Mathematics of Space and Time

mountain-mcescher

Mathematics brings to us the fundamental idea of SEQUENCE. When we count numbers we are following a sequence.

A sequence consists of arrangement of items. The sequence is there because we compare the items in a certain way. There is sequence in time. There is sequence of logic. There is sequence in terms of heights. In fact, sequence is possible in terms of any characteristic.

So, underlying a sequence there is a criterion. It forms the basis of the sequence. Space and time seems to offer the fundamental basis and criteria for sequence.

Both space and time are infinite when undisturbed. When  disturbance takes place space and time seem to become segmented into finite intervals. The “finite interval of space” is the wavelength; the “finite interval of time” is the period.

As the “wavelength” increases or decrease, the “period” also increases and decreases according to a constant ratio. The constant “c”, or “speed of light”, seems to represent this ratio. As wavelength goes to infinite, the period also goes to infinite. It appears that the limiting value of “infinite wavelength over infinite period” is the same constant “c”. This constant may even apply to undisturbed space . This means that space and time are fundamentally entwined in some definite way. Space cannot occur without time; and time cannot occur without space. We define this constant “c” in terms of arbitrary units of length and time. But the constant “c” is not arbitrary.

All sequences seem to be based one way or other on the constant “c”.

To summarize the above, all items in a sequence must have bounds so we can identify and compare them. No bounds apply to undisturbed space and time, which have the characteristic of being infinite. Bounds emerge when there is disturbance of space and time. The disturbance has wave characteristics. Space and time become segmented into sequence of wavelengths and periods. The wavelengths and periods support a constant ratio. We represent this ratio by the constant “c”.

The constant “c” has the unit of “length over time”, which is same as the units of speed. But there is nothing moving in space and time. What we have is disturbance of space and time. Here we may have a real definition of “point”. This “point” has dimensions of wavelength and period.

This “point” starts out with infinite dimension of undisturbed space-time. The “point” reduces in dimension as frequency of disturbance increases. It is possible that “point” at the level of matter is the size of de Broglie’s wavelength.

This makes it possible to do away with the arbitrary notion of Euclidean point.

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