What Makes Your Jaw Drop?

[terdancam]

Had an idea for an interesting thread after reading this in BusinessWeek.

I`ve always thought that the world is divided into two camps............us thickies and the really really clever people who are so clever they are called Mr.Clever and live in Clever Street.

So what piece of scientific stuff have you found out that just makes your jaw drop?

Something that whooshes so far over your head, its flying with the jumbos?

Something that is so amazing that it makes you reevaluate how pointless your own job is!

Heres mine:

"A tuning fork's pitch depends on the size of its tines. With really tiny tines, you can figuratively play molecular music -- as a team from the California Institute of Technology has done. Physicist jack Ya-Tang Yang told the APS meeting that the team has weighed an extremely small mass -- just a few dozen Xenon atoms -- spraying them on silicon-carbide tines a mere 100 nanometers long. The added weight noticeably slows the tines' vibrations, and the mass that was applied is then calculated from the frequency change. So how few atoms can the tuning fork weigh? About 30, or a mass of seven zeptograms (seven trillionths of a nanogram). Detecting such minuscule quantities is essential for drug research, toxin detection, and more."

By Burt Helm Cited:BusinessWeek 11/05/05

[harlowrog]

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[harlowrog]

Had an idea for an interesting thread after reading this in BusinessWeek.

I`ve always thought that the world is divided into two camps............us thickies and the really really clever people who are so clever they are called Mr.Clever and live in Clever Street.

So what piece of scientific stuff have you found out that just makes your jaw drop?

Something that whooshes so far over your head, its flying with the jumbos?

Something that is so amazing that it makes you reevaluate how pointless your own job is!

Heres mine:

"A tuning fork's pitch depends on the size of its tines. With really tiny tines, you can figuratively play molecular music -- as a team from the California Institute of Technology has done. Physicist Jack Ya-Tang Yang told the APS meeting that the team has weighed an extremely small mass -- just a few dozen xenon atoms -- spraying them on silicon-carbide tines a mere 100 nanometers long. The added weight noticeably slows the tines' vibrations, and the mass that was applied is then calculated from the frequency change. So how few atoms can the tuning fork weigh? About 30, or a mass of seven zeptograms (seven trillionths of a nanogram). Detecting such minuscule quantities is essential for drug research, toxin detection, and more."

By Burt Helm Cited:BusinessWeek 11/05/05

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You need to get out more. :duh:

[Anees]

ZZZZZZZZZZZZZZzzzzzzzzzzzzzzzzzzzzzzzzzz (sorry!)

[Monster-Mat]

i know where your coming from, what amazes me are

String Theories

A Good Website

BY WAY OF INTRODUCTION

"There was a time when the newspapers said that only twelve men understood the theory of relativity. I do not believe that there ever was such a time... On the other hand, I think it is safe to say that no one understands quantum mechanics... Do not keep saying to yourself, if you can possibly avoid it, 'But how can it be like that?', because you will get 'down the drain' into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that."

R. P. Feynman (1967)

"The first processes, therefore, in the effectual studies of the sciences, must be ones of simplification and reduction of the results of previous investigations to a form in which the mind can grasp them."

J.C. Maxwell, On Faraday's lines of force

" ...conventional formulations of quantum theory, and of quantum field theory in particular, are unprofessionally vague and ambiguous. Professional theoretical physicists ought to be able to do better. Bohm has shown us a way."

John S. Bell, Speakable and Unspeakable in Quantum Mechanics

"It would seem that the theory [quantum mechanics] is exclusively concerned about 'results of measurement', and has nothing to say about anything else. What exactly qualifies some physical systems to play the role of 'measurer'? Was the wavefunction of the world waiting to jump for thousands of millions of years until a single-celled living creature appeared? Or did it have to wait a little longer, for some better qualified system ... with a Ph.D.? If the theory is to apply to anything but highly idealized laboratory operations, are we not obliged to admit that more or less 'measurement-like' processes are going on more or less all the time, more or less everywhere. Do we not have jumping then all the time?

The first charge against 'measurement', in the fundamental axioms of quantum mechanics, is that it anchors the shifty split of the world into 'system' and 'apparatus'. A second charge is that the word comes loaded with meaning from everyday life, meaning which is entirely inappropriate in the quantum context. When it is said that something is 'measured' it is difficult not to think of the result as referring to some pre-existing property of the object in question. This is to disregard Bohr's insistence that in quantum phenomena the apparatus as well as the system is essentially involved. If it were not so, how could we understand, for example, that 'measurement' of a component of 'angular momentum' ... in an arbitrarily chosen direction ... yields one of a discrete set of values? When one forgets the role of the apparatus, as the word 'measurement' makes all too likely, one despairs of ordinary logic ... hence 'quantum logic'. When one remembers the role of the apparatus, ordinary logic is just fine.

In other contexts, physicists have been able to take words from ordinary language and use them as technical terms with no great harm done. Take for example the 'strangeness', 'charm', and 'beauty' of elementary particle physics. No one is taken in by this 'baby talk' ... Would that it were so with 'measurement'. But in fact the word has had such a damaging effect on the discussion, that I think it should now be banned altogether in quantum mechanics."

J. S. Bell, Against "Measurement"

"Is it not clear from the smallness of the scintillation on the screen that we have to do with a particle? And is it not clear, from the diffraction and interference patterns, that the motion of the particle is directed by a wave? De Broglie showed in detail how the motion of a particle, passing through just one of two holes in screen, could be influenced by waves propagating through both holes. And so influenced that the particle does not go where the waves cancel out, but is attracted to where they cooperate. This idea seems to me so natural and simple, to resolve the wave-particle dilemma in such a clear and ordinary way, that it is a great mystery to me that it was so generally ignored."

J. S. Bell, Speakable and Unspeakable in Quantum Mechanics

"...in physics the only observations we must consider are position observations, if only the positions of instrument pointers. It is a great merit of the de Broglie-Bohm picture to force us to consider this fact. If you make axioms, rather than definitions and theorems, about the "measurement" of anything else, then you commit redundancy and risk inconsistency."

J. S. Bell, Speakable and Unspeakable in Quantum Mechanics

"To outward appearance, the modern world was born of an anti religious movement: man becoming self-sufficient and reason supplanting belief. Our generation and the two that preceded it have heard little of but talk of the conflict between science and faith; indeed it seemed at one moment a foregone conclusion that the former was destined to take the place of the latter. ... After close on two centuries of passionate struggles, neither science nor faith has succeeded in discrediting its adversary.

On the contrary, it becomes obvious that neither can develop normally without the other. And the

reason is simple: the same life animates both. Neither in its impetus nor its achievements can science go to its limits without becoming tinged with mysticism and charged with faith."

Pierre Thierry de Chardin, "The Phenomenon of Man"

A. OVERVIEW OF STRING AND SUPERSTRING THEORIES

String theories aim to unify two apparently disparate physical theories: QFT (Quantum Field Theory) and the General Relativity Theory GRT). QFT stipulates the exchange of point-like particles. These exchanges result in the emergence of the four physical forces (weak, strong, electromagnetic and gravity). As the energy of these interactions increases, the forces tend to merge until they become a single, unified force at very high energies. The pursuit of a Grand Unified Theory or, even, a Theory of Everything - is not a new phenomenon. Einstein's Special Theory of Relativity (SRT) (preceded by Maxwell) unified the electromagnetic forces. Glashow, Salam and Weinberg unified the electroweak forces. In the Standard Model (SM), the strong and electroweak forces attain the same values (i.e., are the same) at high energy and gravitation joins in at even higher energies.

GRT and QFT are mathematically interfaced. Macro-objects (dealt with in the GRT) tend to create infinite spacetime curvature when infinitely compressed (to become point particles). The result is a "quantum foam" which really reflects the probabilities of point particles. But relativistic QFT fails to account for gravity. It copes well with elementary particles but only in an environment with a vanishingly weak force of gravity. Some physicists tried to add a "graviton" (gravity force carrying particle) to QFT - and ended up with numerous singularities (particle interactions at a single point and at a zero distance).

Enter the strings. These are 1-dimensional (length) entities (compared to zero-dimensional points). They move across the surface their "worldsheet". They vibrate and each type of vibration is characterized by a number which we otherwise know as a quantum number (such as spin or mass). Thus, reach vibrational modes, with its distinct set of quantum number corresponds to a specific particle.

String theories strive to get rid of infinities and singularities (such as the aforementioned infinite curvature, or the infinities in the Feynman diagrams). They postulate the existence of matter-forming, minuscule, open or closed, strings with a given - and finite - length. The vibrations of these entities yields both the four elementary forces and four corresponding particles. in other words, particles are excitatory modes of these strings, which otherwise only float in spacetime. The string tension being related to its length, strings need to have a Planck length to be able to account for quantum gravity. One of these states of excitation is a particle with zero mass and 2 spin units - known in Quantum Theory of Gravity (QTG) as "graviton". Moreover, strings tend to curl (though, counterintuitively, they are wrapped around space rather than in it - very much like the topological chimeras the Mobius strip, or the Klein bottle). Mathematics dictate an 11-dimensional universe. Four of its dimensions have "opened" and become accessible to us. The other 7 remain curled up in a "Calabi-Yau space" in which strings vibrate. In later version of string theory (like the M-Theory), there is a 7-dimensional, curled up Calabi-Yau space wrapped on every 4-dimensional point in our universe. But Calabi-Yau spaces are not fixed entities. New ones can be created every time space is "torn" and "repairs" itself in a different curvature. Lastly, strings merge when they interact, which is very useful mathematically-speaking. Technically speaking, one of 2 interacting strings "opens up" in an intermediate phase - and then closes up again.

But what is the contribution of this hidden, strange world and of the curling up solution to our understanding of the world?

String theories do not deal with the world as we know it. They apply in the Planck scale (where quantum gravity prevails). On the other hand, to be of any use, even conceptually, they must encompass matter (fermions). Originally, fermions are thought to have been paired with bosons (force conveying particles) in a super-symmetric, superstring world. Supersymmetry broke down and vanished from our expanding Universe. This necessitated the "elimination" of the extra-dimensions and hence their "compactification" (curling up).

Moreover, some string theories describe closed but openable strings - while others describe closed and NON-openable ones. To incorporate Quantum Mechanics (QM) fully, one needs to resort to outlandish 26 dimensional universes, etc.

Still, string theories are both mathematically simpler than anything else we have to offer - and powerfully explanatory.

Abstract

Strings

Strings are described as probabilistic ripples (waves) of spacetime (NOT in a quantum field) propagating through spacetime at the speed of light. From the point of view of an observer in a gravitational field, strings will appear to be point particles (Special Relativity). The same formalism used to describe ripples in quantum fields (i.e., elementary particles) is, therefore, applied.

Strings collapse (are resolved) and "stabilize" as folds, wrinkles, knots, or flaps of spacetime.

The vibrations of strings in string theories are their probabilities in this theory (described in a wave function).

The allowed, netted resonances (vibrations) of the strings are derived from sub-Planck length quantum fluctuations ("quantum foam"). One of these resonances yields the graviton.

Strings probabilistically vibrate in ALL modes at the same time (superposition) and their endpoints are interference patterns.

D-branes are the probability fields of all possible vibrations.

The Universe

A 12 dimensional universe is postulated, with 9 space dimensions and 3 time dimensions.

Every "packet" of 3 spatial dimensions and 1 temporal dimension curls up and creates a Planck length size "curled Universe".

At every point, there are 2 curled up Universes and 1 expressed Universe (=the Universe as we know it).

The theory is symmetric in relation to all curled Universe ("curl-symmetric").

All the dimensions - whether in the expressed Universe (ours) or in the curled ones - are identical. But the curled Universes are the "branches", the worlds in the Many Worlds interpretation of Quantum Mechanics.

Such a 12 dimensional Universe is reducible to an 11 dimensional M Theory and, from there, to 10 dimensional string theories.

In the Appendix we study an alternative approach to Time:

A time quantum field theory is suggested. Time is produced in a non-scalar field by the exchange of a particle ("Chronon").

We use Perturbation Theory (PT) To compute QM amplitudes. We simply add up contributions from all the orders of quantum processes. To be effective, contributions need to get smaller (until they become negligible) the "higher" we climb the order hierarchy. The computation of the first few diagrams should be yield an outcome asymptotic to "reality". This is necessary because in point-like particle field theories, the number of diagrams required to describe higher orders grows exponentially and demands awesome computing power.

Not so in string theories. Holes and "handles" (protrusions) in the worldsheet replace the diagrams. Each PT order has one diagram - the worldsheet. This does not alleviate the mathematical complexity - solving a 2-handle worldsheet is no less excruciating than solving a classic PT diagram. But if we want to obtain complete knowledge about a quantum system, we need a non-perturbative theory. PT is good only as an approximation in certain circumstances (such as weak coupling).

MORE ON THE INNER WORKINGS OF STRING THEORIES

String vibrate. In other words, they change shape - but revert to their original form. Closed strings are bound by boundary conditions (such as the period of their vibration). Open strings also succumb to boundary conditions known as the Neumann and Dirichlet boundary conditions. Neumann allowed the end point of a string free movement - but with no loss of momentum to the outside. Dirichlet constrained its movement to one "plane" (or manifold) known as a D-brane or Dp-brane (the "p" stands for the number of spatial dimensions of the manifold). Thus, if a spacetime has 11 dimensions - of which 10 are spatial - it would have a D10 D-brane as its upper limit. p could be negative (-1) if all space and time coordinates are fixed (and "instanton"). When p=0, all the spatial coordinates are fixed, the endpoint is at a single spatial point (i.e., a particle). A D0-brane is what we know as a particle and a D1-brane would be a string. D-branes are mobile and interact with closed strings (and particles). Strings (such as the graviton) may open and "affix" their endpoints on a D2-brane (during the interaction).

But these interactions are confined to bosons. When we add fermions to the cocktail, we get supersymmetry and pairs of fermions and bosons. When we try to construct a "supersymmetric" QFT, we need to add 6 dimensions to the 4 we are acquainted with. This contraption cancel the anomalous results we otherwise obtain. In terms of PT, we get only five consistent string theories: I, IIA, IIB, E8XE8 Heterotic, SO(32) Heterotic. In terms of weakly coupled PT, they appear very different. But, in reality, they are all aspects of a single string theory and are related by "string dualities" (i.e., different formalisms that describe the same physical phenomena).

C. A LITTLE HISTORY

From its very inception in 1987, it was clear one of the gauge groups at the heart of E8XE8 is identical to the gauge group of the Standard Model (SM). Thus, matter in one E8 interacted through all the forces and their particles - and matter in the other E8 interacted only through gravity. This did nothing to explain why the breakdown of supersymmetry - and why the SM is so complex and muti-generational. Six of the 10 dimensions curled up into (non-observable) Planck length and compact 6-d balls attached to every 4-d point in our observable universe. This was a throwback to the neat mathematics of Kaluza-Klein. By compactifying 1 dimension in a 5-d universe, they were able to derive both GRT and electromagnetism (as a U(1) gauge theory of rotation around a circle).

We need to compactify the extra dimensions of (10-d and 11-d alike) superstring theories to get to our familiar universe. Various methods of doing this still leave us with a lot of supersymmetry. A few physicists believe that supersymmetry is likely to emerge - even in our pedestrian 4-d world - at ultra high energies. Thus, in order to preserve a minimum of supersymmetry in our 4-d universe, we use Calabi-Yau (CY) manifolds (on which the extra dimensions are compactified) for low energies. A certain CY manifold even yields the transition from the big bang (10 or 11 dimensional) universe to our dimensions-poorer one.

D. DUALITIES

The various string theories are facets of one underlying theory. Dualities are the "translation mechanisms" that bind them together. The T-duality relates theories with dimensions compactified on a circle with the radius R to theories whose dimensions are compactified on a circle with the radius 1/R. Thus, one's curled dimension is the other's uncurled one. The S-duality relates the coupling limits of the various theories. One's upper (strong coupling) limit becomes another's weak coupling limit. The celebrated M Theory is also a duality, in a way.

M Theory is not a string theory, strictly speaking. It is an 11-d supergravity with membranes and solitons (its 5-branes). Only when compactified does it yield a 10-d string theory (the IIA version, to be precise). It is not as counterintuitive as it sounds. If the 11th dimension is of finite length, the endpoints of a line segment define 9-dimensional boundaries (the 10th dimension is time). The intersection of an open membrane with these boundaries creates strings. We can safely say that the five string theories, on the one hand, and M Theory on the other hand constitute classical LIMITS. Perturbation theory was used to derive their corresponding quantum theories - but to little effect. the study of non-perturbative attributes (dualities, supersymmetry and so on) yielded much more and LED us to the conviction that a unified quantum theory underlies these myriad manifestations.

PARTICLES

Every physical theory postulates physical entities, which are really nothing more than conventions of its formalism. The Standard Model (SM) uses fields. The physical properties of these fields (electric, magnetic, etc.) are very reminiscent of the physical properties of the now defunct pre-relativistic ether. Quantized momenta and energy (i.e., elementary particles) are conveyed as ripples in the field. A distinct field is assigned to each particle. Fields are directional. The SM adds scalar fields (=fields without direction) to account for the (directionless) masses of the particles. But scalar fields are as much a field as their non-scalar brethren. Hence the need to assign to them Higgs particles (bosons) as their quanta. SM is, therefore, an isotropy-preserving Quantum Field Theory (QFT).

The problem is that gravity is negligibly weak compared to the enormous energies (masses) of the Higgs, W, Z and Gluon particles. Their interactions with other fields are beyond the coupling strengths (measurement energies) of today's laboratories. The strong and electroweak forces get unified only at 10 to the 16th power GeV. Gravity - at 10 to the 18th power (though some theories suggest a lower limit). This is almost at the Planck scale of energy. There is an enormous gap between the mass of the Higgs particles (200 Gev) and these energies. No one knows why. Supersymmetric and "Technicolor" solutions suggest the existence of additional forces and particles that do not interact with the SM "zoo" at low energies.

But otherwise SM is one of the more successful theories in the history of physics. It renormalized QFT and, thus, re-defined many physical constants. It also eliminated the infinities yielded by QFT calculations. Yet, it failed to renormalize a gravitational QFT.

The result is a schism between the physics of low energies and the physics of high and ultra-high energies. Particle theories look totally disparate depending on the energies of the reactions they study. But, luckily, the reactions of massive particles are negligible in low energies - so renormalizable QFT (e.g., SM) is a fair approximation, althesame. At low energies, the combination of Special Relativity Theory (SRT) and any quantum theory is indistinguishable from a renormalizable QFT. These are the fundaments of a possible unification. Unfortunately, these theories break down at high energy and, though very effective, they are far from being simple or aesthetic (i.e., classic). Too many interactions yielded by the formalism are arbitrarily suppressed below this or that energy threshold. Most of these suppressed interactions are figments of the imagination at the energy scales we are accustomed to or which are attainable in our labs. Not so gravitation - also a non-renormalizable, suppressed (though extremely weak) interaction. Other suppressed reactions threaten to unsettle the whole edifice - yielding such oddities as unstable photons, or neutrinos with masses.

Hence the intuitive appeal of string theories. The vibratory modes of strings appear to us as particles. Gravitation is finally made a part of a finite theory. The drawbacks are the extra-dimensions, which seem to unparsimoniously run contra to Occam's razor - and the outlandishly high energies in which they are supposed to reveal themselves (uncurl). M Theory tries to merge QFT with the classic string theories - but this alleviates only a few marginal issues.

The more philosophically and aesthetically inclined reject the operationalism which characterizes modern physics ("if it works - I am not interested to know WHY it works or even HOW it works"). They demand to know what is the underlying PHYSICAL reality (or at least, physical PRINCIPLE). The great pre-QM (Quantum Mechanics) theories always sprang from such a principle. The general Relativity Theory (GRT) was founded on the principle of the equivalence (i.e., indistinguishability) of gravity and inertia. Even the SM is based on a gauge symmetry. Special Relativity Theory (space-time) constrains QFTs and is, therefore, their "principle". No one is quite sure about string theories.

Arguably, their most important contribution is to have dispensed with Perturbation Theory (PT). PT broke down quantum processes into intermediate stages and generated an "order of complexity". The contributions from simpler phases were computed and added up first, then the same treatment was accorded to the contributions of the more complex phases and so on. It worked with weak forces and many theories which postulate stronger forces (like some string theories) are reducible to PT-solvable theories. But, in general, PT is useless for intermediate and strong forces.

Another possible contribution - though highly theoretical at this stage - is that adding dimensions may act to reduce the energy levels at which grand unification (including gravity) is to be expected. But this is really speculative stuff. No one know how large these extra dimensions are. If too small, particles will be unable to vibrate in them. Admittedly, if sufficiently large, new particles may be discovered as well as new force conveyance modes (including the way gravity is transmitted). But the mathematical fact is that the geometrical form of the curled dimensions determines the possible modes of vibration (i.e., which particle masses and charges are possible).

Strings also constitute a lower limit on quantum fluctuations. This, in due time and with a lot more work (and possibly a new formalism), may explain why our universe is the way it is. Unconstrained quantum fluctuations should have yielded a different universe with a different cosmological constant.

THE MICRO AND THE MACRO

Strings have two types of energy states, depending on the shape of space time. If curled (cylindrical) space-time is "fat" (let's say, the whole universe) there will be closely spaced energy states, which correspond to the number of waves (vibrations) of the string and its length, and widely spaced energy states, which correspond to the number of loops a string makes around curled (cylindrical) space-time (winding modes). If the curled (cylindrical) space time is "thin" (let's say a molecule), a mirror picture emerges. Obviously, in both cases - "fat" space-time and "thin" space-time - the same vibrations and winding states are observed. In other words, the microcosm yields the same physics as the macrocosm.

G. BLACK HOLES

String theory, which is supposed to incorporate quantum gravity, should offer insights regarding black holes. String theories make use of the General Relativity Theory (GRT) formalism and add to it specific matter fields. Thus, many classical black hole solutions satisfy string equations of motion. In an effort to preserve some supersymmetry, superstring theory has devised its own black hole solutions (with D-branes, or "black branes", as the description of certain supersymmetric black holes). A match was even found between types of supersymmetric black holes and supergravity including greybody factors (frequency dependent corrections). String theorists have derived most of Hawking's (and Bekenstein's) work regarding the entropy of black holes from string theories.

This LED to novel ways of thinking about strings. What if "open" strings were really closed ones with one part "hidden" behind a black brane? What if intersecting black branes wrapped around seven curled dimensions gave rise to black holes? The vanishing masses of black branes delineate a cosmological evolutionary tree - from a universe with one topology to another, with another topology. Our world may be the "default" universe on the path of least resistance and minimum energy from one universe to another.

H. FROM SUPERGRAVITY TO MEMBRANES - A RECAP

The particles with half integer spins predicted by supersymmetry are nowhere to be found. Either supersymmetry is a wrong idea or the particles are too heavy (or too something) to be detected by us with our current equipment. The latter (particles too heavy) is possible only if supersymmetry has broken down (which is almost the same as saying that it is wrong). Had it existed, it would probably have encompassed gravity (as does the General Theory of Relativity) in the form of "supergravity". The non-supersymmetric equivalent of supergravity can be gravity as we know it. In terms of particles, supersymmetry in an 11-dimensional universe talks about a supersymmetric gravitino and a spin 2 graviton.

Supersymmetric supergravity was supplanted by 10-dimensional superstring theory because it could not account for handedness in nature (i.e., the preference of left or right in spin direction and in other physical phenomena) and for many quantum effects. From there it was a short - and inevitable - way to membrane theories. Branes with "p" dimensions moved in worldvolumes with p+1 dimensions and wrapped around curled dimensions to produce strings. Strings are, therefore, the equivalents of branes. To be more precise, strongly interacting (10-dimensional) strings are the dual equivalent of weakly interacting five-branes (solitons) (Duff, Scientific American, February 1998). Later, a duality between solitonic and fundamental strings in 6 dimensions (the other 4 curled and the five-brane wrapped around them) was established and then dualities between strings from the 5 string theories. Duff's "duality of dualities" states that the T-duality of a solitonic string is the S-duality of the fundamental string and vice versa. In other words, what appears as the charge of one object can also be construed as the inversion of the length of another (and, hence, the size of the dimension). All these insights - pulled together by Witten - LED to M Theory in 11 dimensions. Later on, matrix theories replaced traditional coordinates in space time with non-commutable matrices. In other words, in an effort to rigorously define M Theory (that is, merge quantum physics with gravity), space time itself has been "sacrificed" or "quantum theorized".

[terdancam]

:shutit:

i remember being gobsmacked by that documentary on String Theory---------and going from your cut and pastes there it reinforces the fact that there are some bloody clever people out there!!

And how clever are the people that designed and built the petronas towers?

I wouldn`t know where to start, drawing or project managing!!!!!!

Obviously just me and you Monster-Mat who like the intelligent and non-mundane stuff out there!

[Monster-Mat]

  :shutit: 

i remember being gobsmacked by that documentary on String Theory---------and going from your cut and pastes there it reinforces the fact that there are some bloody clever people out there!!

And how clever are the people that designed and built the petronas towers?

I wouldn`t know where to start, drawing or project managing!!!!!!

Obviously just me and you Monster-Mat who like the intelligent and non-mundane stuff out there!

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indeed....the world is an amazing place, unfortunatly for the good that a few Humans do, there are thousands that care not a Jot...and are intent on destroying either there fellow man, or the World we rome....

[Mr Morse]

Nanobot technology - nanometer sized "robots" that will eventually be used to fix the ills and ailments in our bodies from the inside....

[Monster-Mat]

Nanobot technology - nanometer sized "robots" that will eventually be used to fix the ills and ailments in our bodies from the inside....

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..........and are able to make clones of themselfs.....is that a good or Bad thing.

[legendswraith]

Quantum mechanics far to much input at the end of the day can we say wormholes and be done with it :D

Chaos theory (this threads going to be mind melting for the latecomers)

The flapping of a single butterfly's wing today produces a tiny change in the state of the atmosphere. Over a period of time, what the atmosphere actually does diverges from what it would have done. So, in a month's time, a tornado that would have devastated the Indonesian coast doesn't happen. Or maybe one that wasn't going to happen, does. (Ian Stewart, Does *** Play Dice? The Mathematics of Chaos, pg. 141)

This phenomenon, common to chaos theory, is also known as sensitive dependence on initial conditions. Just a small change in the initial conditions can drastically change the long-term behavior of a system. Such a small amount of difference in a measurement might be considered experimental noise, background noise, or an inaccuracy of the equipment. Such things are impossible to avoid in even the most isolated lab. With a starting number of 2, the final result can be entirely different from the same system with a starting value of 2.000001. It is simply impossible to achieve this level of accuracy - just try and measure something to the nearest millionth of an inch!

From this idea, Lorenz stated that it is impossible to predict the weather accurately. However, this discovery LED Lorenz on to other aspects of what eventually came to be known as chaos theory.

Lorenz started to look for a simpler system that had sensitive dependence on initial conditions. His first discovery had twelve equations, and he wanted a much more simple version that still had this attribute. He took the equations for convection, and stripped them down, making them unrealistically simple. The system no longer had anything to do with convection, but it did have sensitive dependence on its initial conditions, and there were only three equations this time. Later, it was discovered that his equations precisely described a water wheel.

At the top, water drips steadily into containers hanging on the wheel's rim. Each container drips steadily from a small hole. If the stream of water is slow, the top containers never fill fast enough to overcome friction, but if the stream is faster, the weight starts to turn the wheel. The rotation might become continuous. Or if the stream is so fast that the heavy containers swing all the way around the bottom and up the other side, the wheel might then slow, stop, and reverse its rotation, turning first one way and then the other. (James Gleick, Chaos - Making a New Science, pg. 29)

The equations for this system also seemed to give rise to entirely random behavior. However, when he graphed it, a surprising thing happened. The output always stayed on a curve, a double spiral. There were only two kinds of order previously known: a steady state, in which the variables never change, and periodic behavior, in which the system goes into a loop, repeating itself indefinitely. Lorenz's equations were definitely ordered - they always followed a spiral. They never settled down to a single point, but since they never repeated the same thing, they weren't periodic either. He called the image he got when he graphed the equations the Lorenz attractor. (See figure 2)

In 1963, Lorenz published a paper describing what he had discovered. He included the unpredictability of the weather, and discussed the types of equations that caused this type of behavior. Unfortunately, the only journal he was able to publish in was a meteorological journal, because he was a meteorologist, not a mathematician or a physicist. As a result, Lorenz's discoveries weren't acknowledged until years later, when they were rediscovered by others. Lorenz had discovered something revolutionary; now he had to wait for someone to discover him.

Another system in which sensitive dependence on initial conditions is evident is the flip of a coin. There are two variables in a flipping coin: how soon it hits the ground, and how fast it is flipping. Theoretically, it should be possible to control these variables entirely and control how the coin will end up. In practice, it is impossible to control exactly how fast the coin flips and how high it flips. It is possible to put the variables into a certain range, but it is impossible to control it enough to know the final results of the coin toss.

A similar problem occurs in ecology, and the prediction of biological populations. The equation would be simple if population just rises indefinitely, but the effect of predators and a limited food supply make this equation incorrect. The simplest equation that takes this into account is the following:

next year's population = r * this year's population * (1 - this year's population)

In this equation, the population is a number between 0 and 1, where 1 represents the maximum possible population and 0 represents extinction. R is the growth rate. The question was, how does this parameter affect the equation? The obvious answer is that a high growth rate means that the population will settle down at a high population, while a low growth rate means that the population will settle down to a low number. This trend is true for some growth rates, but not for every one.

One biologist, Robert May, decided to see what would happen to the equation as the growth rate value changes. At low values of the growth rate, the population would settle down to a single number. For instance, if the growth rate value is 2.7, the population will settle down to .6292. As the growth rate increased, the final population would increase as well. Then, something weird happened. As soon as the growth rate passed 3, the line broke in two. Instead of settling down to a single population, it would jump between two different populations. It would be one value for one year, go to another value the next year, then repeat the cycle forever. Raising the growth rate a little more caused it to jump between four different values. As the parameter rose further, the line bifurcated (doubled) again. The bifurcations came faster and faster until suddenly, chaos appeared. Past a certain growth rate, it becomes impossible to predict the behavior of the equation. However, upon closer inspection, it is possible to see white strips. Looking closer at these strips reveals little windows of order, where the equation goes through the bifurcations again before returning to chaos. This self-similarity, the fact that the graph has an exact copy of itself hidden deep inside, came to be an important aspect of chaos.

An employee of IBM, Benoit Mandelbrot was a mathematician studying this self-similarity. One of the areas he was studying was cotton price fluctuations. No matter how the data on cotton prices was analyzed, the results did not fit the normal distribution. Mandelbrot eventually obtained all of the available data on cotton prices, dating back to 1900. When he analyzed the data with IBM's computers, he noticed an astonishing fact:

The numbers that produced aberrations from the point of view of normal distribution produced symmetry from the point of view of scaling. Each particular price change was random and unpredictable. But the sequence of changes was independent on scale: curves for daily price changes and monthly price changes matched perfectly. Incredibly, analyzed Mandelbrot's way, the degree of variation had remained constant over a tumultuous sixty-year period that saw two World Wars and a depression. (James Gleick, Chaos - Making a New Science, pg. 86)

Mandelbrot analyzed not only cotton prices, but many other phenomena as well. At one point, he was wondering about the length of a coastline. A map of a coastline will show many bays. However, measuring the length of a coastline off a map will miss minor bays that were too small to show on the map. Likewise, walking along the coastline misses microscopic bays in between grains of sand. No matter how much a coastline is magnified, there will be more bays visible if it is magnified more.

One mathematician, Helge von Koch, captured this idea in a mathematical construction called the Koch curve. To create a Koch curve, imagine an equilateral triangle. To the middle third of each side, add another equilateral triangle. Keep on adding new triangles to the middle part of each side, and the result is a Koch curve. (See figure 4) A magnification of the Koch curve looks exactly the same as the original. It is another self-similar figure.

The Koch curve brings up an interesting paradox. Each time new triangles are added to the figure, the length of the line gets longer. However, the inner area of the Koch curve remains less than the area of a circle drawn around the original triangle. Essentially, it is a line of infinite length surrounding a finite area.

To get around this difficulty, mathematicians invented fractal dimensions. Fractal comes from the word fractional. The fractal dimension of the Koch curve is somewhere around 1.26. A fractional dimension is impossible to conceive, but it does make sense. The Koch curve is rougher than a smooth curve or line, which has one dimension. Since it is rougher and more crinkly, it is better at taking up space. However, it's not as good at filling up space as a square with two dimensions is, since it doesn't really have any area. So it makes sense that the dimension of the Koch curve is somewhere in between the two.

Fractal has come to mean any image that displays the attribute of self-similarity. The bifurcation diagram of the population equation is fractal. The Lorenz Attractor is fractal. The Koch curve is fractal.

During this time, scientists found it very difficult to get work published about chaos. Since they had not yet shown the relevance to real-world situations, most scientists did not think the results of experiments in chaos were important. As a result, even though chaos is a mathematical phenomenon, most of the research into chaos was done by people in other areas, such as meteorology and ecology. The field of chaos sprouted up as a hobby for scientists working on problems that maybe had something to do with it.

Later, a scientist by the name of Feigenbaum was looking at the bifurcation diagram again. He was looking at how fast the bifurcations come. He discovered that they come at a constant rate. He calculated it as 4.669. In other words, he discovered the exact scale at which it was self-similar. Make the diagram 4.669 times smaller, and it looks like the next region of bifurcations. He decided to look at other equations to see if it was possible to determine a scaling factor for them as well. Much to his surprise, the scaling factor was exactly the same. Not only was this complicated equation displaying regularity, the regularity was exactly the same as a much simpler equation. He tried many other functions, and they all produced the same scaling factor, 4.669.

This was a revolutionary discovery. He had found that a whole class of mathematical functions behaved in the same, predictable way. This universality would help other scientists easily analyze chaotic equations. Universality gave scientists the first tools to analyze a chaotic system. Now they could use a simple equation to predict the outcome of a more complex equation.

Many scientists were exploring equations that created fractal equations. The most famous fractal image is also one of the most simple. It is known as the Mandelbrot set (pictures of the mandelbrot set). The equation is simple: z=z2+c. To see if a point is part of the Mandelbrot set, just take a complex number z. Square it, then add the original number. Square the result, then add the original number. Repeat that ad infinitum, and if the number keeps on going up to infinity, it is not part of the Mandelbrot set. If it stays down below a certain level, it is part of the Mandelbrot set. The Mandelbrot set is the innermost section of the picture, and each different shade of gray represents how far out that particular point is. One interesting feature of the Mandelbrot set is that the circular humps match up to the bifurcation graph. The Mandelbrot fractal has the same self-similarity seen in the other equations. In fact, zooming in deep enough on a Mandelbrot fractal will eventually reveal an exact replica of the Mandelbrot set, perfect in every detail.

Fractal structures have been noticed in many real-world areas, as well as in mathematician's minds. Blood vessels branching out further and further, the branches of a tree, the internal structure of the lungs, graphs of stock market data, and many other real-world systems all have something in common: they are all self-similar.

Scientists at UC Santa Cruz found chaos in a dripping water faucet. By recording a dripping faucet and recording the periods of time, they discovered that at a certain flow velocity, the dripping no longer occurred at even times. When they graphed the data, they found that the dripping did indeed follow a pattern.

The human heart also has a chaotic pattern. The time between beats does not remain constant; it depends on how much activity a person is doing, among other things. Under certain conditions, the heartbeat can speed up. Under different conditions, the heart beats erratically. It might even be called a chaotic heartbeat. The analysis of a heartbeat can help medical researchers find ways to put an abnormal heartbeat back into a steady state, instead of uncontrolled chaos.

Researchers discovered a simple set of three equations that graphed a fern. This started a new idea - perhaps DNA encodes not exactly where the leaves grow, but a formula that controls their distribution. DNA, even though it holds an amazing amount of data, could not hold all of the data necessary to determine where every cell of the human body goes. However, by using fractal formulas to control how the blood vessels branch out and the nerve fibers get created, DNA has more than enough information. It has even been speculated that the brain itself might be organized somehow according to the laws of chaos.

Chaos even has applications outside of science. Computer art has become more realistic through the use of chaos and fractals. Now, with a simple formula, a computer can create a beautiful, and realistic tree. Instead of following a regular pattern, the bark of a tree can be created according to a formula that almost, but not quite, repeats itself.

Music can be created using fractals as well. Using the Lorenz attractor, Diana S. Dabby, a graduate student in electrical engineering at the Massachusetts Institute of Technology, has created variations of musical themes. ("Bach to Chaos: Chaotic Variations on a Classical Theme", Science News, Dec. 24, 1994) By associating the musical notes of a piece of music like Bach's Prelude in C with the x coordinates of the Lorenz attractor, and running a computer program, she has created variations of the theme of the song. Most musicians who hear the new sounds believe that the variations are very musical and creative.

Chaos has already had a lasting effect on science, yet there is much still left to be discovered. Many scientists believe that twentieth century science will be known for only three theories: relativity, quantum mechanics, and chaos. Aspects of chaos show up everywhere around the world, from the currents of the ocean and the flow of blood through fractal blood vessels to the branches of trees and the effects of turbulence. Chaos has inescapably become part of modern science. As chaos changed from a little-known theory to a full science of its own, it has received widespread publicity. Chaos theory has changed the direction of science: in the eyes of the general public, physics is no longer simply the study of subatomic particles in a billion-dollar particle accelerator, but the study of chaotic systems and how they work.

[Monster-Mat]

But, String Theories, can , in Theory explain your Chaos Theory

[shorty]

What I find amazing is if a watch a topless bird jumping up and down it makes all the blood rush from one head to the other :P

[Fidgits]

uh oh - its another of those threads....

i'll tell you the things that amaze me - tomorrow...

[Tony9r]

Quantum Physics... but it mentions a car...

The difference is that the common laws of physics begin to deteriorate on small scales. For example, Nippendenso (Japan Electric) built a car that's only half a millimeters long. One could easily mistake it for a grain of rice if not for its gold color. At the scale of 1 to 1000, physics is already changing. Oil would now gum up the engine, and the tires wouldn't have enough traction to move the car...

Drat, tea time

[Rodders_UK]

I'm very interested in string theory - it's supposed to be the answer to all questions - just wish I understood it more.

I really admire people that design micro-electronics too.

[Fargo]

i know where your coming from, what amazes me are

String Theories

A Good Website

D. DUALITIES

The various string theories are facets of one underlying theory. Dualities are the "translation mechanisms" that bind them together. The T-duality relates theories with dimensions compactified on a circle with the radius R to theories whose dimensions are compactified on a circle with the radius 1/R. Thus, one's curled dimension is the other's uncurled one. The S-duality relates the coupling limits of the various theories. One's upper (strong coupling) limit becomes another's weak coupling limit. The celebrated M Theory is also a duality, in a way.

M Theory is not a string theory, strictly speaking. It is an 11-d supergravity with membranes and solitons (its 5-branes). Only when  compactified does it yield a 10-d string theory (the IIA version, to be precise). It is not as counterintuitive as it sounds. If the 11th dimension is of finite length, the endpoints of a line segment define 9-dimensional boundaries (the 10th dimension is time). The intersection of an open membrane with these boundaries creates strings. We can safely say that the five string theories, on the one hand, and M Theory on the other hand constitute classical LIMITS. Perturbation theory was used to derive their corresponding quantum theories - but to little effect. the study of non-perturbative attributes (dualities, supersymmetry and so on) yielded much more and led us to the conviction that a unified quantum theory underlies these myriad manifestations.

.

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did someone mention Dualities.

Get yah head around Duality in Buddism the enlightenment which the Buddhist path is designed to awaken consists precisely in the realization of this non-dualistic perspective

[legendswraith]

it will take a long time for the physics to be that accurate that chaos theory becomes obsloete and there are still mathematics used in working out the transmission of force from bosons and the receiving of force by fermions and wheretheres room for error chaos theory still has a place. Besides the way chaos theory is introduced is alot more philosophical than metaphysics science is good but a little to hard nosed at times.

I still want to feel the force than work it out on my calculator :D

[legendswraith]

Buddhism isn't that the all life is pain and the cause of pain is desire thing

(runs off to contemplate naval) :duh:

[1sTee]

Rice Krispies still amaze me!!

Just how they make them snap cracle AND pop is just beyond me! :duh:

[Fargo]

Buddhism isn't that the all life is pain and the cause of pain is desire thing

(runs off to contemplate naval) :duh:

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nah man.... you got it all wrongggg,,, now im not a budhist (nor religious in any way) but buddhism i reckon is the way that EVERYone should be living, behaving etc... basically its all about karma baby.. you do good then goos will come.. imagine it if everyone did good, then your gaurenteed to have good come back on you...

[legendswraith]

hope you realise all of this information has had to take up the space that had my childhood memories. Thats another one gone now

[Mr Morse]

Buddhism isn't that the all life is pain and the cause of pain is desire thing

(runs off to contemplate naval) :duh:

←

nah man.... you got it all wrongggg,,, now im not a budhist (nor religious in any way) but buddhism i reckon is the way that EVERYone should be living, behaving etc... basically its all about karma baby.. you do good then goos will come.. imagine it if everyone did good, then your gaurenteed to have good come back on you...

←

Buddhism is (probably?) the only religion where mass extermination has not featured in part of that religion's history, unlike Islam, Judaism, Catholisism, etc etc.

[1sTee]

Buddhism isn't that the all life is pain and the cause of pain is desire thing

(runs off to contemplate naval) :duh:

←

nah man.... you got it all wrongggg,,, now im not a budhist (nor religious in any way) but buddhism i reckon is the way that EVERYone should be living, behaving etc... basically its all about karma baby.. you do good then goos will come.. imagine it if everyone did good, then your gaurenteed to have good come back on you...

←

The film 'Pay it forward' based on the novel by Catherine Ryan Hyde,

Sums this type of philosophy up perfectly.

http://www.payitforwardmovement.org/ 'sigh' what a wonderful place the world would be.

[terdancam]

Rice Krispies still amaze me!!

Just how they make them snap cracle AND pop is just beyond me!  :duh:

←

Holy jobbie, that made me larf.

Guys, i was actually pitching closer to the above rather than to the existensalism you seem to have covered!!!!

Heres some more..........

How does the USS Nimitz float...i still don`t get displacement and how they worked it out!

The microchip.................nope, thats so far beyond me it could be in canada.

How they work out trajectories in space/orbits/planets circling other stars.

How they`ve mapped the human genome.

How they landed a probe on titan :duh: :duh: :duh: :duh:

Laser eye surgery...how do you invent something like that? :winky:

How would you go about splitting an atom exactly....wouldn`t know where to start.

Those make my jaw drop..........!

[legendswraith]

Rice Krispies still amaze me!!

Just how they make them snap cracle AND pop is just beyond me!  :duh:

←

Holy jobbie, that made me larf.

Guys, i was actually pitching closer to the above rather than to the existensalism you seem to have covered!!!!

Heres some more..........

How does the USS Nimitz float...i still don`t get displacement and how they worked it out!

The microchip.................nope, thats so far beyond me it could be in canada.

How they work out trajectories in space/orbits/planets circling other stars.

How they`ve mapped the human genome.

How they landed a probe on titan :duh: :duh: :duh: :duh:

Laser eye surgery...how do you invent something like that? :winky:

How would you go about splitting an atom exactly....wouldn`t know where to start.

Those make my jaw drop..........!

←

the nimitz floats because below decks its a helium atmosphere thats why they all talk squeaky on it :winky:

trajectories of planets is worked out by the magnitude of the light reflected off the planet star etc against a known magnitude i.e sol

GPS as far as i know

with very clever monkey pilots

laser eye surgery was invented in the same manner as getting drunk and licking the scalectric track to see if you get a shock (but in a lab instead and with lasers)

You split an atom by accelerating unstable ions at a radioactive metal this causes the atom to split and release energy

thats my best efforts with out looking it up and its all true