Information theory and dimensionality of space

Area of Science:

• Physics
• Information Theory
• Cosmology

Background:

• Noninteger dimensions are empirically observed in physics.
• Previous studies introduced noninteger dimensions based on experimental needs.
• The theoretical basis for the utility of noninteger dimensions was lacking.

Purpose of the Study:

• To develop an information-theoretic approach for optimal data representation.
• To theoretically explain the physical relevance of noninteger dimensions.
• To apply noninteger dimensions to resolve cosmological measurement discrepancies.

Main Methods:

• Utilizing information theory to define intrinsic data dimensionality.
• Correlating noninteger dimensions with data density.
• Applying the concept of lower density in noninteger dimensions to cosmological data.

Main Results:

• The optimal representation of data intrinsic dimensionality is shown to be noninteger.
• A theoretical justification is provided for the use of noninteger dimensions in physics.
• The lower density associated with noninteger dimensions is used to reconcile differing Hubble constant values.

Conclusions:

• The information-theoretic approach provides a fundamental understanding of noninteger dimensions.
• Noninteger dimensions have measurable physical consequences, including in cosmology.
• This framework offers a novel solution to long-standing problems in measuring the Hubble constant.