Background

String theory is a label applied to a variety of formulations of different natures and purposes. Some applied to subatomic particles and others to astronomical structures and cosmology. A timeline structure is suitable, even essential, for presenting its history.

Prehistory

In 1867 Lord Kelvin (Sir William Thomson) published an article in the Proceedings of the Royal Society of Edinburgh, Vol. VI, 1867, pp. 94-105, in which he proposed that atoms consisted of vortex rings in the ether of space. Such vortex rings could be linked together to form complex structures. The title of Kelvin's article was "On Vortex Atoms."

Atoms were known to exist because of the constant proportions demonstrated in chemical reactions. However this article was from a time before the existence of electrons was known. Experiments by J.J. Thomson in 1897 led to the discovery of the electron as a fundamental building block of matter. Experiments by others led them to the same conclusion and the name electron was coined by someone else.

In 1919 the German mathematician Theodor Kaluza formulated a theory based upon the General Theory of Relativity but involving four spatial dimensions rather than three. From his theory Kaluza got electromagnetism as an implication. This held out the possibility of uniting gravity and electromagnetism. Albert Einstein liked Kaluza's work and supported its publication.

(Kaluza was German but his name was Slavic which leads people to identify him as being Polish but his name is not Polish but instead that of a small Slavic minority in Eastern Germany.)

String Theory

• 1968: Gabriele Veneziano worked for about a year at CERN to develop a theory of the nuclear strong force as manifested in the interaction of hadron particles. A function that he found which played an important role in his theory was:

  B(x, y) = ∫₀¹t^x-1(1 - t)^y-1dt

  In a book of mathematical functions he discovered a name for this function. It was called Euler's beta function. Somehow this story got changed into the notion that he discovered the beta function as a function that would explain the strong force. That version neglects the year he spent deriving the mathematical function. In the book he only found out that the function had a name.

  Who would have thought, from the title of Veneziano's article, "Construction of a Crossing-Symmetric Regge-Behaved Amplitude for Linearly Rising Regge Trajectories," that it would launch a major intellectual effort.

  
  Gabriele Veneziano

  This effort by Veneziano is taken to be the foundation of string theory although at that point it was not known that the analysis could be interpreted as pertaining to strings. Another researcher at CERN, Mahiko Suzuki, at the same time independently developed the same analysis as Veneziano.

• About 1970 three different physicists; Yoichiro Nambu of the University of Chicago, Holger Nielsen of the Niels Bohr Institute and Leonard Susskind, later of Stanford University; discovered that Veneziano's formulation could be derived from particles being strings rather than points. The strings could stretch and contract and also vibrate.
• There was at this time a rivalry between two approaches to particle physics; quantum field theory and the S matrix theory. The S matrix (scattering matrix) per se is just the mathematical values of what happens when the various elemental particles collide or otherwise interact. It was originally formulated by Werner Heisenberg.

  The quantum field approach to particle physics involves Feynman diagrams for the elemental particle interactions, which may involve infinite quantities. The procedure for the removal of these infinities is called renormalization.

  The S matrix theory approach distained visualizations, Feynman diagrams and renormalization and reduced everything to obtaining the matrix of the interactions of particles. The outstanding proponent of S matrix theory was Geoffrey Chew of the University of California at Berkeley. String theory appeared to be a victory for Chew's S matrix theory.

• After attempting to verify that string theory was consistent with Special Relativity and quantum theory it was concluded that such consistency required that the world be of 26 dimensions and that there exist a massless particle that travels at a speed greater than the speed of light. (Such a particle is referred to as a tachyon.) This was not immediately taken as a complete discrediting of the theory.
• Three physicists at the University of Wisconsin, Bunji Sakita, Keiji Kikkawa and Miguel Virasoro, conjectured that the adding closed strings (loops) to the model would solve some of the problems of the Veneziano model. This however would require the consideration of Feynman diagrams for the interactions.
• The string theory of Veneziano pertained only to particles acting through the nuclear strong force. Another problem with Veneziano's theory was that there was no place in it for fermions, particles with half unit spin. Pierre Raymond reformulated the model to take into account particle spin and thus his version included bosons, particles with integral spins, as well as fermions. Thus it was as though string theorists cried:

  The Old String Theory is dead! Long live the New String Theory!

  John Schwarz and Andre Neveu of Princeton University also created such a reformulation of string theory. The new string theory had the advantage that it did not require for consistency with Special Relativity and quantum theory the existence of a tachyon and a world of 26 dimensions. It only required a world of ten dimensions. This modified string theory became known as superstring theory. This was the first, but not the last, case of a name being coined which appears to be meaningful but is nevertheless opaque.

  
  John Schwarz
• The world appears to consist of three spatial dimensions and one temporal dimension. However for the universe to be finite it would have to be curved in a fourth spatial dimension. It is also possible that time is curved and this would require a second temporal dimension. . So it is possible that our four dimensional world actually involves six dimensions. But this is not how string theorists rationalize extra unseen dimensions.

  A world that is a narrow tube would appear to be one dimensional but a position around the circular cross section of the tube would constitute a second dimension. String theorists envision some multi-dimensional compactification of space existing at every point in space.

• Notice that the notion that the world is ten dimensional has only the strange support of that if the world is not ten dimensional then superstring theory is certainly wrong. This is what Richard Feynman, one of the most outstanding physicists of the twentieth century, said concerning superstring theory:

  I don't like that they are not calculating anything. I don't like that they don't check their ideas. I don't like that for anything that disagrees with an experiment, they cook up an explanation--a fix-up to say "Well it still might be true." For example, the theory requires ten dimensions. Well, maybe there is a way of wrapping up six of the dimensions. Yes, that is possible mathematically, but why not seven? When they write their equations, the equations should decide how many of these things get wrapped up, not the desire to agree with experiment. In other words, there is no reason whatsoever in superstring theory that it is not eight of the ten dimensions that get wrapped up and that the result is two dimensions, which would be completely in disagreement with experience. So the fact that it might disagree with experience is very tenuous, it does not produce anything, it has to be excused most of the time. It does not look right.

  This is from Superstrings: A Theory of Everything (1988), pp. 194-195.

• Sheldon Glashow, another outstanding physicist of the twentieth century, says

  But superstring theorists have not yet shown that their theory really works. They cannot demonstrate that the standard theory is a logical outcome of string theory. They cannot even be sure that their formulism includes a description of such things as protons and electrons. And they have not yet made even one teeny-tiny experimental prediction. Worst of all, superstring theory does not follow as logical consequence of some appealing set of hypotheses about nature. Why, you may ask, do the string theorists insist that space is nine-dimensional? Simply because string theory doesn't make sense in any other kind of space. …

  This is from Interactions: A Journey Through the Mind of a Particle Physicist (1988), p. 25.

• During the decade following the formulation of superstring theory there developed possible anomalies between it and quantum theory. Interest in the physics community dropped off. But in 1984 John Schwarz and Michael Green wrote a paper in which they provided strong evidence that superstring theory was consistent and was finite; i.e., did not lead to infinities in calculations. The title of the article was "Anomaly Cancellations in Supersymmetric D=10 Gauge Theory and Superstring Theory."
• Even before this paper was published Edward Witten at Princeton requested a copy and immediately the physicists at Princeton University and the Institute for Advanced Study began working on superstring theory.
• By 1985 four of these string theorists; Edward Witten, Philip Candelas, Gary Horowitz and Andrew Strominger; produced an article entitled "Vacuum Configurations for Superstrings."
• At first string theory thought in terms of the compactification consisting of something like a sphere or a torus, but the authors found that the mathematicians Eugenio Calabi and Shing-tung Yau had formulated and analyzed a special type of six-dimensional manifold that could be involved. An example is shown below.
  

  The article showed that the conditions for superstring theory to imply a version of the standard model were the same as the conditions which defined a Calabi-Yau manifold. Furthermore the parameters of the standard model such as the masses of the particles corresponded to characteristics of the Calabi-Yau manifold.

• In 1986 one of the authors of the above article, Andrew Strominger, published an article entitled, "Superstrings with Torsion," which showed how to formulate a vast variety of superstring theories. So there is a large population of superstring theories and yet not a single do-able experiment that would select one that is relevant for the real world. And perhaps none of them are.
• By 1995 the population of superstring theories had been narrowed down to just five. In March of that year there was a conference on string theory at the University of Southern California in Los Angeles.
  
  Edward Witten

  Edward Witten gave a lecture at that conference in which he outlined the nature that string theory would take in the future. He proposed that there were dualities involved among the five versions of string theory such that they could all be considered as manifestations of a single theory. However the unification of the five versions of string theory came at a price: The number of dimensions of the world has to be eleven rather than ten. But there isn't a consistent string theory of eleven dimensions. There is an eleven dimensional version involving membranes, two dimensional analogues of the one dimensional strings. Witten gave the name M-theory to the theory that was to replace strings. But it was not so different after all. If one dimension of a membrane is wrapped around a circle, say a small circle, it is a tube that effectively is one dimensional.

• One string theorist who listened to Witten's lecture was Joseph Polchinski of the University of California at Santa Barbara. Polchinski went to work to investigate the ideas proposed by Witten. He was able to prove that the dualities between the five versions of string theories would not exist unless there were higher dimensional versions of strings such as membranes. He generalized the two dimensional membranes and called the generalized structures D-branes. These are crucial for tying the M-theory to gauge theories and linking it with the standard model.
• In 1996 Andrew Strominger and Cumrun Vafa discovered that the brane version of string theory of Polchinski allowed one to describe and incorporate a special type of black hole within the theory. The Argentinian physicist, Juan Maldacena, demonstrated how closely brane theory matched the physics of black holes. This is a strange re-interpretation of a theory that was supposed to pertain to subatomic particles as applying to astronomical structures, actually theoretical astonomical structures. It was especially strange in that the formulation of the string theory did not include gravity but the black holes were structures such that the gravitational force is so great that even light cannot escape from them. Somehow string theory became involved in the matter of the thermodynamics of black holes. All of this concerned the interpretation of theoretical formulations of string theory.
• There had been an article entitled "On the Quantum Mechanics of Supermembranes," published in 1988 that attempted to derive quantum theory from an eleven-dimensional membrane theory. The authors; Bernard de Wit, Jens Hoppe and Hermann Nicolai; determined that this could be done if the membranes are represented as matrices.
• In 1996 the physicists; Thomas Banks, Willy Fischer, Stephen Shenker and Leonard Susskind; published an article entitled "M-Theory as a Matrix Model: A Conjecture," in which they propose, as the title indicates, that the 1988 model of de Wit, Hoppe and Nicolai is the M-Theory Witten called for.
• Again it was a matter of

  The Old String Theory is dead! Long live the New String Theory!

The physicist Lee Smolin in his 2006 book Trouble with Physics makes the point that the physics profession is overcommitted to the notion of string theory.

[…]Despite the absence of experimental support and precise formulation, the theory is believed of its adherents with a certainty that seems emotional rather than rational.

[…]Nearly every particle theorist with a permanent position at the prestigious Institute for Advanced Study, including the director, is a string theorist. The same is true of the Kavli Institute for Theoretical Physics. Eight of the nine MacArthur Fellowships awarded to particle physicists since the beginnings of the program in 1981 have also gone to string theorists. And in the country's top physics departments (Berkeley, Caltech, Harvard, MIT, Princeton, and Stanford), twenty out of the twenty-two tenured professors in particle physics who received PhDs after 1981 made their reputations in string theory or related approaches. (Page xx of the Introduction.)

This was as of 2006. Here in 2015 the situation is about the same: String theory on the verge of explaining everything but not having yielded one verifiable prediction. Most theories have a set of free parameters whose values are established by the particular universe we have. Richard Dawid, in his book String Theory and the Scientific Method points out that string theory has no free parameters and it is the only scientific theory with this characteristic.

It seems that

String Theory is an elegant answer in search of an appropriate question.

Perhaps the string theorists have forgotten that the phlogiston theory of heat and the luminiferous aether for the propogation of electromagnetic waves were elegant solutions to real problems, but still they were not right.

Some former string theorists are more trenchant in their criticisms. Peter Woit, in his book Not Even Wrong: The Failure of String Theory and the Search for Unity in Physical Law argues that string theory’s lack of rigor has left its practitioners unable to distinguish between a scientific speculation and a genuine analytical result.. The overall result is a disaster in terms of the waste of funding and scientific talent. Lee Smolin speaks of being challenged at string theory conferences as to his right to being there.

What can be said is that the journey that the term string theory represents is strewn with discarded formulations and interpretations that were once thought to be revolutionary developments in science. These were discarded because of theoretical flaws, but it is unlikely that the an empirical failure of a version of string theory would have resulted in anything other than a reformulation of string theory and a continuation of the quest.

The following is a graph of the number of article published per year in string theory from 1973 to 2008.

Despite more than 800 published articles per year from 1998 and beyond no testable prediction of string theory has, as of 2015, been developed. However, what has come out of the effort is valid propositions in mathematics.

The process sees to involve two parts. The first part involves formulating a model in terms of Lagrangian mechanics and rigorously analyzing it mathematically. The second part involves linking the mathematical results ingenuously but nonrigorously to entities in the physical world. The first part is string theory as such; the second part is more or less yarn theory.

Father Divine, a cult leader of the 1920's through the 50's, once said

The trouble with this world is that there are too many metaphysicians that don't know how to tangibilitate.

The trouble now may be that there are all too many metaphysicians who know how to tangibilitate and they do so freely.

Furthermore, as it is, string theory is an example of an attempt to execute an all-too-prevalent false syllogism in science. The false syllogism is:

Proposition A implies Proposition B
Proposition B is true
Therefore Proposition A is true

To draw that conclusion it would have to be established that Proposition B is true only if Proposition A is true, which is a much stronger proposition than what is used in the false syllogism.

At this stage string theory is collecting witty characterization by people who are not true believers; e.g.,

String theory is The Theory of More than Everything. .,

And then along came the Bogdanov brothers.