Limits of mathematics in cosmology

Ed,

Thanks for the advice, but since some of us are not "taking things too seriously", some of us have to. ;-))

Cheers,

--Lev

OK, Lev,

If you're serious, address all of the above...

I'm prepared to.

Edwin Eugene Klingman

Ed,

With all due respect, as I already mentioned, I see the "above" as a soup of contradictions, so, to be honest, I really lost the interest.

Thanks for asking!

OK Lev,

All of the current explanations of physics are irrelevant. It's in your lap now.

Ed

I don't see what you see in this lambda hopping idea, Lev. It postulates that there is no simultaneous particle position and momentum. If that were true, rest mass would be incalculable, spacetime would not be physically real and general relativity would be falsified.

This looks like another version of Mach's Principle to me, which Einstein has already incorporated into GR.

Tom

Lev,

A large part of the reason that theorists turned to extra dimensions, I think, is the problem you describe as "instantiation." Fact is, we only know motion by what motion is not; i.e., relative motion as an instantaneous relation between bodies obviates time dependence.

Jumps in action demand time dependence. We can't have a jump in zero time, so whatever interval "instantiates" the action is measure zero. Measure zero is on the boundary of whatever internal structure may (or may not) exist at a more fundamental level. This leads in a quite natural way to brane models and holography, because the boundary of the boundary is where we receive information from our vantage of d 1 dimensions.

Tom

Thanks, Lev. I'll order Capek's book. 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

Tom,

The hopping is about the pulsational nature of movement which is predicted by the struct hypothesis: in space, you can observe *only* the instantiated events of the corresponding struct.

Lev,

"Pulsating nature of movement" is exactly what wave phenomena instantiate. It is a field action principle. If particle and wave phenomena are unitary (and we in fact know that they are), the pulse informs us of where the particle is (local information) but not where it was or how fast it was going (nonlocal information). The variables are not hidden in 3 1 dimensions, experiment tells us. The encoding must therefore reside in a high order structure.

Tom

Tom,

"The variables are not hidden in 3 1 dimensions, experiment tells us. The encoding must therefore reside in a high order structure."

What do you mean by each of these two statements?

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