Limits of mathematics in cosmology

Lev,

Thanks for getting me into the right thread.

I don't think that any space at all supports structural events. If we agree that time is identical to information, then only spacetime supports structure, because spacetime _is_ structure; i.e., time structures space.

Tom

Edwin,

Thanks for the recommendation. I know of the book, but have not read it. Another along the same line that I enjoyed was Barry Mazur, _Imagining Numbers_.

Tom

Tom,

I should have mentioned this to you long time ago: since "information" has so many meanings, the phrase "time is identical to information" is quite ambiguous.

Lev,

It isn't ambiguous to me. Time has a very specific physical meaning, its behavior identical to quantum information -- as I have said, as Jacobson-Verlinde find that quantum information is identical to gravity, with entropic properties, I find n-dimensional continuation of the time metric entropic (though I think dissipative is a better term) as well. Think of dissipative structures in biology (Priogine)then extend it to n-dimensional analysis.

Fundamentally, I mean that n-dimensional Euclidean space is embedded in 0 1 spacetime. It is the time metric ( 1) that structures the space; i.e., spacetime curvature determines what we observe, because we distinguish objects by variations in curvature (which also defines variations in velocity, which is a time dependent property). A hypothetical 2 dimension observer needs access to 3 dimensions to detect curvature, and therefore lives in a 2 1 world. In our familiar 3 dimensions, we are 4 dimensional observers living in a 3 1 world.

Think of every massive object as having a horizon that limits the measure of an n-dimension observer, n > 1. Approaching the horizon, the measure becomes infinite, as in a Poincare disc. The observer may even circumnavigate the space without determining a finite shape. To an observer in a higher dimension, though, it is simple to see the fixed point of origin and return --let's call that place "point-like space."

The 2-dimension complex sphere, C*, allows the infinitely continuous expansion of that point-like space over a non-ordered field of definite values. So no matter what Euclidean dimension (d > 1) that one chooses, the 2-dimension field and the 1-dimension metric is sufficient for analysis on d - 1. This means that for d > = 4, the "point like space" is a particle, i.e., of dimension d - 1. 4 dimension observers, obviously, detect only 3 dimension particles. Every n 1 dimension set, however, is structured by time such that d - 1 observers have access to the d manifold that defines the structure.

Because the internal structure beyond that manifold is inaccessible in principle (the dynamics are irreversible) I like the idea of structs as mediators of action so that system processes evolve at different rates; in other words, a time-dependent system does not obligate time-independent structures to follow a linear sequence of evolution. I do think you show this in your pictorial of structs, depicting connected and unconnected channels.

Tom

Tom

Lev,

"Can you say it in a plain language?"

I thought I did. :-)

Okay. I sketched the mathematical basis in another thread. Let me try and explain it without using numbers:

Nonlocality ("Something somewhere is doing we don't know what") is inherently a statistical placeholder for an event of probability unity. What I found is that a continuum of negative mass keeps the energy books balanced between particle and wave phenomena so that the low inertial (baryonic matter) content of our world is explainable as the probability 0.0459 that the universe contains matter at all. WMAP shows ordinary matter content of 4.59%, so the prediction is exact. (Okay, so I can't do it without at least a couple of numbers.)

Because this negative mass continuum coheres in the Hilbert space, however, a continuation of Hilbert space with ordinary Euclidean space implies the smooth mapping of nonlocal information on local configuration space, resulting in identity between quantum unitarity and mass unitarity. The terms square perfectly with Einstein's mass-energy equivalence, in that energy to matter conversion is proportionate, and the absence of a rest state for negative mass implies an accelerating universe.

What this means to our topic of "structure" is that the hyperbolic space of negative mass-energy bounded by the parabolic space of positive mass-energy results in measure zero space (therefore, space without structure)and the only artifact that gives structure to the space, is time.

Tom

Lev,

I agree with you that reality is more about streaming events, than particles, but it seems all three are levels of emergence.

Here is a point I make about the nature of time: If two objects, be they particles or automobiles, collide, it creates an event. Now the physical reality of the objects go from past events to future ones, say from the factory to the scrap heap. On the other hand, the events go from being in the future to being in the past. Tomorrow becomes yesterday.

Now the question is what is more fundamental and what is the higher level of emergence? Being physically extant, we view time as the series of events along which we progress, so time goes from past to future. On the other hand, it would seem quite evident that the only physical reality is what is present. So while we view the present as moving from past to future, what if the present is the constant and it is the events which are transitioning? Does the earth travel/exist along a fourth dimension, from yesterday to tomorrow, or does tomorrow become yesterday because the earth rotates? In the first, time is a fundamental dimension along which events exist and this fourth dimension is correlated to the three coordinates of space to locate the ways in which information of these events radiates. In the second approach, time is an emergent effect of motion in space, similar to temperature, being configurational slices of the continuing transition effect.

Which is not to negate the traditional view of time as progression from past to future, because as cause and effect, both are inseparable.

Consider how this defines the physical relationship between objects and processes: In a factory, the product goes from initiation to completion, but the production process goes the other direction, consuming raw material and expelling finished product. This could even be applied to the mind/brain dichotomy. The brain consumes raw information and formulates conceptual models of that information, called thoughts. So while the brain is always physically present, as least during our lifespan, the mind is a series of conceptual models that congeal out of informational input, which then are displaced by the next thought and recede into the past.

Ultimately, even our lives are units of time which start in the future and recede into the past.

There are a number of psychological implications to this time dichotomy as well. When we view time as the series of events, we exist as a point of reference, moving against our physical context, but when we view it as what is physically real, we exist as a fundamental part of that larger context, as the events of our lives recede into the past.

The existence of time as an emergent phenomena means any concepts associated with time have to be evaluated in that context. Consider the idea of the present as a dimensionless point. If we were to have a dimensionless point of time, that would mean freezing the very motion being measured. In which case, physical reality would effectively vanish, since so much of it, if not all of it, is relational motion. It would be like taking a picture with the shutter speed set at zero. No light and thus no information could travel. So, in this sense, no physical object could have a precise location in space, since that would mean referencing an instantaneous point in time. Without that inherent fuzziness, everything would not be crystal clear, but non-existent.

This then gets to the idea of time as a fundamental dimension, along which all events exist. This becomes a physical impossibility, as it is physically contradictory. It is the motion/energy which creates events, but the process of creation requires replacing what came before. Creation and destruction are two sides of the same coin. The amount of energy remains the same, so the information it forms must change in order to create new information and if it were to cease changing, there would be no relational interchange, so no information could exist. The energy goes from prior configuration to succeeding configurations, while these events go from potential, to actual, to residual.

I could offer more thoughts on this, but will let you consider the idea.

"On the other hand, the events go from being in the future to being in the past. Tomorrow becomes yesterday."

"Ultimately, even our lives are units of time which start in the future and recede into the past."

John,

I believe that this is an illusory perception of reality. If you take the view of reality as a flow of interconnected events (and you agreed with this), there is only one direction of flow: unless you have a very 'primitive', i.e. cyclic, universe, an unlikely scenario, an event that appears in the flow again, does so in a different 'context'. That is why, except for the basic events and very short processes, there are no two absolutely identical objects/processes, even when they belong to the same class, e.g. a protein of a reasonable size, a bacterium, an ant, a tree, a star, or a screw.

Lev,

I would say our perception of time is a flow of interconnected events, but there are some inherent caveats in that. I think it reasonable to say there are many events which are not directly connected, ie, exist outside each other's light cones, such that there is no single timeline tying them all together. Even in the context of Big Bang theory, mutiverses and dark energy provide example of one, completely (theoretical) outside events(multiverse), as well as apparent additional input into the given cause and effect timeline, that of dark energy.

It's not that I'm arguing against the one direction of of the flow of events, but I'm posing the question of: What is it flowing against? What is the constant? Is it these series of occurences, or is it the physical reality of the present? As objects we move from one event to the next, but as processes, we only exist in the present. So are we moving along a metadimension of time, whether Newton's absolute flow, or Einstein's fourth dimension, from past to future, or does the changing configuration of what is cause one event to be replaced by its successor and thus recede into the past?

For much of human existence, we viewed the sun as moving across the sky, from east to west and constructed increasingly complex explanations for this, from Apollo's chariot to epicycles. It was only been within the last five hundred years we understood it was the rotation of the earth, moving the other waqy, west to east, which caused this effect. Could it be the view of time as a dimension along which the present moves is equally reversed?

The effect of time is caused by a multitude of motions, which we tend to intellectually coalesce into one cumulative motion. A good example is how the measure of the cycles of the moon were adapted into units of the solar year and no longer reflect an accurate moon cycle.

One of the main functions of relativity is to try and explain why clocks do record their own time and are not reflective of some universal time.

Have to run.....

Lev,

Sorry for the rushed response this morning. From your essay:

"As we know, objects in nature do not pop up out of nowhere but always take some time to appear,

and in each case, the way an object appears is similar to the way some other, 'similar', objects

appear. In other words, as far as we know, there is no object in nature that does not belong to some

class of closely related objects, be it an atom, a cloud, a star, a black hole, a stone, a worm, a protein,

or a stop sign. Since we view objects as processes, we have

Postulate 1: the universe is a family of evolving and interactive classes of (irreversible)

processes."

In making a distinction between objects and processes, I would view the process as that which creates and the object as that which is created. A process usually creates innumerable distinct, but similar entities, whether it's the rotation of the earth relative to the sun creating days, or an automobile factory creating cars. The processes and entities go in opposite directions though, with the process going from past entities to future ones, while the particular entities go from being in the future to being in the past.

This is not a cyclical process, but a relational one.

Of course there are internal processes within entities, much as your brain is an entity that is also a process of distilling information into useful observations, as well as processes which are entities on a larger scale, such as that car factory being a unit within the larger economic process.

In terms of a clock, the process is the hand which moves from one unit of time to the next, while the units of time go from being in the future to being in the past. It should be noted that clocks evolved from sun dials, so the hand of the clock models the motion of the sun through the phases of the day, but to go back to an earlier point, we now know it's the earth which moves, not the sun, so if we were to translate that to the clock, it's the hand, which represents the present, that is constant and it would be the face of the clock, as the dimension of time, moving counterclockwise.

John,

I'd like to ask you about your idea that time is an emergent phenomenon, like temperature, that arises from the ever-malleable 'substance' of the universe which is generally represented by energy-momentum relations.

In other words, 3-space dimensions exist 'NOW'. These dimensions 'contain' the universe. The future may be implied, but does not exist. The past may be remembered, and the present is in a sense the 'record' of the past. But the physical, energetic universe exists only at this moment, which we know as 'now'.

Aside from questions of directionality, is this a fair characterization of your position?

Edwin Eugene Klingman

John and Edwin,

Please allow my entry here.

I posted the following in http://www.fqxi.org/community/forum/topic/59

"If we admit the idea that duration in time and motion (mass-energy) in space do not interact with duration and motion being simply concurrent realities, then the idea of an infinite past and future time would be easy."

If we allow the idea that duration and motion are separate and non-interacting but concurrent occurrences, then the whole physical/material universe would be just a construct of motion (i.e., energy) with the overall motion (energy) transformations occurring 'alongside' the temporal occurrence.

The whole dynamic existence of corporeal motion transformations would then have the irreversible history, with the temporal (duration) 'transformation' simply an abstraction.

The way I see it, there'd be the separately fixed 3-D space dimension and the 1-D time dimension. The motion and duration occurrences would be the only 'changes' that occur - i.e., the energy transformations and the temporal transformation with the space and time dimensions merely the backgrounds.

castel

castel,

From my reading of what you wrote, we would seem to be in general agreement, in that the changing configuration of what exists is the underlaying reality, while spacetime geometry is a mental model of the narrative process in a spatial context.

The essential reality amounts to a fluctuating vacuum, resulting in an expanding background, interspersed with contracting gravity wells to balance it, resulting in an overall flat space. Time being an emergent effect of this process.

John and Castel,

I will reread Castel's essay, but agree with John that spacetime geometry is a mental model. What I have the most trouble with is the 'fuzzy' now, the "point" when it is all happening. I hope we can make sense of that. I'd like to try to nail down some of the reasons for concluding that now is the ultimate reality.

In GR 'block time' nothing changes. There is no 'now', nor can there be free will if the future already exists (I don't consider splitting universes worth thinking about.) GR 'block time' is surely a mathematical fiction.

However, let's assume that the future does not exist, but that the past really does exist. This would mean that the past physical reality grows larger with each moment. This would imply that new universes materialize every moment, bringing into real physical existence all of the energy and information of the universe, endlessly. This is inconceivable to me.

For these reasons I don't believe that the past or future exist as physical reality, but only as conceptual ordering categories.

What are the problems with 'now'? Some argue that Einstein's special relativity demolished the concept of 'simultaneity' (as in it's simultaneously 'now' over all 3-space.) I disagree. What he did was demolish the picture of a 'God's eye view' of the whole thing in which all reality is seen at once. He replaced this with operational local observations requiring the speed of light be taken into consideration.

If we're in rough agreement on these points, let's move on to the 'fuzzy' now, and try to deal with 'momentary duration' or whatever is implied by the existence of change in space.

Edwin Eugene Klingman

The main problem, if time is not to be considered as an everlasting linear 'dimension' stretching from the eternal past to the far future, seems to be the need for some concept of 'duration' or 'time of change'.

First, does duration exist? That is, is now 'fuzzy' or a perfect 'point'?

If we consider physical reality to be best characterized by energy and momentum, then these seem to imply some finite or infinitesimal time duration that is real in some sense.

But momentum and energy, useful as they are, do not seem to be fundamental. What *does* seem to be fundamental, both in my theory and in the rest of physics, is 'action', in units of Planck's constant, h.

Conceptually, we seem to have a hard time with 'action', and I suspect it's because of this 'built-in' duration. My basic quantum flow condition is presented in my essay,

http://fqxi.org/community/forum/topic/561

as

(dm/dt)(dx)**2 = h

but lets look at Heisenberg's version:

dE dt = h

If a given local event exhibits one Planck unit of action, h, then we see that both the change in energy, dE, and the duration, dt, are somewhat 'fuzzy'.

This is my first cut at understanding the concept of 'duration' as it applies to the reality of 'now' in 3-space. I think that the next effort might be focussed on understanding the meaning of 'local' in the above description.

Edwin Eugene Klingman

My discussion of the 'built-in duration' implied by Planck's constant of action led to the concept of 'local', so I'd like to examine a few relevant concepts here.

Since we are focused on the energy that characterizes the changes in 3-space, then an obvious related concept is that of "energy density" which almost certainly means "local energy density".

There are several things to note here. First, quantum electrodynamics (QED), our most 'successful' theory until recently, was developed with the idea of a "roiling frenzy of quantum foam" (Brian Greene in 'The Elegant Universe'). The major problem here is that circa 1998 we learned from cosmology that the 'vacuum energy' was off by 120 orders of magnitude. That's a big deal. In fact, if you or I were off by that much, we would be expected to recalculate everything that depended on vacuum energy. Wanna bet whether all QED calculations since 1948 were redone? I didn't think so.

Further, Greene makes the following statement:

"...the uncertainly principle tells us that the size of the undulations [in the quantum foam] of the gravitational field gets larger as we focus our attention on smaller regions of space."

This may be what Greene and other QED'ers believe, but this is most definitely *not* what the uncertainty principle tells us. We cannot 'focus' on smaller regions of space! We can 'probe' smaller regions of space via the use of higher energy (shorter wavelength) particles. But in this case *we* are putting the energy into the smaller region of space. Heisenberg's principle did not put the energy there simply because we "focused" our attention on the space.

This is examined in more detail in my book, "Gene Man's World".

Next I'd like to look at the consequences of this misunderstanding of vacuum energy.

Edwin Eugene Klingman

The idea of excessive vacuum energy led to further concepts such as a 'sea of quarks' and the general idea of the 'polarization of the vacuum' due to the virtual particle sea. Brian Greene again:

"Even in an empty region of space... energy and momentum are uncertain. They fluctuate between extremes that get larger as the size of the box gets smaller. It's as if the region of space inside the box is a compulsive 'borrower' of energy and momentum, constantly extracting 'loans' from the universe and subsequently 'paying' them back."

[I don't mean to pick on Greene, but his 'Elegant Universe' has apparently met the approval of most QED'ers, since these comments are over a decade old, with no corrections.]

The above misunderstanding is the source of problems in quantum field theory. [For those who haven't heard, the vaunted dozen place accuracy associated with the hydrogen atom has just been reduced to almost one place accuracy WRT the proton radius seen in muonic hydrogen!] In essence "unlimited credit is the root of the ultraviolet catastrophe", where the ultraviolet catastrophe is the name for the fact that infinite values always show up at high energies. In Gene Man's World I explain that:

"In terms of the 'borrowing analogy', it's as if one believed his local bank had all the money in the world, only to find out that it holds only one peso."

Physicists speak of 'borrowing energy' from the field, yet they seem to believe in 'unlimited credit'. To assume that the (local) region can borrow energy, without specifying where the energy is to come from, is just sloppy thinking. I cannot go to my local bank and borrow billions of dollars. My local bank does not have billions of dollars! Similarly, a particle cannot borrow large amounts of energy from a local region of space that does not have a huge amount of energy. The implication is that no particle can be supported in a volume of space that has no dimensions greater than or equal to the particle wave length. If true, so much for the 'sea of virtual particles' that QED is based on. Since the fqxi comments are not equation or diagram friendly, I simply refer to Gene Man's World for the details of this analysis.

Since the above has been conceptual, I should touch base with experiment. In 2007 a HAPPEX collaboration of over 100 physicists reported Jan 2007 Phys Rev Lett that:

"there is little room for observable nucleon strangeness dynamics."

In other words, they don't see any sign of the strange quarks that they expected to find in the 'sea'.

This hasn't resolved our problems of 'fuzziness' of now, but it's been fun.

Next I want to treat some consequences of the above, but I'll back off now and let others have their say.

Edwin Eugene Klingman

Edwin,

The idea is that time is an effect. How do we experience it? Our lives exist as series of perceptual impressions and so it's natural to think in terms of the narrative effect. So what would a point in time be? It wouldn't be an event, as they require some duration of activity to exist, be perceived and processed into a conceptual impression. This duration is a unit of time, like a second, minute, etc. A point in time would be the hypothetical division between one unit and the next. The assumption is it is dimensionless, but this is mathematically flawed, because anything multiplied by zero, is zero, so any point, spatial or temporal, cannot be dimensionless, or it doesn't exist. There would be nothing to divide one unit from the next. It is though, a handy concept and useful modeling tool, but that doesn't mean a dimensionless point can be real. So if you think about it from that perspective, the real question might be to ask why anyone would think "now" could even be a dimensionless point.

Consider that in terms knowing the position of a particle: Can a particle even be said to have an exact position, if there is no such thing as a dimensionless point in time? It would require isolating the actual object from any motion it might exhibit, should it even exist independent of motion. Think quantum string without the vibrations. We don't even know they exist, except as an explanation for the vibrations. Could it be there is no there there though? We think the noun must precede the verb, but does function follow form? Possibly one motion is simply matched by its opposite. The fact is that the more we explore the evidence, it seems this is the case, though we reject it instinctively. The search for the God Particle continues.

From the perspective of physical reality, there is just a bunch of energy bouncing around. To this energy, there is no time. No beginnings or endings. Events require some frame, or perspective, to be anything other than random activity. The pulsing of activity which brings together form and tears it apart always exists in larger networks of activity. These forms have a beginning and end, these are the units of time, whether lives of beings or the celestial cycles we call days. As they go from potential to actual to residual, the future becomes past. We think of this historical record as constantly increasing, but the reality is this information evaporates, as the energy manifesting it cycles through other forms. So there is no more direction than a hamster running in its wheel. Of course that same activity which destroys, also creates, so we can't have our cake and eat it too.

As for energy of that expansion, for there to be a flat space, where expansion is balanced by contraction, as is observed, it would seem that what falls into gravity wells is distributed back out across the space between them.

When Einstein first understood gravity to be contracting the measure of space, he added the cosmological constant to balance it out. While much is made of the fact that Big Bang theorists predicted the existence of background radiation, it should be also noted they seriously missed explaining how flat it is, as well as explaining the curvature of the redshift. Rather than reexamine the theory, two major patches, inflation and dark energy, were added. As you say, " if you or I were off by that much, we would be expected to recalculate everything that depended on" Big Bang theory.

Now Einstein himself proposed that for the universe to be balanced, there had to be an effect known as the Cosmological Constant. Every successive measure of redshift since 1998 has more accurately shown this redshift to equal what Einstein predicted, rather than that predicted by BBT. It is generally accepted that the space we observe is flat, that expansion and gravity balance out. That means there is no observed overall expansion, only expansion between the gravity wells. So why is it that we have both theory and observation that support a balanced universe, yet there isn't even a suggestion of discussion about the possibility?

We keep building ever more powerful telescopes and as far as they can see there are mature galaxies and galaxy structures and the only response seems to be; My, they grew up fast! Yes, they say those most distant galaxies only show the light of the lightest elements, so they must be young, but given the distance, wouldn't any light from heavier elements have been completely shifted off into black body radiation? Which is what we see a preponderance of, from the edges of the visible universe, but that's supposed to be the afterglow of the Big Bang.

Now that have built this theory of the entire universe as a single entity, going from its birth to its death, we can't help but suppose there are other such entities out there. What if the space we exist in is simply infinite and we are constrained by the horizon line of how far light travels before it falls completely off the visible spectrum? Do we really understand the properties of light well enough to insist this redshift could only be due to recessional velocity? The theory is that space itself expands and that is why we appear to be at the center, but if it was an optical effect, due to distance, the result would be the same appearance. When gravity wells bend light, such that the source appears to move, we know it is only the path of the light being bent. Wouldn't it be simple enough to consider a similar effect causes the other galaxies to appear to recede, as opposed to assuming they must actually recede? We only have a few decades of observation to go on.

If space itself were to expand, why wouldn't the speed of light increase proportionally, since it is our most elementary ruler of galactic space? What would determine C otherwise?The Doppler effect, as it is properly understood, isn't due to the expansion of the frame, but movement within the frame.

I better leave it at this, for the moment.

John,

Apparently, the idea is more like - the space dimension, the time dimension, the ethereal substance of existence, the ephemeral instance of existence, the motion, and the duration are all co-existential essences.

To KISS all these (as per Occam's suggestion), the space dimension would simply be the 3-d volumetric container of the ethereal substance of existence; the time dimension would simply be the 'container' of the ephemeral instance of existence; the motion simply renders the mass-energy definitions to the substance in space; while the duration simply renders the definitions to the instance in time.

It is not necessary to ascribe motion (curvature, expansion, etc.) to space. It is enough to have the motion transformations (curvature of motion, acceleration, etc.) - actually the correct picture than the pseudo-picture of the curvature/acceleration of space or space-time.

It is not necessary to have duration reversals in time either. Duration reversal is never a possible effect on duration, since we only a single temporal vector in the time dimension.

KISSing the view for space makes the space dimension the unchanging essence that gets occupied by the ethereal substance which is rendered its definitions by the motion transformations.

KISSing the view for time makes the time dimension the unchanging essence by which we regard the ephemeral instance according to the effects of duration. In the question "What time is it?" - we actually mean the span of duration that has been effected relative to a certain point in time.

One common problem in discussions is the problem of language - our manner of conveying ideas. There is the logical language (properly, the language of words) and there is the mathematical/rational language (properly, the language of numbers). The use of appropriate language to make the discussions understandable is important. This is probably why we have the thread topic "Limits of mathematics in cosmology".

There is a confusion in the use of the mathematical languages in the discussions. The mathematical languages used are either for that of the geometrical or dimensional measurements or for that of the dynamical/mechanical/kinematical or vectorial measurements.

The dimensional measurements are properly for the measurement of the static realities in nature (volumes and lengths in the space and time dimensions). The vectorial measurements are properly for the measurement of the changes in the realities in nature (motion transformations and duration transformation). It becomes a big problem when the mathematical languages are improperly used - the ideas get interchanged and/or confused (mixed up).

If we talk about the dimensions, we need to admit that the dimensions are the unchanging realities. And if we talk about motion and duration, we need to admit that the motion and duration are the carriers or vectors of the change in nature, the essences of the change in nature.

The language of space-time transformations just don't cut the standard for the language. Thus, the idea of space-time transformations is a confusion.

It is more appropriate to consider the transformations in space (not 'of' space) that are effected by motion and the transformation in time (not 'of' time) that is effected by duration, with motion and duration as separate but concurrent realities.

So, duration is not the effect of motion per se. We measure motion against the background space and time dimensions. And we measure duration against the background time dimension with relations that regard certain motions. But motion and duration are concurrent realities, the former with the corporeality and the latter as a purely abstract reality. It does look proper that one would be emergent because of the other, after all they simply co-exists as the two main aspects of the change that occur in nature.

A prime example of the Maths is E=mc2. This formula expresses the idea of velocity or motion transformation that relates the transformation effects in terms of mass and energy.

castel

corrections -

(Duration reversal is never a possible effect on duration, since we only HAVE a single temporal vector in the time dimension.)

and

(It does NOT look proper that one would be emergent because of the other, after all they simply co-exist as the two main aspects of the change that occur in nature.)

Sorry about that...

castel