Limits of mathematics in cosmology

Lev,

I mean that nonlocal communication must instantiate measure criteria not accessible to our low energy domain. Pp. 8 -- 10 of my "time barrier" preprint linked earlier, explains the technical details.

Tom

Tom,

Can you say it in a plain language?

Thanks Tom,

By the way, if you have not already read Paul J Nahin's book, "An Imaginary Tale: The Story of (sqrt of minus one)" I think you would really enjoy it.

Edwin Eugene Klingman

"I don't agree, however, that " ... successive moments of duration are untranslatable into spatial imagery ..." when we allow n-dimension calculus. We simply make the space as big as it needs to be."

Tom,

(You replied in the wrong thread, so I am trying to continue the right one.)

The issue is not resolved with the increase in the dimensionality of the space.

The issue has to do with the ability of any space to support structural events. That is the whole crux of the matter!

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.

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

Edwin,

Basically, but remember the concept of "now" is part of the temporal construct. As such, it's generally considered as a dimensionless point between past and future, since any attempt to measure it constricts down to nothing and logic likes measurements. So in that sense, I'd tend to use the term "extant." Sort of a fuzzy "now," because motion is a prerequisite for change and if we constrict duration to nothing, there is no motion.

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