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Tiny Geometries
…partially inspired by Ray Lynch’s wonderful piece of music “Tiny Geometries” on his album “Deep Breakfast”.
Tiny geometries,
At existence’s core,
Time and space intermixed,
Seething evermore1.
With bits of time
And bits of space
No further divisible2
This the secret, this the door,
To wherefores still invisible3.
Through superposition,
Dawns reality4.
The rare near impossible,
The norm, certainty5.
Dimensions saved,
Held from collapse
Through time irreversible.
Space of no utility,
Both back and forth traversable6.
In shrunken dimensions
Particles arise7—
Tremors in loops of string
All structure supplies8.
What hidden laws,
What mysteries
Ordain the permissible?
Will we through knowledge glean the Whys,
Or sigh, things inexplicable?
©2009, Richard Puetter
All rights reserved.
Notes
Dear reader, this is another “physics” poem. Sorry, but they appeal to me so much. There are many popular writings that will help those unfamiliar with these topics. Topics covered here are quantum gravity, string theory, and the making of Universes through the superposition of all possible states. There are good articles on Wikipedia on these topics and in the science magazine Scientific American. I am also willing to answer to the best of my ability questions sent to me via e-mail.
Very best regards,
Rick
[1]The properties of matter are currently thought to be determined by geometric structures in miniscule "folded-dimensions". So, on the microscopic scale, tiny geometries determine all. Time and space always intermix because of special relativity, but on the smallest scales, time can "briefly" run backwards and be reversible (cause and effect need not be time-ordered at least not for short periods), i.e., "effects" can actually precede "causes".
[2]There is a smallest unit of time, the Planck time (roughly 5.4x10-44 sec), and a smallest unit of space (Planck length, approximately 1.6x10-33 cm), the distance light travels in a Planck time.
[3]In quantum mechanics time and space are continuous, i.e., there is no smallest unit of either quantity, which is convenient since quantum field equations can then be functions of a continuous coordinate system. However, in quantum gravity, time and space themselves must be quantized. This poses serious problems since now standard tricks cannot be used to write down the field equations as the coordinate system itself is discrete.
[4]Reality is a superposition of all possible states. One approach in trying to understand the properties of our 4-dimensional Universe (I’m referring to 1 time dimension and 3 space dimensions and momentarily ignoring rolled up small dimensions from which matter may be comprised—see note [7]), is to form a superposition of all possible 4-dimensional universes, and then take the average as this should provide a accurate picture of reality.
[5]This is a common tautology in statistical mechanics. Since the average of the superposition of all possible states is the most likely reality (by astronomically large probabilities, i.e., a certainty), the nature of reality reflects the typical state in the ensemble of all possible states. So the norm reflects the average (i.e., reality) and one will never see a reality characteristic of an atypical state.
[6]Studies that try to understand the properties of our 4-dimensional space-time have found that without one of the dimensions (i.e., what we call time) being irreversible, the average of the ensemble of all possible Universes typically collapses to lower dimensional structures. So it seems that one of the only ways quantum mechanically to build a 4-dimensional universe is to have one of the dimensions irreversible, e.g., one can only go forward and not back in this dimension, just like we have with time. Indeed, this may be the single, most important property that distinguishes space and time. In space, you can go back and forth. In time, you cannot.
[7]In modern string theory the particles of matter are made up of strings that live in “folded-up” dimensions, i.e., dimensions that are microscopically small and which have not participated in the expansion of the Universe as have our more familiar 3 spatial dimensions.
[8]Vibrations in the string structures of string theory and the geometric properties of these strings are now thought to give rise to all of the different families of fundamental particles.