A short overview of M-theory?

Question

Inspired by this question, let me ask a similar question. Is it possible to do the same (give a description of M-theory your grandmother could understand)for M theory? While I know even experts don't understand it properly, I still hope some basic ideas may be expressed. Is it just a hypothetical non-perturbative formulation of quantume gravity whose different limits for varisous coupling constants are five string theories and 11d supergravity or theorists know about it in more detail?

Edit: As far as my grandmother is concerned let me inform that she has a Phd (HEP her specialization) and quite a smart woman. She has also a good knowledge of GR. So she won't mind technical staff. What she finds frustrating is that there is no rigorous definition of M-theory available to her. In her age (80) she doesn't hope to understand every details of M-theory but she certainly can find some definition of M-theory helpful.
This post imported from StackExchange Physics at 2014-04-10 16:25 (UCT), posted by SE-user user1355

Comments

@Moshe: Fair enough, but I think at least some introductory definition will suffice, like what are the basic degrees of freedom, what are the relevant observables etc.

This post imported from StackExchange Physics at 2014-04-10 16:25 (UCT), posted by SE-user user1355

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What would your answer be for QFT? My main point that we are not talking about a specific model, it is a framework. The standard model has quarks and gluons, relativistic QFT has locality and Lorentz invariance. M-theory is more like the latter, and you are asking questions appropriate for the former.

This post imported from StackExchange Physics at 2014-04-10 16:25 (UCT), posted by SE-user user566

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I understand it now. So it should be thought as a general framework rather than a specific model. Please bear with me. I want to learn.

This post imported from StackExchange Physics at 2014-04-10 16:25 (UCT), posted by SE-user user1355

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No, thanks for your questions and for not getting impatient, I was afraid I was starting to sound evasive.

This post imported from StackExchange Physics at 2014-04-10 16:25 (UCT), posted by SE-user user566

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Let me also say that historically M-theory first referred to the 11 dimensional theory, what I called the most symmetric situation. In that more restricted sense your questions are answered by Mitchell Porter below. These days, my impression is that most people use the name to refer to the whole framework, which is what I was discussing. Confusing, I'm sure...

This post imported from StackExchange Physics at 2014-04-10 16:25 (UCT), posted by SE-user user566

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Dear sb1, you're surely not asking whether theorists know more about string theory than the just fact that it has 6 limits, are you? There are about 30,000 papers filled with knowledge on string theory, and even if you compressed it as much as possible, there would still be 50,000 pages of important insights and knowledge about string/M-theory. I don't believe that your grandmother could understand them so your comment about its being a candidate or having 6 limits may be the maximum explanation to be hopeful about, but that surely doesn't mean that people don't know more than that.

This post imported from StackExchange Physics at 2014-04-10 16:25 (UCT), posted by SE-user Luboš Motl

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@Luboš Motl : I am sure people know much much more about it than those 6 limits. please relax. Afterall that's why I asked the question. When it comes to string/M-theory many people are totally clueless. Please excuse the ignorances. A sincere apology if it hurts the sensitivity of any hard working theorist.

This post imported from StackExchange Physics at 2014-04-10 16:25 (UCT), posted by SE-user user1355

Answer 1

Here is something, which may be aiming a little low...

The main two ways we describe our universe, quantum mechanics and general relativity, contradict each other when applied simultaneously. This seems to point out that the quantum nature of spacetime itself needs to be understood better.

One way to resolve theoretical problems with our current understanding of spacetime is to embed it in a larger theoretical structure, which has powerful underlying symmetries. Those symmetries cannot be too restrictive: they should be enough not only to make the model well-behaved, but also to be consistent with the not-quite-so-symmetric world we see around us.

This way of thinking has led to the theoretical structure of string theory and then M-theory. To study the structure of the theory, it is useful to first concentrate on the most symmetric situations, even though these are the most removed from our world. At first, this led to study of supersymmetric string theories in 10 dimensions (higher dimensional theories are more symmetric - their Lorentz invariance is larger and more restrictive). Later it turned out that those are all secretly related to an even larger and more symmetric structure, dubbed M-theory, which describes all the previously known string theories as well as 11-dimensional supergravity.

The story is not finished, we only have bits and pieces of the underlying structure that is M-theory. But, we do have many indications we are on the right track. As always with deep structures we found side benefits in the form of unexpected applications in mathematics and physics.

One of the unexpected discoveries is that quantum gravity is not all that different from other parts of physics, and sometimes conventional physics can be reformulated in different variables to make it equivalent to a quantum gravitational theory. Using classical and semi-classical gravity calculations then helps us explore conventional physics in regimes otherwise inaccessible. This is the whole subject of holography and its applications.

So, what we seem to have found is, instead of a specific model to describe our universe at short distances (or high energies), a whole new language in which we describe and discuss physics - and not just high energy physics. Where precisely this is going to lead is anyone’s guess.

Now, if your grandmother feels patronized, has more knowledge of physics and would like to ask more specific questions, I can try to add more details. It is a very large subject...

(see also the answers to this similar question)

This post imported from StackExchange Physics at 2014-04-10 16:25 (UCT), posted by SE-user user566

Comments

Fair enough, I am hoping to see something about the basic objects, states, observables, dynamics and so on. Of course the OP may have something else in mind, and that should be answered

This post imported from StackExchange Physics at 2014-04-10 16:25 (UCT), posted by SE-user MBN

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I've added some more explanation. I think that "grandmother" would want me to stay non-technical, but you can ask a more technical questions if you wish.

This post imported from StackExchange Physics at 2014-04-10 16:25 (UCT), posted by SE-user user566

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@Moshe: I have edited my question. Please give a rigorous definition of M-theory. The time you have given for this answer is very much appreciated.

This post imported from StackExchange Physics at 2014-04-10 16:25 (UCT), posted by SE-user user1355

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@sb1 I wish I could give you a rigorous definition. To use GR as an analogy, now we have the equivalent of post Newtonian approximation and a few special cases like the Schwarzschild solution, and you want the principle of equivalence. Give it some time, it will come and the wait will be worth it.

This post imported from StackExchange Physics at 2014-04-10 16:25 (UCT), posted by SE-user user566

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I also realize this sounds kind if vague, so maybe I will think about something more to say. But, the question you are asking - what is the essential defining characteristics of string/M - theory is quite deep, and the real answer is unknown.

This post imported from StackExchange Physics at 2014-04-10 16:25 (UCT), posted by SE-user user566

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@anna v: I added a paragraph. The history is interesting: the origins of the subject are as a model of the strong interactions as you point out, then it was thought as model of quantum gravity, now we have come full circle and realize those are not really distinct alternatives.

This post imported from StackExchange Physics at 2014-04-10 16:25 (UCT), posted by SE-user user566

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Moshe, that is very interesting, but we would also like to see what M-theory actually is.

This post imported from StackExchange Physics at 2014-04-10 16:25 (UCT), posted by SE-user MBN

Answer 2

M-theory is a conjectured 11-dimensional theory with the property that, compactified on a circle, it becomes Type IIA string theory, and, compactified on a line segment, it becomes E₈ x E₈ heterotic string theory. At some level of description, it should consist of 2- and 5-dimensional supermembranes coupled to the fields of 11-dimensional supergravity. An exact formulation is not known, but arXiV:1012.0459 reviews recent progress.

This post imported from StackExchange Physics at 2014-04-10 16:25 (UCT), posted by SE-user Mitchell Porter

Comments

Explain M-Theory to a grandmother, who was a graduate student in theoretical physics after 1980 :).

This post imported from StackExchange Physics at 2014-04-10 16:25 (UCT), posted by SE-user orbifold

Answer 3

I tend to explain this with analogues with instruments. I say imagine a string, like a guitar string or a piano string. However, this string has some interesting properties. The tension in the string is due to the quantum uncertainty principle. Because quantum mechanics says we are not able to identify the position of the string to complete precision while also knowing its momentum, this means there is a constant wavy motion which occurs. This waviness happens whether we are pulling on the string or not. So the string has its own tension.

Now for the open string there are these flapping open ends, a bit like bullwhips cracking in space. This means that waves are reflected off the ends and waves going up and down are the same. This is different from a closed string, which is a loop that have waves going clockwise and counter-clockwise (left & right) which are independent. Now let us suppose we take that open string and put in on a sound board. The end points are now held fixed and a wave which approaches the endpoint is reflected off by this fixed point. However, the sound board, which we will now call a membrane, or D-brane, may adjust in response. So that reflected wave on the string may be changed in a way so that it has an independent part from the incoming wave. This means the wave dynamics on that open string tied to D-brane becomes similar to the wave dynamics on the closed string.

In this way the behavior of quantum strings with respect to these D-branes, which are similar to Fermi surfaces or “defects” in space (with a follow on discussion on Fermi surfaces etc) can be transformed from one type to the other.

I mean really, if you are talking to “grandmas” discussions about symmetries and the like will be little more than soporific. Gotta keep it really simple, even if maybe slightly wrong. In the case of sb1's gramma this could be a sort of spring board for going into deeper discussions. However, this gives at least a physical sense of M-theory.

This post imported from StackExchange Physics at 2014-04-10 16:25 (UCT), posted by SE-user Lawrence B. Crowell

Comments

Maybe you have to keep logging in? This is a nice analogue and in any case is the one that gave the terminology.Maybe you could change the board to a stretched membrane, like a tympanum. A strings is one of the original harmonic oscillators. Which leads me to a question I do not dare ask in "questions": The harmonic oscillator is ubiquitous in physics because it is actually the first term in a Tailor expansion of a symmetric potential. Potentials can have many forms. Has anybody been considering higher terms in this framework?

This post imported from StackExchange Physics at 2014-04-10 16:25 (UCT), posted by SE-user anna v

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The soundboard analogue works because the soundboard, whether that is in a piano or a violin, is not perfectly rigid. So a left moving wave scatters off into a right moving wave by inducing wave mechanics on the D-brane. This means the right moving wave is not just a case of $k~\rightarrow~-k$, but where is a slight change in the wave structure. So there are differences between right and left movers. Maybe the foundations of M-theory are to be found in understanding how a Stradivari or Guarnari instrument has such exquisite clarity of sound.

This post imported from StackExchange Physics at 2014-04-10 16:25 (UCT), posted by SE-user Lawrence B. Crowell