Amherst College (Box 2262)

Amherst, MA 01002

e-mail: rlolders@unix.amherst.edu

I am an independent reseacher in the field of cosmology. I am loosely affiliated with Amherst College in Amherst, Massachusetts and do my research there and at the University of Massachusetts.

I am most interested in fractal cosmological models that involve self-similarity. For approximately 20 years I have worked on a particular model referred to as the Self-Similar Cosmological Paradigm. The paradigm proposes the following basic ideas.

- Nature is organized into discrete Scales, e.g., the atomic, stellar and galactic Scales.
- The physics on each Scale is rigorously similar to that on all other Scales.
- For each fundamental system on one Scale there is an analogue system on all other Scales.
- Length (R), time (T) and mass(M) parameters for
analogues on neighboring Scales are related by the following
discrete self-similar scale transformation equations:
R

_{n}= KR_{n-1 }T

_{n}= KT_{n-1 }M

_{n}= K^{D}M_{n-1}

where K and D are empirically determined dimensionless constants equal to about 5.2x1017 and 3.174, respectively.

- The hierarchy of Scales is unbounded, such that there is no largest or smallest object (or Scale) in nature.

A 2-part review paper on this paradigm has been published in the *International Journal of Theoretical Physics*, Vol. 28, No. 6, pgs. 669-694 and No. 12, pgs. 1503-1532, 1989. Enventually these papers will be available at this web site.

The initial purpose of this web page is to provide interested persons with access to my papers on this, and related, topics.

Comments/criticism sent to me via e-mail will be greatly appreciated.

e-mail: rlolders@unix.amherst.edu

- THE SELF-SIMILAR COSMOLOGICAL MODEL: INTRODUCTION AND EMPIRICAL TESTS

*International Journal of Theoretical Physics,***28**(6), 669-694, 1989.

Part 1 of an introductory review of the Self-Similar Cosmological Model, emphasizing the basic ideas and many retrodictive tests.

- A FRACTAL UNIVERSE?

Non-technical discussion of hints that nature might have a fractal structure with discrete Self-Similarity.

- SUCCESSFUL PREDICTIONS OF THREE STELLAR SCALE ENIGMAS

*International Journal of Theoretical Physics,***35**(12), 2475-2481, 1996.

This paper demostrates the predictive power of the Self-Similar Cosmological Model. Three stellar scale mysteries: (1) an unexpected cutoff in the stellar mass function, (2) the unexpected discovery of planets orbiting neutron stars, and (3) the surprising result that Dark Matter objects of about 0.2 solar masses make up at least 50% of the Galaxy, were predicted by the fractal cosmological paradigm.

- A REVIEW OF MASS ESTIMATES FOR GALACTIC DARK MATTER OBJECTS

*Chaos, Solitons and Fractals*, submitted.

An updated review (see #52 for an earlier review) of mass estimates for galactic dark matter objects (MACHOs). The estimates come primarily from gravitational microlensing experiments. The data are consistent with predictions of the Self-Similar Cosmological Paradigm. Trends in the data are discussed, as well as empirical support for a predicted correlation between stellar mass functions and dark matter mass functions.

- AN APPARENT GAP IN THE STELLAR MASS DISTROIBUTIONS AT » 0.7M
_{¤}AND A POSSIBLE EXPLAINATION

*Astrophysics and Space Sciences*, in press.

The Self-Similar Cosmologicl Paradigm definitively predicts that stellar mass functions have anomalous deficits at about 0.73M_{¤}. This prediction is based on the fact that there are no atoms with masses of 5 atomic mass units, hence a gap in the atomic mass function. Mass functions for several stellar samples appear to have the predicted deficit. Prospects for further testing of this prediction are considered.

- CRITICAL TEST OF A FRACTAL PARADIGM: DEFICIT OF PLANETARY SYSTEMS ORBITING RED DWARF STARS

*Astrophysics and Space Sciences*, under review.

The Self-Similar Cosmological Paradigm predicts that lowest mass M-dwarf stars have anormalously few planetary companions, data so far support this prediction.

- THE LEGEND OF COSMOLOGICAL HOMOGENEITY

Various lines of evidence suggest that on the largest scales the structure of the cosmos is fractal, not homogeneous.

- JANUS-FACED COSMOLOGY

*Sky and Telescope*, April, 1998.

Discusses the contradiction between the overly optimistic public face of cosmology and the real situation in the fiels, where we cannot even give a basic description of the cosmos because 90% to 99% of its composition is enigmatic "dark matter". And that is just for starters.

- M-SET AS METAPHOR

Fractal Cosmology for English majors; the beauty and infinite wonders of the mandelbrot set.

- THE GALACTIC DARK MATTER: PREDICTIONS AND OBSERVATIONS

*Astrophysics and Space Science*,**257**(2), 271-278, 1998.

The Self-Similar Cosmological Model's crucial predictions regarding the masses and physical states of the galactic dark matter objects are shown to agree with available experimental evidence, while the Standard Big Bang Model's predictions are not supported. Additional SSCM predictions are discussed.

Links to other websites devoted to fractal paradigms:

- http://rloldershaw.people.amherst.edu/stars2/
- http://www.daec.obspm.fr/users/nottale/ukmenure.htm
- http://www.math.yale.edu/mandelbrot/

Visitors since 09 Feb 2001.

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