# Space Dimensions

## 1. Space Types

Newtonian space and time areseparate, unchanging, passive, and absolute backgrounds for matter and motions.

Leibnizian space and time areobject and event relations.

Machian space and time arerelative to matter and energy amounts and relative positions.

Einsteinian space and timeinterrelate, change, are active, and have relative backgrounds for matter andmotions.

Quantum-mechanical space andtime are discrete, and entangled objects stay in direct contact over any spaceand time amount.

## 2. Space-Time

Time and space dimensionsinteract to make one unified space-time. Time dimension relates to spacedimensions by light speed: space-dimension length divided by light speed istime, and time-dimension time times light speed is length. Only light speedmatches experiment and makes special relativity true. All objects move throughspace-time at light speed. Space-time has no time flow or direction, sospace-time represents all previous and future times in the same way as spatial dimensionsrepresent all points in all directions.

## 3. Properties of Dimensions

At scales above subatomicdistances, space dimensions are continuous and homogeneous.

Time dimension is isochronic.Physical processes are the same forward and backward in time. Motions have timesymmetry, which is equivalent to the law of energy conservation.

Space dimensions areisotropic. Physical processes are the same in any space direction anddimension, so directions are equivalent. Motions have spatial symmetry, whichis equivalent to the law of momentum conservation. Only infinite universes canbe isotropic, so finite universes cannot be isotropic.

Physical processes are thesame right-handed or left-handed, so rotation directions are equivalent.Motions have rotational symmetry, which is equivalent to the law ofangular-momentum conservation [Feynman, 1965].

### 3.1. Time

Change shows time. Timeorders changes.

Time flows forward, notbackward. Time flows the same everywhere. Time changes are never symmetric.

However, in space-time, justas all space exists everywhere, all time exists always and everywhere.Space-time does not flow.

### 3.2. Curvature

Space-time dimensions can bestraight or curved.

### 3.3. Quantum Effects

At quantum-mechanicalsizes, space and time dimensions can superimpose and interchange, so dimensionsare neither space nor time.

### 3.4. Lattice

Perhaps, space is a lattice,with particles at nodes. Lattices can have different spatial frequencies andwavelengths.

## 4. Why Space Has Three Dimensions

Universe has three longspatial real-number dimensions (and one long time real-number dimension).

### 4.1. Forces and Energies

If universe has no timedimension and any number of space dimensions, or any number of time dimensionsand no space dimension, motion, energy, momentum, and space-time do not exist.

If universe has one or moretime dimensions and more than three spatial dimensions, gravity andelectromagnetism strengths decrease more quickly with distance, so star andplanet orbits and electron orbits, respectively, are too lightly bound and areunstable. With one or more time dimensions and fewer than three spatialdimensions, gravity and electromagnetism strengths decrease less quickly withdistance, so stars and planets and electrons quickly move to center, and stars,planets, and electrons do not exist.

If universe has more than onetime dimension and one space dimension, fields are unstable. If universe hasmore than one time dimension and more than one space dimension, physical eventsare unpredictable.

### 4.2. Electromagnetism

Electron current, magneticfield, and atom radius define three space dimensions, so electromagnetismrequires at least three spatial dimensions. Space cannot have more than threespatial dimensions, because then electron current, magnetic field, and atomradius have two or more independent relations for electric and magnetic fields.

### 4.3. Entropy

Perhaps, because fewerdimensions make lower entropy, universe has four-dimensional space-time becausethat has lowest entropy consistent with maximum energy. Perhaps, universe hasoptimum number, length, and geometry of space-time dimensions to allow highestnumber of states, most stability, and most symmetries.

### 4.4. Quantum Loop Theory

Quantum-loop intersectiontopology, knots, and kinks define space dimensions, so quantum loops definethree infinite spatial dimensions.

## 5.0. Can Dimensions Change?

Perhaps, dimension number,length, and geometry were or are in flux. Dimension number varies from zero toinfinite. Dimension lengths vary from zero to infinite length. Dimensiongeometries vary from linear to curved to curled up. Perhaps, dimensions evolveby physical processes to stable numbers, lengths, and geometries. Perhaps,energy and matter distributions dynamically determine dimension number, length,and geometry. Perhaps, multiverses or different universe regions have differentdimensions. Perhaps, beginning universe had zero dimensions.

### 5.1. Hidden Dimensions

Perhaps, space has hiddendimensions, so separate universes are at the same space point.

Perhaps, to allowsupersymmetry and supergravity, space-time has extra Grassmann dimensions.

### 5.2. Short Dimensions

Perhaps, space has curled-upreal-number dimensions.

### 5.3. Imaginary-Number Dimensions

Perhaps, space has infiniteand/or curled-up imaginary-number dimensions, and particles are adjacent inthat dimension while apart in real dimensions. Time imaginary-number dimensionhas no direction. Imaginary-number time can be decreasing or increasing, justlike spatial dimensions.

### 5.4. String Theory

String and brane theoriesrequire three infinite spatial dimensions and seven or eight curled-up spatialdimensions.

## Bibliography

Feynman, Richard (1965) TheCharacter of Physical Law. New York: Modern Library.

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Copyright © 2012 JohnFranklin Moore. All rights reserved.