Einstein-s “twin-brothers” – we certainly SHOULD take into
consideration what was DIFFERENT in functionality of SUB-processes for
both.
Now I believe that one of the brothers, which
will be placed into the conditions of LOWER gravitation – will REALLY have
FASTER “pace” of PROCESSES based on gravitation (as a base-sub-process).
This
was PROVED by some experiments with laser clocks on orbit, comparing
to the pre-synchronized twin-clocks on the
surface.
But it is NOT about “relativism” yet.
“Relativism” is about the MOVEMENTS (relative speed of
systems).
So the question is: could some processes
“feel” that their system is MOVING RELATIVELY TO “physical vacuum” (or
“plankeons”)?
Some smart … could ask “and what
about the principle of Galileo”?
Meaning that
systems, moving in “emptiness” should NOT (by Galileo opinion) have means
to “know” about its constant-movement (“by
inertia”).
My current answers could be
next.
First, like it is now understood, “physical
vacuum” is NOT “emptiness”. So, it is EVIDENTLY NOT such simple model
as “something unchangeable moving in emptiness”. If we select the
model of crystal-like physical “vacuum” – big-body movements in it
will look like a model of something “liquid”, filtering through
“channels” with “jumping vacancies”…
In such
conditions of “inertial” movement – the Galileo principle definitely could
“work” only under some “conditions”, like low-speed, really big body, etc.
In most of the OTHER “conditions of movement” we could NOT guarantee that
sub-processes (of interactions with “lattice” trough which it is
“filtered”) will be the same.
So, reaching some speed
of “filtering” – we reach a conditions under which we should spend MORE
energy to add the SAME increment of speed (supposing that our big-body get
some “external impulses” to increase our speed of “filtering”). Of course
such dependence between the same amount of increment of “absolute” speed”
and necessary impulse of energy for it - will be “essentially
non-linear”.
I can not exclude a possibility that it
could be exactly like in Lorenz-Einstein equations (by math-form of
dependence from speed). But, of course, the reason does NOT lie in “increasing of
mass with speed”…
More likely, the limit of “energy
transmission” (near the v=c) is reached because our external impulses
could NOT FULLY catch-up with our body, so it could not completely transfer
the
impulse. Thus we should spend MORE energy to reach the same increment of
speed of our body.
So, that already looks like
our body COULD “feel” its ABSOLUTE speed (?)
And
now the question is: could we state that this BASE-SUB-PROCESS - absolute
movement against “physical vacuum” – be “responsible” for VARIATIONS of
measures of ALL high-level-processes “constructed” on this
“basis”?
My answer is YES. Different speed of
absolute movement COULD, in some conditions, INFLUENCE processes in
“inertial systems”.
A more interesting question
(to which I do not have answer yet) – is the absolute speed
influence ALL high-level processes or NOT? We now know that
“life-time” of some “elementary particle” depend on the (absolute)
SPEED of its movement. Indirectly this hints, that some internal
processes in UNSTABLE “elementary particles” go DIFFERENTLY when this
particle (interacting system of “vacancies”) is MOVING through
“vacuum” (“propagated inside discrete vacuum”, “transmitted between
nodes”, “reincarnated”).
The puzzle remains in
constructing DETAILED model of why such “propagation” add them MORE
STABILITY…
And we should keep in mind, that if some
particle ALREADY has HIGH SPEED – this means that it also had BIGGER
INTERNAL ENERGY. And thus as a SYSTEM it should have MORE “time” until
this energy “dissipate” (what is usually the reason of instability of some
systems). But this is already “alternative” explanation. Or, possibly,
just “other side” of INTERACTIONS with “vacuum” during
“propagation”.
But it happens NOT “thanks to
Einstein”, NOT because “…metric of space-time is changing at very fast
speeds…”.
Ok, we have tried to
find out which of the “base-sub-processes” could WORK
DIFFERENTLY in different LOCAL CONDITIONS. We “have found”, that “absolute
speed” could also be used as a “base-sub-process” – and thus with
DIFFERENT speed of the systems we should get DIFFERENT “local measures of
time”.
This only proves our main principle of
local causality of ALL high-level processes based on unified local
sub-processes. “Time” (in practical sense) is only ONE OF such
“high-level processes” (clocks, for example) which DEPENDS on the LOCAL
CONDITIONS in which base-sub-processes are going.
The
age (“personal biological clocks”) of one of the “Einstein twin-brothers”
– too…
And
what amazes me most is: how could Einstein get
the CORRECT result of his “imaginary
experiment”, NOT “knowing a damn” about how it was REALLY going? Was it just
a 50/50 chance – and he made a “good guess”? Or is there some hidden “deep
connection” between “Special
Relativity” and “Local Process-Causality”? :O)
We will try to find it
later…
But before, we will not
miss another chance to “give a kick” to Minkovsky and all his “math-brothers”.
In Minkovsky’s “metric spaces” there also
exist some “movements”. But this “math-movements” (parallel transfer and
rotation of “math-points”(?)) are completely “torn off” from ANY MATTER and
thus do NOT have any PHYSICAL ESSENCE (media) under it. So those “metric
spaces” do NOT have any BASE-SUB-PROCESSES under their “movements”. And
thus there could NOT exist any PHYSICAL CHANGES as “inescapable” source of
ANY REAL MOVEMENTS.
I understood that such
explanations would not convince mathematicians. But author have hope to
convince at least physicists.
For mathematiiancs I have
one “consolation”. Sometimes completely abstract MODELS could give
the SAME RESULT like in a real physical experiment. But this does NOT means that
in REALITY it all happens “exactly as in a
math-model”…
So now we will
spend some efforts to discuss relations between REAL process and its
“REFLECTION” (model).
I am purposely not writing:
a “math-reflection”, because the philosophical and physical version of this
term is much “wider”. For example, in human brain interesting
kind of “reflection” takes place. But there (in the brain) exist different levels of
“reflections” (“abstractions”). And this is certainly no place to
start discussing details of all levels of reflections :O). I have
mentioned the brain because for such systems the problem
(property) of “functional similarity” between the “world in reflection”
and “primary world” already aroused. Just because such reflecting-systems are so
complicated - it could have a “life of its own”. And sometimes this
“internal life” gives “nearly the same results” as the
“source-system”.
But this does NOT mean that the
INTERNAL STRUCTURE of the reflecting SYSTEM is “exactly the same” as that
of
the source-system. There exists only FUNCTIONAL SIMILARITY. And only
PARTIAL.
So
everyone who tried to convince us that
mathematics is “the same thing” as the REAL WORLD – made the same mistake as
the one who think that functional similarity means the STRUCTURAL
similarity.
Of course
it is often the case. Like in the
detailed model of a steam locomotive :O)
But in more
complicated models (reflections) the internal STRUCTURE of the model is often “simplified”… Or, sometimes, (like in
the human brain) it is
COMPLETELY DIFFERENT.
Of course it is “amazing” how
completely different structure - could give the SAME functional
results…
But the fact remains. Possibly “functional
similarity” also means some kind of system-structure similarity. Or, in
some sense, a “functional topology”…
But let
mathematicians play with such toys. Here we just state, that functional
similarity and physical-structure similarity – are NOT “the same thing”
sometimes.
I have another
consolation for mathematicians. It looks like some of the current “pure
math-abstractions” gives MUCH MORE REAL “functional results” than its
current “physical interpretations” (done on the wrong physical
assumptions). Most evident example is the Fourier-transformation.
It is declared, that with the Fourier-transformation you could extrapolate
nearly ANY function by the SUPERPOSITION of the finite number of sine-curves.
I am nearly sure, that the Fourier-transformation could NOT be just a
“math-trick”, but comes-out as REAL PHYSICAL PROCESSES-description. Meaning
that “in reality” it happens “the same way”.
If ALL
the “fundamental particles” are some “soliton-like” periodic PROCESSES –
then it is “evident” why could ANY real physical process be described
(modeled) as a reverse-Fourier-transformation?
Well,
at least we do have one useful “math-reflection” .
The second “useful”
math-reflection was “imaginary coordinates” or “imaginary
planes”.
But it is NOT so simple, as with the
Fourier-transformation.
Correct explanations of the
PHYSICAL meaning of “imaginary plane” are in attempts of some
“math-physics” to ADD DIMENSIONS(?) to some modeled processes and thus get
much more REAL results than those which he gets while using old
Newtonian ONE-modAl and CONTINUAL model of “field of continual
points”.
And it makes NO DIFFERENCE if we will use
Minkovsky-s “metric spaces”. REAL PROCESSES, real “movements” will ALWAYS
have MORE “dimensions” (independent PHYSICAL parameters), than any
abstraction of “metric spaces”.
Feeble attempts to
save “self-respect” of math-physic by madly adding “other dimensions of
(empty?) space” – will NOT solve it as a PHYSICAL
problem.
When someone insists that Newtonian-like math-physical
equations have “wonderful solution in spaces of MORE DIMENSIONS” – he “subconsciously” trying to “jump-out” of the PHYSICAL LIMITATIONS
imposed by the CONTINUAL-filed-of-points MODEL.
Most useless such Newtonian-like models
with “continual logic” of “infinitesimal variables” - are on the BORDERS
of MEASURE (in the philosophic sense).
Simply speaking,
“math-physicists” should NOT, like maniacs, continue to think about the electron
(for example) as a “DIMENSIONLESS MATH-POINT”, and try to use math-models with “mad-amount” of “other SPACE
dimensions” of “imaginary coordinates” for its PHYSICAL
description.
Is not it
more “sane” to say to yourself that the electron is STRUCTURED – and try to
create MULTI-MODAL DISCRETE models of its STRUCTURE with
SUB-STRUCTURE?
First step in correct direction was
done by Maxwell. But his equations where only TWO-MODAL (electricity and
magnetism) – but still based on Newtonian “continual field of points”. It
is not widely known, but Maxwell also tried to construct some PHYSICAL
model correspondents to his equations. But because of wrong “assumptions”
his physical model did not “worked”. Yes, it is not so easy as writing
equations…
In short, my
objections against using “imaginary planes” is – it is just “crutches” in
situations when the use of ONE-MODAL and Newtonian “fields of
infinitesimal points” INEVITABLY leads to complete PHYSICAL DEAD
END.
Einstein found nearly
the same (as “imaginable planes”) “way out” of the Newtonian “dead end”. He
“simply” declared that “space-time” was “curved”. Never mind that this “way
out” was NOT MATERIALISTIC. Einstein ignored such “rubbish”. But special
“insult” (from my point) was fact, that the man who
considered himself a PHYSICIST
– had NOT even tried to offer ANY PHYSICAL MODEL for his MATH-equations…
Maxwell at least tried… Nils Bohr too…
But the
“humor” of situation is that (as I hinted above), applying his
“deformation of space-time” he did a kind of “math-reflection” of
Newtonian-like description of ANY processes – to some OTHER FUNCTIONAL
MODEL, which allowed him to give MORE REAL RESULTS (!) than by “classic”
model.
I am sure that this
FUNCTIONAL RESEMBLANCE of Einstein’s “curved spaces” to REAL PROCESSES –
does NOT mean that REALITY is “made the same way” as Einstein’s “curved
space-time”…
I have already given examples that some
“reflecting systems” (brain) produce NEARLY THE SAME functional result as
DIFFERENTLY constructed
SYSTEMS.
So, the first “step
to reality” will be in attempt to “throw-out the crutches” of “imaginary
planes”.
Any model which does not “work” without
“imaginary planes” should be changed so that ADDITIONAL “degree of
freedom” is added there NOT by “additional dimension of the imaginary
coordinate” – but as additional “dimension” of PHYSICAL “coordinate”
(parameter of PROCESSES).
And there are TWO ways of
doing it.
Maxwell-like adding of MODALITY (new
quality of processes).
Or “discretization” of BORDERS
of sub-elements and as a result GOING TO STRUCTURAL SUB-LEVEL of modeling.
For example, when modeling flows of liquid through some channels it is enough to
think about water as “continuum of size-less points”. But for the model
of “super-sound” processes we should go to the structural sub-level and make
model of “media of discrete points with gaps”.
If
someone has read Gerlovin’s book about “hierarchy of spaces” – I could
give hints about how his ideas could be “returned back to the ground”. Each
time he is talking about adding new “space-dimension” – we should think about
adding new description and functionality to a MORE FUNDAMENTAL STRUCTURAL
SUB-LEVEL…
Now about the
meaning of some other “math-tricks”.
It has become “fashionable”
in modern
“math-physical researches” to seek an additional
“physical sense” in “higher-dimensional spaces”. First, they take
some well-known physical dependencies (from nuclear physics mostly) – and
“reflect” it on the “space of MORE dimensions”. Next they are trying to find some “topological analog” for this “reflection”, like “ellipsoid in
n-dimensional space” or “group of
automorphisms”.
When they think that they “have
found” some “topological analog” – they are trying to make some
“conclusions” about SOURCE (real physical)
dependencies.
Most of the “result conclusions” are so
TRIVIAL, that any self-respecting PHYSICIST could make them WITHOUT all that
“math-madness”. Mostly it is something like: “…this group of elementary
particles should be the part of some wider multiplet…”.
And the “procedure” itself reminds me of
attempts to understand what the man is thinking now – trying to
“attentively inspect” the configuration of his dynamic encephalogram
(external electric potentials of the human brain). I am strongly convinced (I
have made such brain researches myself), that without REAL
understanding of FUNCTIONING, model of SYSTEM STRUCTURE, knowing of
structural ELEMENTS (sub-structure), knowledge of “internal links and
loops” – such “external inspection” of such COMPLICATED STRUCTURES is
USELESS…
Ok, you could certainly “inspect” something
by the method of a “black box”. And when we have REAL subject to which we
could really apply “input values” and measure “output values” – it is
the correct method of getting PRIMARILY propositions about the INTERNAL
STRUCTURE. But without attempts to understand this internal structure – we
will never get none of the “internal qualities” of that “black
box”.
In the case when we “inspect” NOT the REAL
“black box”, but try to get some IMAGINARY “outputs” from IMAGINARY
“black box” (something about we do not know a damn) – it does not looks
like a “good method of research” of REAL
STRUCTURE.
But again, it is not such a simple
case.
I have already shown examples when the “reflection
of reflection” could give a CORRECT RESULT (!).
The
problem is that we should NOT think that this way we have found out “how it
REALLY works”…
Since it is already “evident”
that “double reflections” (and sometimes even the “single reflection”) could
ADD NEW PROPERTIES to the reflected math-model, which (new property)
have ONLY reflection itself, but NOT the “source”.
I
call it the “extension of reality in its reflection”, when talking about
reflections of REALITY. But some kind of “extensions” is added to the
reflected MATH-MODELS too! And this is, possibly, the reason why the
“jokes” like the “case of Einstein” are possible at all. And, by the way,
“the case” with our possibility to “understand” and GET CORRECT RESULTS
with something like our brains
:O)
So, I hope, I have
explained why most of the “math-physicist” think that ANYTHING they could
“imagine” – is the “reality itself”. And only “stupid materialists” just
could not create something like a “time-machine” to “happily prove” their
“math-models”.
Yes, I know that in theirs nightmares
they see how they return to REALITY. But when he wake up, some
other “pure mathematician” call him and propose “another interesting method
of reflection” – and reality is forgot until the next
nightmare…
Lets try to make it
“clear” about “General Relativity” (GR) again. I think I have “proofs” that
a “reflection with adding dimension” was made in
GR. Then attempts were made to
get some properties of the “source”, using the method of “topological
analogy”. This is the most “mystic” part of the “story”, because I still
could not understand HOW the CORRECT (mostly) results were received by such
“method”. Possibly I am “overestimating” the rate of “convincing-ness” of
GR-equations and the “conclusions” were really made “from the ceiling”? I
have to re-read it (GR) again…
But the most convincing
(for me) argument, that GR is a “double reflection with adding
properties” – is its (GR) conclusion that INERTIA is something
“immaterial”, explained just by the “geometry of (blank)
space-time”.
I have just the
opposite conviction. INERTIA is the manifestation of INTERACTIONS on the BASE-LEVEL of
hierarchy of PROCESSES. Probably, on the level of interactions
between “elementary particles” and “physical vacuum”. As it happens to “spin-networks” of Yang-Mills.
Only on that
structural level we could explain “equivalence” between “inert” and
“gravitational” masses – by the SAME physical STRUCTURE of INTERACTIONS in
BOTH cases.
The only difference in the “structure of
interactions” in both cases I see in the fact, that “inert-interaction” is
“external force” applied around the “borders” of interacted “enigmas”
(sub-structure of “bodies”) – while “gravitational interaction” is
“internal force” applied to the whole structure at once. And thus the
difference in the “picture” of gravi and inert interactions should be only
in the resulted DEFORMATION of “body” in INERT-interaction. So both values are
really “equivalent” ONLY for the “material POINT” abstraction. For real
“bodies” the difference is
“visible”.
To explain more
general meaning of INERTIA we should possibly remind
ourselves of Newton’s
“Perseverare in statu quo” (the persistence in resisting to attempts to
change the current state). Meaning that MATERIAL body not only “passively”
keeps its parameters – but also “resists” to chang them (whatever Newton
meant under “resistance”).
More simple explanation
of INERTIA I see in the STRUCTURAL approach to ANY
INTERACTIONS.
As you know, Newton formulated
his three “rules” ONLY to the STRUCTURE-LESS “material
points”.
So, with such approach, inertia was
something “unexplainable” or even “mystic” to
him.
But if we
suppose that ANY
“material part of ANYTHING” SHOULD HAVE some STRUCTURE – then
INERTIA becomes evident PROCESS of PROPAGATION of CHANGES through
this SYSTEM.
At any “frozen” state of system
there is a PART of the system in which the CHANGES have already HAPPENED – and
the OTHER PART, to which those changes have NOT been TRANSFERRED
YET.
If we are talking about changes in SPEED of
ELEMENTS of system (what Newton’s laws is about) – this looks like some
PART of the “body” has already started moving – but some distant part
still has the OLD SPEED, and thus is trying to “resist changes”
:O)
So, it looks like Newton’s attempt to deal ONLY
with “unstructured points” – give us very “simplified” version of
Newton’s first
“law” (“law of inertial motion”). Though it would be better to state
that: INERTIA is a property of ANY SYSTEM – Newton formulated the
“limit-case of the second law” (while we do NOT have “force” – we could NOT
change the speed of the element). For this we should NOT add a SEPARATE
“law”.
I
only wanted to explain the correct meaning of INERTIA as a property of
STRETCHED SYSTEM – and thus IMPOSSIBILITY to explain inertia as a
“property of POINT”! Especially as “point of space-time”
:O)
Leibnitz described the inertial mass as a
“quantitative measure of the MATTER or substance of the selected
system”.
Possibly it is “more convenient” to evaluate
the “amount of matter” of some system by the “curvature of space-time” in
the same locality? You know how to organize its (“curvature”) MEASUREMENT?
Especially when this “space” is IMMATERIAL…
We
could find nearly
the same line of objections in the book by our (Russian)
philosopher B.G. Kuznetsov:
"Mass
gives the body his DIFFERENCE from the PLACE or SPACE or BLANKNESS. Mass
is a MEASURE of MATERIAL EXISTENCE (different from geometric properties).
Mass (and its structure) allows us to DISTINCT the body from “media”,
allows to make the body “individual” … ensure its self-identity. If the
MASS ensures the (external) INTERACTIONS, then it COULD NOT be the
property of SINGLE BODY (or “mass-point”). Mass gives meaning not only to
the
“position in space” but even to the EXISTENCE (interactions) of the "body", which,
in such interpretation, could ONLY be the material STRUCTURE (but NOT a
"dimensionless point" of "blank space")…”
And thus we could NOT “assign” INERTIA to be the
“geometric property of space” – without applying to that “space” the
MATERIAL PROPERTIES and the capability to INTERACT with
“bodies”.
So, the “space-time” of GR – is exactly
this DISCRETE and STRUCTURAL “physical vacuum”…
ONLY this “way” we could try to seek any PHYSICAL meaning of this
“reflection”.
--------------------------------------------------------------------------------------
CONCLUSION
Those
who had
enough patience to reach this place in the text, possibly want me to give
recommendations about “returning back to reality from all those
reflections”…
Ok, try to look trough the above text and find
the words about:
- principle of local causality;
- principle of local `time` as a measure of
changes, evaluated by local base sub-processes
.
I am not sure in
which math-forms this “principles” will be formulated in the nearest future
(not only by me).
It will be more clear in a few
years from now (2006).
It could be some variants of
the formalisms of “Lattice functions”.
And, of course,
the Yang-Mills theory of “spin-network space” could get some “extended”
versions (provided
by Rovelli, possibly).
Looks like I
had “proved”, that some kind of “double-reflections” will still be
“tested”. And valued as a "big step to understanding reality" :O) (some
other versions of "strings" or "branas").
And other
kinds of “reflections” - Fourier-reflection, or Laplace-reflection, or some
kind of “discrete-reflection” - will still be “fruitful abstractions”,
even as physical models of some real processes.
And
of course for me, as a specialist in computer-modeling (simulating) the
most “natural” way of developments lies in “functional
models” based on the paradigm of “cell-automata”.
But
for a real advancement in this direction we should first prove to all
“math-physicists” that the model can “work” (give correct results) even if
we do NOT know ALL Newtonian-like-equations of
it…
The “catastrophe” for them (in such approach) will
be the impossibility (to them) to apply ANY “properties” to the computer-model. While “pure math” allows this, computer-models will NOT
“work” with the assumptions, that do not fit in the STRUCTURE of a
modeled SYSTEM… Well, it does NOT mean that ALL computer-models will
always be "reality itself"...
---------------------
Valeriy V. Pimenov.
December
2006.
Moscow,
ROSCOSMOS.
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