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Final Answers
© 2000-2017   Gérard P. Michon, Ph.D.

String Theory
and other  "Theories of Everything"

The Universe is not only queerer than we
suppose, it's queerer than we
  can  suppose.
J.B.S. Haldane (1892-1964)
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Related articles on this site:

Related Links (Outside this Site)

The Official String Theory Website  by  Patricia Schwarz.
Reminiscences of Collaborations with Joël Scherk  by  John H. Schwarz.
The Second Superstring Revolution  by  John H. Schwarz.
String Theory:  A Historical Overview  by   Jason Scott.

Militant Blogs

Not Even Wrong  by  Peter Woit  (Columbia University)
Backreaction  by  Sabine Hossenfelder (Bee)  and  Stefan Scherer.
Cosmic Variance   by   CarrollHewettWechsler  and  Troden.
Asymptotia  by  Clifford Johnson  (USC).
TGD Diary  by  Matti Pitkanen  (TGD = Topological Geometrodynamics).
A Quantum Diaries Survivor  by  Tommaso Dorigo  (Padova, Fermilab, CERN)
The Reference Frame  by  Lubos Motl  (formerly at Harvard)
Mass  by  Carl Brannen
Rantings of an Angry Physicist  by  a student  of  Steve Carlip  at UC Davis.

Popular Blog Articles

Quantum Diaries:  The  Year of Physics  (2005)  chronicled by 33 physicists.
The Higgs Boson Particle  in  Life, the Universe and Everything  by  JSKot.

Garrett Lisi :  TOE without Strings
Home   [ Videos: Snowboarding  |  E8 ]

An Exceptionally Simple Theory of Everything  by  Garrett Lisi  (2007-11-06)   ;-)
Reactions by   Garrett Lisi himself, Sabine Hossenfelder (Bee), Peter Woit, Casey Kazan, Lubos Motl, Cosmic Variance, etc.

Textbooks on String Theory :   [ discussion | QFT prerequisite ]

Videos :

String Theory and the Universe  by  Edward Witten  (IOP, 2010-07-01)
The Coming Revolutions in Theoretical Physics  by  David Gross  (2007-10-19)
What is F-theory?  by  Dave Morrison  (2014-09-09)
What every physicist should know about String Theory   Ed Witten  (June 2015).
The importance of superstring theory (3:10)  Murray Gell-Mann  (2016-05-12).
Testing superstring theory (3:27)  by  Murray Gell-Mann  (2016-05-12).
The Case for String Theory  by  Tony Padilla  (Sixty Symbols, 2017-01-30).
Spacetime Versus the Quantum  by  Joe Polchinski  (KITP, UCSB, 2014-12-04)
Introduction to Gauge-Gravity Duality,  by  Joe Polchinski   | 1 | 2 | 3 | 4 | 5 |
Loop Quantum Gravity  by  Carlo Rovelli :   | 1 | 2 | 3 |
String Theory and M-Theory  by  Leonard Susskind  (Stanford, Fall 2010)
[ 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 ]
Topics in String Theory  by  Leonard Susskind  (Stanford, Winter 2011)
[ 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 ]

The Elegant Universe   by  Brian Greene
A 3-hour NOVA miniseries.   [  Video  |  For Teachers  |  Full Screen  ]

In order of appearance :  Steven Weinberg,  Michael Green,  Jim Gates,  Peter Galison, Marcia Bartusiak, Joseph Polchinski, Walter Lewin, Amanda Peet, Nima Arkani-Hamed, Edward Farhi, Michael Duff, Ed Witten, Joe Lykken, Sheldon Glashow, Gabriele Veneziano, Lenny Susskind, John Schwarz, Cumrun Vafa, David Gross, Savas Dimopoulos, Burt Ovrut, Nathan Seiberg, Gary Horowitz, Alan Guth, Paul Steinhardt, Maria Spiropulu.

Biographies   |   Viewpoints   |   Glossary   |   Dimensions   |   Resonance


String Theory,  Superstrings,  M-Theory

The current epistemological status of String Theory is probably best grasped by comparing it with another theory devised in simpler times:  The Dirac equation was a clever example of a theory consistent with the axioms of both quantum mechanics and special relativity.  Some of the concepts involved in its interpretation may not have survived the test of time but it was instrumental in predicting the existence of antimatter and it helped demonstrate that any quantum theory consistent with special relativity would likewise involve antimatter  (which was duly observed, by  Carl Anderson, a couple of years after P.A.M. Dirac predicted it).
Similarly, String Theory is a quantum theory consistent with General Relativity.  Unlike the Dirac equation, however, it has failed to make any definite physical prediction so far.  Therefore, it's currently a legitimate target for critics who call it "nonphysical" or "unscientific"  (arguably, a theory must have falsifiable consequences to be call "scientific" outside of the realm of pure mathematics).
Over the years, this state of affairs has slowly transformed "String Theory" into a general study of all possible quantum theories compatible with General Relativity.  It's not just a theory of "strings" anymore.  It is hoped that, sooner or later, String Theory will achieve at least the same philosophical status as either Newtonian mechanics or Dirac's equation.  It may or may not turn out to be the advertised "theory of everything" but its logical structure would at least reveal some testable features of our physical universe.
The social impact of String Theory among the "community" of theoretical physicists can hardly be overstated...  An entire generation of many of the brightest theoretical physicists have been lured by its mathematical appeal away from other pursuits.  Yet, nobody knows how relevant to physics the resulting body of knowledge really is.  So far, this has been a gamble of unprecedented magnitude without any definite payoff in sight.
The Large Hadron Collider (LHC) is touted as bringing new hope for fresh experimental data in particle physics.  It should soon provide proof of the existence of the long-awaited  Higgs Boson  and determine its mass  (which will round up the structure of the standard model).  However, the LHC cannot provide a test of String Theory, for two reasons:  The experimental consequences of String Theory are not yet clear  (they are not ready to be compared with observation) and, anyway, such direct consequences would be in a range of energy far beyond what's accessible to the LHC  (or any other particle accelerator like it).  Of course, there might well be  indirect  consequences which could take center stage and bring new excitement in the world of particle physics... 


LHC-inspired Google Logo 
 (Used by Google on 2008-09-10)

On the day LHC was supposed to starts operations  (2008-09-10)  Google  flaunted the above version of their logo worldwide.  The discovery of the Higgs boson was announced 4 years later  (2012-07-04).  The 2012 Nobel prize was then widely expected to go to Peter Higgs  (it went to Serge Haroche and David Wineland instead, for unrelated work).  Peter Higgs  and François Englert  were duly awarded the 2013 Nobel prize for physics.

(2008-07-23)   Unification of Physical Concepts
Why use the same units for all kinds of distances, large and small?

The ancient Egyptians measured large horizontal distances by rolling a wheel whose diameter was measured in the units they used for small vertical distances...  The countless appearances of the number  p  (the ratio of the circumference of a circle to its diameter)  in the Egyptian pyramids can be puzzling to whoever has been exposed to  unified  Euclidean space since childhood.  To Egyptian architects, the relevant dimensions were integers!

 Robert Copley,
 called Grosseteste 
Robert Grosseteste (1168-1253) is credited with the idea that the homogeneous and isotropic space of Euclidean geometry can be a backdrop for light and matter  (De Luce = About Light, c. 1235).

Blurring the distinction between horizontal and vertical distances is philosophically pleasing, although this does not make practical differences go away...  There's very little difference between right and left but there's a huge difference between up and down  (just try falling up).  The distinction between the horizontal and vertical directions  (near the surface of the Earth)  seems to vanish at  high energies :  If you shoot a gun indoors, the bullet always moves in a straight line and at the same speed no matter where you aim.  Outdoors, distances are larger and there's enough time for the pull of gravity to influence the bullet noticeably.  Very fast "bullets"  (photons or particles moving at nearly the speed of light)  are not noticeably influenced by gravity, except over astronomical distances.

"Unifying" two physical concepts is not at all a denial of their differences, it's the creation of a common consistent framework where those differences can be charted and where their interplay becomes clear.  If you have a rigid stick with one fixed end, our "unified" notion of Euclidean distance will tell you how the vertical position of the moving end varies when its horizontal position changes.

Similarly, the unification of space and time in the context of Special Relativity does not equate the two notions but it describes circumstances  (motion of the observer)  where one is traded for the other.  Loosely speaking, the speed of light  (Einstein's constant c)  is built into relativistic spacetime in very much the same way  p  was built into the architecture of the ancient Egyptians...  The numerical value of  c  is merely a consequence of our traditional ways to measure spatial distances, on one hand, and time intervals, on the other.  Rulers and clocks.

Historically, unifying separate physical concepts has always resulted in a deeper understanding of Nature.  Arguably, the most satisfying such event was the unification of electricity and magnetism by Maxwell (1861) as he found a simple way to amend the law of Ampère into a consistent picture of electromagnetism which  demanded  the existence of electromagnetic waves propagating at a constant speed c.  The fact that this ought to be so for all observers in uniform motion with respect to each other directly led to special relativity.

Unifying quests are so appealing that many mathematical physicist share a blind faith:  The forces of nature must ultimately be unified;  at high enough energies all interactions ought to look alike  (just like the aforementioned great speed of bullets blurs the distinction between horizontal and vertical directions).  Some evidence indicates that it may well be so.  However, the greatest goal of physics will be achieved if we have  consistent  descriptions of all physical phenomena, not necessarily  unified  ones.

(2008-07-09)   Kaluza-Klein Theory
A universe with 5 dimensions to unify gravity and electromagnetism.

 George Uhlenbeck 
 1900-1988  When Oskar Klein told of his ideas which would not only unify the
Maxwell with the Einstein equations but also bring in the quantum
theory, I felt a kind of ecstasy:  Now, one understands the world
George Uhlenbeck  (1900-1988)  Summer of 1926.

 Theodor Kaluza 
 c. 1929
Theodor Kaluza
    Classical relativistic  spacetime  has 4 dimensions; one dimension of time and 3 dimensions of space.  In 1919, the German physicist  Theodor Kaluza (1885-1954)  suggested that one extra geometrical dimension could be added to account for electromagnetic phenomena and describe them in purely geometrical terms, in much the same way  Einstein's General Relativity  describes gravity.

    Oskar Klein (c. 1950)
Oskar Klein
In the summer of 1926, Paul Ehrenfest (1880-1933)  invited to Leiden the Swedish physicist Oskar Klein (1894-1977) to present his refinement of the Kaluza theory and the idea that  extra spatial dimensions  might be a good way of unifying  Relativity  with  Quantum Theory.  Klein envisioned that a topologically  curled  extra dimension wouldn't be perceived as a spatial dimension on a normal scale, pretty much like the two-dimensional surface of a garden hose may look like a single-dimensional wire, if observed from a large enough distance.

For a while, this stirred the enthusiasm of Albert Einstein (1879-1955) himself and caused the special type of  ecstasy  described in the above quote by  George Uhlenbeck  (who was Ehrenfest's assistant at Leiden in 1926).

However, the excitement over this  5-dimensional physical universe  of 1926  (the so-called  Kaluza-Klein  Universe)  was short-lived, since some consequences of Oskar Klein's proposal turn out to be entirely off-base.

What's still with us today is Klein's fundamental ideas about how extra dimensions might provide a quantum theory compatible with  General Relativity.  The concept was revived in the 1970s and in the 1980s, as extra geometrical dimensions are a prerequisite for what's now called  String Theory.  Such dimensions are still visualized as  rolled up,  although they need not have a  compact  topology.

The 2009 Oskar Klein Memorial LectureMy Life as a Boson   by  Peter Higgs
Hidden Dimensions: Exploring Hyperspace  World Science Festival  (2010-06-05).

(2011-04-20)   Physics of hadrons in the 1960's.  Regge trajectories.
The light-cone frame  ("infinite momentum") & constant-tension strings.

... / ...

Tullio Regge (1931-)   |   Reggeology by Lubos Motl

(2007-08-17)   The Magic of Euler's Beta and Gamma Functions
Veneziano's 4-particle amplitude (1968).  Dual resonance model.

     Gabriele Veneziano
Gabriele Veneziano
In 1968, Gabriele Veneziano (1942-) took a boat trip from Israel to Italy  en route  to his first postdoctoral job at CERN.

At the time, Veneziano had already been working for about a year  (with M. Ademollo, H. Rubinstein and M. Virasono)  on the complementary duality of the Regge and resonance description of pion-nucleon exchange, which had been proposed by R. Dolen, D. Horn and C. Schmid.

Veneziano and his three colleagues had been putting together a model of the relevant scattering amplitude in the process.  On the boat, Veneziano realized that the essential features of that scattering amplitude would be captured by a simple expression involving Euler's Beta function and Gamma function, namely:

A ( s , t )   »   B ( 1 - a(s) , 1 - a(t) )    =     G( 1 - a(s) )   G( 1 - a(t) )
G( 2 - a(s) - a(t) )

The attractive closed form of the  Veneziano amplitude  contrasted sharply with the usual intractability which physicists had to deal with for strong nuclear interactions.  The formula created a widespread  stir.

     Leonard Susskind
Leonard Susskind
(2007-08-17)   The Idea of a Fundamental String  (1969)
Leonard Susskind (1940-)  Nielsen and Nambu.

Lenny Susskind has been at Stanford since 1979  (Felix Bloch Professor of Theoretical Physics, since 2000).


In 1969, Susskind pondered  Veneziano's formula  for months, trying to make some clear physical sense out of it.  He finally came to the conclusion that an entity was described which could stretch and vibrate just like an open-ended elastic  string.  (I'm told that the expression is now interpreted as the scattering amplitude for four open-string tachyons).

 Yoichiro Nambu
Yoichiro Nambu
   Holger Nielsen
Holger Bech Nielsen

Two other physicists working on the same premises arrived independently at similar conclusions shortly thereafter:  Holger Nielsen (1941-) at the Niels Bohr Institute,  and  Yoichiro Nambu (1921-) the inventor of the  color charge  (University of Chicago).

In  2008,  Nambu was awarded the Nobel prize in Physics for his introduction (in 1960) of mass-producing  spontaneous symmetry breaking  in particle physics  (he had been inspired by an analogy with the theory of superconductivity).

     Joel Scherk
Joël Scherk
(2007-08-17)   Could that be a... graviton ?   (1974)
Joël Scherk (1946-1979)  &  John H. Schwarz (1941-).

 John H. Schwarz
John H. Schwarrtz
As they were trying to use the newly minted  string theory  to describe the  strong nuclear force, Joël Scherk and John Schwarz kept bumping into a massless elementary particle of spin 2 which did not fit whatever was known about strong interactions.  After failing to conjure up ways to get rid of this nuisance, they came to the conclusion that this unavoidable entity could very well be the  graviton  itself  (that same idea is also credited to the Japanese physicist Tamiaki Yoneya, b. 1947)...  Thus, string theory  had to  encompass gravity and seemed destined to describe  fundamental  strings with a much smaller size and a much greater tension than previously thought  (in the restricted context of strong interactions).

Working with Eugène Cremmer and Bernard Julia, Scherk devised an 11-dimensional theory of supergravity  and proposed (with Cremmer) the mechanism of spontaneous compactification in  quantum field theory.  Scherk was a diabetic and he died in tragic circumstances, as he passed out when nobody was around to give him a shot of insulin.

After the death of Scherk, Schwartz found only one person willing to help with the work they had started together:  Michael Green...

John H. Schwarz:  String People   |   JHS / 60
Murray Gell-Mann and String Theory (27:11)  by  John Schwarz  (2013-10-12).

(2007-08-17)   Theory of Everything ?   (1984)
Michael B. Green (1946-)   &  John H. Schwarz (1941-).

 Michael B. Green
Michael B. Green
Arguably,  Superstring Theory  was born in the Summer of 1984, when  Michael Green  and  John Schwarz finally established the consistency of a theory rich enough to encompass all known forces of nature.  This was the first credible candidate for a  Theory of Everything  (TOE).

At the time, it appeared that the ultimate puzzle was being solved for good.

At Princeton,  Ed Witten  built immediately on the breakthrough of  Green & Schwarz.  On Monday, November 12, 1984, for the annual Marston Morse Memorial lecture, Witten delivered a fast-paced speech entitled  "Index Theorems and Superstrings"  at the Institute for Advanced Study.  Witten was speaking for the record, not for the immediate benefit of the 200 top-level scientists who were attending  (there were no questions from them).

When  Stephen Hawking  (b. 1942)  stepped down as  Lucasian Professor of Mathematics  in Cambridge  (on 2009-09-30)  Michael B. Green  was appointed  (on 2009-10-19, as of 2009-11-01)  to the prestigious chair, once held by  Newton, Airy, Babbage, Stokes, Larmor and Dirac.  With effect from 2015-07-01, Green's successor is Michael Cates (b. 1961).

(2017-08-07)   Two Kinds of Heterotic Strings   (1985)
Hybrids of a closed superstring and a bosonic string.

Heterotic string theory was first developed in 1985,  by the so-called  Princeton String Quartet  composed of:

Heterotic string theory

(2008-08-29)   String Quintet
Too much of a good thing:  5  consistent  string theories.

No fewer than  five  consistent string theories have been devised:

  • Type I :   The earliest theory.  It allows both open and closed strings  (the other theories allow only closed strings). 
  • Type II A :   The only  nonchiral  string theory. 
  • Type II B :   The  chiral  version of the previous one.  Both of them feature  two  supersymmetries between fermions and bosons  (the other three superstring theories have only one such supersymmetry). 
  • SO(32) Heterotic Strings :   The term "heterotic" means that the two directions along a string represent two different particles. 
  • E8 x E8 Heterotic Strings :   Based on two copies of the largest  exceptional Lie group  (E8).

The difference between the various string theories  by  Randall Scalise

    Ed Witten
Ed Witten
(2007-08-17)   Ed Witten's  M-Theory  (1995)
Is  "M"  magic, mystery, matrix, murky  or membrane ?

In 1995, Edward Witten (1951-) combined into a single 11-dimensional framework the 5 competing 10-dimensional string theories and the  11-dimensional theory of supergravity  which had been devised in 1978 by Joël Scherk (1946-1979) Eugène Cremmer (1942-) and Bernard Julia (1952-).

Even before that  tour de forceEd Witten  was widely recognized as the dominant string theorist of that era.  (He became a Fields Medalist in 1990.)

Video :   A New Look at the Path-Integral of Quantum Mechanics  by  Ed Witten   (2010-08-16).

    Lisa Randall 
 interviewed by Charlie Rose
Lisa Randall
    Burt A. Ovrut
Burt A. Ovrut
(2009-10-22)   Brane world  scenarios
In M-Theory, branes are the membranes of which parallel universes are made of.

... / ...

Membranes (M-Theory)   |   Brane Cosmology

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