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Hi all, I'm glad that I came to this forum
Dr. E wrote: "Finally we have been liberated from frozen time and the block universe, with a simple postulate and equation..."
This is not very reasonable. The block universe is a deductive consequence of Einstein's 1905 constant-speed-of-light postulate: if you don't like the consequence, logic says you should replace the premise. Banesh Hoffmann gives you a clue:
http://www.amazon.com/Relativity-Its-Roots-Banesh-Hoffmann/dp/0486406768
"Relativity and Its Roots" By Banesh Hoffmann
"Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether."
Pentcho Valev pvalev@yahoo.com
Dr. Barbour, I can accept your idea that time is an illusion, but surely you must accept the possibility that all external reality is an illusion. A human being with normal intelligence and an active mind but with no access to the external world via the famous five senses would have no way of knowing, much less proving the reality of the external world. Such an unfortunate individual would only know that he thinks (a la Descartes).
You may respond that all of us, indeed most of us do in fact have the 5 transducers that pass along signals from the external world into our brains so that we can know of its existence. However, we are removed from immediate experience of the hypothetical external reality by the, dare I call it time it takes the signals to move from the sense organs to the brain to be perceived.
How can we know that the signals our 5 senses relay to our brains are from a physical reality at all. Perhaps, as conjectured by Bishop Berkeley there is no proof that an independent external world exists. Rather something, call it a spiritual reality or advanced aliens from somewhere else, something transmits the signals we receive through our onboard transducers giving us the impression there is an external physical reality.
How can we know such a reality is real? How can we trust our senses on faith that they are reporting the true reality? Perhaps time is not real as our senses tell us it is; but matter may not be real as well; the forces of electromagnetism, gravity, strong, and weak that we have "observed" may not be real either.
80 nanoseconds of "time" separates our mental selves from any immediate awareness of external reality. Our consciousness seems to be suspended in "time" in a sense, floating through a reality that we have no trustworthy resources for defining scientifically; rather, we merely believe on sensorial faith that it exists.
As long as I must assume that there is a physical reality, I may as well go the whole distance and assume that their is an independent feature within it that we refer to as time.
Please help me understand how my thinking may be incorrect.
Dear Julian,
As with your recent talk at the Perimeter Institute on the same subject, I enjoyed your essay. I also very much agree with you that duration/interval does not exist and is merely an out-flow of motion. I have a question though. Do you still believe that instants and instantaneous magnitudes exist? If you perhaps do, and I get the impression from reading your essay that this is the case, I think that your view about time has some issues. Firstly, as they would constitute the building blocks of time, if one assumes the existence of instants (and instantaneous magnitudes), one also necessarily assumes the existence of time. Secondly, to deny the existence of interval, and yet hold onto instants, is not consistent, as, by definition, an interval is simply a duration bounded by two instants; as long as the instants are still there, the interval will be too. Indeed, if such instants existed, it can be shown that they would render change, motion, and as such, the idea of a clock, impossible.
Best wishes
http://www.taylorgolfclubs.com
Connections
The binding of existence
This is a story, built upon knowledge, intuition, and speculation. In the end, it is built upon some known theoretically successfully tested truths, and some unknowns conveyed in a formula that I consider trumps any objections - as we ponder the scope of existence. First we know of existence, by way of our self-awareness, coupled with scientific knowledge. Second by way of the unknowns i.e., "Infinity", that must incongruously play with us (self-aware-finite creatures), in some connected manner.
This Second irascibly indefinable thing called "Infinity", simply stumps our "finite" minds every time, when we attempt to figure out its mathematical infinities. As it must. As if it did not stump our efforts to understand it, it would become defined, and anything defined, is "Finite.". So we have an absolute conundrum that operates our existence. But we are still connected, in a union, both finite and infinite, through the known attributes we have scientifically tested to be true. As without "Infinity", there can be no "Finite." And remember Infinity, has no bounds, no time, no space, no beginning and no end.
This is plainly contrary to finite logic, but Infinity simply is contrary. Always has been. And always will be. But it is also the very milk of our very finite existences... We are Connected... Our actions matter, as I will soon explain - in summary.
INFINITY: Irascible and fundamentally a necessary fickle fact. An argument that no mathematics or thought equation can defend against... To challenge this premise is to supersede infinity's very nature. It will never ever happen.
Therefore we are circumscribed to live within, the physics - largely of Newtonian and Einstein's mathematics. I would caution to note: that these finite mathematics are subject to change that currently work fairly well for our finite existence as we mathematically calculate how to penetrate and maneuver the Stars, or add 2 plus 2 to equal 4. But they do not work to unravel Quantum Mechanics (in total), and the cache of oddities, such as "Superposition's", whereby subatomic particles are in several places at one time, until they are interrupted by measurement. Or do these current finite mathematics explain "Entanglement", which allows for two subatomic elements to be millions of miles apart, however if one changes its state of "spin" or "electrical" charge the other particle millions of miles away responds instantly. Yes, this violates the concept of the speed of light as the fasted method of action in the Universe.
As Einstein called "Entanglement" Spooky, but none the less real. This seemingly violates the speed of light. But hold on, the Speed of Light travels, Entanglement implies "Connection". Or what is known as Local action.
Space is the key to this thought equation. Since space is "Infinite" to the "Finite" Observer. Space in this context is also in union with waves - as well as particles. However waves may connect all things instantly, just as waves may allow for "Superposition's."
The answer is simply that: This makes us both Local and Non-Local at the same time. Waves and or theoretical "Strings" perhaps in some union - connect our space and possibly time in ways we do not fully comprehend. If true, our infinite extended connections are observed from a finite realm only. It might be important to note here: That simply no distance is allowed in an Infinite realm, as infinity is immune to classification, therefore it is all things and no things at the same time. Make sense? It usually should not, as finite logic has a difficult time with this both intuitively and implicitly mathematically. Make sense yet?
Probably not, as this means that "Everything is Nothing and Nothing is Everything." Hence there are no real "infinites" to calculate in an Infinite realm. But this last statement is a clear oxymoron, as it should be, as infinity does not have mathematics or anything defined based in or of it. As this would imply a finite realm. It is simply infinite, and does not apply to our finite realm of mathematics.
Mathematics is purely the purview of the finite.
When I said there are really no infinities in the infinite realm. I meant it. But to us, within the finite realm or finite conscious state, as observers, Infinities are what - infinity, space and time are made of. Once again, the ultimate and infinite conundrum. However, how does this allow for the stuff of existence, such as "us", or cars, and trees and so on to exist? Well we do need infinity to have a finite realm, as I said.
That is the puzzle? That must never be answered technically, nor can it, again from a finite perspective or finite observer. This mind trap we are caught in trying to view infinity - would seem to drive one mad to think that Infinity, Space and Time have no beginning or an end.
But get use to it.
Infinity is indelible. Terms like "time" and "space" are non-words to describe Infinity correctly, as Infinity never had a beginning or an end. The space and time word terms we use within the realm of Infinities definition, or lack thereof, could not and do not exist. Unlike the finite world, which has an Alpha and Omega. (Dust to Dust, Evolution, and Space to move to, and a length of Time that life gives us to observe.
And - That is that...
We are here by way of connections of an indefinable Infinity, which has always been, and will always be. Make no mistake about it. This will provide us and others forever to give sentiency a journey to discover anew. New science from physics to health, coupled with new modes of life, new cultures to come. Save an Asteroid impacting the Earth, or a Super-Volcano taking us to our end of time as sentient beings. But others will arise, no doubt by way of times finite arrow.
The finite with a beginning and end is necessary, to find hope. Just imagine living for eternity without end. That proposition, would invoke a person to lose goals, have no new hopes, and actually impart a crazy madness of hopelessness. As you would be in the ultimate Trap, or Jail forever, if self-aware. What would be the point? One would ask themselves... And therefore, Life and Death, are necessary.
Dust to Dust and then perhaps? Take your best shot at a faithful guess! The options are many, the realities may be few. No one really knows. No one...
Plainly beyond us, the Infinite and Finite will ebb and flow, and new existences will arise through an endless connection to everything for all time...
Essential Points:
1. The Science is: That Infinity is incomprehensible to any complete understanding and, the Finite is limited to understanding all things, perhaps itself and certainly infinity. The connection between the finite and the infinite operate as if Everything is Nothing and Nothing is Everything... Have fun with that analogy! As for me, it holds true, as it confirms to me that cognitive logic eventually meets the illogic of Infinity. This lets us clearly know we will never actually know honestly and truthfully the great questions of life: As to know "ALL" or "Truth" would be to actually define a place and a time, which can only be finite. And that would defy the rules of Infinity, which cannot be technically ever defined. Otherwise it is no longer infinite; it would then become as a mere canvas with parameters. And Infinity is incomprehensible. End of Story - Yesterday, Today and Tomorrow... In other words Forever!
2. The Moral is: That Legacies matter. Build a good one. The Butterfly Effect is always on... And that is what really matters.
All the best in our journey's, Russ Otter
Dear All,
There is no space unless one chooses to measure and there is no time until one chooses to count. Time is the space between all of us in relative duality and there is "absolutely" no space-time but singularity or the conscience or universal i.
Conscience is the cosmological constant.
The absolute mathematical truth of singularity or universal i can be deduced as follows as well.
If 0 x 0 = 0 is true, then 0 / 0 = 0 is also true
If 0 x 1 = 0 is true, then 0 / 0 = 1 is also true
If 0 x 2 = 0 is true, then 0 / 0 = 2 is also true
If 0 x i = 0 is true, then 0 / 0 = i is also true
If 0 x ~ = 0 is true, then 0 / 0 = ~ is also true
It seems that mathematics, the universal language, is also pointing to the absolute truth that 0 = 1 = 2 = i = ~ (zero = i = infinity), where "i" can be any thing from zero to infinity. We have been looking at only first half of the if true statements in the relative world. As we can see it is not complete with out the then true statements whic are equally true. As all numbers are equal mathematically, so is all creation equal "absolutely".
Love,
Sridattadev.
Dear all,
it has come to my mind that time infact is a quantity in a noncontinuous space or there is no time at all.
Stretching of space in this view means only ther is more and more time between two discontinuous points of space, which applies: there is more and more time in universe, and that makes sense and also complyes with the arrow of time.
Space travel accours (for particles) as discrete jumps from position 1 to position 2,... the positions themselves are drifting apart from each other, but not space, bur time is the added quantity between them.
Best
W
TIME THEORY OF EVERYTHING
Created and Written by KHALID MASOOD
TIME COSMOLOGY: Time to re-study Time.
TIME THEORY OF EVERYTHING is The Time Universe Theory.
At the heart of physical science is physics, and at the heart of physics is TIME.
I propose, only Time exists in the Universe.
Time Creates Space, Life, Consciousness, and the Universe itself.
Time tells matter how to create, matter tells time how to survive!
No particles, no waves, not both and no vibrating or dancing strings. Only "FLUCTUATING EXTREME LEVELS OF ENERGY" write Everything of the Universe, including our consciousness and also Theory of Everything!!!
The only truth about the physical universe is that the universe is not physical. Life and matter of the universe, is nothing but a physical illusion.
The smartest phenomenon of the universe is the universe itself.
On the whole universe is shapeless, massless and weightless.I CAN PICK IT UP!!!
Einsteins second law, m = E/ c^2 i.e. m = E/ c2 [ How mass drives from
pure Energy] raises the question whether mass can be understood more deeply
as energy. And can we build, as Wheeler put it, "Mass Without Mass"? are the
best predictions in favour of my "Time Theory of Everything."
In my view the first question is How pure energy drives from time?. The
universe is not what it used to be, nor what it appears to be, as Frank W
ilczek of MIT quoted in first chapter Getting to it of his book titled "The
Lightness of Being" [ mass, ether, and the unification of forces ] also
supports my theory. Infinity is finity on the whole.
There is nothing original under the physical phenomena. All physical
properties of the universe are secondary in nature.There is a universe behind
the physical universe which is dark and primary universe. If a Theory of
Everything is Holy Grail of cosmology, Time Theory of Everything is Holy
Grail of Modern Physics!
Physicists are hunting for an elusive particle that would reveal the presence
of a new kind of field that permeates all of reality. Finding that Higgs
field will give us a more complete understanding about how the elusive
universe works!
I believe in bold imagination in research. I believe the universe is not acadamic,
and is not bound by our physical theories. Capture Higgs particle, eyes on a
prize particle, the search for the Higgs boson [God Particle] and creation
of micro black holes is nonsense idea.
Higgs boson is not destiny. We have to re-study TIME and ETERNITY. Higgs boson should be named TIME (particle)!
Basic and primary stuff of the universe is not physical. All matter, energy,
and fundamental forces of nature are secondary and referred by a unified
primary force of nature. There is a co-ordination force in between God
and all secondary forces of nature, which is more important than Higgs boson.
I suggest this force is TIME. Time is invisible presence and the only basic
building block of the universe and everything in it.
Time is so central to the state of physics today, so crucial to our final
understanding of the structure of matter, yet so elusive,
that I have given it a nickname: 'The God Force'!
Time is at the very heart of physical discovery from the nature of matter
to the origin of the universe.
It is also a fundamental driver of everything in the universe many of
tomorrows discoveries and technologies will emerge from Time physics.
MOTHER OF ALL FUNDAMENTAL FORCES.
[A union of forces and time]
Time is mother of all fundamental forces.
"Forces-time" in which time exists as fifth force with four fundamental
forces.
Deep down, the particles and forces of the universe are a manifestation of
time.
TIME is a coordination force of the universe and multiverse referred by
nature.
Nothing has independent existence except time.
Password of time is in the Mind of God!
Tell me about the nature of time, I will create the Universe!!!
If all cosmologists of the world say a foolish thing it is still a foolish
thing!
I WILL CHANGE THE HISTORY OF TIME !
God does not play particles' game with the Universe.
Spacetime has no Time Dimension.
The theory of time "t" as a fourth dimension of space, three dimensions of space and one dimension of time is wrong.
All dimensions of space are time's dimensions. Time is not the 4th dimension.
Space is not 3D T, space is 3TD. Time is the distance between two dimensions.
Time is the longest and shortest distance between two dimensions.
Time is mother of all dimensions. Dimensions are the result of time.
TIME IS NOT A MANUFACTURED QUANTITY. Time has independent existence and
is fundamental. Space is a manufactured quantity and secondary form of time.
Space is only a kind of time.
I believe in infinite extra spatial dimensions of time only, and I know what
these dimensions are, but I don't believe time as extra dimension with space.
I dont believe in extra dimensions of space, I believe in extra dimensions
of time. The universe exists in three or 10 dimensions of time.
[as string theory proposed, 10 of space and one of time dimension] There
isnt just one dimension of time, says Itzhak Bars of the University of
Southern California in Los Angeles.There are two. One whole dimension has
until now gone entirely unnoticed by us. Two time / 2T Physics [New
scientist 13 October 2007, Hypertime, Cover story] Why we need two dimensions
of time? Why not we need 11 and many more dimensions of time?
A NEW HYPOTHESIS:
[EXTREME LEVEL COSMOLOGY]
EXTREME LEVEL THEORY:
The study of the theory that all fundamental particles and vibrating one-
dimensional strings are fluctuations of zero-dimensional and unidimensional
Extreme Levels Of Energy.
Extreme Level Fluctuations create the universe.
No-particle proposal:
Elemental building blocks of Nature are not particles.
I dont believe particles in any shape or dimensions as basic building blocks
of matter, energy, and everything in the universe. I have an alternative
Fluctuating Extreme Levels hypothesis which is a part of my Time Theory of
Everything [Extreme Level Theory] Extreme Level Theory suggests that basic
building blocks of everything in the universe are composed of Fluctuating
Extreme Levels of energy. In Extreme Level Theory of time, Extreme Levels
correspond to different entities and quantities. If Extreme Level Theory
proves correct, photons, electrons and neutrinos are different due to changes
in the fluctuations of extreme levels. Prior to Extreme Level Theory,
subatomic particles were envisioned as tiny balls or points of energy.
Extreme Level Theory works on the premise that the tiniest subatomic bits
that make up the elements of atoms actually behave like Fluctuating Extreme
Levels and not like vibrating or dancing strings. Photon is no more now a particle, a wave, or has features of both.
Photon exist at fluctuating extreme level of energy.
About the "Origin of Mass"
For decades, the prevailing view in physics agrees that the Higgs field gives mass to matter, with the mediated by a boson particle called Higgs.
But no one has seen the Higgs boson yet, despite the considerable time and money spent in his quest to particle accelerators.
Time Field:
The mass comes from the interaction of matter with the "Time Field" or "field Time" and not from field Higgs. There is no Higgs field.
Time field is "zero point field" and zero energy state of time-space.
Time field is the lowest energy [zero-energy] state of time. That is extreme level of time in my T.T.O.E.
TIME THEORY OF GRAVITY
TIME GRAVITY
I believe in my 'physical' motto: "Time tells space how to create, space
tells time how to expand and bend."
Deep down, the particles and forces of the universe are a manifestation of
time.
Time is the distance between two places.
Time is the longest and shortest distance between two places.
Gravity is a manifestation of Time-space.
P.S: It's Time-space and not space-Time. TIME COMES FIRST.
Our entire research focus must be on "How time interact with matter and
energy?" and "Time, matter and energy, how they interact with each other?"
Time can take the form of motion, light, electricity, radiation, GRAVITY.....
just about anything honestly.
Time theory of gravity is the best rival of General Theory of Relativity and
Quantum Loop Gravity.
TIME THEORY OF EVERYTHING will change the phenomena of new physics-extra dimensions, entanglement, entropy and information, black holes, tunneling, Bose-Einstein Condensates, chaos and complexity, dark matter, dark energy and meaning of Matter, Energy, Natural Forces, Consciousness, Life & Extraterrestrial Life and Death.
It's not time, it's matter which is disappearing from the universe.
Time is God, God Time.
THE UNIVERSE IS A TIME MACHINE!!!
God can't exists outside of Time. Nothing exists outside of Time.
I am part of the universe, as my heart is part of me. Therefore I am part of God.
Khalid Masood
khalidcustoms@gmail.com
Finally I can make some sense of Einstein's theories, knowing that a great deal of the problems do not sprout from my weak mind, but rather a flaw in underlying assumptions. I am a physicist by any means, but I do excel at logic puzzles- and I have been playing with this one for a while. After picking up an article by Mr Barbour, and thinking for some time that Einstein had to be wrong about his assumptions on distance, time, or both, I am finally getting some relief. I agree with Mr. Barbour that we should take Mach's theories to the next level, knowing that Einstein got almost got us to the finish line, and hold everything relative. In that kind of universe, time has to go!
What I want to know, is what does the size and expanse of the universe look like after removing time? I would tend to think that our current measurements of the expanse of space, along with our calculations of age both for the universe and the Earth, have to be thrown out. If that is the case, doesn't the universe get a lot smaller, and become a place that we cannot think of in terms of "how many miles to cross" or even in travel time. Also, doesn't this approach solve the issue of locality and move us vastly closer to a unified theory? If so, why has it taken so long to gain wide acceptance, I mean I am just a normal guy and I found profound and obvious logical error in current and accepted equations? I can understand making an assumption, or hypothesis, and then trying to prove it. But at some point someone had to say, wait, we have made fully 19 assumptions on which to build the current model, when do we say that we won't likely resolve them via observation, and maybe, just maybe, some of them are wrong and won't ever be proven.
Sorry to ramble, but it's exciting to find that I wasn't so crazy. And forgive me if I made some incorrect or very elementary mistakes. Again, I am just very good at logical puzzles, and no scientists, not even much of a math guy, but as I understand it, Physics is more about balance, and logic. So thank for any input you can provide.
Dear Julian,
Your fundamental paper is erudite, insightful and beautifully written. However, there is a key point that I find unconvincing. You derive equation (3) in order to show that time is not an absolute but depends on other basic quantities, each of which is independent of time. It seems to me that using the same logic one could argue that E = mc2 shows that energy is a superfluous concept reducible to mass, or vice versa. Such examples can be multiplied, each purporting to show that a fundamental concept can be dispensed with by means of a set of other fundamental concepts, depending on the particular equation and which concept is chosen for elimination.
Thus your equation could be reformulated to dispense with mass or distance, just as easily as time. An equation of physics is merely a conversion factor, it does not allow us to define one concept in terms of another.
Best regards
Tad Boniecki
Hi Julian.
In Nov 2011 last year I wrote a notes in my book note about my perspective about time which is already in my mind months before. And right now i'm surprised after reading your ides in the internet that your idea that the time is just an illusion, is the same idea as mine.
I'm so excited since i'm not a physicists.
I was thinking that what we call "TIME" since human being exist on the planet is just our perspective about "CHANGE" from the motion of heavenly body to the atomic particle we see right now.
That is why according to Einstein, the "time" OR "change" on the space around stronger gravity is "SLOWER" than around the "WEAKER" gravity.
["SLOWER" means comparing to our daily perspective of "TIME"]. Because the TIME is change itself, and change request space or degree of freedom, until the center of the black hole, when the singularity creates, our conventional perspective about "TIME" should be stopped, or even transformed or should be redefined into another manifestations.
To avoid repetition, I selected Amrit's Dec 28,2008 @ 15:25 GMT comments because they are identical to my belief.
I also have these comments:
The first obstacle for an observer to overcome is the tendency to project and mistake abstractions of thought to be physically part of the observed.
The laws and mathematical models of physics and the concept of time evolved in the minds of observers and are part of our understanding of physical reality but not a physical part of it.
Time is a mental construct that an observer must have to understand a real physical item of focus because that item is always in relative motion to every other physical thing.
Time has the purpose of helping us understand relative motion and all of the changes that result. The physical reality of the universe has no purpose. It simply exists and has always existed in one form or another.
All that is physically real including space is a form of energy.
How they change form is for physicists to figure out.
Time as a Derived Physical Quantity
Consider a physical system whose state changes and let us call it a Dynamical System.
Let a closed Dynamical System, S, whose state be described by a state function, П€. П€ can take on the following specific states: П€1,.. П€2,.. П€i,..П€j,..П€k,... where i, j, k,.. are positive integers. Then one can define Time increment (Time or duration), Оґt, as follows:
Suppose S initially takes up the state П€i, and then it changes to П€j (written as П€i в†' П€j), then a certain time increment, Оґt, is said to have elapsed; where Оґt = 0 if i = j, and Оґt в‰ 0 if i в‰ j.
A Time increment defined in this way is therefore a Derived Physical Quantity, and
1) If S does not exist, then Time, Оґt, does not exist.
2) Time is quantized if the states П€i, П€j,... etc are discrete.
3) If П€ changes in the sequence "П€i в†' П€j в†' П€k", then the 2 "Оґt's" (associated with the 2 "в†'") are perceived as being equal in magnitude since, in reality, only П€i, П€j and П€k, but not something in-between, that are observable. It is therefore meaningless to say that the "in-betweens" can be of different magnitudes. But we are quite sure that the "in-betweens", the "Оґt's", do exist because their end-points exist.
4) If П€ changes in sequence given by "П€i в†' П€k в†' П€j", where i, j and k all have different values, then the 2 "Оґt's" are taken as having the same sign (direction). This follows naturally from the way "Оґt" is defined above since the 2 "Оґt's" are defined in exactly the same manner, if one has a positive (or negative) sign, so does the other.
Following the above, if П€ changes in sequence given by "П€i в†' П€k в†' П€j в†' П€i", we should perceive S having returned to its previous state of П€i, instead of perceiving as Time having gone backwards. Time, therefore, is unidirectional.
Recall the Definition: A Dynamical System is a Physical System whose state changes. Nevertheless, we still want to ask the question: Why does it change? Why is it not non-changing and stay the same always?
The fact that it changes allows us to postulate the existence for some physical agent О', which when acts on S at П€i, makes possible of the appearance of S at П€j, and accompanying such a change, there is an elapse of time Оґt-- By definition.
Hence, О' : SП€i в†' SП€j where i в‰ j--------------- [S1]
Now, S denotes the Dynamical System, П€ is a mathematical entity we use to describe S (or the state of S), i, j, k,... etc are labels we attach to П€ in order to distinguish the different states of S.
From statement [S1], it is reasonable to assume the existence of a corresponding mathematical operator Г‚, of A, such that
Г‚П€i = П€j--------------------------------- [E1]
This is merely rewriting statement S1 in equation form.
After acting on S at П€i, A persists-- There is no reason why it should vanish suddenly in a close system-- and continues to act on S at П€j. Hence we have
О' : SП€j в†' SП€k where j в‰ k--------------- [S2]
О' : SП€k в†'SП€l where k в‰ l--------------- [S3]
О' : SП€l в†'SП€m where l в‰ m------------- [S4]
and so on.
From these we can get
Г‚П€j = П€k--------------------------------- [E2]
Г‚П€k = П€l--------------------------------- [E3]
Г‚П€l = П€m ------------------------------- [E4]
and so on.
Given the set of equations [E1], [E2], [E3],..., can we say anything about Г‚П€?
Is it correct to say that Г‚П€ = aП€, where "a" is a function independent of П€?
Let в„ќ be the set {П€1, П€2,... П€i,...П€j,...П€k,....}
в„ќ = (All possible П€'s}
So, Г‚ maps each П€ of в„ќ into another П€ of в„ќ and, by inspection, it looks plausible that the Г‚П€ = aП€ is a solution to the set of equations {E1], {E2], ...
I cannot give a rigorous mathematical proof that this is so but maybe a more concrete example could show that this is highly plausible:
Let в„‚ be a set of all boys in a class
в„‚ = {All b's in a class), where b = boy
Specifically, the boys are Stephen, John, Martin, Robert, Ian, Phillip,...
Therefore,
в„‚ = {s, j, m, r, i, p,.... }
Now, T is the teacher who is directing the boys to play a game of passing on a relay-stick. When one particular boy gets the stick, the teacher decides to whom it should be handed to according to a set of rules the teacher has in his head.
We do not yet know what that set of rules is but we can note down how the relay-stick is passed along among the boys. For example, initially Martin is holding the stick and the teacher instructs him to pass it to Stephen. So,
Tm = s
And then the teacher instruct Stephen to pass it to Phillip and so on...
Ts = p
Tp = r
Tr = j
and so on.
From the above, what can we say about "Tb"? We know that it has to be a "b" (boy) but there are constraints. The only way to make an consistent equation is to have
Tb = (attachment)b
In this particular example, the attachment might be a description of the set of rules the teacher uses to decide how the boys should pass the stick along. If the rules are known, all the teacher's instructions can be worked out without actually following the passing of the relay-stick.
Now going back to Г‚П€. By analogy, it seems reasonable to assume that the operator equation, Г‚П€ = aП€, where the attachment is "a", is the solution to the set of equations {E1], [E2], [E3],... What's more, from what we already know about operator equations, the relationship between the attachment "a" and П€ should be one of multiplication (algebraic or matrix).
Assuming that the above arguments are valid it appears that, just from the definition of a Dynamical System being a physical system that changes, one can show that the driver of that change, the physical agent A, should have a corresponding operator Г‚ that is governed by an equation that is in the form of an operator equation, Г‚П€ = aП€, where "a" should reflect the nature of Г‚, and therefore of A.
Kan at kanak53@hotmail.com
The following is to be added to the last paragraph"
"In other words, it is the change in the physical system that gives rise to the equation Âψ = aψ.
Knowing that total energy normally determines how a physical system evolves, it seems reasonable to identify A with the Hamiltonian and  with the Hamiltonian operator."
The arrow of time--
With a point moving on a line as the model of time ("dt"), there are both the possibilities of time moving backward or forward. However, a different kind of model where it's impossible that time move backward would be a "stream," as computer scientists call it. Such a model can be built using nonstandard analysis and non-wellfounded sets.
First:
clockTime = (nonstandardFuture, standardPresent, nonstandardPast)
In nonstandard analysis "clockTime" would be a nonstandard monad, wherein "standardPresent" is a number from the real numbers surrounded by a halo of infinitesimally close nonstandard numbers. Given that time is one dimensional, this halo comprises (a) nonstandard numbers infinitesimally before standardPresent, called here the "nonstandardFuture," as well as (b) nonstandard numbers infinitesimally behind "standardPresent," called here the "nonstandardPast."
Second:
properTime = (clockTime, properTime)
This is an equation solved by a non-wellfounded set. If you continually substitute for "properTime" on the RHS of the equation the expression "(clockTime, properTime)", again and again for each equation you write down, you can see the stream emerge. It is impossible that such a stream go backward. Here, the problem of the arrow of time simply does not exist.
However, now there must be more to be say about how a particle gets assigned a properTime and how the properTimes are geared to each other. (The possibilities are geared to each other.)
More on these issues here:
http://fqxi.org/community/forum/topic/2420
And here:
https://leebloomquist.wordpress.com
