Thursday, January 11, 2007

String Theory for My Friends

I’m always delighted when friends make requests for specific PVBlogs. This morning at Starbucks Mark asked for a white paper on string theory. Now, I have the greatest respect for Mark for that magical day in 1955 when he went head-to-head against Jim Brown in a lacrosse match. Some don’t know that Brown was an All-American in lacrosse at Syracuse as well as football. He outweighed Mark by 40-50 pounds of muscle, but Mark made up for it by being … ummm…. slower. Mark is one brave guy. Anyway, in honor of that RPI versus Syracuse lacrosse match, here is a bit of string theory for Mark and the rest of the Starbuckers.

String was invented by the Egyptians back around 4000 B.C. as a thin, flexible version of rope which may be used to tie, bind, or hang other objects. String can be made from a variety of fibres including date palms, flax, grass, papyrus, leather, water reeds or animal hair. The use of the rope version pulled by thousands of workers allowed the Egyptians to move the heavy stones required to build their monuments. (ref. Wikipedia)

Ropes and strings can also be used as flogging device with widely different impact depending on length, weight, number of strands and the presence or absensce of knots. Thus aboard ships, a rope's end or starter was frequently used to administer the lightest discipline to sailors, while the fearsome cat o' nine tails was used for more severe punishment. Mark may have some experience with cats from his days in the navy.

The mathematics of strings began with Euclid who noticed that strings may form a variety of geometrical shapes. Here is a question for the reader: Given a length of string, how many squares may be constructed? How many rectangles?

A few centuries later, Georg Riemann, a student of Carl Gauss, noticed that a string laid on the surface of a sphere can no longer be formed into a perfect square. This seminal discovery led immediately to the invention of non-Euclidian differential geometry and the theory of complex manifolds utilizing the Riemann curvature tensor.

This was a very good thing because, when Einstein derived his theory of General Relativity, in 1915, he needed a mathematical formulation of curved spaces. Einstein rejected the Newtonian theory of gravitational forces believing instead that the Earth sucks. (Sorry…. just a little joke.) No, Einsten believed that matter and energy bend space into a spherical shape and that matter and energy in turn move along the surface of the sphere, like following the piece of string. John Wheeler described it by saying that “matter tells space-time how to curve, and space-time tells matter how to move.” So-long to straight line motion unless there is no mass around.

Once the field equations of General Relativity were in place, Einstein became aware of some disturbing features. He first realized that the presence of matter in the universe meant that a static universe is impossible; it would ultimately collapse. (That sucked!) This was a real philosophical problem for any scientist, even a radical like Einstein, who was raised with Aristotle’s model of an unchanging universe. Einstein was so disturbed by his collapsing universe solution that he concluded the equations needed another term to counteract the attractive force of gravity. He invented the “cosmological constant” term that acted like anti-gravity and allowed the universe to be permanently static.

Not long after, in 1922, the Russian Alexander Friedmann showed that Einstein’s equations also admitted a solution corresponding to an expanding universe and by 1927 Georges Lemaitre had worked out the details. Einstein rejected the solution as un-physical although mathematically correct. But only two years later Edwin Hubble published data showing that stars and galaxies are all receeding, leading to the obvious conclusion that sometime in the past the universe must have burst on the scene from a miniscule point. Lemaitre called it a cosmic egg; Fred Hoyle called it, dismissively, the “Big Bang.” Einstein figuratively kicked himself in the butt for insisting on the cosmological constant and a static universe.

Now what about that Big Bang? Physicists have concluded that at the instant after the bang, the universe must have been so dense and filled with energy to such a degree that gravity had quantum properties. Unfortunately a quantum theory of gravity does not exist. Enter string theory. Underlying the fundamental particles (quarks, etc), string theory assumes there are more fundamental entities having some properties of strings.

The basic strings are mighty small, with a length equal to the “Planck length” (about 10 to the negative 33-power centimeters). Like a violin string under tension, the quantum strings support standing waves, and the fundamental particles of matter are thought to correspond to different vibration frequencies. This is not such an unusual idea as it is related to the wave-particle duality of quantum physics. We do not “see” the stringiness in experiments because its dimension is so very small.

The mass-frequency relationship is easily derived. The Planck-Einstein photo-electric effect showed that energy is related to frequency by the simple relation E = hf, where h is Planck’s constant and f is the frequency. Add to this Einstein’s mass-energy relationship, E = mcc, and we obtain an equation that defines particle mass from the string frequency: m = hf/cc. For the electron, the wave frequency is about 10 to the 21-power cycles/sec, and the proton frequency is about 1840 times higher.

The basic idea is pretty simple, but the theory quickly becomes muy complex. Some of the fundamentals are unsettling (eg 10 dimensions of space) and some are contradictory (eg faster than light particles). But the major problem for string theory is that it has yet to make a testable prediction, and the current thinking is that the theory allows an astronomically large number of physical possibilities so it seems impossible to ever test it. Peter Woit has called the theory “Not Even Wrong,” the title of his recent book. Normally this situation would cause physicists to run for the exits, but string theorists seem to be a hardier lot, not easily frightened.

I’m skeptical.


Blogger Yolo Cowboy said...

I loved the special on string theory that ran on PBS. Not knowing a darn thing about math using ten dimensions, or math using lots of parentheses and letters for that matter, I think the hole in string theory is the theory takes place is structures so small, way beyond sub atomic, that you can't view them. If you cannot observe something, or prove that it exists, is it science or philosophy?

7:42 PM  
Anonymous Anonymous said...

Thanks for the String Theory Piece Bill. Concise summary, nicely done.

Living close to Fermi Lab made it possible for me to take advantage of their public relations outreach efforts over the years and have conversational contact with people seriously immersed in the search for more knowledge in the area of high energy physics. To hear them conjecturing across a cafeteria table about sensible extrapolations in theory based on what is established and being experimentally tested, was eye-opening. Because with each other, they don't have to waste time and words constantly stating that these so-called "particles", are not tiny, solid, things; they mostly seem to agree that a particle is more like "something happening for a while" and when enough such events occur in close enough relative proximity, we detect and conceive of their combined happenings as a larger particle - a proton, for example, could just be the detectable aspect of quarks interacting. (It's important to note that if true, that would mean "protons" don't exist - only quarks interacting in what we have classified as a "proton" way. More about such later here.)

In common line with this view, most modern day educational introductory exposures to chemistry DO leave students with at least a vague impression that matter is actually just a form of energy where the energy's continuing manifestation is motion confined to a very small space.

Even in relaxed settings, these scientists tended to balk at conjectural discussions reaching out more than a logical step or two beyond what is known - accordingly, the most unorthodox physics I heard conjectured by serious credentialed physicists were A) the possibilities that all particles could be patterned disturbances of a dynamic (positionally unfixed) aether of virtual particles (unliked the fixed aether discarded after the world's most famous failed experiment early in the last century) and B) the possibility that the ultimate trivial (simplest) "particle" might (more importantly) be the ultimately simplest unit of existence, leading to musing over whether or not "volumetric space" is itself comprised of "particles" (which, recall, may just be "happenings" instead of "things") Science fiction buffs might consider such theorizing tame and dull, but not these folks - they seem perpetually enthused.

Their sense of wonder at what they are doing, doesn't hinge on the possibility of uncovering a window to an elaborate social reality symbolizing the supremacy of mankind or evidence that a supernatural conscious force in the Universe is the benefactor or tormentor of intelligent natural life forms. To these scientists, a most basic constituent of existence would represent the building block for the genesis of all that is or can be. It's roughly analogous to revering the nearly limitless message conveying potential of a written language's character set's combinatorial possibilities, more than, say, the work's of Shakespeare. Because, the higher order complexity of Hamlet resides in elaborately ordered series of the character set's trivial symbols. And so potentially does every other language-conveyable idea. Still, I admit I had to hear the phrase, "most basic units of existence" several times to think of it seriously, as a candidate for particledom. It has helped me departicalize my "picture" of sub-atomic particles though. Shedding the macroscopic imagery is difficult - ironically the best way to start to build a "picture" of these tiny realms is to remind yourself of what each particle IS NOT!

We must also remember Richard Feynman's admonition that, "If you think you understand quantum mechanics, you don't understand quantum mechanics."

All this being said, string theory can be thought of as a continuation of the search for the most basic units of existence, which started in the modern era with the development of the atomic model. I've been slowly putting together a short description of the implications of what we "know" about energy & matter for friends who are non-scientists to use in developing a less macroscopically conceived model of what is going on at the atomic model layer and on down.

Not an easy vision to maintain for any of us. We ironically dismiss the most potentially insightful revelations as being remotely abstract - overlooking the essence of existence as though we could not be the products of such a freak show. We hear about the latest discoveries in the basic particle realm and although their significance each registers with us intellectually, we don't acknowledge that the totality of what the discoveries imply, transcends our familiar and comfortably approximate notion of reality. It never ceases to amaze me how even scientists default to talking and thinking about quantum scale events in macroscopic reality terms. Unless they are in the middle of writing a book or paper about the subject. And they are often hesitant in media interviews to even mention implications that would not be politically correct or which would turn over sacred apple carts.

Your "so long to straight line motion" line is refreshingly haunting in it's implications, because, Where is there NO gravity? Absolute straightness ITSELF is revealed to be an unrealizable concept. Our notion of motion may not even be the essence of movement.

Meanwhile, we are psychologically chained to the idea of an enveloping metric space and intellectually almost limited to understanding anything only to the degree we can compare it to something else in units of some biological sensory capability which we have.


10:33 PM  
Anonymous Anonymous said...

I really appreciate both your efforts to enlighten us on the subtleties of string theory. I am not yet, however, a true believer.

I find it difficult to reconcile the concept of these sub-atomic particles promiscuously going into and out of existence, with matter as we know it enduring for millennia, or indeed for billions of years.

Does anyone think that the Large Hadron Collider, due to go online this year, will allow us to firm up, clarify or discard any of the theoretical underpinnings of string theory?


10:35 PM  
Anonymous Anonymous said...

It seems to me that, unlike the gradual proof stepped assemblage of Atomic Theory and quantum mechanics, they have with String Theory gone too many theoretical steps beyond what is experimentally provable.

Also, you help me get my premise across by saying "with matter as we know it, enduring..... ". Starting with the totally unsupportable elusion that matter has anything even approaching "solidity" it is not clear that the energy that any piece of matter is made out of, discretely remains the constituting energy that makes up that matter over time.

As for whether the Large Hadron Collider will allow us to firm up, clarify or discard any of the theoretical underpinnings of string theory: They hope it will. But probably not a great deal, although ANY proof would be a big deal.


6:38 PM  
Blogger Bill Lama said...

Dear Phil and Norm,
I truly appreciate your responses to my little piece of string theory. I try to interject some humor to interest my non-scientific friends (all of the Starbuckers) but am actually hoping to get some concepts across to them. Phil's explications are a profound addition to my feeble efforts, and Norm's questions are really good ones.

Phil, Do you still live near Fermi Lab? What a marvelous opportunity to hear real scientists discuss their work. I have thought about traveling to Pasadena to sit in on the Cal Tech Physics Dept colloquia (A school chum heads their quantum computer group) but dread fighting the traffic from Palos Verdes.

I certainly agree that, generally speaking, a particle is more like "something happening for a while." The vast majority of "particles" are short lived thingies. However, to my mind there are exceptions. While a proton may be described as the "combination" of 3 quarks (2 ups plus 1 down) it seems overly humble to call it transitory when the estimated half life is greater than 10^32 years.

I am also fond of the Standard Model of particle physics, particularly for its picture of particles as "patterned disturbances of a dynamic (positionally unfixed) aether of virtual particles," the patterns defined by the symmetry groups. I am also impressed by the "nearly limitless message conveying porential of a written language," and regard that miracle as a gift from God, Who also gave us Newton and Shakespeare.

String theory is certainly a continuation of the search begun by Democritus, but it is motivated by the holy grail: Unification. Most stringers are obsessed with rounding out the Standard Model to include gravitation, ie to quantize gravity and create a "theory of everything." However, their approach has been most unusual, not building on the foundational theory supported by a plethora of experiments and letting theory and experiment evolve together. Rather, string theory has been developed from the top down, relying on the beauty of the mathematics.

Thank you for completing the square on my "so long to straight line motion" line -- indeed, there is nowhere without gravity, so straight line motion is an approximation at best.

I was particularly intrigued by your reading of Einstein: "The increasing presence of those aspects of existence which we partially apprehend and call 'matter' and 'energy' are always associated with increasing local curvature of that aspect of existence which we partially apprehend and call 'space' and this happens so consistently that we can quantitatively predict how this effect will cause the aspects of existence we partially apprehend as 'trajectory' and 'shape' to diverge from the values that would otherwise be expected if the unadulterated structure of metric space was actually a Euclidian 3 axes Cartesian coordinate phenomenon."

I do understand, but it is a bit like reading Thomas Aquinas, and impatience keeps me from the original in both cases. (And I'm lazy.)

I loved your closing thought: "Still, what could be more charming than to be able to contemplate being the ultimate self-aware product of the randomly patterned entanglements of incomprehensibly trivial units of existence?" To me, the charm is only enhanced by comprehending the Creator, Who made it all possible.

As for the Large Hadron Collider (Norm) every new tool reveals new phenomena and new particles (patterned entanglements) and I expect the LHC to be no different. However, its upper energy limit is to be around 14 TeV (14 x 10^12 eV) that gets nowhere near the Planck energy (10^19 GeV = 10^28 eV) where strings live or even the Grand Unification energies (10^15 GeV = 10^24 eV). Still, it should be interesting.

Stringing along with my friends,

6:44 PM  
Anonymous Anonymous said...

Hello Bill:

Keep these coming --- I really enjoy them....


6:46 PM  
Anonymous Anonymous said...

Phil you are right absolute straightness is like absolute motionless.

No such thing.

And I agree they have gone way beyond what is or will be provable in the near future, however at the beginning of the last century data suggested the structure of an atom with negatively charged particles orbiting around a positively charged core would be physically unstable.

Maybe string theory will hold up and be proven by the beginning of the next century.

While I have commented on science and other self evident subjects it seems to threaten Bill so he deletes them and Bill like the speed of light is constant in this.


7:42 PM  
Blogger Bill Lama said...

You just can't resist taking a shot. But I'm going to let it stay since the rest of your comment was rational and not insulting.

8:59 PM  

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