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Showing posts with label Klein. Show all posts
Showing posts with label Klein. Show all posts

Wednesday, January 18, 2012

A Historical Look at Kaluza-Klein Particles?

In 1919, Kaluza sent Albert Einstein a preprint --- later published in 1921 --- that considered the extension of general relativity to five dimensions. He assumed that the 5-dimensional field equations were simply the higher-dimensional version of the vacuum Einstein equation, and that all the metric components were independent of the fifth coordinate. The later assumption came to be known as the cylinder condition. This resulted in something remarkable: the fifteen higher-dimension field equations naturally broke into a set of ten formulae governing a tensor field representing gravity, four describing a vector field representing electromagnetism, and one wave equation for a scalar field. Furthermore, if the scalar field was constant, the vector field equations were just Maxwell's equations in vacuo, and the tensor field equations were the 4-dimensional Einstein field equations sourced by an EM field. In one fell swoop, Kaluza had written down a single covariant field theory in five dimensions that yielded the four dimensional theories of general relativity and electromagnetism. Naturally, Einstein was very interested in this preprint (Link is now dead but what is said here is very important and may help with imagery needed?)

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After having formulated general relativity Albert Einstein did not immediately focus on the unification of electromagnetism and gravity in a classical field theory - the issue that would characterize much of his later work. It was still an open question to him whether relativity and electrodynamics together would cast light on the problem of the structure of matter [?]. Rather, in a 1916 paper on gravitational waves he anticipated a different development: since the electron in its atomic orbit would radiate gravitationally, something that cannot occur in reality", he expected quantum theory would have to change not only the "Maxwellian electrodynamics, but also the new theory of gravitation" [?]2. Einstein's position, however, gradually changed. From about 1919 onwards, he took a strong interest in the unification programme3. In later years, after about 1926, he hoped that he would and a particular classical unified field theory that could undercut quantum theory. Such a theory would have to contain the material objects -sources and fields- and their dynamics. He would even expect the distinction between these concepts to fade: \a complete field theory knows only fields and not the concepts of particle and motion" [?]. We will study how he wanted to realize these principles in classical Kaluza-Klein theory, and try to see what his objectives and results were.See: Einstein and the Kaluza-Klein particle

moving on further in the article toward the end...

Bergmann, now in Syracuse, wrote Einstein and asked if they could have a discussion sometime:

As anyone can only be a crank about his own ideas, and as you are someone who combines steadfastness with the ability to acknowledge his hypothesis could go wrong (usually one can only and just one of these qualities, mostly the latter) I would appreciate very much talking to you and hearing your observations; whether we appreciate the same or not, what we want is sufficiently related that we could easily come to an understanding." [?] 2

Einstein replies:
You are looking for an independent and new way to solve the fundamental problems. With this endeavor no one can help you, least of all someone who has somewhat fixed ideas. For instance, you know that on the basis of certain considerations I am convinced that the probability concept should not be primarily included in the description of reality, whereas you seem to believe that one should first formulate a field theory and subsequently 'quantize' it. This is in keeping with the view of most contemporaries. Your effort to abstractly carry through a field theory without having at your disposal the formal nature of the field quantities in advance, does not seem favorable to me, for it is formally too poor and vague."17 [?] 2

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Missing Energy Kicks New Physics Models Off The Board


The signature of large missing energy and jets is arguably one of the most important avenues for the study of potential new physics signatures at today's hadron colliders.

The above concept marks an interesting turn of events: the years of the glorification of charged leptons as the single most important tools for the discovery of rare production processes appears behind us. The W and Z discovery in 1983 by UA1 at CERN, or the top quark discovery by CDF and DZERO in 1995 at Fermilab, would have been impossible without the precise and clean detection of electrons and muons. However, with time we have understood that missing energy may be a more powerful tool for new discoveries.

Missing energy arises when a violent collision between the projectiles -protons against antiprotons at the Tevatron collider, or protons against protons at the world's most powerful accelerator, the LHC- produces an asymmetric flow of energetic bodies out of the collision point in the plane orthogonal to the beams: a transverse imbalance. This is a clear signal that something is leaving the detector unseen. And it turns out that there is a host of new physics signals which can do precisely that.

A large amount of missing transverse energy may be the result of the decay of a leptoquarks into jets and neutrinos, when the latter leave undetected; or from the silent escape of a supersymmetric neutral particle -the neutralino- produced in the chain of decays following the production of squarks and gluinos; or it may even be due to the escape of particles in a fourth dimension of space -an alternative dubbed "large extra dimensions".
(see more in linked title above)

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I have been slowly moving through the explanations for the extra-dimensions that are being explained by Matt Strassler:

In this article and the next, we will learn why extra dimensions lead to “Kaluza-Klein (KK) partner” particles (described in the previous article in this series, which you should read before this one.)  If a known type of  particle of mass m can travel in a dimension of which we are unaware — an “extra” dimension — then we will eventually discover many other types of particles, similar to the known one but heavier, with masses M>m.
See: Kaluza-Klein Partners — Why? Step 1

Friday, January 13, 2012

The Smoking Gun

One string theorist even went so far to conclude that a string theory calculation of Kaluza-Klein modes was the "smoking gun" that proved our theory was the same as the string theory that string theorists had already been studying.Warped Passages: Unraveling The Mysteries of the Universes Hidden Dimensions by Lisa Randall Pg 436, Para 4

Putting this together with what is real in our reality is of importance as well. While I may have my own metaphysical development and model building characteristics it was important that I learn the scientific one so that I could see where I may have been wrong in my own development scenario. Wrong in my own intuitions.

 Meanwhile I’m continuing to develop the Extra Dimensions series of articles, and I’ve now followed up my examples of extra dimensions with a next installment, a first discussion of what scientists would look for in trying to identify that our world actually has one or more extra dimensions .  The new article describes one of the key clues that would indicate their presence.  But this is far from the end of the story: I owe you more articles, explaining why extra dimensions would generate this clue, outlining how we try to search for this clue experimentally, and mentioning other possible clues that might arise.  All in due course…The Smoking Gun for Extra Dimensions by Theoretical Physicist Matt Strassler

Some may of not been forced to question them-self  with what it is that we have to ask of ourselves,  as we delve into the world of the sciences and philosophies. To ask ourselves whether we had always been dealing with the truth of our getting to the heart of things.

A professor may have asked what it is exactly what I wanted out of all of this,  and to him I have to relay a dream that has manifested because of his question.

In the dream I have been provided a forum for discussing my ideas.....but when it came to the time for speaking,  my preparations,  I felt lost as to where to begin. So it seems I have come to this point in time, as to "shit or get off the pot" as to what it is I wish to share of importance?

Giving these subjects the numbers of years since 2001, one would have thought  had served my own internship, but alas I remain ever the student with no classification. Yet it is the developing of the concepts with what is real in the push to experiment as to find what the real world examples are showing as attributes in the experimental processes as they unfold.

 In this example I’m going to map speed to the pitch of the note, length/postion to the duration of the note and number of turns/legs/puffs to the loudness of the note.See: How to make sound out of anything.


Who of us has the foresight to see where the process of the experiment had been developed to share an idea about what it was that we wanted to discover of nature? To see in the mind of the developers as to why the equipment has been superimposed from the schematics of theories to be tested as to discover what we may found in our model building.

Does all this prepare you to looking at the universe different?

 The Lagrange Points


In the above contour plot we see that L4 and L5 correspond to hilltops and L1, L2 and L3 correspond to saddles (i.e. points where the potential is curving up in one direction and down in the other). This suggests that satellites placed at the Lagrange points will have a tendency to wander off (try sitting a marble on top of a watermelon or on top of a real saddle and you get the idea). A detailed analysis (PDF link) confirms our expectations for L1, L2 and L3, but not for L4 and L5. When a satellite parked at L4 or L5 starts to roll off the hill it picks up speed. At this point the Coriolis force comes into play - the same force that causes hurricanes to spin up on the earth - and sends the satellite into a stable orbit around the Lagrange point. See: Space Travel and Propulsion Methods

I have to say who has not been touched as if we put on a pair of rose colored glasses to see the Lagrangian world as if the gravitons populated  locations of influence. As if they were descriptive as overlapping nodes of sound as to support some acoustical idea about levitation? Satellites that travel through space or held in position as our space station is.

 
Like different musical instruments, different types of stars produce different types of sound waves. Small stars produce a sound with a higher pitch than bigger stars, just like the 'piccolo' produces a higher sound than the cello

Thus it is as ones can see differently that I look upon the world as to discover what things we may not know of our own selves that we had missed in understanding our own physical evolution, that it is more then the matter with which we use and are made up of?


This recording was produced by converting into audible sounds some of the radar echoes received by Huygens during the last few kilometres of its descent onto Titan. As the probe approaches the ground, both the pitch and intensity increase. Scientists will use intensity of the echoes to speculate about the nature of the surface. Radar echos from Titan's surface

Tuesday, November 15, 2011

Point Particles and String Amplitudes



For myself understanding the dimensional relationship toward the QFT perspective of particle research and development,  it has been a difficult road to understanding this relation. It is not just the idea of what transpires as we architecturally build the world\universe we live in,  but to understand nature's expression as we see the movement in the universe as we research and experimental with particle  decay products.


Click on Image to go to appropriate site for image dedication

So there is a lot being said about what is contained in the first paragraph of this opening blog post that will never be understood by other layman like myself, or, other experts considering the developmental phases I have been going through. Are my  ruminations consistent,  or,  have they haphazardly layered a trail of confusion  to have it said that what danger lurks in this determination of what is written here is to confuse.

Should I put aside all that I have learn in context of theoretical developments?


Albrecht Dürer(self portrait at 28) See also: Albrecht Durer and His Magic Square


No.  I can assure you that I have been at this a number of years now to say that with what I am doing now is filling  in the gaps of where I have been to where I am going in terms of better explaining myself in a scientific context that is acceptable to the notion of what might have transpired in the 21 st century for some. It has been in learning string theory.  Yes, I have listened to all the articulations of the back and forth of what the basis of this theoretical determination is "as a mathematical foundation"  has yet to prove it''s validity as a method by which to explain the nature of the universe?

 
Physicists Andrew Strominger and Cumrin Vafa, showed that this exact entropy formula can be derived microscopically (including the factor of 1/4) by counting the degeneracy of quantum states of configurations of strings and D-branes which correspond to black holes in string theory. This is compelling evidence that D-branes can provide a short distance weak coupling description of certain black holes! For example, the class of black holes studied by Strominger and Vafa are described by 5-branes, 1-branes and open strings traveling down the 1-brane all wrapped on a 5-dimensional torus, which gives an effective one dimensional object -- a black hole. 


How am I to dismiss the logic of approach? We are learning to count in dimensional referencing? It is mathematically orientated is it not? But indeed,  Planck scale presents a problem.  So by what foundation can  it ever play as a method by which such discussion of the universe in expression? How can it have such validation as a geometrical expression of the nature of particle expression by virtue of the dimensional development along side of topological arrangement and correlations?


The crystalline state is the simplest known example of a quantum , a stable state of matter whose generic low-energy properties are determined by a higher organizing principle and nothing else. Prof. Robert B. Laughlin
 
This is just the road I took and it allowed me to see what can ever transpired as a expression of a understanding of symmetry breaking. It is an understanding of this correlation toward the "false vacuum to the true."  This was an expression of the space we are "living in" as an understanding of the timing in relation to the expression of this universe. One just had to know indeed their was indeed a higher order? A Klein bottle perhaps in  following the lines on the surface?

 Using the anti–de Sitter/conformal field theory correspondence to relate fermionic quantum critical fields to a gravitational problem, we computed the spectral functions of fermions in the field theory. By increasing the fermion density away from the relativistic quantum critical point, a state emerges with all the features of the Fermi liquid. See:String Theory, Quantum Phase Transitions, and the Emergent Fermi Liquid
What can we say then is emergent? So you are learning to count in geometrical expressions as a placement of the Genus figures? So what correlations can be drawn toward the beginning of such counting?

For me it was necessary to carry on the tradition of geometrical seeing what was revealed in relativity development(Grossman and Riemann) to know that such an expression had to be moved into the world of the very small.

The Landscape Again and again....


It had to have a relativistic interpretation of the way in which such energies could detail the understanding of particles in expression. But also, of the energies involved. So this "Royal road to geometry" in relation to topology,  had to be understood by myself as I understood the Genus placements in the valleys of expression. The landscape.

I knew where such new physics needs to be in relation to what is happening as we look at the experiments of LHC . Of course I have to better understand the Jet manifestation in order to reveal some of the thinking that has been produced in my journeys.

Wednesday, March 09, 2011

ICECUBE

 For me, the idea of a backdrop measure, as if Thomas Young experimentally fires his photon gun, the collision points at the LHC provide dimensional references(flight paths) to events that are measured  by comparison of LHC too,  muon detection facilitations as if,  Cosmic Rays collisions in faster then light medium of ice, resulting in ICECUBE data. Cerenkov. Muon detection scenarios are useful tools to speeds through earth and matters for  consideration anyway. Think of Volcano here or looking through pyramids.

That's the plan anyway right?
 
“IceCube: An instrument for neutrino astronomy,” by Francis Halzen and Spencer R. Klein
IceCube completed, University of Wisconsin press release
Ice Cube completed, Berkeley Lab press release
IceCube website

Wednesday, November 10, 2010

It's Neither World, not Nether

Netherworld is often used as a synonym for Underworld.

Okay this may seem like a strange title, but believe me when I say how fascinating that such dynamics in meeting "each other: will allow something to "pop" right out of existence.

Underworld is a region in some religions and in mythologies which is thought to be under the surface of the earth.[1] It could be a place where the souls of the recently departed go, and, in some traditions, it is identified with Hell or the realm of death. In other traditions, however, such as animistic traditions, it could be seen as the place where life appears to have originated from (such as plant life, water, etc.) and a place to which life must return at life's end, with no negative undertones.

I mean I am not quite sure how this post must materialize, to conclude "non-existence" until it is clear, that such dynamics  will allow such a thing to happen, that one could say indeed,  they have completed their journey.

Now can I say that this is the process of the universe,  I can't be sure.I know that in the "mediation process" for concluding the experience,  such an experience has to come undone. Again this is such a strange thing in my mind that I had to say that "I was the experience" until such a time, that going along with other things in sameness of dynamics, that it was hard at first to see this dynamics in play as being apart from it.  I could actually only say enough of this experience to concluded  the realization of coming undone. Hmm...

To solidify this until understanding, I relived these things until I saw the last of the tension ebb away to allow  "a tension" to become undone. As if such tension "had to exist" until the very bubble that harbored and allowed all of the world of our expediency no longer supported such a viable option as that bubble.

I know this is not such a cute analogy but to get to the essence of the story then it has to be understood that underneath "this experience"  is a dynamcial revelation of sorts that hides the equation of such an experience?

You should know then that I see this very schematics of the world as having this nature to it that we may describe reality as something closer to the definition of it's very existence and that such a attempt at describing nature was to get to the very end of what begins? Imagine arriving at the juxtaposition of such a point?

How are We to Contained Experience?

In mathematics, the Klein bottle ([klaɪ̯n]) is a non-orientable surface, informally, a surface (a two-dimensional manifold) with no identifiable "inner" and "outer" sides. Other related non-orientable objects include the Möbius strip and the real projective plane. Whereas a Möbius strip is a two-dimensional surface with boundary, a Klein bottle has no boundary. (For comparison, a sphere is an orientable surface with no boundary.)
By adding a fourth dimension to the three dimensional space, the self-intersection can be eliminated. Gently push a piece of the tube containing the intersection out of the original three dimensional space. A useful analogy is to consider a self-intersecting curve on the plane; self-intersections can be eliminated by lifting one strand off the plane.
This immersion is useful for visualizing many properties of the Klein bottle. For example, the Klein bottle has no boundary, where the surface stops abruptly, and it is non-orientable, as reflected in the one-sidedness of the immersion.

The geometry was revealing as I tried to encapsulate this point, so as to see where such a description fell away from all that we can contain of the world. That we can truly say we had indeed let go. To imagine then that one's grip on things became ever tighter, while wishing to let the strength of this while becoming ever stronger to fall away.

"While Gassner was watching television, the natural motion of the Earth must have carried him through a small non-orientable pocket of the universe," said Boris Harkov, a mathematician at the Massachusetts Institute of Technology in Cambridge. "That's the only reasonable explanation."

One way to test the orientation of the universe is to hurl a right-handed glove into the air and see if it falls back to Earth as a left-handed glove--if it does, the universe must be non-orientable. Since Gassner's announcement, physicists have been carrying out such experiments, both outdoors and in Gassner's TV room, but so far all tests have come back negative. Still, many researchers are optimistic. "I'm confident that the glove will flip soon," said Chen Xiang, an experimental physicist at Brookhaven National Laboratory in New York. The Klarreich Occasionally


Ultimate realization that what is negative is a positive toward completion.That is how one might define the whole perspective of validation of no longer being negative?

As if one wold realize that such a tension revealed in the Tao, no longer existed in the picture as a demonstration of the Tao now gone.
Now, such a object seemed part of the experience,  as to the unfolding, yet in my inadequate understanding how could such a thing be taken down to such a point as to say it no longer existed. How can I say say such a geometry was part of that process while I struggle to define such an action as falling away or reducing it to such a point of nothing?

It's enough then that one sees "around that point"  that the ultimate quest envisions such  an "undoing" that we see where the relevance of such a tension can and should no longer exist?

The Experience Most Fitting then ?

As I relayed earlier I experience many things until I understood this undoing, that such reason then to awareness of "what should be" was capsulized in only one example. How shall I say it then that I understood all that befell me to dissolution to show that such a demonstration was complete. I would still be here? That such an equation of resistance could have been imparted not only in the equation, but in the telling of the experience too?

While I show by experience such an example it should be taken that in this example I have changed the name of the person in order to protect our association. Shall I be so forthcoming that only the "object of relation" shall be the only thing identifiable  so as to know that this association is very real to me, and only to me by that person's identification as an experience that is real? Aw....well anyway "more then one" for sure, as to the way in which I use that experience to demonstrate.

It all began, as I noticed a tension in his voice, as he slipped into the realization of something that had happen to him earlier in that day. I was taken to a "good observation point" so that I might admit to seeing what he was seeing.  As hard as I looked at first I could not tell what he was so upset about that I tried ever harder  to see, that slowly I understood then what he was pointing at. Why such a tension could exist in him and his voice, that such a rectification and adjustment was needed in order to make this right.

As I relay this situation it was apparent at the time of such a demonstration, as to a example that this situation popped up,  as such a reason to be demonstrated that to make it right, had to be the undoing of what made it wrong you see. To make the point ever driven home for realization was to demonstrate that such undoing had to rectify the situation of where it began, so of course,  all actions taken to get it fixed. Could it have ever been undone?

Well as if I understood why such an experience came frothing to the surface of awareness I thought to conclude this example by what I saw, that it took me by realization that "in turning" to back up, a hand imprint in oil was left on the back of the seat in order for the person to complete the job. A "new point of tension" by not washing their hands, or not covering  pristine upholstery that was just purchased, was created.

All of this has to be undone in order for one to say that this experience has popped out of existence you see?

That was how such a demonstration was shown to be reasonable in my mind for such an equation to manifest such a description about that experience that I could say that it was reasonable to me that I had understood.

Was it a good example rests on you to be sure.

***
Physically, the effect can be interpreted as an object moving from the "false vacuum" (where = 0) to the more stable "true vacuum" (where = v). Gravitationally, it is similar to the more familiar case of moving from the hilltop to the valley. In the case of Higgs field, the transformation is accompanied with a "phase change", which endows mass to some of the particles

"Quantum Field Theory

Quantum Vacuum:

In classical physics, empty space is called the vacuum. The classical vacuum is utterly featureless. However, in quantum theory, the vacuum is a much more complex entity. The uncertainty principle allows virtual particles (each corresponding to a quantum field) continually materialize out of the vacuum, propagate for a short time and then vanish. " http://universe-review.ca/R15-12-QFT.htm#vacuum

"The idea behind the Coleman-De Luccia instanton, discovered in 1987, is that the matter in the early universe is initially in a state known as a false vacuum. A false vacuum is a classically stable excited state which is quantum mechanically unstable." http://www.damtp.cam.ac.uk/research/gr/public/qg_qc.html

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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