Preamble: When absolute space and absolute time were falsified in the
early 20th century, the concept of absolute spacetime scale became
very suspect. Note that the source-free equations of general
relativity (Einstein's equations) and electromagnetism (Maxwell's
equations) are both scale invariant. On the other hand, absolute size
scale seemed to be required empirically. After all, galaxies are very
big, neutron stars are middle-sized and atomic nuclei are very small.
Are they not? Here I will propose a possible resolution to this
paradox.

Context: If our global spacetime has a new symmetry principle called
discrete scale invariance (synonymous with discrete dilation
invariance or discrete self-similarity), then the group structure of
this global spacetime is the Relativistic Similarity Group (aka the
Weyl Group: = Poincare Group + dilation invariance), but it is
globally symmetric under *discrete* transformations of scale, as
opposed to the more familiar and scale-restricted examples of
continuous scale invariance.

The physical embodiment of the new discrete symmetry principle would
be an infinite hierarchical universe of physical systems manifesting
discrete self-similarity. When one observes nature objectively,
emphasizing empirical knowledge and treating most theoretical
assumptions as open to question, then that is precisely what we
appear
to have: a discrete hierarchy of self-similar systems
(i.e., ...galactic systems, composed of stellar systems, composed of
atomic systems, ...). There is considerable evidence for discrete
self-
similarity among analogues on the different cosmological scales. A
veritable cornucopia of observational and theoretical support for
this
paradigm can be found atwww.amherst.edu/~rloldershaw.

In such a universe, a galaxy could be viewed as a galaxy, a neutron
star, or an atomic nucleus depending on the cosmological reference
scale chosen by the observer.

An empirically-based scientific idea this radical has not come along
in a very long time. Absolute scale, beyond the restricted "absolute"
scale that applies only *within* individual cosmological scales,
would
be relegated to the dustbin of history.

Knecht

www.amherst.edu/~rloldershaw

Knecht

www.amherst.edu/~rloldershaw



Knecht ( Robert)

Knecht ( Robert)
You seem to be dealing not in physical science,
but more into philosophy, maybe?
Like :
what is space
and
does it have measurable limits or not?
Questions too broad to have simple answers.

Fractal scales deal in relative measure
and so much in the limits of measuring sticks...
Fractal theoretical zooming in complex dynamics seems to
be stopped only by lack of computing techniques for too big or two small
numbers.
Roger Bagula

On Oct 22, 8:44 pm, Roger Bagula <rlbag...@sbcglobal.net> wrote:



Knecht ( Robert)
You seem to be dealing not in physical science,
but more into philosophy, maybe?
Like :
what is space
and
does it have measurable limits or not?
Questions too broad to have simple answers.




"Space is blue and birds fly in it." - Pauli?



Fractal scales deal in relative measure
and so much in the limits of measuring sticks...
Fractal theoretical zooming in complex dynamics seems to
be stopped only by lack of computing techniques for too big or two small
numbers.
Roger Bagula




There are mathematical fractals and there are physical fractals. There
are fractals with continuous scale invariance and there are fractals
with discrete scale invariance. There are fractals with finite numbers
of levels and there are fractals with infinite numbers of levels.

The application of fractal mathematics and fractal physical models in
the fields of physics and natural philosophy has hardly begun. Nature
abounds with self-similarity and yet most physics books do not even
list self-similarity or hierarchical in their index sections. The term
fractal usually only merits a brief and superficial treatment. What
does that tell you? Those who think physics, and the science of
fractals, are "almost finished" may be in for quite a surprise!

Perhaps their world view *is* almost finished, and now we are on the
threshold of a new fractal paradigm that will finally offer the
unification that natural philosophers have dreamed of for centuries.

Knecht
www.amherst.edu/~rloldershaw




Knecht,

Where do Penrose tilings fit in here?
The problem is of a mathematics not of symmetry,
but of symmetry breaking and the conservation of information
seems to be telling us we haven't got close to understanding nature yet.

I agree that at the moment science is not at an end,
but probably at a new beginning.
Roger Bagula- Hide quoted text -

On Oct 24, 10:39 am, Roger Bagula <rlbag...@sbcglobal.net> wrote:

Where do Penrose tilings fit in here?
The problem is of a mathematics not of symmetry,
but of symmetry breaking and the conservation of information
seems to be telling us we haven't got close to understanding nature yet.

I agree that at the moment science is not at an end,
but probably at a new beginning.
Roger Bagula- Hide quoted text -

Hi Roger,

Thanks for the comments. I have printed them out and I will study them
carefully tonight (actually more like early AM) with my end-of-the-day-
cigar.

But I cannot resist one quick argument. You and virtually all well-
trained physical scientists these days focus almost exclusively on
mathematics. Since you are a mathematician, that makes sense. But
physicists are supposed to be studying nature. When will they realize
that their mathematical myopia is preventing them from understanding
their subject: nature.

Anyone who bothers to study the real world, rather than mathematical
idealizations and abstractions, cannot fail to notice some very
fundamental properties of nature.

1. Nature has a hierarchical organization (how can this be almost
totally ignored?!).

2. Nature's hierarchy is highly stratified (how can this be almost
totally ignored?!).

3. There is compelling evidence for self-similarity between and within
the major stratifications, i.e., Atomic, Stellar and Galactic Scales
(how can this be almost totally ignored?!).

It is like the physicists are so focused on the mathematical trees
that they cannot see the forest, or the planet, or the Solar System,
or the Galaxy,... . And ironically, if they would only take a step
back from their scribblings and look at nature holistically, they
would see a very promising path toward understanding many of their
most irritating mathematical problems: like how to reconcile general
relativity and quantum mechanics.

I do not get it. How can scientists profess to sincerely want to
understand nature, and then turn around and literally ignore its most
fundamental properties?

Then again, maybe the explanation is obvious. When one pushes the
reductionist approach to the extreme and concentrates on individual
isolated systems, then myopia is the unfortunate result.

I am currently reading Prigogine's book; "The End of Certainty", and
am happy to see that I am not the only one out here calling for a more
realistic and holistic physics that puts observations ahead of
theoretical epicycles.

Knecht
www.amherst.edu/~rloldershaw

Anyone who bothers to study the real world, rather than mathematical
idealizations and abstractions, cannot fail to notice some very
fundamental properties of nature.

And you need to study it in order to get those mathematical
idealizations/abstractions in the first place if you want them
to have anything to do with reality.

1. Nature has a hierarchical organization (how can this be almost
totally ignored?!).

2. Nature's hierarchy is highly stratified (how can this be almost
totally ignored?!).

3. There is compelling evidence for self-similarity between and within
the major stratifications, i.e., Atomic, Stellar and Galactic Scales
(how can this be almost totally ignored?!).

You sure? There seem to be some effects that appear on one
scale that don't on the other. For example, quantum particles
can do "odd" things that macroscopic objects just don't seem
to do, at least not easily.

It is like the physicists are so focused on the mathematical trees
that they cannot see the forest, or the planet, or the Solar System,
or the Galaxy,... . And ironically, if they would only take a step
back from their scribblings and look at nature holistically, they
would see a very promising path toward understanding many of their
most irritating mathematical problems: like how to reconcile general
relativity and quantum mechanics.

How does this new approach work, exactly? I'm curious. Can
it be turned into mathematical models of the universe?

I do not get it. How can scientists profess to sincerely want to
understand nature, and then turn around and literally ignore its most
fundamental properties?

Then again, maybe the explanation is obvious. When one pushes the
reductionist approach to the extreme and concentrates on individual
isolated systems, then myopia is the unfortunate result.

However, how can you experiment with the entire universe?
Man is a very small and limited creature. Universe is huge
and vast beyond all imagination. Whaddya do?

As for whether or not scale is absolute, the question you
asked in the subject line, that is still an open problem. Some
theories predict things cannot be smaller than a certain "Planck"
length, around 10^-33 cm. You mentioned this was a problem
with "string theory" type approaches. Not so, it's a fundamental
limit of quantum mechanics. Either new physics takes over when
the scale gets smaller, or that's simply as small as you can go,
in which case scale is indeed absolute.