Exploring M-Theory Philosophical Implications

[fuzzyfelt]

Confused and just wondering if i could be pointed in the right direction to find philosophical implications of m-theory

 

[evthis]

m-theory? What is m-theory?

 

[HallsofIvy]

According to a google search, it is apparently the 11-dimensional variety of string theory.

 

[fuzzyfelt]

M-theory is something I was interested in back when it had correlations with post-modernism, and am now rediscovering it and trying to remember my previous knowledge of it and its implications, and trying to understand the developments that have taken place in the interim and looking to find what philosophical implications have been made of these.
Forgive my fogginess, but roughly it deals with the idea that there are multi dimensional membranes. Some are tiny strings that through their vibrations, tension and twists create matter and forces. That our universe is a larger membrane. It requires other dimensions than the ones we are aware of to work.
There are a couple of forums here devoted to them and anyone there I'm sure would answer this better than I could.

 

[fuzzyfelt]

Perhaps I have used the wrong term, perhaps 'm-theory' is out-dated too. Could someone possibly direct me toward any thoughts on strings, membranes, that sort of thing.

 

[selfAdjoint]

Up on the Strings, Branes, and LQG forum, they have a collection of links that could help you. But the best introduction if you don't have the math is Greene's wonderful book The Elegant Universe.

 

[fuzzyfelt]

thank you selfadjoint. I shall have a good look. Do you think they are likely to have links about what philosophers make of their theories, or do you, or anyone, think there is a better way to ask the question? Or a better place to post?

 

[Problem+Solve=Reason]

What is the dimension we are in now? And further more, what would the other required dimentions consist of?

 

[fuzzyfelt]

Exactly, thanks. Are there imperitive rules and are there others yet to be determined, and in which direction are the ones yet to be determined pointing toward?
Being new to this, I did post my first question about dimensions in their forum, but didn't see it up- posted badly or just tooo silly. It was along these lines- are dimensions nescessarily restricted to the usual 11 or 26 that is usually discussed or is this the smallest amount needed for the equations to work? That is, are other dimensions possible within the existing framework? Or are the dimensions definitely fiexed and finite?
Further, they talk of the greater dimensions only existing as bound up within, and in answer to your first question, what they all agree upon, is the 4 dimensions- spot, line, volumne and time, (visually speaking) that we percieve.
If so, there are usual questions of within what does our universe exist...Or is our 4d universe with hidden dimensions within it, it? Why would this be the case, and how is this elegant?
In a not very good attempt to answe your second question, the other dimensions are simply tightly wrapped up and effect us by allowing the dualities that instigate matter and forces. I would like to understand this and dualities and symmetry breaking much better. Any thoughts?

 

[selfAdjoint]

...are dimensions nescessarily restricted to the usual 11 or 26 that is usually discussed or is this the smallest amount needed for the equations to work? That is, are other dimensions possible within the existing framework? Or are the dimensions definitely fiexed and finite?

The 10, 11, and 26 are indeed the minimum needed for the string math to work in different circumstances. Dimensions aside from these might exist, but we would surely notice if energy leaked away into them, for example. On the other hand if they were rigorously separated from the ones our physics happens in, how could we ever detect them? And if we couldn't detect them, why speculate about them?

Further, they talk of the greater dimensions only existing as bound up within, and in answer to your first question, what they all agree upon, is the 4 dimensions- spot, line, volumne and time, (visually speaking) that we percieve.

Surely your own life doesn't break into some fixed "spot, line, volume and time"? Rather you exist in a three dimensional space where points, lines and volumes can be defined ad lib, in any size and orientation you might choose. The time coordinate is somewhat problematical, but under the laws of relativity it too is dependent on your choice of coordinates.

If so, there are usual questions of within what does our universe exist...Or is our 4d universe with hidden dimensions within it, it? Why would this be the case, and how is this elegant?

It is not nevessary for our universe to lie in a larger space, so we don't assume it is. See my response aboe on unphysical dimensions. As for compacting the extra string dimensions, Greene calls it elegant, but he is a string physicist . I think if physicists were given a chance to eliminate the compacted dimensions, they'd leap at it. Something like that came out a couple of years ago, called "deconstruction", the extra dimensions could be converted into parameters in the theory. There was a lot of excitement for a while, but I haven't heard anything about it lately.

In a not very good attempt to answe your second question, the other dimensions are simply tightly wrapped up and effect us by allowing the dualities that instigate matter and forces. I would like to understand this and dualities and symmetry breaking much better. Any thoughts?

Yup, that's where the action is. It's hard to do it without the math, but with the math at least T-duality becomes almost trivial. You have a compacted dimension of radius R (a very tiny number) and certain physical equations hold there. If you plug 1/R into the equations (a very big number), and simplify algebraically, they become the right equations for large space. It happens automatically,"just like magic". So you can relate a theory that's just about a tiny corner to a theory that's about a big world.

 

[fuzzyfelt]

thank you again, Selfadjoint. I've been reading up and come across some of your other posts and am feeling very humble about my own. Thank you for being so helpful.
Also, I didn't mean to be rude about the aesthetics of physicists , the ideas are so appealing to me because it involves so many beautiful parts, and I think Keats was right. Just having a little appreciating them. I'll be back with more questions after I've read a little more.

 

[fuzzyfelt]

I'm pretty sure I'm understanding things a lot more, but i haven't found a description of supersymmetry, just that it is to do with spin ... would someone help me please? And does they asnwer mean that, for example, particles and sparticles are composite opposites?

 

[selfAdjoint]

I'm pretty sure I'm understanding things a lot more, but i haven't found a description of supersymmetry, just that it is to do with spin ... would someone help me please? And does they asnwer mean that, for example, particles and sparticles are composite opposites?

Well you know that all the particles we know of are divided into two kinds by their spin. Those whose spin is a whole number, 0 or 1 or 2, are called bosons, and those whose spin are a whole number + 1/2, as 1/2 or 3/2, are called fermions. And it works out that bosons and fermions behave differently; bosons will cluster and can even form Bose-Einstein Condensates (BEC) where they actually share their individuality in one "big particle". Fermions on the other hand obey the Pauli exclusion principle, under which no two of them can have all the same characteristics.

The two collections of particles seemed arbitrary, and theorists looked for a general principle that could yield them. The old mathematics of Grassmann variables showed a way. In the supersymmetric theory, every boson has a matching fermion and vice versa. The bosic photon has a fermionic photino to partner it, and the fermionic electron has a bosonic selectron. There are regular naming conventions for these extra particles.

Supersymmetry has a number of other properties that will affect the theories you impose it on. So both the existing standard model and string theory have their supersymmetric extensions, and it has been applied to gravity too. Really it is independent of these theories; it can go on to anyone of them.

 

[fuzzyfelt]

That really helps thankyou. I shall absorb this and ask more again later.

 

[fuzzyfelt]

Back from holidays, drove past CERN, nice part of the world, pity about all the cheese and veal, and have more questions as promised...
About supersymmetry, I guess according to superstrings-M, is it right that there are higher levels of energy as the dimensions increase and this leads to stronger symmetry and, vice versa, lower levles of energy, smaller dimensions, weaker symmetry? What is the order of the different degrees of symmetry, is each dimension designated a degree of symmetry and if so which degree of symmetry belongs with each dimension? I like the way Selfadjoint answers my questions with interesting things rather than with equations and words like 'Jacobean matrix of the first partials of the polynomials', but any answers would be very much appreciated.
Also, what is a soliton?
And, in a perfect world would all uncompacted or compacted dimensions allow all lower dimensions within them? Sorry, i can't think of a better way to ask that!

 

[selfAdjoint]

Thanks for the compliment Fi. There is not more energy in the extra dimensons, just more room to spread the energy around in. The extra dimensions do allow for greater symmetry, and this works itself into string physics via the string's world sheet, which turns out to have more symmetries than you would expect from a two dimensional surface in three dimensional space. And these extra symmetries take string physics into the hot area of new mathematics and have contributed to its continuing popularity, when according to some it is spinning its wheels and going nowhere.

A soliton is a kind of wave that neither disperses or crests, as most real-world waves eventually do. This is because for the soliton, the dispersing forces ("Spead out, wave!") are in continuing dynamic balance with the cresting forces ("Peak up, wave!"). Obviously this is rather special physics, and it only occurs with certain types of differential equations. But such things do exist both in canals (where the first soliton was discovered in the 19th century) and in our oceans, atmospheres, electronic devices, and maybe our quantum physics.

Sorry but I didn't quite understand your question about compaction.

 

[fuzzyfelt]

Thankyou, sorry to trouble you with these questions, just trying to see if i am on the right track. I am feeling brave enough to deal with hamilton, lorentz, chiralities should this make it easier.

 

[fuzzyfelt]

I can't find where i read it- I'm very lost about all of it, but maybe the word wasn't soliton- it was describing the unification of strings into m that resulted in among other things a 5 dimensional 'soliton'(?).
I know physicists would rather do without them, but I am intrigued by the other dimensions that are required.
I've had trouble getting the books I've ordered and not sure how dated some of the stuff I've read on the internet is- does Vafa still think there are 12 dimensions? And is there an in depth over-view of the dimensions i could read. Something that describes each dimension and what exists in them and because of which symmetry. For example, someone said that the 0branes could be time/space, is this considered far fetched, and if not does symmetry apply to them, and what type of symmetry. As they are the smallest dimension have they the least symmetry, and what sort of form does it take? And does m theory rule out the existence of a first dimension since strings are 2branes with a dimension curled in? When it says SUSY=n1 what does that mean? Or I think somethimes it says something like =4d SuSy.And then there are very odd things mentioned like the reverse side of a flat brane having supersymmetry.
Fairly obviously i didn't do any maths at all in my final years of school. I did do a lot of art. I've been busy having babies and entertaining them and now my youngest is about to start school I'm ready to paint again, and the bits of this that I do understand have inspired me. I will paint what I feel I've learned because what I do see is beautiful, but if this really were a very important theory, it would be important to interpret it correctly too. Or maybe that should be left to someone who did at least do year 12 maths!

 

[selfAdjoint]

Imkagine you're in an airplane, and it's fliying straight and level. So your "up", "down", "left", "right", "ahead", and "back" are aligned pretty much with the directions those words suggest on the surface of the earth. Now let the plane bank, "ahead" and "back" are still the same but "left" now points down at an angle toward the earth, while "right" points up at the same angle to the sky, while "up" and "down" are also rotated ny the same angle from their "true" positions. Suppose the plane goes into a vertical dive, now "ahead" has switched places with "down", and so on.

What this is all to suggest to you is that there is no first dimension and that dimensions are highly interchangable, depending on what coordinates you draw. So of the ten dimensions of superstring theory, 9 of them are space dimensions and 6 of those are compacted, but the question which 6 is meaningless, you could swap the labels of the dimensions around without changing anything. I think you really have to grasp this point, see it as a picture in your head if you think that way, before you try to think about branes.

 

[fuzzyfelt]

I'm not sure i get exactly what you are saying. I think i get that you mean that extra dimensions simply allow extra coordinates, i don't quite get that they are interchangable depending upon point of view. I mean, it does make sense, but why then are higher dimensions spoken of as having greater symmetry? doesn't that mean that their is a difference between them and lower dimensions, even if that changes? And when you say there is no first dimension do you mean that there is no need to label any dimension as first etc., or do you mean that one cannot exist alone? Sorry to be slow here.
Interchangeable works for me, and it doesn't matter too much if the dimensions are really just mathmatical devices, they can be portrayed as such. Aside from traditional landscapes- back as a kid in 1985 for assessment, it sounds a bit simplistic now, we were asked to do a painting based on post-modernist thought - unification (that unifying theories had met dead ends - my assumption was that this was regarding political, religous, etc. theories), fragmentation, eclecticism, infinities. My sources were artists like A.R. Penck who were exhibiting at the Venice Bienalle around that time, and found myself painting looped strings on space/time coordinates which worked really nicely except that I used black to signify infinities and black frowned upon unless it is representing something incredibly profound, which the irony of an infinity of unifying ideas it seems is not- Rothko had better uses for black. I hadn't heard of the trials of string theory at the time, but obviously I must have been influenced by sources that had, so I was working backward. Postmodernism was disenchanted with unifying theories and unlike modernism that believed in them and who's motto was form follows function, postmodernism's motto was form follows fun. Since then I did read about the t and s dualities, thought they were amazing and did do some paintings with them, but kids, moving countries and oils don't readily mix, so really trying to understand it all went onto the back burner for a more appropriate time.
I wish i did have a greater knowledge of physics because artists are meant to reflect the thought that influences society, and progress in physics is at the forefront of that.

 

[fuzzyfelt]

I accidentally deleted my post and re wrote it with haste, forgetting to thank selfadjoint again for his time and patience!

 

[selfAdjoint]

I'm not sure i get exactly what you are saying. I think i get that you mean that extra dimensions simply allow extra coordinates, i don't quite get that they are interchangable depending upon point of view. I mean, it does make sense, but why then are higher dimensions spoken of as having greater symmetry? doesn't that mean that their is a difference between them and lower dimensions, even if that changes?

In the three dimensions our senses perceive, you can have a certain set of rotations, for example, and they form a group, which is notated SO(3). In four dimensional Minkowski spacetime of special relativity the corresponding group is SO(1,3), the Poincare group. And SO(3) is a subgroup of SO(1,3); every 3-D rotation is also a 4-D Poincare transformation, but SO(1,3) has more transformations, Lorentz transformations in it which can not be accomplished in 3-space. Similarly the group SO(1,9) of orthogonal transformations on the 10 dimensions of superstring theory has transformations that cannot be accomplished in any smaller space. More dimensions = more ways to turn and wiggle.

And when you say there is no first dimension do you mean that there is no need to label any dimension as first etc., or do you mean that one cannot exist alone? Sorry to be slow here.

No need to label is what I meant, or rather that any labelling is arbitrary and interchangeable with any other. We have no evidence of a one dimensional continuum existing without others.

angeable works for me, and it doesn't matter too much if the dimensions are really just mathmatical devices, they can be portrayed as such. Aside from traditional landscapes- back as a kid in 1985 for assessment, it sounds a bit simplistic now, we were asked to do a painting based on post-modernist thought - unification (that unifying theories had met dead ends - my assumption was that this was regarding political, religous, etc. theories), fragmentation, eclecticism, infinities. My sources were artists like A.R. Penck who were exhibiting at the Venice Bienalle around that time, and found myself painting looped strings on space/time coordinates which worked really nicely except that I used black to signify infinities and black frowned upon unless it is representing something incredibly profound, which the irony of an infinity of unifying ideas it seems is not- Rothko had better uses for black. I hadn't heard of the trials of string theory at the time, but obviously I must have been influenced by sources that had, so I was working backward. Postmodernism was disenchanted with unifying theories and unlike modernism that believed in them and who's motto was form follows function, postmodernism's motto was form follows fun. Since then I did read about the t and s dualities, thought they were amazing and did do some paintings with them, but kids, moving countries and oils don't readily mix, so really trying to understand it all went onto the back burner for a more appropriate time.

This is very interesting. These hidden influences are an important subcurrent of cultural history. Many people have commented on the coincidence of the twin revolutions of Einstein and Picasso appearing at the same time. Now there is a book claiming that Picasso frequented a circle of thinkers in Paris where Einstein's ideas were discussed.

I wish i did have a greater knowledge of physics because artists are meant to reflect the thought that influences society, and progress in physics is at the forefront of that.

Hang around on PF a while and you'll soak up as much of the variety of modern physics as you can take. No guarantees, but no upper limit, either.

 

[fuzzyfelt]

thankyou, thankyou, thankyou, wow that's terrific, the answers to questions i didn't know how to ask and would never have imagined the answer. I will hang around here a while and soak up as much as I can, but you've left me with a lot so i shan't be bothering you for a while. Maybe we read the same thing about Picasso, I've heard it said that cubism was an attempt to paint various dimensions at once. This on top of making the viewer more aware of the viewing process, and combining it with masterly balanced design principles! Very excited now, thankyou selfadjoint.

 

[fuzzyfelt]

Just a quick question- my books have arrived, The Elegant Universe and a couple of others (they were a gift so I had to wait), and I've been enjoying them and the many symmetries I am coming across, including the marvellous SO ones. Just wondering, I haven't seen one but I'm guessing someone has made a list of known symmetries, any idea how I could find one? And, what does SO stand for? And SU and E and U,etc.

 

[selfAdjoint]

Just a quick question- my books have arrived, The Elegant Universe and a couple of others (they were a gift so I had to wait), and I've been enjoying them and the many symmetries I am coming across, including the marvellous SO ones. Just wondering, I haven't seen one but I'm guessing someone has made a list of known symmetries, any idea how I could find one? And, what does SO stand for? And SU and E and U,etc.

O stands for Orthogonal; it applies to Real number coordinates and means to transform vectors without changing their lengths or the angles at which they intersect. U stands for Unitary and applies to complex number coordinates; it also preserves lengths and angles. S stands for special; when the transformations of O or U type are written as Matrices, the S means the matrices have determinants equal to plus one. E means exceptional, and I can't give you a simple description of that one.

Most of the continuous symmetries used in physics are included here. For example SO(3) is the rotations in three dimensional space, SO(1,3) is the Poincare group of Lorentz transformation and rotations on Minkowski space. SU(2) is the group of transformations of two component spinors, and SU(3) is the group of the "color" force in QCD. SU(4) would be the transformations of four component Dirac spinors, but there is a theorem that SO(4) = SU(2)XSU(2), which means that in transforming four component spinors, the first two components transform as a two component spinor and so do the second two components, independently.

 

[fuzzyfelt]

thank you so much yet again SelfAdjoint. So pleased to hear there aren't a whole lot more of them to learn about. And I'm so pleased these amazing things are really starting to make some sense to me!

 

[Sempiternity]

At first, I was somewhat surprised at the speculation of the existence of M-theory at the beginning of the topic. I was under the impression that M-theory was more widely known. Nevertheless, selfAdjoint has done well at explaining.

Another book I highly recommend reading is Parallel Worlds by Michio Kaku. A chapter is dedicated to the development, history, reasoning, and concepts of the M-theory, which works to unify the formulated string theories in a single theory of membranes. Michio Kaku notes that string theory was once a set of various formulas and "rules of thumb" until he and his colleague, Keiji Kikkawa, formulated the field theory of strings, which summarized all the information within string theory. When the M-theory was proposed by Dr. Edward Witten, it was seen it compiled all the string theories into a single theory.

Soon afterward, it was found that all five string theories could be shown to be the same--just different approximations of the same mysterious eleven-dimensional theory. Since membranes of different sorts can exist in eleven dimensions, Witten called this theory M-Theory. But not only did it unify the five different string theories, as a bonus it also explained the mystery of supergravity.

However, M-Theory thus far does not have a set field theory like string theory does (developed by Michio Kaku and Keiji Kikkawa). This is where current progress lies: in search of a field theory of M-theory

Last, I said that M-theory was not really a theory at all, since its basic equations were not known. Unlike string theory (which could be expressed in terms of the simple string field equations I wrote down years ago that encapsulated the entire theory), membranes had no field theory at all...

The origin of this revolution is that string theory is still evolving backward. Even today, no one knows the simple physical principles that underlie the entire theory.

http://en.wikipedia.org/wiki/M-Theory
http://www.theory.caltech.edu/people/jhs/strings/str154.html

 

[ohwilleke]

Philosophically, M-Theory is interesting because:

* The world could have many more dimensions than we perceive.
* The "stuff" of which the universe is made could be very simple and homogeneous.
* All forces and matter are simply different forms of the same thing.
* There is a huge variety of possible stuff in nature not yet discovered which has no great relevance to how the world works.

 

[fuzzyfelt]

Thank you Sempiternity and ohwilleke, it is hard, starting with such a little understanding, to judge what sort of level to read, and indeed, which authors to trust and to trust my understanding of what they say. Of Course, it would be hard to go astray reading someone of the calibre of Kaku, and thanks for your recommendation, I'll read it. Selfadjoint has been wonderful, looking back at what I've written its hard to believe he's persisted with me! I've been coming to grips with the very basics, like the gauge fields, (thats fascinating that M-theory doesn't have a field theory), angular momentum, complex numbers...all these things are so amazing! I do wonder if what i did read about complex numbers was a little over the top, i think it said the time dimension is complex (-ict), which made me wonder why it is listed amongst the orthogonals? (Another stupid question, and the answer doesn't really worry me much, it is more about whether I have understood what orthogonals and complex numbers are). And, ohwilleke, that's a really nice summation, the light at the end of the tunnel, I hope I will come to understand that well.

 

[selfAdjoint]

In relativity the interval squared is $$-ct^2 - x^2 + y^2 + z^2$$. Physicists in the early 20th century (up till about 1940) thought of this as the inner product of a four vector $$(ict,x,y,z)$$ with itself. But introducing complex coordinates here raised more problems than it solved; you cn't be just a little bit complex. So now they explain the negative sign this way. There is a fundamental Minkowski metric tensor
$$\eta =\left( \begin{array}{cccc} -1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 &0 & 0 & 1 \end{array} \right)$$

and the inner product is $$\eta_ab u^au^b$$. Then the matrix-vector arithmetic slips the minus sing in without invoking complex numbers.

 

[fuzzyfelt]

Wow, is there anything you don't have an answer for? Thank you again, I'll work on understanding your answer,
Fi

 

[StarshipX]

If I'm not mistaken, Superstring/M-theory is an extension of general relativity. http://arxiv.org/PS_cache/hep-th/pdf/0504/0504089.pdf extends the methods of differential geometry.

 

[selfAdjoint]

If I'm not mistaken, Superstring/M-theory is an extension of general relativity. http://arxiv.org/PS_cache/hep-th/pdf/0504/0504089.pdf extends the methods of differential geometry.

Not quite right. Superstring theories have "flat" Minkowski spacetime as a background, and they produce a particle, the graviton, which couples to matter according to the same equations as Einstein's curvature. But there are difficulties with accepting this straight off as a theory of gravity.

Some approaches to M-theory construct a spacetime as part of the theory. This is "background independent" but I have never heard that the spacetime constructed was that of general relativity.

ADDED: The paper hep-th/0504089 does not discuss strings or M-theory, but complexifed general relativity, a completely different subject.

 

[fuzzyfelt]

Many caveats- I've been concentrating on the small picture, out of my depth, etc., but looking very simplisticly at the different theories above, with a quasi platonicish/zenish view, would it be correct to say that if this universe were some imperfect extension, the perfect point of departure in strings belongs at the beginning of this universe, and with twistors in complex space?

 

[selfAdjoint]

Many caveats- I've been concentrating on the small picture, out of my depth, etc., but looking very simplisticly at the different theories above, with a quasi platonicish/zenish view, would it be correct to say that if this universe were some imperfect extension, the perfect point of departure in strings belongs at the beginning of this universe, and with twistors in complex space?

I'm not sure I understand this question, but let me try, are you asking, given that there is something prior to spacetime, is the application of that priorness localized at the beginning of spacetime (the "big bang"), or is it being applied at every moment and point throughout the universe. Did the prior thing, strings or twistors or whatever, generate spacetime and then go idle, or does spacetime continually come out of strings or twistors or whatever.

I believe the theories I mentioned, would require the second option. The strings or twistors are evolving and as they do they generate the evolving spacetime. Or rather the spacetime we see is just a low energy approximation to the evolving prior physics, now and always.