Tiny Geometries

the mysterious structures latent in the Universe

Free computer wallpaper from plasmator.net. Image available at http://www.plasmator.net/wallpaper/GridBall.jpg

 

Tiny Geometries

 

     …partially inspired by Ray Lynch’s wonderful piece of music “Tiny Geometries” on his album “Deep Breakfast”.

(see, for example, http://www.last.fm/music/Ray+Lynch/_/Tiny+Geometries)

 

 

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.

Author's Note

6-5-6-5-4-4-7-7-8 meter, abcbdefbf rhyme, with f repeating identically in all three verses. Yep, pretty complicated, just like Nature.

I will answer manyantler's questions here since I think there will be others interested in the answers as well.

First, I'd like to comment on Zeta-Reticuli, which is a double star (binary) system in our galaxy. It is not a galaxy of it's own. Galaxies have hundreds of millions to tens of billions of stars. So a two-star system doesn't qualify as a galaxy. Also, binary star systems are very common. Single stars, like our sun, are in the minority. Double stars, triple stars, quadruple star, etc. happen all the time. When star systems form, the massive systems generally form more than one star. When the system isn't massive enough to form multiple stars, solar systems form out of what's left over. So it is thought that lower mass stars, like our sun, will generally be found with solar systems (planets). In the more massive systems, those with multiple stars, any planets in solar systems are likely to be thrown out of the system by gravitational interaction with the stars of the system. So these would most likely not have planets except way out, past the orbits of the multiple star systems (in such systems the multiple stars orbit around each other).

Now as to how we know the age of our sun, that is rather simple actually. Scientist have extremely good models of stellar structure and stellar evolution. We can predict from first principles all of the different kinds of stars that we see in the sky. We know how massive they are, how hot they are, and how long they live before they turn into a supernova. Extensive observations of clusters of stars can see all of the different kind of stars and can see that the more massive stars have already turned off of the main sequence (this is when stars burn hydrogen in their cores) and have gone into the red-giant phase. This is exactly as predicted by our models and we can use this to date the age of globular clusters (large groupings of stars that have all formed at roughly same time). This precise agreement with theory gives great confidence that we know what is going on in stars. We can also look at the heavy elements produced in stars in their normal burning cycle and in the supernovae phase. This, too, agrees with theory and is another check that we have it right. So from all of this we know that our sun is roughly 5 billion years old. This also agrees well with our independent dating of the age of the earth at roughtly 4.5 billion years old. So this is yet another independent check that we understand the structure and evolutionn of stars. So in another 5 billion years our sun will also turn off the main sequence (it will have exhausted all the hydrogen in its core) and begin to expand and become a red-giant, engulfing the earth (our orbital distance will actually be inside the sun). However before that happens, in about 2-3 billion years, our galaxy, the Milky Way, will have collided with Andromeda, the other large galaxy in our local group of about 20 or so galaxies. This collision will probably knock the sun out of its orbit in our galaxy, but it would probably be too weak to strip off the planets from the sun (at least the inner planets). The collision will be generally disruptive of the galaxy and as the stars from each of the two colliding galaxies coalesce, a new, combined, bigger galaxy will form. From observations, astronomers can see that this is a common occurance in the Universe. Galaxies collide all the time and it is an extremely violent event.

Reviews

[Greg Close]

Rick - really like the style and love the topic. Nothing like a poem about subatomic particles to get my juices flowing. This actually reminded me of a Rush lyric by Neil Peart for the song Natural Science (Permanent Waves, rel. 1980). For no particular reason, just in general flow of the rhythm and the deft but accessible scientific bent of the subject matter.

[JC]

WOW.... everything about this is complicated. Although I will admit to knowing anything on the subject, I did like the rhyming scheme and meter.

Thanks for the invite!

JC

[Nancy Lee Shrader]

Well Done Rick. Such a difficult write done so well. Keep it up.

[papaed]

Wonderful! Any one who has read or studied any of this has asked the question... will we every understand the whys? Once again an engrossing subject and a captivating read. The concept that time cannot be reversible or the whole space-time structure may collapse is not surprising, but a new thought in this context for me. However, how the matter in strings is thought to not participate in their expansion of the universe seems to place it outside of the 'time' part of the previous thought. How can that be? The 'why' is understandable only if some 'how' can be explained. Thanks so much for the stimulation.

papaed

[Legion]

Well, I like it. Always with the question why? No matter what answer(s) we find, it will only bring more questions. A good write. I haven't been on much of late. Trying to move into a new house as well as new responsibilities in my job. Hope to correct that problem soon though. Keep up the good work.

[Andrew (not Andy, A.J. ..]

Ye cods Rick, this was confusing!
I liked the poem, but all the notes did was confuse me further and distract me from the poem(by the way, there was less poem than notes)
Anyway, that's the only thing that confused me (other than the Author's note) so good job! Keep writing.
--Andrew

[Dianah]

Wow...what a poem. I thought I understood it until I read the notes.(only joking) I find physics totally fascinating and love reading poetry about it...so refreshing. Thanks for your review of 'Nothing is solid'.
I am someone who picks up bits of Scientific knowledge from TV programmes and the odd Science mag I read I appreciate comments from a pro. Thanks.

Dianah

[Ellen Hammond]

Wow an outstanding poem and a physics lesson too. I will not pretend to understand all the data but the poem structure is, rhyme and flow is wonderful. Thanks for the thoughts to ponder.

[Mark]

Might as well have been written in cuneiform, ole son. Didn't get a word of it, content-wise...But you knew that would be the case, didn't you? As a poem, I enjoyed the flow of the words, with their contrived but still regular rhyming pattern. My greatest kudos go to the poet, whose mission seems to be to strive to make the incomprehenble less so, which may be the common purpose of all us poets, wot?

[Sheila Kline]

Absolutely a complicated meter scheme, but am I surprised? NO!! A topic that I know virtually little of except the meaning of the word, and basic principles of GEOMETRY...no more!...but, yet your write is most intriguing and interesting as I scan through your explanations.
The picture certainly defines much as it is truly representative of the web of knowns intricately woven to the knowns, but still possibly meandering out to the field of the unknowns...ah, discovery yet to be found by the physicist as you!
I find the write interesting, and will surely require a bit...no a lot more...study to understand, but I am willing to partake in it!
Thank you for sharing yet another fascinating topic to broaden my field of understanding into this wonderful world of time and space!....as you ascertain it! Your write is indeed fascinating, and I find the second verse to be most intriguing!....
"Through superposition...all preordained?
Dawns reality...ah ha it sinks in!
The norm certainty...we have come to expect the average?, that which is deemed acceptable?..by what rules/laws/set of standards?
Held from collapse
Through time irreversable.....cannot go back and change, woven together?
and the closing..just love the explanation of time vs space

The rare near impossible.....not impossible, but near impossible.....I like the way it is not absolutely "proven"...the near.

Wonderful, and stunning write from the brilliant mind of Scientist Rick Putter!