فضای کمی: مدلی از جهان - انحنای فضا - بیگ بنگ - جرم سیاه

THE POINT. QUANTIZING SPACE AND TIME Physical space, with everything that is contained in it, forms the Universe. It is a material space, unlike mathematical spaces. Any space consists of points. The point is the basic brick out of which the entire universe is made. All structures that exist in space consist of points. In a geometric space points are undefined and no dimension is associated with them; they are infinitely small. To form a segment of a given size an infinite number of points is needed. No matter how small an infinitesimal element dx might be, it consists of an infinite number of points. In a continuous mathematical space, no physical properties are associated with a point. All points are identical. The dimensionless point cannot be represented graphically nor visualized mentally. It is infinitesimally small, it vaporizes into nonexistence, through an absolute zoom. We'll never encounter it, we'll never locate it. We might as well say it doesn't exist. In mathematics such points form a space which is continuous, infinite and boundless. Fallacy: How can we form objects of size (length, area, volume) out of dimensionless points? An infinite number of non-dimensions cannot generate dimensions. One cannot form segments, areas or volumes by endlessly melding dimensionless points together. Or, to put it otherwise: No combination of dimensionless things can result in anything with a dimension. We are forced to assign a dimension to the point, a radius, however small. The point thus becomes a quantum of space; its diameter represents the smallest possible infinitesimal element.