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Showing posts with label Antony Garrett Lisi. Show all posts
Showing posts with label Antony Garrett Lisi. Show all posts

Friday, June 29, 2012

A Inherent Pattern of Consciousness


This image depicts the interaction of nine plane waves—expanding sets of ripples, like the waves you would see if you simultaneously dropped nine stones into a still pond. The pattern is called a quasicrystal because it has an ordered structure, but the structure never repeats exactly. The waves produced by dropping four or more stones into a pond always form a quasicrystal.

Because of the wavelike properties of matter at subatomic scales, this pattern could also be seen in the waveform that describes the location of an electron. Harvard physicist Eric Heller created this computer rendering and added color to make the pattern’s structure easier to see. See: What Is This? A Psychedelic Place Mat?
See Also: 59. Medieval Mosque Shows Amazing Math Discovery





A CG movie inspired by the Persian Architecture, by Cristóbal Vila. Go to www.etereaestudios.com for more info.






Circle Limit III, 1959




In 1941, Escher wrote his first paper, now publicly recognized, called Regular Division of the Plane with Asymmetric Congruent Polygons, which detailed his mathematical approach to artwork creation. His intention in writing this was to aid himself in integrating mathematics into art. Escher is considered a research mathematician of his time because of his documentation with this paper. In it, he studied color based division, and developed a system of categorizing combinations of shape, color and symmetrical properties. By studying these areas, he explored an area that later mathematicians labeled crystallography.

Around 1956, Escher explored the concept of representing infinity on a two-dimensional plane. Discussions with Canadian mathematician H.S.M. Coxeter inspired Escher's interest in hyperbolic tessellations, which are regular tilings of the hyperbolic plane. Escher's works
Circle Limit I–IV demonstrate this concept. In 1995, Coxeter verified that Escher had achieved mathematical perfection in his etchings in a published paper. Coxeter wrote, "Escher got it absolutely right to the millimeter."


Snow Crystal Photo Gallery I
 
If you have never studied the structure of Mandala origins of the Tibetan Buddhist you might never of recognize the structure given to this 2 dimensional surface?  Rotate the 2d surface to the side view. It becomes a recognition of some Persian temple perhaps? I mean,  the video really helps one to see this,  and to understand the structural integrity is built upon.

So too, do we recognize this "snow flake"  as some symmetrical realization of it's individuality as some mathematical form constructed in nature?

I previous post I gave some inclination to the idea of time travel and how this is done within the scope of consciousness. In the same vein, I want you to realize that such journeys to our actualized past can bring us in contact with a book of Mandalas that helped me to realize and reveals a key of symmetrical expressions of the lifetime, or lifetimes.

Again in relation how science sees subjectivity I see that this is weak in expression in terms of how it can be useful in an objective sense as to be repeatable. But it helps too, to trace this beginning back to a source that while perceived as mathematical , shows the the mathematical relation embedded in nature.




See: Nature = Mathematics?

Thursday, April 19, 2012

Model Building in Life

"...underwriting the form languages of ever more domains of mathematics is a set of deep patterns which not only offer access to a kind of ideality that Plato claimed to see the universe as created with in the Timaeus; more than this, the realm of Platonic forms is itself subsumed in this new set of design elements-- and their most general instances are not the regular solids, but crystallographic reflection groups. You know, those things the non-professionals call . . . kaleidoscopes! * (In the next exciting episode, we'll see how Derrida claims mathematics is the key to freeing us from 'logocentrism'-- then ask him why, then, he jettisoned the deepest structures of mathematical patterning just to make his name...)

* H. S. M. Coxeter, Regular Polytopes (New York: Dover, 1973) is the great classic text by a great creative force in this beautiful area of geometry (A polytope is an n-dimensional analog of a polygon or polyhedron. Chapter V of this book is entitled 'The Kaleidoscope'....)"


I just wanted to show you what has been physically reproduced in cultures. This in order to highlight some of the things that were part of our own make up,  so you get that what has transpired in our societies has been part of something hidden within our own selves.

As I have said before it has become something of an effort for me to cataloged knowledge on some of  the things I learn.  The ways in which to keep the information together. I am not saying everyone will do this in there own way but it seems to me that as if some judgement about our selves is hidden in the way we had gathered information about our own lives then it may have been put together like some kaleidoscope.


Online Etymology Dictionary-1817, lit. "observer of beautiful forms," coined by its inventor, Sir David Brewster (1781-1868), from Gk. kalos "beautiful" + eidos "shape" (see -oid) + -scope, on model of telescope, etc. Figurative meaning "constantly changing pattern" is first attested 1819 in Lord Byron, whose publisher had sent him one.

So to say then past accomplishments were part of the designs, what had we gained about our own lives then?  What page in the book of Mandalas can you have said that any one belonged to you? It was that way for me in that I saw the choices. These I thought I had built on my own, as some inclination of a method and way to deliver meaning into my own life. Then through exploration it seem to contain the energy of all that I had been before as to say that in this life now, that energy could unfold?




Scan of painting 19th century Tibetan Buddhist thangka painting
Maṇḍala (मण्डल) is a Sanskrit word meaning "circle." In the Buddhist and Hindu religious traditions their sacred art often takes a mandala form. The basic form of most Hindu and Buddhist mandalas is a square with four gates containing a circle with a center point. Each gate is in the shape of a T.[1][2] Mandalas often exhibit radial balance.[3]


These mandalas, concentric diagrams, have spiritual and ritual significance in both Buddhism and Hinduism.[4][5] The term is of Hindu origin and appears in the Rig Veda as the name of the sections of the work, but is also used in other Indian religions, particularly Buddhism. In the Tibetan branch of Vajrayana Buddhism, mandalas have been developed into sandpainting. They are also a key part of anuttarayoga tantra meditation practices.


In various spiritual traditions, mandalas may be employed for focusing attention of aspirants and adepts, as a spiritual teaching tool, for establishing a sacred space, and as an aid to meditation and trance induction. According to the psychologist David Fontana, its symbolic nature can help one "to access progressively deeper levels of the unconscious, ultimately assisting the meditator to experience a mystical sense of oneness with the ultimate unity from which the cosmos in all its manifold forms arises."[6] The psychoanalyst Carl Jung saw the mandala as "a representation of the unconscious self,"[citation needed] and believed his paintings of mandalas enabled him to identify emotional disorders and work towards wholeness in personality.[7]


In common use, mandala has become a generic term for any plan, chart or geometric pattern that represents the cosmos metaphysically or symbolically, a microcosm of the Universe from the human perspective.[citation needed]


So what does this mean then that you see indeed some subjects that are allocated toward design of to say that it may be an art of a larger universal understanding that hidden in our natures the will to provide for something schematically inherent? Our nature,  as to the way in which we see the world. The way in which we see science. What cosmic plan then to say the universe would unfold this way, or  to seek the inner structure and explanations as to the way the universe began. The way we emerged into consciousness of who you are?

 The kaleidoscope was perfected by Sir David Brewster, a Scottish scientist, in 1816. This technological invention, whose function is literally the production of beauty, or rather its observation, was etymologically a typical aesthetic form of the nineteenth century - one bound up with disinterested contemplation. (The etymology of the word is formed from kalos (beautiful), eidos (form) and scopos (watcher) - "watcher of beautiful shapes".) The invention is enjoying a second life today - as the model for many contemporary abstract works. In Olafur Eliasson's Kaleidoscope (2001), the viewer takes the place of the pieces of glass, producing a myriad of images. In an inversion of the situation involved in the classic kaleidoscope, the watcher becomes the watched. In Jim Drain's Kaleidoscope (2003), the viewer is also plunged physically inside the myriad of abstract forms, and his image becomes a part of the environment. Spin My Wheel (2003), by Lori Hersberger, also forms a painting that is developed in space, spilling beyond the frame of the picture, its projected image constantly changing, dissolving the surrounding world with an infinite play of reflections in fragments of broken mirror. The viewer becomes one of the subjects of the piece. (Not the subject, as in Eliasson's work, but one of its subjects.)
See: The End of Perspective-Vincent Pécoil.

Would there be then some algorithmic style to the code written in your life as to have all the things you are as some pattern as to the way in which you will live your life? I ask then what would seem so strange that you might not paint a picture of it? Not encode your life in some mathematical principle as to say that life emerge for you in this way?


Although Aristotle in general had a more empirical and experimental attitude than Plato, modern science did not come into its own until Plato's Pythagorean confidence in the mathematical nature of the world returned with Kepler, Galileo, and Newton. For instance, Aristotle, relying on a theory of opposites that is now only of historical interest, rejected Plato's attempt to match the Platonic Solids with the elements -- while Plato's expectations are realized in mineralogy and crystallography, where the Platonic Solids occur naturally.Plato and Aristotle, Up and Down-Kelley L. Ross, Ph.D.



See Also:

Sunday, January 15, 2012

WHAT IS YOUR FAVORITE DEEP, ELEGANT, OR BEAUTIFUL EXPLANATION?

Scientists' greatest pleasure comes from theories that derive the solution to some deep puzzle from a small set of simple principles in a surprising way. These explanations are called "beautiful" or "elegant". Historical examples are Kepler's explanation of complex planetary motions as simple ellipses, Bohr's explanation of the periodic table of the elements in terms of electron shells, and Watson and Crick's double helix. Einstein famously said that he did not need experimental confirmation of his general theory of relativity because it "was so beautiful it had to be true." See:2012 : WHAT IS YOUR FAVORITE DEEP, ELEGANT, OR BEAUTIFUL EXPLANATION?
See which comments resonate with you. Some of my picks as I go through was by :

Raphael Bousso
Professor of Theoretical Physics, Berkeley



My Favorite Annoying Elegant Explanation: Quantum Theory .......General Relativity, in turn, is only a classical theory. It rests on a demonstrably false premise: that position and momentum can be known simultaneously. This may a good approximation for apples, planets, and galaxies: large objects, for which gravitational interactions tend to be much more important than for the tiny particles of the quantum world. But as a matter of principle, the theory is wrong. The seed is there. General Relativity cannot be the final word; it can only be an approximation to a more general Quantum Theory of Gravity.

But what about Quantum Mechanics itself? Where is its seed of destruction? Amazingly, it is not obvious that there is one. The very name of the great quest of theoretical physics—"quantizing General Relativity"—betrays an expectation that quantum theory will remain untouched by the unification we seek. String theory—in my view, by far the most successful, if incomplete, result of this quest—is strictly quantum mechanical, with no modifications whatsoever to the framework that was completed by Heisenberg, Schrödinger, and Dirac. In fact, the mathematical rigidity of Quantum Mechanics makes it difficult to conceive of any modifications, whether or not they are called for by observation.

Yet, there are subtle hints that Quantum Mechanics, too, will suffer the fate of its predecessors. The most intriguing, in my mind, is the role of time. In Quantum Mechanics, time is an essential evolution parameter. But in General Relativity, time is just one aspect of spacetime, a concept that we know breaks down at singularities deep inside black holes. Where time no longer makes sense, it is hard to see how Quantum Mechanics could still reign. As Quantum Mechanics surely spells trouble for General Relativity, the existence of singularities suggests that General Relativity may also spell trouble for Quantum Mechanics. It will be fascinating to watch this battle play out.



President, The Royal Society; Professor of Cosmology & Astrophysics; Master, Trinity...

Physical Reality Could Be Hugely More Extensive Than the Patch of Space and Time Traditionally Called 'The Universe' .....As an analogy (which I owe to Paul Davies) consider the form of snowflakes. Their ubiquitous six-fold symmetry is a direct consequence of the properties and shape of water molecules. But snowflakes display an immense variety of patterns because each is molded by its distinctive history and micro-environment: how each flake grows is sensitive to the fortuitous temperature and humidity changes during its growth.

If physicists achieved a fundamental theory, it would tell us which aspects of nature were direct consequences of the bedrock theory (just as the symmetrical template of snowflakes is due to the basic structure of a water molecule) and which cosmic numbers are (like the distinctive pattern of a particular snowflake) the outcome of environmental contingencies. .


Theoretical physicist

An Explanation of Fundamental Particle Physics That Doesn't Exist Yet.....What is tetrahedral symmetry doing in the masses of neutrinos?! Nobody knows. But you can bet there will be a good explanation. It is likely that this explanation will come from mathematicians and physicists working closely with Lie groups. The most important lesson from the great success of Einstein's theory of General Relativity is that our universe is fundamentally geometric, and this idea has extended to the geometric description of known forces and particles using group theory. It seems natural that a complete explanation of the Standard Model, including why there are three generations of fermions and why they have the masses they do, will come from the geometry of group theory. This explanation does not yet exist, but when it does it will be deep, elegant, and beautiful—and it will be my favorite.


Mathematician, Harvard; Co-author, The Shape of Inner Space

A Sphere....Most scientific facts are based on things that we cannot see with the naked eye or hear by our ears or feel by our hands. Many of them are described and guided by mathematical theory. In the end, it becomes difficult to distinguish a mathematical object from objects in nature.

One example is the concept of a sphere. Is the sphere part of nature or it is a mathematical artifact? That is difficult for a mathematician to say. Perhaps the abstract mathematical concept is actually a part of nature. And it is not surprising that this abstract concept actually describes nature quite accurately.



theoretical physicist; Professor, Department of Physics, University of California,...
 Gravity Is Curvature Of Spacetime … Or Is It?......We do not yet know the full shape of the quantum theory providing a complete accounting for gravity. We do have many clues, from studying the early quantum phase of cosmology, and ultrahigh energy collisions that produce black holes and their subsequent disintegrations into more elementary particles. We have hints that the theory draws on powerful principles of quantum information theory. And, we expect that in the end it has a simple beauty, mirroring the explanation of gravity-as-curvature, from an even more profound depth.



Albert Einstein Professor in Science, Departments of Physics and Astrophysical...
Quasi-elegance....As a young student first reading Weyl's book, crystallography seemed like the "ideal" of what one should be aiming for in science: elegant mathematics that provides a complete understanding of all physical possibilities. Ironically, many years later, I played a role in showing that my "ideal" was seriously flawed. In 1984, Dan Shechtman, Ilan Blech, Denis Gratias and John Cahn reported the discovery of a puzzling manmade alloy of aluminumand manganese with icosahedral symmetry. Icosahedral symmetry, with its six five-fold symmetry axes, is the most famous forbidden crystal symmetry. As luck would have it, Dov Levine (Technion) and I had been developing a hypothetical idea of a new form of solid that we dubbed quasicrystals, short for quasiperiodic crystals. (A quasiperiodic atomic arrangement means the atomic positions can be described by a sum of oscillatory functions whose frequencies have an irrational ratio.) We were inspired by a two-dimensional tiling invented by Sir Roger Penrose known as the Penrose tiling, comprised of two tiles arranged in a five-fold symmetric pattern. We showed that quasicrystals could exist in three dimensions and were not subject to the rules of crystallography. In fact, they could have any of the symmetries forbidden to crystals. Furthermore, we showed that the diffraction patterns predicted for icosahedral quasicrystals matched the Shechtman et al. observations. Since 1984, quasicrystals with other forbidden symmetries have been synthesized in the laboratory. The 2011 Nobel Prize in Chemistry was awarded to Dan Shechtman for his experimental breakthrough that changed our thinking about possible forms of matter. More recently, colleagues and I have found evidence that quasicrystals may have been among the first minerals to have formed in the solar system.

The crystallography I first encountered in Weyl's book, thought to be complete and immutable, turned out to be woefully incomplete, missing literally an uncountable number of possible symmetries for matter. Perhaps there is a lesson to be learned: While elegance and simplicity are often useful criteria for judging theories, they can sometimes mislead us into thinking we are right, when we are actually infinitely wrong.




Physicist, Harvard University; Author, Warped Passages; Knocking On Heaven's Door

The Higgs Mechanism......Fortunately that time has now come for the Higgs mechanism, or at least the simplest implementation which involves a particle called the Higgs boson. The Large Hadron Collider at CERN near Geneva should have a definitive result on whether this particle exists within this coming year. The Higgs boson is one possible (and many think the most likely) consequence of the Higgs mechanism. Evidence last December pointed to a possible discovery, though more data is needed to know for sure. If confirmed, it will demonstrate that the Higgs mechanism is correct and furthermore tell us what is the underlying structure responsible for spontaneous symmetry breaking and spreading "charge" throughout the vacuum. The Higgs boson would furthermore be a new type of particle (a fundamental boson for those versed in physics terminology) and would be in some sense a new type of force. Admittedly, this is all pretty subtle and esoteric. Yet I (and much of the theoretical physics community) find it beautiful, deep, and elegant.

Symmetry is great. But so is symmetry breaking. Over the years many aspects of particle physics were first considered ugly and then considered elegant. Subjectivity in science goes beyond communities to individual scientists. And even those scientists change their minds over time. That's why experiments are critical. As difficult as they are, results are much easier to pin down than the nature of beauty. A discovery of the Higgs boson will tell us how that is done when particles acquire their masses.



Professor of Quantum Mechanical Engineering, MIT; Author, Programming the Universe
 The True Rotational Symmetry of Space.....Although this excercise might seem no more than some fancy and painful basketball move, the fact that the true symmetry of space is rotation not once but twice has profound consequences for the nature of the physical world at its most microscopic level. It implies that 'balls' such as electrons, attached to a distant point by a flexible and deformable 'strings,' such as magnetic field lines, must be rotated around twice to return to their original configuration. Digging deeper, the two-fold rotational nature of spherical symmetry implies that two electrons, both spinning in the same direction, cannot be placed in the same place at the same time. This exclusion principle in turn underlies the stability of matter. If the true symmetry of space were rotating around only once, then all the atoms of your body would collapse into nothingness in a tiny fraction of a second. Fortunately, however, the true symmetry of space consists of rotating around twice, and your atoms are stable, a fact that should console you as you ice your shoulder.

Remember even though I pick some of these explanations does not mean I discount all others. It's just that some are picked for what they are saying in highlighted quotations. Lisi's statement on string theory is of course in my opinion far from the truth, yet,  he captures a geometrical truth that I feel exists.:) You sort of get the jest of where I am coming from in the summation of Paul Steinhardt

Monday, July 12, 2010

Theory of Everything

From Wikipedia, the free encyclopedia

Beyond the Standard Model
CMS Higgs-event.jpg
Standard Model
The theory of everything (TOE) is a putative theory of theoretical physics that fully explains and links together all known physical phenomena, and, ideally, has predictive power for the outcome of any experiment that could be carried out in principle. Initially, the term was used with an ironic connotation to refer to various overgeneralized theories. For example, a great-grandfather of Ijon Tichy—a character from a cycle of Stanisław Lem's science fiction stories of the 1960s—was known to work on the "General Theory of Everything". Physicist John Ellis[1] claims to have introduced the term into the technical literature in an article in Nature in 1986.[2] Over time, the term stuck in popularizations of quantum physics to describe a theory that would unify or explain through a single model the theories of all fundamental interactions of nature.

There have been many theories of everything proposed by theoretical physicists over the last century, but none has been confirmed experimentally. The primary problem in producing a TOE is that the accepted theories of quantum mechanics and general relativity are hard to combine. Their mutual incompatibility argues that they are incomplete, or at least not fully understood taken individually. (For more, see unsolved problems in physics).

Based on theoretical holographic principle arguments from the 1990s, many physicists believe that 11-dimensional M-theory, which is described in many sectors by matrix string theory, in many other sectors by perturbative string theory is the complete theory of everything, although there is no widespread consensus and M-theory is not a completed theory but rather an approach for producing one.

Contents


 Historical antecedents

Laplace famously suggested that a sufficiently powerful intellect could, if it knew the position and velocity of every particle at a given time, along with the laws of nature, calculate the position of any particle at any other time:
An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.
Essai philosophique sur les probabilités, Introduction. 1814
Although modern quantum mechanics suggests that uncertainty is inescapable, a unifying theory governing probabilistic assignments may nevertheless exist.

 Ancient Greece to Einstein

Since ancient Greek times, philosophers have speculated that the apparent diversity of appearances conceals an underlying unity, and thus that the list of forces might be short, indeed might contain only a single entry. For example, the mechanical philosophy of the 17th century posited that all forces could be ultimately reduced to contact forces between tiny solid particles.[3] This was abandoned after the acceptance of Isaac Newton's long-distance force of gravity; but at the same time, Newton's work in his Principia provided the first dramatic empirical evidence for the unification of apparently distinct forces: Galileo's work on terrestrial gravity, Kepler's laws of planetary motion, and the phenomenon of tides were all quantitatively explained by a single law of universal gravitation.

In 1820, Hans Christian Ørsted discovered a connection between electricity and magnetism, triggering decades of work that culminated in James Clerk Maxwell's theory of electromagnetism. Also during the 19th and early 20th centuries, it gradually became apparent that many common examples of forces—contact forces, elasticity, viscosity, friction, pressure—resulted from electrical interactions between the smallest particles of matter. In the late 1920s, the new quantum mechanics showed that the chemical bonds between atoms were examples of (quantum) electrical forces, justifying Dirac's boast that "the underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known".[4]

Attempts to unify gravity with electromagnetism date back at least to Michael Faraday's experiments of 1849–50.[5] After Albert Einstein's theory of gravity (general relativity) was published in 1915, the search for a unified field theory combining gravity with electromagnetism began in earnest. At the time, it seemed plausible that no other fundamental forces exist. Prominent contributors were Gunnar Nordström, Hermann Weyl, Arthur Eddington, Theodor Kaluza, Oskar Klein, and most notably, many attempts by Einstein and his collaborators. In his last years, Albert Einstein was intensely occupied in finding such a unifying theory. None of these attempts were successful.[6]

 New discoveries

The search for a unifying theory was interrupted by the discovery of the strong and weak nuclear forces, which could not be subsumed into either gravity or electromagnetism. A further hurdle was the acceptance that quantum mechanics had to be incorporated from the start, rather than emerging as a consequence of a deterministic unified theory, as Einstein had hoped. Gravity and electromagnetism could always peacefully coexist as entries in a list of Newtonian forces, but for many years it seemed that gravity could not even be incorporated into the quantum framework, let alone unified with the other fundamental forces. For this reason, work on unification for much of the twentieth century, focused on understanding the three "quantum" forces: electromagnetism and the weak and strong forces. The first two were unified in 1967–68 by Sheldon Glashow, Steven Weinberg, and Abdus Salam as the "electroweak" force.[7] However, while the strong and electroweak forces peacefully coexist in the Standard Model of particle physics, they remain distinct. Several Grand Unified Theories (GUTs) have been proposed to unify them. Although the simplest GUTs have been experimentally ruled out, the general idea, especially when linked with supersymmetry, remains strongly favored by the theoretical physics community.[8]

 Modern physics

In current mainstream physics, a Theory of Everything would unify all the fundamental interactions of nature, which are usually considered to be four in number: gravity, the strong nuclear force, the weak nuclear force, and the electromagnetic force. Because the weak force can transform elementary particles from one kind into another, the TOE should yield a deep understanding of the various different kinds of particles as well as the different forces. The expected pattern of theories is:

Theory of Everything


Gravity
Electronuclear force (GUT)

Strong force
SU(3)
Electroweak force
SU(2) x U(1)

Weak force
SU(2)
Electromagnetism
U(1)


Electric force
Magnetic force
In addition to the forces listed here, modern cosmology might require an inflationary force, dark energy, and also dark matter composed of fundamental particles outside the scheme of the standard model. The existence of these has not been proven and there are alternative theories such as modified Newtonian dynamics.[citation needed]

Electroweak unification is a broken symmetry: the electromagnetic and weak forces appear distinct at low energies because the particles carrying the weak force, the W and Z bosons, have a mass of about 100 GeV, whereas the photon, which carries the electromagnetic force, is massless. At higher energies Ws and Zs can be created easily and the unified nature of the force becomes apparent. Grand unification is expected to work in a similar way, but at energies of the order of 1016 GeV, far greater than could be reached by any possible Earth-based particle accelerator. By analogy, unification of the GUT force with gravity is expected at the Planck energy, roughly 1019 GeV.

It may seem premature to be searching for a TOE when there is as yet no direct evidence for an electronuclear force, and while in any case there are many different proposed GUTs. In fact the name deliberately suggests the hubris involved. Nevertheless, most physicists believe this unification is possible, partly due to the past history of convergence towards a single theory. Supersymmetric GUTs seem plausible not only for their theoretical "beauty", but because they naturally produce large quantities of dark matter, and the inflationary force may be related to GUT physics (although it does not seem to form an inevitable part of the theory). And yet GUTs are clearly not the final answer. Both the current standard model and proposed GUTs are quantum field theories which require the problematic technique of renormalization to yield sensible answers. This is usually regarded as a sign that these are only effective field theories, omitting crucial phenomena relevant only at very high energies. Furthermore, the inconsistency between quantum mechanics and general relativity implies that one or both of these must be replaced by a theory incorporating quantum gravity.

Unsolved problems in physics
Is string theory, superstring theory, or M-theory, or some other variant on this theme, a step on the road to a "theory of everything", or just a blind alley? Question mark2.svg
The mainstream theory of everything at the moment is superstring theory / M-theory; current research on loop quantum gravity may eventually play a fundamental role in a TOE, but that is not its primary aim.[9] These theories attempt to deal with the renormalization problem by setting up some lower bound on the length scales possible. String theories and supergravity (both believed to be limiting cases of the yet-to-be-defined M-theory) suppose that the universe actually has more dimensions than the easily observed three of space and one of time. The motivation behind this approach began with the Kaluza-Klein theory in which it was noted that applying general relativity to a five dimensional universe (with the usual four dimensions plus one small curled-up dimension) yields the equivalent of the usual general relativity in four dimensions together with Maxwell's equations (electromagnetism, also in four dimensions). This has led to efforts to work with theories with large number of dimensions in the hopes that this would produce equations that are similar to known laws of physics. The notion of extra dimensions also helps to resolve the hierarchy problem, which is the question of why gravity is so much weaker than any other force. The common answer involves gravity leaking into the extra dimensions in ways that the other forces do not.[citation needed]

In the late 1990s, it was noted that one problem with several of the candidates for theories of everything (but particularly string theory) was that they did not constrain the characteristics of the predicted universe. For example, many theories of quantum gravity can create universes with arbitrary numbers of dimensions or with arbitrary cosmological constants. Even the "standard" ten-dimensional string theory allows the "curled up" dimensions to be compactified in an enormous number of different ways (one estimate is 10500 ) each of which corresponds to a different collection of fundamental particles and low-energy forces. This array of theories is known as the string theory landscape.

A speculative solution is that many or all of these possibilities are realised in one or another of a huge number of universes, but that only a small number of them are habitable, and hence the fundamental constants of the universe are ultimately the result of the anthropic principle rather than a consequence of the theory of everything. This anthropic approach is often criticised[who?] in that, because the theory is flexible enough to encompass almost any observation, it cannot make useful (as in original, falsifiable, and verifiable) predictions. In this view, string theory would be considered a pseudoscience, where an unfalsifiable theory is constantly adapted to fit the experimental results.

 With reference to Gödel's incompleteness theorem

A small number of scientists claim that Gödel's incompleteness theorem proves that any attempt to construct a TOE is bound to fail. Gödel's theorem, informally stated, asserts that any formal theory expressive enough for elementary arithmetical facts to be expressed and strong enough for them to be proved is either inconsistent (both a statement and its denial can be derived from its axioms) or incomplete, in the sense that there is a true statement about natural numbers that can't be derived in the formal theory. In his 1966 book The Relevance of Physics, Stanley Jaki pointed out that, because any "theory of everything" will certainly be a consistent non-trivial mathematical theory, it must be incomplete. He claims that this dooms searches for a deterministic theory of everything.[10] In a later reflection, Jaki states that it is wrong to say that a final theory is impossible, but rather that "when it is on hand one cannot know rigorously that it is a final theory." [11]
Freeman Dyson has stated that
Gödel’s theorem implies that pure mathematics is inexhaustible. No matter how many problems we solve, there will always be other problems that cannot be solved within the existing rules. [...] Because of Gödel's theorem, physics is inexhaustible too. The laws of physics are a finite set of rules, and include the rules for doing mathematics, so that Gödel's theorem applies to them.
—NYRB, May 13, 2004
Stephen Hawking was originally a believer in the Theory of Everything but, after considering Gödel's Theorem, concluded that one was not obtainable.
Some people will be very disappointed if there is not an ultimate theory, that can be formulated as a finite number of principles. I used to belong to that camp, but I have changed my mind.
Jürgen Schmidhuber (1997) has argued against this view; he points out that Gödel's theorems are irrelevant for computable physics.[12] In 2000, Schmidhuber explicitly constructed limit-computable, deterministic universes whose pseudo-randomness based on undecidable, Gödel-like halting problems is extremely hard to detect but does not at all prevent formal TOEs describable by very few bits of information.[13][14]
Related critique was offered by Solomon Feferman,[15] among others. Douglas S. Robertson offers Conway's game of life as an example:[16] The underlying rules are simple and complete, but there are formally undecidable questions about the game's behaviors. Analogously, it may (or may not) be possible to completely state the underlying rules of physics with a finite number of well-defined laws, but there is little doubt that there are questions about the behavior of physical systems which are formally undecidable on the basis of those underlying laws.

Since most physicists would consider the statement of the underlying rules to suffice as the definition of a "theory of everything", these researchers argue that Gödel's Theorem does not mean that a TOE cannot exist. On the other hand, the physicists invoking Gödel's Theorem appear, at least in some cases, to be referring not to the underlying rules, but to the understandability of the behavior of all physical systems, as when Hawking mentions arranging blocks into rectangles, turning the computation of prime numbers into a physical question.[17] This definitional discrepancy may explain some of the disagreement among researchers.
Another approach to working with the limits of logic implied by Gödel's incompleteness theorems is to abandon the attempt to model reality using a formal system altogether. Process Physics[18] is a notable example of a candidate TOE that takes this approach, where reality is modeled using self-organizing (purely semantic) information.

 Potential status of a theory of everything

No physical theory to date is believed to be precisely accurate. Instead, physics has proceeded by a series of "successive approximations" allowing more and more accurate predictions over a wider and wider range of phenomena. Some physicists believe that it is therefore a mistake to confuse theoretical models with the true nature of reality, and hold that the series of approximations will never terminate in the "truth". Einstein himself expressed this view on occasions.[19] On this view, we may reasonably hope for a theory of everything which self-consistently incorporates all currently known forces, but should not expect it to be the final answer. On the other hand it is often claimed that, despite the apparently ever-increasing complexity of the mathematics of each new theory, in a deep sense associated with their underlying gauge symmetry and the number of fundamental physical constants, the theories are becoming simpler. If so, the process of simplification cannot continue indefinitely.

There is a philosophical debate within the physics community as to whether a theory of everything deserves to be called the fundamental law of the universe.[20] One view is the hard reductionist position that the TOE is the fundamental law and that all other theories that apply within the universe are a consequence of the TOE. Another view is that emergent laws (called "free floating laws" by Steven Weinberg[citation needed]), which govern the behavior of complex systems, should be seen as equally fundamental. Examples are the second law of thermodynamics and the theory of natural selection. The point being that, although in our universe these laws describe systems whose behaviour could ("in principle") be predicted from a TOE, they would also hold in universes with different low-level laws, subject only to some very general conditions. Therefore it is of no help, even in principle, to invoke low-level laws when discussing the behavior of complex systems. Some[who?] argue that this attitude would violate Occam's Razor if a completely valid TOE were formulated. It is not clear that there is any point at issue in these debates (e.g., between Steven Weinberg and Philip Anderson[citation needed]) other than the right to apply the high-status word "fundamental" to their respective subjects of interest.

Although the name "theory of everything" suggests the determinism of Laplace's quotation, this gives a very misleading impression. Determinism is frustrated by the probabilistic nature of quantum mechanical predictions, by the extreme sensitivity to initial conditions that leads to mathematical chaos, and by the extreme mathematical difficulty of applying the theory. Thus, although the current standard model of particle physics "in principle" predicts all known non-gravitational phenomena, in practice only a few quantitative results have been derived from the full theory (e.g., the masses of some of the simplest hadrons), and these results (especially the particle masses which are most relevant for low-energy physics) are less accurate than existing experimental measurements. The true TOE would almost certainly be even harder to apply. The main motive for seeking a TOE, apart from the pure intellectual satisfaction of completing a centuries-long quest, is that all prior successful unifications have predicted new phenomena, some of which (e.g., electrical generators) have proved of great practical importance. As in other cases of theory reduction, the TOE would also allow us to confidently define the domain of validity and residual error of low-energy approximations to the full theory which could be used for practical calculations.

Some of the biggest problems facing current TOE attempts are related to Einstein's theories of relativity. None of the current attempted TOEs give a structure of matter that gives rise to the special relativity corrections to mass, length and time when a particle moves. Those corrections are just imposed as if it is some unknown property of space. Also Einstein introduced an approximation when he derived his gravitational field equations in his general theory of relativity.[21] Trying to match a theory to an approximation is always going to be difficult. It is believed[who?] that success will be easier when those two factors are taken into consideration.

 Theory of everything and philosophy

The status of a physical TOE is open to philosophical debate. For example, if physicalism is true, a physical TOE will coincide with a philosophical theory of everything. Some philosophers (Aristotle, Plato, Hegel, Whitehead, et al.) have attempted to construct all-encompassing systems. Others are highly dubious about the very possibility of such an exercise. Stephen Hawking wrote in A Brief History of Time that even if we had a TOE, it would necessarily be a set of equations. He wrote, “What is it that breathes fire into the equations and makes a universe for them to describe?”[22]. Of course, the ultimate irreducible brute fact would then be "why those equations?" One possible solution to the last question might be to adopt the point of view of ultimate ensemble, or modal realism, and say that those equations are not unique.

 See also

 References

  1. ^ Ellis, John (2002). "Physics gets physical (correspondence)". Nature 415: 957. 
  2. ^ Ellis, John (1986). "The Superstring: Theory of Everything, or of Nothing?". Nature 323: 595–598. doi:10.1038/323595a0. 
  3. ^ Shapin, Steven (1996). The Scientific Revolution. University of Chicago Press. ISBN 0226750213. 
  4. ^ Dirac, P.A.M. (1929). "Quantum mechanics of many-electron systems". Proceedings of the Royal Society of London A 123: 714. doi:10.1098/rspa.1929.0094. 
  5. ^ Faraday, M. (1850). "Experimental Researches in Electricity. Twenty-Fourth Series. On the Possible Relation of Gravity to Electricity". Abstracts of the Papers Communicated to the Royal Society of London 5: 994–995. doi:10.1098/rspl.1843.0267. 
  6. ^ Pais (1982), Ch. 17.
  7. ^ Weinberg (1993), Ch. 5
  8. ^ There is one GUT not linked to super symmetry that has not been eliminated by experiment. That is the four universe theory of George Ryazanov. It has been tested once in a lab at Hebrew University informally. The results were reported to be positive. But the test has not been repeated elsewhere. See http://george-ryazanov.com/book4/03-Physics_of_Unity.html. However Ryazanov's theory does involve Lorentz violation. If the Fermi Glast project does not find Lorentz violation, this will be a blow to the Ryazanov Theory.
  9. ^ Potter, Franklin (15 February 2005). "Leptons And Quarks In A Discrete Spacetime". Frank Potter's Science Gems. http://www.sciencegems.com/discretespace.pdf. Retrieved 2009-12-01. 
  10. ^ Jaki, S.L. (1966). The Relevance of Physics. Chicago Press. 
  11. ^ Stanley L. Jaki (2004) "A Late Awakening to Gödel in Physics," p. 8-9.
  12. ^ Schmidhuber, Jürgen (1997). A Computer Scientist's View of Life, the Universe, and Everything. Lecture Notes in Computer Science. Springer. pp. 201–208. doi:10.1007/BFb0052071. ISBN 978-3-540-63746-2. http://www.idsia.ch/~juergen/everything/. 
  13. ^ Schmidhuber, Jürgen (2000). "Algorithmic Theories of Everything". arΧiv:quant-ph/0011122 [quant-ph]. 
  14. ^ Schmidhuber, Jürgen (2002). "Hierarchies of generalized Kolmogorov complexities and nonenumerable universal measures computable in the limit". International Journal of Foundations of Computer Science 13 (4): 587–612. doi:10.1142/S0129054102001291. 
  15. ^ Feferman, Solomon (17 November 2006). "The nature and significance of Gödel’s incompleteness theorems". Institute for Advanced Study. http://math.stanford.edu/~feferman/papers/Godel-IAS.pdf. Retrieved 2009-01-12. 
  16. ^ Robertson, Douglas S. (2007). "Goedel’s Theorem, the Theory of Everything, and the Future of Science and Mathematics". Complexity 5: 22–27. doi:10.1002/1099-0526(200005/06)5:5<22::AID-CPLX4>3.0.CO;2-0. 
  17. ^ Hawking, Stephen (20 July 2002). "Gödel and the end of physics". http://www.damtp.cam.ac.uk/strings02/dirac/hawking/. Retrieved 2009-12-01. 
  18. ^ Cahill, Reginald (2003). "Process Physics". Process Studies Supplement. Center for Process Studies. pp. 1–131. http://www.ctr4process.org/publications/ProcessStudies/PSS/2003-5-CahillR-Process_Physics.shtml. Retrieved 2009-07-14. 
  19. ^ Einstein, letter to Felix Klein, 1917. (On determinism and approximations.) Quoted in Pais (1982), Ch. 17.
  20. ^ Weinberg (1993), Ch 2.
  21. ^ Equation 20 in Einstein, Albert (1916), "Die Grunlage der allgemeinen Relativätstheorie", Annalen der Physik 49: 769 
  22. ^ as quoted in [Artigas, The Mind of the Universe, p.123]

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