We each struggle with the concepts of time, and we each face and resolve as best we can the difficulties and dilemmas we experience in our effort to grasp this sometimes enemy sometimes friend. What I am offering here may or may not clarify some things about what you are thinking about time. And the long final section of this posting I owe to string theorist Leonard Susskind and to the excellent review of his book by John Walker -- touching on the idea of infinite numbers of universes.

I'll indulge your quandary. You indulge my response. I’m not sure it will be fun, but it could be fun.

You refer to one of several of Zeno's paradoxes, nearly all of which involve infinite series. No one doubts that you grow older, that you eventually "reach" a destination, nor that the last halfway of a task gets completed.

I mention task thingies, since when I was younger than you, Dad brought in a load of loose hay, pitchforks and all, and my 9 year-old brother and I (I was 10 going on 11) were to stay out of trouble by unloading the wagon of loose hay, and stacking it so it would not slide over and Dad showed us how to pitch a fork full of hay, and "tie-in" the stack of loose hay. We were energetic, but it was a big task.

I proposed, out load, that we would unload half today, and half of what’s left tomorrow. And Dad said "Oh? How long will it take you if you unload half everyday?”

My mind raced ahead to the last single twig of hay, and although we could have thrown that single twig, that straw-like stem, on to the stack with almost no effort, the rules called for me to break it in half, and half.. . and half. "Forever." I said.

"Yes. that is why you boys will have it unloaded by the time I get back from work tonight." Dad said.

I realized then that not only would it take forever to unload the hay wagon, but that it would soon require reaching down into the tiniest pieces of matter, molecules, elements, atoms, and electrons, neutrons, protons, and what was smaller, neutrinos?. . . . but I knew about electrons and protons. I thought it might be hard to ‘find’ tomorrow's half somewhere on the hay wagon, when we got nearly finished unloading it some time from now.

I am going to break apart a little of what you wrote and it won’t hurt. Many have been down this road. Newton, Einstein, Galileo, Hawking, and anyone with a potentially good mind – even if their expression of this road seemed to themselves, upon refection, confusing. There is no promise that if you read further, the road will become clear. I will shoot for ‘clearer’ or less confusing. . .

I quote you, Corbow6
Anyway, since time is based on numbers you can never truly grow older because there is no defined beginning, middle, or end to time since it is said to be infinite.

Hold on. TIME is not “based” on numbers.
Numbers are abstractions.
And Time may be an abstraction, too!

But we do have imaginary numbers, and if you have imaginary numbers, then some really bright students speak of the “Real” numbers; numbers that are almost ‘tangible’ (to some) and even such things as Cardinal and Ordinal numbers.

Instead of infinitely divisible infinitesimal or fractional numbers, what about tiny integer unit systems where there is nothing but the whole full “distance” between the numbers, and there can be no such thing as 1.500001, barely beyond halfway to 2.

Numbers are not real things but because we use numbers in our ‘incomplete’ and incomplete-able mathematics so usefully in understanding the universe around us, they seem so. . Not to stretch these words,( themselves abstractions), too far, there are many formulations or descriptions of time that speak of and contain expressions for imaginary time.

In my very limited view of Time and other things, I prefer to ascribe time to be itself an abstraction projected, as it were, from the three familiar X, Y, Z dimensions of space into that 4th dimension. In my simple minded description for this instance, time is nothing without the happenings in space.

IMAGE: Wikipedia Note the character is a 5 ft 4 inch tall insertion at correct scale. Yes, this is Big Ben!

Some would say “actions” in “space” and I agree that if there were no actions in space; no matter in translation; no radiation in traverse, even with wavelengths the length of the width of the visible universe; no Brownian motion at a molecular level, no restless mutterings of the quarks or gluons or what ever strong forces are composed of; nor vibratory twitterings of the tiny 11 or whatever dimensional strings – then time does not pass, nor exist.

In my limited view, Time is based on “changes” between real physical things.

Does Time have an independent existence? (Some students scream YES!!!!) (But not I.) I say No.

And further, I say that “actions” can only progress in one direction. The down hill course of energy. The second law of thermodynamics. The course of entropy.

The “change” we measure and turn into seconds of time is the change between chunks of matter, or matter and energy, or chunks of energy with respect to each other. Viewed from an energy standpoint, time passes when the energy changes, and that change is always, and naturally, the down-hill course of energy. From one level to a lower level.

Life uses some of this energy for a while, borrows it, organizes with that energy, improbable structures, but the course of the energy is always from a higher level to a lower level. And it is a struggle, always. We experience the changes in this ‘order’ of energy configuration, or order, from one level to the next lower level as the passage of time.

“Time travel” is possible. You and I do it every day. We get older. We travel forward, with entropy, we head on toward the ‘future’ which arrives instant after instant so it is always the present for us. What time ‘passes’ is that change of relationships in matter and energy; matter and energy changing with respect to each other. Often predictably, often probabilistically, and always the down hill path of energy.

(Image: Wikipedia, Salvador Dali, "The Persistence of Memeory" Fair use doctrine, educational historical.)

Why would Time not be infinitely divisible? It has to do with the amount of change.

Of course, our “numbers” are infinitely divisible. But if time, is as I suggest, exists only when something changes; something ‘physical’ changes, what is the smallest unit or step of ‘change’ we can have?

What is the smallest “change” possible? I think if we find a discrete chunk of time that can’t be further infinitely sub-divided, we have gotten down to the single ‘pixel’ scale of the universe.

Defining and characterizing what is the smallest amount of energy (therefore "change") that can exist leads to disturbing things.

These discrete little quantities; these little bundles, these “quanta” are the foundation of our understanding of some aspects of electronics, and of atomic structure and in no small measure, of the vast universe.

I apologize for the quality of the images .

What is the least (smallest) amount of time that can be considered in connection with change?

(Wikipedia images)
where:

h = h /2 pi is the reduced Planck constant

G is the gravitational constant

c is the speed of light in a vacuum

t p is in seconds.

The two digits between the parentheses(40) denote the uncertainty in the last two digits of the value (5.39121) (+/- 0.00040)

These are thought to be the smallest non trivial values that are connected to “physical” things in the universe. In my view Time is not infinitely divisible in any real sense of the term divisible.

Now, I have said my bit and want to progress to something ‘different’. I mentioned above the pixel level of the universe.

I am going to excerpt part of an exceptional book review, by an exceptional individual who is living in Switzerland, and maintains the ant-lab website: www.fourmilab.ch The ch is Switzerland. The review was written by John Walker, and I hope to extract and excerpt from it what you might really enjoy. John Walker made the statement on his site that these reviews when posted are in the public domain.

Susskind, Leonard, The Cosmic Landscape. New York: Little, Brown, 2006. ISBN 0-316-15579-9.

The book is subtitled “String Theory and the Illusion of Intelligent Design”

Susskind is eloquent in describing why the discovery that the cosmological constant, which virtually every theoretical physicist would have bet had to be precisely zero, is (apparently) a small tiny positive number, seemingly fine tuned to one hundred and twenty decimal places “hit us like the proverbial ton of bricks” (p. 185)—here was a number which, not only did theory suggest should be 120 orders of magnitude greater, but which, had it been slightly larger than its minuscule value, would have precluded structure formation (and hence life) in the universe. One can imagine some as-yet-undiscovered mathematical explanation why a value is precisely zero (and, indeed, physicists did: it's called supersymmetry, and searching for evidence of it is one of the reasons they're spending billions of taxpayer funds to build the Large Hadron Collider), but when you come across a dial set with the almost ridiculous precision of 120 decimal places and it's a requirement for our own existence, thoughts of a benevolent Creator tend to creep into the mind of even the most doctrinaire scientific secularist. This is how the appearance of “intelligent design” (as the author defines it) threatens to get into the act, and the book is an exposition of the argument string theorists and cosmologists have developed to contend that such apparent design is entirely an illusion.

The origin of life on Earth due to deliberate seeding with engineered organisms by intelligent extraterrestrials is a theory of intelligent design which has no supernatural component, evidence of which may be discovered by science in the future, and which is sufficiently plausible to have persuaded Francis Crick, co-discoverer of the structure of DNA, was the most likely explanation.

If you observe a watch, you're entitled to infer the existence of a watchmaker, but there's no reason to believe he's a magician, just a craftsman.

If we're to compare these theories, let us begin by stating them both succinctly:

Theory 1: Intelligent Design. An intelligent being created the universe and chose the initial conditions and physical laws so as to permit the existence of beings like ourselves.

Theory 2: String Landscape. The laws of physics and initial conditions of the universe are chosen at random from among 10500 possibilities, only a vanishingly small fraction of which (probably no more than one in 10120 can support life. The universe we observe, which is infinite in extent and may contain regions where the laws of physics differ, is one of an infinite number of causally disconnected “pocket universes“ which spontaneously form from quantum fluctuations in the vacuum of parent universes, a process which has been occurring for an infinite time in the past and will continue in the future, time without end. Each of these pocket universes which, together, make up the “megaverse”, has its own randomly selected laws of physics, and hence the overwhelming majority are sterile. We find ourselves in one of the tiny fraction of hospitable universes because if we weren't in such an exceptionally rare universe, we wouldn't exist to make the observation.

Since there are an infinite number of universes, however, every possibility not only occurs, but occurs an infinite number of times, so not only are there an infinite number of inhabited universes, there are an infinite number identical to ours, including an infinity of identical copies of yourself wondering if this paragraph will ever end. Not only does the megaverse spawn an infinity of universes, each universe itself splits into two copies every time a quantum measurement occurs. Our own universe will eventually spawn a bubble which will destroy all life within it, probably not for a long, long time, but you never know. Evidence for all of the other universes is hidden behind a cosmic horizon and may remain forever inaccessible to observation.

Paging Friar Ockham! If unnecessarily multiplying hypotheses are stubble indicating a fuzzy theory, it's pretty clear which of these is in need of the razor! Further, while one can imagine scientific investigation discovering evidence for Theory 1, almost all of the mechanisms which underlie Theory 2 remain, barring some conceptual breakthrough equivalent to looking inside a black hole,[are] forever hidden from science by an impenetrable horizon through which no causal influence can propagate. So severe is this problem that chapter 9 of the book is devoted to the question of how far theoretical physics can go in the total absence of experimental evidence.

What's more, unlike virtually every theory in the history of science, which attempted to describe the world we observe as accurately and uniquely as possible, Theory 2 predicts every conceivable universe and says, hey, since we do, after all, inhabit a conceivable universe, it's consistent with the theory. To one accustomed to the crystalline inevitability of Newtonian gravitation, general relativity, quantum electrodynamics, or the laws of thermodynamics, this seems by comparison like a California blonde saying “whatever”—the cosmology of despair.

Scientists will, of course, immediately rush to attack Theory 1, arguing that a being such as that it posits would necessarily be “indistinguishable from magic”, capable of explaining anything, and hence unfalsifiable and beyond the purview of science. (Although note that on pp. 192–197 Susskind argues that Popperian falsifiability [Karl Popper] should not be a rigid requirement for a theory to be deemed scientific. See Lee Smolin's Scientific Alternatives to the Anthropic Principle for the argument against the string landscape theory on the grounds of falsifiability, and the 2004 Smolin/Susskind debate for a more detailed discussion of this question.)

But let us look more deeply at the attributes of what might be called the First Cause of Theory 2.

It not only permeates all of our universe, potentially spawning a bubble which may destroy it and replace it with something different, it pervades the abstract landscape of all possible universes, populating them with an infinity of independent and diverse universes over an eternity of time: omnipresent in spacetime. When a universe is created, all the parameters which ultimately govern its ultimate evolution (under the probabilistic laws of quantum mechanics, to be sure) are fixed at the moment of creation: omnipotent to create any possibility, perhaps even varying the mathematical structures underlying the laws of physics.

As a budded off universe evolves, whether a sterile formless void or teeming with intelligent life, no information is ever lost in its quantum evolution, not even down a black hole or across a cosmic horizon, and every quantum event splits the universe and preserves all possible outcomes. The ensemble of universes is thus omniscient of all its contents. Throw in intelligent and benevolent, and you've got the typical deity, and since you can't observe the parallel universes where the action takes place, you pretty much have to take it on faith. Where have we heard that before?

Lest I be accused of taking a cheap shot at string theory, or advocating a deistic view of the universe, consider the following creation story which, after John A. Wheeler, I shall call “Creation without the Creator.”

Many extrapolations of continued exponential growth in computing power envision a technological singularity in which super-intelligent computers designing their own successors rapidly approach the ultimate physical limits on computation. Such computers would be sufficiently powerful to run highly faithful simulations of complex worlds, including intelligent beings living within them which need not be aware they were inhabiting a simulation, but thought they were living at the “top level”, who eventually passed through their own technological singularity, created their own simulated universes, populated them with intelligent beings who, in turn,…world without end. Of course, each level of simulation imposes a speed penalty (though, perhaps not much in the case of quantum computation), but it's not apparent to the inhabitants of the simulation since their own perceived time scale is in units of the “clock rate” of the simulation.

If an intelligent civilisation develops to the point where it can build these simulated universes, will it do so? Of course it will—just look at the fascination crude video game simulations have for people today. Now imagine a simulation as rich as reality and unpredictable as tomorrow, actually creating an inhabited universe—who could resist?

As unlimited computing power becomes commonplace, kids will create innovative universes and evolve them for billions of simulated years for science fair projects. Call the mean number of simulated universes created by intelligent civilisations in a given universe (whether top-level or itself simulated) the branching factor. If this is greater than one, and there is a single top-level non-simulated universe, then it will be outnumbered by simulated universes which grow exponentially in numbers with the depth of the simulation.

Hence, by the Copernican principle, or principle of mediocrity, we should expect to find ourselves in a simulated universe, since they vastly outnumber the single top-level one, which would be an exceptional place in the ensemble of real and simulated universes. Now here's the point: if, as we should expect from this argument, we do live in a simulated universe, then our universe is the product of intelligent design and Theory 1 is an absolutely correct description of its origin.

Suppose this is the case: We're inside a simulation designed by a freckle-faced superkid for extra credit in her fifth grade science class. Is this something we could discover, or must it, like so many aspects of Theory 2, be forever hidden from our scientific investigation? Surprisingly, this variety of Theory 1 is quite amenable to experiment: neither revelation nor faith is required.

What would we expect to see if we inhabited a simulation? Well, there would probably be a discrete time step and granularity in position fixed by the time and position resolution of the simulation—check, and check: the Planck time and distance appear to behave this way in our universe.

There would probably be an absolute speed limit to constrain the extent we could directly explore and impose a locality constraint on propagating updates throughout the simulation—check: speed of light.

There would be a limit on the extent of the universe we could observe—check: the Hubble radius is an absolute horizon we cannot penetrate, and the last scattering surface of the cosmic background radiation limits electromagnetic observation to a still smaller radius.

There would be a limit on the accuracy of physical measurements due to the finite precision of the computation in the simulation—check: Heisenberg uncertainty principle—and, as in games, randomness would be used as a fudge when precision limits were hit—check: quantum mechanics.

Might we expect surprises as we subject our simulated universe to ever more precise scrutiny, perhaps even astonishing the being which programmed it with our cunning and deviousness (as the author of any software package has experienced at the hands of real-world users)?

Who knows, we might run into round-off errors which “hit us like a ton of bricks”! Suppose there were some quantity, say, that was supposed to be exactly zero but, if you went and actually measured the geometry way out there near the edge and crunched the numbers, you found out it differed from zero in the 120th decimal place.

Why, you might be as shocked as the naïve Perl programmer who ran the program “printf("%.18f", 0.2)” and was aghast when it printed “0.200000000000000011” until somebody explained that with about 56 bits of mantissa in IEEE double precision floating point, you only get about 17 decimal digits (log10 256) of precision.

So, what does a round-off in the 120th digit imply? Not Theory 2, with its infinite number of infinitely reproducing infinite universes, but simply that our Theory 1 intelligent designer used 400 bit numbers (log2 10120) in the simulation and didn't count on our noticing—remember you heard it here first, and if pointing this out causes the simulation to be turned off, sorry about that, folks!

Surprises from future experiments which would be suggestive (though not probative) that we're in a simulated universe would include failure to find any experimental signature of quantum gravity (general relativity could be classical in the simulation, since potential conflicts with quantum mechanics would be hidden behind event horizons in the present-day universe, and extrapolating backward to the big bang would be meaningless if the simulation were started at a later stage, say at the time of big bang nucleosynthesis), and discovery of limits on the ability to superpose wave functions for quantum computation which could result from limited precision in the simulation as opposed to the continuous complex values assumed by quantum mechanics.

An interesting theoretical program would be to investigate feasible experiments which, by magnifying physical effects similar to proposed searches for quantum gravity signals, would detect round-off errors of magnitude comparable to the cosmological constant.

But seriously, this is an excellent book and anybody who's interested in the strange direction in which the string theorists are veering these days ought to read it; it's well-written, authoritative, reasonably fair to opposing viewpoints (although I'm surprised the author didn't address the background spacetime criticism of string theory raised so eloquently by Lee Smolin), and provides a roadmap of how string theory may develop in the coming years.

The only nagging question you're left with after finishing the book is whether after thirty years of theorising which comes to the conclusion that everything is predicted and nothing can be observed, it's about science any more.

My paraphrase of John Walker's review of Susskind's book ends here.

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Corbow6, I hope you were able to enjoy John Walker’s review as much as I, and see that maybe time travel to the hypothetical past would be impossibly hard in the simulation.

I suggest you read the “old” SF book Eon, 1985 by Greg Bear. It will give you an entertaining look at a line of time I do not accept, but I liked the read.

image www. gregbear. com

It, “time” will seem confusing for a long “time.” Enjoy.

Corbow6's statement and my response to it is above.

Corbow6 writes:

Anyway, since time is based on numbers you can never truly grow older because there is no defined beginning, middle, or end to time since it is said to be infinite. But then I got to thinking about time travel, and I believe it would technically be time travel, but it wouldn’t in the sense that wherever you travel wouldn’t be your timeline. If there are an infinite number of timelines it would make sense because it would account for every single point on any given timeline, so if you could find which dimension you want it would be as if you had traveled backwards in time. Infinity covers everything, so there would theoretically be an infinite number of points for every place you wanted to travel. Could be easy….could be hard. Who knows?

If you do things right. You will get older. You are too young to not grow older, and change will change you.