Reinstating the Timespace Continuum
Some months ago I was pondering how space and time interacted on a fundamental/local level whilst walking home from the shop. I imagined that the ground was divided into a grid of squares, which had numbers on them. To begin with all of the squares were numbered '1', the next second they were numbered '2' and so on... I thought to myself, if I am moving at one square per second then the relationship between my movement and time is symmetric. If I stand still the numbers on the grid change regardless, and the only difference in me moving is which square I stand on at any given second.
In this image we see a man walking. The first line of our space time matrix shows the local time at 1 second. If the man were standing still we could say that he is moving in a vertical direction, downwards with time. If the man moves one square per second then his progression takes a diagonal route down through the matrix (the coloured line). Therefore in order to counteract the downward motion of time, this person would have to be traveling very fast indeed. This is the basic concept behind Einstein's Theory of Relativity, where all speeds are charcterised by a direction in 4-dimensional space-time. I had never fully understood that statement until I began thinking of time in this manner.
As we can see, the diagram divides up the differing speeds into angles of 45 degrees. Ordinary motion takes place at 45 degree angles to time, and light speed travel takes place at a further 45 degrees, making a total of 90 degrees. This is what I think Einstein had originally intended for his diagram of space-time, where 90º equals the sum of all possible speeds, there being no room left for any further acceleration. However, in Minkowskian diagrams the speed of light is often characterised by an angle of 45º, for convenience sake. Although this method allows for further areas of acceleration, these are usually discounted by conjectured time-paradoxes.
This diagram endeavors to show how the different speeds correspond to directions in 4D space-time. The top of the central spike being the sum of all possible speeds is depicted as being at 90º to the slower time-based regions. This diagram also bears relation to the Mexican Hat theory, where the physical laws only appear symmetrical when viewed from the top of the graph i.e. the region of most energy.
With the recent discovery of the neutrino particle traveling faster-than-light, we must logically assume that more potentially feasible regions of acceleration exist in the graphs than previously thought. My own musings on this subject lead to the development of instructive matrices utilising the 45º angle for the 'c' axis, not out of mere mathematical convenience but because that is what makes most logical sense.
The numbers in the first column show the flow rate of time, as observed by an individual (known as A) at rest, where as the diagonal line - consisting entirely of 1s - shows the amount of time experienced by an individual (known as B) traveling at the speed of light. As we can see, if B travels along the diagonal line for 3 seconds and then drops out of light speed, time resumes its normal vertical (downward) tracking. B is now on a different column to A, which expresses the fact that he has moved in space. However, both are on the same row, and indeed can never be on separate rows, because only the present moment exists. Comparing A's clock with B's clock will show a difference of 3 seconds, but the number above and to the right will show the universal time, as marked by all objects in space.
When I speak of 'universal time', I do not refer to the Newtonian concept of absolute time, which is demonstrably false, but rather to the shared commonality of what is known as 'the present' with respect to all reference frames; both of scale and acceleration. While the concept of what constitutes the present may expand i.e. dilate, at speeds approaching that of light, the free-scale nature of space-time prevents this scaled-expansion from being in anyway important to its over-all conception of what constitutes the present.
Einstein's Theory of Relativity states that because the laws of physics are the same (therefore constant) in all reference frames, the point of view of one reference frame is as good as another. So if time has appeared to stop in one reference frame, then this means that time has indeed stopped across the entire spectrum of space and time, based solely on this one reference frame's point of view. This I feel is a grievous error, because as the above matrix shows time is implicit in all motion. If time stops we can still ask how long it stopped for.
In contrast, relativists have always assumed that due to the constancy of physical laws in all reference frames that the space-time continuum must be disconnected and broken up into individual non-relatable fragments. This is to forget that space and time are fundamentally related, that they are a continuum, and that movement in one represents duration in another.
Interestingly, this very matrix appears in a table by 15th Century mathematician and polymath Sir John Dee. Dee claimed to use the table to communicate with angels. Metatron is the leader of the angels, and is also the name of a potent device in the Transformers series; the Metatron Cube. Another device of importance in this series is the Matrix of Leadership. Therefore, being a child of the 80's and a spirited fan of science fiction, I dub the above matrix, the Matrix of Leadership.
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