Discussion of "Time and Classical and Quantum Mechanics: 
Indeterminacy vs. Discontinuity."
by
D. A. White
dpedtech@dpedtech.com

Recently a young scientist and thinker from New Zealand, Peter Lynds, published a paper in Found. Phys. Lett., 1 Feb., 2001, proposing what he claims is a new interpretation of time.  He also claims that Zeno thought of the idea about 2500 years ago.  Maybe there's nothing new under the sun, just fresh viewpoints.  "Time" is definitely an important feature not only at the foundations of both classical and modern physics but also in the daily lives of most people in our society.  Modern physics is a vast and rapidly developing field of great power, elegance, sophistication, and complexity.  Most physicists simply have no time to take a closer look at the foundations of the edifice they are busily erecting, but just assume that things are pretty much OK and charge on ahead with their work.  Thus my first comment on the paper by Mr. Lynds is to congratulate him for having the courage and interest to choose one of the foundation concepts of a basic science -- even of our whole civilization -- and attempting to look it squarely in the face.  Let's see what he sees and what he doesn't see in the mirror.

The first thing he rightly sees is that "time" is a fuzzy and problematic concept.  He attempts to resolve the problem of time by postulating a "new" kind of indeterminacy that he claims is different from the quantum indeterminacy that was uncovered by Heisenberg.  Lynds argues that, even paying no heed to quantum issues, no matter how small the displacement in which you view a moving object, the object is still moving, and thus has not only an imprecise position but also encompasses a finite interval of time.  He argues that time has no specific direction, is co-conditioned by distance, and guarantees a "necessary trade off of all precisely determined physical values at a time, for their continuity through time." (quoted from his abstract.)  

Most of this is not news.  Many aspects of modern quantum physics are considered unquantized.  For example, velocity and EM frequencies are not considered quantized in free space.  On the other hand they may become quantized under certain boundary conditions.  And they do have upper and lower limits.  I would submit that the above quoted phrase from Mr. Lynds' abstract is a bit self-contradictory and circular.  First, the phrase "at a time" is meaningless because he has not defined time and he himself disallows using "precise static instants" of time, such as "at a time" presumably is meant to be.  If he intends by his statement that time be considered a primitive undefined axiom, then he may just say so and skip the rest of his paper.  Second, the whole argument of his paper is intended to show that precisely determined physical values are impossible.  I do not think modern physicists would disagree with that, since they know they depend on instruments of measurement subject to specific resolutions in order to determine physical values with precision.  If we already agree we can not define a measurement precisely, speaking of a trade off is meaningless.  In quantum mechanics a probability wave is absolutely precise.  It has a total probability of 1.  All the rest is figuring out the relative weights of the components depending on how you look at the system.  I never heard that time was an exception.  It is a codependent component that never exists by itself.  For example, you can say (D p) (D x) >= h, or you can say (D E) (D t) >= h.  Here we talk about an uncertainty trade off of time interval versus energy, or momentum, or displacement, or whatever you like.  Theoretically you can take the displacement or time interval down as small as you please as long as you let the momentum or energy change compensate by expanding as needed.  As in calculus you can not take the interval to zero or the uncertainty expression becomes meaningless.  As Lynds rightly says, you work with intervals.  If we take the time interval down to around 10^-81 s, then the energy shift must be equivalent to converting a sun-size star (around 10^30 kg) entirely from mass to energy (E = mc^2).  If you tried to "observe" an electron within an interval of 10^-12 m, the range of a nucleon, the velocity would go superluminal, which is why bound electrons form blurry clouds around nucleons.

So, without picking too hard at the details of his arguments, I would suggest that Mr. Lynds has overlooked several important considerations in his paper.  Let me discuss a few briefly.  My point is not to criticize Mr. Lynds (who at least took a shot at an excellent target) as to bring up some foundational issues that come along with the problem of time and are also frequently overlooked by physicists.

(1)	What is time?  In his paper Mr. Lynds seems to indicate that we can not define time precisely.  Maybe that is why he did not attempt to define it.  He may be right quantitatively, but I believe we can at least construct qualitative definitions of time.  We can also use quantitative methods to support our qualitative definitions within the range of our technical expertise.  For example, try this: "The notion of time is a symbolic way of indicating the presence of dis-equilibrium in a system."  Instead of "dis-equilibrium" we could say "resistance".  We can explore such a definition of time qualitatively by examining various types or aspects of dis-equilibrium.  We can explore time quantitatively by comparing different dimensions of dis-equilibrium with conventional standards.  Our definition is both general and precise.  It also brings up several other relevant issues that Mr. Lynds forgot to mention in his paper.  The above definition may not be the only one or even the best one.  It is simply an example to show what I mean by giving a definition of time.

(2)	What is a qualitative notion of time?  Mr. Lynds focuses on the problem of precision in measuring time, but does not consider that there may be a variety of qualitatively different notions of time -- Ta, Tb, Tc, Td, ..... --, some of which may admit absolute precision within the defined frames of their operation.  We could define a mathematical time that only exists in the particular mathematical realm that it occupies.   For example, each moment in our mathematical time might be represented by an integer.  A physical system (with irregular intervals but precise moments!) might involve the tossing of a coin.  Each "time" the coin lands "head" up constitutes a moment in our temporal scheme, and any other state doesn't count.  The system gains equilibrium when we stop tossing coins.  Time then stops also.

(3)	Where is the observer, and what is his role?  Mr. Lynds actually mentions the observer casually and hypothetically in his relativity examples and also refers vaguely in passing to the flowing notion of time "as our subjective conscious perceptions often seem to suggest." (p. 3) But he does not pursue this key issue.  As my comments under points (1) and (2) above suggest, time is probably best thought of as a mental construct more than anything else. When we say that time is a "way of indicating dis-equilibrium", the question arises: who does the indicating?  Whatever definition you use, I think you'll find that "time" is a code word in physics for the involvement of the observer.  Nobody has ever seen mind or consciousness.  Nobody has ever seen "time" either.  We can see a person who is conscious, but not consciousness.  We can see a clock "telling" time, and we can see things change as the clock also moves, but we do not see time itself.  We also do not see space.  We can see things in space, but not space all by its self.  Remove all the "things" and the "space" disappears.  It is very possible that this means space and time are mental constructs created by the observer in order to interpret his experiences.  If Einstein is right that physical space/time geometry is mass-energy, and our above analysis is right that space/time is a mental construct, then perhaps all that mass-energy "out there" in the universe is nothing but the observer's own creative potential.  When you look out at the "vast" universe in which you seem to "exist", what you see is a reflection of your self, just as you are.  What if you don't believe me?  Well, that is how you define your own creative potential.  And that is what you experience.  So the relativity of the observer goes far beyond the consideration of time, or Planck's constant, or quantum uncertainty.  But any consideration of time involves an observer.

(4)	How do you deal with unannounced viewpoint shifts?	Many of the perplexing problems in modern physics arise from the physicist making unannounced viewpoint shifts.  Such shifts often occur as an unconscious habit.  We all have habits, and habits are not necessarily bad.  They are behavioral automatons that can minimize waste of attention energy while carrying out lots of useful low level or even high level functions.  You construct your life and the physical universe out of various embedded behavioral automatons.  They function as conditioned loops that will go on and on as long as they are not interfered with.  However, if you as observer shift your viewpoint, a previously useful automaton can become a nuisance.  But the automaton does not know that it is now a nuisance, because its behavior loop is insulated from the rest of the system.  It's autistic, so to speak.  This keeps it stuck to its knitting, but hard of hearing.  Zeno's paradoxes give us a good look at how this works.  The story of Achilles and the Tortoise (or the Dichotomy) traps your attention into focusing on the relative intervals between the two racers.  The paradox arises not from a problem with time, but from an unannounced shift of attention to a different reference frame.  We can assume that the two racers move at constant but different velocities (Achilles being, let's say, twice as fast as the Tortoise so the race is basically the same as the Dichotomy).  Then the distance between them will keep halving indefinitely and they will never exactly be at the same point.  However, this viewpoint requires the observer to squeeze his notion of time (and/or space) intervals into shorter and shorter "segments", a procedure that runs against the ordinary observer's habit of attention.  Most people set their clocks by a regular oscillation such as day and night, pulse beat, and so on.  This causes them to shift automatically into the assumption that Achilles passes the Tortoise in two units of automaton observer time.  That is true from the viewpoint of the observer's habitual automaton clock.  So our observer is perplexed when Zeno tells him that Achilles can never beat the Tortoise.  When the observer shifts to Zeno's viewpoint, he has to agree with Zeno.  But that viewpoint feels weird and unfamiliar.  The point here has nothing to do with quantum mechanics or unusual properties of time.  It has to do with the critical importance of the observer's viewpoint, something which Mr. Lynds and many physicists unfortunately tend to lose track of in the course of their explorations.  The situation is not so much that time is non-precise as that time looks different from different points of view because it is a mental construct in the observer's consciousness.  In each of Zeno's conflicting viewpoints time can be mathematically precise.  Physicists use lots of interesting tools such as renormalization to switch viewpoints when things get inconvenient.  This is OK so long as you know when you are doing it.  It's also helpful to let readers know what's going on.  Unfortunately Mr. Lynds follows Zeno and argues (Section 3.1, par. 2 et al.) that if some value were precisely determined, "it could never change, as it would firstly have to proceed to another precise value.  But before it could do this, it would firstly have to proceed to half of that value...."  And so on.  Then he claims it "can be demonstrated that if a physical value were precisely determined, it could never change."  I challenge him to "demonstrate" that claim.  If you try to demonstrate that claim, you are stuck.  How can you demonstrate within a finite lifetime that something will NEVER change?  If you can't demonstrate it, then it is at best an overstated claim.  Of course you are only stuck if you believe the notions that he asks you to believe.  This is really tangled Zenoism.  Mr. Lynds might claim that all physical values eventually change.  Then in order to challenge him we have to find a counter example of a physical value that doesn't change.  The physical constants such as the speed of light in a pure vacuum, the charge quantum, and so on, are pretty good candidates for non-changing physical values, though we know there are always vacuum fluctuations that cause tiny perturbations in light speed.  Never say never.

(5)	What is change (motion), and what is non-change (rest)?	Mr. Lynds seems confused about the nature of change and non-change and the relations of these to time.  From our previous definition of time, we could say that an object or system in equilibrium is at rest.  This is a relative state of rest, since components of the system probably would continue some motion.  However, the system as a whole would be incapable of accomplishing work according to thermodynamics.  Another form of quasi-rest involves systems that oscillate or loop in some way.  But we see that change, motion, energy, work, and all such concepts in physics are anchored in our definition of time.  In perfect equilibrium time stops.  In the absence of all phenomena, time also stops.  (Actually there is probably a threshold slightly above equilibrium or total absence in which time stops.)  The straw dog "precise static instant in time" that Mr. Lynds speaks of is precisely not "IN" time. It is "OUTSIDE" time.  As a simple experiment to experience this, try going to sleep.  During deep sleep you will "notice" that you have no concept of time.  When you are awake, you can construct or reconstruct whatever notions of time you feel you need in order to "get on" with your life.  We do an unannounced viewpoint shift whenever we assume that time continues while we are asleep. Then we organize a lot of evidence in our lives to prove that that belief is true in spite of Zeno laughing at us from beyond the grave.  This unannounced viewpoint shift is a common feature of thermodynamics.  In spite of the statistical existence of Poincare peaks and other such "spontaneous" equilibrium upsetting fluctuations in a system, many physicists insist on odd notions such as the "heat death of the universe." They neglect to point out that they are playing cosmologist one "moment" and then jumping back into their little human clocks. What if the cosmos has no trouble at all snoozing through to the next Poincare peak? What if the cosmos has a few nonlinear negentropic butterfly aces hiding up its sleeve that can quickly stack the random shuffling of the cosmic deck?

(6)	What is the relation between certainty and continuity?  Mr. Lynds believes that "nature has wisely traded" certainty for continuity.  I suspect nature at least allows both, just like it allows fermions and bosons, particles and waves.  What the observer sees when he looks at the world is up to the observer to decide.  Natural numbers are so called because they seem right there in nature.  They are absolutely precise.  They never change place when they are ordinals.  But they are nevertheless mental constructs, not physical objects.  We also have so-called "real" numbers that turn out to consist largely of infinite (undefined) "quantities" of undefined numbers.  I call them "peanut" numbers, because they are like the little styrofoam dumbbells that protect shipped items from rattling around in their boxes.  Natural numbers are always discrete, and you always know where they are and their exact values.  But real numbers are slippery and stretchy, and can sequence to form a smooth continuum.  There are even shadow doppelgangers for every finite real decimal.  The mental number constructs generate a viewpoint that confuses most people about the nature of the physical world. People look at "individual" macroscopic or quantum-level objects, and they imagine that such things are as reliable as the discrete natural numbers.  This is a mirage.  All apparently solid and discrete objects are rapidly dispersing wave packets.  They don't stick around.  They stretch and slip and melt away.  On the other hand, the non-local probability waves of phenomena last forever, and extend continuously as fields through all points of time and space.  So the question is not one of "nature" doing a trade off.  It is more that the observer does a switcheroo on himself when he shifts from mental space (thinking) to world space (experiencing).  It is like looking in a mirror.  There are different kinds of mirrors.  Reflections from ordinary bathroom mirrors switch left and right positions in space.  Reflections from phase conjugate mirrors switch forward and backward directions in time.  Reflections from "observer" mind-body mirrors switch discrete certainty and continuity of impressions in consciousness.

(7)	What is a measurement?  Mr. Lynds talks about precision in measurements, but he does not go to the root of the measurement problem.  A measurement is a comparison between an object designated as a standard and an object under observation.  Both the standard and the object of observation are completely arbitrary.  The observer decides what standard to use and what object to observe.  Everybody knows, or should know, that we choose standards and observations as a matter of convenience and preference.  It is total bias, absolute prejudice.  It also sometimes lapses into automated habits of comparison.  A common convention in physics is to divide a measurement into three components.  (a) A "unit" such as meters or seconds refers to the standard object used in the comparison. (b) A "scale" such as a power of ten refers roughly to the size comparison between the standard object and the object of study. (c) A "ratio" within the scale range gives a more or less precise comparison against the scale of the object of comparison to the rough scale.  For example, the speed of light often is written as 2.9979...x10^8 m/s.  Here the (m/s) indicates a totally arbitrary velocity unit in the form of a meter per second. Meters and seconds are internationally defined arbitrary standards.  The scale is 10^8, or 10*10*10*10*10*10*10*10 = 100,000,000, or a hundred million.  We work in the conventionally accepted arbitrary base ten system.  Our computers translate this into binary.  The ratio 2.9979... tells us approximately how many of these scaled units of the standard it takes to match the observed phenomenon.  This is also in base ten to match our scale convention.  Everybody knows that the measurement depends on the precision design of our standard, our measurement of the standard (we make a copy for personal use), our measurement of the phenomenon with our copy of the standard, and general level of sloppiness in transcribing and communicating the whole rigmarole.  So we do our best, and nobody pretends that anything is or even could be measured precisely within infinitesimal tolerances, though some pretty amazing measuring has been done. Nature "measures" by the principles of least action and equilibrium (non-action).  The main problem with precise human measurement comes from the quantum uncertainties that are inherent in the co-conditioned structure of phenomena.  Things just don't stand all alone by themselves.  They are connected.  Planck found a constant (h) while studying energy.  But this constant did not refer to a single isolated "thing" or even to a fixed set of things.  We can analyze it in different ways depending on our viewpoint as an observer.  What are we looking for, at, as?  Planck's (h) can involve mass, distance, time, momentum, energy, and perhaps any number of other things.  Depending on viewpoint, these are linked together, and then the "trade off" begins.  If you want to observe an electron (directly or indirectly), you must do so via a photon.  The mass of the electron is small enough that the photon seriously disturbs it when the interaction takes place.  So you have to choose what you want to see clearly -- momentum or position, energy or time, and so on.  The rest gets fuzzy.  This is how ordinary attention works as well.  Look at the palm of your hand.  Do you see wrinkles?  Now focus your attention on something right next to your palm.  You can still see the palm, but the wrinkles get fuzzy.  Do you see that this all has more to do with the observer than with Planck's constant or time? Explore.  Whatever you put your attention on will become clearer, and whatever is NOT in focus is, well, not in focus -- simply because your attention is not focused on it!!  So who do you blame?  If you don't understand something, put your attention on it honestly and directly and you will see the answer.  This is a very general principle for us because it is based on the nature of us observers according to how our habit automatons currently are configured.  Some creatures habitually put attention on several objects at a time or on peripheral areas.  Their nervous systems are configured differently.  Go to the zoo and check out the animals.  Go to the park and check out the plants.  How do they configure attention?  (Clue: We speak of phototropism and geotropism.)

(8)	What is the core quantum issue?		We discover here the principle of observer quantum relativity.  You can configure your perception -- and even your beliefs -- any way you like within the range of your psycho-physical resolution.  In his later years at Princeton when he was probing for a Unified Field Theory, Einstein got to know a graduate student named Leo Baranski.  Baranski wrote an unusual doctoral dissertation at Princeton (1960) entitled: "Temporal Characteristics of Dynamic Contour Perception."  Einstein was impressed with Baranski's research, and they worked together for a while.  Baranski's main thesis basically was that all we know or can know of the world is gained via our perception, but our perception has certain constraints, some of which seem quantum in nature.  For example, our perception of motion (and hence time) is limited to a certain resolution.  Testing various size objects under various illuminations Baranski found that anything moving faster than about 15 */s (degrees/second) through our field of perception becomes fuzzy or may not even be perceived.  (We can get up to about 30 */s if the object is first presented as a still frame.)  The implications of this research are significant to say the least and should be replicated and widely studied.  For some odd reason his discoveries seem to have been quietly deep-sixed. ...(subluminal blip)... You can probably figure out why without even looking at the details.  ...(   )...  On the other hand, you probably wouldn't want to know. ...(  )... It might seriously erode your current world view. ...( )... The implications of quantized perception of motion regarding the notion of time are fundamental to any theory of time and also to the "management" of society. ...()...  Mr. Lynds puts no attention on this primary issue, which may be why he got published and Dr. Baranski disappeared in a somewhat untimely way. ...... 

(9)	What is directionality?	Mr. Lynds asserts (Sect. 4.1) that "it is the relative order of events that is relevant, not the direction of time itself."  His point seems to be that he doesn't like "imaginary" time or time forking off in an orthogonal direction.  Nevertheless, the computer he wrote his paper on undoubtedly processes data in a limited spacelike manner called parallel processing.  When a serial string of data moves in parallel through a chip or bus, the time dimension forks 90 degrees.  I do not know what Mr. Lynds means by the "relative order of events".  The usual position in physics is that an event occurs, and it is what it is.  Different observers will perceive it from different viewpoints, and we can set up reference frames and do transformations on them and so forth, but the event still is what it is.  The event may look VERY different to different observers.  That may include the "relative order of events" as well.  So what is it relevant to?  I would say the order is relevant to the observer's viewpoint.  Time, being a mental construct according to our definition, is entirely relative to the standard chosen by the observer.  Nature has no standard.  Nature just is.  From a certain viewpoint an observer might even see something he calls chronons.  Others would not.  "Imaginary" time refers to a mathematical (mental) construction that is useful for plotting objects in reference frames and has nothing to do with the objects themselves.  As an exploration draw three dots randomly on a sheet of paper.  See how many different ways you can look at them.  Can you see them form a circle?  Can you get them to look like just two dots?  Can you line them up?  Can you get them to look like a single dot?  Can you make them disappear?  Time is like space, and can transform into space and other things too. Directionality implies possible or actual motion relative to an observer.  I suggest Mr. Lynd's sentence left out the words "to an observer" after the word "relevant" (and/or relative) in the phrase I quoted above.  Antiparticles appear to move "backwards" in time because they behave in reverse relative to our biased conventional viewpoint.  To them we seem made of antimatter.

(10)	Is it all just a movie?	The static freeze frame notion that Mr. Lynds speaks of with distaste is also a clear possibility.  After all, Hollywood so permeates our lives these days, we should not find it too surprising if the "real" world turns out also to be a kind of high-tech "Mickey Mouse" cartoon movie. Some of the pictures emanating from the sci-fi mavens are even suggesting that idea.  If a movie is all made of nothing but still frames, how can we experience it as a moving picture that emulates our real world experience?  Mr. Lynds thinks that if we have still frames, then that's all we have -- forever -- and physics dies like a photon frozen in a de-pumped quantum phase conjugate gas chamber.  Maybe that's not the whole story.  The still frames on the celluloid won't make a movie come alive.  It takes a movie reel, a projector, a bulb, a screen, and an audience, and maybe some other components as well.  What if the still frames of the collapsed wave functions exist on multidimensional probability reels?  For the movie to come alive an observer has to choose a reel with his will and then illuminate it by strobing his attention through it.  The strobing attention projects images into the "Mind's Eye", the screen of silent awareness that forms a backdrop to all physical phenomena and experiences.  The screen of undefined awareness provides continuity between frames.  Yes, I know this sounds a bit hokey, but in terms of physics it means we have a (real or virtual) macroscopic quantum phase conjugation bubble created with correlated photons.  The object photons correlate with the observer antiphotons.  The object electrons correlate with the observer quasi-positrons.  The object electrons emit photons and absorb antiphotons.  The quasi-positrons absorb photons and emit antiphotons.  Because we are a bit shy about our "bodies" we call the antiphoton beams "attention". Time arises as a side effect of the observer resisting something he sees but doesn't prefer.  Educational psychologist Harry Palmer points out that when you resist something it tends to persist.  When something persists, we get time.  We do time.  If we don't resist, then nothing persists.  The still frame flashes for a moment and is gone.  The connection from one frame to the next is arbitrarily based on the decision of the observer to follow a particular probability reel with attention.  Barring that there is nothing to connect one moment to the next.  Moments are all flashes of light in some configuration.  What you put your attention on is up to you.  As an experiment go into a dark room and seal off all light sources.  Hide in a closet or under a blanket.  Open your eyes and observe carefully.  What do you see?  Is it really dark in there?  Or is it filled with flashes of light?  Do the flashes have size?  Do they have any direction?  Do they change? Or is it a kind of sparkly steady-state background like the cosmic background radiation?  Does it have zero-point fluctuations? ......

I am glad that so many noted members of the physics community have been willing to look at Mr. Lynds' ideas and encourage him to whack away at the foundations.  One of the things I liked best about Richard Feynman was his talent for pointing out a key issue in physics or a weird phenomenon and saying honestly, "Nobody has any idea why."  If an electron has no nuclear forces, what holds all its negative charge together?  "The question has never been answered," he says (Lectures, 2:1-2.), and then he entertains us with a bunch of really creative ideas.

DAW
Aug, 2003