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String theory developed over a period of more than 40 years, in a kind of haphazard evolution, with theoretical roots stretching all the way back to the decade of the 1940s. It lacks a single unifying physical principle (like, for example Einstein's Principle of Equivalence, on which his theory of gravity is based), and has never managed to make contact with actual, concrete space-time physics, or to make testable predictions. Proponents of String Theory generally point to two achievements: (1) String theory is one of a small handful of proposed viable quantum theories of gravity; and, (2) the new areas of mathematics invented for string theory have proven useful in branches of physics totally removed from fundamental particle physics. It might also be noted that one of the ancestors of string theory was Duality (late 1960s), an approach that provided connections between two apparently totally different physical problems, one difficult to solve, one easy to solve. A modern version of this kind of situation exists in string theory, the so-called AdS/CFT correspondence, which is the subject of intense current interest.
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The very attractive founding idea of string theory was that all “fundamental” particles are in fact different quantum modes of the same physical object, a one-dimensional string with a length of no more than the Planck length (10-35 meters). The possible modes would be the quantum equivalents of vibrations or rotations. From this alone, you can see that getting strings to behave like fermions was a major problem at first.
Critics of string theory point to the fact that string theories are inherently multi-dimensional (9 or 10 space dimensions) and have to be “compacted” to 3 space dimensions to be relevant to physics... but there turn out to be at least 10500 different ways to do this, with no way to know which one is the way that leads to the space-time we live in. They also note that string theory is built on supersymmetry, and that there is no experimental evidence whatsoever that supersymmetry is correct. [String theories originally described only bosons, and supersymmetry is necessary to allow inclusion of fermions.]
In a way, string theory generalizes Feynman's perturbative approach, replacing the point fermions and bosons by closed strings, and thus removing all of the sources of infinities in Feynman's approach (no point particles or point vertices). But this means there is no non-perturbative version of string theory! What do you do with strings when facing a problem where a perturbation series cannot converge? Another vexing problem is that the string theory description of gravity does not satisfy background independence: a spacetime has to be input instead of emerging from the calculation.
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One type of experiment that can possibly be
done at the LHC, and that is relevant to string theories, is a
search for so-called KK partners of some existing particle.
Such partners, if found, would provide at least some evidence
that extra, compacted space dimensions do exist. For an
explanation of how this works, at the level of an introductory
undergraduate survey physics class, look here,
then here
and then here.
Needless to say, no evidence whatsoever of such KK partners
has been observed to date in LHC runs. In string theory, by
the way, superpartners are also claimed as evidence
for extra dimensions. However, superpartners will result from
any theory of fundamental processes that incorporates
supersymmetry, and do not directly provide confirmation for
any aspect of string theory.
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 The distinctive Kaluza-Klein tower is a result of standing waves in a compacted dimension. |
As the decade of the 1990s began, leading string theorist Edward Witten pointed out that the six different versions of string theory that were known by that time could probably be viewed as limiting cases of a more general theory with one extra dimension, which he called M-theory. [He said it was premature to decide what the “M” stood for.] Witten's surmise seems to be correct.
 What is a "heterotic" string? |
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Is there a future
for string theory? At the moment, it's highly debatable. Here
is a somewhat old, but clear, summary of various developments
in string theory during its long history. About the most
hopeful quote I have seen concerning string theory recently is
from string theory pioneer Andrew Strominger, who said in
2016, “String theory may not be the fabled theory of
everything, but it is definitely a theory of something.”
It remains to find out what. It would not, for example,
make much sense to cut away everything else in the theory, and
use strings only for quantum gravity.
Steven Weinberg on the problems of String Theory: here.
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 Juan Maldacena (1968 - ) |
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 Theodor Kaluza (1885 - 1954) & Oskar Klein (1894 - 1977) |
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