# What is string theory in a nutshell

### String theory (as M-theory) in a nutshell

When I talk about string theories in the following, I mean M-theory (which initially means the sum of all string theories).

In the meantime (around 2010), however, the M-theory is more likely to be what is the focus of all efforts around string theory today: Any consistent quantum theory that includes 11-dimensional supergravity as a low-energy limit case. [Steven Gubser, a young string theorist, tells us this on page 65 of his book The Little Book of String Theory (2010).]

In the low-energy borderline case comes the person who only considers the simplest of all oscillation states that are possible for a string.

What string theorists had achieved by around 2005 is outlined (from the point of view of their proponents) in the paper Stringscape.

As cosmic law of natureI denote the totality of all physical laws that apply anywhere in the cosmos - globally or locally. Note:

String theory assumes that

• the cosmic law of nature can be described mathematically,
• that it can be described as the set of solutions to a finite system of equations, which to understand does not require any method of thinking that could overwhelm people, and
• the set of all unconditionally valid mathematical laws represents an axiom valid in the entire cosmos (even if we only know a few of these laws explicitly).

Kurt Gödel has shown that no formal calculus can - if it at least correctly models all natural numbers including their behavior under addition and multiplication - be complete and free of contradictions at the same time.

In other words: There is no formal logic that assigns exactly one of the truth values ​​TRUE or FALSE to every conceivable formal statement.

In other words: the set of all statements that formal mathematical methodology can prove to be TRUE is a real subset of the totality of all statements that are actually TRUE.

So it's an exciting question:

Where do string theorists get their bold opinion

the sought-after world formula

can solution set of a system only finite many Be equations?

Steven Hawking is now wondering that too (read his article Gödel and the end of Physics).

The fact is that the M-theory equation system has not yet been worked out.

So far, string theorists have really only looked at equations of one type: equations that are most likely to be believed would

• sensibly restrict the huge number of conceivable world models
• and yet confirm and complete previously recognized models.

And indeed: String theory confirms the standard model of elementary particle physics. In adding and merging other models - that of general relativity and that of quantum mechanics - string theory has so far been rather weak on the chest.

Essential statements of string theory are:

• The smallest building blocks of the cosmos seem to be vibrating (only in exceptional cases also completely resting) portions of energy (so-called branes) that cannot be further subdivided, which are best imagined as membranes - as something that goes beyond the point of space-time at which it is can have up to 7 additional dimensions. It's not clear if these are just conceptual in nature.
• If these are really spatial dimensions, it cannot be ruled out that all branes have maximum dimensions - then the same - and that one or more of these dimensions are so strongly compacted that they can be ignored or only then recognized as present, if you calculate accordingly precisely.
• The string theorists hope that the system of equations defining the M-theory, which has only been worked out in fragments so far, will be the implicit formulation of all the physical laws applicable in the cosmos.

This formulation has exactly one parameter, which is called the string coupling constant (it describes the probability with which a string is temporarily divided into a virtual string pair). If you choose a specific value for this, the system of equations changes into one that describes a certain type of universe - a consistent, possible version of all physical laws.

The higher the value of the string coupling constant, the more the strings interact, and the less well perturbation calculus converges (a method of calculation that is often the only one with which one has a chance of mathematically analyzing the world model in question and according to its physical statement accessible).

The main problem for string theorists is

not to know,

what coupling constant our universe has
:

Strings are at least 15 orders of magnitude too small to be experimental physics
could measure how strongly they bind to one another.

• What is particularly interesting about string theory is that it knows numerous pairs of models that are dual to one another (two models are called dual to one another if they describe identical physics).

It is remarkable and helpful that models can be dual to one another even if they look completely different - so you would never get the idea that they could be equivalent to one another:

• Identical physics describes e.g. every pair of models in which the diameter R. the compacted dimensions of one is inverse to the diameter of the compacted dimensions of the other. To have discovered that is worth a lot, because:

The difficulty of obtaining useful calculation results in one or the other model is all the more varied the clearer it is R. of value 1 differs. Which of the two ways is the cheaper one can depend on the problem.

• Another duality is particularly interesting, the so-called supersymmetry:

Not all of the world models provided by the M-theory are supersymmetric (a model is called supersymmetric if it can be converted into an equivalent by a certain transformation, such that what the bosons are in one model, the fermions in the other and vice versa ).

Such duality is astonishing when you consider that bosons behave very differently than fermions (the Pauli principle applies to all fermions, but does not apply to bosons).

Since only supersymmetric world models reproduce the proven standard model of elementary particle physics, there is much to suggest that our universe is supersymmetrical is.

• In the range of energies below 103 GeV - these are areas in which it is a question of distances that are not smaller than 10-18 cm are - 10-dimensional superstring theory is equivalent to 11-dimensional supergravity theory.

Up until 1995, the latter was regarded as an unlikely competitor of string theory and was only promoted by two researchers: Michael Duff and Paul Townsend. They were only taken seriously after Witten had discovered that models coming through their theory are just another form of true string theory models - but a form that significantly alleviates certain computational problems.

The fact that supergravity models know one space dimension more than the corresponding superstring models, and also the observation that this additional space dimension corresponds to an additional component of the state of the strings in the superstring model, suggests in my eyes that all of them are beyond the usual 3 + 1 Dimensions of space-time beyond additional dimensions could be of a purely conceptual nature. This would explain why experimental physics has not yet found it.

The dualities of string theory reveal an astonishing relationship between world models, which can show almost no similarity. Just think of a pair of models ( Mss, Msg ), in which Mss is a model of superstring theory and Msg an equivalent model of the supergravity theory: They differ
• due to often extremely different string coupling constants,
• by the fact that Msg Gravity taken into account, Mss but not,
• by the number and shape of their additional spatial dimensions,
• through their ontology,
• and a lot more.

Nevertheless, both describe identical physics (at least the same, as far as one can see so far).

This reminds me strongly of Niels Bohr, who is supposed to have said once: Physics cannot fathom how nature works: it can only examine how nature shows itself to us.

String theory makes it clear to us that nature can show it to us in different ways, like certain fish that live in coral reefs and always shape themselves according to shape and color in such a way that they are almost indistinguishable from the background of their surroundings.