Thursday, June 28, 2012

Einstein and Space-Time Continuum

Artist concept of Gravity Probe B orbiting the Earth
to measure space-time, a four-dimensional description
of the universe including height, width, length, and time.
Matter changes the geometry of spacetime, this (curved) geometry being interpreted as gravity. The grid lines do not represent the curvature of space but instead represent the coordinate system imposed on the curved spacetime, which would be rectilinear in a flat spacetime. (wikipedia)

Space-time continuum (spacetime) is common parlance in today's scientific talk but during most of the history of humanity this has not been so.

The geocentric world view that ruled until the beginning of 16th century AD is natural to us. Our brains conceptualized the world on the basis of what we could observe around us and up there on the sky.

Our everyday experience also makes it natural to think that time progresses at a fixed rate of days and nights, months and years, hours, minutes and seconds. Saying otherwise sounds rather counter-intuitive if not outright crazy.
In non-relativistic classical mechanics, the use of Euclidean space instead of spacetime is appropriate, as time is treated as universal and constant, being independent of the state of motion of an observer.
In relativistic contexts, time cannot be separated from the three dimensions of space, because the observed rate at which time passes for an object depends on
  • the object's velocity relative to the observer and also on
  • on the strength of gravitational fields, which can slow the passage of time.

Euclidian space
Euclidean space is the three dimensional geometric world in which we recognize width, length and height. That space is so familiar to us and is ruled by the fundamental axiom that parallel lines never cross. From this it has been possible for humanity to build Euclidian geometry to measure spatial things for example with the help of trigonometry.

Measuring spatial things was figured out already by the ancients already in the earliest cultures so that Pharaonic Egyptians living on the shores of the Nile, the Sumerians in Mesopotamia (the Land between the Rivers), the inhabitants of Hindus Valley, and the gifted people inhabiting Yellow River Valley in China. Engineers and architects and government officials used ropes and sticks and advanced calculations to control the proportions of temples and public buildings, the taxation of cultivated land and other things.

The honour of the name for geometry of parallel lines not crossing goes to the Greek genius Euclid who lived in Alexandria, Egypt, during the rule of king Ptolemy I (323-283 BC).

Albert Einstein
Portrait of Albert Einstein 1921
It has taken some very advanced and expensive instruments and experiments to verify that Einstein actually was right when he claimed just by figuring things out in his brilliant mind that even time itself is relative to space and movement.

Theory of Relativity has since become a common word in everyday parlance implying something incredibly clever and hard to understand.

Allow me to remind the reader of a blog talking about Theology that Albert Einstein (1879-1955) belongs to the chosen people of God of Israel. Founders of the modern State of Israel actually invited him to become the first President - an invitation he declined the job being taken by another eminent scientist, Chaim Weizmann. Einstein can thus be considered one of the divine gifts God has bestowed upon the humanity He has made out of dust - star dust that is!

Single manifold
We all enjoy the pure logic, pure science of Euclidian space - and then some Mr Einstein has to go to mess up the beautiful theory that during millennia has so brilliantly served humanity. Single manifold, is it single or many?
From a Euclidean space perspective, the universe has three dimensions of space and one dimension of time. By combining space and time into a single manifold, physicists have significantly simplified a large number of physical theories, as well as described in a more uniform way the workings of the universe at both the supergalactic and subatomic levels.

When dimensions are understood as mere components of the grid system, rather than physical attributes of space, it is easier to understand the alternate dimensional views as being simply the result of coordinate transformations.
Note the word simply so innocently used by the anonymous contributor to the wikipedia article I am digesting here!

Spacetime in Cosmology
In cosmology, the concept of spacetime combines space and time to a single abstract universe.

Mathematically it is a manifold consisting of "events" which are described by some type of coordinate system. Typically three spatial dimensions (length, width, height), and one temporal dimension (time) are required.

Dimensions are independent components of a coordinate grid needed to locate a point in a certain defined "space". For example, on the globe the latitude and longitude are two independent coordinates which together uniquely determine a location.

In spacetime, a coordinate grid that spans the 3+1 dimensions locates events (rather than just points in space), i.e. time is added as another dimension to the coordinate grid. This way the coordinates specify where and when events occur.

However, the unified nature of spacetime and the freedom of coordinate choice it allows imply that to express the temporal coordinate in one coordinate system requires both temporal and spatial coordinates in another coordinate system.

Unlike in normal spatial coordinates, there are still restrictions for how measurements can be made spatially and temporally (Spacetime intervals). These restrictions correspond roughly to a particular mathematical model which differs from Euclidean space in its manifest symmetry.

Read the entire wikipedia article from here.

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